0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s 0.12/0.33 % Computer : n014.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 10:38:40 EDT 2023 0.12/0.33 % CPUTime : 14.48/14.09 ============================== Prover9 =============================== 14.48/14.09 Prover9 (32) version 2009-11A, November 2009. 14.48/14.09 Process 29067 was started by sandbox on n014.cluster.edu, 14.48/14.09 Mon Jul 3 10:38:52 2023 14.48/14.09 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1440 -f /tmp/Prover9_28914_n014.cluster.edu". 14.48/14.09 ============================== end of head =========================== 14.48/14.09 14.48/14.09 ============================== INPUT ================================= 14.48/14.09 14.48/14.09 % Reading from file /tmp/Prover9_28914_n014.cluster.edu 14.48/14.09 14.48/14.09 set(prolog_style_variables). 14.48/14.09 set(auto2). 14.48/14.09 % set(auto2) -> set(auto). 14.48/14.09 % set(auto) -> set(auto_inference). 14.48/14.09 % set(auto) -> set(auto_setup). 14.48/14.09 % set(auto_setup) -> set(predicate_elim). 14.48/14.09 % set(auto_setup) -> assign(eq_defs, unfold). 14.48/14.09 % set(auto) -> set(auto_limits). 14.48/14.09 % set(auto_limits) -> assign(max_weight, "100.000"). 14.48/14.09 % set(auto_limits) -> assign(sos_limit, 20000). 14.48/14.09 % set(auto) -> set(auto_denials). 14.48/14.09 % set(auto) -> set(auto_process). 14.48/14.09 % set(auto2) -> assign(new_constants, 1). 14.48/14.09 % set(auto2) -> assign(fold_denial_max, 3). 14.48/14.09 % set(auto2) -> assign(max_weight, "200.000"). 14.48/14.09 % set(auto2) -> assign(max_hours, 1). 14.48/14.09 % assign(max_hours, 1) -> assign(max_seconds, 3600). 14.48/14.09 % set(auto2) -> assign(max_seconds, 0). 14.48/14.09 % set(auto2) -> assign(max_minutes, 5). 14.48/14.09 % assign(max_minutes, 5) -> assign(max_seconds, 300). 14.48/14.09 % set(auto2) -> set(sort_initial_sos). 14.48/14.09 % set(auto2) -> assign(sos_limit, -1). 14.48/14.09 % set(auto2) -> assign(lrs_ticks, 3000). 14.48/14.09 % set(auto2) -> assign(max_megs, 400). 14.48/14.09 % set(auto2) -> assign(stats, some). 14.48/14.09 % set(auto2) -> clear(echo_input). 14.48/14.09 % set(auto2) -> set(quiet). 14.48/14.09 % set(auto2) -> clear(print_initial_clauses). 14.48/14.09 % set(auto2) -> clear(print_given). 14.48/14.09 assign(lrs_ticks,-1). 14.48/14.09 assign(sos_limit,10000). 14.48/14.09 assign(order,kbo). 14.48/14.09 set(lex_order_vars). 14.48/14.09 clear(print_given). 14.48/14.09 14.48/14.09 % formulas(sos). % not echoed (10484 formulas) 14.48/14.09 14.48/14.09 ============================== end of input ========================== 14.48/14.09 14.48/14.09 % From the command line: assign(max_seconds, 1440). 14.48/14.09 14.48/14.09 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 14.48/14.09 14.48/14.09 % Formulas that are not ordinary clauses: 14.48/14.09 1 (all A all B (r2_hidden(A,B) -> -r2_hidden(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 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]. 14.48/14.09 3 $T # label(t3_tarski) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 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]. 14.48/14.09 5 $T # label(dt_k3_tarski) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 6 (all A all B k2_tarski(A,B) = k2_tarski(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 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]. 14.48/14.09 8 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 9 $T # label(t1_tarski) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 10 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 11 $T # label(t6_tarski) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 12 $T # label(t4_tarski) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 13 $T # label(t8_tarski) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 17 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 20 (all A all B r1_tarski(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 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]. 14.48/14.09 22 $T # label(t5_tarski) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 29 (exists A -v1_xboole_0(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 30 $T # label(dt_k5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 33 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 36 (all A all B k3_xboole_0(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 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]. 14.48/14.09 38 (all A (A = k1_xboole_0 <-> v1_xboole_0(A))) # label(d5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 39 (all A all B -r2_xboole_0(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 40 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 46 (all A all B k2_xboole_0(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 49 (all A all B r3_xboole_0(A,A)) # label(reflexivity_r3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 56 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 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]. 14.48/14.09 58 (all A (A = k1_xboole_0 <-> (all B -r2_hidden(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 59 (exists A v1_xboole_0(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 60 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 61 (all A all B -(v1_xboole_0(B) & r2_hidden(A,B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 62 (all A k1_xboole_0 = k3_xboole_0(A,k1_xboole_0)) # label(t2_boole) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 63 (all A k4_xboole_0(k1_xboole_0,A) = k1_xboole_0) # label(t4_boole) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 64 (all A A = k2_xboole_0(A,k1_xboole_0)) # label(t1_boole) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 65 (all A all B -(v1_xboole_0(B) & A != B & v1_xboole_0(A))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 66 (all A k5_xboole_0(A,k1_xboole_0) = A) # label(t5_boole) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 67 (all A A = k4_xboole_0(A,k1_xboole_0)) # label(t3_boole) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 68 (all A (v1_xboole_0(A) -> k1_xboole_0 = A)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 77 (all A r1_xboole_0(A,k1_xboole_0)) # label(t65_xboole_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 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]. 14.48/14.09 79 (all A -r2_xboole_0(A,k1_xboole_0)) # label(t62_xboole_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 97 (all A k1_xboole_0 = k5_xboole_0(A,A)) # label(t92_xboole_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 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]. 14.48/14.09 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]. 14.48/14.09 100 (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]. 14.48/14.09 101 (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]. 14.48/14.09 102 (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]. 14.48/14.09 103 (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]. 14.48/14.09 104 (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]. 14.48/14.09 105 (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]. 14.48/14.09 106 (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]. 14.48/14.09 107 (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]. 14.48/14.09 108 (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]. 14.48/14.09 109 (all A r1_tarski(k1_xboole_0,A)) # label(t2_xboole_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 110 (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]. 14.48/14.09 111 (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]. 14.48/14.09 112 (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]. 14.48/14.09 113 (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]. 14.48/14.09 114 (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]. 14.48/14.09 115 (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]. 14.48/14.09 116 (all A all B r1_tarski(k4_xboole_0(A,B),A)) # label(t36_xboole_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 117 (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]. 14.48/14.09 118 (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]. 14.48/14.09 119 (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]. 14.48/14.09 120 (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]. 14.48/14.09 121 (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]. 14.48/14.09 122 (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]. 14.48/14.09 123 (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]. 14.48/14.09 124 (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]. 14.48/14.09 125 (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]. 14.48/14.09 126 (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]. 14.48/14.09 127 (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]. 14.48/14.09 128 (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]. 14.48/14.09 129 (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]. 14.48/14.09 130 (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]. 14.48/14.09 131 (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]. 14.48/14.09 132 (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]. 14.48/14.09 133 (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]. 14.48/14.09 134 (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]. 14.48/14.09 135 (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]. 14.48/14.09 136 (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]. 14.48/14.09 137 (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]. 14.48/14.09 138 (all A (k1_xboole_0 != A -> r2_xboole_0(k1_xboole_0,A))) # label(t61_xboole_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 139 (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]. 14.48/14.09 140 (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]. 14.48/14.09 141 (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]. 14.48/14.09 142 (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]. 14.48/14.09 143 (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]. 14.48/14.09 144 (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]. 14.48/14.09 145 (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]. 14.48/14.09 146 (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]. 14.48/14.09 147 (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]. 14.48/14.09 148 (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]. 14.48/14.09 149 (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]. 14.48/14.09 150 (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]. 14.48/14.09 151 (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]. 14.48/14.09 152 (all A all B (r1_tarski(A,B) -> B = k2_xboole_0(A,B))) # label(t12_xboole_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 153 (all A all B r1_tarski(A,k2_xboole_0(A,B))) # label(t7_xboole_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 154 (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]. 14.48/14.09 155 (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]. 14.48/14.09 156 (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]. 14.48/14.09 157 (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]. 14.48/14.09 158 (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]. 14.48/14.09 159 (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]. 14.48/14.09 160 (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]. 14.48/14.09 161 (all A all B r1_xboole_0(k4_xboole_0(A,B),B)) # label(t79_xboole_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 162 (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]. 14.48/14.09 163 (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]. 14.48/14.09 164 (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]. 14.48/14.09 165 (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]. 14.48/14.09 166 (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]. 14.48/14.09 167 (all A (r1_tarski(A,k1_xboole_0) -> A = k1_xboole_0)) # label(t3_xboole_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 168 (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]. 14.48/14.09 169 (all A all B r1_tarski(k3_xboole_0(A,B),A)) # label(t17_xboole_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 170 (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]. 14.48/14.09 171 (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]. 14.48/14.09 172 (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]. 14.48/14.09 173 (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]. 14.48/14.09 174 (all A all B -(r2_xboole_0(B,A) & r1_tarski(A,B))) # label(t60_xboole_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 175 (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]. 14.48/14.09 176 (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]. 14.48/14.09 177 (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]. 14.48/14.09 178 (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]. 14.48/14.09 179 (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]. 14.48/14.09 180 (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]. 14.48/14.09 181 (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]. 14.48/14.09 182 (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]. 14.48/14.09 183 (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]. 14.48/14.09 184 (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]. 14.48/14.09 185 (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]. 14.48/14.09 186 (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]. 14.48/14.09 187 $T # label(t15_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 188 (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]. 14.48/14.09 189 (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]. 14.48/14.09 190 $T # label(t77_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 191 (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]. 14.48/14.09 192 (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]. 14.48/14.09 193 (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]. 14.48/14.09 194 (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]. 14.48/14.09 195 (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]. 14.48/14.09 196 (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]. 14.48/14.09 197 (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]. 14.48/14.09 198 (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]. 14.48/14.09 199 (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]. 14.48/14.09 200 (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]. 14.48/14.09 201 $T # label(t85_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 202 (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]. 14.48/14.09 203 (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]. 14.48/14.09 204 (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]. 14.48/14.09 205 (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]. 14.48/14.09 206 (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]. 14.48/14.09 207 (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]. 14.48/14.09 208 (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]. 14.48/14.09 209 (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]. 14.48/14.09 210 (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]. 14.48/14.09 211 (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]. 14.48/14.09 212 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 213 (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]. 14.48/14.09 214 (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]. 14.48/14.09 215 $T # label(t78_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 216 (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]. 14.48/14.09 217 (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]. 14.48/14.09 218 (all A all B -v1_xboole_0(k4_tarski(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.09 219 (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]. 14.48/14.09 220 (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]. 14.48/14.09 221 (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]. 14.48/14.09 222 (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]. 14.48/14.09 223 (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]. 14.48/14.09 224 (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]. 14.48/14.09 225 $T # label(t4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 226 (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]. 14.48/14.10 227 (all A (r1_tarski(A,k2_zfmisc_1(A,A)) -> k1_xboole_0 = A)) # label(t116_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 228 (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]. 14.48/14.10 229 (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]. 14.48/14.10 230 $T # label(t7_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 231 (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]. 14.48/14.10 232 (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]. 14.48/14.10 233 (all A k3_tarski(k1_tarski(A)) = A) # label(t31_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 234 $T # label(t76_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 235 (all A all B r1_tarski(k1_tarski(A),k2_tarski(A,B))) # label(t12_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 236 (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]. 14.48/14.10 237 (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]. 14.48/14.10 238 (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]. 14.48/14.10 239 (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]. 14.48/14.10 240 (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]. 14.48/14.10 241 $T # label(t89_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 242 (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]. 14.48/14.10 243 (all A all B (r1_tarski(k1_tarski(A),k1_tarski(B)) -> B = A)) # label(t6_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 244 $T # label(t11_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 245 $T # label(t62_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 246 (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]. 14.48/14.10 247 (all A all B (r1_tarski(k1_tarski(A),k1_tarski(B)) -> A = B)) # label(t24_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 248 (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]. 14.48/14.10 249 (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]. 14.48/14.10 250 $T # label(t3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 251 (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]. 14.48/14.10 252 (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]. 14.48/14.10 253 (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]. 14.48/14.10 254 (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]. 14.48/14.10 255 (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]. 14.48/14.10 256 (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]. 14.48/14.10 257 (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]. 14.48/14.10 258 (all A r1_tarski(k1_tarski(A),k1_zfmisc_1(A))) # label(t80_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 259 (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]. 14.48/14.10 260 (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]. 14.48/14.10 261 (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]. 14.48/14.10 262 (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]. 14.48/14.10 263 (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]. 14.48/14.10 264 $T # label(t5_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 265 (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]. 14.48/14.10 266 (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]. 14.48/14.10 267 (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]. 14.48/14.10 268 (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]. 14.48/14.10 269 (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]. 14.48/14.10 270 (all A all B (r2_hidden(A,B) -> r1_tarski(A,k3_tarski(B)))) # label(t92_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 271 (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]. 14.48/14.10 272 $T # label(t71_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 273 (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]. 14.48/14.10 274 (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]. 14.48/14.10 275 $T # label(t91_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 276 (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]. 14.48/14.10 277 (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]. 14.48/14.10 278 (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]. 14.48/14.10 279 (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]. 14.48/14.10 280 (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]. 14.48/14.10 281 (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]. 14.48/14.10 282 (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]. 14.48/14.10 283 (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]. 14.48/14.10 284 (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]. 14.48/14.10 285 $T # label(t88_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 286 (all A all B (r2_hidden(A,B) <-> r1_tarski(k1_tarski(A),B))) # label(t37_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 287 (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]. 14.48/14.10 288 (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]. 14.48/14.10 289 (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]. 14.48/14.10 290 (all A r1_tarski(A,k1_zfmisc_1(k3_tarski(A)))) # label(t100_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 291 (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]. 14.48/14.10 292 (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]. 14.48/14.10 293 (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]. 14.48/14.10 294 (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]. 14.48/14.10 295 (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]. 14.48/14.10 296 $T # label(t133_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 297 (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]. 14.48/14.10 298 (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]. 14.48/14.10 299 $T # label(t61_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 300 (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]. 14.48/14.10 301 (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]. 14.48/14.10 302 (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]. 14.48/14.10 303 (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]. 14.48/14.10 304 $T # label(t87_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 305 (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]. 14.48/14.10 306 (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]. 14.48/14.10 307 $T # label(dt_k3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 308 (all A all B k1_xboole_0 != k2_xboole_0(k1_tarski(A),B)) # label(t49_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 309 (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]. 14.48/14.10 310 (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]. 14.48/14.10 311 (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]. 14.48/14.10 312 (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]. 14.48/14.10 313 (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]. 14.48/14.10 314 (all A k3_tarski(k1_zfmisc_1(A)) = A) # label(t99_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 315 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 316 (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]. 14.48/14.10 317 (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]. 14.48/14.10 318 (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]. 14.48/14.10 319 (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]. 14.48/14.10 320 (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]. 14.48/14.10 321 (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]. 14.48/14.10 322 (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]. 14.48/14.10 323 $T # label(dt_k4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 324 (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]. 14.48/14.10 325 (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]. 14.48/14.10 326 (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]. 14.48/14.10 327 $T # label(t90_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 328 (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]. 14.48/14.10 329 (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]. 14.48/14.10 330 (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]. 14.48/14.10 331 (all A -v1_xboole_0(k1_tarski(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 332 (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]. 14.48/14.10 333 (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]. 14.48/14.10 334 (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]. 14.48/14.10 335 (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]. 14.48/14.10 336 (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]. 14.48/14.10 337 (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]. 14.48/14.10 338 (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]. 14.48/14.10 339 $T # label(t5_subset_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 340 (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]. 14.48/14.10 341 (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]. 14.48/14.10 342 $T # label(t9_subset_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 343 (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]. 14.48/14.10 344 (all A k1_subset_1(A) = k3_subset_1(A,k2_subset_1(A))) # label(t21_subset_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 345 (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]. 14.48/14.10 346 (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]. 14.48/14.10 347 (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]. 14.48/14.10 348 (all A k1_xboole_0 = k1_subset_1(A)) # label(d3_subset_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 349 (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]. 14.48/14.10 350 (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]. 14.48/14.10 351 (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]. 14.48/14.10 352 $T # label(t12_subset_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 353 (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]. 14.48/14.10 354 (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]. 14.48/14.10 355 (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]. 14.48/14.10 356 (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]. 14.48/14.10 357 $T # label(t37_subset_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 358 $T # label(t23_subset_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 359 (all A k2_subset_1(A) = k3_subset_1(A,k1_subset_1(A))) # label(t22_subset_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 360 $T # label(t2_subset_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 361 (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]. 14.48/14.10 362 (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]. 14.48/14.10 363 (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]. 14.48/14.10 364 $T # label(t14_subset_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 365 (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]. 14.48/14.10 366 (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]. 14.48/14.10 367 (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]. 14.48/14.10 368 (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]. 14.48/14.10 369 (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]. 14.48/14.10 370 (all A -v1_xboole_0(k1_zfmisc_1(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 371 (all A m1_subset_1(k2_subset_1(A),k1_zfmisc_1(A))) # label(dt_k2_subset_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 372 (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]. 14.48/14.10 373 (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]. 14.48/14.10 374 (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]. 14.48/14.10 375 (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]. 14.48/14.10 376 (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]. 14.48/14.10 377 $T # label(t20_subset_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 378 (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]. 14.48/14.10 379 (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]. 14.48/14.10 380 (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]. 14.48/14.10 381 (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]. 14.48/14.10 382 (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]. 14.48/14.10 383 $T # label(t1_subset_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 384 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r1_tarski(B,C) & r1_xboole_0(D,C) -> r1_tarski(B,k3_subset_1(A,D))))))))) # label(t47_subset_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 385 (all A all B (m1_subset_1(B,A) -> (A != k1_xboole_0 -> m1_subset_1(k1_tarski(B),k1_zfmisc_1(A))))) # label(t55_subset_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 386 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> (r1_subset_1(A,B) -> r1_subset_1(B,A)))) # label(symmetry_r1_subset_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 387 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k4_xboole_0(B,C) = k6_subset_1(A,B,C))) # label(redefinition_k6_subset_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 388 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k7_subset_1(A,B,C) = k5_xboole_0(B,C))) # label(redefinition_k7_subset_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 389 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k4_subset_1(A,B,B) = B)) # label(idempotence_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 390 (all A (-$T -> (all B (m1_subset_1(B,A) -> B = k8_subset_1(A))))) # label(d6_subset_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 391 $T # label(t11_subset_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 392 (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]. 14.48/14.10 393 (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]. 14.48/14.10 394 (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]. 14.48/14.10 395 (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]. 14.48/14.10 396 (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]. 14.48/14.10 397 (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]. 14.48/14.10 398 (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]. 14.48/14.10 399 (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]. 14.48/14.10 400 (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]. 14.48/14.10 401 $T # label(t45_subset_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 402 (all A k2_subset_1(A) = A) # label(d4_subset_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 403 (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]. 14.48/14.10 404 (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]. 14.48/14.10 405 (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]. 14.48/14.10 406 (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]. 14.48/14.10 407 $T # label(t27_subset_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 408 (all A exists B m1_subset_1(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 409 (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]. 14.48/14.10 410 (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]. 14.48/14.10 411 (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]. 14.48/14.10 412 $T # label(t24_subset_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 413 (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]. 14.48/14.10 414 $T # label(t13_subset_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 415 (all A m1_subset_1(k1_xboole_0,k1_zfmisc_1(A))) # label(t4_subset_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 416 (all A m1_subset_1(k8_subset_1(A),A)) # label(dt_k8_subset_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 417 (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]. 14.48/14.10 418 $T # label(t19_subset_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 419 $T # label(d1_subset_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 420 (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]. 14.48/14.10 421 (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]. 14.48/14.10 422 (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]. 14.48/14.10 423 (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]. 14.48/14.10 424 (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]. 14.48/14.10 425 $T # label(t6_subset_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 426 (all A all B -v1_xboole_0(k2_tarski(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 427 (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]. 14.48/14.10 428 (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]. 14.48/14.10 429 (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]. 14.48/14.10 430 (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]. 14.48/14.10 431 (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]. 14.48/14.10 432 (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]. 14.48/14.10 433 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 434 (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]. 14.48/14.10 435 (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]. 14.48/14.10 436 $T # label(t3_subset_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 437 (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]. 14.48/14.10 438 (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]. 14.48/14.10 439 (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]. 14.48/14.10 440 (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]. 14.48/14.10 441 $T # label(t16_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 442 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (B = k1_tarski(A) -> k7_setfam_1(A,B) = k1_tarski(k1_xboole_0)))) # label(t55_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 443 (all A all B all C (k4_setfam_1(A,B) = C <-> (all D (r2_hidden(D,C) <-> (exists E exists F (r2_hidden(F,B) & D = k4_xboole_0(E,F) & r2_hidden(E,A))))))) # label(d6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 444 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> m1_subset_1(k5_setfam_1(A,B),k1_zfmisc_1(A)))) # label(dt_k5_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 445 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r1_tarski(k7_setfam_1(A,B),k7_setfam_1(A,C)) -> r1_tarski(B,C)))))) # label(t51_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 446 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r1_tarski(B,C) -> r1_tarski(k8_setfam_1(A,C),k8_setfam_1(A,B))))))) # label(t59_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 447 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> m1_subset_1(k6_setfam_1(A,B),k1_zfmisc_1(A)))) # label(dt_k6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 448 $T # label(t43_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 449 $T # label(t14_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 450 (all A all B (B != k1_xboole_0 -> k1_setfam_1(k2_setfam_1(k1_tarski(A),B)) = k2_xboole_0(A,k1_setfam_1(B)))) # label(t35_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 451 (all A all B r1_setfam_1(A,A)) # label(reflexivity_r1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 452 $T # label(t15_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 453 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> ((all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(D,C) <-> r2_hidden(D,B)))) -> B = C))))) # label(t44_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 454 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> k7_setfam_1(A,k4_subset_1(k1_zfmisc_1(A),B,C)) = k4_subset_1(k1_zfmisc_1(A),k7_setfam_1(A,B),k7_setfam_1(A,C)))))) # label(t54_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 455 $T # label(dt_k2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 456 (all A all B all C (k3_setfam_1(A,B) = C <-> (all D (r2_hidden(D,C) <-> (exists E exists F (r2_hidden(E,A) & r2_hidden(F,B) & D = k3_xboole_0(E,F))))))) # label(d5_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 457 (all A all B (r2_hidden(A,B) -> r1_tarski(k1_setfam_1(B),A))) # label(t4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 458 $T # label(t1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 459 $T # label(d7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 460 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k7_setfam_1(A,C) = k7_setfam_1(A,B) -> B = C))))) # label(t53_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 461 (all A all B (r2_setfam_1(A,B) <-> (all C -((all D -(r1_tarski(D,C) & r2_hidden(D,A))) & r2_hidden(C,B))))) # label(d3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 462 (all A all B (r1_tarski(A,B) -> r1_tarski(k1_setfam_1(B),k1_setfam_1(A)) | k1_xboole_0 = A)) # label(t7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 463 (exists A (-v1_xboole_0(A) & v1_setfam_1(A))) # label(rc1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 464 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> m1_subset_1(k7_setfam_1(A,B),k1_zfmisc_1(k1_zfmisc_1(A))))) # label(dt_k7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 465 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> -(B != k1_xboole_0 & k7_setfam_1(A,B) = k1_xboole_0))) # label(t46_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 466 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> B = k7_setfam_1(A,k7_setfam_1(A,B)))) # label(involutiveness_k7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 467 (all A (v2_setfam_1(A) <-> (all B (-v1_xboole_0(B) -> -r2_hidden(B,A))))) # label(d11_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 468 (all A all B all C (r1_tarski(k3_tarski(A),B) & r2_hidden(C,A) -> r1_tarski(C,B))) # label(t56_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 469 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k1_xboole_0 != B -> k6_subset_1(A,k2_subset_1(A),k6_setfam_1(A,B)) = k5_setfam_1(A,k7_setfam_1(A,B))))) # label(t48_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 470 (all A all B k3_setfam_1(B,A) = k3_setfam_1(A,B)) # label(commutativity_k3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 471 (all A (-v1_xboole_0(A) & v1_setfam_1(A) -> (all B (m1_subset_1(B,A) -> -v1_xboole_0(B))))) # label(cc1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 472 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> k3_tarski(B) = k5_setfam_1(A,B))) # label(redefinition_k5_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 473 (all A r1_setfam_1(A,k2_setfam_1(A,A))) # label(t29_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 474 $T # label(dt_k4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 475 (all A (-v1_xboole_0(A) -> -v1_xboole_0(k1_tarski(A)) & v1_setfam_1(k1_tarski(A)))) # label(fc2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 476 (all A (r2_hidden(k1_xboole_0,A) -> k1_xboole_0 = k1_setfam_1(A))) # label(t5_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 477 (all A k1_setfam_1(k1_tarski(A)) = A) # label(t11_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 478 (exists A -v2_setfam_1(A)) # label(rc2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 479 (all A all B ((all C (r2_hidden(C,A) -> r1_tarski(B,C))) -> r1_tarski(B,k1_setfam_1(A)) | A = k1_xboole_0)) # label(t6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 480 $T # label(dt_k3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 481 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) & v1_xboole_0(B) -> v1_xboole_0(k7_setfam_1(A,B)))) # label(fc1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 482 (all A (-v2_setfam_1(A) -> (exists B (m1_subset_1(B,A) & -v1_xboole_0(B))))) # label(rc3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 483 (all A r1_setfam_1(k1_xboole_0,A)) # label(t20_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 484 $T # label(t22_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 485 (all A all B (r1_tarski(A,B) -> r1_setfam_1(A,B))) # label(t17_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 486 (all A all B k3_xboole_0(A,B) = k1_setfam_1(k2_tarski(A,B))) # label(t12_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 487 (all A all B k3_tarski(k3_setfam_1(A,B)) = k3_xboole_0(k3_tarski(A),k3_tarski(B))) # label(t39_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 488 $T # label(t28_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 489 $T # label(t42_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 490 (all A r1_setfam_1(k4_setfam_1(A,A),A)) # label(t31_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 491 (all A (r1_setfam_1(A,k1_xboole_0) -> A = k1_xboole_0)) # label(t21_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 492 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r1_tarski(k7_setfam_1(A,B),C) <-> r1_tarski(B,k7_setfam_1(A,C))))))) # label(t52_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 493 (all A r1_setfam_1(k3_setfam_1(A,A),A)) # label(t30_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 494 (all A all B (-r1_xboole_0(A,B) -> k1_setfam_1(k3_setfam_1(A,B)) = k3_xboole_0(k1_setfam_1(A),k1_setfam_1(B)))) # label(t34_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 495 (all A (-r2_hidden(k1_xboole_0,A) <-> v1_setfam_1(A))) # label(d9_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 496 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> k6_setfam_1(A,B) = k1_setfam_1(B))) # label(redefinition_k6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 497 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (B = k1_xboole_0 -> k8_setfam_1(A,B) = A) & (k1_xboole_0 != B -> k6_setfam_1(A,B) = k8_setfam_1(A,B)))) # label(d10_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 498 (all A all B all C (r1_setfam_1(A,B) & r1_setfam_1(B,C) -> r1_setfam_1(A,C))) # label(t23_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 499 (all A all B all C (C = k2_setfam_1(A,B) <-> (all D (r2_hidden(D,C) <-> (exists E exists F (r2_hidden(F,B) & k2_xboole_0(E,F) = D & r2_hidden(E,A))))))) # label(d4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 500 $T # label(t27_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 501 (all A all B (k1_xboole_0 != B -> k1_setfam_1(k4_setfam_1(k1_tarski(A),B)) = k4_xboole_0(A,k3_tarski(B)))) # label(t37_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 502 (all A all B all C (r1_tarski(C,k3_tarski(k2_xboole_0(A,B))) & (all D (r2_hidden(D,B) -> r1_xboole_0(D,C))) -> r1_tarski(C,k3_tarski(A)))) # label(t57_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 503 $T # label(t26_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 504 (all A all B all C (r1_setfam_1(C,k2_tarski(A,B)) -> (all D -(r2_hidden(D,C) & -r1_tarski(D,A) & -r1_tarski(D,B))))) # label(t25_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 505 $T # label(t45_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 506 (all A all B (r1_setfam_1(A,B) -> r1_tarski(k3_tarski(A),k3_tarski(B)))) # label(t18_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 507 (all A all B k2_setfam_1(A,B) = k2_setfam_1(B,A)) # label(commutativity_k2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 508 (all A all B all C (r1_tarski(A,C) & r2_hidden(A,B) -> r1_tarski(k1_setfam_1(B),C))) # label(t8_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 509 (all A all B ((A != k1_xboole_0 -> ((all C (r2_hidden(C,B) <-> (all D (r2_hidden(D,A) -> r2_hidden(C,D))))) <-> B = k1_setfam_1(A))) & (A = k1_xboole_0 -> (B = k1_setfam_1(A) <-> k1_xboole_0 = B)))) # label(d1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.10 510 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (C = k7_setfam_1(A,B) <-> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(D,C) <-> r2_hidden(k3_subset_1(A,D),B))))))))) # label(d8_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 511 $T # label(t50_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 512 $T # label(dt_k1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 513 (all A all B (r2_setfam_1(B,A) -> r1_tarski(k1_setfam_1(B),k1_setfam_1(A)) | k1_xboole_0 = A)) # label(t19_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 514 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (B != k1_xboole_0 -> k6_setfam_1(A,k7_setfam_1(A,B)) = k6_subset_1(A,k2_subset_1(A),k5_setfam_1(A,B))))) # label(t47_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 515 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> m1_subset_1(k8_setfam_1(A,B),k1_zfmisc_1(A)))) # label(dt_k8_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 516 (all A all B (k1_xboole_0 != B -> k4_xboole_0(A,k1_setfam_1(B)) = k3_tarski(k4_setfam_1(k1_tarski(A),B)))) # label(t38_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 517 (all A all B (v1_setfam_1(A) & v1_setfam_1(B) -> v1_setfam_1(k2_xboole_0(A,B)))) # label(fc4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 518 (all A all B ((all C -((all D -(r2_hidden(D,B) & r1_tarski(C,D))) & r2_hidden(C,A))) <-> r1_setfam_1(A,B))) # label(d2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 519 (all A r1_tarski(k1_setfam_1(A),k3_tarski(A))) # label(t3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 520 (all A all B all C (r2_hidden(A,B) & r1_xboole_0(A,C) -> r1_xboole_0(k1_setfam_1(B),C))) # label(t9_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 521 (all A all B (r1_setfam_1(B,k1_tarski(A)) -> (all C (r2_hidden(C,B) -> r1_tarski(C,A))))) # label(t24_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 522 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r2_hidden(B,A) -> ((all D (r2_hidden(D,C) -> r2_hidden(B,D))) <-> r2_hidden(B,k8_setfam_1(A,C)))))) # label(t58_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 523 (all A (-v2_setfam_1(A) -> -v1_xboole_0(A))) # label(cc2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 524 $T # label(t33_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 525 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> -v1_xboole_0(k2_tarski(A,B)) & v1_setfam_1(k2_tarski(A,B)))) # label(fc3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 526 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r2_hidden(k3_subset_1(A,C),k7_setfam_1(A,B)) <-> r2_hidden(C,B)))))) # label(t49_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 527 (all A all B r1_tarski(k1_setfam_1(k4_setfam_1(A,B)),k4_xboole_0(k1_setfam_1(A),k1_setfam_1(B)))) # label(t41_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 528 $T # label(t32_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 529 (all A all B -(k1_xboole_0 != B & -r1_tarski(k2_xboole_0(k1_setfam_1(A),k1_setfam_1(B)),k1_setfam_1(k2_setfam_1(A,B))) & k1_xboole_0 != A)) # label(t40_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 530 (all A all B r2_setfam_1(B,B)) # label(reflexivity_r2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 531 (all A all B -(k1_xboole_0 != A & k1_setfam_1(k2_xboole_0(A,B)) != k3_xboole_0(k1_setfam_1(A),k1_setfam_1(B)) & k1_xboole_0 != B)) # label(t10_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 532 $T # label(t13_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 533 (all A all B k3_xboole_0(A,k3_tarski(B)) = k3_tarski(k3_setfam_1(k1_tarski(A),B))) # label(t36_setfam_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 534 (all A all B all C (r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) -> m1_subset_1(A,C))) # label(t4_subset) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 535 (all A all B all C -(v1_xboole_0(C) & m1_subset_1(B,k1_zfmisc_1(C)) & r2_hidden(A,B))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 536 (all A all B (m1_subset_1(A,B) -> v1_xboole_0(B) | r2_hidden(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 537 (all A all B (r2_hidden(A,B) -> m1_subset_1(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 538 (all A all B (m1_subset_1(A,k1_zfmisc_1(B)) <-> r1_tarski(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 539 (all A all B (v1_relat_1(B) -> r1_tarski(k10_relat_1(B,A),k1_relat_1(B)))) # label(t167_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 540 (all A all B (v1_relat_1(B) -> (r1_tarski(A,k1_relat_1(B)) -> A = k1_relat_1(k7_relat_1(B,A))))) # label(t91_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 541 $T # label(t70_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 542 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(B,C) -> r1_tarski(k7_relat_1(B,A),k7_relat_1(C,A))))))) # label(t105_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 543 (all A all B (v1_relat_1(B) -> k3_xboole_0(k2_relat_1(B),A) = k2_relat_1(k8_relat_1(A,B)))) # label(t119_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 544 (all A ((all B -(r2_hidden(B,A) & (all C all D B != k4_tarski(C,D)))) <-> v1_relat_1(A))) # label(d1_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 545 (all A k8_relat_1(A,k1_xboole_0) = k1_xboole_0) # label(t138_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 546 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k8_relat_1(A,C) = k8_relat_1(B,k8_relat_1(A,C))))) # label(t129_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 547 (all A all B all C (v1_relat_1(C) -> (k1_tarski(k4_tarski(A,B)) = C -> k2_tarski(A,B) = k3_relat_1(C)))) # label(t32_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 548 $T # label(t7_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 549 (all A all B all C (v1_relat_1(C) -> k3_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)) = k7_relat_1(C,k3_xboole_0(A,B)))) # label(t108_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 550 $T # label(t61_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 551 (all A (v1_relat_1(A) -> k5_relat_1(A,k1_xboole_0) = k1_xboole_0 & k1_xboole_0 = k5_relat_1(k1_xboole_0,A))) # label(t62_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 552 (all A all B (v1_relat_1(B) -> (r1_tarski(k1_relat_1(B),A) -> B = k7_relat_1(B,A)))) # label(t97_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 553 (all A all B all C (v1_relat_1(C) -> r1_tarski(k4_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)),k9_relat_1(C,k4_xboole_0(A,B))))) # label(t155_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 554 (exists A (v1_xboole_0(A) & v1_relat_1(A))) # label(rc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 555 (all A (v1_relat_1(A) -> ((all B all C -r2_hidden(k4_tarski(B,C),A)) -> A = k1_xboole_0))) # label(t56_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 556 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(B,C) -> r1_tarski(k10_relat_1(B,A),k10_relat_1(C,A))))))) # label(t179_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 557 (all A (v1_xboole_0(A) -> v1_relat_1(A))) # label(cc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 558 $T # label(t8_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 559 $T # label(dt_k9_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 560 (all A all B all C all D (v1_relat_1(D) -> (r2_hidden(k4_tarski(A,B),D) & r2_hidden(B,C) <-> r2_hidden(k4_tarski(A,B),k5_relat_1(D,k6_relat_1(C)))))) # label(t75_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 561 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(A,B) -> r1_tarski(k1_relat_1(A),k1_relat_1(B)) & r1_tarski(k2_relat_1(A),k2_relat_1(B))))))) # label(t25_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 562 (all A (v1_relat_1(A) -> (v3_relat_1(A) <-> r1_tarski(k2_relat_1(A),k1_tarski(k1_xboole_0))))) # label(d15_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 563 (all A all B all C (v1_relat_1(C) -> k2_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)) = k9_relat_1(C,k2_xboole_0(A,B)))) # label(t153_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 564 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k2_xboole_0(k3_relat_1(A),k3_relat_1(B)) = k3_relat_1(k2_xboole_0(A,B)))))) # label(t33_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 565 (all A (-v1_xboole_0(A) & v1_relat_1(A) -> -v1_xboole_0(k1_relat_1(A)))) # label(fc5_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 566 (all A all B (v3_relat_1(A) & v1_relat_1(A) -> v3_relat_1(k7_relat_1(A,B)) & v1_relat_1(k7_relat_1(A,B)))) # label(fc13_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 567 (all A (v1_relat_1(A) -> k1_relat_1(A) = k10_relat_1(A,k2_relat_1(A)))) # label(t169_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 568 (all A all B (v1_relat_1(B) -> v1_relat_1(k8_relat_1(A,B)))) # label(dt_k8_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 569 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k2_xboole_0(k2_relat_1(A),k2_relat_1(B)) = k2_relat_1(k2_xboole_0(A,B)))))) # label(t26_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 570 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C all D (k7_relat_1(A,D) = k7_relat_1(B,D) & r1_tarski(C,D) -> k7_relat_1(B,C) = k7_relat_1(A,C))))))) # label(t188_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 571 (all A all B (v1_relat_1(B) -> k1_relat_1(k7_relat_1(B,A)) = k3_xboole_0(k1_relat_1(B),A))) # label(t90_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 572 (all A (v1_relat_1(A) -> k9_relat_1(A,k1_relat_1(A)) = k2_relat_1(A))) # label(t146_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 573 (all A all B (v1_relat_1(B) -> r1_tarski(k1_relat_1(k7_relat_1(B,A)),A))) # label(t87_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 574 $T # label(t114_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 575 (all A all B (v1_relat_1(B) -> (k1_xboole_0 = k9_relat_1(B,A) <-> r1_xboole_0(k1_relat_1(B),A)))) # label(t151_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 576 (all A all B (v1_relat_1(B) -> r1_tarski(k2_relat_1(k7_relat_1(B,A)),k2_relat_1(B)))) # label(t99_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 577 (all A all B (v1_relat_1(B) -> r1_tarski(k3_xboole_0(k1_relat_1(B),A),k9_relat_1(k4_relat_1(B),k9_relat_1(B,A))))) # label(t163_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 578 (all A (v1_relat_1(A) -> ((all B (r2_hidden(B,k2_relat_1(A)) -> k1_xboole_0 = B)) <-> v3_relat_1(A)))) # label(t184_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 579 (all A all B all C (v1_relat_1(C) -> k7_relat_1(k8_relat_1(A,C),B) = k8_relat_1(A,k7_relat_1(C,B)))) # label(t140_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 580 (exists A (v3_relat_1(A) & v1_relat_1(A))) # label(rc3_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 581 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k4_xboole_0(k1_relat_1(A),k1_relat_1(B)),k1_relat_1(k4_xboole_0(A,B))))))) # label(t15_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 582 (all A all B (v1_relat_1(B) -> r1_tarski(k2_relat_1(k8_relat_1(A,B)),A))) # label(t116_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 583 $T # label(t58_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 584 (all A all B (v1_relat_1(B) -> (r1_tarski(A,k2_relat_1(B)) -> A = k2_relat_1(k8_relat_1(A,B))))) # label(t120_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 585 (all A (v1_relat_1(A) -> A = k8_relat_1(k2_relat_1(A),A))) # label(t126_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 586 (exists A (v1_relat_1(A) & -v1_xboole_0(A))) # label(rc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 587 $T # label(t83_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 588 (all A (A = k1_relat_1(k6_relat_1(A)) & k2_relat_1(k6_relat_1(A)) = A)) # label(t71_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 589 (all A all B (v1_relat_1(B) -> v1_relat_1(k4_xboole_0(B,A)))) # label(t10_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 590 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k10_relat_1(C,A),k10_relat_1(C,B))))) # label(t178_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 591 $T # label(t11_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 592 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k4_xboole_0(k4_relat_1(A),k4_relat_1(B)) = k4_relat_1(k4_xboole_0(A,B)))))) # label(t41_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 593 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k9_relat_1(C,A),k9_relat_1(D,B))))))) # label(t158_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 594 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(A,B) <-> (all C all D (r2_hidden(k4_tarski(C,D),A) -> r2_hidden(k4_tarski(C,D),B)))))))) # label(d3_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 595 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k7_relat_1(C,A),k7_relat_1(D,B))))))) # label(t106_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 596 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k2_relat_1(k5_relat_1(A,B)),k2_relat_1(B)))))) # label(t45_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 597 $T # label(t85_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 598 (all A (v1_relat_1(A) -> (all B all C (v1_relat_1(C) -> ((all D all E (r2_hidden(k4_tarski(D,E),A) & r2_hidden(D,B) <-> r2_hidden(k4_tarski(D,E),C))) <-> k7_relat_1(A,B) = C))))) # label(d11_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 599 (all A all B all C (v1_relat_1(C) -> k7_relat_1(C,k4_xboole_0(A,B)) = k4_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)))) # label(t109_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 600 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k10_relat_1(A,k1_relat_1(B)) = k1_relat_1(k5_relat_1(A,B)))))) # label(t182_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 601 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k7_relat_1(C,A),k7_relat_1(C,B))))) # label(t104_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 602 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 603 (all A (v1_relat_1(A) -> r1_tarski(A,k2_zfmisc_1(k1_relat_1(A),k2_relat_1(A))))) # label(t21_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 604 (all A (-v1_xboole_0(A) & v1_relat_1(A) -> -v1_xboole_0(k2_relat_1(A)))) # label(fc6_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 605 (all A (v1_xboole_0(A) -> v1_relat_1(k4_relat_1(A)) & v1_xboole_0(k4_relat_1(A)))) # label(fc11_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 606 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k9_relat_1(C,A),k9_relat_1(C,B))))) # label(t156_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 607 (all A k10_relat_1(k1_xboole_0,A) = k1_xboole_0) # label(t172_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 608 (all A (v1_relat_1(A) -> A = k4_relat_1(k4_relat_1(A)))) # label(involutiveness_k4_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 609 (all A all B (v1_relat_1(B) -> ((all C (r2_hidden(C,A) -> r2_hidden(k4_tarski(C,C),B))) -> r1_tarski(k6_relat_1(A),B)))) # label(t73_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 610 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 611 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(A),k1_relat_1(B)) -> k1_relat_1(A) = k1_relat_1(k5_relat_1(A,B))))))) # label(t46_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 612 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k7_relat_1(A,k1_relat_1(B)) = k7_relat_1(A,k1_relat_1(k7_relat_1(B,k1_relat_1(A)))))))) # label(t189_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 613 (all A all B (v1_relat_1(B) -> k7_relat_1(B,A) = k7_relat_1(k7_relat_1(B,A),A))) # label(t101_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 614 (exists A (v1_relat_1(A) & (all B all C (r2_hidden(B,f1_s1_relat_1) & r2_hidden(C,f2_s1_relat_1) & p1_s1_relat_1(B,C) <-> r2_hidden(k4_tarski(B,C),A))))) # label(s1_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 615 (all A v1_relat_1(k6_relat_1(A))) # label(dt_k6_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 616 (all A all B (v1_relat_1(B) -> -(k1_xboole_0 != A & k1_xboole_0 = k9_relat_1(B,A) & r1_tarski(A,k1_relat_1(B))))) # label(t152_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 617 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k9_relat_1(B,k2_relat_1(A)) = k2_relat_1(k5_relat_1(A,B)))))) # label(t160_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 618 (all A (v1_xboole_0(A) -> v1_relat_1(k2_relat_1(A)) & v1_xboole_0(k2_relat_1(A)))) # label(fc8_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 619 (all A all B (v1_relat_1(B) -> k8_relat_1(A,B) = k8_relat_1(A,k8_relat_1(A,B)))) # label(t128_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 620 $T # label(t164_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 621 (all A all B (v1_relat_1(B) & v1_xboole_0(A) -> v1_relat_1(k5_relat_1(A,B)) & v1_xboole_0(k5_relat_1(A,B)))) # label(fc9_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 622 (all A (v1_relat_1(A) -> (v2_relat_1(A) <-> -r2_hidden(k1_xboole_0,k2_relat_1(A))))) # label(d9_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 623 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k5_relat_1(C,A),k5_relat_1(C,B))))))))) # label(t48_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 624 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k3_xboole_0(k4_relat_1(A),k4_relat_1(B)) = k4_relat_1(k3_xboole_0(A,B)))))) # label(t39_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 625 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(C)) & r2_hidden(A,B) <-> r2_hidden(A,k1_relat_1(k7_relat_1(C,B)))))) # label(t86_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 626 (all A all B (v1_relat_1(B) -> v1_relat_1(k3_xboole_0(A,B)))) # label(t9_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 627 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k5_relat_1(A,C),k5_relat_1(B,C))))))))) # label(t49_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 628 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k7_relat_1(C,A) = k7_relat_1(k7_relat_1(C,B),A)))) # label(t103_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 629 (all A all B (v1_relat_1(B) -> k5_relat_1(B,k6_relat_1(A)) = k8_relat_1(A,B))) # label(t123_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 630 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k7_relat_1(k7_relat_1(C,A),B) = k7_relat_1(C,A)))) # label(t102_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 631 $T # label(t57_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 632 (all A (v1_relat_1(A) -> v1_relat_1(k4_relat_1(A)))) # label(dt_k4_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 633 $T # label(t162_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 634 (all A all B (v1_relat_1(B) -> k10_relat_1(B,k3_xboole_0(k2_relat_1(B),A)) = k10_relat_1(B,A))) # label(t168_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 635 (all A (v1_relat_1(A) -> (all B (k1_relat_1(A) = B <-> (all C (r2_hidden(C,B) <-> (exists D r2_hidden(k4_tarski(C,D),A)))))))) # label(d4_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 636 (all A all B (v1_relat_1(B) -> r1_tarski(k9_relat_1(B,A),k2_relat_1(B)))) # label(t144_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 637 $T # label(t2_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 638 (all A all B (v1_relat_1(B) -> r1_tarski(k10_relat_1(B,A),k10_relat_1(B,k2_relat_1(B))))) # label(t170_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 639 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> r1_tarski(k4_xboole_0(k5_relat_1(A,B),k5_relat_1(A,C)),k5_relat_1(A,k4_xboole_0(B,C))))))))) # label(t53_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 640 $T # label(t17_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 641 $T # label(t35_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 642 (all A all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> k8_relat_1(A,B) = B))) # label(t125_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 643 (all A (v1_relat_1(A) -> (all B ((all C (r2_hidden(C,B) <-> (exists D r2_hidden(k4_tarski(D,C),A)))) <-> k2_relat_1(A) = B)))) # label(d5_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 644 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k10_relat_1(B,k10_relat_1(C,A)) = k10_relat_1(k5_relat_1(B,C),A))))) # label(t181_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 645 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k5_relat_1(B,k8_relat_1(A,C)) = k8_relat_1(A,k5_relat_1(B,C)))))) # label(t139_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 646 (all A all B all C (v1_relat_1(C) -> ((exists D (r2_hidden(k4_tarski(A,D),C) & r2_hidden(D,B) & r2_hidden(D,k2_relat_1(C)))) <-> r2_hidden(A,k10_relat_1(C,B))))) # label(t166_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 647 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k5_relat_1(k4_relat_1(B),k4_relat_1(A)) = k4_relat_1(k5_relat_1(A,B)))))) # label(t54_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 648 $T # label(t69_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 649 (all A all B (v1_relat_1(B) -> (k7_relat_1(B,A) = k1_xboole_0 <-> r1_xboole_0(k1_relat_1(B),A)))) # label(t95_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 650 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k5_relat_1(A,C),k5_relat_1(B,D))))))))))) # label(t50_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 651 (all A all B all C (v1_relat_1(C) -> k3_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)) = k8_relat_1(k3_xboole_0(A,B),C))) # label(t135_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 652 (all A all B (v1_relat_1(B) & v1_relat_1(A) -> v1_relat_1(k3_xboole_0(A,B)))) # label(fc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 653 (all A all B (v1_relat_1(B) -> k2_relat_1(k7_relat_1(B,A)) = k9_relat_1(B,A))) # label(t148_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 654 (all A (v1_relat_1(A) -> k9_relat_1(A,k1_xboole_0) = k1_xboole_0)) # label(t149_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 655 (all A all B (v1_relat_1(B) & v1_relat_1(A) -> v1_relat_1(k4_xboole_0(A,B)))) # label(fc3_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 656 (all A all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> k5_relat_1(B,k6_relat_1(A)) = B))) # label(t79_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 657 (all A all B v1_relat_1(k2_zfmisc_1(A,B))) # label(t6_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 658 (all A all B (v1_relat_1(B) -> k7_relat_1(B,A) = k3_xboole_0(B,k2_zfmisc_1(A,k2_relat_1(B))))) # label(t96_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 659 (all A all B (v1_relat_1(B) & v1_xboole_0(A) -> v1_relat_1(k5_relat_1(B,A)) & v1_xboole_0(k5_relat_1(B,A)))) # label(fc10_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 660 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k9_relat_1(C,B)) <-> (exists D (r2_hidden(D,k1_relat_1(C)) & r2_hidden(D,B) & r2_hidden(k4_tarski(D,A),C)))))) # label(t143_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 661 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k9_relat_1(C,k9_relat_1(B,A)) = k9_relat_1(k5_relat_1(B,C),A))))) # label(t159_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 662 (all A (v1_relat_1(A) -> k5_relat_1(k6_relat_1(k1_relat_1(A)),A) = A)) # label(t78_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 663 (all A all B all C all D all E (v1_relat_1(E) -> (k2_tarski(k4_tarski(A,B),k4_tarski(C,D)) = E -> k2_tarski(A,C) = k1_relat_1(E) & k2_relat_1(E) = k2_tarski(B,D)))) # label(t24_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 664 (all A all B all C (v1_relat_1(C) -> (k1_tarski(k4_tarski(A,B)) = C -> k2_relat_1(C) = k1_tarski(B) & k1_relat_1(C) = k1_tarski(A)))) # label(t23_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 665 (all A all B (v1_relat_1(B) -> r1_tarski(k3_xboole_0(k2_relat_1(B),A),k10_relat_1(k4_relat_1(B),k10_relat_1(B,A))))) # label(t183_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 666 (all A (v1_relat_1(A) -> k1_xboole_0 = k8_relat_1(k1_xboole_0,A))) # label(t137_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 667 (all A all B all C (v1_relat_1(C) -> k2_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)) = k7_relat_1(C,k2_xboole_0(A,B)))) # label(t107_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 668 (all A k1_xboole_0 = k9_relat_1(k1_xboole_0,A)) # label(t150_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 669 (all A all B (v1_relat_1(B) -> -(r2_hidden(A,k2_relat_1(B)) & (all C -r2_hidden(C,k1_relat_1(B)))))) # label(t19_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 670 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k1_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k1_relat_1(A),k1_relat_1(B)))))) # label(t13_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 671 $T # label(t1_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 672 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k8_relat_1(A,C) = k8_relat_1(A,k8_relat_1(B,C))))) # label(t130_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 673 (all A (v1_relat_1(A) -> k3_relat_1(A) = k3_relat_1(k4_relat_1(A)))) # label(t38_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 674 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> ((all D all E (r2_hidden(E,A) & r2_hidden(k4_tarski(D,E),B) <-> r2_hidden(k4_tarski(D,E),C))) <-> C = k8_relat_1(A,B)))))) # label(d12_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 675 (all A (v1_relat_1(A) -> (all B all C (k9_relat_1(A,B) = C <-> (all D (r2_hidden(D,C) <-> (exists E (r2_hidden(k4_tarski(E,D),A) & r2_hidden(E,B))))))))) # label(d13_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 676 (all A (v1_relat_1(A) -> k3_xboole_0(A,k2_zfmisc_1(k1_relat_1(A),k2_relat_1(A))) = A)) # label(t22_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 677 $T # label(t12_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 678 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(k1_relat_1(A),k2_relat_1(B)) -> k2_relat_1(A) = k2_relat_1(k5_relat_1(B,A))))))) # label(t47_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 679 (all A (v1_relat_1(A) -> k1_xboole_0 = k7_relat_1(A,k1_xboole_0))) # label(t110_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 680 $T # label(t63_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 681 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> ((all D all E (r2_hidden(k4_tarski(D,E),C) <-> (exists F (r2_hidden(k4_tarski(D,F),A) & r2_hidden(k4_tarski(F,E),B))))) <-> C = k5_relat_1(A,B)))))))) # label(d8_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 682 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C all D (k7_relat_1(A,D) = k7_relat_1(B,D) & k7_relat_1(B,C) = k7_relat_1(A,C) -> k7_relat_1(B,k2_xboole_0(C,D)) = k7_relat_1(A,k2_xboole_0(C,D)))))))) # label(t185_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 683 (all A all B (v1_relat_1(B) -> (r1_tarski(A,B) -> v1_relat_1(A)))) # label(t3_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 684 $T # label(t59_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 685 (all A all B all C (v1_relat_1(C) -> r1_tarski(k9_relat_1(k7_relat_1(C,A),B),k9_relat_1(C,B)))) # label(t161_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 686 (all A all B all C (v1_relat_1(C) -> k8_relat_1(k2_xboole_0(A,B),C) = k2_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)))) # label(t134_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 687 (all A all B (v1_relat_1(B) -> r1_tarski(k8_relat_1(A,B),B))) # label(t117_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 688 (all A (v1_relat_1(A) -> k10_relat_1(A,k1_xboole_0) = k1_xboole_0)) # label(t171_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 689 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k4_xboole_0(k2_relat_1(A),k2_relat_1(B)),k2_relat_1(k4_xboole_0(A,B))))))) # label(t28_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 690 $T # label(t142_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 691 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_xboole_0(k2_relat_1(A),k1_relat_1(B)) -> k5_relat_1(A,B) = k1_xboole_0))))) # label(t67_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 692 $T # label(t165_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 693 $T # label(t68_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 694 (all A all B (v1_relat_1(B) & v1_relat_1(A) -> v1_relat_1(k2_xboole_0(A,B)))) # label(fc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 695 (all A (v1_relat_1(A) -> k1_relat_1(k4_relat_1(A)) = k2_relat_1(A) & k2_relat_1(k4_relat_1(A)) = k1_relat_1(A))) # label(t37_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 696 (all A all B (v1_relat_1(B) -> k9_relat_1(B,k3_xboole_0(k1_relat_1(B),A)) = k9_relat_1(B,A))) # label(t145_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 697 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (B = A <-> (all C all D (r2_hidden(k4_tarski(C,D),B) <-> r2_hidden(k4_tarski(C,D),A)))))))) # label(d2_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 698 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k10_relat_1(C,A),k10_relat_1(D,B))))))) # label(t180_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 699 (all A all B (v1_relat_1(B) -> (r1_xboole_0(k2_relat_1(B),A) <-> k10_relat_1(B,A) = k1_xboole_0))) # label(t173_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 700 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k2_xboole_0(k5_relat_1(A,B),k5_relat_1(A,C)) = k5_relat_1(A,k2_xboole_0(B,C)))))))) # label(t51_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 701 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> ((all C all D (r2_hidden(k4_tarski(D,C),A) <-> r2_hidden(k4_tarski(C,D),B))) <-> k4_relat_1(A) = B))))) # label(d7_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 702 (all A (v1_relat_1(A) -> (all B (r1_xboole_0(B,k1_relat_1(A)) -> k7_relat_1(A,B) = k1_xboole_0)))) # label(t187_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 703 $T # label(t42_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 704 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> r1_tarski(k5_relat_1(k8_relat_1(A,B),C),k5_relat_1(B,C)))))) # label(t121_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 705 (all A (v1_relat_1(A) -> (all B all C (k10_relat_1(A,B) = C <-> (all D (r2_hidden(D,C) <-> (exists E (r2_hidden(E,B) & r2_hidden(k4_tarski(D,E),A))))))))) # label(d14_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 706 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k5_relat_1(k7_relat_1(B,A),C) = k7_relat_1(k5_relat_1(B,C),A))))) # label(t112_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 707 (all A all B all C (v1_relat_1(C) -> k7_relat_1(k7_relat_1(C,A),B) = k7_relat_1(C,k3_xboole_0(A,B)))) # label(t100_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 708 (all A k1_xboole_0 = k7_relat_1(k1_xboole_0,A)) # label(t111_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 709 (all A all B all C all D v1_relat_1(k2_tarski(k4_tarski(A,B),k4_tarski(C,D)))) # label(t5_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 710 (all A all B (v1_relat_1(B) -> -(r1_tarski(A,k2_relat_1(B)) & k10_relat_1(B,A) = k1_xboole_0 & A != k1_xboole_0))) # label(t174_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 711 $T # label(t16_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 712 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> r1_tarski(k5_relat_1(B,k7_relat_1(C,A)),k5_relat_1(B,C)))))) # label(t93_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 713 $T # label(t84_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 714 (all A all B (v1_relat_1(A) & v1_relat_1(B) -> v1_relat_1(k5_relat_1(A,B)))) # label(dt_k5_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 715 (all A (v1_relat_1(A) -> (k2_relat_1(A) = k1_xboole_0 | k1_relat_1(A) = k1_xboole_0 -> k1_xboole_0 = A))) # label(t64_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 716 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> r1_tarski(k5_relat_1(B,k8_relat_1(A,C)),k5_relat_1(B,C)))))) # label(t122_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 717 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(B,C) -> r1_tarski(k8_relat_1(A,B),k8_relat_1(A,C))))))) # label(t132_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 718 $T # label(dt_k10_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 719 (all A (v1_relat_1(A) -> r1_tarski(k2_relat_1(A),k3_relat_1(A)) & r1_tarski(k1_relat_1(A),k3_relat_1(A)))) # label(t29_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 720 (all A (v1_xboole_0(A) -> v1_relat_1(k1_relat_1(A)) & v1_xboole_0(k1_relat_1(A)))) # label(fc7_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 721 $T # label(t36_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 722 (all A all B all C (v1_relat_1(C) -> k2_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)) = k10_relat_1(C,k2_xboole_0(A,B)))) # label(t175_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 723 (all A k6_relat_1(A) = k4_relat_1(k6_relat_1(A))) # label(t72_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 724 (all A (v1_relat_1(A) -> k2_xboole_0(k1_relat_1(A),k2_relat_1(A)) = k3_relat_1(A))) # label(d6_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 725 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> r1_tarski(k5_relat_1(A,k3_xboole_0(B,C)),k3_xboole_0(k5_relat_1(A,B),k5_relat_1(A,C))))))))) # label(t52_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 726 (all A (v1_relat_1(A) -> A = k7_relat_1(A,k1_relat_1(A)))) # label(t98_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 727 (all A all B all C (v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),C) -> r2_hidden(A,k3_relat_1(C)) & r2_hidden(B,k3_relat_1(C))))) # label(t30_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 728 (all A all B (v1_relat_1(A) -> v1_relat_1(k7_relat_1(A,B)))) # label(dt_k7_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 729 $T # label(t43_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 730 (all A all B (v1_relat_1(B) -> r1_tarski(k9_relat_1(B,A),k9_relat_1(B,k1_relat_1(B))))) # label(t147_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 731 $T # label(dt_k3_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 732 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(B,C) -> r1_tarski(k9_relat_1(B,A),k9_relat_1(C,A))))))) # label(t157_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 733 (all A (v1_relat_1(A) -> (k1_xboole_0 = k2_relat_1(A) <-> k1_relat_1(A) = k1_xboole_0))) # label(t65_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 734 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(C,B) & r1_tarski(k1_relat_1(C),A) -> r1_tarski(C,k7_relat_1(B,A))))))) # label(t186_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 735 (all A all B (v1_relat_1(B) -> r1_tarski(k2_relat_1(k8_relat_1(A,B)),k2_relat_1(B)))) # label(t118_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 736 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k1_relat_1(k5_relat_1(A,B)),k1_relat_1(A)))))) # label(t44_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 737 (all A (v1_relat_1(A) -> A = k5_relat_1(A,k6_relat_1(k2_relat_1(A))))) # label(t80_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 738 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k2_relat_1(k8_relat_1(B,C))) <-> r2_hidden(A,k2_relat_1(C)) & r2_hidden(A,B)))) # label(t115_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 739 (all A all B (v1_relat_1(B) -> r1_tarski(k7_relat_1(B,A),B))) # label(t88_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 740 (all A all B (v1_relat_1(B) -> -(v3_relat_1(B) & -v3_relat_1(k7_relat_1(B,A))))) # label(t190_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 741 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k1_relat_1(k3_xboole_0(A,B)),k3_xboole_0(k1_relat_1(A),k1_relat_1(B))))))) # label(t14_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 742 (all A all B (v1_relat_1(B) -> k8_relat_1(A,B) = k3_xboole_0(B,k2_zfmisc_1(k1_relat_1(B),A)))) # label(t124_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 743 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k3_relat_1(k3_xboole_0(A,B)),k3_xboole_0(k3_relat_1(A),k3_relat_1(B))))))) # label(t34_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 744 (all A all B all C all D (v1_relat_1(D) -> (r2_hidden(k4_tarski(A,B),D) & r2_hidden(A,C) <-> r2_hidden(k4_tarski(A,B),k5_relat_1(k6_relat_1(C),D))))) # label(t74_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 745 (all A all B v1_relat_1(k1_tarski(k4_tarski(A,B)))) # label(t4_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 746 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(A,B) -> r1_tarski(k3_relat_1(A),k3_relat_1(B))))))) # label(t31_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 747 (all A all B all C (v1_relat_1(C) -> r1_tarski(k9_relat_1(C,k3_xboole_0(A,B)),k3_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B))))) # label(t154_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 748 (all A all B (v1_relat_1(B) -> -(r2_hidden(A,k1_relat_1(B)) & (all C -r2_hidden(C,k2_relat_1(B)))))) # label(t18_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 749 (all A all B (v1_relat_1(B) -> r1_tarski(k5_relat_1(B,k6_relat_1(A)),B) & r1_tarski(k5_relat_1(k6_relat_1(A),B),B))) # label(t76_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 750 (all A all B all C (v1_relat_1(C) -> r1_tarski(k4_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)),k10_relat_1(C,k4_xboole_0(A,B))))) # label(t177_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 751 (all A all B (v1_relat_1(B) -> (r1_tarski(k1_relat_1(B),A) -> k5_relat_1(k6_relat_1(A),B) = B))) # label(t77_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 752 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k2_relat_1(k3_xboole_0(A,B)),k3_xboole_0(k2_relat_1(A),k2_relat_1(B))))))) # label(t27_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 753 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> r1_tarski(k5_relat_1(k7_relat_1(B,A),C),k5_relat_1(B,C)))))) # label(t92_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 754 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k5_relat_1(A,k5_relat_1(B,C)) = k5_relat_1(k5_relat_1(A,B),C))))))) # label(t55_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 755 $T # label(t113_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 756 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k8_relat_1(A,C),k8_relat_1(B,C))))) # label(t131_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 757 (all A all B (v1_relat_1(B) -> ((all C all D (r2_hidden(k4_tarski(C,D),B) <-> r2_hidden(C,A) & C = D)) <-> k6_relat_1(A) = B))) # label(d10_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 758 (all A all B all C (v1_relat_1(C) -> r1_tarski(k10_relat_1(C,k3_xboole_0(A,B)),k3_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B))))) # label(t176_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 759 (all A all B all C (v1_relat_1(C) -> k8_relat_1(k3_xboole_0(A,B),C) = k8_relat_1(A,k8_relat_1(B,C)))) # label(t127_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 760 (all A all B (v1_relat_1(B) -> k7_relat_1(B,A) = k5_relat_1(k6_relat_1(A),B))) # label(t94_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 761 (all A all B (v1_relat_1(B) -> r1_tarski(k1_relat_1(k7_relat_1(B,A)),k1_relat_1(B)))) # label(t89_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 762 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k8_relat_1(A,C),k8_relat_1(B,D))))))) # label(t133_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 763 (all A all B all C (v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),C) -> r2_hidden(A,k1_relat_1(C)) & r2_hidden(B,k2_relat_1(C))))) # label(t20_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 764 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k4_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k4_relat_1(A),k4_relat_1(B)))))) # label(t40_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 765 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (k5_relat_1(B,D) = k6_relat_1(A) & k6_relat_1(k1_relat_1(D)) = k5_relat_1(C,B) & r1_tarski(k2_relat_1(C),A) & A = k1_relat_1(B) -> D = C))))))) # label(t82_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 766 (all A all B all C (v1_relat_1(C) -> k4_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)) = k8_relat_1(k4_xboole_0(A,B),C))) # label(t136_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 767 $T # label(t141_relat_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 768 (all A k6_relat_1(A) = k2_funct_1(k6_relat_1(A))) # label(t67_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 769 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(k5_relat_1(B,A)) = k1_relat_1(B) -> r1_tarski(k2_relat_1(B),k1_relat_1(A))))))) # label(t27_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 770 $T # label(t109_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 771 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(k5_relat_1(C,B))) -> k1_funct_1(B,k1_funct_1(C,A)) = k1_funct_1(k5_relat_1(C,B),A)))))) # label(t22_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 772 (exists A (v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A))) # label(rc4_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 773 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> r1_tarski(k9_relat_1(k8_relat_1(A,C),B),k9_relat_1(C,B)))) # label(t120_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 774 $T # label(t5_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 775 (all A all B (v1_relat_1(B) -> (k10_relat_1(B,k1_tarski(A)) != k1_xboole_0 <-> r2_hidden(A,k2_relat_1(B))))) # label(t142_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 776 $T # label(t103_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 777 $T # label(t69_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 778 (all A v2_funct_1(k6_relat_1(A))) # label(t52_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 779 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) <-> (all B -((all C k10_relat_1(A,k1_tarski(B)) != k1_tarski(C)) & r2_hidden(B,k2_relat_1(A))))))) # label(t144_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 780 $T # label(t98_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.11 781 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_tarski(k9_relat_1(C,k3_xboole_0(A,k10_relat_1(C,B))),k3_xboole_0(k9_relat_1(C,A),B)))) # label(t149_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 782 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> k2_funct_1(A) = k4_relat_1(A)))) # label(d9_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 783 (exists A (v1_funct_1(A) & v1_xboole_0(A) & v1_relat_1(A))) # label(rc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 784 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C ((all D (r2_hidden(D,C) <-> r2_hidden(k1_funct_1(A,D),B) & r2_hidden(D,k1_relat_1(A)))) <-> C = k10_relat_1(A,B))))) # label(d13_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 785 $T # label(t132_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 786 $T # label(d2_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 787 (all A all B -((all C (v1_relat_1(C) & v1_funct_1(C) -> -(B = k1_relat_1(C) & r1_tarski(k2_relat_1(C),A)))) & -(k1_xboole_0 = A & B != k1_xboole_0))) # label(t18_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 788 (all A all B all C (v1_relat_1(C) -> k10_relat_1(k7_relat_1(C,A),B) = k3_xboole_0(A,k10_relat_1(C,B)))) # label(t139_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 789 $T # label(t39_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 790 $T # label(t30_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 791 (all A all B all C (v1_relat_1(C) -> r1_tarski(k3_xboole_0(A,k10_relat_1(C,B)),k10_relat_1(C,k3_xboole_0(k9_relat_1(C,A),B))))) # label(t151_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 792 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> k2_relat_1(k5_relat_1(k2_funct_1(A),A)) = k2_relat_1(A) & k1_relat_1(k5_relat_1(k2_funct_1(A),A)) = k2_relat_1(A)))) # label(t59_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 793 $T # label(t130_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 794 $T # label(t119_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 795 $T # label(t31_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 796 $T # label(d6_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 797 $T # label(t24_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 798 $T # label(t111_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 799 (exists A (v1_funct_1(A) & v2_relat_1(A) & v1_relat_1(A))) # label(rc5_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 800 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k5_relat_1(A,B) = A & k2_relat_1(A) = k1_relat_1(B) -> B = k6_relat_1(k1_relat_1(B))))))) # label(t44_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 801 $T # label(d10_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 802 $T # label(t116_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 803 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(A) = k1_relat_1(B) & (all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(A,C) = k1_funct_1(B,C))) -> A = B))))) # label(t9_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 804 $T # label(t140_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 805 $T # label(t135_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 806 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_tarski(A) = k2_relat_1(B) & k1_tarski(A) = k2_relat_1(C) & k1_relat_1(C) = k1_relat_1(B) -> C = B))))) # label(t17_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 807 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (v2_funct_1(C) & r1_xboole_0(A,B) -> r1_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B))))) # label(t125_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 808 $T # label(t134_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 809 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> k3_xboole_0(k9_relat_1(C,A),B) = k9_relat_1(C,k3_xboole_0(A,k10_relat_1(C,B))))) # label(t150_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 810 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> B = k9_relat_1(k6_relat_1(A),B))) # label(t162_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 811 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> k2_funct_1(k2_funct_1(A)) = A))) # label(t65_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 812 (all A all B (v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(B) & v1_relat_1(A) -> v1_funct_1(k5_relat_1(A,B)) & v1_relat_1(k5_relat_1(A,B)))) # label(fc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 813 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) & r2_hidden(A,k2_relat_1(B)) -> A = k1_funct_1(B,k1_funct_1(k2_funct_1(B),A)) & A = k1_funct_1(k5_relat_1(k2_funct_1(B),B),A)))) # label(t57_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 814 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B all C k4_xboole_0(k9_relat_1(A,B),k9_relat_1(A,C)) = k9_relat_1(A,k4_xboole_0(B,C))) -> v2_funct_1(A)))) # label(t124_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 815 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) -> r1_tarski(k10_relat_1(B,k9_relat_1(B,A)),A)))) # label(t152_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 816 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(k1_funct_1(C,A),k1_relat_1(B)) & r2_hidden(A,k1_relat_1(C)) <-> r2_hidden(A,k1_relat_1(k5_relat_1(C,B)))))))) # label(t21_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 817 $T # label(t4_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 818 $T # label(t45_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 819 $T # label(t36_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 820 $T # label(t80_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 821 (all A (v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) -> v1_relat_1(k4_relat_1(A)) & v1_funct_1(k4_relat_1(A)))) # label(fc3_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 822 $T # label(t104_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 823 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k2_relat_1(B),k1_relat_1(A)) & v2_funct_1(k5_relat_1(B,A)) -> v2_funct_1(B)))))) # label(t47_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 824 $T # label(t95_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 825 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B -(v1_xboole_0(k1_funct_1(A,B)) & r2_hidden(B,k1_relat_1(A)))) <-> v2_relat_1(A)))) # label(d15_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 826 $T # label(t129_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 827 (all A all B (r2_hidden(B,A) -> B = k1_funct_1(k6_relat_1(A),B))) # label(t35_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 828 $T # label(t102_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 829 $T # label(t106_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 830 (all A (v1_xboole_0(A) -> v1_funct_1(A))) # label(cc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 831 $T # label(t11_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 832 (all A (v1_funct_1(k6_relat_1(A)) & v1_relat_1(k6_relat_1(A)))) # label(fc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 833 $T # label(t41_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 834 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k9_relat_1(B,k10_relat_1(B,A)),A))) # label(t145_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 835 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> k3_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)) = k10_relat_1(C,k3_xboole_0(A,B)))) # label(t137_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 836 $T # label(t93_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 837 (all A all B (v1_relat_1(B) -> (r1_tarski(A,k1_relat_1(B)) -> r1_tarski(A,k10_relat_1(B,k9_relat_1(B,A)))))) # label(t146_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 838 $T # label(t74_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 839 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(C)) & k1_funct_1(C,A) = B <-> r2_hidden(k4_tarski(A,B),C)))) # label(t8_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 840 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) -> v2_funct_1(k8_relat_1(A,B))))) # label(t99_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 841 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(C,k1_funct_1(B,A)) = k1_funct_1(k5_relat_1(B,C),A)))))) # label(t23_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 842 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k1_relat_1(k8_relat_1(A,C))) -> k1_funct_1(k8_relat_1(A,C),B) = k1_funct_1(C,B)))) # label(t87_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 843 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(A) & v2_funct_1(B) -> k5_relat_1(k2_funct_1(B),k2_funct_1(A)) = k2_funct_1(k5_relat_1(A,B))))))) # label(t66_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 844 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_relat_1(B),k1_relat_1(A)) & k1_relat_1(C) = k1_relat_1(B) & k5_relat_1(B,A) = k5_relat_1(C,A) & r1_tarski(k2_relat_1(C),k1_relat_1(A)) -> B = C))))) <-> v2_funct_1(A)))) # label(t49_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 845 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B ((all C (r2_hidden(C,B) <-> (exists D (k1_funct_1(A,D) = C & r2_hidden(D,k1_relat_1(A)))))) <-> k2_relat_1(A) = B)))) # label(d5_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 846 $T # label(d7_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 847 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,k2_relat_1(C)) & r1_tarski(k10_relat_1(C,A),k10_relat_1(C,B)) -> r1_tarski(A,B)))) # label(t158_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 848 (all A (v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) -> v1_setfam_1(k2_relat_1(A)))) # label(fc6_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 849 $T # label(t29_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 850 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> v1_relat_1(k8_relat_1(A,B)) & v1_funct_1(k8_relat_1(A,B)))) # label(fc5_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 851 $T # label(t110_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 852 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> k3_xboole_0(k1_relat_1(B),A) = k1_relat_1(k5_relat_1(k6_relat_1(A),B)))) # label(t37_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 853 (all A all B k6_relat_1(k3_xboole_0(A,B)) = k5_relat_1(k6_relat_1(B),k6_relat_1(A))) # label(t43_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 854 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> k3_xboole_0(A,k9_relat_1(B,k1_relat_1(B))) = k9_relat_1(B,k10_relat_1(B,A)))) # label(t148_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 855 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((exists B (k6_relat_1(k1_relat_1(A)) = k5_relat_1(A,B) & v1_funct_1(B) & v1_relat_1(B))) -> v2_funct_1(A)))) # label(t53_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 856 (all A (v1_relat_1(A) & v1_funct_1(A) -> k5_relat_1(A,k6_relat_1(k2_relat_1(A))) = A & k5_relat_1(k6_relat_1(k1_relat_1(A)),A) = A)) # label(t42_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 857 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (v2_funct_1(C) -> k3_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)) = k9_relat_1(C,k3_xboole_0(A,B))))) # label(t121_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 858 $T # label(t1_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 859 $T # label(t136_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 860 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(k2_relat_1(B),k1_relat_1(C)) -> r1_tarski(k10_relat_1(B,A),k10_relat_1(k5_relat_1(B,C),k9_relat_1(C,A)))))))) # label(t160_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 861 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> k2_relat_1(k5_relat_1(A,k2_funct_1(A))) = k1_relat_1(A) & k1_relat_1(A) = k1_relat_1(k5_relat_1(A,k2_funct_1(A)))))) # label(t58_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 862 $T # label(t78_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 863 (all A all B all C (r2_hidden(A,f1_s2_funct_1) & p1_s2_funct_1(A,C) & p1_s2_funct_1(A,B) -> C = B)) & (all A -(r2_hidden(A,f1_s2_funct_1) & (all B -p1_s2_funct_1(A,B)))) -> (exists A (k1_relat_1(A) = f1_s2_funct_1 & (all B (r2_hidden(B,f1_s2_funct_1) -> p1_s2_funct_1(B,k1_funct_1(A,B)))) & v1_funct_1(A) & v1_relat_1(A))) # label(s2_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 864 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(k5_relat_1(B,A)) & k2_relat_1(B) = k1_relat_1(A) -> v2_funct_1(B) & v2_funct_1(A)))))) # label(t48_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 865 $T # label(t115_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 866 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(A) & k2_relat_1(B) = k1_relat_1(A) & k6_relat_1(k2_relat_1(A)) = k5_relat_1(B,A) -> B = k2_funct_1(A)))))) # label(t64_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 867 $T # label(t6_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 868 $T # label(t108_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 869 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,B) -> k7_relat_1(C,A) = k7_relat_1(k7_relat_1(C,A),B) & k7_relat_1(k7_relat_1(C,B),A) = k7_relat_1(C,A)))) # label(t82_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 870 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k2_relat_1(k5_relat_1(C,B))) -> r2_hidden(A,k2_relat_1(B))))))) # label(t25_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 871 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k2_relat_1(A) = k1_relat_1(B) & (all C all D ((k1_funct_1(B,C) = D & r2_hidden(C,k2_relat_1(A)) -> C = k1_funct_1(A,D) & r2_hidden(D,k1_relat_1(A))) & (r2_hidden(D,k1_relat_1(A)) & k1_funct_1(A,D) = C -> D = k1_funct_1(B,C) & r2_hidden(C,k2_relat_1(A))))) <-> B = k2_funct_1(A))))))) # label(t54_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 872 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v3_relat_1(A) <-> (all B (r2_hidden(B,k1_relat_1(A)) -> v1_xboole_0(k1_funct_1(A,B))))))) # label(d14_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 873 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B r1_tarski(k10_relat_1(A,k9_relat_1(A,B)),B)) -> v2_funct_1(A)))) # label(t153_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 874 $T # label(d3_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 875 (all A all B (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)))) # label(fc4_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 876 (all A all B all C (p1_s1_funct_1(A,B) & p1_s1_funct_1(A,C) -> B = C)) -> (exists A (v1_relat_1(A) & v1_funct_1(A) & (all B all C (r2_hidden(k4_tarski(B,C),A) <-> p1_s1_funct_1(B,C) & r2_hidden(B,f1_s1_funct_1))))) # label(s1_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 877 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k2_relat_1(k2_funct_1(A)) = k1_relat_1(A) & k1_relat_1(k2_funct_1(A)) = k2_relat_1(A)))) # label(t55_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 878 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,A) & r2_hidden(B,k1_relat_1(C)) -> r2_hidden(k1_funct_1(C,B),k2_relat_1(k7_relat_1(C,A)))))) # label(t73_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 879 $T # label(t77_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 880 $T # label(t114_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 881 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (A = k2_relat_1(B) & k1_relat_1(D) = A & k5_relat_1(B,C) = k5_relat_1(B,D) & k1_relat_1(C) = A -> D = C))))))) # label(t156_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 882 $T # label(t131_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 883 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k1_relat_1(k8_relat_1(A,B)),k1_relat_1(B)) & r1_tarski(k2_relat_1(k8_relat_1(A,B)),k2_relat_1(B)))) # label(t89_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 884 $T # label(t3_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 885 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(B) = k1_tarski(A) -> k1_tarski(k1_funct_1(B,A)) = k2_relat_1(B)))) # label(t14_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 886 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C -(r2_hidden(C,A) & (all D -(k1_funct_1(B,D) = C & r2_hidden(D,k1_relat_1(B)))))) -> r1_tarski(A,k2_relat_1(B))))) # label(t19_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 887 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k3_xboole_0(k1_relat_1(C),A)) -> k1_funct_1(C,B) = k1_funct_1(k7_relat_1(C,A),B)))) # label(t71_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 888 $T # label(t75_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 889 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k1_relat_1(C)) & r2_hidden(A,k1_relat_1(C)) -> k9_relat_1(C,k2_tarski(A,B)) = k2_tarski(k1_funct_1(C,A),k1_funct_1(C,B))))) # label(t118_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 890 $T # label(t96_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 891 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(A) & k2_relat_1(A) = k1_relat_1(B) & (all C all D (r2_hidden(C,k1_relat_1(A)) & r2_hidden(D,k1_relat_1(B)) -> (C = k1_funct_1(B,D) <-> D = k1_funct_1(A,C)))) & k2_relat_1(B) = k1_relat_1(A) -> B = k2_funct_1(A)))))) # label(t60_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 892 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) <-> (all B exists C r1_tarski(k10_relat_1(A,k1_tarski(B)),k1_tarski(C)))))) # label(t159_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 893 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k1_relat_1(k7_relat_1(C,A))) -> k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B)))) # label(t70_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 894 (all A ((all B all C all D (r2_hidden(k4_tarski(B,D),A) & r2_hidden(k4_tarski(B,C),A) -> D = C)) <-> v1_funct_1(A))) # label(d1_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 895 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(k1_funct_1(C,B),A) & r2_hidden(B,k1_relat_1(C)) <-> r2_hidden(B,k1_relat_1(k8_relat_1(A,C)))))) # label(t86_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 896 (exists A (v1_relat_1(A) & v1_funct_1(A))) # label(rc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 897 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k9_relat_1(C,A),k9_relat_1(C,B)) & v2_funct_1(C) & r1_tarski(A,k1_relat_1(C)) -> r1_tarski(A,B)))) # label(t157_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 898 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (k6_relat_1(A) = B <-> (all C (r2_hidden(C,A) -> C = k1_funct_1(B,C))) & k1_relat_1(B) = A))) # label(t34_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 899 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> k9_relat_1(B,k1_tarski(A)) = k1_tarski(k1_funct_1(B,A))))) # label(t117_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 900 $T # label(t91_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 901 $T # label(t127_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 902 $T # label(t81_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 903 (exists A (v1_funct_1(A) & (all B (r2_hidden(B,f1_s3_funct_1) -> k1_funct_1(A,B) = f2_s3_funct_1(B))) & k1_relat_1(A) = f1_s3_funct_1 & v1_relat_1(A))) # label(s3_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 904 (all A ((all B all C all D (r2_hidden(k4_tarski(B,C),A) & r2_hidden(k4_tarski(B,D),A) -> D = C)) & (all B -((all C all D B != k4_tarski(C,D)) & r2_hidden(B,A))) -> v1_funct_1(A) & v1_relat_1(A))) # label(t2_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 905 (all A all B (v1_relat_1(B) -> ((all C -(r2_hidden(C,A) & k1_xboole_0 = k10_relat_1(B,k1_tarski(C)))) -> r1_tarski(A,k2_relat_1(B))))) # label(t143_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 906 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k6_relat_1(k1_relat_1(A)) = k5_relat_1(A,B) & k2_relat_1(A) = k1_relat_1(B) & v2_funct_1(A) -> B = k2_funct_1(A)))))) # label(t63_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 907 (exists A (v1_relat_1(A) & v1_funct_1(A) & f1_s4_funct_1 = k1_relat_1(A) & (all B (m1_subset_1(B,f1_s4_funct_1) -> k1_funct_1(A,B) = f2_s4_funct_1(B))))) # label(s4_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 908 $T # label(t128_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 909 $T # label(t133_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 910 (all A (k1_xboole_0 != A -> (all B exists C (v1_funct_1(C) & A = k1_relat_1(C) & k1_tarski(B) = k2_relat_1(C) & v1_relat_1(C))))) # label(t15_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 911 $T # label(t107_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 912 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> v2_funct_1(k2_funct_1(A))))) # label(t62_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 913 (exists A (v1_funct_1(A) & v2_funct_1(A) & v1_relat_1(A))) # label(rc3_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 914 $T # label(t88_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 915 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(B) = A & A = k1_relat_1(C) & r1_tarski(k2_relat_1(C),A) & B = k5_relat_1(C,B) & v2_funct_1(B) -> C = k6_relat_1(A)))))) # label(t50_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 916 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,B) -> k8_relat_1(A,C) = k8_relat_1(A,k8_relat_1(B,C)) & k8_relat_1(B,k8_relat_1(A,C)) = k8_relat_1(A,C)))) # label(t97_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 917 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) & r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(k2_funct_1(B),k1_funct_1(B,A)) = A & k1_funct_1(k5_relat_1(B,k2_funct_1(B)),A) = A))) # label(t56_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 918 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k3_xboole_0(k1_relat_1(C),A)) -> k1_funct_1(k5_relat_1(k6_relat_1(A),C),B) = k1_funct_1(C,B)))) # label(t38_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 919 $T # label(t113_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 920 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (k9_relat_1(A,B) = C <-> (all D ((exists E (r2_hidden(E,k1_relat_1(A)) & D = k1_funct_1(A,E) & r2_hidden(E,B))) <-> r2_hidden(D,C))))))) # label(d12_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 921 $T # label(t83_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 922 $T # label(t7_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 923 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k7_relat_1(C,A) = B <-> k3_xboole_0(k1_relat_1(C),A) = k1_relat_1(B) & (all D (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(B,D) = k1_funct_1(C,D)))))))) # label(t68_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 924 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,k2_relat_1(C)) & r1_tarski(B,k2_relat_1(C)) & k10_relat_1(C,A) = k10_relat_1(C,B) -> B = A))) # label(t161_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 925 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k2_funct_1(A)) & v1_funct_1(k2_funct_1(A)))) # label(dt_k2_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 926 $T # label(t94_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 927 $T # label(t101_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 928 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k2_relat_1(B),A) & (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (A = k1_relat_1(D) & k5_relat_1(B,D) = k5_relat_1(B,C) & A = k1_relat_1(C) -> D = C))))) -> A = k2_relat_1(B)))) # label(t33_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 929 $T # label(t32_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 930 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> k3_xboole_0(A,k9_relat_1(C,B)) = k9_relat_1(k8_relat_1(A,C),B))) # label(t126_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 931 $T # label(t13_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 932 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) -> k9_relat_1(B,A) = k10_relat_1(k2_funct_1(B),A)))) # label(t154_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 933 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(k1_funct_1(C,B),A) & r2_hidden(B,k1_relat_1(C)) <-> r2_hidden(B,k1_relat_1(k5_relat_1(C,k6_relat_1(A))))))) # label(t40_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 934 $T # label(t141_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 935 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k1_relat_1(k7_relat_1(B,A)),k1_relat_1(B)) & r1_tarski(k2_relat_1(k7_relat_1(B,A)),k2_relat_1(B)))) # label(t76_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 936 $T # label(dt_k1_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 937 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> r2_hidden(k1_funct_1(B,A),k2_relat_1(B))))) # label(t12_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 938 $T # label(t92_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 939 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,A) -> k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B)))) # label(t72_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 940 $T # label(t90_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 941 (all A ((all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(B) = A & k1_relat_1(C) = A -> C = B))))) -> A = k1_xboole_0)) # label(t16_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 942 $T # label(t100_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 943 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C ((-r2_hidden(B,k1_relat_1(A)) -> (C = k1_funct_1(A,B) <-> C = k1_xboole_0)) & (r2_hidden(B,k1_relat_1(A)) -> (C = k1_funct_1(A,B) <-> r2_hidden(k4_tarski(B,C),A))))))) # label(d4_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 944 $T # label(t79_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 945 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k6_relat_1(k2_relat_1(A)) = k5_relat_1(k2_funct_1(A),A) & k6_relat_1(k1_relat_1(A)) = k5_relat_1(A,k2_funct_1(A))))) # label(t61_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 946 $T # label(t10_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 947 $T # label(t112_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 948 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B all C (k1_funct_1(A,B) = k1_funct_1(A,C) & r2_hidden(C,k1_relat_1(A)) & r2_hidden(B,k1_relat_1(A)) -> B = C)) <-> v2_funct_1(A)))) # label(d8_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 949 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,k2_relat_1(B)) -> A = k9_relat_1(B,k10_relat_1(B,A))))) # label(t147_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 950 $T # label(t28_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 951 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) -> v2_funct_1(k7_relat_1(B,A))))) # label(t84_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 952 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) -> k9_relat_1(k2_funct_1(B),A) = k10_relat_1(B,A)))) # label(t155_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 953 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> ((all D (r2_hidden(k1_funct_1(A,D),k1_relat_1(B)) & r2_hidden(D,k1_relat_1(A)) <-> r2_hidden(D,k1_relat_1(C)))) & (all D (r2_hidden(D,k1_relat_1(C)) -> k1_funct_1(B,k1_funct_1(A,D)) = k1_funct_1(C,D))) -> C = k5_relat_1(A,B)))))))) # label(t20_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 954 $T # label(t26_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 955 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) -> k4_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)) = k9_relat_1(C,k4_xboole_0(A,B))))) # label(t123_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 956 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B all C k9_relat_1(A,k3_xboole_0(B,C)) = k3_xboole_0(k9_relat_1(A,B),k9_relat_1(A,C))) -> v2_funct_1(A)))) # label(t122_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 957 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> k4_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)) = k10_relat_1(C,k4_xboole_0(A,B)))) # label(t138_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 958 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k2_relat_1(k5_relat_1(B,A)) = k2_relat_1(A) & v2_funct_1(A) -> r1_tarski(k1_relat_1(A),k2_relat_1(B))))))) # label(t51_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 959 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k8_relat_1(A,C) = B <-> (all D (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(B,D) = k1_funct_1(C,D))) & (all D (r2_hidden(k1_funct_1(C,D),A) & r2_hidden(D,k1_relat_1(C)) <-> r2_hidden(D,k1_relat_1(B))))))))) # label(t85_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 960 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(A) & v2_funct_1(B) -> v2_funct_1(k5_relat_1(A,B))))))) # label(t46_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 961 (all A (v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) -> v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A))) # label(cc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 962 $T # label(d11_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 963 $T # label(t105_funct_1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 964 (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]. 14.48/14.12 965 (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]. 14.48/14.12 966 $T # label(t5_relat_2) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 967 (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]. 14.48/14.12 968 (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]. 14.48/14.12 969 $T # label(t16_relat_2) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 970 (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]. 14.48/14.12 971 (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]. 14.48/14.12 972 $T # label(t4_relat_2) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 973 (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]. 14.48/14.12 974 (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]. 14.48/14.12 975 (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]. 14.48/14.12 976 (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]. 14.48/14.12 977 $T # label(t3_relat_2) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 978 (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]. 14.48/14.12 979 (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]. 14.48/14.12 980 (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]. 14.48/14.12 981 (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]. 14.48/14.12 982 $T # label(t2_relat_2) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 983 (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]. 14.48/14.12 984 (all A (v1_relat_1(A) -> (v2_relat_2(A) -> v2_relat_2(k4_relat_1(A))))) # label(t28_relat_2) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 985 (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]. 14.48/14.12 986 (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]. 14.48/14.12 987 $T # label(t21_relat_2) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 988 $T # label(t9_relat_2) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 989 (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]. 14.48/14.12 990 (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]. 14.48/14.12 991 $T # label(t11_relat_2) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 992 (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]. 14.48/14.12 993 (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]. 14.48/14.12 994 (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]. 14.48/14.12 995 $T # label(t13_relat_2) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 996 (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]. 14.48/14.12 997 (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]. 14.48/14.12 998 (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]. 14.48/14.12 999 $T # label(t8_relat_2) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 1000 $T # label(t14_relat_2) # label(axiom) # label(non_clause). [assumption]. 14.48/14.12 1001 (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]. 14.48/14.13 1002 (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]. 14.48/14.13 1003 (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]. 14.48/14.13 1004 $T # label(t1_relat_2) # label(axiom) # label(non_clause). [assumption]. 14.48/14.13 1005 $T # label(t15_relat_2) # label(axiom) # label(non_clause). [assumption]. 14.48/14.13 1006 (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]. 14.48/14.13 1007 (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]. 14.48/14.13 1008 (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]. 14.48/14.13 1009 $T # label(t7_relat_2) # label(axiom) # label(non_clause). [assumption]. 14.48/14.13 1010 (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]. 14.48/14.13 1011 (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]. 14.48/14.13 1012 (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]. 14.48/14.13 1013 (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]. 14.48/14.13 1014 (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]. 14.48/14.13 1015 $T # label(t12_relat_2) # label(axiom) # label(non_clause). [assumption]. 14.48/14.13 1016 (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]. 14.48/14.13 1017 $T # label(t6_relat_2) # label(axiom) # label(non_clause). [assumption]. 14.48/14.13 1018 (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]. 14.48/14.13 1019 (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]. 14.48/14.13 1020 (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]. 14.48/14.13 1021 (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]. 14.48/14.13 1022 (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]. 14.48/14.13 1023 $T # label(t10_relat_2) # label(axiom) # label(non_clause). [assumption]. 14.48/14.13 1024 (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]. 14.48/14.13 1025 (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]. 14.48/14.13 1026 (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]. 14.48/14.13 1027 (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]. 14.48/14.13 1028 (exists A (v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A))) # label(rc4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.13 1029 (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]. 14.48/14.13 1030 (all A exists B m1_ordinal1(B,A)) # label(existence_m1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.13 1031 (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]. 14.48/14.13 1032 (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]. 14.48/14.13 1033 (exists A (v2_ordinal1(A) & v3_ordinal1(A) & v1_ordinal1(A))) # label(rc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.13 1034 (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]. 14.48/14.13 1035 (all A k2_xboole_0(A,k1_tarski(A)) = k1_ordinal1(A)) # label(d1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.13 1036 (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]. 14.48/14.13 1037 $T # label(t43_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.13 1038 (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]. 14.48/14.13 1039 (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]. 14.48/14.13 1040 (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]. 14.48/14.13 1041 (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]. 14.48/14.13 1042 $T # label(t11_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.13 1043 (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]. 14.48/14.13 1044 (exists A (v1_ordinal1(A) & v3_ordinal1(A) & v2_ordinal1(A) & -v1_xboole_0(A))) # label(rc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.13 1045 $T # label(t18_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.13 1046 (all A (v1_ordinal1(A) & v2_ordinal1(A) <-> v3_ordinal1(A))) # label(d4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.13 1047 (all A all B (v3_ordinal1(B) -> (r2_hidden(A,B) -> v3_ordinal1(A)))) # label(t23_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.13 1048 (all A all B -(r1_tarski(B,A) & r2_hidden(A,B))) # label(t7_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.48/14.13 1049 (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]. 14.48/14.13 1050 (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]. 14.48/14.13 1051 (all A (v1_ordinal1(A) & v2_ordinal1(A) -> v3_ordinal1(A))) # label(cc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1052 (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]. 14.57/14.13 1053 $T # label(t28_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1054 (all A (v3_ordinal1(A) -> v2_ordinal1(A) & v1_ordinal1(A))) # label(cc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1055 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> r3_xboole_0(A,B))))) # label(t25_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1056 (all A -(all B (v3_ordinal1(B) -> r2_hidden(B,A)))) # label(t38_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1057 $T # label(t17_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1058 (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]. 14.57/14.13 1059 (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]. 14.57/14.13 1060 $T # label(dt_k1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1061 (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]. 14.57/14.13 1062 $T # label(t44_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1063 $T # label(t1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1064 $T # label(t2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1065 (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]. 14.57/14.13 1066 (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]. 14.57/14.13 1067 (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]. 14.57/14.13 1068 (all A k1_ordinal1(A) != A) # label(t14_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1069 (all A all B (k1_ordinal1(B) = k1_ordinal1(A) -> A = B)) # label(t12_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1070 (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]. 14.57/14.13 1071 $T # label(t16_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1072 (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]. 14.57/14.13 1073 (all A m1_ordinal1(k1_xboole_0,A)) # label(t45_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1074 $T # label(d5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1075 (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]. 14.57/14.13 1076 (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]. 14.57/14.13 1077 (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]. 14.57/14.13 1078 (all A -(all B (v3_ordinal1(B) <-> r2_hidden(B,A)))) # label(t37_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1079 (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]. 14.57/14.13 1080 (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]. 14.57/14.13 1081 (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]. 14.57/14.13 1082 $T # label(t20_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1083 (all A r2_hidden(A,k1_ordinal1(A))) # label(t10_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1084 (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]. 14.57/14.13 1085 (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]. 14.57/14.13 1086 (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]. 14.57/14.13 1087 (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]. 14.57/14.13 1088 (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]. 14.57/14.13 1089 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> r1_ordinal1(A,A))) # label(reflexivity_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1090 (all A (k3_tarski(A) = A <-> v4_ordinal1(A))) # label(d6_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1091 $T # label(t40_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1092 (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]. 14.57/14.13 1093 (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]. 14.57/14.13 1094 $T # label(t9_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1095 $T # label(t8_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1096 (all A -v1_xboole_0(k1_ordinal1(A))) # label(fc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1097 (all A (v3_ordinal1(A) -> v3_ordinal1(k3_tarski(A)))) # label(t30_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1098 (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]. 14.57/14.13 1099 (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]. 14.57/14.13 1100 $T # label(t15_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1101 (all A (v1_xboole_0(A) -> v2_ordinal1(A) & v3_ordinal1(A) & v1_ordinal1(A))) # label(cc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1102 (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]. 14.57/14.13 1103 (all A (v1_ordinal1(A) <-> (all B (r2_hidden(B,A) -> r1_tarski(B,A))))) # label(d2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1104 (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]. 14.57/14.13 1105 (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]. 14.57/14.13 1106 (all A (v3_ordinal1(A) -> v3_ordinal1(k1_ordinal1(A)))) # label(t29_ordinal1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1107 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]. 14.57/14.13 1108 (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]. 14.57/14.13 1109 $T # label(t7_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1110 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (all E (v1_funct_1(E) & v1_relat_1(E) -> (r3_wellord1(B,C,E) & r3_wellord1(A,B,D) -> r3_wellord1(A,C,k5_relat_1(D,E))))))))))))) # label(t51_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1111 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> (all B ((all C (r2_hidden(C,k3_relat_1(A)) & r1_tarski(k1_wellord1(A,C),B) -> r2_hidden(C,B))) -> r1_tarski(k3_relat_1(A),B)))))) # label(t41_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1112 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r3_wellord1(A,B,C) & v2_wellord1(A) -> (all D -(r2_hidden(D,k3_relat_1(A)) & (all E -(k9_relat_1(C,k1_wellord1(A,D)) = k1_wellord1(B,E) & r2_hidden(E,k3_relat_1(B))))))))))))) # label(t60_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1113 $T # label(t4_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1114 (all A all B (v1_relat_1(A) -> v1_relat_1(k2_wellord1(A,B)))) # label(dt_k2_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1115 (all A all B all C (v1_relat_1(C) -> (v2_wellord1(C) & r2_hidden(B,k3_relat_1(C)) & (all D (r2_hidden(D,k1_wellord1(C,A)) -> r2_hidden(k4_tarski(D,B),C) & B != D)) & r2_hidden(A,k3_relat_1(C)) -> r2_hidden(k4_tarski(A,B),C)))) # label(t42_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1116 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_wellord1(A) & r3_wellord1(A,B,C) -> (all D -(r2_hidden(D,k3_relat_1(A)) & (all E -(r4_wellord1(k2_wellord1(A,k1_wellord1(A,D)),k2_wellord1(B,k1_wellord1(B,E))) & r2_hidden(E,k3_relat_1(B))))))))))))) # label(t61_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1117 $T # label(t14_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1118 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> (all B -(r2_hidden(B,k3_relat_1(A)) & r4_wellord1(A,k2_wellord1(A,k1_wellord1(A,B)))))))) # label(t57_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1119 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r4_wellord1(A,B) <-> (exists C (v1_relat_1(C) & r3_wellord1(A,B,C) & v1_funct_1(C)))))))) # label(d8_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1120 (all A all B all C all D (v1_relat_1(D) -> (all E (v1_relat_1(E) -> (r2_hidden(A,k3_relat_1(D)) & r2_hidden(B,k3_relat_1(E)) & r4_wellord1(k2_wellord1(D,k1_wellord1(D,A)),k2_wellord1(E,k1_wellord1(E,C))) & r4_wellord1(D,k2_wellord1(E,k1_wellord1(E,B))) & r2_hidden(C,k3_relat_1(E)) & v2_wellord1(E) & v2_wellord1(D) -> r1_tarski(k1_wellord1(E,C),k1_wellord1(E,B)) & r2_hidden(k4_tarski(C,B),E)))))) # label(t62_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1121 (all A all B (v1_relat_1(B) -> (v8_relat_2(B) -> v8_relat_2(k2_wellord1(B,A))))) # label(t24_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1122 (all A all B (v1_relat_1(B) -> (v2_wellord1(B) -> k3_relat_1(k2_wellord1(B,k1_wellord1(B,A))) = k1_wellord1(B,A)))) # label(t40_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1123 (all A all B all C (v1_relat_1(C) -> (v2_wellord1(C) -> r3_xboole_0(k1_wellord1(C,A),k1_wellord1(C,B))))) # label(t33_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1124 (all A all B all C (v1_relat_1(C) -> k2_wellord1(k2_wellord1(C,A),B) = k2_wellord1(C,k3_xboole_0(A,B)))) # label(t26_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1125 (all A all B (v1_relat_1(B) & v1_relat_1(A) -> v1_relat_1(k3_wellord1(A,B)) & v1_funct_1(k3_wellord1(A,B)))) # label(dt_k3_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1126 $T # label(dt_k1_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1127 (all A all B (v1_relat_1(B) -> (v1_relat_2(B) -> v1_relat_2(k2_wellord1(B,A))))) # label(t22_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1128 (all A (v1_relat_1(A) -> (v8_relat_2(A) & v1_wellord1(A) & v6_relat_2(A) & v4_relat_2(A) & v1_relat_2(A) <-> v2_wellord1(A)))) # label(d4_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1129 (all A all B (v1_relat_1(B) -> (r1_tarski(A,k3_relat_1(B)) & v2_wellord1(B) -> k3_relat_1(k2_wellord1(B,A)) = A))) # label(t39_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1130 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k3_relat_1(C)) & r2_hidden(B,k3_relat_1(C)) & v2_wellord1(C) -> (r1_tarski(k1_wellord1(C,A),k1_wellord1(C,B)) <-> B = A | r2_hidden(A,k1_wellord1(C,B)))))) # label(t38_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1131 $T # label(t44_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1132 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> k3_relat_1(A) = k1_xboole_0 | (all B -((all C -(r2_hidden(C,k3_relat_1(A)) & r2_hidden(k4_tarski(B,C),A) & (all D -(r2_hidden(k4_tarski(B,D),A) & D != B & -r2_hidden(k4_tarski(C,D),A) & r2_hidden(D,k3_relat_1(A)))))) & (exists C (-r2_hidden(k4_tarski(C,B),A) & r2_hidden(C,k3_relat_1(A)))) & r2_hidden(B,k3_relat_1(A))))))) # label(t12_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1133 $T # label(t46_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1134 $T # label(t56_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1135 (all A all B (v1_relat_1(B) -> (v1_wellord1(B) -> v1_wellord1(k2_wellord1(B,A))))) # label(t31_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1136 (all A all B (v1_relat_1(B) -> (r2_wellord1(B,A) -> (all C -(k1_xboole_0 != C & (all D -((all E (r2_hidden(E,C) -> r2_hidden(k4_tarski(D,E),B))) & r2_hidden(D,C))) & r1_tarski(C,A)))))) # label(t9_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1137 (all A all B (v1_relat_1(B) -> r1_tarski(k1_wellord1(B,A),k3_relat_1(B)))) # label(t13_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1138 (all A (v1_relat_1(A) -> A = k2_wellord1(A,k3_relat_1(A)))) # label(t30_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1139 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> (all B -((all C -(r2_hidden(C,B) & (all D (r2_hidden(D,B) -> r2_hidden(k4_tarski(C,D),A))))) & k1_xboole_0 != B & r1_tarski(B,k3_relat_1(A))))))) # label(t10_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1140 (all A (v1_relat_1(A) -> (v1_wellord1(A) <-> r1_wellord1(A,k3_relat_1(A))))) # label(t5_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1141 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r4_wellord1(B,C) & r4_wellord1(A,B) -> r4_wellord1(A,C)))))))) # label(t52_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1142 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r3_wellord1(A,B,C) -> (all D all E (r2_hidden(k4_tarski(D,E),A) -> r2_hidden(k4_tarski(k1_funct_1(C,D),k1_funct_1(C,E)),B) & k1_funct_1(C,D) != k1_funct_1(C,E) | E = D))))))))) # label(t45_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1143 (all A all B all C (v1_relat_1(C) -> (v2_wellord1(C) & r2_hidden(B,k1_wellord1(C,A)) & r2_hidden(A,k3_relat_1(C)) -> k1_wellord1(C,B) = k1_wellord1(k2_wellord1(C,k1_wellord1(C,A)),B)))) # label(t35_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1144 $T # label(t1_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1145 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r3_wellord1(A,B,C) <-> v2_funct_1(C) & (all D all E (r2_hidden(k4_tarski(D,E),A) <-> r2_hidden(k4_tarski(k1_funct_1(C,D),k1_funct_1(C,E)),B) & r2_hidden(E,k3_relat_1(A)) & r2_hidden(D,k3_relat_1(A)))) & k3_relat_1(B) = k2_relat_1(C) & k1_relat_1(C) = k3_relat_1(A)))))))) # label(d7_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1146 (all A (v1_relat_1(A) -> (all B (r8_relat_2(A,B) & r4_relat_2(A,B) & r6_relat_2(A,B) & r1_wellord1(A,B) & r1_relat_2(A,B) <-> r2_wellord1(A,B))))) # label(d5_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1147 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v2_wellord1(A) & r4_wellord1(A,B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k3_wellord1(A,B) = C <-> r3_wellord1(A,B,C))))))))) # label(d9_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1148 (all A (v1_relat_1(A) -> -(v2_wellord1(A) & k3_relat_1(A) != k1_xboole_0 & (all B -((all C (r2_hidden(C,k3_relat_1(A)) -> r2_hidden(k4_tarski(B,C),A))) & r2_hidden(B,k3_relat_1(A))))))) # label(t11_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1149 (all A (v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_wellord1(A) & k1_relat_1(B) = k3_relat_1(A) & (all C all D (r2_hidden(k4_tarski(C,D),A) -> D = C | r2_hidden(k4_tarski(k1_funct_1(B,C),k1_funct_1(B,D)),A) & k1_funct_1(B,D) != k1_funct_1(B,C))) & r1_tarski(k2_relat_1(B),k3_relat_1(A)) -> (all C (r2_hidden(C,k3_relat_1(A)) -> r2_hidden(k4_tarski(C,k1_funct_1(B,C)),A)))))))) # label(t43_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1150 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (v2_wellord1(B) & r1_tarski(A,k3_relat_1(B)) & r3_wellord1(B,C,D) -> r3_wellord1(k2_wellord1(B,A),k2_wellord1(C,k9_relat_1(D,A)),k7_relat_1(D,A)) & r4_wellord1(k2_wellord1(B,A),k2_wellord1(C,k9_relat_1(D,A)))))))))) # label(t59_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1151 (all A all B (v1_relat_1(B) -> r2_hidden(A,k3_relat_1(B)) | k1_xboole_0 = k1_wellord1(B,A))) # label(t2_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1152 (all A all B (v1_relat_1(B) -> (v4_relat_2(B) -> v4_relat_2(k2_wellord1(B,A))))) # label(t25_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1153 (all A (v1_relat_1(A) -> (all B all C (C = k1_wellord1(A,B) <-> (all D (r2_hidden(D,C) <-> D != B & r2_hidden(k4_tarski(D,B),A))))))) # label(d1_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1154 (all A (v1_relat_1(A) -> r4_wellord1(A,A))) # label(t48_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1155 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k2_wellord1(C,A) = k2_wellord1(k2_wellord1(C,B),A)))) # label(t29_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1156 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> -(v2_wellord1(A) & -r4_wellord1(A,B) & (all C -(r2_hidden(C,k3_relat_1(A)) & r4_wellord1(k2_wellord1(A,k1_wellord1(A,C)),B))) & (all C -(r2_hidden(C,k3_relat_1(B)) & r4_wellord1(A,k2_wellord1(B,k1_wellord1(B,C))))) & v2_wellord1(B)))))) # label(t63_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1157 (all A all B (v1_relat_1(B) -> k2_wellord1(k2_wellord1(B,A),A) = k2_wellord1(B,A))) # label(t28_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1158 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r3_wellord1(A,B,C) -> (v1_wellord1(A) -> v1_wellord1(B)) & (v4_relat_2(A) -> v4_relat_2(B)) & (v6_relat_2(A) -> v6_relat_2(B)) & (v8_relat_2(A) -> v8_relat_2(B)) & (v1_relat_2(A) -> v1_relat_2(B))))))))) # label(t53_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1159 (all A (v1_relat_1(A) -> ((all B -(r1_tarski(B,k3_relat_1(A)) & k1_xboole_0 != B & (all C -(r1_xboole_0(k1_wellord1(A,C),B) & r2_hidden(C,B))))) <-> v1_wellord1(A)))) # label(d2_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1160 (all A (v1_relat_1(A) -> (all B k2_wellord1(A,B) = k3_xboole_0(A,k2_zfmisc_1(B,B))))) # label(d6_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1161 (all A all B (v1_relat_1(B) -> k7_relat_1(k8_relat_1(A,B),A) = k2_wellord1(B,A))) # label(t17_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1162 (all A all B all C (v1_relat_1(C) -> -(v2_wellord1(C) & r2_hidden(B,k3_relat_1(C)) & r4_wellord1(k2_wellord1(C,k1_wellord1(C,A)),k2_wellord1(C,k1_wellord1(C,B))) & A != B & r2_hidden(A,k3_relat_1(C))))) # label(t58_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1163 (all A all B (v1_relat_1(B) -> (v2_wellord1(B) -> v2_wellord1(k2_wellord1(B,A))))) # label(t32_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1164 (all A all B all C (v1_relat_1(C) -> r1_tarski(k1_wellord1(k2_wellord1(C,A),B),k1_wellord1(C,B)))) # label(t21_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1165 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k3_relat_1(k2_wellord1(C,B))) -> r2_hidden(A,k3_relat_1(C)) & r2_hidden(A,B)))) # label(t19_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1166 $T # label(t6_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1167 (all A all B all C (v1_relat_1(C) -> (r2_hidden(B,k3_relat_1(C)) & r2_hidden(A,k3_relat_1(C)) & v2_wellord1(C) -> (r2_hidden(k4_tarski(A,B),C) <-> r1_tarski(k1_wellord1(C,A),k1_wellord1(C,B)))))) # label(t37_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1168 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v2_wellord1(A) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r3_wellord1(A,B,D) & r3_wellord1(A,B,C) -> D = C)))))))))) # label(t55_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1169 (all A all B (v1_relat_1(B) -> (v6_relat_2(B) -> v6_relat_2(k2_wellord1(B,A))))) # label(t23_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1170 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_wellord1(A) & r3_wellord1(A,B,C) -> v2_wellord1(B)))))))) # label(t54_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1171 (all A all B (v1_relat_1(B) -> k2_wellord1(B,A) = k8_relat_1(A,k7_relat_1(B,A)))) # label(t18_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1172 (all A all B (v1_relat_1(B) -> (v2_wellord1(B) & r1_tarski(A,k3_relat_1(B)) -> (-((all C -(r2_hidden(C,k3_relat_1(B)) & k1_wellord1(B,C) = A)) & k3_relat_1(B) != A) <-> (all C (r2_hidden(C,A) -> (all D (r2_hidden(k4_tarski(D,C),B) -> r2_hidden(D,A))))))))) # label(t36_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1173 $T # label(t34_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1174 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,C) & r2_hidden(A,k2_zfmisc_1(B,B)) <-> r2_hidden(A,k2_wellord1(C,B))))) # label(t16_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1175 (all A all B all C (v1_relat_1(C) -> k2_wellord1(k2_wellord1(C,B),A) = k2_wellord1(k2_wellord1(C,A),B))) # label(t27_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1176 $T # label(t3_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1177 (all A all B (v1_relat_1(B) -> r1_tarski(k2_wellord1(B,A),k2_zfmisc_1(A,A)) & r1_tarski(k2_wellord1(B,A),B))) # label(t15_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1178 (all A (v1_relat_1(A) -> (all B ((all C -(r1_tarski(C,B) & C != k1_xboole_0 & (all D -(r1_xboole_0(k1_wellord1(A,D),C) & r2_hidden(D,C))))) <-> r1_wellord1(A,B))))) # label(d3_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1179 (all A all B (v1_relat_1(B) -> -((all C -(r4_wellord1(k2_wellord1(B,k1_wellord1(B,C)),k2_wellord1(B,A)) & r2_hidden(C,k3_relat_1(B)))) & -r4_wellord1(B,k2_wellord1(B,A)) & v2_wellord1(B) & r1_tarski(A,k3_relat_1(B))))) # label(t64_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1180 (all A (v1_relat_1(A) -> (r2_wellord1(A,k3_relat_1(A)) <-> v2_wellord1(A)))) # label(t8_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1181 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r3_wellord1(A,B,C) -> r3_wellord1(B,A,k2_funct_1(C))))))))) # label(t49_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1182 (all A all B (v1_relat_1(B) -> r1_tarski(k3_relat_1(k2_wellord1(B,A)),A) & r1_tarski(k3_relat_1(k2_wellord1(B,A)),k3_relat_1(B)))) # label(t20_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1183 (all A (v1_relat_1(A) -> r3_wellord1(A,A,k6_relat_1(k3_relat_1(A))))) # label(t47_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1184 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r4_wellord1(A,B) -> r4_wellord1(B,A)))))) # label(t50_wellord1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1185 (all A m2_relset_1(k6_relat_1(A),A,A)) # label(t29_relset_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1186 (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]. 14.57/14.13 1187 (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]. 14.57/14.13 1188 (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]. 14.57/14.13 1189 (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]. 14.57/14.13 1190 (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]. 14.57/14.13 1191 (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]. 14.57/14.13 1192 (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]. 14.57/14.13 1193 (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]. 14.57/14.13 1194 (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]. 14.57/14.13 1195 $T # label(t43_relset_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1196 $T # label(t5_relset_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1197 (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]. 14.57/14.13 1198 (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]. 14.57/14.13 1199 $T # label(t44_relset_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1200 (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]. 14.57/14.13 1201 (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]. 14.57/14.13 1202 (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]. 14.57/14.13 1203 $T # label(t20_relset_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1204 (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]. 14.57/14.13 1205 (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]. 14.57/14.13 1206 (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]. 14.57/14.13 1207 (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]. 14.57/14.13 1208 (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]. 14.57/14.13 1209 (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]. 14.57/14.13 1210 (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]. 14.57/14.13 1211 (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]. 14.57/14.13 1212 (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]. 14.57/14.13 1213 (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]. 14.57/14.13 1214 (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]. 14.57/14.13 1215 (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]. 14.57/14.13 1216 $T # label(t42_relset_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1217 (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]. 14.57/14.13 1218 (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]. 14.57/14.13 1219 $T # label(t7_relset_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1220 $T # label(t40_relset_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1221 (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]. 14.57/14.13 1222 (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]. 14.57/14.13 1223 (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]. 14.57/14.13 1224 (all A all B m2_relset_1(k1_xboole_0,A,B)) # label(t25_relset_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1225 (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]. 14.57/14.13 1226 (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]. 14.57/14.13 1227 $T # label(t18_relset_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1228 (all A all B exists C m2_relset_1(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1229 (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]. 14.57/14.13 1230 (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]. 14.57/14.13 1231 (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]. 14.57/14.13 1232 (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]. 14.57/14.13 1233 (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]. 14.57/14.13 1234 (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]. 14.57/14.13 1235 (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]. 14.57/14.13 1236 $T # label(t1_relset_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.13 1237 (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]. 14.57/14.13 1238 (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]. 14.57/14.13 1239 (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]. 14.57/14.13 1240 (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]. 14.57/14.14 1241 (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]. 14.57/14.14 1242 (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]. 14.57/14.14 1243 (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]. 14.57/14.14 1244 $T # label(t2_relset_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1245 (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]. 14.57/14.14 1246 (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]. 14.57/14.14 1247 $T # label(t21_relset_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1248 (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]. 14.57/14.14 1249 (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]. 14.57/14.14 1250 (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]. 14.57/14.14 1251 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1252 (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]. 14.57/14.14 1253 $T # label(t37_relset_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1254 (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]. 14.57/14.14 1255 (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]. 14.57/14.14 1256 (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]. 14.57/14.14 1257 (all A r1_tarski(k6_relat_1(A),k2_zfmisc_1(A,A))) # label(t28_relset_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1258 (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]. 14.57/14.14 1259 (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]. 14.57/14.14 1260 (all A (-v1_xboole_0(A) -> k6_relat_1(A) != k1_xboole_0)) # label(t46_relset_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1261 (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]. 14.57/14.14 1262 (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]. 14.57/14.14 1263 $T # label(t41_relset_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1264 (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]. 14.57/14.14 1265 (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]. 14.57/14.14 1266 (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]. 14.57/14.14 1267 (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]. 14.57/14.14 1268 $T # label(t3_relset_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1269 (all A all B exists C m1_relset_1(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1270 (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]. 14.57/14.14 1271 (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]. 14.57/14.14 1272 (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]. 14.57/14.14 1273 (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]. 14.57/14.14 1274 $T # label(t177_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1275 (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]. 14.57/14.14 1276 (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]. 14.57/14.14 1277 $T # label(d2_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1278 $T # label(t90_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1279 (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]. 14.57/14.14 1280 (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]. 14.57/14.14 1281 (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]. 14.57/14.14 1282 $T # label(t166_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1283 (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]. 14.57/14.14 1284 $T # label(t118_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1285 $T # label(t42_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1286 (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]. 14.57/14.14 1287 $T # label(t149_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1288 (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]. 14.57/14.14 1289 (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]. 14.57/14.14 1290 $T # label(t151_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1291 (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]. 14.57/14.14 1292 $T # label(t12_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1293 (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]. 14.57/14.14 1294 (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]. 14.57/14.14 1295 (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]. 14.57/14.14 1296 $T # label(t182_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1297 (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]. 14.57/14.14 1298 $T # label(t111_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1299 $T # label(t133_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1300 (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]. 14.57/14.14 1301 (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]. 14.57/14.14 1302 $T # label(t161_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1303 $T # label(t152_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1304 (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]. 14.57/14.14 1305 (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]. 14.57/14.14 1306 $T # label(t75_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1307 (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]. 14.57/14.14 1308 (all A all B k3_partfun1(k1_xboole_0,A,B) = k1_xboole_0) # label(t91_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1309 (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]. 14.57/14.14 1310 $T # label(d1_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1311 (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]. 14.57/14.14 1312 (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]. 14.57/14.14 1313 (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]. 14.57/14.14 1314 (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]. 14.57/14.14 1315 (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]. 14.57/14.14 1316 (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]. 14.57/14.14 1317 (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]. 14.57/14.14 1318 $T # label(t150_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1319 $T # label(t165_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1320 (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]. 14.57/14.14 1321 (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]. 14.57/14.14 1322 (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]. 14.57/14.14 1323 $T # label(t20_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1324 $T # label(t40_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1325 (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]. 14.57/14.14 1326 (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]. 14.57/14.14 1327 $T # label(t137_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1328 (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]. 14.57/14.14 1329 (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]. 14.57/14.14 1330 (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]. 14.57/14.14 1331 (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]. 14.57/14.14 1332 (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]. 14.57/14.14 1333 (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]. 14.57/14.14 1334 $T # label(t170_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1335 $T # label(t179_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1336 (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]. 14.57/14.14 1337 $T # label(t108_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1338 $T # label(t155_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1339 (all A k1_tarski(k1_xboole_0) = k4_partfun1(A,k1_xboole_0)) # label(t123_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1340 (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]. 14.57/14.14 1341 (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]. 14.57/14.14 1342 (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]. 14.57/14.14 1343 $T # label(t23_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1344 (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]. 14.57/14.14 1345 (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]. 14.57/14.14 1346 (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]. 14.57/14.14 1347 $T # label(t164_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1348 (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]. 14.57/14.14 1349 $T # label(t52_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1350 $T # label(t16_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1351 $T # label(t6_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1352 (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]. 14.57/14.14 1353 (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]. 14.57/14.14 1354 $T # label(t173_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1355 (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]. 14.57/14.14 1356 (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]. 14.57/14.14 1357 $T # label(t134_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1358 $T # label(t22_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1359 (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]. 14.57/14.14 1360 (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]. 14.57/14.14 1361 $T # label(t15_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1362 $T # label(t183_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1363 (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]. 14.57/14.14 1364 (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]. 14.57/14.14 1365 (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]. 14.57/14.14 1366 $T # label(t110_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1367 $T # label(t129_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1368 (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]. 14.57/14.14 1369 $T # label(t124_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1370 (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]. 14.57/14.14 1371 (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]. 14.57/14.14 1372 (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]. 14.57/14.14 1373 (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]. 14.57/14.14 1374 (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]. 14.57/14.14 1375 (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]. 14.57/14.14 1376 (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]. 14.57/14.14 1377 (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]. 14.57/14.14 1378 (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]. 14.57/14.14 1379 (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]. 14.57/14.14 1380 (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]. 14.57/14.14 1381 (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]. 14.57/14.14 1382 (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]. 14.57/14.14 1383 (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]. 14.57/14.14 1384 (all A k4_partfun1(k1_xboole_0,A) = k1_tarski(k1_xboole_0)) # label(t122_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1385 (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]. 14.57/14.14 1386 (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]. 14.57/14.14 1387 (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]. 14.57/14.14 1388 (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]. 14.57/14.14 1389 $T # label(t98_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1390 (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]. 14.57/14.14 1391 (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]. 14.57/14.14 1392 $T # label(t106_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1393 $T # label(t184_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1394 (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]. 14.57/14.14 1395 $T # label(t5_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1396 (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]. 14.57/14.14 1397 $T # label(t167_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1398 $T # label(t105_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1399 $T # label(t181_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1400 (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]. 14.57/14.14 1401 (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]. 14.57/14.14 1402 (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]. 14.57/14.14 1403 $T # label(t13_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1404 $T # label(t102_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1405 (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]. 14.57/14.14 1406 (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]. 14.57/14.14 1407 (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]. 14.57/14.14 1408 (all A k6_relat_1(A) = k6_partfun1(A)) # label(redefinition_k6_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1409 (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]. 14.57/14.14 1410 (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]. 14.57/14.14 1411 (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]. 14.57/14.14 1412 (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]. 14.57/14.14 1413 $T # label(t160_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1414 (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]. 14.57/14.14 1415 $T # label(t107_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1416 $T # label(t18_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1417 (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]. 14.57/14.14 1418 (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]. 14.57/14.14 1419 $T # label(t156_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1420 (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]. 14.57/14.14 1421 (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]. 14.57/14.14 1422 (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]. 14.57/14.14 1423 $T # label(t89_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1424 (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]. 14.57/14.14 1425 (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]. 14.57/14.14 1426 (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]. 14.57/14.14 1427 (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]. 14.57/14.14 1428 (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]. 14.57/14.14 1429 (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]. 14.57/14.14 1430 $T # label(t157_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1431 (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]. 14.57/14.14 1432 (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]. 14.57/14.14 1433 $T # label(t104_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1434 $T # label(t4_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1435 $T # label(t101_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1436 (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]. 14.57/14.14 1437 $T # label(t103_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1438 (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]. 14.57/14.14 1439 (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]. 14.57/14.14 1440 $T # label(dt_k4_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1441 $T # label(t154_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1442 (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]. 14.57/14.14 1443 (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]. 14.57/14.14 1444 $T # label(t109_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1445 (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]. 14.57/14.14 1446 (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]. 14.57/14.14 1447 (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]. 14.57/14.14 1448 (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]. 14.57/14.14 1449 (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]. 14.57/14.14 1450 (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]. 14.57/14.14 1451 (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]. 14.57/14.14 1452 $T # label(t8_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.14 1453 (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]. 14.57/14.15 1454 $T # label(t153_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1455 $T # label(t163_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1456 (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]. 14.57/14.15 1457 $T # label(t7_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1458 $T # label(t19_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1459 $T # label(t14_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1460 $T # label(t11_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1461 (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]. 14.57/14.15 1462 (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]. 14.57/14.15 1463 (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]. 14.57/14.15 1464 (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]. 14.57/14.15 1465 $T # label(dt_k5_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1466 (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]. 14.57/14.15 1467 $T # label(t178_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1468 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (all E (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]. 14.57/14.15 1469 $T # label(t48_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1470 (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]. 14.57/14.15 1471 (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]. 14.57/14.15 1472 $T # label(t50_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1473 (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]. 14.57/14.15 1474 $T # label(t100_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1475 $T # label(t159_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1476 (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]. 14.57/14.15 1477 (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]. 14.57/14.15 1478 $T # label(t17_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1479 $T # label(t180_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1480 $T # label(t41_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1481 $T # label(t21_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1482 (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]. 14.57/14.15 1483 (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]. 14.57/14.15 1484 $T # label(t9_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1485 $T # label(t88_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1486 (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]. 14.57/14.15 1487 (all A all B -v1_xboole_0(k4_partfun1(A,B))) # label(fc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1488 (all A -((all B -(r2_hidden(B,A) & (all C all D all E (r2_hidden(E,B) & r2_hidden(D,E) & r2_hidden(C,D) -> r1_xboole_0(C,A))))) & k1_xboole_0 != A)) # label(t4_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1489 (all A all B all C all D all E all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,D) -> (F = k4_mcart_1(G,H,I,J) -> E = J))))))))) -> k1_xboole_0 = C | E = k11_mcart_1(A,B,C,D,F) | D = k1_xboole_0 | B = k1_xboole_0 | k1_xboole_0 = A))) # label(t82_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1490 (all A all B all C all D all E all F (r1_tarski(C,D) & r1_tarski(E,F) & r1_tarski(A,B) -> r1_tarski(k3_zfmisc_1(A,C,E),k3_zfmisc_1(B,D,F)))) # label(t77_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1491 (all A all B all C all D all E all F all G all H (k4_zfmisc_1(E,F,G,H) = k4_zfmisc_1(A,B,C,D) -> k4_zfmisc_1(A,B,C,D) = k1_xboole_0 | H = D & G = C & F = B & E = A)) # label(t57_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1492 (all A all B -(-(all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> C = k4_tarski(k1_mcart_1(C),k2_mcart_1(C)))) & B != k1_xboole_0 & k1_xboole_0 != A)) # label(t24_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1493 (all A all B all C all D all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> m1_subset_1(k10_mcart_1(A,B,C,D,E),C))) # label(dt_k10_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1494 (all A all B all C all D -(k1_xboole_0 != A & B != k1_xboole_0 & (exists E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) & (exists F exists G exists H exists I (-(H = k10_mcart_1(A,B,C,D,E) & k11_mcart_1(A,B,C,D,E) = I & G = k9_mcart_1(A,B,C,D,E) & k8_mcart_1(A,B,C,D,E) = F) & k4_mcart_1(F,G,H,I) = E)))) & k1_xboole_0 != D & k1_xboole_0 != C)) # label(t59_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1495 (all A all B all C all D k3_zfmisc_1(k2_tarski(A,B),k1_tarski(C),k1_tarski(D)) = k2_tarski(k3_mcart_1(A,C,D),k3_mcart_1(B,C,D))) # label(t40_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1496 $T # label(t30_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1497 (all A all B all C -(B != k1_xboole_0 & k1_xboole_0 != C & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> k7_mcart_1(A,B,C,D) = k2_mcart_1(D) & k2_mcart_1(k1_mcart_1(D)) = k6_mcart_1(A,B,C,D) & k1_mcart_1(k1_mcart_1(D)) = k5_mcart_1(A,B,C,D))) & k1_xboole_0 != A)) # label(t50_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1498 (all A all B all C all D all E all F all G all H (k4_mcart_1(E,F,G,H) = k4_mcart_1(A,B,C,D) -> B = F & G = C & D = H & A = E)) # label(t33_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1499 (all A all B all C all D (k4_zfmisc_1(A,B,C,D) != k1_xboole_0 <-> A != k1_xboole_0 & B != k1_xboole_0 & k1_xboole_0 != C & k1_xboole_0 != D)) # label(t55_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1500 $T # label(dt_k3_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1501 (all A all B all C all D all E all F all G all H (r1_tarski(E,F) & r1_tarski(G,H) & r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k4_zfmisc_1(A,C,E,G),k4_zfmisc_1(B,D,F,H)))) # label(t88_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1502 (all A all B all C all D all E all F (m1_subset_1(D,k1_zfmisc_1(A)) & m1_subset_1(E,k1_zfmisc_1(B)) & m1_subset_1(F,k1_zfmisc_1(C)) -> m1_subset_1(k13_mcart_1(A,B,C,D,E,F),k1_zfmisc_1(k3_zfmisc_1(A,B,C))))) # label(dt_k13_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1503 (all A all B all C all D k2_tarski(k3_mcart_1(A,B,D),k3_mcart_1(A,C,D)) = k3_zfmisc_1(k1_tarski(A),k2_tarski(B,C),k1_tarski(D))) # label(t41_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1504 (all A k20_mcart_1(A) = k2_mcart_1(k2_mcart_1(A))) # label(d17_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1505 (all A all B all C all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> m1_subset_1(k7_mcart_1(A,B,C,D),C))) # label(dt_k7_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1506 (all A all B -(B != k1_xboole_0 & -(all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> k2_mcart_1(C) != C & C != k1_mcart_1(C))) & k1_xboole_0 != A)) # label(t26_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1507 (all A k1_mcart_1(k1_mcart_1(A)) = k17_mcart_1(A)) # label(d14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1508 $T # label(dt_k20_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1509 (all A all B all C all D k4_mcart_1(A,B,C,D) = k3_mcart_1(k4_tarski(A,B),C,D)) # label(t32_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1510 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (all E (m1_subset_1(E,k1_zfmisc_1(B)) -> (all F (m1_subset_1(F,k1_zfmisc_1(C)) -> (all G (m1_subset_1(G,k3_zfmisc_1(A,B,C)) -> (r2_hidden(G,k3_zfmisc_1(D,E,F)) -> r2_hidden(k5_mcart_1(A,B,C,G),D) & r2_hidden(k6_mcart_1(A,B,C,G),E) & r2_hidden(k7_mcart_1(A,B,C,G),F)))))))))) # label(t76_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1511 (all A all B all C all D -(B != k1_xboole_0 & k1_xboole_0 != D & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> k9_mcart_1(A,B,C,D,E) = k2_mcart_1(k1_mcart_1(k1_mcart_1(E))) & k11_mcart_1(A,B,C,D,E) = k2_mcart_1(E) & k10_mcart_1(A,B,C,D,E) = k2_mcart_1(k1_mcart_1(E)) & k8_mcart_1(A,B,C,D,E) = k1_mcart_1(k1_mcart_1(k1_mcart_1(E))))) & k1_xboole_0 != C & A != k1_xboole_0)) # label(t61_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1512 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(k2_tarski(B,C),k1_tarski(D))) -> k2_mcart_1(A) = D & (B = k1_mcart_1(A) | C = k1_mcart_1(A)))) # label(t17_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1513 (all A all B all C all D all E all F all G all H (m1_subset_1(G,k1_zfmisc_1(C)) & m1_subset_1(H,k1_zfmisc_1(D)) & m1_subset_1(F,k1_zfmisc_1(B)) & m1_subset_1(E,k1_zfmisc_1(A)) -> m1_subset_1(k14_mcart_1(A,B,C,D,E,F,G,H),k1_zfmisc_1(k4_zfmisc_1(A,B,C,D))))) # label(dt_k14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1514 (all A all B all C all D -(k1_xboole_0 != B & D != k1_xboole_0 & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,A) -> (k8_mcart_1(A,B,C,D,E) = F <-> (all G all H all I all J (k4_mcart_1(G,H,I,J) = E -> F = G))))))) & k1_xboole_0 != C & k1_xboole_0 != A)) # label(d8_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1515 (all A all B all C all D all E all F k3_zfmisc_1(k2_tarski(A,B),k2_tarski(C,D),k2_tarski(E,F)) = k6_enumset1(k3_mcart_1(A,C,E),k3_mcart_1(A,D,E),k3_mcart_1(A,C,F),k3_mcart_1(A,D,F),k3_mcart_1(B,C,E),k3_mcart_1(B,D,E),k3_mcart_1(B,C,F),k3_mcart_1(B,D,F))) # label(t46_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1516 (all A all B all C all D -(A != k1_xboole_0 & k1_xboole_0 != C & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> E = k4_mcart_1(k8_mcart_1(A,B,C,D,E),k9_mcart_1(A,B,C,D,E),k10_mcart_1(A,B,C,D,E),k11_mcart_1(A,B,C,D,E)))) & D != k1_xboole_0 & k1_xboole_0 != B)) # label(t60_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1517 (all A all B all C all D all E k2_enumset1(k3_mcart_1(A,B,D),k3_mcart_1(A,C,D),k3_mcart_1(A,B,E),k3_mcart_1(A,C,E)) = k3_zfmisc_1(k1_tarski(A),k2_tarski(B,C),k2_tarski(D,E))) # label(t45_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1518 (all A -(k1_xboole_0 != A & (all B -((all C all D (r2_hidden(D,B) & r2_hidden(C,D) -> r1_xboole_0(C,A))) & r2_hidden(B,A))))) # label(t3_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1519 (all A ((exists B exists C k4_tarski(B,C) = A) -> A = k4_tarski(k1_mcart_1(A),k2_mcart_1(A)))) # label(t8_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1520 (all A all B all C -(B != k1_xboole_0 & k1_xboole_0 != C & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> k3_mcart_1(k5_mcart_1(A,B,C,D),k6_mcart_1(A,B,C,D),k7_mcart_1(A,B,C,D)) = D)) & k1_xboole_0 != A)) # label(t48_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1521 (all A all B all C all D all E all F all G all H (-r1_xboole_0(k4_zfmisc_1(A,B,C,D),k4_zfmisc_1(E,F,G,H)) -> -r1_xboole_0(A,E) & -r1_xboole_0(B,F) & -r1_xboole_0(D,H) & -r1_xboole_0(C,G))) # label(t64_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1522 (all A k1_mcart_1(k2_mcart_1(A)) = k19_mcart_1(A)) # label(d16_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1523 (all A all B all C all D -(r2_hidden(A,k3_zfmisc_1(B,C,D)) & (all E all F all G -(r2_hidden(E,B) & A = k3_mcart_1(E,F,G) & r2_hidden(G,D) & r2_hidden(F,C))))) # label(t72_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1524 (all A all B all C all D k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,B),C),D) = k4_zfmisc_1(A,B,C,D)) # label(t53_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1525 (all A all B all C all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> m1_subset_1(k6_mcart_1(A,B,C,D),B))) # label(dt_k6_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1526 (all A all B all C (r2_hidden(A,k2_zfmisc_1(B,C)) -> A != k1_mcart_1(A) & k2_mcart_1(A) != A)) # label(t67_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1527 (all A all B all C all D all E (m1_subset_1(E,k3_zfmisc_1(A,B,C)) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (k3_mcart_1(F,G,H) = E -> H = D))))))) -> A = k1_xboole_0 | D = k7_mcart_1(A,B,C,E) | C = k1_xboole_0 | k1_xboole_0 = B))) # label(t71_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1528 (all A all B all C all D all E all F (m1_subset_1(D,k1_zfmisc_1(A)) & m1_subset_1(E,k1_zfmisc_1(B)) & m1_subset_1(F,k1_zfmisc_1(C)) -> k3_zfmisc_1(D,E,F) = k13_mcart_1(A,B,C,D,E,F))) # label(redefinition_k13_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1529 (all A all B all C all D all E ((all F (r2_hidden(F,A) <-> (exists G exists H exists I exists J (r2_hidden(G,B) & r2_hidden(H,C) & k4_mcart_1(G,H,I,J) = F & r2_hidden(J,E) & r2_hidden(I,D))))) -> k4_zfmisc_1(B,C,D,E) = A)) # label(t85_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1530 (all A all B all C all D all E all F all G all H (r2_hidden(C,G) & r2_hidden(D,H) & r2_hidden(B,F) & r2_hidden(A,E) <-> r2_hidden(k4_mcart_1(A,B,C,D),k4_zfmisc_1(E,F,G,H)))) # label(t84_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1531 (all A ((exists B exists C A = k4_tarski(B,C)) -> (all B (B = k2_mcart_1(A) <-> (all C all D (A = k4_tarski(C,D) -> D = B)))))) # label(d2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1532 (all A all B all C all D all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> m1_subset_1(k11_mcart_1(A,B,C,D,E),D))) # label(dt_k11_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1533 (all A all B all C all D all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> -(k1_xboole_0 != A & B != k1_xboole_0 & k1_xboole_0 != C & D != k1_xboole_0 & (exists F exists G exists H exists I (E = k4_mcart_1(F,G,H,I) & -(F = k8_mcart_1(A,B,C,D,E) & G = k9_mcart_1(A,B,C,D,E) & I = k11_mcart_1(A,B,C,D,E) & k10_mcart_1(A,B,C,D,E) = H)))))) # label(t78_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1534 (all A all B all C all D -(k1_xboole_0 != A & k1_xboole_0 != D & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,D) -> (k11_mcart_1(A,B,C,D,E) = F <-> (all G all H all I all J (k4_mcart_1(G,H,I,J) = E -> J = F))))))) & k1_xboole_0 != C & B != k1_xboole_0)) # label(d11_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1535 (all A all B all C all D all E all F (r2_hidden(A,D) & r2_hidden(B,E) & r2_hidden(C,F) <-> r2_hidden(k3_mcart_1(A,B,C),k3_zfmisc_1(D,E,F)))) # label(t73_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1536 (all A all B all C all D ((all E (r2_hidden(E,A) <-> (exists F exists G exists H (r2_hidden(F,B) & k3_mcart_1(F,G,H) = E & r2_hidden(H,D) & r2_hidden(G,C))))) -> A = k3_zfmisc_1(B,C,D))) # label(t74_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1537 (all A -((all B -((all C (r2_hidden(C,B) -> r1_xboole_0(C,A))) & r2_hidden(B,A))) & k1_xboole_0 != A)) # label(t2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1538 (all A all B (k2_zfmisc_1(A,B) != k1_xboole_0 -> (all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> k1_mcart_1(C) != C & k2_mcart_1(C) != C)))) # label(t66_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1539 (all A all B all C k4_tarski(k4_tarski(A,B),C) = k3_mcart_1(A,B,C)) # label(d3_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1540 (all A all B all C all D k4_zfmisc_1(A,B,C,D) = k3_zfmisc_1(k2_zfmisc_1(A,B),C,D)) # label(t54_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1541 (all A all B all C all D k2_enumset1(k4_tarski(A,C),k4_tarski(A,D),k4_tarski(B,C),k4_tarski(B,D)) = k2_zfmisc_1(k2_tarski(A,B),k2_tarski(C,D))) # label(t25_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1542 (all A all B all C all D all E all F (k19_mcart_1(k4_tarski(F,k4_tarski(D,E))) = D & k20_mcart_1(k4_tarski(F,k4_tarski(D,E))) = E & B = k18_mcart_1(k4_tarski(k4_tarski(A,B),C)) & A = k17_mcart_1(k4_tarski(k4_tarski(A,B),C)))) # label(t89_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1543 (all A all B all C all D k3_zfmisc_1(k1_tarski(A),k1_tarski(B),k2_tarski(C,D)) = k2_tarski(k3_mcart_1(A,B,C),k3_mcart_1(A,B,D))) # label(t42_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1544 $T # label(dt_k17_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1545 $T # label(t21_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1546 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> k2_mcart_1(k1_funct_1(A,C)) = k1_funct_1(B,C))) & k1_relat_1(A) = k1_relat_1(B) <-> k16_mcart_1(A) = B))))) # label(d13_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1547 (all A all B all C all D (-(-r1_tarski(A,k4_zfmisc_1(C,D,A,B)) & -r1_tarski(A,k4_zfmisc_1(D,A,B,C)) & -r1_tarski(A,k4_zfmisc_1(B,C,D,A)) & -r1_tarski(A,k4_zfmisc_1(A,B,C,D))) -> A = k1_xboole_0)) # label(t63_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1548 (all A -(A != k1_xboole_0 & (all B -((all C all D -((r2_hidden(D,A) | r2_hidden(C,A)) & k4_tarski(C,D) = B)) & r2_hidden(B,A))))) # label(t9_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1549 (all A all B all C all D all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> m1_subset_1(k9_mcart_1(A,B,C,D,E),B))) # label(dt_k9_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1550 (all A all B (k4_zfmisc_1(A,A,A,A) = k4_zfmisc_1(B,B,B,B) -> A = B)) # label(t58_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1551 (all A all B (k3_zfmisc_1(A,A,A) = k3_zfmisc_1(B,B,B) -> A = B)) # label(t38_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1552 (all A all B all C all D all E all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,D) -> (k4_mcart_1(G,H,I,J) = F -> I = E))))))))) -> A = k1_xboole_0 | k1_xboole_0 = C | E = k10_mcart_1(A,B,C,D,F) | k1_xboole_0 = D | k1_xboole_0 = B))) # label(t81_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1553 $T # label(dt_k19_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1554 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k15_mcart_1(A)) & v1_relat_1(k15_mcart_1(A)))) # label(dt_k15_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1555 (all A all B all C all D k4_mcart_1(A,B,C,D) = k4_tarski(k4_tarski(k4_tarski(A,B),C),D)) # label(t31_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1556 (all A all B all C all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> m1_subset_1(k5_mcart_1(A,B,C,D),A))) # label(dt_k5_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1557 (all A -((all B -(r2_hidden(B,A) & (all C all D all E all F -((r2_hidden(D,A) | r2_hidden(C,A)) & B = k4_mcart_1(C,D,E,F))))) & A != k1_xboole_0)) # label(t34_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1558 (all A all B all C all D all E all F (k3_zfmisc_1(A,B,C) = k3_zfmisc_1(D,E,F) -> k3_zfmisc_1(A,B,C) = k1_xboole_0 | A = D & F = C & E = B)) # label(t37_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1559 $T # label(dt_k1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1560 (all A all B all C all D all E all F -((exists G (m1_subset_1(G,k3_zfmisc_1(A,B,C)) & (exists H (-(k6_mcart_1(D,E,F,H) = k6_mcart_1(A,B,C,G) & k7_mcart_1(A,B,C,G) = k7_mcart_1(D,E,F,H) & k5_mcart_1(D,E,F,H) = k5_mcart_1(A,B,C,G)) & G = H & m1_subset_1(H,k3_zfmisc_1(D,E,F)))))) & F != k1_xboole_0 & E != k1_xboole_0 & D != k1_xboole_0 & k1_xboole_0 != C & k1_xboole_0 != B & A != k1_xboole_0)) # label(t75_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1561 (all A all B all C all D all E (m1_subset_1(E,k1_zfmisc_1(A)) -> (all F (m1_subset_1(F,k1_zfmisc_1(B)) -> (all G (m1_subset_1(G,k1_zfmisc_1(C)) -> (all H (m1_subset_1(H,k1_zfmisc_1(D)) -> (all I (m1_subset_1(I,k4_zfmisc_1(A,B,C,D)) -> (r2_hidden(I,k4_zfmisc_1(E,F,G,H)) -> r2_hidden(k8_mcart_1(A,B,C,D,I),E) & r2_hidden(k10_mcart_1(A,B,C,D,I),G) & r2_hidden(k11_mcart_1(A,B,C,D,I),H) & r2_hidden(k9_mcart_1(A,B,C,D,I),F)))))))))))) # label(t87_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1562 (all A all B (k2_mcart_1(k4_tarski(A,B)) = B & k1_mcart_1(k4_tarski(A,B)) = A)) # label(t7_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1563 (all A all B all C all D k1_tarski(k4_mcart_1(A,B,C,D)) = k4_zfmisc_1(k1_tarski(A),k1_tarski(B),k1_tarski(C),k1_tarski(D))) # label(t65_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1564 (all A all B all C all D all E (r2_hidden(A,k2_zfmisc_1(k2_tarski(B,C),k2_tarski(D,E))) -> (C = k1_mcart_1(A) | k1_mcart_1(A) = B) & (k2_mcart_1(A) = D | k2_mcart_1(A) = E))) # label(t19_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1565 (all A all B all C (r2_hidden(k1_mcart_1(A),B) & r2_hidden(k2_mcart_1(A),C) -> (all D all E k4_tarski(D,E) != A) | r2_hidden(A,k2_zfmisc_1(B,C)))) # label(t11_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1566 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(B,k2_tarski(C,D))) -> (D = k2_mcart_1(A) | k2_mcart_1(A) = C) & r2_hidden(k1_mcart_1(A),B))) # label(t16_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1567 (all A -(k1_xboole_0 != A & (all B -(r2_hidden(B,A) & r1_xboole_0(B,A))))) # label(t1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1568 (all A all B all C k1_tarski(k3_mcart_1(A,B,C)) = k3_zfmisc_1(k1_tarski(A),k1_tarski(B),k1_tarski(C))) # label(t39_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1569 $T # label(dt_k4_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1570 (all A all B all C -(k1_xboole_0 != A & C != k1_xboole_0 & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> D != k7_mcart_1(A,B,C,D) & k6_mcart_1(A,B,C,D) != D & k5_mcart_1(A,B,C,D) != D)) & k1_xboole_0 != B)) # label(t51_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1571 (all A all B all C all D all E all F all G all H (k4_zfmisc_1(A,B,C,D) = k4_zfmisc_1(E,F,G,H) -> k1_xboole_0 = D | E = A & B = F & C = G & H = D | C = k1_xboole_0 | B = k1_xboole_0 | k1_xboole_0 = A)) # label(t56_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1572 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(k1_tarski(B),k2_tarski(C,D))) -> k1_mcart_1(A) = B & (k2_mcart_1(A) = D | k2_mcart_1(A) = C))) # label(t18_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1573 (all A all B all C all D all E all F (k3_mcart_1(A,B,C) = k3_mcart_1(D,E,F) -> A = D & F = C & E = B)) # label(t28_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1574 $T # label(t27_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1575 (all A ((exists B exists C k4_tarski(B,C) = A) -> A != k1_mcart_1(A) & k2_mcart_1(A) != A)) # label(t20_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1576 (all A all B all C all D (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(D,k1_zfmisc_1(B)) -> k2_zfmisc_1(C,D) = k12_mcart_1(A,B,C,D))) # label(redefinition_k12_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1577 (all A ((exists B exists C A = k4_tarski(B,C)) -> (all B ((all C all D (k4_tarski(C,D) = A -> B = C)) <-> B = k1_mcart_1(A))))) # label(d1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1578 $T # label(dt_k2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1579 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(B,C) = k1_mcart_1(k1_funct_1(A,C)))) & k1_relat_1(B) = k1_relat_1(A) <-> k15_mcart_1(A) = B))))) # label(d12_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1580 $T # label(t22_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1581 (all A all B all C -(k1_xboole_0 != C & (exists D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) & (exists E exists F exists G (k3_mcart_1(E,F,G) = D & -(k7_mcart_1(A,B,C,D) = G & k6_mcart_1(A,B,C,D) = F & E = k5_mcart_1(A,B,C,D)))))) & k1_xboole_0 != B & k1_xboole_0 != A)) # label(t47_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1582 (all A k18_mcart_1(A) = k2_mcart_1(k1_mcart_1(A))) # label(d15_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1583 $T # label(dt_k18_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1584 (all A all B all C all D all E all F (-r1_xboole_0(k3_zfmisc_1(A,B,C),k3_zfmisc_1(D,E,F)) -> -r1_xboole_0(A,D) & -r1_xboole_0(C,F) & -r1_xboole_0(B,E))) # label(t52_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1585 (all A all B all C all D all E (m1_subset_1(E,k3_zfmisc_1(A,B,C)) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (E = k3_mcart_1(F,G,H) -> D = G))))))) -> k1_xboole_0 = B | C = k1_xboole_0 | k6_mcart_1(A,B,C,E) = D | A = k1_xboole_0))) # label(t70_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1586 (all A all B all C all D all E all F (k3_zfmisc_1(D,E,F) = k3_zfmisc_1(A,B,C) -> A = k1_xboole_0 | k1_xboole_0 = C | C = F & E = B & D = A | k1_xboole_0 = B)) # label(t36_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1587 (all A all B all C all D all E (m1_subset_1(E,k3_zfmisc_1(A,B,C)) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (E = k3_mcart_1(F,G,H) -> D = F))))))) -> A = k1_xboole_0 | k1_xboole_0 = B | k1_xboole_0 = C | D = k5_mcart_1(A,B,C,E)))) # label(t69_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1588 (all A -((all B -((all C all D all E all F all G (r2_hidden(C,D) & r2_hidden(D,E) & r2_hidden(E,F) & r2_hidden(G,B) & r2_hidden(F,G) -> r1_xboole_0(C,A))) & r2_hidden(B,A))) & k1_xboole_0 != A)) # label(t6_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1589 (all A all B all C all D all E -((all F all G all H all I -(r2_hidden(F,B) & r2_hidden(G,C) & r2_hidden(H,D) & r2_hidden(I,E) & k4_mcart_1(F,G,H,I) = A)) & r2_hidden(A,k4_zfmisc_1(B,C,D,E)))) # label(t83_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1590 (all A all B all C all D (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(D,k1_zfmisc_1(B)) -> m1_subset_1(k12_mcart_1(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(A,B))))) # label(dt_k12_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1591 (all A all B all C (-(-r1_tarski(A,k3_zfmisc_1(A,B,C)) & -r1_tarski(A,k3_zfmisc_1(B,C,A)) & -r1_tarski(A,k3_zfmisc_1(C,A,B))) -> k1_xboole_0 = A)) # label(t49_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1592 (all A all B all C -(k1_xboole_0 != C & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> (all E (m1_subset_1(E,C) -> (E = k7_mcart_1(A,B,C,D) <-> (all F all G all H (D = k3_mcart_1(F,G,H) -> H = E))))))) & B != k1_xboole_0 & k1_xboole_0 != A)) # label(d7_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1593 (all A all B all C all D all E all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,D) -> (k4_mcart_1(G,H,I,J) = F -> G = E))))))))) -> k1_xboole_0 = A | k1_xboole_0 = B | k1_xboole_0 = D | E = k8_mcart_1(A,B,C,D,F) | C = k1_xboole_0))) # label(t79_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1594 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k16_mcart_1(A)) & v1_relat_1(k16_mcart_1(A)))) # label(dt_k16_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1595 (all A all B all C all D all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> m1_subset_1(k8_mcart_1(A,B,C,D,E),A))) # label(dt_k8_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1596 (all A -((all B -((all C all D all E all F (r2_hidden(F,B) & r2_hidden(E,F) & r2_hidden(D,E) & r2_hidden(C,D) -> r1_xboole_0(C,A))) & r2_hidden(B,A))) & k1_xboole_0 != A)) # label(t5_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1597 (all A all B all C -(C != k1_xboole_0 & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> (all E (m1_subset_1(E,B) -> ((all F all G all H (D = k3_mcart_1(F,G,H) -> G = E)) <-> k6_mcart_1(A,B,C,D) = E))))) & k1_xboole_0 != B & A != k1_xboole_0)) # label(d6_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1598 (all A all B all C all D -(A != k1_xboole_0 & C != k1_xboole_0 & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> E != k9_mcart_1(A,B,C,D,E) & k11_mcart_1(A,B,C,D,E) != E & E != k10_mcart_1(A,B,C,D,E) & E != k8_mcart_1(A,B,C,D,E))) & k1_xboole_0 != D & k1_xboole_0 != B)) # label(t62_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1599 (all A all B all C all D k4_mcart_1(A,B,C,D) = k4_tarski(k3_mcart_1(A,B,C),D)) # label(d4_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1600 (all A all B all C (r2_hidden(A,k2_zfmisc_1(k1_tarski(B),C)) -> B = k1_mcart_1(A) & r2_hidden(k2_mcart_1(A),C))) # label(t12_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1601 (all A all B all C (r2_hidden(A,k2_zfmisc_1(B,C)) -> k4_tarski(k1_mcart_1(A),k2_mcart_1(A)) = A)) # label(t23_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1602 (all A all B all C all D all E all F all G all H (m1_subset_1(E,k1_zfmisc_1(A)) & m1_subset_1(H,k1_zfmisc_1(D)) & m1_subset_1(G,k1_zfmisc_1(C)) & m1_subset_1(F,k1_zfmisc_1(B)) -> k14_mcart_1(A,B,C,D,E,F,G,H) = k4_zfmisc_1(E,F,G,H))) # label(redefinition_k14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1603 (all A all B all C all D all E all F all G all H -(B != k1_xboole_0 & k1_xboole_0 != E & k1_xboole_0 != F & k1_xboole_0 != G & H != k1_xboole_0 & (exists I ((exists J (m1_subset_1(J,k4_zfmisc_1(E,F,G,H)) & -(k9_mcart_1(A,B,C,D,I) = k9_mcart_1(E,F,G,H,J) & k10_mcart_1(E,F,G,H,J) = k10_mcart_1(A,B,C,D,I) & k11_mcart_1(E,F,G,H,J) = k11_mcart_1(A,B,C,D,I) & k8_mcart_1(E,F,G,H,J) = k8_mcart_1(A,B,C,D,I)) & J = I)) & m1_subset_1(I,k4_zfmisc_1(A,B,C,D)))) & k1_xboole_0 != D & C != k1_xboole_0 & A != k1_xboole_0)) # label(t86_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1604 (all A all B all C (k3_zfmisc_1(A,B,C) != k1_xboole_0 <-> k1_xboole_0 != C & k1_xboole_0 != B & A != k1_xboole_0)) # label(t35_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1605 (all A all B all C -(-(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> (all E (m1_subset_1(E,A) -> ((all F all G all H (k3_mcart_1(F,G,H) = D -> E = F)) <-> k5_mcart_1(A,B,C,D) = E))))) & C != k1_xboole_0 & k1_xboole_0 != B & A != k1_xboole_0)) # label(d5_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1606 (all A all B all C all D all E all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,D) -> (F = k4_mcart_1(G,H,I,J) -> H = E))))))))) -> k1_xboole_0 = C | D = k1_xboole_0 | E = k9_mcart_1(A,B,C,D,F) | k1_xboole_0 = B | k1_xboole_0 = A))) # label(t80_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1607 (all A all B all C all D all E k2_enumset1(k3_mcart_1(A,C,E),k3_mcart_1(B,C,E),k3_mcart_1(A,D,E),k3_mcart_1(B,D,E)) = k3_zfmisc_1(k2_tarski(A,B),k2_tarski(C,D),k1_tarski(E))) # label(t43_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1608 (all A all B all C all D all E k2_enumset1(k3_mcart_1(A,C,D),k3_mcart_1(B,C,D),k3_mcart_1(A,C,E),k3_mcart_1(B,C,E)) = k3_zfmisc_1(k2_tarski(A,B),k1_tarski(C),k2_tarski(D,E))) # label(t44_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1609 (all A all B all C all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> -(A != k1_xboole_0 & B != k1_xboole_0 & (exists E exists F exists G (D = k3_mcart_1(E,F,G) & -(E = k5_mcart_1(A,B,C,D) & F = k6_mcart_1(A,B,C,D) & G = k7_mcart_1(A,B,C,D)))) & C != k1_xboole_0))) # label(t68_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1610 (all A all B all C all D -(k1_xboole_0 != A & B != k1_xboole_0 & D != k1_xboole_0 & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,B) -> ((all G all H all I all J (k4_mcart_1(G,H,I,J) = E -> H = F)) <-> k9_mcart_1(A,B,C,D,E) = F))))) & k1_xboole_0 != C)) # label(d9_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1611 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(k2_tarski(B,C),D)) -> r2_hidden(k2_mcart_1(A),D) & (B = k1_mcart_1(A) | C = k1_mcart_1(A)))) # label(t15_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1612 (all A all B all C all D -(-(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,C) -> (k10_mcart_1(A,B,C,D,E) = F <-> (all G all H all I all J (E = k4_mcart_1(G,H,I,J) -> I = F))))))) & D != k1_xboole_0 & C != k1_xboole_0 & B != k1_xboole_0 & k1_xboole_0 != A)) # label(d10_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1613 (all A all B all C (r2_hidden(A,k2_zfmisc_1(B,C)) -> r2_hidden(k1_mcart_1(A),B) & r2_hidden(k2_mcart_1(A),C))) # label(t10_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1614 (all A all B all C (r2_hidden(A,k2_zfmisc_1(k1_tarski(B),k1_tarski(C))) -> k2_mcart_1(A) = C & B = k1_mcart_1(A))) # label(t14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1615 (all A all B all C (r2_hidden(A,k2_zfmisc_1(B,k1_tarski(C))) -> k2_mcart_1(A) = C & r2_hidden(k1_mcart_1(A),B))) # label(t13_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1616 (all A -((all B -(r2_hidden(B,A) & (all C all D all E -(k3_mcart_1(C,D,E) = B & (r2_hidden(D,A) | r2_hidden(C,A)))))) & A != k1_xboole_0)) # label(t29_mcart_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1617 $T # label(t19_wellord2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1618 (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]. 14.57/14.15 1619 (all A v1_relat_1(k1_wellord2(A))) # label(dt_k1_wellord2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1620 (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]. 14.57/14.15 1621 (all A v4_relat_2(k1_wellord2(A))) # label(t5_wellord2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1622 $T # label(t21_wellord2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1623 (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]. 14.57/14.15 1624 (all A all B (r2_tarski(A,B) <-> r2_wellord2(A,B))) # label(redefinition_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1625 (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]. 14.57/14.15 1626 (all A v8_relat_2(k1_wellord2(A))) # label(t3_wellord2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1627 (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]. 14.57/14.15 1628 (all A (v3_ordinal1(A) -> v1_wellord1(k1_wellord2(A)))) # label(t6_wellord2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1629 (all A (v1_relat_1(A) -> v3_ordinal1(k2_wellord2(A)))) # label(dt_k2_wellord2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1630 (all A v1_relat_2(k1_wellord2(A))) # label(t2_wellord2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1631 (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]. 14.57/14.15 1632 (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]. 14.57/14.15 1633 $T # label(t23_wellord2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1634 (all A exists B (v1_relat_1(B) & r2_wellord1(B,A))) # label(t26_wellord2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1635 (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]. 14.57/14.15 1636 (all A all B r2_wellord2(A,A)) # label(reflexivity_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1637 (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]. 14.57/14.15 1638 $T # label(t15_wellord2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1639 (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]. 14.57/14.15 1640 (all A all B (r2_wellord2(A,B) -> r2_wellord2(B,A))) # label(symmetry_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1641 $T # label(t18_wellord2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1642 (all A (v3_ordinal1(A) -> v2_wellord1(k1_wellord2(A)))) # label(t7_wellord2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1643 (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]. 14.57/14.15 1644 $T # label(t20_wellord2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1645 $T # label(t1_wellord2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1646 (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]. 14.57/14.15 1647 $T # label(t16_wellord2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1648 $T # label(t24_wellord2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1649 (all A (v3_ordinal1(A) -> v6_relat_2(k1_wellord2(A)))) # label(t4_wellord2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.15 1650 (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]. 14.57/14.15 1651 (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]. 14.57/14.16 1652 (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]. 14.57/14.16 1653 (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]. 14.57/14.16 1654 (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]. 14.57/14.16 1655 (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]. 14.57/14.16 1656 $T # label(t52_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1657 $T # label(t63_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1658 $T # label(t117_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1659 (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]. 14.57/14.16 1660 (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]. 14.57/14.16 1661 (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]. 14.57/14.16 1662 (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]. 14.57/14.16 1663 (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]. 14.57/14.16 1664 (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]. 14.57/14.16 1665 (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]. 14.57/14.16 1666 (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]. 14.57/14.16 1667 $T # label(t68_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1668 $T # label(t56_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1669 $T # label(t103_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1670 (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]. 14.57/14.16 1671 $T # label(t101_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1672 $T # label(t39_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1673 (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]. 14.57/14.16 1674 $T # label(t58_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1675 (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]. 14.57/14.16 1676 (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]. 14.57/14.16 1677 $T # label(t114_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1678 (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]. 14.57/14.16 1679 $T # label(t90_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1680 $T # label(t112_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1681 (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]. 14.57/14.16 1682 (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]. 14.57/14.16 1683 $T # label(t2_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1684 (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]. 14.57/14.16 1685 (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]. 14.57/14.16 1686 $T # label(t57_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1687 (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]. 14.57/14.16 1688 $T # label(t144_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1689 (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]. 14.57/14.16 1690 $T # label(t105_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1691 (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]. 14.57/14.16 1692 $T # label(t104_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1693 (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]. 14.57/14.16 1694 $T # label(t10_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1695 (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]. 14.57/14.16 1696 (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]. 14.57/14.16 1697 $T # label(t93_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1698 (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]. 14.57/14.16 1699 (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]. 14.57/14.16 1700 (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]. 14.57/14.16 1701 (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]. 14.57/14.16 1702 (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]. 14.57/14.16 1703 $T # label(t122_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1704 (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]. 14.57/14.16 1705 $T # label(t89_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1706 $T # label(t33_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1707 (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]. 14.57/14.16 1708 (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]. 14.57/14.16 1709 (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]. 14.57/14.16 1710 (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]. 14.57/14.16 1711 (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]. 14.57/14.16 1712 (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]. 14.57/14.16 1713 (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]. 14.57/14.16 1714 (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]. 14.57/14.16 1715 (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]. 14.57/14.16 1716 (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]. 14.57/14.16 1717 $T # label(t72_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1718 (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]. 14.57/14.16 1719 (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]. 14.57/14.16 1720 (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]. 14.57/14.16 1721 $T # label(t78_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1722 (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]. 14.57/14.16 1723 (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]. 14.57/14.16 1724 (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]. 14.57/14.16 1725 (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]. 14.57/14.16 1726 $T # label(t100_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1727 (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]. 14.57/14.16 1728 (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]. 14.57/14.16 1729 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]. 14.57/14.16 1730 $T # label(t109_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1731 (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]. 14.57/14.16 1732 $T # label(t125_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1733 (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]. 14.57/14.16 1734 (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]. 14.57/14.16 1735 $T # label(t15_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1736 (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]. 14.57/14.16 1737 (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]. 14.57/14.16 1738 (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]. 14.57/14.16 1739 (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]. 14.57/14.16 1740 $T # label(t137_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1741 $T # label(t139_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1742 (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]. 14.57/14.16 1743 (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]. 14.57/14.16 1744 (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]. 14.57/14.16 1745 (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]. 14.57/14.16 1746 (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]. 14.57/14.16 1747 (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]. 14.57/14.16 1748 (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]. 14.57/14.16 1749 (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]. 14.57/14.16 1750 (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]. 14.57/14.16 1751 (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]. 14.57/14.16 1752 (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]. 14.57/14.16 1753 (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]. 14.57/14.16 1754 (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]. 14.57/14.16 1755 (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]. 14.57/14.16 1756 $T # label(t13_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1757 $T # label(t84_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1758 $T # label(t54_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1759 (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]. 14.57/14.16 1760 $T # label(dt_k1_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1761 $T # label(t102_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1762 (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]. 14.57/14.16 1763 (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]. 14.57/14.16 1764 (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]. 14.57/14.16 1765 (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]. 14.57/14.16 1766 (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]. 14.57/14.16 1767 (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]. 14.57/14.16 1768 (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]. 14.57/14.16 1769 (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]. 14.57/14.16 1770 (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]. 14.57/14.16 1771 (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]. 14.57/14.16 1772 $T # label(t129_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1773 (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]. 14.57/14.16 1774 (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]. 14.57/14.16 1775 (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]. 14.57/14.16 1776 $T # label(t128_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1777 (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]. 14.57/14.16 1778 (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]. 14.57/14.16 1779 $T # label(t150_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1780 (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]. 14.57/14.16 1781 (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]. 14.57/14.16 1782 $T # label(t98_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1783 (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]. 14.57/14.16 1784 $T # label(t42_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1785 (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]. 14.57/14.16 1786 (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]. 14.57/14.16 1787 (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]. 14.57/14.16 1788 $T # label(t127_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1789 (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]. 14.57/14.16 1790 $T # label(t138_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1791 (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]. 14.57/14.16 1792 (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]. 14.57/14.16 1793 $T # label(t126_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1794 (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]. 14.57/14.16 1795 $T # label(t157_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1796 $T # label(t71_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1797 (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]. 14.57/14.16 1798 (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]. 14.57/14.16 1799 (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]. 14.57/14.16 1800 (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]. 14.57/14.16 1801 (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]. 14.57/14.16 1802 (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]. 14.57/14.16 1803 (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]. 14.57/14.16 1804 (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]. 14.57/14.16 1805 $T # label(t97_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1806 $T # label(t124_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1807 $T # label(t96_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1808 $T # label(t91_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1809 $T # label(t99_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1810 $T # label(t69_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1811 (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]. 14.57/14.16 1812 $T # label(t147_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1813 $T # label(t140_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1814 (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]. 14.57/14.16 1815 (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]. 14.57/14.16 1816 (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]. 14.57/14.16 1817 $T # label(t94_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1818 (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]. 14.57/14.16 1819 (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]. 14.57/14.16 1820 (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]. 14.57/14.16 1821 (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]. 14.57/14.16 1822 (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]. 14.57/14.16 1823 (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]. 14.57/14.16 1824 $T # label(t95_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1825 (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]. 14.57/14.16 1826 (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]. 14.57/14.16 1827 (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]. 14.57/14.16 1828 $T # label(t80_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1829 (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]. 14.57/14.16 1830 (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]. 14.57/14.16 1831 (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]. 14.57/14.16 1832 (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]. 14.57/14.16 1833 $T # label(t110_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1834 (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]. 14.57/14.16 1835 (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]. 14.57/14.16 1836 (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]. 14.57/14.16 1837 (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]. 14.57/14.16 1838 $T # label(t111_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1839 $T # label(t1_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1840 (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]. 14.57/14.16 1841 (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]. 14.57/14.16 1842 (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]. 14.57/14.16 1843 (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]. 14.57/14.16 1844 (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]. 14.57/14.16 1845 (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]. 14.57/14.16 1846 (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]. 14.57/14.16 1847 (all A -v1_xboole_0(k1_funct_2(A,A))) # label(fc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1848 (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]. 14.57/14.16 1849 $T # label(t163_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1850 (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]. 14.57/14.16 1851 (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]. 14.57/14.16 1852 $T # label(t106_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1853 $T # label(t123_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.16 1854 (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]. 14.57/14.16 1855 (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]. 14.57/14.17 1856 (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]. 14.57/14.17 1857 $T # label(t81_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1858 (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]. 14.57/14.17 1859 (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]. 14.57/14.17 1860 (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]. 14.57/14.17 1861 (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]. 14.57/14.17 1862 (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]. 14.57/14.17 1863 $T # label(t107_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1864 $T # label(t108_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1865 (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]. 14.57/14.17 1866 $T # label(t153_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1867 $T # label(t135_funct_2) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1868 (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]. 14.57/14.17 1869 (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]. 14.57/14.17 1870 (all A all B (r1_tarski(A,B) -> k6_relat_1(A) = k7_relat_1(k6_relat_1(B),A))) # label(t1_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1871 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k9_relat_1(k3_funct_3(B),A),k1_zfmisc_1(k1_relat_1(B))))) # label(t27_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1872 (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) -> k5_relat_1(k13_funct_3(B,D),k15_funct_3(A,C)) = k13_funct_3(k5_relat_1(B,A),k5_relat_1(D,C)))))))))) # label(t91_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1873 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> k2_relat_1(k15_funct_3(A,B)) = k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B)))))) # label(t88_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1874 (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,A,C) & m2_relset_1(E,A,C) & v1_funct_1(E) -> -((B = k1_xboole_0 -> k1_xboole_0 = A) & -(v1_funct_2(k13_funct_3(D,E),A,k2_zfmisc_1(B,C)) & m2_relset_1(k13_funct_3(D,E),A,k2_zfmisc_1(B,C)) & v1_funct_1(k13_funct_3(D,E))) & (k1_xboole_0 = C -> A = k1_xboole_0)))))) # label(t78_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1875 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k3_xboole_0(k1_relat_1(B),k1_relat_1(C))) -> k4_tarski(k1_funct_1(B,A),k1_funct_1(C,A)) = k1_funct_1(k13_funct_3(B,C),A)))))) # label(t68_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1876 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (r1_tarski(B,k1_zfmisc_1(k1_relat_1(A))) & v2_funct_1(A) -> k9_relat_1(k1_funct_3(A),B) = k10_relat_1(k3_funct_3(A),B))))) # label(t37_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1877 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k3_tarski(k9_relat_1(k1_funct_3(B),A)),k9_relat_1(B,k3_tarski(A))))) # label(t15_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1878 (all A all B (v1_funct_1(k5_funct_3(A,B)) & v1_funct_2(k5_funct_3(A,B),B,k2_tarski(np__0,np__1)) & m2_relset_1(k5_funct_3(A,B),B,k2_tarski(np__0,np__1)))) # label(dt_k5_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1879 $T # label(t26_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1880 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k9_relat_1(k1_funct_3(B),A),k1_zfmisc_1(k2_relat_1(B))))) # label(t12_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1881 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (C = k7_funct_3(A,B) <-> k1_relat_1(C) = k2_zfmisc_1(A,B) & (all D all E (r2_hidden(D,A) & r2_hidden(E,B) -> k1_funct_1(C,k4_tarski(D,E)) = D))))) # label(d5_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1882 (all A all B k6_relat_1(k2_zfmisc_1(A,B)) = k13_funct_3(k9_funct_3(A,B),k10_funct_3(A,B))) # label(t73_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1883 (exists A (k2_zfmisc_1(f1_s2_funct_3,f2_s2_funct_3) = k1_relat_1(A) & (all B all C (r2_hidden(C,f2_s2_funct_3) & r2_hidden(B,f1_s2_funct_3) -> f3_s2_funct_3(B,C) = k1_funct_1(A,k4_tarski(B,C)))) & v1_funct_1(A) & v1_relat_1(A))) # label(s2_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1884 $T # label(t67_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1885 (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) -> k13_funct_3(k5_relat_1(C,A),k5_relat_1(C,B)) = k5_relat_1(C,k13_funct_3(A,B)))))))) # label(t75_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1886 $T # label(t63_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1887 (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) & m2_relset_1(E,A,C) & v1_funct_2(E,A,C) -> r1_tarski(k2_relat_1(k13_funct_3(D,E)),k2_zfmisc_1(B,C)))))) # label(t80_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1888 (all A all B (v1_funct_1(k8_funct_3(A,B)) & v1_relat_1(k8_funct_3(A,B)))) # label(dt_k8_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1889 (all A (v1_funct_1(k12_funct_3(A)) & m2_relset_1(k12_funct_3(A),A,k2_zfmisc_1(A,A)) & v1_funct_2(k12_funct_3(A),A,k2_zfmisc_1(A,A)))) # label(dt_k12_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1890 (all A (v1_funct_1(A) & v1_relat_1(A) -> r1_tarski(k2_relat_1(k1_funct_3(A)),k1_zfmisc_1(k2_relat_1(A))))) # label(t10_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1891 (all A all B all C (k1_funct_1(k4_funct_3(B,C),A) = np__1 -> r2_hidden(A,B))) # label(t42_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1892 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,C) & m2_relset_1(E,A,C) -> (all F (m1_subset_1(F,A) -> k4_tarski(k8_funct_2(A,B,D,F),k8_funct_2(A,C,E,F)) = k8_funct_2(A,k2_zfmisc_1(B,C),k14_funct_3(A,B,C,D,E),F))))))))))))) # label(t79_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1893 $T # label(t55_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1894 (all A all B k5_funct_3(A,B) = k4_funct_3(A,B)) # label(redefinition_k5_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1895 (all A all B r1_tarski(k2_relat_1(k4_funct_3(A,B)),k2_tarski(np__0,np__1))) # label(t48_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1896 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,k1_zfmisc_1(k1_relat_1(B))) -> k9_relat_1(B,k3_tarski(A)) = k3_tarski(k9_relat_1(k1_funct_3(B),A))))) # label(t16_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1897 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> ((k1_xboole_0 = B -> k1_xboole_0 = A) -> v1_funct_2(k1_funct_3(C),k1_zfmisc_1(A),k1_zfmisc_1(B)) & m2_relset_1(k1_funct_3(C),k1_zfmisc_1(A),k1_zfmisc_1(B)) & v1_funct_1(k1_funct_3(C))))) # label(t22_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1898 (all A all B k7_funct_3(A,B) = k9_funct_3(A,B)) # label(redefinition_k9_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1899 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v2_funct_1(A) -> r1_tarski(k9_relat_1(k1_funct_3(A),B),k10_relat_1(k3_funct_3(A),B)))))) # label(t36_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1900 (all A all B all C all D (r2_hidden(A,f1_s1_funct_3) & p1_s1_funct_3(A,B,C) & p1_s1_funct_3(A,B,D) & r2_hidden(B,f2_s1_funct_3) -> C = D)) & (all A all B -(r2_hidden(B,f2_s1_funct_3) & (all C -p1_s1_funct_3(A,B,C)) & r2_hidden(A,f1_s1_funct_3))) -> (exists A (v1_relat_1(A) & v1_funct_1(A) & k1_relat_1(A) = k2_zfmisc_1(f1_s1_funct_3,f2_s1_funct_3) & (all B all C (r2_hidden(C,f2_s1_funct_3) & r2_hidden(B,f1_s1_funct_3) -> p1_s1_funct_3(B,C,k1_funct_1(A,k4_tarski(B,C))))))) # label(s1_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1901 (all A all B (v1_relat_1(k7_funct_3(A,B)) & v1_funct_1(k7_funct_3(A,B)))) # label(dt_k7_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1902 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k3_tarski(k9_relat_1(k3_funct_3(B),A)),k10_relat_1(B,k3_tarski(A))))) # label(t29_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1903 $T # label(t58_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1904 $T # label(t44_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1905 $T # label(t45_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1906 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k9_relat_1(k3_funct_3(B),A),k10_relat_1(k1_funct_3(B),A)))) # label(t33_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1907 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_2(E,A,C) & m2_relset_1(E,A,C) & v1_funct_1(E) -> k7_funct_2(A,k2_zfmisc_1(B,C),B,k14_funct_3(A,B,C,D,E),k9_funct_3(B,C)) = D & k7_funct_2(A,k2_zfmisc_1(B,C),C,k14_funct_3(A,B,C,D,E),k10_funct_3(B,C)) = E)))))))) # label(t82_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1908 (all A all B (A != k1_xboole_0 -> k2_relat_1(k8_funct_3(A,B)) = B)) # label(t62_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1909 (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(k13_funct_3(A,B)),k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B))))))) # label(t71_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1910 (all A all B (v1_relat_1(k4_funct_3(A,B)) & v1_funct_1(k4_funct_3(A,B)))) # label(dt_k4_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1911 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (all F (v1_funct_1(F) & m2_relset_1(F,A,C) & v1_funct_2(F,A,C) -> (all G (m2_relset_1(G,A,C) & v1_funct_2(G,A,C) & v1_funct_1(G) -> (k13_funct_3(D,F) = k13_funct_3(E,G) -> B = k1_xboole_0 & k1_xboole_0 != A | k1_xboole_0 != A & k1_xboole_0 = C | G = F & D = E))))))))) # label(t83_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1912 (all A all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> k3_xboole_0(k10_relat_1(C,A),k10_relat_1(D,B)) = k10_relat_1(k13_funct_3(C,D),k2_zfmisc_1(A,B)))))))) # label(t77_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1913 $T # label(t65_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1914 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> k2_zfmisc_1(k10_relat_1(C,A),k10_relat_1(D,B)) = k10_relat_1(k15_funct_3(C,D),k2_zfmisc_1(A,B)))))) # label(t94_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1915 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C (r1_tarski(C,k2_relat_1(A)) -> k1_funct_1(B,C) = k10_relat_1(A,C))) & k1_zfmisc_1(k2_relat_1(A)) = k1_relat_1(B) <-> B = k3_funct_3(A)))))) # label(d2_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1916 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k3_tarski(k10_relat_1(k3_funct_3(B),A)),k9_relat_1(B,k3_tarski(A))))) # label(t31_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1917 $T # label(t41_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1918 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> k2_zfmisc_1(k9_relat_1(C,A),k9_relat_1(D,B)) = k9_relat_1(k15_funct_3(C,D),k2_zfmisc_1(A,B)))))) # label(t93_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1919 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k1_relat_1(C) = k2_zfmisc_1(A,B) & k1_relat_1(D) = k2_zfmisc_1(A,B) & (all E all F (r2_hidden(F,B) & r2_hidden(E,A) -> k1_funct_1(D,k4_tarski(E,F)) = k1_funct_1(C,k4_tarski(E,F)))) -> C = D))))) # label(t6_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1920 (all A all B all C (-v1_xboole_0(B) & v1_funct_1(C) & m1_relset_1(C,A,B) & v1_funct_2(C,A,B) -> k2_funct_3(A,B,C) = k1_funct_3(C))) # label(redefinition_k2_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1921 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) & r1_tarski(A,k2_relat_1(k5_relat_1(B,C))) -> r1_tarski(k10_relat_1(C,A),k2_relat_1(B))))))) # label(t4_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1922 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(k3_funct_3(B))) -> k10_relat_1(B,A) = k1_funct_1(k3_funct_3(B),A)))) # label(t24_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1923 (all A (v1_relat_1(A) & v1_funct_1(A) -> m2_relset_1(k3_funct_3(A),k1_zfmisc_1(k2_relat_1(A)),k1_zfmisc_1(k1_relat_1(A))) & v1_funct_2(k3_funct_3(A),k1_zfmisc_1(k2_relat_1(A)),k1_zfmisc_1(k1_relat_1(A))) & v1_funct_1(k3_funct_3(A)))) # label(t39_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1924 $T # label(d4_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1925 (all A all B all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,C) & m2_relset_1(D,A,C) -> r1_tarski(k10_relat_1(k1_funct_3(D),B),k1_zfmisc_1(A)))))) # label(t14_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1926 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,k1_relat_1(B)) & r1_tarski(k9_relat_1(B,A),k1_relat_1(C)) -> r1_tarski(A,k1_relat_1(k5_relat_1(B,C)))))))) # label(t3_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1927 $T # label(t57_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1928 (all A all B k8_funct_3(A,B) = k10_funct_3(A,B)) # label(redefinition_k10_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1929 (all A all B all C all D all E all F (v1_funct_1(E) & v1_funct_2(E,A,C) & m1_relset_1(E,A,C) & v1_funct_1(F) & v1_funct_2(F,B,D) & m1_relset_1(F,B,D) -> v1_funct_1(k16_funct_3(A,B,C,D,E,F)) & m2_relset_1(k16_funct_3(A,B,C,D,E,F),k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) & v1_funct_2(k16_funct_3(A,B,C,D,E,F),k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)))) # label(dt_k16_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1930 $T # label(t64_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1931 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,k1_zfmisc_1(k2_relat_1(B))) -> k10_relat_1(B,k3_tarski(A)) = k3_tarski(k9_relat_1(k3_funct_3(B),A))))) # label(t30_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1932 (all A all B all C (k4_funct_3(C,B) = k4_funct_3(A,B) & r1_tarski(C,B) & r1_tarski(A,B) -> C = A)) # label(t47_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1933 $T # label(t85_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1934 (all A (v1_funct_1(k11_funct_3(A)) & v1_relat_1(k11_funct_3(A)))) # label(dt_k11_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1935 (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(C) = A & A = k1_relat_1(B) -> k1_relat_1(k13_funct_3(B,C)) = A))))) # label(t70_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1936 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(B)) -> (r2_hidden(A,C) -> r2_hidden(k1_funct_1(k6_funct_3(B,C),A),B)))) # label(t56_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1937 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> m2_relset_1(k6_funct_3(A,B),B,A) & v1_funct_2(k6_funct_3(A,B),B,A) & v1_funct_1(k6_funct_3(A,B)))) # label(dt_k6_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1938 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> k15_funct_3(A,B) = k13_funct_3(k5_relat_1(k9_funct_3(k1_relat_1(A),k1_relat_1(B)),A),k5_relat_1(k10_funct_3(k1_relat_1(A),k1_relat_1(B)),B)))))) # label(t87_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1939 (all A (v1_relat_1(A) & v1_funct_1(A) -> k1_funct_1(k1_funct_3(A),k1_xboole_0) = k1_xboole_0)) # label(t9_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1940 (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(k4_tarski(C,D),k2_zfmisc_1(k1_relat_1(A),k1_relat_1(B))) -> k4_tarski(k1_funct_1(A,C),k1_funct_1(B,D)) = k1_funct_1(k15_funct_3(A,B),k4_tarski(C,D)))))))) # label(t86_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1941 (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 (v1_relat_1(D) & v1_funct_1(D) -> (k1_relat_1(C) = k1_relat_1(D) & k13_funct_3(D,C) = k13_funct_3(A,B) & k1_relat_1(A) = k1_relat_1(B) -> D = A & C = B))))))))) # label(t74_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1942 (all A all B all C all D all E (m1_relset_1(D,A,B) & v1_funct_1(E) & v1_funct_2(E,A,C) & m1_relset_1(E,A,C) & v1_funct_2(D,A,B) & v1_funct_1(D) & -v1_xboole_0(C) & -v1_xboole_0(B) -> k14_funct_3(A,B,C,D,E) = k13_funct_3(D,E))) # label(redefinition_k14_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1943 (all A all B all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,C) & m2_relset_1(D,A,C) -> (r1_tarski(B,k1_zfmisc_1(A)) -> k2_funct_2(A,C,D,k3_tarski(B)) = k3_tarski(k9_relat_1(k1_funct_3(D),B))))))) # label(t17_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1944 (all A all B (A != k1_xboole_0 -> B = k2_relat_1(k7_funct_3(B,A)))) # label(t60_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1945 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & -v1_xboole_0(B) -> v1_funct_2(k2_funct_3(A,B,C),k1_zfmisc_1(A),k1_zfmisc_1(B)) & m2_relset_1(k2_funct_3(A,B,C),k1_zfmisc_1(A),k1_zfmisc_1(B)) & v1_funct_1(k2_funct_3(A,B,C)))) # label(dt_k2_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1946 (all A k11_funct_3(A) = k12_funct_3(A)) # label(redefinition_k12_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1947 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> r1_tarski(k9_relat_1(k13_funct_3(B,C),A),k2_zfmisc_1(k9_relat_1(B,A),k9_relat_1(C,A))))))) # label(t76_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1948 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> k1_funct_3(k5_relat_1(A,B)) = k5_relat_1(k1_funct_3(A),k1_funct_3(B)))))) # label(t20_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1949 (all A (v1_funct_1(A) & v1_relat_1(A) -> r1_tarski(k2_relat_1(k3_funct_3(A)),k1_zfmisc_1(k1_relat_1(A))))) # label(t25_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1950 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (r1_tarski(B,k1_zfmisc_1(k1_relat_1(A))) -> r1_tarski(k10_relat_1(k3_funct_3(A),B),k9_relat_1(k1_funct_3(A),B)))))) # label(t35_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1951 $T # label(t54_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1952 (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) -> k5_relat_1(k15_funct_3(B,D),k15_funct_3(A,C)) = k15_funct_3(k5_relat_1(B,A),k5_relat_1(D,C)))))))))) # label(t92_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1953 (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) -> (k13_funct_3(A,B) = C <-> (all D (r2_hidden(D,k1_relat_1(C)) -> k4_tarski(k1_funct_1(A,D),k1_funct_1(B,D)) = k1_funct_1(C,D))) & k3_xboole_0(k1_relat_1(A),k1_relat_1(B)) = k1_relat_1(C)))))))) # label(d8_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1954 (all A all B r1_tarski(k2_relat_1(k7_funct_3(A,B)),A)) # label(t59_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1955 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,k1_zfmisc_1(k2_relat_1(B))) -> k3_tarski(k10_relat_1(k1_funct_3(B),A)) = k10_relat_1(B,k3_tarski(A))))) # label(t19_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1956 (all A all B all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_2(E,A,C) & m2_relset_1(E,A,C) & v1_funct_1(E) -> (all F (v1_funct_2(F,B,D) & m2_relset_1(F,B,D) & v1_funct_1(F) -> k16_funct_3(A,B,C,D,E,F) = k13_funct_3(k5_relat_1(k9_funct_3(A,B),E),k5_relat_1(k10_funct_3(A,B),F)))))))))) # label(t98_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1957 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k1_funct_3(A)) & m2_relset_1(k1_funct_3(A),k1_zfmisc_1(k1_relat_1(A)),k1_zfmisc_1(k2_relat_1(A))) & v1_funct_2(k1_funct_3(A),k1_zfmisc_1(k1_relat_1(A)),k1_zfmisc_1(k2_relat_1(A))))) # label(t21_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1958 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) -> k10_relat_1(k1_funct_3(B),A) = k9_relat_1(k3_funct_3(B),A)))) # label(t34_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1959 (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_1(E) & v1_funct_2(E,A,C) & m2_relset_1(E,A,C) -> k5_relat_1(k12_funct_3(A),k16_funct_3(A,A,B,C,D,E)) = k13_funct_3(D,E))))) # label(t99_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1960 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C (r1_tarski(C,k1_relat_1(A)) -> k1_funct_1(B,C) = k9_relat_1(A,C))) & k1_relat_1(B) = k1_zfmisc_1(k1_relat_1(A)) <-> k1_funct_3(A) = B))))) # label(d1_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1961 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (C = k8_funct_3(A,B) <-> k1_relat_1(C) = k2_zfmisc_1(A,B) & (all D all E (r2_hidden(D,A) & r2_hidden(E,B) -> E = k1_funct_1(C,k4_tarski(D,E))))))) # label(d6_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1962 (all A all B (v1_funct_1(k9_funct_3(A,B)) & v1_funct_2(k9_funct_3(A,B),k2_zfmisc_1(A,B),A) & m2_relset_1(k9_funct_3(A,B),k2_zfmisc_1(A,B),A))) # label(dt_k9_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1963 (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) -> (all F (v1_funct_1(F) & m2_relset_1(F,C,D) & v1_funct_2(F,C,D) -> -((B = k1_xboole_0 -> A = k1_xboole_0) & k16_funct_3(A,C,B,D,E,F) != k13_funct_3(k5_relat_1(k9_funct_3(A,C),E),k5_relat_1(k10_funct_3(A,C),F)) & (k1_xboole_0 = D -> k1_xboole_0 = C)))))) # label(t97_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1964 (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) -> (all F (v1_funct_2(F,C,D) & m2_relset_1(F,C,D) & v1_funct_1(F) -> v1_funct_1(k15_funct_3(E,F)) & m2_relset_1(k15_funct_3(E,F),k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) & v1_funct_2(k15_funct_3(E,F),k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)))))) # label(t95_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1965 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k10_relat_1(C,A),k2_relat_1(B)) & r1_tarski(A,k2_relat_1(C)) -> r1_tarski(A,k2_relat_1(k5_relat_1(B,C)))))))) # label(t5_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1966 $T # label(t51_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1967 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C (r2_hidden(C,A) -> k4_tarski(C,C) = k1_funct_1(B,C))) & A = k1_relat_1(B) <-> k11_funct_3(A) = B))) # label(d7_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1968 (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) -> (k2_zfmisc_1(k1_relat_1(A),k1_relat_1(B)) = k1_relat_1(C) & (all D all E (r2_hidden(E,k1_relat_1(B)) & r2_hidden(D,k1_relat_1(A)) -> k1_funct_1(C,k4_tarski(D,E)) = k4_tarski(k1_funct_1(A,D),k1_funct_1(B,E)))) <-> C = k15_funct_3(A,B)))))))) # label(d9_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1969 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m2_relset_1(E,A,C) & v1_funct_2(E,A,C) & v1_funct_1(E) -> -((C = k1_xboole_0 -> k1_xboole_0 = A) & -(D = k5_relat_1(k13_funct_3(D,E),k9_funct_3(B,C)) & k5_relat_1(k13_funct_3(D,E),k10_funct_3(B,C)) = E) & (B = k1_xboole_0 -> k1_xboole_0 = A)))))) # label(t81_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1970 (all A all B k6_relat_1(k2_zfmisc_1(A,B)) = k15_funct_3(k6_relat_1(A),k6_relat_1(B))) # label(t90_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1971 (all A all B (m2_relset_1(B,A,k2_tarski(np__0,np__1)) & v1_funct_2(B,A,k2_tarski(np__0,np__1)) & v1_funct_1(B) -> k4_funct_3(k3_funct_2(A,k2_tarski(np__0,np__1),B,k1_tarski(np__1)),A) = B)) # label(t49_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1972 (all A all B all C all D all E (-v1_xboole_0(C) & v1_funct_1(E) & v1_funct_2(E,A,C) & m1_relset_1(E,A,C) & m1_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) & -v1_xboole_0(B) -> v1_funct_1(k14_funct_3(A,B,C,D,E)) & v1_funct_2(k14_funct_3(A,B,C,D,E),A,k2_zfmisc_1(B,C)) & m2_relset_1(k14_funct_3(A,B,C,D,E),A,k2_zfmisc_1(B,C)))) # label(dt_k14_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1973 (all A (v1_funct_1(A) & v1_relat_1(A) -> k1_relat_1(A) = k2_funct_2(k2_zfmisc_1(k1_relat_1(A),k2_relat_1(A)),k1_relat_1(A),k9_funct_3(k1_relat_1(A),k2_relat_1(A)),A))) # label(t100_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1974 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k1_funct_3(A)) & v1_funct_1(k1_funct_3(A)))) # label(dt_k1_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1975 $T # label(t40_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1976 (all A all B r1_tarski(k2_relat_1(k8_funct_3(A,B)),B)) # label(t61_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1977 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(A,k1_relat_1(k1_funct_3(B))) -> k1_funct_1(k1_funct_3(B),A) = k9_relat_1(B,A)))) # label(t8_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1978 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r1_tarski(k2_relat_1(D),B) & r1_tarski(k2_relat_1(C),A) & k1_relat_1(C) = k1_relat_1(D) -> k5_relat_1(k13_funct_3(C,D),k9_funct_3(A,B)) = C & D = k5_relat_1(k13_funct_3(C,D),k10_funct_3(A,B))))))) # label(t72_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1979 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) -> k5_relat_1(k3_funct_3(B),k3_funct_3(A)) = k3_funct_3(k5_relat_1(A,B))))))) # label(t38_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1980 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(B) -> v1_funct_1(k13_funct_3(A,B)) & v1_relat_1(k13_funct_3(A,B)))) # label(dt_k13_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1981 (all A all B (v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_relat_1(A) -> v1_relat_1(k15_funct_3(A,B)) & v1_funct_1(k15_funct_3(A,B)))) # label(dt_k15_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1982 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(A,B) & B = k1_relat_1(D) & k1_relat_1(C) = B -> k4_tarski(k1_funct_1(C,A),k1_funct_1(D,A)) = k1_funct_1(k13_funct_3(C,D),A)))))) # label(t69_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1983 (all A all B all C all D all E all F (v1_funct_1(E) & v1_funct_2(E,A,C) & m1_relset_1(E,A,C) & v1_funct_1(F) & m1_relset_1(F,B,D) & v1_funct_2(F,B,D) -> k15_funct_3(E,F) = k16_funct_3(A,B,C,D,E,F))) # label(redefinition_k16_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1984 $T # label(t46_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1985 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k10_relat_1(k3_funct_3(B),A),k1_zfmisc_1(k2_relat_1(B))))) # label(t28_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1986 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(C) = B & (all D (r2_hidden(D,B) -> (r2_hidden(D,A) -> np__1 = k1_funct_1(C,D)) & (-r2_hidden(D,A) -> np__0 = k1_funct_1(C,D)))) <-> C = k4_funct_3(A,B)))) # label(d3_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1987 $T # label(t7_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1988 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k3_tarski(k10_relat_1(k1_funct_3(B),A)),k10_relat_1(B,k3_tarski(A))))) # label(t18_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1989 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> (all F (v1_funct_1(F) & v1_funct_2(F,C,D) & m2_relset_1(F,C,D) -> (all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,C) -> k4_tarski(k8_funct_2(A,B,E,G),k8_funct_2(C,D,F,H)) = k1_funct_1(k16_funct_3(A,C,B,D,E,F),k4_tarski(G,H)))))))))))))))))) # label(t96_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1990 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (A = k1_relat_1(B) & k1_relat_1(C) = A -> k5_relat_1(k12_funct_3(A),k15_funct_3(B,C)) = k13_funct_3(B,C)))))) # label(t89_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1991 (all A all B (v1_funct_1(k10_funct_3(A,B)) & v1_funct_2(k10_funct_3(A,B),k2_zfmisc_1(A,B),B) & m2_relset_1(k10_funct_3(A,B),k2_zfmisc_1(A,B),B))) # label(dt_k10_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1992 (all A all B all C (r2_hidden(A,k4_xboole_0(B,C)) -> k1_funct_1(k4_funct_3(C,B),A) = np__0)) # label(t43_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1993 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) & r1_tarski(A,k1_zfmisc_1(k1_relat_1(B))) -> k9_relat_1(B,k3_tarski(A)) = k3_tarski(k10_relat_1(k3_funct_3(B),A))))) # label(t32_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1994 $T # label(t50_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1995 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k3_funct_3(A)) & v1_funct_1(k3_funct_3(A)))) # label(dt_k3_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1996 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (all F (v1_funct_1(F) & v1_funct_2(F,A,C) & m2_relset_1(F,A,C) -> (all G (v1_funct_1(G) & v1_funct_2(G,A,C) & m2_relset_1(G,A,C) -> (k14_funct_3(A,B,C,E,G) = k14_funct_3(A,B,C,D,F) -> E = D & F = G))))))))))))) # label(t84_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1997 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k6_funct_3(A,B) = k7_relat_1(k6_relat_1(A),B))) # label(t53_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1998 $T # label(t11_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 1999 $T # label(t23_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 2000 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,k1_relat_1(k5_relat_1(B,C))) -> r1_tarski(k9_relat_1(B,A),k1_relat_1(C))))))) # label(t2_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 2001 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k6_funct_3(A,B) = k6_relat_1(B))) # label(redefinition_k6_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 2002 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k10_relat_1(k1_funct_3(B),A),k1_zfmisc_1(k1_relat_1(B))))) # label(t13_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 2003 $T # label(t52_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 2004 (all A r1_tarski(k2_relat_1(k11_funct_3(A)),k2_zfmisc_1(A,A))) # label(t66_funct_3) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 2005 $T # label(t4_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 2006 $T # label(t10_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 2007 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (v3_binop_1(B,A) <-> (all C (m1_subset_1(C,A) -> k1_binop_1(B,C,C) = C))))) # label(d4_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 2008 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (v1_binop_1(C,A) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k2_binop_1(A,A,A,C,D,k2_binop_1(A,A,A,B,E,F)) = k2_binop_1(A,A,A,B,k2_binop_1(A,A,A,C,D,E),k2_binop_1(A,A,A,C,D,F)))))))) <-> r6_binop_1(A,C,B))))))))) # label(t24_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 2009 (all A all B (m1_subset_1(B,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> ((all D (m1_subset_1(D,A) -> D = k1_binop_1(C,D,B))) <-> r2_binop_1(A,B,C)))))) # label(d6_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 2010 (exists A (v1_funct_1(A) & (all B (m1_subset_1(B,f1_s2_binop_1) -> (all C (m1_subset_1(C,f1_s2_binop_1) -> k2_binop_1(f1_s2_binop_1,f1_s2_binop_1,f1_s2_binop_1,A,B,C) = f2_s2_binop_1(B,C))))) & m2_relset_1(A,k2_zfmisc_1(f1_s2_binop_1,f1_s2_binop_1),f1_s2_binop_1) & v1_funct_2(A,k2_zfmisc_1(f1_s2_binop_1,f1_s2_binop_1),f1_s2_binop_1))) # label(s2_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 2011 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (v1_binop_1(B,A) -> ((all D (m1_subset_1(D,A) -> D = k1_binop_1(B,C,D))) <-> r3_binop_1(A,C,B))))))) # label(t12_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 2012 $T # label(t21_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.17 2013 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (r1_binop_1(A,C,B) & r2_binop_1(A,D,B) -> C = D))))))) # label(t17_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2014 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> ((exists C (m1_subset_1(C,A) & r3_binop_1(A,C,B))) -> (all C (m1_subset_1(C,A) -> (C = k3_binop_1(A,B) <-> r3_binop_1(A,C,B))))))) # label(d8_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2015 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (r2_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> k2_binop_1(A,A,A,C,D,B) = D))))))))) # label(d17_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2016 (all A all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> (v1_binop_1(B,A) -> (r2_binop_1(A,C,B) <-> r1_binop_1(A,C,B))))))) # label(t16_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2017 $T # label(t8_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2018 (all A (m1_relset_1(A,k2_zfmisc_1(k1_xboole_0,k1_xboole_0),k1_xboole_0) -> (v1_funct_2(A,k2_zfmisc_1(k1_xboole_0,k1_xboole_0),k1_xboole_0) & v1_funct_1(A) -> v1_funct_2(A,k2_zfmisc_1(k1_xboole_0,k1_xboole_0),k1_xboole_0) & v2_binop_1(A,k1_xboole_0) & v1_binop_1(A,k1_xboole_0) & v1_xboole_0(A) & v1_funct_1(A)))) # label(cc1_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2019 (all A all B (m1_subset_1(B,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (r1_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> D = k1_binop_1(C,B,D)))))))) # label(d5_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2020 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (v1_binop_1(B,A) -> (r3_binop_1(A,C,B) <-> (all D (m1_subset_1(D,A) -> D = k1_binop_1(B,D,C))))))))) # label(t13_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2021 (all A all B (m1_subset_1(B,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (r1_binop_1(A,B,C) & r2_binop_1(A,B,C) <-> r3_binop_1(A,B,C)))))) # label(d7_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2022 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (v2_binop_1(B,A) <-> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> k1_binop_1(B,C,k1_binop_1(B,D,E)) = k1_binop_1(B,k1_binop_1(B,C,D),E)))))))))) # label(d3_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2023 (all A all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (r3_binop_1(A,C,B) & r3_binop_1(A,D,B) -> C = D))))))) # label(t18_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2024 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (v1_binop_1(B,A) <-> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> k1_binop_1(B,C,D) = k1_binop_1(B,D,C)))))))) # label(d2_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2025 (all A (-v1_xboole_0(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (r4_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k2_binop_1(A,A,A,C,k2_binop_1(A,A,A,B,D,E),k2_binop_1(A,A,A,B,D,F)) = k2_binop_1(A,A,A,B,D,k2_binop_1(A,A,A,C,E,F))))))))))))))) # label(d18_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2026 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (v3_binop_1(B,A) <-> (all C (m1_subset_1(C,A) -> C = k2_binop_1(A,A,A,B,C,C)))))))) # label(d15_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2027 $T # label(t19_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2028 (all A (-v1_xboole_0(A) -> (all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (r7_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> k8_funct_2(A,A,B,k2_binop_1(A,A,A,C,D,E)) = k2_binop_1(A,A,A,C,k8_funct_2(A,A,B,D),k8_funct_2(A,A,B,E))))))))))))) # label(d20_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2029 $T # label(t22_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2030 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (r5_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k2_binop_1(A,A,A,B,k2_binop_1(A,A,A,C,D,E),F) = k2_binop_1(A,A,A,C,k2_binop_1(A,A,A,B,D,F),k2_binop_1(A,A,A,B,E,F))))))))))))))) # label(d19_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2031 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C k1_binop_1(A,B,C) = k1_funct_1(A,k4_tarski(B,C))))) # label(d1_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2032 $T # label(t7_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2033 (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) -> (v2_binop_1(B,A) <-> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> k2_binop_1(A,A,A,B,C,k2_binop_1(A,A,A,B,D,E)) = k2_binop_1(A,A,A,B,k2_binop_1(A,A,A,B,C,D),E)))))))))))) # label(d14_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2034 $T # label(t3_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2035 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (v1_binop_1(C,A) -> (r4_binop_1(A,C,B) <-> r5_binop_1(A,C,B))))))))) # label(t28_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2036 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (v1_binop_1(B,A) <-> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> k2_binop_1(A,A,A,B,D,C) = k2_binop_1(A,A,A,B,C,D)))))))))) # label(d13_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2037 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (v1_binop_1(C,A) -> (r6_binop_1(A,C,B) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k2_binop_1(A,A,A,B,k2_binop_1(A,A,A,C,D,F),k2_binop_1(A,A,A,C,E,F)) = k2_binop_1(A,A,A,C,k2_binop_1(A,A,A,B,D,E),F))))))))))))))) # label(t25_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2038 (all A all B all C all D all E all F (-v1_xboole_0(A) & -v1_xboole_0(B) & v1_funct_1(D) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & m1_subset_1(F,B) & m1_subset_1(E,A) & v1_funct_2(D,k2_zfmisc_1(A,B),C) -> k2_binop_1(A,B,C,D,E,F) = k1_binop_1(D,E,F))) # label(redefinition_k2_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2039 $T # label(t9_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2040 $T # label(t6_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2041 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (r6_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k1_binop_1(B,D,k1_binop_1(C,E,F)) = k1_binop_1(C,k1_binop_1(B,D,E),k1_binop_1(B,D,F)) & k1_binop_1(C,k1_binop_1(B,D,F),k1_binop_1(B,E,F)) = k1_binop_1(B,k1_binop_1(C,D,E),F)))))))))))) # label(t23_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2042 $T # label(t20_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2043 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (v1_binop_1(B,A) -> (r2_binop_1(A,C,B) <-> r3_binop_1(A,C,B))))))) # label(t15_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2044 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k1_binop_1(B,D,k1_binop_1(C,E,F)) = k1_binop_1(C,k1_binop_1(B,D,E),k1_binop_1(B,D,F)))))))) <-> r4_binop_1(A,B,C)))))) # label(d9_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2045 (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 (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) -> k2_binop_1(A,B,C,D,F,G) = k2_binop_1(A,B,C,E,F,G))))) -> D = E))))))))))) # label(t2_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2046 (all A (m1_subset_1(A,f1_s1_binop_1) -> (all B (m1_subset_1(B,f1_s1_binop_1) -> (exists C (m1_subset_1(C,f1_s1_binop_1) & p1_s1_binop_1(A,B,C))))))) -> (exists A (m2_relset_1(A,k2_zfmisc_1(f1_s1_binop_1,f1_s1_binop_1),f1_s1_binop_1) & (all B (m1_subset_1(B,f1_s1_binop_1) -> (all C (m1_subset_1(C,f1_s1_binop_1) -> p1_s1_binop_1(B,C,k2_binop_1(f1_s1_binop_1,f1_s1_binop_1,f1_s1_binop_1,A,B,C)))))) & v1_funct_2(A,k2_zfmisc_1(f1_s1_binop_1,f1_s1_binop_1),f1_s1_binop_1) & v1_funct_1(A))) # label(s1_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2047 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (r5_binop_1(A,B,C) & r4_binop_1(A,B,C) <-> r6_binop_1(A,B,C)))))) # label(d11_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2048 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (r5_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k1_binop_1(B,k1_binop_1(C,D,E),F) = k1_binop_1(C,k1_binop_1(B,D,F),k1_binop_1(B,E,F))))))))))))) # label(d10_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2049 $T # label(t1_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2050 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (r7_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> k1_funct_1(B,k1_binop_1(C,D,E)) = k1_binop_1(C,k1_funct_1(B,D),k1_funct_1(B,E))))))))))) # label(d12_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2051 $T # label(t5_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2052 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> (v1_binop_1(B,A) -> (r1_binop_1(A,C,B) <-> r3_binop_1(A,C,B))))))) # label(t14_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2053 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (v1_binop_1(C,A) -> (r6_binop_1(A,C,B) <-> r5_binop_1(A,C,B))))))))) # label(t27_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2054 $T # label(dt_k1_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2055 (all A all B all C all D all E all F (v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & m1_subset_1(F,B) & m1_subset_1(E,A) & -v1_xboole_0(B) & -v1_xboole_0(A) -> m1_subset_1(k2_binop_1(A,B,C,D,E,F),C))) # label(dt_k2_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2056 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (r3_binop_1(A,C,B) <-> (all D (m1_subset_1(D,A) -> k1_binop_1(B,C,D) = D & D = k1_binop_1(B,D,C)))))))) # label(t11_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2057 (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 (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (v1_binop_1(C,A) -> (r4_binop_1(A,C,B) <-> r6_binop_1(A,C,B))))))))) # label(t26_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2058 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> ((all D (m1_subset_1(D,A) -> k2_binop_1(A,A,A,C,B,D) = D)) <-> r1_binop_1(A,B,C)))))))) # label(d16_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2059 (all A all B (m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> m1_subset_1(k3_binop_1(A,B),A))) # label(dt_k3_binop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2060 (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]. 14.57/14.18 2061 (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]. 14.57/14.18 2062 (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]. 14.57/14.18 2063 (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]. 14.57/14.18 2064 (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]. 14.57/14.18 2065 (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]. 14.57/14.18 2066 (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]. 14.57/14.18 2067 (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]. 14.57/14.18 2068 (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]. 14.57/14.18 2069 (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]. 14.57/14.18 2070 (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]. 14.57/14.18 2071 (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]. 14.57/14.18 2072 (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]. 14.57/14.18 2073 (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]. 14.57/14.18 2074 (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]. 14.57/14.18 2075 (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]. 14.57/14.18 2076 (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]. 14.57/14.18 2077 (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]. 14.57/14.18 2078 (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]. 14.57/14.18 2079 (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]. 14.57/14.18 2080 (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]. 14.57/14.18 2081 (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]. 14.57/14.18 2082 $T # label(t8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2083 (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]. 14.57/14.18 2084 (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]. 14.57/14.18 2085 (exists A (v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A))) # label(rc1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2086 $T # label(t5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2087 (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]. 14.57/14.18 2088 (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]. 14.57/14.18 2089 (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]. 14.57/14.18 2090 (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]. 14.57/14.18 2091 (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]. 14.57/14.18 2092 (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]. 14.57/14.18 2093 (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]. 14.57/14.18 2094 (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]. 14.57/14.18 2095 (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]. 14.57/14.18 2096 (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]. 14.57/14.18 2097 (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]. 14.57/14.18 2098 (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]. 14.57/14.18 2099 (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]. 14.57/14.18 2100 $T # label(dt_k2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2101 (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]. 14.57/14.18 2102 (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]. 14.57/14.18 2103 (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]. 14.57/14.18 2104 (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]. 14.57/14.18 2105 (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]. 14.57/14.18 2106 $T # label(t40_funcop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2107 $T # label(dt_k3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2108 (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]. 14.57/14.18 2109 (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]. 14.57/14.18 2110 (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]. 14.57/14.18 2111 (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]. 14.57/14.18 2112 (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]. 14.57/14.18 2113 (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]. 14.57/14.18 2114 (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]. 14.57/14.18 2115 (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]. 14.57/14.18 2116 (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]. 14.57/14.18 2117 (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]. 14.57/14.18 2118 (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]. 14.57/14.18 2119 (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]. 14.57/14.18 2120 (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]. 14.57/14.18 2121 (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]. 14.57/14.18 2122 (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]. 14.57/14.18 2123 (all A k1_funcop_1(k12_funct_3(A)) = k12_funct_3(A)) # label(t9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2124 (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]. 14.57/14.18 2125 (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]. 14.57/14.18 2126 (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]. 14.57/14.18 2127 (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]. 14.57/14.18 2128 (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]. 14.57/14.18 2129 (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]. 14.57/14.18 2130 (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]. 14.57/14.18 2131 (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]. 14.57/14.18 2132 (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]. 14.57/14.18 2133 (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]. 14.57/14.18 2134 (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]. 14.57/14.18 2135 $T # label(dt_k4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2136 (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]. 14.57/14.18 2137 (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]. 14.57/14.18 2138 (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]. 14.57/14.18 2139 (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]. 14.57/14.18 2140 (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]. 14.57/14.18 2141 $T # label(t50_funcop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2142 (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]. 14.57/14.18 2143 (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]. 14.57/14.18 2144 (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]. 14.57/14.18 2145 (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]. 14.57/14.18 2146 (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]. 14.57/14.18 2147 (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]. 14.57/14.18 2148 $T # label(t62_funcop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2149 (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]. 14.57/14.18 2150 (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]. 14.57/14.18 2151 (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]. 14.57/14.18 2152 $T # label(t68_funcop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2153 (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]. 14.57/14.18 2154 (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]. 14.57/14.18 2155 (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]. 14.57/14.18 2156 (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]. 14.57/14.18 2157 (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]. 14.57/14.18 2158 (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]. 14.57/14.18 2159 (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]. 14.57/14.18 2160 (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]. 14.57/14.18 2161 $T # label(t33_funcop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.18 2162 (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]. 14.57/14.18 2163 (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]. 14.57/14.18 2164 (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]. 14.57/14.18 2165 (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]. 14.57/14.18 2166 (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]. 14.57/14.19 2167 $T # label(dt_k5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.19 2168 (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]. 14.57/14.19 2169 (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]. 14.57/14.19 2170 (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]. 14.57/14.19 2171 (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]. 14.57/14.19 2172 $T # label(t12_funcop_1) # label(axiom) # label(non_clause). [assumption]. 14.57/14.19 2173 (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]. 14.57/14.19 2174 (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]. 14.57/14.19 2175 (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]. 14.57/14.19 2176 (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]. 14.57/14.19 2177 $T # label(dt_k4_funct_4) # label(axiom) # label(non_clause). [assumption]. 14.57/14.19 2178 (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]. 14.57/14.19 2179 (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]. 14.57/14.19 2180 (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]. 14.57/14.19 2181 (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]. 14.57/14.19 2182 (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]. 14.57/14.19 2183 (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]. 14.57/14.19 2184 (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]. 14.57/14.19 2185 (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]. 14.57/14.19 2186 (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]. 14.57/14.19 2187 (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]. 14.57/14.19 2188 (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]. 14.57/14.19 2189 (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]. 14.57/14.19 2190 (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]. 14.57/14.19 2191 (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]. 14.57/14.19 2192 (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]. 14.57/14.19 2193 (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]. 14.57/14.19 2194 (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]. 14.57/14.19 2195 (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]. 14.57/14.19 2196 (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]. 14.57/14.19 2197 (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]. 14.57/14.19 2198 (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]. 14.57/14.19 2199 (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]. 14.57/14.19 2200 (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]. 14.57/14.19 2201 (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]. 14.57/14.19 2202 (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]. 14.57/14.19 2203 (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]. 14.57/14.19 2204 (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]. 14.57/14.19 2205 (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]. 14.57/14.19 2206 (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]. 14.57/14.19 2207 (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]. 14.57/14.19 2208 (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]. 14.57/14.19 2209 (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]. 14.57/14.19 2210 (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]. 14.57/14.19 2211 (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]. 14.57/14.19 2212 (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]. 14.57/14.19 2213 (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]. 14.57/14.19 2214 (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]. 14.57/14.19 2215 (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]. 14.63/14.19 2216 (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]. 14.63/14.19 2217 (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]. 14.63/14.19 2218 (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]. 14.63/14.19 2219 (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]. 14.63/14.19 2220 (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]. 14.63/14.19 2221 (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]. 14.63/14.19 2222 (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]. 14.63/14.19 2223 (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]. 14.63/14.19 2224 (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]. 14.63/14.19 2225 (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]. 14.63/14.19 2226 (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]. 14.63/14.19 2227 (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]. 14.63/14.19 2228 (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]. 14.63/14.19 2229 (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]. 14.63/14.19 2230 (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]. 14.63/14.19 2231 (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]. 14.63/14.19 2232 (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]. 14.63/14.19 2233 (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]. 14.63/14.19 2234 (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]. 14.63/14.19 2235 (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]. 14.63/14.19 2236 (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]. 14.63/14.19 2237 (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]. 14.63/14.19 2238 (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]. 14.63/14.19 2239 (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]. 14.63/14.19 2240 (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]. 14.63/14.19 2241 (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]. 14.63/14.19 2242 (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]. 14.63/14.19 2243 (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]. 14.63/14.19 2244 (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]. 14.63/14.19 2245 (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]. 14.63/14.19 2246 (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]. 14.63/14.19 2247 (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]. 14.63/14.19 2248 (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]. 14.63/14.19 2249 (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]. 14.63/14.19 2250 (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]. 14.63/14.19 2251 (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]. 14.63/14.19 2252 (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]. 14.63/14.19 2253 (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]. 14.63/14.19 2254 (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]. 14.63/14.19 2255 (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]. 14.63/14.19 2256 (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]. 14.63/14.19 2257 (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]. 14.63/14.19 2258 (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]. 14.63/14.19 2259 (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]. 14.63/14.19 2260 (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]. 14.63/14.19 2261 (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]. 14.63/14.19 2262 (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]. 14.63/14.19 2263 (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]. 14.63/14.19 2264 (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]. 14.63/14.19 2265 (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]. 14.72/14.31 2266 (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]. 14.72/14.31 2267 (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]. 14.72/14.31 2268 (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]. 14.72/14.31 2269 (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]. 14.72/14.31 2270 $T # label(t3_funct_4) # label(axiom) # label(non_clause). [assumption]. 14.72/14.31 2271 (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]. 14.72/14.31 2272 (all A (v3_ordinal1(A) -> (all B (m1_ordinal1(B,A) -> v1_ordinal2(B))))) # label(cc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.72/14.31 2273 (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]. 14.72/14.31 2274 $T # label(t18_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.72/14.31 2275 (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]. 14.72/14.31 2276 (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]. 14.72/14.31 2277 (all A v3_ordinal1(k7_ordinal2(A))) # label(dt_k7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.72/14.31 2278 (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]. 14.72/14.31 2279 (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]. 14.72/14.31 2280 (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]. 14.72/14.31 2281 (all A (v3_ordinal1(A) -> A = k3_tarski(k1_ordinal1(A)))) # label(t2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.72/14.31 2282 (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]. 14.72/14.31 2283 (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]. 14.72/14.31 2284 (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]. 14.72/14.31 2285 $T # label(t33_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.72/14.31 2286 (all A (v3_ordinal1(A) -> r1_ordinal1(k3_tarski(A),A))) # label(t5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.72/14.31 2287 $T # label(t41_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.72/14.31 2288 (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]. 14.72/14.31 2289 (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]. 14.72/14.31 2290 (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]. 14.72/14.31 2291 $T # label(t64_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.72/14.31 2292 (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]. 14.72/14.31 2293 (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]. 14.72/14.31 2294 (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]. 14.72/14.31 2295 (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]. 14.76/14.33 2296 (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]. 14.76/14.33 2297 (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]. 14.76/14.33 2298 (all A r1_tarski(k2_ordinal2(A),A)) # label(t9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.76/14.33 2299 (all A k1_setfam_1(k2_ordinal2(A)) = k6_ordinal2(A)) # label(d6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.76/14.33 2300 (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]. 14.76/14.33 2301 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]. 14.76/14.33 2302 (all A (v3_ordinal1(A) -> A = k2_ordinal2(A))) # label(t10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.76/14.33 2303 $T # label(t8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.76/14.33 2304 (all A (v3_ordinal1(A) -> r1_tarski(k1_ordinal1(A),k1_zfmisc_1(A)))) # label(t3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.76/14.33 2305 (all A (v3_ordinal1(A) -> k14_ordinal2(A,k4_ordinal2) = k1_ordinal1(A))) # label(t48_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.76/14.33 2306 $T # label(dt_k2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.76/14.33 2307 (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]. 14.76/14.33 2308 (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]. 14.76/14.33 2309 (all A (v3_ordinal1(A) -> k1_xboole_0 = k15_ordinal2(A,k1_xboole_0))) # label(t55_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.76/14.33 2310 (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]. 14.76/14.33 2311 (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]. 14.76/14.33 2312 (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]. 14.76/14.33 2313 (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]. 14.76/14.33 2314 (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]. 14.76/14.33 2315 (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]. 14.76/14.33 2316 (all A (v4_ordinal2(A) <-> r2_hidden(A,k5_ordinal2))) # label(d21_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.76/14.33 2317 (exists A (v1_ordinal1(A) & v4_ordinal1(A) & v3_ordinal1(A) & v2_ordinal1(A))) # label(rc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.76/14.33 2318 (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]. 14.76/14.33 2319 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]. 14.76/14.33 2320 (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]. 14.76/14.33 2321 (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]. 14.76/14.33 2322 (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]. 14.76/14.33 2323 $T # label(dt_k5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.76/14.33 2324 (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]. 14.76/14.33 2325 (all A (v3_ordinal1(A) -> k1_ordinal1(A) = k7_ordinal2(k1_tarski(A)))) # label(t31_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.76/14.33 2326 (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]. 14.76/14.33 2327 (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]. 14.76/14.33 2328 (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]. 14.76/14.33 2329 (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]. 14.76/14.33 2330 $T # label(t37_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.76/14.33 2331 (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]. 14.76/14.33 2332 (all A v3_ordinal1(k6_ordinal2(A))) # label(dt_k6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.76/14.33 2333 (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]. 14.76/14.33 2334 (all A r1_tarski(k3_ordinal2(A),k2_ordinal2(A))) # label(t15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.76/14.33 2335 (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]. 14.76/14.33 2336 $T # label(t43_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.76/14.33 2337 (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]. 14.76/14.33 2338 (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]. 14.76/14.33 2339 (all A (v3_ordinal1(A) -> A = k14_ordinal2(A,k1_xboole_0))) # label(t44_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.76/14.33 2340 (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]. 14.80/14.35 2341 (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]. 14.80/14.35 2342 (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]. 14.80/14.35 2343 (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]. 14.80/14.35 2344 (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]. 14.80/14.35 2345 (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]. 14.80/14.35 2346 (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]. 14.80/14.35 2347 (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]. 14.80/14.35 2348 (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]. 14.80/14.35 2349 (all A (v3_ordinal1(A) -> A = k14_ordinal2(k1_xboole_0,A))) # label(t47_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.80/14.35 2350 (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]. 14.80/14.35 2351 $T # label(t21_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.80/14.35 2352 (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]. 14.80/14.35 2353 (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]. 14.80/14.36 2354 (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]. 14.80/14.36 2355 (all A (v3_ordinal1(A) -> k15_ordinal2(k1_xboole_0,A) = k1_xboole_0)) # label(t52_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.80/14.36 2356 (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]. 14.80/14.36 2357 (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]. 14.80/14.36 2358 (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]. 14.80/14.36 2359 (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]. 14.80/14.36 2360 $T # label(dt_k3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.80/14.36 2361 $T # label(t6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.80/14.36 2362 (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]. 14.80/14.36 2363 (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]. 14.80/14.36 2364 (all A r1_tarski(k3_ordinal2(A),A)) # label(t13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.80/14.36 2365 (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]. 14.80/14.36 2366 (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]. 14.80/14.36 2367 (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]. 14.80/14.36 2368 (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]. 14.80/14.41 2369 (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]. 14.80/14.41 2370 (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]. 14.80/14.41 2371 (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]. 14.80/14.41 2372 (all A (v3_ordinal1(A) -> k16_ordinal2(A,k1_xboole_0) = k4_ordinal2)) # label(t60_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.80/14.41 2373 (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]. 14.80/14.41 2374 (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]. 14.80/14.41 2375 $T # label(t36_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.80/14.41 2376 $T # label(t20_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.80/14.41 2377 $T # label(t39_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.80/14.41 2378 (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]. 14.80/14.41 2379 $T # label(t40_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.80/14.41 2380 (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]. 14.80/14.41 2381 (all A (v3_ordinal1(A) -> k7_ordinal2(A) = A)) # label(t26_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.80/14.41 2382 (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]. 14.80/14.41 2383 (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]. 14.80/14.41 2384 (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]. 14.80/14.41 2385 (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]. 14.80/14.41 2386 (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]. 14.80/14.41 2387 $T # label(t42_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.80/14.41 2388 $T # label(t12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.80/14.41 2389 (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]. 14.80/14.41 2390 (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]. 14.80/14.41 2391 (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]. 14.80/14.41 2392 $T # label(dt_k1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.80/14.41 2393 (all A r1_ordinal1(k6_ordinal2(A),k7_ordinal2(A))) # label(t32_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.80/14.41 2394 $T # label(t38_ordinal2) # label(axiom) # label(non_clause). [assumption]. 14.80/14.41 2395 $T # label(t2_finset_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.41 2396 $T # label(t1_finset_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.41 2397 (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]. 14.80/14.41 2398 (all A (-v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)))) # label(fc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.41 2399 (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]. 14.80/14.41 2400 (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]. 14.80/14.41 2401 (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]. 14.80/14.41 2402 (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]. 14.80/14.41 2403 (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]. 14.80/14.41 2404 $T # label(t8_finset_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.41 2405 (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]. 14.80/14.41 2406 $T # label(t6_finset_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.41 2407 (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]. 14.80/14.41 2408 (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]. 14.80/14.41 2409 $T # label(t5_finset_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.41 2410 (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]. 14.80/14.41 2411 (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]. 14.80/14.41 2412 (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]. 14.80/14.41 2413 (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]. 14.80/14.41 2414 $T # label(t7_finset_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.41 2415 $T # label(t11_finset_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.41 2416 (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]. 14.80/14.41 2417 (all A all B all C v1_finset_1(k1_enumset1(A,B,C))) # label(fc3_finset_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.41 2418 (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]. 14.80/14.41 2419 (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]. 14.80/14.41 2420 $T # label(t12_finset_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.41 2421 (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]. 14.80/14.41 2422 (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]. 14.80/14.41 2423 (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]. 14.80/14.41 2424 (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]. 14.80/14.41 2425 (all A (v1_finset_1(k1_zfmisc_1(A)) <-> v1_finset_1(A))) # label(t24_finset_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.41 2426 (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]. 14.80/14.41 2427 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]. 14.80/14.42 2428 (all A (v1_xboole_0(A) -> v1_finset_1(A))) # label(cc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2429 (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]. 14.80/14.42 2430 $T # label(t3_finset_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2431 (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]. 14.80/14.42 2432 (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]. 14.80/14.42 2433 (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]. 14.80/14.42 2434 (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]. 14.80/14.42 2435 (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]. 14.80/14.42 2436 (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]. 14.80/14.42 2437 $T # label(t4_finset_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2438 $T # label(t9_finset_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2439 (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]. 14.80/14.42 2440 (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]. 14.80/14.42 2441 (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]. 14.80/14.42 2442 (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]. 14.80/14.42 2443 (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]. 14.80/14.42 2444 (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]. 14.80/14.42 2445 (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]. 14.80/14.42 2446 (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]. 14.80/14.42 2447 (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]. 14.80/14.42 2448 $T # label(t10_finset_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2449 (exists A (-v1_xboole_0(A) & v1_finset_1(A))) # label(rc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2450 (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]. 14.80/14.42 2451 (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]. 14.80/14.42 2452 (all A all B (v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k1_funct_2(A,B)))) # label(t16_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2453 (all A (m1_subset_1(A,f1_s4_fraenkel) -> (all B (m1_subset_1(B,f2_s4_fraenkel) -> (p2_s4_fraenkel(A,B) <-> p1_s4_fraenkel(A,B)))))) -> a_0_6_fraenkel = a_0_7_fraenkel # label(s4_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2454 (all A (r2_hidden(A,a_0_36_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s20_fraenkel) & f4_s20_fraenkel = C & p1_s20_fraenkel(B,C) & A = f3_s20_fraenkel(B,C) & m1_subset_1(C,f2_s20_fraenkel))))) # label(fraenkel_a_0_36_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2455 (all A (r2_hidden(A,a_0_34_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s19_fraenkel) & m1_subset_1(C,f2_s19_fraenkel) & p2_s19_fraenkel(B,C) & A = f3_s19_fraenkel(B,C))))) # label(fraenkel_a_0_34_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2456 (all A ((exists B (m1_subset_1(B,f1_s6_fraenkel) & f2_s6_fraenkel(B) = A & p1_s6_fraenkel(B))) <-> r2_hidden(A,a_0_10_fraenkel))) # label(fraenkel_a_0_10_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2457 (all A all B all C (m1_fraenkel(C,A,B) & -v1_xboole_0(B) -> (all D (m2_fraenkel(D,A,B,C) -> v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B))))) # label(dt_m2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2458 (all A ((exists B (m1_subset_1(B,f1_s5_fraenkel) & p1_s5_fraenkel(B) & A = f2_s5_fraenkel(B))) <-> r2_hidden(A,a_0_8_fraenkel))) # label(fraenkel_a_0_8_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2459 (all A (m1_subset_1(A,f1_s12_fraenkel) -> (all B (m1_subset_1(B,f2_s12_fraenkel) -> (p1_s12_fraenkel(A,B) -> p2_s12_fraenkel(f3_s12_fraenkel(A,B))))))) -> (all A (r2_hidden(A,a_0_20_fraenkel) -> p2_s12_fraenkel(A))) # label(s12_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2460 (all A ((exists B (A = f3_s6_fraenkel(B) & p1_s6_fraenkel(B) & m1_subset_1(B,f1_s6_fraenkel))) <-> r2_hidden(A,a_0_11_fraenkel))) # label(fraenkel_a_0_11_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2461 (all A (m1_subset_1(A,f1_s9_fraenkel) -> (r2_hidden(A,f3_s9_fraenkel) -> (p2_s9_fraenkel(A) <-> p1_s9_fraenkel(A))))) & k7_relat_1(f5_s9_fraenkel,f3_s9_fraenkel) = k7_relat_1(f4_s9_fraenkel,f3_s9_fraenkel) -> a_0_16_fraenkel = a_0_17_fraenkel # label(s9_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2462 (all A (r2_hidden(A,a_0_20_fraenkel) <-> (exists B exists C (m1_subset_1(C,f2_s12_fraenkel) & p1_s12_fraenkel(B,C) & f3_s12_fraenkel(B,C) = A & m1_subset_1(B,f1_s12_fraenkel))))) # label(fraenkel_a_0_20_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2463 (all A (-v1_xboole_0(A) -> (all B all C all D (r1_tarski(C,B) & r1_tarski(D,A) -> k1_funct_2(C,D) = k1_xboole_0 | (all E (m1_subset_1(E,k1_funct_2(C,D)) -> v1_funct_1(E) & m2_relset_1(E,B,A))))))) # label(t6_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2464 $T # label(t4_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2465 (all A all B all C (m1_fraenkel(C,A,B) -> v1_fraenkel(C) & -v1_xboole_0(C))) # label(dt_m1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2466 (exists A (m1_subset_1(A,k5_finsub_1(f1_s24_fraenkel)) & (all B (m1_subset_1(B,f1_s24_fraenkel) -> ((exists C (m1_subset_1(C,f2_s24_fraenkel) & B = f4_s24_fraenkel(C) & p1_s24_fraenkel(B,C) & r2_hidden(C,f3_s24_fraenkel))) <-> r2_hidden(B,A)))))) # label(s24_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2467 (all A all B (v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k1_funct_2(A,B)) & v1_fraenkel(k1_funct_2(A,B)))) # label(fc2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2468 (all A (r2_hidden(A,a_0_37_fraenkel) <-> (exists B (f3_s20_fraenkel(B,f4_s20_fraenkel) = A & p1_s20_fraenkel(B,f4_s20_fraenkel) & m1_subset_1(B,f1_s20_fraenkel))))) # label(fraenkel_a_0_37_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2469 (all A all B all C (m1_fraenkel(C,A,B) & -v1_xboole_0(B) -> (all D (m2_fraenkel(D,A,B,C) <-> m1_subset_1(D,C))))) # label(redefinition_m2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2470 (all A ((exists B (r1_tarski(k2_funct_2(f1_s25_fraenkel,f2_s25_fraenkel,B,f3_s25_fraenkel),f4_s25_fraenkel) & A = f5_s25_fraenkel(B) & m2_fraenkel(B,f1_s25_fraenkel,f2_s25_fraenkel,k1_fraenkel(f1_s25_fraenkel,f2_s25_fraenkel)))) <-> r2_hidden(A,a_0_40_fraenkel))) # label(fraenkel_a_0_40_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2471 (all A (r2_hidden(A,a_0_38_fraenkel) <-> (exists B (r2_hidden(B,f2_s21_fraenkel) & A = f3_s21_fraenkel(B) & m1_subset_1(B,f1_s21_fraenkel))))) # label(fraenkel_a_0_38_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2472 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> m1_fraenkel(k2_setwiseo(k1_zfmisc_1(k2_zfmisc_1(A,B)),C),A,B))) # label(t10_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2473 v1_finset_1(f2_s21_fraenkel) -> v1_finset_1(a_0_38_fraenkel) # label(s21_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2474 (exists A (-v1_xboole_0(A) & v1_fraenkel(A))) # label(rc1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2475 (all A (-v1_xboole_0(A) -> (all B all C all D (r1_tarski(D,A) & r1_tarski(C,B) -> k1_xboole_0 = k1_funct_2(C,D) | (all E (m1_subset_1(E,k1_funct_2(C,D)) -> (exists F (m2_fraenkel(F,B,A,k1_fraenkel(B,A)) & E = k7_relat_1(F,C))))))))) # label(t14_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2476 (all A all B (-v1_xboole_0(B) -> k1_fraenkel(A,B) = k1_funct_2(A,B))) # label(redefinition_k1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2477 (all A (m1_subset_1(A,f1_s1_fraenkel) -> (p1_s1_fraenkel(A) -> p2_s1_fraenkel(A)))) -> r1_tarski(a_0_0_fraenkel,a_0_1_fraenkel) # label(s1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2478 (all A (m1_subset_1(A,f1_s26_fraenkel) -> -((all B (m1_subset_1(B,f2_s26_fraenkel) -> -p1_s26_fraenkel(A,B))) & r2_hidden(A,f3_s26_fraenkel)))) -> (exists A ((all B (m1_subset_1(B,f1_s26_fraenkel) -> (r2_hidden(B,f3_s26_fraenkel) -> p1_s26_fraenkel(B,k8_funct_2(f1_s26_fraenkel,f2_s26_fraenkel,A,B))))) & m2_relset_1(A,f1_s26_fraenkel,f2_s26_fraenkel) & v1_funct_2(A,f1_s26_fraenkel,f2_s26_fraenkel) & v1_funct_1(A))) # label(s26_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2479 (all A (v1_fraenkel(A) -> (all B (r1_tarski(B,A) -> v1_fraenkel(B))))) # label(t17_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2480 (all A (r2_hidden(A,a_0_32_fraenkel) <-> (exists B (m1_subset_1(B,f1_s17_fraenkel) & f3_s17_fraenkel(B) = A & r2_hidden(f3_s17_fraenkel(B),f2_s17_fraenkel) & p1_s17_fraenkel(B))))) # label(fraenkel_a_0_32_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2481 (all A (m1_subset_1(A,f1_s23_fraenkel) -> (all B (m1_subset_1(B,f1_s23_fraenkel) -> (all C (m1_subset_1(C,f1_s23_fraenkel) -> (p1_s23_fraenkel(A,B) & p1_s23_fraenkel(B,C) -> p1_s23_fraenkel(A,C)))))))) & (all A (m1_subset_1(A,f1_s23_fraenkel) -> p1_s23_fraenkel(A,A))) -> (all A (m1_subset_1(A,f1_s23_fraenkel) -> -((all B (m1_subset_1(B,f1_s23_fraenkel) -> -(p1_s23_fraenkel(B,A) & (all C (m1_subset_1(C,f1_s23_fraenkel) -> (r2_hidden(C,f2_s23_fraenkel) & p1_s23_fraenkel(C,B) -> p1_s23_fraenkel(B,C)))) & r2_hidden(B,f2_s23_fraenkel)))) & r2_hidden(A,f2_s23_fraenkel)))) # label(s23_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2482 (all A ((exists B (m1_subset_1(B,f3_s13_fraenkel) & r2_hidden(B,a_0_22_fraenkel) & p2_s13_fraenkel(B) & A = B)) <-> r2_hidden(A,a_0_21_fraenkel))) # label(fraenkel_a_0_21_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2483 (all A (r2_hidden(A,a_0_19_fraenkel) -> p2_s11_fraenkel(A))) -> (all A (m1_subset_1(A,f1_s11_fraenkel) -> (all B (m1_subset_1(B,f2_s11_fraenkel) -> (p1_s11_fraenkel(A,B) -> p2_s11_fraenkel(f3_s11_fraenkel(A,B))))))) # label(s11_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2484 (all A (r2_hidden(A,a_0_0_fraenkel) <-> (exists B (m1_subset_1(B,f1_s1_fraenkel) & A = f2_s1_fraenkel(B) & p1_s1_fraenkel(B))))) # label(fraenkel_a_0_0_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2485 (all A (r2_hidden(A,a_0_33_fraenkel) <-> (exists B (m1_subset_1(B,f1_s18_fraenkel) & A = f3_s18_fraenkel(B) & p1_s18_fraenkel(B) & -r2_hidden(f3_s18_fraenkel(B),f2_s18_fraenkel))))) # label(fraenkel_a_0_33_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2486 (all A (r2_hidden(A,a_0_39_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s22_fraenkel) & m1_subset_1(C,f2_s22_fraenkel) & A = f5_s22_fraenkel(B,C) & r2_hidden(C,f4_s22_fraenkel) & r2_hidden(B,f3_s22_fraenkel))))) # label(fraenkel_a_0_39_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2487 (all A (r2_hidden(A,a_0_23_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s13_fraenkel) & p2_s13_fraenkel(f4_s13_fraenkel(B,C)) & p1_s13_fraenkel(B,C) & A = f4_s13_fraenkel(B,C) & m1_subset_1(C,f2_s13_fraenkel))))) # label(fraenkel_a_0_23_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2488 (all A ((exists B (m1_subset_1(B,f1_s14_fraenkel) & p2_s14_fraenkel(B) & p1_s14_fraenkel(B) & f2_s14_fraenkel(B) = A)) <-> r2_hidden(A,a_0_26_fraenkel))) # label(fraenkel_a_0_26_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2489 (all A ((exists B exists C (m1_subset_1(B,f1_s11_fraenkel) & m1_subset_1(C,f2_s11_fraenkel) & p1_s11_fraenkel(B,C) & A = f3_s11_fraenkel(B,C))) <-> r2_hidden(A,a_0_19_fraenkel))) # label(fraenkel_a_0_19_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2490 (all A (m1_subset_1(A,f1_s7_fraenkel) -> (all B (m1_subset_1(B,f2_s7_fraenkel) -> f3_s7_fraenkel(A,B) = f4_s7_fraenkel(A,B))))) -> a_0_12_fraenkel = a_0_13_fraenkel # label(s7_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2491 (all A (m1_subset_1(A,f1_s19_fraenkel) -> (all B (m1_subset_1(B,f2_s19_fraenkel) -> (p2_s19_fraenkel(A,B) <-> p1_s19_fraenkel(A,B) & B = f4_s19_fraenkel))))) -> a_0_34_fraenkel = a_0_35_fraenkel # label(s19_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2492 (all A (r2_hidden(A,a_0_6_fraenkel) <-> (exists B exists C (f3_s4_fraenkel(B,C) = A & p1_s4_fraenkel(B,C) & m1_subset_1(C,f2_s4_fraenkel) & m1_subset_1(B,f1_s4_fraenkel))))) # label(fraenkel_a_0_6_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2493 (all A ((exists B exists C (m1_subset_1(C,f2_s16_fraenkel) & A = f3_s16_fraenkel(B,C) & p1_s16_fraenkel(B,C) & m1_subset_1(B,f1_s16_fraenkel))) <-> r2_hidden(A,a_0_30_fraenkel))) # label(fraenkel_a_0_30_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2494 v1_finset_1(f4_s22_fraenkel) & v1_finset_1(f3_s22_fraenkel) -> v1_finset_1(a_0_39_fraenkel) # label(s22_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2495 $T # label(t9_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2496 (all A all B v1_fraenkel(k1_funct_2(A,B))) # label(fc1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2497 (all A (m1_subset_1(A,f1_s6_fraenkel) -> (p1_s6_fraenkel(A) -> f2_s6_fraenkel(A) = f3_s6_fraenkel(A)))) -> a_0_11_fraenkel = a_0_10_fraenkel # label(s6_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2498 (all A (r2_hidden(A,a_0_22_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s13_fraenkel) & m1_subset_1(C,f2_s13_fraenkel) & p1_s13_fraenkel(B,C) & A = f4_s13_fraenkel(B,C))))) # label(fraenkel_a_0_22_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2499 (all A ((exists B exists C (f3_s16_fraenkel(B,C) = A & p2_s16_fraenkel(B,C) & m1_subset_1(C,f2_s16_fraenkel) & m1_subset_1(B,f1_s16_fraenkel))) <-> r2_hidden(A,a_0_31_fraenkel))) # label(fraenkel_a_0_31_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2500 (all A (m1_subset_1(A,f1_s27_fraenkel) -> -((all B (m1_subset_1(B,f2_s27_fraenkel) -> -p1_s27_fraenkel(A,B))) & r2_hidden(A,f3_s27_fraenkel)))) -> (exists A (m2_fraenkel(A,f1_s27_fraenkel,f2_s27_fraenkel,k1_fraenkel(f1_s27_fraenkel,f2_s27_fraenkel)) & (all B (m1_subset_1(B,f1_s27_fraenkel) -> (r2_hidden(B,f3_s27_fraenkel) -> p1_s27_fraenkel(B,k8_funct_2(f1_s27_fraenkel,f2_s27_fraenkel,A,B))))))) # label(s27_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2501 $T # label(t13_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2502 (all A (r2_hidden(A,a_0_24_fraenkel) <-> (exists B (m1_subset_1(B,f1_s14_fraenkel) & A = f2_s14_fraenkel(B) & p1_s14_fraenkel(B) & r2_hidden(B,a_0_25_fraenkel))))) # label(fraenkel_a_0_24_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2503 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (k7_relat_1(C,E) = k7_relat_1(D,E) -> (all F (m1_subset_1(F,A) -> (r2_hidden(F,E) -> k8_funct_2(A,B,D,F) = k8_funct_2(A,B,C,F)))))))))))))) # label(t3_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2504 (all A all B exists C m1_fraenkel(C,A,B)) # label(existence_m1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2505 $T # label(t1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2506 (all A (-v1_xboole_0(A) -> (all B all C all D (m2_fraenkel(D,B,A,k1_fraenkel(B,A)) -> k7_relat_1(D,C) = k7_relat_1(D,k3_xboole_0(B,C)))))) # label(t15_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2507 (all A (r2_hidden(A,a_0_3_fraenkel) <-> (exists B exists C (m1_subset_1(C,f2_s2_fraenkel) & f3_s2_fraenkel(B,C) = A & p2_s2_fraenkel(B,C) & m1_subset_1(B,f1_s2_fraenkel))))) # label(fraenkel_a_0_3_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2508 $T # label(t7_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2509 (all A (r2_hidden(A,a_0_4_fraenkel) <-> (exists B (m1_subset_1(B,f1_s3_fraenkel) & A = f2_s3_fraenkel(B) & p1_s3_fraenkel(B))))) # label(fraenkel_a_0_4_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2510 (all A (r2_hidden(A,a_0_9_fraenkel) <-> (exists B (A = f3_s5_fraenkel(B) & p1_s5_fraenkel(B) & m1_subset_1(B,f1_s5_fraenkel))))) # label(fraenkel_a_0_9_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2511 (all A (m1_subset_1(A,f1_s16_fraenkel) -> (all B (m1_subset_1(B,f2_s16_fraenkel) -> -(p1_s16_fraenkel(A,B) & (all C (m1_subset_1(C,f1_s16_fraenkel) -> -(f3_s16_fraenkel(A,B) = f3_s16_fraenkel(C,B) & p2_s16_fraenkel(C,B))))))))) -> r1_tarski(a_0_30_fraenkel,a_0_31_fraenkel) # label(s16_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2512 $T # label(t2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2513 (all A ((exists B exists C (m1_subset_1(B,f1_s8_fraenkel) & p1_s8_fraenkel(B,C) & f3_s8_fraenkel(B,C) = A & m1_subset_1(C,f2_s8_fraenkel))) <-> r2_hidden(A,a_0_14_fraenkel))) # label(fraenkel_a_0_14_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2514 (all A (r2_hidden(A,a_0_1_fraenkel) <-> (exists B (m1_subset_1(B,f1_s1_fraenkel) & f2_s1_fraenkel(B) = A & p2_s1_fraenkel(B))))) # label(fraenkel_a_0_1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2515 (all A (m1_subset_1(A,f1_s2_fraenkel) -> (all B (m1_subset_1(B,f2_s2_fraenkel) -> (p1_s2_fraenkel(A,B) -> p2_s2_fraenkel(A,B)))))) -> r1_tarski(a_0_2_fraenkel,a_0_3_fraenkel) # label(s2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2516 (all A (r2_hidden(A,a_0_27_fraenkel) <-> (exists B exists C (m1_subset_1(C,f2_s15_fraenkel) & A = f3_s15_fraenkel(B,C) & p1_s15_fraenkel(B,C) & r2_hidden(B,a_0_28_fraenkel) & m1_subset_1(B,f1_s15_fraenkel))))) # label(fraenkel_a_0_27_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2517 (all A (r2_hidden(A,a_0_16_fraenkel) <-> (exists B (m1_subset_1(B,f1_s9_fraenkel) & k8_funct_2(f1_s9_fraenkel,f2_s9_fraenkel,f4_s9_fraenkel,B) = A & p1_s9_fraenkel(B) & r2_hidden(B,f3_s9_fraenkel))))) # label(fraenkel_a_0_16_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2518 (all A (r2_hidden(A,a_0_15_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s8_fraenkel) & m1_subset_1(C,f2_s8_fraenkel) & A = f3_s8_fraenkel(C,B) & p2_s8_fraenkel(B,C))))) # label(fraenkel_a_0_15_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2519 (all A all B r1_tarski(k1_funct_2(A,B),k1_zfmisc_1(k2_zfmisc_1(A,B)))) # label(t5_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2520 (all A ((exists B (m1_subset_1(B,f1_s10_fraenkel) & p1_s10_fraenkel(B) & A = B)) <-> r2_hidden(A,a_0_18_fraenkel))) # label(fraenkel_a_0_18_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2521 (all A (r2_hidden(A,a_0_5_fraenkel) <-> (exists B (f2_s3_fraenkel(B) = A & p2_s3_fraenkel(B) & m1_subset_1(B,f1_s3_fraenkel))))) # label(fraenkel_a_0_5_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2522 (all A (r2_hidden(A,a_0_13_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s7_fraenkel) & p1_s7_fraenkel(B,C) & A = f4_s7_fraenkel(B,C) & m1_subset_1(C,f2_s7_fraenkel))))) # label(fraenkel_a_0_13_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2523 (all A ((exists B (r2_hidden(B,f3_s9_fraenkel) & p2_s9_fraenkel(B) & k8_funct_2(f1_s9_fraenkel,f2_s9_fraenkel,f5_s9_fraenkel,B) = A & m1_subset_1(B,f1_s9_fraenkel))) <-> r2_hidden(A,a_0_17_fraenkel))) # label(fraenkel_a_0_17_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2524 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_fraenkel(k1_tarski(A)))) # label(t8_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2525 (all A (m1_subset_1(A,f1_s8_fraenkel) -> (all B (m1_subset_1(B,f2_s8_fraenkel) -> (p2_s8_fraenkel(A,B) <-> p1_s8_fraenkel(A,B)))))) & (all A (m1_subset_1(A,f1_s8_fraenkel) -> (all B (m1_subset_1(B,f2_s8_fraenkel) -> f3_s8_fraenkel(B,A) = f3_s8_fraenkel(A,B))))) -> a_0_14_fraenkel = a_0_15_fraenkel # label(s8_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2526 (all A (r2_hidden(A,a_0_25_fraenkel) <-> (exists B (m1_subset_1(B,f1_s14_fraenkel) & p2_s14_fraenkel(B) & B = A)))) # label(fraenkel_a_0_25_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2527 (all A (m1_subset_1(A,f1_s5_fraenkel) -> f2_s5_fraenkel(A) = f3_s5_fraenkel(A))) -> a_0_8_fraenkel = a_0_9_fraenkel # label(s5_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2528 (all A ((exists B (m1_subset_1(B,f1_s19_fraenkel) & f3_s19_fraenkel(B,f4_s19_fraenkel) = A & p1_s19_fraenkel(B,f4_s19_fraenkel))) <-> r2_hidden(A,a_0_35_fraenkel))) # label(fraenkel_a_0_35_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2529 (all A (r2_hidden(A,a_0_7_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s4_fraenkel) & m1_subset_1(C,f2_s4_fraenkel) & p2_s4_fraenkel(B,C) & f3_s4_fraenkel(B,C) = A)))) # label(fraenkel_a_0_7_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2530 (all A (m1_subset_1(A,f1_s3_fraenkel) -> (p1_s3_fraenkel(A) <-> p2_s3_fraenkel(A)))) -> a_0_5_fraenkel = a_0_4_fraenkel # label(s3_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2531 (all A ((exists B exists C (m1_subset_1(B,f1_s15_fraenkel) & p2_s15_fraenkel(B) & p1_s15_fraenkel(B,C) & A = f3_s15_fraenkel(B,C) & m1_subset_1(C,f2_s15_fraenkel))) <-> r2_hidden(A,a_0_29_fraenkel))) # label(fraenkel_a_0_29_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2532 (all A ((exists B (A = B & p2_s15_fraenkel(B) & m1_subset_1(B,f1_s15_fraenkel))) <-> r2_hidden(A,a_0_28_fraenkel))) # label(fraenkel_a_0_28_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2533 (all A all B all C (v1_fraenkel(C) & -v1_xboole_0(C) -> ((all D (m1_subset_1(D,C) -> v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D))) <-> m1_fraenkel(C,A,B)))) # label(d2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2534 $T # label(t12_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2535 (all A all B all C (m1_fraenkel(C,A,B) & -v1_xboole_0(B) -> (exists D m2_fraenkel(D,A,B,C)))) # label(existence_m2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2536 (all A (v1_fraenkel(A) -> (all B (m1_subset_1(B,A) -> v1_relat_1(B) & v1_funct_1(B))))) # label(cc1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2537 (all A (v1_fraenkel(A) <-> (all B (r2_hidden(B,A) -> v1_funct_1(B) & v1_relat_1(B))))) # label(d1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2538 (all A (r2_hidden(A,a_0_12_fraenkel) <-> (exists B exists C (m1_subset_1(C,f2_s7_fraenkel) & p1_s7_fraenkel(B,C) & f3_s7_fraenkel(B,C) = A & m1_subset_1(B,f1_s7_fraenkel))))) # label(fraenkel_a_0_12_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2539 (all A all B (-v1_xboole_0(B) -> m1_fraenkel(k1_fraenkel(A,B),A,B))) # label(dt_k1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2540 (all A ((exists B exists C (m1_subset_1(B,f1_s2_fraenkel) & m1_subset_1(C,f2_s2_fraenkel) & f3_s2_fraenkel(B,C) = A & p1_s2_fraenkel(B,C))) <-> r2_hidden(A,a_0_2_fraenkel))) # label(fraenkel_a_0_2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2541 v1_finset_1(f3_s25_fraenkel) & v1_finset_1(f4_s25_fraenkel) & (all A (m2_fraenkel(A,f1_s25_fraenkel,f2_s25_fraenkel,k1_fraenkel(f1_s25_fraenkel,f2_s25_fraenkel)) -> (all B (m2_fraenkel(B,f1_s25_fraenkel,f2_s25_fraenkel,k1_fraenkel(f1_s25_fraenkel,f2_s25_fraenkel)) -> (k7_relat_1(A,f3_s25_fraenkel) = k7_relat_1(B,f3_s25_fraenkel) -> f5_s25_fraenkel(B) = f5_s25_fraenkel(A)))))) -> v1_finset_1(a_0_40_fraenkel) # label(s25_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2542 (all A (-v1_xboole_0(A) -> (all B m1_fraenkel(k1_funct_2(B,A),B,A)))) # label(t11_fraenkel) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2543 $T # label(dt_k1_numbers) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2544 (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]. 14.80/14.42 2545 $T # label(dt_k4_numbers) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2546 $T # label(dt_k3_numbers) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2547 $T # label(dt_k2_numbers) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2548 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)))) # label(fc3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2549 (exists A (v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) & -v3_xreal_0(A) & -v1_xboole_0(A))) # label(rc2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2550 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) & v2_xreal_0(A) -> v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v3_xreal_0(k6_xcmplx_0(B,A)) & -v2_xreal_0(k6_xcmplx_0(B,A)) & -v1_xboole_0(k6_xcmplx_0(B,A)))) # label(fc18_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2551 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> r1_xreal_0(A,A))) # label(reflexivity_r1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2552 (all A (v1_xreal_0(A) & v3_xreal_0(A) -> -v1_xboole_0(A) & v1_xreal_0(A) & -v2_xreal_0(A) & v1_xcmplx_0(A))) # label(cc5_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2553 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)))) # label(fc4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2554 (all A all B (v1_xreal_0(B) & -v3_xreal_0(B) & -v2_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(k3_xcmplx_0(B,A)) & -v2_xreal_0(k3_xcmplx_0(B,A)) & v1_xreal_0(k3_xcmplx_0(B,A)))) # label(fc22_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2555 (all A all B (v1_xreal_0(A) & v3_xreal_0(A) & -v3_xreal_0(B) & v1_xreal_0(B) -> v1_xcmplx_0(k6_xcmplx_0(B,A)) & -v3_xreal_0(k6_xcmplx_0(B,A)) & v2_xreal_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & -v1_xboole_0(k6_xcmplx_0(B,A)))) # label(fc20_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2556 (all A all B (-v3_xreal_0(B) & v1_xreal_0(B) & -v2_xreal_0(A) & v1_xreal_0(A) -> -v2_xreal_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc21_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2557 (exists A (-v1_xboole_0(A) & v1_xcmplx_0(A) & -v2_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(A))) # label(rc3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2558 (all A all B (v1_xreal_0(A) & -v2_xreal_0(B) & v1_xreal_0(B) & v2_xreal_0(A) -> v1_xcmplx_0(k6_xcmplx_0(A,B)) & v2_xreal_0(k6_xcmplx_0(A,B)) & -v3_xreal_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & -v1_xboole_0(k6_xcmplx_0(A,B)))) # label(fc17_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2559 (all A all B (v1_xreal_0(B) & -v2_xreal_0(B) & -v3_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(k7_xcmplx_0(B,A)) & v1_xreal_0(k7_xcmplx_0(B,A)) & -v2_xreal_0(k7_xcmplx_0(B,A)))) # label(fc28_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2560 (all A (v1_xreal_0(A) -> (-r1_xreal_0(np__0,A) <-> v3_xreal_0(A)))) # label(d4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2561 (all A (v1_xreal_0(A) & -v2_xreal_0(A) -> v1_xreal_0(k4_xcmplx_0(A)) & -v3_xreal_0(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)))) # label(fc13_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2562 (all A (v1_xreal_0(A) -> (-r1_xreal_0(A,np__0) <-> v2_xreal_0(A)))) # label(d3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2563 (all A (v1_xreal_0(A) & -v3_xreal_0(A) -> v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & -v2_xreal_0(k4_xcmplx_0(A)))) # label(fc14_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2564 (all A (v1_xreal_0(A) -> v1_xcmplx_0(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(A)))) # label(fc2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2565 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)))) # label(fc5_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2566 (all A all B (v1_xreal_0(B) & -v3_xreal_0(B) & v2_xreal_0(A) & v1_xreal_0(A) -> v2_xreal_0(k2_xcmplx_0(B,A)) & -v3_xreal_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & -v1_xboole_0(k2_xcmplx_0(B,A)))) # label(fc10_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2567 (all A (-v1_xboole_0(A) & -v3_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A))) # label(cc4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2568 (all A all B (v1_xreal_0(B) & -v3_xreal_0(B) & -v3_xreal_0(A) & v1_xreal_0(A) -> v1_xreal_0(k7_xcmplx_0(A,B)) & -v3_xreal_0(k7_xcmplx_0(A,B)) & v1_xcmplx_0(k7_xcmplx_0(A,B)))) # label(fc29_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2569 (all A (r2_hidden(A,k1_numbers) <-> v1_xreal_0(A))) # label(d1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2570 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r2_hidden(A,k2_arytm_2) & r2_hidden(B,k2_arytm_2) -> ((exists C ((exists D (r1_arytm_2(C,D) & D = B & C = A & m1_subset_1(D,k2_arytm_2))) & m1_subset_1(C,k2_arytm_2))) <-> r1_xreal_0(A,B))) & (r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) -> (r1_xreal_0(A,B) <-> (exists C (m1_subset_1(C,k2_arytm_2) & (exists D (k4_tarski(np__0,C) = A & r1_arytm_2(D,C) & k4_tarski(np__0,D) = B & m1_subset_1(D,k2_arytm_2))))))) & -(-(r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_arytm_2)) & -(r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(B,k2_arytm_2) <-> r1_xreal_0(A,B)) & -(r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)))))))) # label(d2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2571 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> r1_xreal_0(A,B) | r1_xreal_0(B,A))) # label(connectedness_r1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2572 (all A (v4_ordinal2(A) -> v1_xreal_0(A))) # label(cc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2573 (all A all B (-v3_xreal_0(B) & v1_xreal_0(B) & -v3_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & -v3_xreal_0(k3_xcmplx_0(A,B)))) # label(fc24_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2574 (exists A (v1_xcmplx_0(A) & v1_xreal_0(A) & -v3_xreal_0(A) & -v2_xreal_0(A) & v1_xboole_0(A))) # label(rc4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2575 (all A all B (-v2_xreal_0(A) & -v2_xreal_0(B) & v1_xreal_0(B) & v1_xreal_0(A) -> v1_xcmplx_0(k7_xcmplx_0(A,B)) & -v3_xreal_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)))) # label(fc30_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2576 (all A all B (v2_xreal_0(A) & v1_xreal_0(B) & -v3_xreal_0(B) & v1_xreal_0(A) -> -v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & -v3_xreal_0(k2_xcmplx_0(A,B)) & v2_xreal_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)))) # label(fc9_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2577 (all A all B (v1_xreal_0(A) & v3_xreal_0(A) & -v2_xreal_0(B) & v1_xreal_0(B) -> -v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & -v2_xreal_0(k2_xcmplx_0(A,B)) & v3_xreal_0(k2_xcmplx_0(A,B)))) # label(fc11_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2578 (all A all B (v1_xreal_0(A) & -v2_xreal_0(B) & v1_xreal_0(B) & -v3_xreal_0(A) -> v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & -v3_xreal_0(k6_xcmplx_0(A,B)))) # label(fc15_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2579 (all A all B (-v2_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) & v1_xreal_0(A) -> v1_xcmplx_0(k3_xcmplx_0(A,B)) & -v3_xreal_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)))) # label(fc23_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2580 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & -v3_xreal_0(B) & -v3_xreal_0(A) -> v1_xreal_0(k2_xcmplx_0(A,B)) & -v3_xreal_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)))) # label(fc7_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2581 (all A (v1_xreal_0(A) & -v2_xreal_0(A) & -v3_xreal_0(A) -> v1_xboole_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A))) # label(cc8_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2582 (all A all B (v1_xreal_0(A) & -v3_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) -> v1_xcmplx_0(k6_xcmplx_0(B,A)) & -v2_xreal_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)))) # label(fc16_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2583 (all A (v1_xreal_0(A) & v1_xboole_0(A) -> -v2_xreal_0(A) & -v3_xreal_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A))) # label(cc7_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2584 (all A (v2_xreal_0(A) & v1_xreal_0(A) -> -v3_xreal_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A) & -v1_xboole_0(A))) # label(cc3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2585 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) & -v2_xreal_0(A) -> v1_xreal_0(k2_xcmplx_0(A,B)) & -v2_xreal_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)))) # label(fc8_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2586 (all A all B (v1_xreal_0(A) & -v3_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) -> v1_xcmplx_0(k7_xcmplx_0(A,B)) & -v2_xreal_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)))) # label(fc27_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2587 (all A (-v2_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(A)) & -v2_xreal_0(k5_xcmplx_0(A)))) # label(fc25_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2588 (exists A (v1_xcmplx_0(A) & v1_xreal_0(A))) # label(rc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2589 (all A (v1_xreal_0(A) & -v3_xreal_0(A) -> v1_xcmplx_0(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(A)) & -v3_xreal_0(k5_xcmplx_0(A)))) # label(fc26_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2590 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> v1_xreal_0(k7_xcmplx_0(A,B)) & v1_xcmplx_0(k7_xcmplx_0(A,B)))) # label(fc6_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2591 (all A all B (v3_xreal_0(A) & -v3_xreal_0(B) & v1_xreal_0(B) & v1_xreal_0(A) -> -v2_xreal_0(k6_xcmplx_0(A,B)) & v3_xreal_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)) & -v1_xboole_0(k6_xcmplx_0(A,B)))) # label(fc19_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2592 (all A (v1_xreal_0(A) -> v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)))) # label(fc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2593 (all A all B (v1_xreal_0(A) & -v2_xreal_0(B) & v1_xreal_0(B) & v3_xreal_0(A) -> v1_xcmplx_0(k2_xcmplx_0(B,A)) & -v2_xreal_0(k2_xcmplx_0(B,A)) & v3_xreal_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & -v1_xboole_0(k2_xcmplx_0(B,A)))) # label(fc12_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2594 (all A (-v1_xboole_0(A) & -v2_xreal_0(A) & v1_xreal_0(A) -> v3_xreal_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A))) # label(cc6_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2595 (all A (v1_xreal_0(A) -> v1_xcmplx_0(A))) # label(cc2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2596 $T # label(t31_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2597 $T # label(t1_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2598 (exists A (v1_xreal_0(A) & v1_int_1(A) & v1_xcmplx_0(A) & m1_subset_1(A,k1_numbers))) # label(rc1_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2599 (all A (v1_xreal_0(A) -> k1_int_1(k1_int_1(A)) = k1_int_1(A))) # label(t63_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2600 (all A (v1_xreal_0(A) -> (v1_int_1(A) <-> k2_int_1(A) = A))) # label(t54_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2601 (all A (v1_xreal_0(A) -> -(v1_int_1(A) & -r1_xreal_0(k2_int_1(A),k1_int_1(A))) & -(-v1_int_1(A) & r1_xreal_0(k2_int_1(A),k1_int_1(A))))) # label(t60_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2602 (all A (v1_xreal_0(A) -> (v1_int_1(A) <-> np__0 = k4_int_1(A)))) # label(t71_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2603 $T # label(t25_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2604 (all A all B (v1_int_1(B) & m1_subset_1(A,k5_numbers) -> v1_int_1(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)))) # label(fc6_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2605 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> -((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(C = k6_xcmplx_0(B,A) & r1_xreal_0(np__1,C)))) & -r1_xreal_0(B,A)))))) # label(t78_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2606 (all A (v1_int_1(A) -> (r1_xreal_0(np__0,A) -> r2_hidden(A,k5_numbers)))) # label(t16_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2607 (all A all B (v1_int_1(A) & v1_int_1(B) -> v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_int_1(k6_xcmplx_0(A,B)))) # label(fc4_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2608 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (all D (v1_int_1(D) -> (r1_int_1(A,B,C) & r1_int_1(B,D,C) -> r1_int_1(A,D,C)))))))))) # label(t36_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2609 (all A (v1_xreal_0(A) -> r1_xreal_0(np__0,k4_int_1(A)) & -r1_xreal_0(np__1,k4_int_1(A)))) # label(t69_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2610 (all A (v1_int_1(A) -> v1_xreal_0(k4_xcmplx_0(A)) & v1_int_1(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)))) # label(fc3_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2611 (all A (v1_xreal_0(A) -> -(-v1_int_1(A) & r1_xreal_0(k2_int_1(A),A)) & -(v1_int_1(A) & -r1_xreal_0(k2_int_1(A),A)))) # label(t55_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2612 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> v1_int_1(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)))) # label(fc9_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2613 (exists A (m1_subset_1(A,k1_zfmisc_1(k4_numbers)) & (all B (v1_int_1(B) -> (p1_s1_int_1(B) <-> r2_hidden(B,A)))))) # label(s1_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2614 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> ((exists D (k6_xcmplx_0(A,B) = k3_xcmplx_0(C,D) & v1_int_1(D))) <-> r1_int_1(A,B,C)))))))) # label(d3_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2615 $T # label(t3_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2616 $T # label(t49_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2617 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> k5_int_1(A,B) = k1_int_1(k7_xcmplx_0(A,B)))))) # label(d7_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2618 $T # label(t12_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2619 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (B != np__0 -> k6_xcmplx_0(A,k3_xcmplx_0(k5_int_1(A,B),B)) = k6_int_1(A,B)) & (B = np__0 -> np__0 = k6_int_1(A,B)))))) # label(d8_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2620 (all A (v1_xreal_0(A) -> k3_int_1(A) = k4_int_1(A))) # label(redefinition_k4_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2621 (exists A v1_int_1(A)) # label(rc2_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2622 (all A (v1_xreal_0(A) -> k2_int_1(A) = k2_int_1(k2_int_1(A)))) # label(t64_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2623 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (all D (v1_int_1(D) -> (all E (v1_int_1(E) -> (C = k3_xcmplx_0(A,B) & r1_int_1(D,E,C) -> r1_int_1(D,E,A)))))))))))) # label(t41_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2624 (all A all B (v1_int_1(B) & m1_subset_1(A,k5_numbers) -> v1_xreal_0(k3_xcmplx_0(B,A)) & v1_int_1(k3_xcmplx_0(B,A)) & v1_xcmplx_0(k3_xcmplx_0(B,A)))) # label(fc7_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2625 (all A (v1_xreal_0(A) -> k2_int_1(k1_int_1(A)) = k1_int_1(A))) # label(t65_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2626 (all A all B (v1_int_1(B) & v1_int_1(A) -> v1_int_1(k5_int_1(A,B)))) # label(dt_k5_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2627 (all A (v4_ordinal2(A) -> v1_int_1(A))) # label(cc3_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2628 (all A (v1_xreal_0(A) -> -(v1_int_1(A) & -r1_xreal_0(A,k1_int_1(A))) & -(-v1_int_1(A) & r1_xreal_0(A,k1_int_1(A))))) # label(t48_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2629 (all A all B (v1_int_1(B) & v1_int_1(A) -> v1_int_1(k6_int_1(A,B)))) # label(dt_k6_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2630 (all A (v1_int_1(A) -> (A != np__0 -> np__1 = k5_int_1(A,A)))) # label(t76_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2631 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (-r1_xreal_0(B,A) -> r1_xreal_0(k2_xcmplx_0(A,np__1),B)))))) # label(t20_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2632 (all A (v1_xreal_0(A) -> (v1_int_1(A) <-> k1_int_1(A) = k2_int_1(A)))) # label(t59_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2633 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (r1_xreal_0(A,B) & r1_xreal_0(A,C) -> r1_xreal_0(k2_xcmplx_0(A,np__1),C) | C = B | r1_xreal_0(k2_xcmplx_0(A,np__1),B)))))))) # label(t45_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2634 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (r1_xreal_0(B,A) & r1_xreal_0(C,A) -> r1_xreal_0(B,k6_xcmplx_0(A,np__1)) | B = C | r1_xreal_0(C,k6_xcmplx_0(A,np__1))))))))) # label(t44_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2635 (all A (v1_xreal_0(A) -> (v1_int_1(A) -> v1_int_1(k2_xcmplx_0(A,np__1)) & v1_int_1(k6_xcmplx_0(A,np__1))))) # label(t17_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2636 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (all D (v1_int_1(D) -> (all E (v1_int_1(E) -> (r1_int_1(D,E,C) & r1_int_1(A,B,C) -> r1_int_1(k3_xcmplx_0(A,D),k3_xcmplx_0(B,E),C)))))))))))) # label(t39_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2637 $T # label(t53_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2638 $T # label(t29_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2639 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> ((exists C (v1_int_1(C) & B = k3_xcmplx_0(A,C))) <-> r2_int_1(A,B)))))) # label(d9_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2640 (all A (v1_int_1(A) -> k6_int_1(A,A) = np__0)) # label(t77_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2641 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (C = k2_xcmplx_0(B,A) -> r1_xreal_0(B,C)))))))) # label(t19_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2642 $T # label(t73_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.42 2643 (all A ((all B (r2_hidden(B,A) <-> -(all C (m2_subset_1(C,k1_numbers,k5_numbers) -> B != k1_real_1(C) & C != B)))) <-> k4_numbers = A)) # label(d1_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2644 $T # label(t67_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2645 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> r1_xreal_0(np__0,k5_int_1(A,B)))))) # label(t82_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2646 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> (r1_xreal_0(A,B) & -r1_xreal_0(k2_xcmplx_0(A,np__1),B) <-> k2_int_1(A) = B))))) # label(d5_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2647 p1_s4_int_1(f1_s4_int_1) & (all A (v1_int_1(A) -> (p1_s4_int_1(A) -> p1_s4_int_1(k2_xcmplx_0(A,np__1)) & p1_s4_int_1(k6_xcmplx_0(A,np__1))))) -> (all A (v1_int_1(A) -> p1_s4_int_1(A))) # label(s4_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2648 $T # label(t26_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2649 (all A (v1_xreal_0(A) -> (k1_int_1(A) = A <-> v1_int_1(A)))) # label(t47_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2650 $T # label(t56_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2651 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (k1_real_1(np__1) = B & k1_real_1(np__1) = A | np__1 = B & A = np__1 <-> np__1 = k3_xcmplx_0(A,B)))))) # label(t22_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2652 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (r1_int_1(A,B,C) <-> r1_int_1(k2_xcmplx_0(A,C),B,C)))))))) # label(t42_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2653 $T # label(t4_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2654 $T # label(t5_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2655 $T # label(t9_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2656 $T # label(t13_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2657 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (r1_xreal_0(A,B) -> r2_hidden(k6_xcmplx_0(B,A),k5_numbers)))))) # label(t18_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2658 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> r1_int_1(A,A,B))))) # label(t32_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2659 (all A (m1_subset_1(A,k5_numbers) -> v3_ordinal1(A) & v1_xreal_0(A) & v1_int_1(A) & -v3_xreal_0(A) & v1_xcmplx_0(A) & v4_ordinal2(A) & v2_ordinal1(A) & v1_ordinal1(A))) # label(cc2_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2660 (all A all B (v1_int_1(A) & v1_int_1(B) -> v1_int_1(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc2_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2661 (all A (v1_int_1(A) -> np__0 = k5_int_1(A,np__0))) # label(t75_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2662 $T # label(t2_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2663 (all A (v1_int_1(A) -> (p1_s5_int_1(A) -> r1_xreal_0(f1_s5_int_1,A)))) & (exists A (v1_int_1(A) & p1_s5_int_1(A))) -> (exists A (v1_int_1(A) & p1_s5_int_1(A) & (all B (v1_int_1(B) -> (p1_s5_int_1(B) -> r1_xreal_0(A,B)))))) # label(s5_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2664 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(k4_int_1(A),np__0) & v1_int_1(A)) & -(-v1_int_1(A) & r1_xreal_0(k4_int_1(A),np__0)))) # label(t72_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2665 (all A (v1_xreal_0(A) -> (all B (v4_ordinal2(B) -> (B = A | A = k4_xcmplx_0(B) -> v1_int_1(A)))))) # label(t7_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2666 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (all D (v1_int_1(D) -> (all E (v1_int_1(E) -> (r1_int_1(A,B,C) & r1_int_1(D,E,C) -> r1_int_1(k6_xcmplx_0(A,D),k6_xcmplx_0(B,E),C)))))))))))) # label(t38_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2667 (all A all B (v1_int_1(A) & v1_int_1(B) -> v1_int_1(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)))) # label(fc1_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2668 p1_s2_int_1(f1_s2_int_1) & (all A (v1_int_1(A) -> (r1_xreal_0(f1_s2_int_1,A) & p1_s2_int_1(A) -> p1_s2_int_1(k2_xcmplx_0(A,np__1))))) -> (all A (v1_int_1(A) -> (r1_xreal_0(f1_s2_int_1,A) -> p1_s2_int_1(A)))) # label(s2_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2669 (all A (v1_xreal_0(A) -> -r1_xreal_0(k2_int_1(A),k6_xcmplx_0(A,np__1)) & -r1_xreal_0(k2_xcmplx_0(k2_int_1(A),np__1),A))) # label(t57_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2670 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (all D (v1_int_1(D) -> (all E (v1_int_1(E) -> (r1_int_1(A,B,C) & r1_int_1(D,E,C) -> r1_int_1(k2_xcmplx_0(A,D),k2_xcmplx_0(B,E),C)))))))))))) # label(t37_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2671 $T # label(t10_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2672 (all A all B (v1_int_1(B) & v1_int_1(A) -> r2_int_1(A,A))) # label(reflexivity_r2_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2673 $T # label(t30_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2674 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> k2_xcmplx_0(k2_int_1(A),B) = k2_int_1(k2_xcmplx_0(A,B)))))) # label(t58_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2675 (all A (v1_int_1(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) -> r1_xreal_0(A,k1_int_1(B))))))) # label(t81_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2676 $T # label(t24_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2677 (all A (v1_xreal_0(A) -> -r1_xreal_0(A,k6_xcmplx_0(k1_int_1(A),np__1)) & -r1_xreal_0(k2_xcmplx_0(A,np__1),k1_int_1(A)))) # label(t50_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2678 (all A (v1_xreal_0(A) -> v1_int_1(k1_int_1(A)))) # label(dt_k1_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2679 (all A (v1_xreal_0(A) -> -r1_xreal_0(k2_xcmplx_0(k1_int_1(A),np__1),A))) # label(t52_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2680 $T # label(t11_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2681 (all A (v1_xreal_0(A) -> np__0 = k1_int_1(k4_int_1(A)))) # label(t70_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2682 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (r1_int_1(A,B,C) -> r1_int_1(B,A,C)))))))) # label(t35_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2683 $T # label(t46_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2684 (all A (r2_hidden(A,k4_numbers) <-> v1_int_1(A))) # label(d2_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2685 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> (k1_int_1(A) = B <-> -r1_xreal_0(B,k6_xcmplx_0(A,np__1)) & r1_xreal_0(B,A)))))) # label(d4_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2686 (all A (v1_int_1(A) -> r1_int_1(A,np__0,A) & r1_int_1(np__0,A,A))) # label(t33_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2687 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (k1_real_1(np__1) = B & A = np__1 | A = k1_real_1(np__1) & B = np__1 <-> k3_xcmplx_0(A,B) = k1_real_1(np__1)))))) # label(t23_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2688 $T # label(dt_k3_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2689 $T # label(t15_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2690 (all A (v1_xreal_0(A) -> r1_xreal_0(k1_int_1(A),k2_int_1(A)))) # label(t61_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2691 (all A (v1_xreal_0(A) -> v1_xcmplx_0(k3_int_1(A)) & v1_xreal_0(k3_int_1(A)))) # label(fc10_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2692 (all A (m1_subset_1(A,k4_numbers) -> v1_int_1(A))) # label(cc1_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2693 $T # label(t14_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2694 (all A (v1_int_1(A) -> (-r1_xreal_0(np__0,A) -> r1_xreal_0(A,k1_real_1(np__1))))) # label(t21_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2695 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> k1_int_1(k2_xcmplx_0(A,B)) = k2_xcmplx_0(k1_int_1(A),B))))) # label(t51_int_1) # label(axiom) # label(non_clause). [assumption]. 14.80/14.43 2696 (exists A (v1_int_1(A) & p1_s6_int_1(A))) & (all A (v1_int_1(A) -> (p1_s6_int_1(A) -> r1_xreal_0(A,f1_s6_int_1)))) -> (exists A (v1_int_1(A) & (all B (v1_int_1(B) -> (p1_s6_int_1(B) -> r1_xreal_0(B,A)))) & p1_s6_int_1(A))) # label(s6_int_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2697 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (-r1_xreal_0(B,A) -> r1_xreal_0(A,k6_xcmplx_0(B,np__1))))))) # label(t79_int_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2698 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> r1_int_1(A,B,np__1))))) # label(t34_int_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2699 (all A (v1_xreal_0(A) -> (k1_int_1(A) = k2_int_1(A) <-> k2_xcmplx_0(k1_int_1(A),np__1) != k2_int_1(A)))) # label(t66_int_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2700 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (all D (v1_int_1(D) -> (r1_int_1(A,k6_xcmplx_0(C,B),D) <-> r1_int_1(k2_xcmplx_0(A,B),C,D)))))))))) # label(t40_int_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2701 (all A (v1_int_1(A) -> (p1_s3_int_1(A) & r1_xreal_0(A,f1_s3_int_1) -> p1_s3_int_1(k6_xcmplx_0(A,np__1))))) & p1_s3_int_1(f1_s3_int_1) -> (all A (v1_int_1(A) -> (r1_xreal_0(A,f1_s3_int_1) -> p1_s3_int_1(A)))) # label(s3_int_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2702 (all A all B (m1_subset_1(A,k5_numbers) & v1_int_1(B) -> v1_int_1(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)))) # label(fc8_int_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2703 (all A (m1_subset_1(A,k5_numbers) -> -v2_xreal_0(k4_xcmplx_0(A)) & v1_int_1(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)))) # label(fc5_int_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2704 (all A (v1_xreal_0(A) -> k2_int_1(A) = k1_int_1(k2_int_1(A)))) # label(t62_int_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2705 (all A (v1_xreal_0(A) -> (r1_xreal_0(np__0,A) -> m2_subset_1(k1_int_1(A),k1_numbers,k5_numbers) & m2_subset_1(k2_int_1(A),k1_numbers,k5_numbers) & r1_xreal_0(np__0,k1_int_1(A)) & r1_xreal_0(np__0,k2_int_1(A))))) # label(t80_int_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2706 (all A (v1_xreal_0(A) -> k6_xcmplx_0(A,k1_int_1(A)) = k3_int_1(A))) # label(d6_int_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2707 (all A (v1_xreal_0(A) -> -((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> A != B & A != k1_real_1(B))) & v1_int_1(A)))) # label(t8_int_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2708 (all A (v1_int_1(A) -> v1_xcmplx_0(A) & v1_xreal_0(A))) # label(cc4_int_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2709 $T # label(t27_int_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2710 (all A (v1_xreal_0(A) -> m1_subset_1(k4_int_1(A),k1_numbers))) # label(dt_k4_int_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2711 $T # label(t28_int_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2712 (all A (v1_xreal_0(A) -> (np__0 != A -> k1_int_1(k7_xcmplx_0(A,A)) = np__1))) # label(t74_int_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2713 (all A (v1_xreal_0(A) -> k2_xcmplx_0(k1_int_1(A),k4_int_1(A)) = A)) # label(t68_int_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2714 (all A (v1_xreal_0(A) -> v1_int_1(k2_int_1(A)))) # label(dt_k2_int_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2715 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (r1_int_1(A,B,C) <-> r1_int_1(k6_xcmplx_0(A,C),B,C)))))))) # label(t43_int_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2716 $T # label(t6_int_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2717 (all A (v1_membered(A) -> (all B (v1_membered(B) -> ((all C (v1_xcmplx_0(C) -> -(r2_hidden(C,A) & r2_hidden(C,B)))) <-> r1_xboole_0(A,B)))))) # label(d16_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2718 (all A all B (v2_membered(B) & r2_hidden(B,A) -> v2_membered(k1_setfam_1(A)))) # label(t27_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2719 (all A (-v1_xboole_0(A) & v4_membered(A) -> (exists B (v1_int_1(B) & r2_hidden(B,A))))) # label(t9_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2720 (all A (v3_membered(A) -> (all B (v3_membered(B) -> ((all C (v1_rat_1(C) -> (r2_hidden(C,A) <-> r2_hidden(C,B)))) <-> B = A))))) # label(d13_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2721 (all A (v2_membered(A) -> (all B (m1_subset_1(B,A) -> v1_xcmplx_0(B) & v1_xreal_0(B))))) # label(cc11_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2722 (all A (v1_membered(A) -> (all B (m1_subset_1(B,A) -> v1_xcmplx_0(B))))) # label(cc10_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2723 (all A all B (v2_membered(A) -> v2_membered(k3_xboole_0(A,B)) & v1_membered(k3_xboole_0(A,B)))) # label(fc29_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2724 (all A (v2_membered(A) -> v1_membered(A))) # label(cc4_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2725 (all A all B (v1_membered(B) & v1_membered(A) -> v1_membered(k2_xboole_0(A,B)))) # label(fc22_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2726 (all A ((all B (r2_hidden(B,A) -> v1_rat_1(B))) <-> v3_membered(A))) # label(d3_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2727 (exists A ((all B (v1_int_1(B) -> (p1_s4_membered(B) <-> r2_hidden(B,A)))) & v4_membered(A))) # label(s4_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2728 (all A all B all C (v1_xcmplx_0(B) & v1_xcmplx_0(C) & v1_xcmplx_0(A) -> v1_membered(k1_enumset1(A,B,C)))) # label(fc17_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2729 (all A all B (v1_membered(B) & v1_membered(A) -> v1_membered(k5_xboole_0(A,B)))) # label(fc42_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2730 (all A (v4_membered(A) -> r1_tarski(A,k4_numbers))) # label(t4_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2731 (all A all B (r2_hidden(B,A) & v3_membered(B) -> v3_membered(k1_setfam_1(A)))) # label(t28_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2732 (all A all B (v1_membered(A) -> v1_membered(k3_xboole_0(B,A)))) # label(fc28_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2733 (all A (v2_membered(A) -> (all B (v2_membered(B) -> (A = B <-> (all C (v1_xreal_0(C) -> (r2_hidden(C,A) <-> r2_hidden(C,B))))))))) # label(d12_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2734 (all A (v1_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v1_membered(B))))) # label(cc16_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2735 (all A all B (r2_hidden(B,A) & v5_membered(B) -> v5_membered(k1_setfam_1(A)))) # label(t30_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2736 (all A (v4_membered(A) <-> (all B (r2_hidden(B,A) -> v1_int_1(B))))) # label(d4_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2737 (all A all B all C (v1_xreal_0(A) & v1_xreal_0(B) & v1_xreal_0(C) -> v1_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)))) # label(fc18_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2738 (all A (v3_membered(A) -> (all B (v3_membered(B) -> (r1_xboole_0(A,B) <-> (all C (v1_rat_1(C) -> -(r2_hidden(C,B) & r2_hidden(C,A))))))))) # label(d18_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2739 (all A all B (v4_membered(A) & v4_membered(B) -> v1_membered(k5_xboole_0(A,B)) & v2_membered(k5_xboole_0(A,B)) & v3_membered(k5_xboole_0(A,B)) & v4_membered(k5_xboole_0(A,B)))) # label(fc45_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2740 (all A ((all B (r2_hidden(B,A) -> v4_membered(B))) -> v4_membered(k3_tarski(A)))) # label(t24_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2741 (all A all B (r2_hidden(B,A) & v1_membered(B) -> v1_membered(k1_setfam_1(A)))) # label(t26_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2742 (all A all B (v4_membered(A) -> v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)))) # label(fc34_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2743 (all A (m1_subset_1(A,k1_zfmisc_1(k5_numbers)) -> v4_membered(A) & v5_membered(A) & v3_membered(A) & v2_membered(A) & v1_membered(A))) # label(cc9_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2744 (all A (m1_subset_1(A,k1_zfmisc_1(k4_numbers)) -> v2_membered(A) & v3_membered(A) & v4_membered(A) & v1_membered(A))) # label(cc8_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2745 (all A (v4_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v1_membered(B) & v3_membered(B) & v4_membered(B) & v2_membered(B))))) # label(cc19_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2746 (all A all B (v2_membered(A) & v2_membered(B) -> v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)))) # label(fc23_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2747 (all A (v5_membered(A) -> (all B (m1_subset_1(B,A) -> v1_xreal_0(B) & v1_rat_1(B) & v1_int_1(B) & v4_ordinal2(B) & v1_xcmplx_0(B))))) # label(cc14_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2748 (all A all B all C (v1_rat_1(A) & v1_rat_1(B) & v1_rat_1(C) -> v1_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)))) # label(fc19_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2749 (all A all B (r2_hidden(B,A) & v4_membered(B) -> v4_membered(k1_setfam_1(A)))) # label(t29_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2750 (all A (v3_membered(A) -> v2_membered(A))) # label(cc3_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2751 (all A (v1_xboole_0(A) -> v1_membered(A) & v2_membered(A) & v5_membered(A) & v4_membered(A) & v3_membered(A))) # label(cc15_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2752 (all A ((all B (r2_hidden(B,A) -> v5_membered(B))) -> v5_membered(k3_tarski(A)))) # label(t25_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2753 (exists A (v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) & v1_membered(A) & -v1_xboole_0(A))) # label(rc1_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2754 (all A all B (v1_int_1(A) & v1_int_1(B) -> v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v1_membered(k2_tarski(A,B)))) # label(fc15_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2755 (all A all B (v4_membered(A) -> v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)) & v1_membered(k4_xboole_0(A,B)))) # label(fc40_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2756 (all A (-v1_xboole_0(A) & v5_membered(A) -> (exists B (v4_ordinal2(B) & r2_hidden(B,A))))) # label(t10_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2757 (all A (m1_subset_1(A,k1_zfmisc_1(k2_numbers)) -> v1_membered(A))) # label(cc5_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2758 (all A all B (v1_membered(B) -> (r1_tarski(A,B) -> v1_membered(A)))) # label(t16_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2759 (all A (v3_membered(A) -> (all B (v3_membered(B) -> (r1_tarski(A,B) <-> (all C (v1_rat_1(C) -> (r2_hidden(C,A) -> r2_hidden(C,B))))))))) # label(d8_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2760 (all A all B all C (v4_ordinal2(A) & v4_ordinal2(B) & v4_ordinal2(C) -> v1_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)) & v5_membered(k1_enumset1(A,B,C)) & v4_membered(k1_enumset1(A,B,C)))) # label(fc21_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2761 (all A all B (v2_membered(B) -> (r1_tarski(A,B) -> v2_membered(A)))) # label(t17_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2762 (all A ((all B (r2_hidden(B,A) -> v2_membered(B))) -> v2_membered(k3_tarski(A)))) # label(t22_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2763 (all A all B (v5_membered(B) & v5_membered(A) -> v1_membered(k5_xboole_0(A,B)) & v2_membered(k5_xboole_0(A,B)) & v4_membered(k5_xboole_0(A,B)) & v5_membered(k5_xboole_0(A,B)) & v3_membered(k5_xboole_0(A,B)))) # label(fc46_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2764 (all A all B (v3_membered(B) & v3_membered(A) -> v2_membered(k5_xboole_0(A,B)) & v3_membered(k5_xboole_0(A,B)) & v1_membered(k5_xboole_0(A,B)))) # label(fc44_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2765 (all A (v1_membered(A) -> ((all B (v1_xcmplx_0(B) -> r2_hidden(B,A))) -> k2_numbers = A))) # label(t11_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2766 (all A all B (v1_xcmplx_0(B) & v1_xcmplx_0(A) -> v1_membered(k2_tarski(A,B)))) # label(fc12_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2767 (all A all B (v3_membered(B) & v3_membered(A) -> v3_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v1_membered(k2_xboole_0(A,B)))) # label(fc24_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2768 (all A (v2_membered(A) -> r1_tarski(A,k1_numbers))) # label(t2_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2769 (all A (v5_membered(A) -> ((all B (v4_ordinal2(B) -> r2_hidden(B,A))) -> A = k5_numbers))) # label(t15_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2770 (all A (v3_membered(A) -> r1_tarski(A,k3_numbers))) # label(t3_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2771 (exists A ((all B (v4_ordinal2(B) -> (r2_hidden(B,A) <-> p1_s5_membered(B)))) & v5_membered(A))) # label(s5_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2772 (all A (v5_membered(A) -> v4_membered(A))) # label(cc1_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2773 (exists A (v1_membered(A) & (all B (v1_xcmplx_0(B) -> (r2_hidden(B,A) <-> p1_s1_membered(B)))))) # label(s1_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2774 (all A all B (v1_rat_1(A) & v1_rat_1(B) -> v3_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v1_membered(k2_tarski(A,B)))) # label(fc14_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2775 (all A (v3_membered(A) -> (all B (m1_subset_1(B,A) -> v1_xreal_0(B) & v1_rat_1(B) & v1_xcmplx_0(B))))) # label(cc12_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2776 (all A all B (v3_membered(A) -> v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)))) # label(fc39_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2777 (exists A (v3_membered(A) & (all B (v1_rat_1(B) -> (p1_s3_membered(B) <-> r2_hidden(B,A)))))) # label(s3_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2778 (all A (v4_ordinal2(A) -> v2_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) & v5_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v1_membered(k1_tarski(A)))) # label(fc11_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2779 (all A all B (v5_membered(A) -> v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) & v5_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)))) # label(fc35_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2780 (all A (v5_membered(A) -> r1_tarski(A,k5_numbers))) # label(t5_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2781 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> v2_membered(A) & v1_membered(A))) # label(cc6_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2782 (all A all B (v5_membered(A) -> v1_membered(k3_xboole_0(B,A)) & v5_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)))) # label(fc36_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2783 (all A (v4_membered(A) -> v3_membered(A))) # label(cc2_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2784 (all A (v4_membered(A) -> (all B (m1_subset_1(B,A) -> v1_xcmplx_0(B) & v1_rat_1(B) & v1_int_1(B) & v1_xreal_0(B))))) # label(cc13_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2785 (exists A ((all B (v1_xreal_0(B) -> (r2_hidden(B,A) <-> p1_s2_membered(B)))) & v2_membered(A))) # label(s2_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2786 (all A (v4_membered(A) -> ((all B (v1_int_1(B) -> r2_hidden(B,A))) -> k4_numbers = A))) # label(t14_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2787 (all A (v4_membered(A) -> (all B (v4_membered(B) -> (r1_tarski(A,B) <-> (all C (v1_int_1(C) -> (r2_hidden(C,A) -> r2_hidden(C,B))))))))) # label(d9_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2788 (all A (v1_membered(A) -> (all B (v1_membered(B) -> ((all C (v1_xcmplx_0(C) -> (r2_hidden(C,A) -> r2_hidden(C,B)))) <-> r1_tarski(A,B)))))) # label(d6_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2789 (all A all B (v4_membered(A) & v4_membered(B) -> v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v1_membered(k2_xboole_0(A,B)))) # label(fc25_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2790 (all A (v5_membered(A) -> (all B (v5_membered(B) -> (r1_xboole_0(A,B) <-> (all C (v4_ordinal2(C) -> -(r2_hidden(C,A) & r2_hidden(C,B))))))))) # label(d20_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2791 (all A ((all B (r2_hidden(B,A) -> v1_xreal_0(B))) <-> v2_membered(A))) # label(d2_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2792 (all A all B all C (v1_int_1(A) & v1_int_1(C) & v1_int_1(B) -> v1_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)) & v4_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)))) # label(fc20_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2793 (all A all B (v2_membered(A) -> v2_membered(k4_xboole_0(A,B)) & v1_membered(k4_xboole_0(A,B)))) # label(fc38_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2794 (all A ((all B (r2_hidden(B,A) -> v4_ordinal2(B))) <-> v5_membered(A))) # label(d5_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2795 (all A (v3_membered(A) & -v1_xboole_0(A) -> (exists B (r2_hidden(B,A) & v1_rat_1(B))))) # label(t8_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2796 (all A all B (v2_membered(A) & v2_membered(B) -> v1_membered(k5_xboole_0(A,B)) & v2_membered(k5_xboole_0(A,B)))) # label(fc43_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2797 (all A all B (v3_membered(A) -> v1_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)))) # label(fc31_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2798 (all A (v1_membered(A) -> (all B (v1_membered(B) -> (B = A <-> (all C (v1_xcmplx_0(C) -> (r2_hidden(C,A) <-> r2_hidden(C,B))))))))) # label(d11_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2799 (all A all B (v5_membered(A) & v5_membered(B) -> v4_membered(k2_xboole_0(A,B)) & v5_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v1_membered(k2_xboole_0(A,B)))) # label(fc26_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2800 (all A all B (v1_membered(A) -> v1_membered(k4_xboole_0(A,B)))) # label(fc37_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2801 (all A (v1_rat_1(A) -> v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)))) # label(fc9_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2802 (all A (v1_xreal_0(A) -> v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)))) # label(fc8_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2803 (all A (-v1_xboole_0(A) & v1_membered(A) -> (exists B (r2_hidden(B,A) & v1_xcmplx_0(B))))) # label(t6_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2804 (all A (v4_membered(A) -> (all B (v4_membered(B) -> (B = A <-> (all C (v1_int_1(C) -> (r2_hidden(C,A) <-> r2_hidden(C,B))))))))) # label(d14_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2805 (all A all B (v5_membered(B) -> (r1_tarski(A,B) -> v5_membered(A)))) # label(t20_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2806 (all A all B (v3_membered(A) -> v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)))) # label(fc32_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2807 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)))) # label(fc13_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2808 (all A (v3_membered(A) -> ((all B (v1_rat_1(B) -> r2_hidden(B,A))) -> k3_numbers = A))) # label(t13_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2809 (all A all B (v3_membered(B) -> (r1_tarski(A,B) -> v3_membered(A)))) # label(t18_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2810 (all A all B (v4_membered(B) -> (r1_tarski(A,B) -> v4_membered(A)))) # label(t19_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2811 (all A all B (v4_membered(A) -> v3_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v1_membered(k3_xboole_0(A,B)))) # label(fc33_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2812 (all A ((all B (r2_hidden(B,A) -> v1_membered(B))) -> v1_membered(k3_tarski(A)))) # label(t21_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2813 (all A (v2_membered(A) -> ((all B (v1_xreal_0(B) -> r2_hidden(B,A))) -> A = k1_numbers))) # label(t12_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2814 (all A (v5_membered(A) -> (all B (v5_membered(B) -> ((all C (v4_ordinal2(C) -> (r2_hidden(C,A) -> r2_hidden(C,B)))) <-> r1_tarski(A,B)))))) # label(d10_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2815 (all A (v4_membered(A) -> (all B (v4_membered(B) -> ((all C (v1_int_1(C) -> -(r2_hidden(C,B) & r2_hidden(C,A)))) <-> r1_xboole_0(A,B)))))) # label(d19_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2816 (all A (v1_int_1(A) -> v2_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v1_membered(k1_tarski(A)))) # label(fc10_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2817 (all A all B (v4_ordinal2(B) & v4_ordinal2(A) -> v4_membered(k2_tarski(A,B)) & v5_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v1_membered(k2_tarski(A,B)))) # label(fc16_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2818 (all A (v5_membered(A) -> (all B (v5_membered(B) -> (A = B <-> (all C (v4_ordinal2(C) -> (r2_hidden(C,A) <-> r2_hidden(C,B))))))))) # label(d15_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2819 (all A (v3_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v1_membered(B) & v2_membered(B) & v3_membered(B))))) # label(cc18_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2820 (all A (v2_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v1_membered(B) & v2_membered(B))))) # label(cc17_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2821 (all A all B (v2_membered(A) -> v2_membered(k3_xboole_0(B,A)) & v1_membered(k3_xboole_0(B,A)))) # label(fc30_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2822 (all A (v2_membered(A) -> (all B (v2_membered(B) -> (r1_xboole_0(A,B) <-> (all C (v1_xreal_0(C) -> -(r2_hidden(C,A) & r2_hidden(C,B))))))))) # label(d17_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2823 (all A all B (v1_membered(A) -> v1_membered(k3_xboole_0(A,B)))) # label(fc27_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2824 (all A (v1_xcmplx_0(A) -> v1_membered(k1_tarski(A)))) # label(fc7_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2825 (all A (v1_membered(A) -> r1_tarski(A,k2_numbers))) # label(t1_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2826 (all A ((all B (r2_hidden(B,A) -> v3_membered(B))) -> v3_membered(k3_tarski(A)))) # label(t23_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2827 (all A (m1_subset_1(A,k1_zfmisc_1(k3_numbers)) -> v1_membered(A) & v2_membered(A) & v3_membered(A))) # label(cc7_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2828 (all A all B (v5_membered(A) -> v3_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)) & v5_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v1_membered(k4_xboole_0(A,B)))) # label(fc41_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2829 (all A (v5_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v2_membered(B) & v5_membered(B) & v4_membered(B) & v3_membered(B) & v1_membered(B))))) # label(cc20_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2830 (all A (v2_membered(A) -> (all B (v2_membered(B) -> ((all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r2_hidden(C,B)))) <-> r1_tarski(A,B)))))) # label(d7_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2831 (all A ((all B (r2_hidden(B,A) -> v1_xcmplx_0(B))) <-> v1_membered(A))) # label(d1_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2832 (all A (-v1_xboole_0(A) & v2_membered(A) -> (exists B (v1_xreal_0(B) & r2_hidden(B,A))))) # label(t7_membered) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2833 (all A (v3_ordinal1(A) -> r2_hidden(A,k2_card_1(A)))) # label(t36_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2834 (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]. 14.87/14.43 2835 (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]. 14.87/14.43 2836 (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]. 14.87/14.43 2837 $T # label(t2_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2838 (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]. 14.87/14.43 2839 (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]. 14.87/14.43 2840 (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]. 14.87/14.43 2841 (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]. 14.87/14.43 2842 (all A exists B (r2_wellord2(A,B) & v3_ordinal1(B))) # label(t4_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2843 (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]. 14.87/14.43 2844 (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]. 14.87/14.43 2845 (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]. 14.87/14.43 2846 (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]. 14.87/14.43 2847 $T # label(t57_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2848 (all A r2_hidden(k1_card_1(k1_xboole_0),k2_card_1(A))) # label(t33_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2849 $T # label(dt_k3_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2850 (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]. 14.87/14.43 2851 (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]. 14.87/14.43 2852 (all A (v1_card_1(A) -> r2_hidden(A,k2_card_1(A)))) # label(t32_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2853 $T # label(t18_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2854 (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]. 14.87/14.43 2855 $T # label(t7_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2856 (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]. 14.87/14.43 2857 (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]. 14.87/14.43 2858 (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]. 14.87/14.43 2859 $T # label(t67_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2860 (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]. 14.87/14.43 2861 (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]. 14.87/14.43 2862 $T # label(t11_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2863 $T # label(t6_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2864 $T # label(t1_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2865 (exists A v1_card_1(A)) # label(rc1_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2866 $T # label(t53_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2867 $T # label(t77_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2868 (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]. 14.87/14.43 2869 (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]. 14.87/14.43 2870 (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]. 14.87/14.43 2871 (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]. 14.87/14.43 2872 $T # label(d3_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2873 (all A (r2_hidden(A,k5_ordinal2) -> v1_card_1(A))) # label(t65_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2874 $T # label(t9_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2875 (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]. 14.87/14.43 2876 (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]. 14.87/14.43 2877 (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]. 14.87/14.43 2878 (all A k4_card_1(k1_tarski(A)) = np__1) # label(t79_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2879 (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]. 14.87/14.43 2880 $T # label(t62_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2881 $T # label(t63_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2882 (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]. 14.87/14.43 2883 (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]. 14.87/14.43 2884 $T # label(t20_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2885 (all A v1_card_1(k2_card_1(A))) # label(dt_k2_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2886 (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]. 14.87/14.43 2887 (all A (v3_ordinal1(A) -> r1_ordinal1(k1_card_1(A),A))) # label(t24_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2888 $T # label(t31_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2889 $T # label(t10_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2890 (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]. 14.87/14.43 2891 (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]. 14.87/14.43 2892 $T # label(t37_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2893 (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]. 14.87/14.43 2894 $T # label(d10_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2895 (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]. 14.87/14.43 2896 $T # label(t75_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2897 (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]. 14.87/14.43 2898 (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]. 14.87/14.43 2899 (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]. 14.87/14.43 2900 (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]. 14.87/14.43 2901 (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]. 14.87/14.43 2902 (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]. 14.87/14.43 2903 $T # label(t3_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2904 (all A (v1_finset_1(A) -> v1_finset_1(k2_card_1(A)))) # label(t82_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.43 2905 (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]. 14.87/14.43 2906 (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]. 14.87/14.44 2907 (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]. 14.87/14.44 2908 $T # label(t17_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 2909 (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]. 14.87/14.44 2910 $T # label(t12_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 2911 (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]. 14.87/14.44 2912 (all A k1_card_1(k1_tarski(A)) = k4_ordinal2) # label(t50_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 2913 (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]. 14.87/14.44 2914 $T # label(d9_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 2915 (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]. 14.87/14.44 2916 (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]. 14.87/14.44 2917 (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]. 14.87/14.44 2918 (all A v1_card_1(k1_card_1(A))) # label(dt_k1_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 2919 (all A -r2_wellord2(A,k1_zfmisc_1(A))) # label(t29_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 2920 $T # label(t16_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 2921 $T # label(t5_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 2922 (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]. 14.87/14.44 2923 $T # label(t54_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 2924 $T # label(t19_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 2925 $T # label(d2_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 2926 (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]. 14.87/14.44 2927 $T # label(t70_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 2928 (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]. 14.87/14.44 2929 $T # label(t55_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 2930 (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]. 14.87/14.44 2931 (all A (r2_wellord2(A,k1_xboole_0) <-> k1_xboole_0 = A)) # label(t46_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 2932 $T # label(d4_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 2933 (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]. 14.87/14.44 2934 (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]. 14.87/14.44 2935 $T # label(t15_card_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 2936 (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]. 14.87/14.44 2937 (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]. 14.87/14.44 2938 (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]. 14.87/14.44 2939 (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]. 14.87/14.44 2940 (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]. 14.87/14.44 2941 (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]. 14.87/14.44 2942 (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]. 14.87/14.44 2943 (all A -v1_xboole_0(k13_finseq_1(A))) # label(fc9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 2944 (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]. 14.87/14.44 2945 (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]. 14.87/14.44 2946 $T # label(t1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 2947 (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]. 14.87/14.44 2948 (all A k5_finseq_1(A) = k1_tarski(k4_tarski(np__1,A))) # label(d5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 2949 (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]. 14.87/14.44 2950 (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]. 14.87/14.44 2951 (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]. 14.87/14.44 2952 (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]. 14.87/14.44 2953 (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]. 14.87/14.44 2954 (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]. 14.87/14.44 2955 (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]. 14.87/14.44 2956 (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]. 14.87/14.44 2957 $T # label(t22_finseq_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 2958 (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]. 14.87/14.44 2959 (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]. 14.87/14.44 2960 (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]. 14.87/14.44 2961 (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]. 14.87/14.44 2962 (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]. 14.87/14.44 2963 (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]. 14.87/14.44 2964 (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]. 14.87/14.44 2965 (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]. 14.87/14.44 2966 (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]. 14.87/14.44 2967 (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]. 14.87/14.44 2968 (all A r2_hidden(k1_xboole_0,k13_finseq_1(A))) # label(t66_finseq_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 2969 (all A exists B m2_finseq_1(B,A)) # label(existence_m2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 2970 (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]. 14.87/14.44 2971 (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]. 14.87/14.44 2972 (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]. 14.87/14.44 2973 (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]. 14.87/14.44 2974 (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]. 14.87/14.44 2975 (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]. 14.87/14.44 2976 $T # label(t49_finseq_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 2977 $T # label(dt_k5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 2978 $T # label(t67_finseq_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 2979 (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]. 14.87/14.44 2980 (all A m2_finseq_1(k14_finseq_1(A),k5_numbers)) # label(dt_k14_finseq_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 2981 (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]. 14.87/14.44 2982 (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]. 14.87/14.44 2983 (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]. 14.87/14.44 2984 (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]. 14.87/14.44 2985 (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]. 14.87/14.44 2986 (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]. 14.87/14.44 2987 (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]. 14.87/14.44 2988 (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]. 14.87/14.44 2989 (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]. 14.87/14.44 2990 $T # label(t28_finseq_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 2991 (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]. 14.87/14.44 2992 $T # label(t13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 2993 (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]. 14.87/14.44 2994 (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]. 14.87/14.44 2995 (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]. 14.87/14.44 2996 $T # label(t34_finseq_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 2997 (all A k1_tarski(k4_tarski(np__1,A)) = k9_finseq_1(A)) # label(t52_finseq_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 2998 (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]. 14.87/14.44 2999 (all A (v4_ordinal2(A) -> v1_finset_1(k1_finseq_1(A)))) # label(fc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 3000 (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]. 14.87/14.44 3001 (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]. 14.87/14.44 3002 (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]. 14.87/14.44 3003 (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]. 14.87/14.44 3004 (all A (v4_ordinal2(A) -> k4_card_1(k2_finseq_1(A)) = A)) # label(t78_finseq_1_AndLHS) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 3005 (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]. 14.87/14.44 3006 (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]. 14.87/14.44 3007 (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]. 14.87/14.44 3008 (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]. 14.87/14.44 3009 (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]. 14.87/14.44 3010 (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]. 14.87/14.44 3011 (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]. 14.87/14.44 3012 $T # label(t53_finseq_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 3013 (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]. 14.87/14.44 3014 (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]. 14.87/14.44 3015 $T # label(dt_k11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 3016 (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]. 14.87/14.44 3017 (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]. 14.87/14.44 3018 (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]. 14.87/14.44 3019 $T # label(t54_finseq_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 3020 (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]. 14.87/14.44 3021 (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]. 14.87/14.44 3022 (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]. 14.87/14.44 3023 (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]. 14.87/14.44 3024 (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]. 14.87/14.44 3025 (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]. 14.87/14.44 3026 (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]. 14.87/14.44 3027 (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]. 14.87/14.44 3028 (exists A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A))) # label(rc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 3029 (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]. 14.87/14.44 3030 (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]. 14.87/14.44 3031 (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]. 14.87/14.44 3032 (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]. 14.87/14.44 3033 (all A k6_finseq_1(A) = k1_xboole_0) # label(d6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 3034 (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]. 14.87/14.44 3035 (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]. 14.87/14.44 3036 (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]. 14.87/14.44 3037 (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]. 14.87/14.44 3038 (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]. 14.87/14.44 3039 (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]. 14.87/14.44 3040 (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]. 14.87/14.44 3041 (all A (v1_relat_1(A) -> v1_relat_1(k17_finseq_1(A)))) # label(dt_k17_finseq_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 3042 (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]. 14.87/14.44 3043 (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]. 14.87/14.44 3044 (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]. 14.87/14.44 3045 (all A m2_finseq_1(k1_xboole_0,A)) # label(t29_finseq_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 3046 (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]. 14.87/14.44 3047 (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]. 14.87/14.44 3048 $T # label(t2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 3049 (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]. 14.87/14.44 3050 (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]. 14.87/14.44 3051 (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]. 14.87/14.44 3052 (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]. 14.87/14.44 3053 (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]. 14.87/14.44 3054 (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]. 14.87/14.44 3055 (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]. 14.87/14.44 3056 (exists A (v1_funct_1(A) & v2_finseq_1(A) & v1_relat_1(A))) # label(rc5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 3057 (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]. 14.87/14.44 3058 (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]. 14.87/14.44 3059 $T # label(t30_finseq_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 3060 (all A k9_finseq_1(A) = k5_finseq_1(A)) # label(redefinition_k9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 3061 (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]. 14.87/14.44 3062 (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]. 14.87/14.44 3063 (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]. 14.87/14.44 3064 (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]. 14.87/14.44 3065 (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]. 14.87/14.44 3066 (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]. 14.87/14.44 3067 (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]. 14.87/14.44 3068 (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]. 14.87/14.44 3069 (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]. 14.87/14.44 3070 (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]. 14.87/14.44 3071 (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]. 14.87/14.44 3072 (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]. 14.87/14.44 3073 (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]. 14.87/14.44 3074 (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]. 14.87/14.44 3075 (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]. 14.87/14.44 3076 (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]. 14.87/14.44 3077 (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]. 14.87/14.44 3078 $T # label(t31_finseq_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 3079 $T # label(dt_k10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 3080 (all A exists B m1_finseq_1(B,A)) # label(existence_m1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 3081 (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]. 14.87/14.44 3082 $T # label(dt_k13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 3083 (all A (v4_ordinal2(A) -> k1_finseq_1(A) = k2_finseq_1(A))) # label(redefinition_k2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.44 3084 (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]. 14.87/14.44 3085 (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]. 14.87/14.44 3086 (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]. 14.87/14.44 3087 (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]. 14.87/14.44 3088 (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]. 14.87/14.45 3089 $T # label(t51_finseq_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3090 (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]. 14.87/14.45 3091 (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]. 14.87/14.45 3092 $T # label(dt_k1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3093 (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]. 14.87/14.45 3094 $T # label(t70_finseq_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3095 (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]. 14.87/14.45 3096 (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]. 14.87/14.45 3097 (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]. 14.87/14.45 3098 $T # label(t48_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3099 $T # label(t147_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3100 $T # label(t49_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3101 (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]. 14.87/14.45 3102 (all A (-v1_xboole_0(A) -> (exists B m1_orders_1(B,A)))) # label(existence_m1_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3103 $T # label(t168_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3104 (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]. 14.87/14.45 3105 (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]. 14.87/14.45 3106 (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]. 14.87/14.45 3107 $T # label(t30_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3108 (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]. 14.87/14.45 3109 $T # label(t83_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3110 $T # label(t79_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3111 (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]. 14.87/14.45 3112 (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]. 14.87/14.45 3113 $T # label(dt_k1_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3114 (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]. 14.87/14.45 3115 $T # label(t28_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3116 (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]. 14.87/14.45 3117 $T # label(t35_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3118 (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]. 14.87/14.45 3119 (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]. 14.87/14.45 3120 $T # label(t46_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3121 $T # label(t52_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3122 (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]. 14.87/14.45 3123 (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]. 14.87/14.45 3124 $T # label(t80_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3125 (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]. 14.87/14.45 3126 (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]. 14.87/14.45 3127 (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]. 14.87/14.45 3128 $T # label(t45_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3129 $T # label(t33_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3130 $T # label(t123_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3131 $T # label(t8_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3132 (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]. 14.87/14.45 3133 $T # label(t53_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3134 $T # label(t167_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3135 (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]. 14.87/14.45 3136 (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]. 14.87/14.45 3137 $T # label(t73_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3138 $T # label(t156_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3139 $T # label(t39_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3140 (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]. 14.87/14.45 3141 (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]. 14.87/14.45 3142 (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]. 14.87/14.45 3143 (all A (v1_relat_1(A) -> (v2_orders_1(A) -> v1_orders_1(A)))) # label(t109_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3144 (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]. 14.87/14.45 3145 (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]. 14.87/14.45 3146 $T # label(t59_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3147 $T # label(t29_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3148 $T # label(t55_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3149 $T # label(t169_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3150 $T # label(t122_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3151 (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]. 14.87/14.45 3152 $T # label(t51_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3153 (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]. 14.87/14.45 3154 (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]. 14.87/14.45 3155 (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]. 14.87/14.45 3156 $T # label(t170_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3157 $T # label(t145_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3158 (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]. 14.87/14.45 3159 $T # label(t67_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3160 $T # label(t2_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3161 $T # label(t70_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3162 (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]. 14.87/14.45 3163 $T # label(t118_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3164 (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]. 14.87/14.45 3165 $T # label(t54_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3166 $T # label(t58_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3167 (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]. 14.87/14.45 3168 $T # label(t3_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3169 $T # label(t117_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3170 $T # label(t61_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3171 $T # label(t78_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3172 $T # label(t75_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3173 $T # label(t77_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3174 $T # label(t88_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3175 (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]. 14.87/14.45 3176 (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]. 14.87/14.45 3177 $T # label(t144_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3178 (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]. 14.87/14.45 3179 (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]. 14.87/14.45 3180 (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]. 14.87/14.45 3181 (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]. 14.87/14.45 3182 $T # label(t24_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3183 (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]. 14.87/14.45 3184 (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]. 14.87/14.45 3185 (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]. 14.87/14.45 3186 $T # label(t25_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3187 $T # label(t72_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3188 (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]. 14.87/14.45 3189 $T # label(t82_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3190 (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]. 14.87/14.45 3191 (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]. 14.87/14.45 3192 (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]. 14.87/14.45 3193 (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]. 14.87/14.45 3194 $T # label(t1_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3195 (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]. 14.87/14.45 3196 (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]. 14.87/14.45 3197 (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]. 14.87/14.45 3198 $T # label(t40_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3199 $T # label(t85_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3200 (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]. 14.87/14.45 3201 (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]. 14.87/14.45 3202 (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]. 14.87/14.45 3203 (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]. 14.87/14.45 3204 (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]. 14.87/14.45 3205 (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]. 14.87/14.45 3206 (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]. 14.87/14.45 3207 (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]. 14.87/14.45 3208 $T # label(t41_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3209 (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]. 14.87/14.45 3210 $T # label(t84_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3211 $T # label(t16_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3212 $T # label(t64_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3213 $T # label(t66_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3214 $T # label(t63_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3215 $T # label(t23_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3216 $T # label(t116_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3217 (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]. 14.87/14.45 3218 $T # label(t57_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3219 $T # label(t60_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3220 $T # label(t153_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3221 (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]. 14.87/14.45 3222 $T # label(t31_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3223 (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]. 14.87/14.45 3224 (all A (v2_orders_1(k6_partfun1(A)) & v1_orders_1(k6_partfun1(A)))) # label(t120_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3225 (all A (-v1_xboole_0(A) -> -v1_xboole_0(k1_orders_1(A)))) # label(fc1_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3226 (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]. 14.87/14.45 3227 (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]. 14.87/14.45 3228 (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]. 14.87/14.45 3229 $T # label(t74_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3230 $T # label(t44_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3231 (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]. 14.87/14.45 3232 (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]. 14.87/14.45 3233 (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]. 14.87/14.45 3234 (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]. 14.87/14.45 3235 (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]. 14.87/14.45 3236 $T # label(t101_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3237 $T # label(t34_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3238 (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]. 14.87/14.45 3239 (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]. 14.87/14.45 3240 $T # label(t121_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3241 (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]. 14.87/14.45 3242 $T # label(t90_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3243 (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]. 14.87/14.45 3244 $T # label(t102_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3245 $T # label(t71_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3246 $T # label(t56_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3247 $T # label(t32_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3248 $T # label(t15_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3249 $T # label(t22_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3250 (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]. 14.87/14.45 3251 (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]. 14.87/14.45 3252 (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]. 14.87/14.45 3253 (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]. 14.87/14.45 3254 (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]. 14.87/14.45 3255 $T # label(t20_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3256 (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]. 14.87/14.45 3257 $T # label(t76_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3258 $T # label(t43_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.87/14.45 3259 (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]. 14.87/14.45 3260 (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]. 14.87/14.45 3261 (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]. 14.87/14.45 3262 (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]. 14.93/14.48 3263 $T # label(t47_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.48 3264 $T # label(t171_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.48 3265 $T # label(t21_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.48 3266 $T # label(t65_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.48 3267 (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]. 14.93/14.48 3268 (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]. 14.93/14.48 3269 (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]. 14.93/14.48 3270 $T # label(t50_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.48 3271 (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]. 14.93/14.48 3272 $T # label(t19_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.48 3273 (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]. 14.93/14.48 3274 $T # label(t26_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.48 3275 (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]. 14.93/14.48 3276 (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]. 14.93/14.48 3277 $T # label(t42_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.48 3278 $T # label(t103_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.48 3279 $T # label(t10_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.48 3280 (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]. 14.93/14.48 3281 $T # label(t38_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.48 3282 $T # label(t148_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.48 3283 (all A (-v1_xboole_0(A) -> r2_hidden(A,k1_orders_1(A)))) # label(t7_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.48 3284 (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]. 14.93/14.48 3285 $T # label(t87_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.48 3286 (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]. 14.93/14.48 3287 (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]. 14.93/14.48 3288 (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]. 14.93/14.48 3289 $T # label(t9_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.48 3290 $T # label(t89_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.48 3291 (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]. 14.93/14.50 3292 $T # label(t37_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.50 3293 $T # label(t11_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.50 3294 (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]. 14.93/14.50 3295 $T # label(t18_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.50 3296 $T # label(t155_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.50 3297 $T # label(t36_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.50 3298 (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]. 14.93/14.50 3299 (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]. 14.93/14.50 3300 $T # label(t172_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.50 3301 $T # label(t27_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.50 3302 (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]. 14.93/14.50 3303 (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]. 14.93/14.50 3304 $T # label(t81_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.50 3305 (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]. 14.93/14.50 3306 $T # label(t69_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.50 3307 $T # label(t68_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.50 3308 $T # label(t86_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.50 3309 $T # label(t62_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.50 3310 $T # label(t154_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.50 3311 $T # label(t17_orders_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.50 3312 (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]. 14.93/14.50 3313 (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]. 14.93/14.50 3314 (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]. 14.93/14.50 3315 (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]. 14.93/14.50 3316 (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]. 14.93/14.50 3317 $T # label(t39_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.50 3318 (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]. 14.93/14.50 3319 $T # label(t21_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.50 3320 (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]. 14.93/14.50 3321 (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]. 14.93/14.50 3322 (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]. 14.93/14.50 3323 $T # label(t9_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.50 3324 (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]. 14.93/14.50 3325 (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]. 14.93/14.50 3326 (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]. 14.93/14.50 3327 (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]. 14.93/14.50 3328 (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]. 14.93/14.50 3329 (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]. 14.93/14.50 3330 (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]. 14.93/14.50 3331 $T # label(t10_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.50 3332 (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]. 14.93/14.50 3333 $T # label(t15_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.50 3334 (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]. 14.93/14.50 3335 (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]. 14.93/14.50 3336 $T # label(t2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.50 3337 (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]. 14.93/14.50 3338 (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]. 14.93/14.50 3339 (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]. 14.93/14.50 3340 (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]. 14.93/14.50 3341 (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]. 14.93/14.50 3342 (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]. 14.93/14.50 3343 $T # label(d2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.50 3344 (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]. 14.93/14.50 3345 (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]. 14.93/14.50 3346 (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]. 14.93/14.50 3347 (all A all B (m1_eqrel_1(B,A) -> v1_setfam_1(B))) # label(cc2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.50 3348 (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]. 14.93/14.50 3349 $T # label(t26_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.50 3350 (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]. 14.93/14.50 3351 (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]. 14.93/14.50 3352 (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]. 14.93/14.50 3353 (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]. 14.93/14.50 3354 (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]. 14.93/14.50 3355 (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]. 14.93/14.50 3356 (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]. 14.93/14.50 3357 (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]. 14.93/14.50 3358 (all A k1_eqrel_1(A) = k2_zfmisc_1(A,A)) # label(d1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.50 3359 (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]. 14.93/14.50 3360 (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]. 14.93/14.50 3361 (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]. 14.93/14.50 3362 (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]. 14.93/14.50 3363 $T # label(t3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.50 3364 (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]. 14.93/14.50 3365 (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]. 14.93/14.50 3366 $T # label(t41_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.50 3367 (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]. 14.93/14.51 3368 (all A m2_relset_1(k1_eqrel_1(A),A,A)) # label(dt_k1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3369 (all A exists B m1_eqrel_1(B,A)) # label(existence_m1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3370 $T # label(t8_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3371 (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]. 14.93/14.51 3372 (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]. 14.93/14.51 3373 (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]. 14.93/14.51 3374 (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]. 14.93/14.51 3375 (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]. 14.93/14.51 3376 (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]. 14.93/14.51 3377 (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]. 14.93/14.51 3378 (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]. 14.93/14.51 3379 (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]. 14.93/14.51 3380 $T # label(t1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3381 (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]. 14.93/14.51 3382 (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]. 14.93/14.51 3383 (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]. 14.93/14.51 3384 (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]. 14.93/14.51 3385 (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]. 14.93/14.51 3386 (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]. 14.93/14.51 3387 (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]. 14.93/14.51 3388 (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]. 14.93/14.51 3389 (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]. 14.93/14.51 3390 (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]. 14.93/14.51 3391 $T # label(t5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3392 (all A all B all C (r2_hidden(k4_tarski(A,B),C) -> r2_hidden(A,k1_funct_5(C)) & r2_hidden(B,k2_funct_5(C)))) # label(t4_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3393 (all A all B (r1_tarski(k4_xboole_0(k1_funct_5(A),k1_funct_5(B)),k1_funct_5(k4_xboole_0(A,B))) & r1_tarski(k4_xboole_0(k2_funct_5(A),k2_funct_5(B)),k2_funct_5(k4_xboole_0(A,B))))) # label(t8_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3394 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_relat_1(C),k4_partfun1(A,B)) -> r1_tarski(k2_relat_1(k6_funct_5(C)),B) & r1_tarski(k2_relat_1(k4_funct_5(C)),B)))) # label(t47_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3395 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_relat_1(C),k1_funct_2(A,B)) -> A = k1_xboole_0 | C = k5_funct_5(k6_funct_5(C)) & C = k3_funct_5(k4_funct_5(C))))) # label(t55_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3396 (all A all B (r1_tarski(k5_xboole_0(k2_funct_5(A),k2_funct_5(B)),k2_funct_5(k5_xboole_0(A,B))) & r1_tarski(k5_xboole_0(k1_funct_5(A),k1_funct_5(B)),k1_funct_5(k5_xboole_0(A,B))))) # label(t9_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3397 (all A all B all C all D (k1_funct_5(k2_tarski(k4_tarski(A,B),k4_tarski(C,D))) = k2_tarski(A,C) & k2_funct_5(k2_tarski(k4_tarski(A,B),k4_tarski(C,D))) = k2_tarski(B,D))) # label(t16_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3398 (all A all B (k1_funct_5(k2_xboole_0(A,B)) = k2_xboole_0(k1_funct_5(A),k1_funct_5(B)) & k2_funct_5(k2_xboole_0(A,B)) = k2_xboole_0(k2_funct_5(A),k2_funct_5(B)))) # label(t6_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3399 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(A,k1_relat_1(k5_funct_5(B))) -> v1_relat_1(k1_funct_1(k5_funct_5(B),A)) & v1_funct_1(k1_funct_1(k5_funct_5(B),A))))) # label(t40_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3400 (all A all B all C (B != A -> r2_wellord2(k1_funct_2(C,k2_tarski(A,B)),k1_zfmisc_1(C)) & k1_card_1(k1_funct_2(C,k2_tarski(A,B))) = k1_card_1(k1_zfmisc_1(C)))) # label(t72_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3401 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) & r1_tarski(k1_relat_1(D),k2_zfmisc_1(A,B)) & k3_funct_5(D) = k3_funct_5(C) -> C = D))))) # label(t59_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3402 (all A (k1_xboole_0 = k1_funct_5(A) <-> k1_xboole_0 = k2_funct_5(A))) # label(t19_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3403 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C -((all D (v1_relat_1(D) & v1_funct_1(D) -> -(k1_relat_1(D) = k2_funct_5(k3_xboole_0(k1_relat_1(A),k2_zfmisc_1(k1_tarski(C),k2_funct_5(k1_relat_1(A))))) & (all E (r2_hidden(E,k1_relat_1(D)) -> k1_funct_1(D,E) = k1_funct_1(A,k4_tarski(C,E)))) & k1_funct_1(B,C) = D))) & r2_hidden(C,k1_funct_5(k1_relat_1(A))))) & k1_relat_1(B) = k1_funct_5(k1_relat_1(A)) <-> B = k3_funct_5(A)))))) # label(d3_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3404 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_relat_1(C),k1_funct_2(A,B)) -> r1_tarski(k2_relat_1(k4_funct_5(C)),B) & r1_tarski(k2_relat_1(k6_funct_5(C)),B)))) # label(t48_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3405 (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 (v1_relat_1(E) & (exists F (E = k1_funct_1(A,D) & r2_hidden(F,k1_relat_1(E)) & r2_hidden(D,k1_relat_1(A)) & C = k4_tarski(D,F))) & v1_funct_1(E))))) & (all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(C,k1_relat_1(B)) & D = k1_funct_1(A,k1_mcart_1(C)) -> k1_funct_1(D,k2_mcart_1(C)) = k1_funct_1(B,C)))) <-> B = k4_funct_5(A)))))) # label(d4_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3406 (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)))) -> k1_xboole_0 = k4_funct_5(A) & k6_funct_5(A) = k1_xboole_0))) # label(t35_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3407 (exists A (v1_relat_1(A) & v1_funct_1(A) & (all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(B,f1_s1_funct_5) -> k1_funct_1(A,B) = f2_s1_funct_5(B)))) & f1_s1_funct_5 = k1_relat_1(A))) # label(s1_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3408 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r1_tarski(k2_relat_1(D),k1_funct_2(A,B)) & k6_funct_5(D) = k6_funct_5(C) & r1_tarski(k2_relat_1(C),k1_funct_2(A,B)) -> C = D | A = k1_xboole_0))))) # label(t54_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3409 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k4_funct_5(A)) & v1_funct_1(k4_funct_5(A)))) # label(dt_k4_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3410 (all A (v1_funct_1(A) & v1_relat_1(A) -> k1_funct_5(k1_relat_1(k2_funct_4(A))) = k2_funct_5(k1_relat_1(A)) & k1_funct_5(k1_relat_1(A)) = k2_funct_5(k1_relat_1(k2_funct_4(A))))) # label(t20_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3411 $T # label(t22_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3412 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k1_relat_1(C) = k2_zfmisc_1(A,B) & k3_funct_5(D) = k3_funct_5(C) & k1_relat_1(D) = k2_zfmisc_1(A,B) -> C = D))))) # label(t51_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3413 (all A (v1_relat_1(A) -> k1_relat_1(A) = k1_funct_5(A) & k2_funct_5(A) = k2_relat_1(A))) # label(t21_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3414 $T # label(t25_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3415 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k6_funct_5(A)) & v1_relat_1(k6_funct_5(A)))) # label(dt_k6_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3416 (all A (v1_relat_1(A) & v1_funct_1(A) -> k1_relat_1(k5_funct_5(A)) = k2_funct_5(k1_relat_1(A)))) # label(t30_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3417 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_relat_1(C),k4_partfun1(A,B)) -> r2_hidden(k1_xboole_0,k2_relat_1(C)) | k3_funct_5(k4_funct_5(C)) = C & k5_funct_5(k6_funct_5(C)) = C))) # label(t58_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3418 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k3_funct_5(A)) & v1_relat_1(k3_funct_5(A)))) # label(dt_k3_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3419 $T # label(t24_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3420 $T # label(t2_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3421 $T # label(t14_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3422 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> -(k2_zfmisc_1(A,B) != k1_xboole_0 & (all E (v1_funct_1(E) & v1_relat_1(E) -> -(E = k1_funct_1(k3_funct_5(D),C) & B = k1_relat_1(E) & r1_tarski(k2_relat_1(E),k2_relat_1(D)) & (all F (r2_hidden(F,B) -> k1_funct_1(D,k4_tarski(C,F)) = k1_funct_1(E,F)))))) & r2_hidden(C,A) & k1_relat_1(D) = k2_zfmisc_1(A,B)))) # label(t36_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3423 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r1_tarski(k2_relat_1(D),k4_partfun1(A,B)) & k6_funct_5(D) = k6_funct_5(C) & r1_tarski(k2_relat_1(C),k4_partfun1(A,B)) -> r2_hidden(k1_xboole_0,k2_relat_1(C)) | r2_hidden(k1_xboole_0,k2_relat_1(D)) | D = C))))) # label(t62_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3424 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k2_zfmisc_1(A,B) = k1_relat_1(C) -> r1_tarski(k2_relat_1(k5_funct_5(C)),k1_funct_2(A,k2_relat_1(C))) & r1_tarski(k2_relat_1(k3_funct_5(C)),k1_funct_2(B,k2_relat_1(C)))))) # label(t42_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3425 $T # label(t3_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3426 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k5_funct_5(A)) & v1_funct_1(k5_funct_5(A)))) # label(dt_k5_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3427 $T # label(dt_k1_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3428 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(k4_tarski(A,B),k1_relat_1(C)) & D = k1_funct_1(k5_funct_5(C),B) -> k1_funct_1(C,k4_tarski(A,B)) = k1_funct_1(D,A) & r2_hidden(A,k1_relat_1(D))))))) # label(t29_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3429 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> -(k2_zfmisc_1(A,B) = k1_relat_1(D) & r2_hidden(C,B) & (all E (v1_relat_1(E) & v1_funct_1(E) -> -((all F (r2_hidden(F,A) -> k1_funct_1(D,k4_tarski(F,C)) = k1_funct_1(E,F))) & r1_tarski(k2_relat_1(E),k2_relat_1(D)) & k1_relat_1(E) = A & E = k1_funct_1(k5_funct_5(D),C)))) & k2_zfmisc_1(A,B) != k1_xboole_0))) # label(t39_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3430 (all A all B (r1_tarski(A,B) -> r1_tarski(k1_funct_5(A),k1_funct_5(B)) & r1_tarski(k2_funct_5(A),k2_funct_5(B)))) # label(t5_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3431 (all A all B all C all D (r2_wellord2(C,D) & r2_wellord2(A,B) -> r2_wellord2(k1_funct_2(A,C),k1_funct_2(B,D)) & k1_card_1(k1_funct_2(B,D)) = k1_card_1(k1_funct_2(A,C)))) # label(t67_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3432 (all A all B k1_tarski(k2_funcop_1(A,B)) = k1_funct_2(A,k1_tarski(B))) # label(t66_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3433 (all A all B all C (r2_wellord2(k1_funct_2(k2_zfmisc_1(A,B),C),k1_funct_2(A,k1_funct_2(B,C))) & k1_card_1(k1_funct_2(k2_zfmisc_1(A,B),C)) = k1_card_1(k1_funct_2(A,k1_funct_2(B,C))))) # label(t70_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3434 (all A all B (k1_tarski(B) = k2_funct_5(k1_tarski(k4_tarski(A,B))) & k1_funct_5(k1_tarski(k4_tarski(A,B))) = k1_tarski(A))) # label(t15_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3435 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_relat_1(C),k1_funct_2(A,B)) -> k1_relat_1(k4_funct_5(C)) = k2_zfmisc_1(k1_relat_1(C),A) & k1_relat_1(k6_funct_5(C)) = k2_zfmisc_1(A,k1_relat_1(C))))) # label(t33_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3436 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (C = k1_funct_1(k3_funct_5(B),A) & r2_hidden(A,k1_relat_1(k3_funct_5(B))) -> k1_relat_1(C) = k2_funct_5(k3_xboole_0(k1_relat_1(B),k2_zfmisc_1(k1_tarski(A),k2_funct_5(k1_relat_1(B))))) & r1_tarski(k2_relat_1(C),k2_relat_1(B)) & (all D (r2_hidden(D,k1_relat_1(C)) -> k1_funct_1(B,k4_tarski(A,D)) = k1_funct_1(C,D) & r2_hidden(k4_tarski(A,D),k1_relat_1(B)))) & r1_tarski(k1_relat_1(C),k2_funct_5(k1_relat_1(B)))))))) # label(t38_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3437 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(A,k1_relat_1(k3_funct_5(B))) -> v1_relat_1(k1_funct_1(k3_funct_5(B),A)) & v1_funct_1(k1_funct_1(k3_funct_5(B),A))))) # label(t37_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3438 (all A all B (r1_tarski(k2_funct_5(k2_zfmisc_1(A,B)),B) & r1_tarski(k1_funct_5(k2_zfmisc_1(A,B)),A))) # label(t12_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3439 (all A (k2_funct_5(A) = k1_xboole_0 | k1_xboole_0 = k1_funct_5(A) -> (all B all C -r2_hidden(k4_tarski(B,C),A)))) # label(t18_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3440 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k2_zfmisc_1(A,B) = k1_relat_1(C) -> C = k6_funct_5(k5_funct_5(C)) & C = k4_funct_5(k3_funct_5(C))))) # label(t56_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3441 $T # label(t23_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3442 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k1_relat_1(D) = k2_zfmisc_1(A,B) & k5_funct_5(D) = k5_funct_5(C) & k1_relat_1(C) = k2_zfmisc_1(A,B) -> C = D))))) # label(t52_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3443 (all A (v1_relat_1(A) & v1_funct_1(A) -> r1_tarski(k2_relat_1(k3_funct_5(A)),k4_partfun1(k2_funct_5(k1_relat_1(A)),k2_relat_1(A))) & r1_tarski(k2_relat_1(k5_funct_5(A)),k4_partfun1(k1_funct_5(k1_relat_1(A)),k2_relat_1(A))))) # label(t43_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3444 (all A all B all C (r1_xboole_0(A,B) -> r2_wellord2(k1_funct_2(k2_xboole_0(A,B),C),k2_zfmisc_1(k1_funct_2(A,C),k1_funct_2(B,C))) & k1_card_1(k1_funct_2(k2_xboole_0(A,B),C)) = k1_card_1(k2_zfmisc_1(k1_funct_2(A,C),k1_funct_2(B,C))))) # label(t69_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3445 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(C) = k2_zfmisc_1(A,B) -> k1_relat_1(k5_funct_5(C)) = B & k1_relat_1(k3_funct_5(C)) = A | k1_xboole_0 = k2_zfmisc_1(A,B)))) # label(t31_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3446 (all A all B (-(k2_zfmisc_1(B,A) = k1_xboole_0 & k1_xboole_0 = k2_zfmisc_1(A,B) & k1_xboole_0 = A) -> k2_funct_5(k2_zfmisc_1(A,B)) = B & B = k1_funct_5(k2_zfmisc_1(B,A)))) # label(t11_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3447 (all A all B all C (A != B -> k1_card_1(k2_zfmisc_1(C,C)) = k1_card_1(k1_funct_2(k2_tarski(A,B),C)) & r2_wellord2(k1_funct_2(k2_tarski(A,B),C),k2_zfmisc_1(C,C)))) # label(t73_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3448 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),k1_relat_1(C)) -> v1_funct_1(k1_funct_1(k3_funct_5(C),A)) & v1_relat_1(k1_funct_1(k3_funct_5(C),A)) & r2_hidden(A,k1_relat_1(k3_funct_5(C)))))) # label(t26_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3449 (all A ((all B all C -r2_hidden(k4_tarski(B,C),A)) -> k2_funct_5(A) = k1_xboole_0 & k1_xboole_0 = k1_funct_5(A))) # label(t17_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3450 (all A all B all C (k1_card_1(k1_funct_2(A,k2_zfmisc_1(B,C))) = k1_card_1(k2_zfmisc_1(k1_funct_2(A,B),k1_funct_2(A,C))) & r2_wellord2(k1_funct_2(A,k2_zfmisc_1(B,C)),k2_zfmisc_1(k1_funct_2(A,B),k1_funct_2(A,C))))) # label(t71_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3451 (all A all B all C (r1_tarski(A,k2_zfmisc_1(B,C)) -> r1_tarski(k1_funct_5(A),B) & r1_tarski(k2_funct_5(A),C))) # label(t13_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3452 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(k5_funct_5(B))) & C = k1_funct_1(k5_funct_5(B),A) -> k1_funct_5(k3_xboole_0(k1_relat_1(B),k2_zfmisc_1(k1_funct_5(k1_relat_1(B)),k1_tarski(A)))) = k1_relat_1(C) & (all D (r2_hidden(D,k1_relat_1(C)) -> k1_funct_1(B,k4_tarski(D,A)) = k1_funct_1(C,D) & r2_hidden(k4_tarski(D,A),k1_relat_1(B)))) & r1_tarski(k2_relat_1(C),k2_relat_1(B)) & r1_tarski(k1_relat_1(C),k1_funct_5(k1_relat_1(B)))))))) # label(t41_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3453 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k1_funct_1(C,A) = D & r2_hidden(B,k1_relat_1(D)) & r2_hidden(A,k1_relat_1(C)) -> r2_hidden(k1_funct_1(D,B),k2_relat_1(k4_funct_5(C))) & k1_funct_1(D,B) = k1_funct_1(k4_funct_5(C),k4_tarski(A,B)) & r2_hidden(k4_tarski(A,B),k1_relat_1(k4_funct_5(C)))))))) # label(t45_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3454 (all A (v1_relat_1(A) & v1_funct_1(A) -> k3_funct_5(k2_funct_4(A)) = k5_funct_5(A))) # label(d5_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3455 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k4_funct_5(C) = k4_funct_5(D) & r1_tarski(k2_relat_1(D),k4_partfun1(A,B)) & r1_tarski(k2_relat_1(C),k4_partfun1(A,B)) -> r2_hidden(k1_xboole_0,k2_relat_1(C)) | C = D | r2_hidden(k1_xboole_0,k2_relat_1(D))))))) # label(t61_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3456 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(k4_tarski(A,B),k1_relat_1(C)) & k1_funct_1(k3_funct_5(C),A) = D -> k1_funct_1(D,B) = k1_funct_1(C,k4_tarski(A,B)) & r2_hidden(B,k1_relat_1(D))))))) # label(t27_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3457 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B all C -r2_hidden(k4_tarski(B,C),k1_relat_1(A))) -> k1_xboole_0 = k5_funct_5(A) & k1_xboole_0 = k3_funct_5(A)))) # label(t34_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3458 (all A all B all C all D (k1_card_1(B) = k1_card_1(A) & k1_card_1(D) = k1_card_1(C) -> k1_card_1(k1_funct_2(A,C)) = k1_card_1(k1_funct_2(B,D)))) # label(t68_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3459 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),k1_relat_1(C)) -> v1_relat_1(k1_funct_1(k5_funct_5(C),B)) & v1_funct_1(k1_funct_1(k5_funct_5(C),B)) & r2_hidden(B,k1_relat_1(k5_funct_5(C)))))) # label(t28_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3460 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k1_funct_2(C,A),k1_funct_2(C,B)))) # label(t63_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3461 (all A all B (r1_tarski(k1_funct_5(k3_xboole_0(A,B)),k3_xboole_0(k1_funct_5(A),k1_funct_5(B))) & r1_tarski(k2_funct_5(k3_xboole_0(A,B)),k3_xboole_0(k2_funct_5(A),k2_funct_5(B))))) # label(t7_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3462 $T # label(dt_k2_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3463 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> k4_funct_5(k3_funct_5(C)) = C & k6_funct_5(k5_funct_5(C)) = C))) # label(t57_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3464 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k5_funct_5(C) = k5_funct_5(D) & r1_tarski(k1_relat_1(D),k2_zfmisc_1(A,B)) & r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> D = C))))) # label(t60_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3465 (all A all B (k1_card_1(k1_funct_2(k1_tarski(B),A)) = k1_card_1(A) & r2_wellord2(A,k1_funct_2(k1_tarski(B),A)))) # label(t65_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3466 (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(k5_funct_5(C)),B) & r1_tarski(k1_relat_1(k3_funct_5(C)),A)))) # label(t32_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3467 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k4_funct_5(C) = k4_funct_5(D) & r1_tarski(k2_relat_1(D),k1_funct_2(A,B)) & r1_tarski(k2_relat_1(C),k1_funct_2(A,B)) -> A = k1_xboole_0 | C = D))))) # label(t53_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3468 (all A (v1_relat_1(A) & v1_funct_1(A) -> k6_funct_5(A) = k2_funct_4(k4_funct_5(A)))) # label(d6_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3469 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(A,k1_relat_1(C)) & r2_hidden(B,k1_relat_1(D)) & k1_funct_1(C,A) = D -> r2_hidden(k1_funct_1(D,B),k2_relat_1(k6_funct_5(C))) & k1_funct_1(D,B) = k1_funct_1(k6_funct_5(C),k4_tarski(B,A)) & r2_hidden(k4_tarski(B,A),k1_relat_1(k6_funct_5(C)))))))) # label(t46_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3470 (all A all B (B = k2_funct_5(A) <-> (all C ((exists D r2_hidden(k4_tarski(D,C),A)) <-> r2_hidden(C,B))))) # label(d2_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3471 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_relat_1(C),k4_partfun1(A,B)) -> r1_tarski(k1_relat_1(k4_funct_5(C)),k2_zfmisc_1(k1_relat_1(C),A)) & r1_tarski(k1_relat_1(k6_funct_5(C)),k2_zfmisc_1(A,k1_relat_1(C)))))) # label(t44_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3472 (all A k1_funct_2(k1_xboole_0,A) = k1_tarski(k1_xboole_0)) # label(t64_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3473 (all A all B ((all C (r2_hidden(C,B) <-> (exists D r2_hidden(k4_tarski(C,D),A)))) <-> k1_funct_5(A) = B)) # label(d1_funct_5) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3474 (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]. 14.93/14.51 3475 (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]. 14.93/14.51 3476 (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]. 14.93/14.51 3477 $T # label(t67_finseq_2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3478 (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]. 14.93/14.51 3479 (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]. 14.93/14.51 3480 (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]. 14.93/14.51 3481 (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]. 14.93/14.51 3482 (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]. 14.93/14.51 3483 (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]. 14.93/14.51 3484 $T # label(dt_m1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.51 3485 (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]. 14.93/14.51 3486 (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]. 14.93/14.51 3487 (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]. 14.93/14.51 3488 (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]. 14.93/14.51 3489 (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]. 14.93/14.51 3490 (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]. 14.93/14.51 3491 (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]. 14.93/14.51 3492 (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]. 14.93/14.51 3493 (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]. 14.93/14.51 3494 (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]. 14.93/14.51 3495 (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]. 14.93/14.51 3496 (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]. 14.93/14.51 3497 (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]. 14.93/14.51 3498 (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]. 14.93/14.51 3499 (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]. 14.93/14.51 3500 (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]. 14.93/14.51 3501 (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]. 14.93/14.51 3502 (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]. 14.93/14.51 3503 (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]. 14.93/14.51 3504 (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]. 14.93/14.51 3505 (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]. 14.93/14.51 3506 (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]. 14.93/14.51 3507 (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]. 14.93/14.51 3508 (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]. 14.93/14.51 3509 (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]. 14.93/14.51 3510 (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]. 14.93/14.52 3511 (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]. 14.93/14.52 3512 (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]. 14.93/14.52 3513 (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]. 14.93/14.52 3514 (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]. 14.93/14.52 3515 (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]. 14.93/14.52 3516 (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]. 14.93/14.52 3517 (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]. 14.93/14.52 3518 (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]. 14.93/14.52 3519 (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]. 14.93/14.52 3520 (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]. 14.93/14.52 3521 (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]. 14.93/14.52 3522 (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]. 14.93/14.52 3523 (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]. 14.93/14.52 3524 (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]. 14.93/14.52 3525 (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]. 14.93/14.52 3526 (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]. 14.93/14.52 3527 (all A k2_finseq_2(np__0,A) = k1_xboole_0) # label(t72_finseq_2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3528 (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]. 14.93/14.52 3529 (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]. 14.93/14.52 3530 (all A (v4_ordinal2(A) -> k3_finseq_1(k1_finseq_2(A)) = A)) # label(t55_finseq_2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3531 (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]. 14.93/14.52 3532 (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]. 14.93/14.52 3533 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]. 14.93/14.52 3534 $T # label(t103_finseq_2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3535 (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]. 14.93/14.52 3536 (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]. 14.93/14.52 3537 $T # label(t12_finseq_2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3538 (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]. 14.93/14.52 3539 (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]. 14.93/14.52 3540 (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]. 14.93/14.52 3541 (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]. 14.93/14.52 3542 (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]. 14.93/14.52 3543 (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]. 14.93/14.52 3544 (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]. 14.93/14.52 3545 (all A k13_finseq_1(A) = k3_finseq_2(A)) # label(redefinition_k3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3546 (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]. 14.93/14.52 3547 (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]. 14.93/14.52 3548 (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]. 14.93/14.52 3549 (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]. 14.93/14.52 3550 (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]. 14.93/14.52 3551 (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]. 14.93/14.52 3552 (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]. 14.93/14.52 3553 (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]. 14.93/14.52 3554 $T # label(t7_finseq_2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3555 (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]. 14.93/14.52 3556 (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]. 14.93/14.52 3557 (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]. 14.93/14.52 3558 (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]. 14.93/14.52 3559 (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]. 14.93/14.52 3560 (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]. 14.93/14.52 3561 (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]. 14.93/14.52 3562 $T # label(t106_finseq_2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3563 (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]. 14.93/14.52 3564 (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]. 14.93/14.52 3565 (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]. 14.93/14.52 3566 (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]. 14.93/14.52 3567 (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]. 14.93/14.52 3568 (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]. 14.93/14.52 3569 (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]. 14.93/14.52 3570 (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]. 14.93/14.52 3571 (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]. 14.93/14.52 3572 (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]. 14.93/14.52 3573 (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]. 14.93/14.52 3574 (all A exists B (m1_finseq_2(B,A) & -v1_xboole_0(B))) # label(rc1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3575 (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]. 14.93/14.52 3576 (all A k10_finseq_1(A,A) = k2_finseq_2(np__2,A)) # label(t75_finseq_2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3577 (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]. 14.93/14.52 3578 (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]. 14.93/14.52 3579 (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]. 14.93/14.52 3580 (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]. 14.93/14.52 3581 (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]. 14.93/14.52 3582 (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]. 14.93/14.52 3583 (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]. 14.93/14.52 3584 (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]. 14.93/14.52 3585 (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]. 14.93/14.52 3586 (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]. 14.93/14.52 3587 (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]. 14.93/14.52 3588 (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]. 14.93/14.52 3589 $T # label(t108_finseq_2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3590 (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]. 14.93/14.52 3591 (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]. 14.93/14.52 3592 (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]. 14.93/14.52 3593 (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]. 14.93/14.52 3594 (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]. 14.93/14.52 3595 (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]. 14.93/14.52 3596 (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]. 14.93/14.52 3597 (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]. 14.93/14.52 3598 (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]. 14.93/14.52 3599 (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]. 14.93/14.52 3600 $T # label(t29_finseq_2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3601 (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]. 14.93/14.52 3602 (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]. 14.93/14.52 3603 (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]. 14.93/14.52 3604 (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]. 14.93/14.52 3605 (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]. 14.93/14.52 3606 (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]. 14.93/14.52 3607 (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]. 14.93/14.52 3608 (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]. 14.93/14.52 3609 (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]. 14.93/14.52 3610 (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]. 14.93/14.52 3611 $T # label(t53_finseq_2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3612 $T # label(t17_finseq_2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3613 (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]. 14.93/14.52 3614 (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]. 14.93/14.52 3615 (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]. 14.93/14.52 3616 (all A exists B m1_finseq_2(B,A)) # label(existence_m1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3617 (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]. 14.93/14.52 3618 (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]. 14.93/14.52 3619 (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]. 14.93/14.52 3620 (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]. 14.93/14.52 3621 (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]. 14.93/14.52 3622 (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]. 14.93/14.52 3623 (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]. 14.93/14.52 3624 (all A k9_finseq_1(A) = k2_finseq_2(np__1,A)) # label(t73_finseq_2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3625 (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]. 14.93/14.52 3626 (all A k2_finseq_2(np__3,A) = k11_finseq_1(A,A,A)) # label(t76_finseq_2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3627 (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]. 14.93/14.52 3628 (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]. 14.93/14.52 3629 (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]. 14.93/14.52 3630 (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]. 14.93/14.52 3631 (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]. 14.93/14.52 3632 (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]. 14.93/14.52 3633 (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]. 14.93/14.52 3634 (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]. 14.93/14.52 3635 (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]. 14.93/14.52 3636 (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]. 14.93/14.52 3637 (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]. 14.93/14.52 3638 (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]. 14.93/14.52 3639 (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]. 14.93/14.52 3640 (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]. 14.93/14.52 3641 (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]. 14.93/14.52 3642 (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]. 14.93/14.52 3643 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) -> (all B (r2_hidden(B,k1_relat_1(A)) -> k1_funct_1(A,B) = k1_card_1(k1_funct_1(k2_card_3(A),B)))))) # label(t40_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3644 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> -((all C all D k4_tarski(C,D) != A) & r2_hidden(A,k3_card_3(k2_card_3(B)))))) # label(t32_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3645 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (B = k2_card_3(A) <-> k1_relat_1(B) = k1_relat_1(A) & (all C (r2_hidden(C,k1_relat_1(A)) -> k2_zfmisc_1(k1_funct_1(A,C),k1_tarski(C)) = k1_funct_1(B,C)))))))) # label(d3_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3646 $T # label(t2_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3647 (all A (v1_funct_1(A) & v1_relat_1(A) -> (r2_hidden(k1_xboole_0,k2_relat_1(A)) <-> k4_card_3(A) = k1_xboole_0))) # label(t37_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3648 (all A (v1_funct_1(A) & v1_card_3(A) & v1_relat_1(A) -> (r2_hidden(k1_xboole_0,k2_relat_1(A)) <-> np__0 = k7_card_3(A)))) # label(t44_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3649 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(k1_card_1(A),k1_card_1(B)) -> r2_hidden(A,B)))))) # label(t59_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3650 $T # label(t7_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3651 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & v1_setfam_1(B) -> v1_fraenkel(k4_card_3(C)) & -v1_xboole_0(k4_card_3(C)))) # label(fc4_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3652 (all A (v2_relat_1(A) & v1_funct_1(A) & v1_relat_1(A) -> -v1_xboole_0(k4_card_3(A)) & v1_fraenkel(k4_card_3(A)))) # label(fc5_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3653 (all A all B all C r1_tarski(k5_card_3(C,k3_xboole_0(A,B)),k3_xboole_0(k5_card_3(C,A),k5_card_3(C,B)))) # label(t28_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3654 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k1_card_3(A)) & v1_card_3(k1_card_3(A)) & v1_funct_1(k1_card_3(A)))) # label(dt_k1_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3655 (all A all B all C k2_xboole_0(k5_card_3(C,A),k5_card_3(C,B)) = k5_card_3(C,k2_xboole_0(A,B))) # label(t27_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3656 $T # label(t1_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3657 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k1_relat_1(C)) & r2_hidden(A,k1_relat_1(C)) -> r1_xboole_0(k1_funct_1(k2_card_3(C),A),k1_funct_1(k2_card_3(C),B)) | B = A))) # label(t13_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3658 (all A all B r1_tarski(k1_card_1(k5_card_3(B,A)),k1_card_1(A))) # label(t31_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3659 $T # label(t23_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3660 $T # label(dt_k4_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3661 (all A all B r1_tarski(k3_card_3(k2_funcop_1(A,B)),B)) # label(t15_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3662 (all A all B k2_funcop_1(k1_tarski(A),k2_zfmisc_1(B,k1_tarski(A))) = k2_card_3(k2_funcop_1(k1_tarski(A),B))) # label(t12_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3663 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_card_3(B) & v1_relat_1(B) -> (k1_relat_1(A) = k1_relat_1(B) & (all C (r2_hidden(C,k1_relat_1(A)) -> k1_card_1(k1_funct_1(A,C)) = k1_funct_1(B,C))) <-> k1_card_3(A) = B))))) # label(d2_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3664 $T # label(dt_k3_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3665 $T # label(t41_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3666 (all A all B k1_card_3(k2_funcop_1(A,B)) = k2_funcop_1(A,k1_card_1(B))) # label(t10_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3667 $T # label(t5_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3668 (all A (v1_relat_1(A) & v1_card_3(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_card_3(B) -> (r1_tarski(A,B) -> r1_tarski(k6_card_3(A),k6_card_3(B))))))) # label(t46_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3669 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> k6_card_3(k2_funcop_1(A,B)) = k2_card_2(A,B))))) # label(t52_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3670 $T # label(t6_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3671 (all A (v1_relat_1(A) & v1_card_3(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_card_3(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> r1_tarski(k1_funct_1(A,C),k1_funct_1(B,C)))) & k1_relat_1(B) = k1_relat_1(A) -> r1_tarski(k6_card_3(A),k6_card_3(B))))))) # label(t43_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3672 (all A all B (v1_card_1(B) -> v1_relat_1(k2_funcop_1(A,B)) & v1_card_3(k2_funcop_1(A,B)) & v1_ordinal2(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)))) # label(fc2_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3673 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k2_card_3(A)) & v1_relat_1(k2_card_3(A)))) # label(dt_k2_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3674 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v1_card_3(A) <-> (all B (r2_hidden(B,k1_relat_1(A)) -> v1_card_1(k1_funct_1(A,B))))))) # label(d1_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3675 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> v1_finset_1(k4_classes1(A)))) # label(t57_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3676 (all A all B (v1_funct_1(A) & v1_card_3(A) & v1_relat_1(A) -> v1_funct_1(k7_relat_1(A,B)) & v1_card_3(k7_relat_1(A,B)) & v1_relat_1(k7_relat_1(A,B)))) # label(fc1_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3677 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k4_card_3(B)) <-> k1_relat_1(A) = k1_relat_1(B) & (all C (r2_hidden(C,k1_relat_1(B)) -> r2_hidden(k1_funct_1(A,C),k1_funct_1(B,C))))))))) # label(t18_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3678 (all A (v1_relat_1(A) & v1_funct_1(A) -> r1_tarski(k1_card_1(k3_card_3(A)),k6_card_3(k1_card_3(A))))) # label(t54_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3679 (all A (v1_card_1(A) -> k6_card_3(k2_funcop_1(k1_xboole_0,A)) = np__0)) # label(t48_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3680 (all A -(v6_ordinal1(A) & (all B -((all C -((all D -((all E (r2_hidden(E,C) -> r1_tarski(D,E))) & r2_hidden(D,C))) & k1_xboole_0 != C & r1_tarski(C,B))) & k3_tarski(A) = k3_tarski(B) & r1_tarski(B,A))))) # label(t61_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3681 $T # label(dt_k5_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3682 (all A all B k1_funct_2(A,B) = k4_card_3(k2_funcop_1(A,B))) # label(t20_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3683 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(A) = k1_relat_1(B) & (all C (r2_hidden(C,k1_relat_1(A)) -> r1_tarski(k1_funct_1(A,C),k1_funct_1(B,C)))) -> r1_tarski(k4_card_3(A),k4_card_3(B))))))) # label(t38_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3684 (all A k5_card_3(A,k1_xboole_0) = k1_xboole_0) # label(t24_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3685 (all A all B all C (C = k5_card_3(A,B) <-> (all D ((exists E (v1_funct_1(E) & r2_hidden(E,B) & D = k1_funct_1(E,A) & v1_relat_1(E))) <-> r2_hidden(D,C))))) # label(d6_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3686 (all A (v1_card_1(A) -> (all B A = k6_card_3(k2_funcop_1(k1_tarski(B),A))))) # label(t50_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3687 (all A all B all C r1_tarski(k5_xboole_0(k5_card_3(B,A),k5_card_3(B,C)),k5_card_3(B,k5_xboole_0(A,C)))) # label(t30_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3688 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) -> r1_tarski(k1_card_1(k3_card_3(A)),k6_card_3(A)))) # label(t55_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3689 (all A (v1_card_1(A) -> (all B k7_card_3(k2_funcop_1(k1_tarski(B),A)) = A))) # label(t51_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3690 (all A (v1_relat_1(A) & v1_funct_1(A) -> k3_tarski(k2_relat_1(A)) = k3_card_3(A))) # label(d4_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.52 3691 (all A (v1_card_3(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_card_3(B) & v1_relat_1(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> r1_tarski(k1_funct_1(A,C),k1_funct_1(B,C)))) & k1_relat_1(B) = k1_relat_1(A) -> r1_tarski(k7_card_3(A),k7_card_3(B))))))) # label(t45_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3692 $T # label(t4_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3693 (all A (v1_card_3(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_card_3(B) & v1_relat_1(B) -> (k1_relat_1(B) = k1_relat_1(A) & (all C (r2_hidden(C,k1_relat_1(A)) -> r2_hidden(k1_funct_1(A,C),k1_funct_1(B,C)))) -> r2_hidden(k6_card_3(A),k7_card_3(B))))))) # label(t56_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3694 (all A (v1_card_1(A) -> (all B (v6_ordinal1(B) & (all C (r2_hidden(C,B) -> r2_hidden(k1_card_1(C),A))) -> r1_tarski(k1_card_1(k3_tarski(B)),A))))) # label(t62_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3695 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> k5_card_3(A,k2_tarski(B,C)) = k2_tarski(k1_funct_1(B,A),k1_funct_1(C,A)))))) # label(t26_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3696 (all A (v1_relat_1(A) & v1_card_3(A) & v1_funct_1(A) -> v1_card_1(k6_card_3(A)))) # label(dt_k6_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3697 (exists A (v1_relat_1(A) & v1_card_3(A) & v1_funct_1(A))) # label(rc1_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3698 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) -> k1_card_1(k3_card_3(k2_card_3(A))) = k6_card_3(A))) # label(d7_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3699 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> k7_card_3(k2_funcop_1(A,B)) = k3_card_2(B,A))))) # label(t53_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3700 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(B,A) = k5_card_3(A,k4_card_3(B)) | k4_card_3(B) = k1_xboole_0))) # label(t22_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3701 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> k1_tarski(k1_funct_1(B,A)) = k5_card_3(A,k1_tarski(B)))) # label(t25_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3702 (all A all B (A != k1_xboole_0 -> k3_card_3(k2_funcop_1(A,B)) = B)) # label(t16_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3703 $T # label(t42_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3704 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(k2_mcart_1(A),k1_relat_1(B)) & r2_hidden(k1_mcart_1(A),k1_funct_1(B,k2_mcart_1(A))) & A = k4_tarski(k1_mcart_1(A),k2_mcart_1(A)) <-> r2_hidden(A,k3_card_3(k2_card_3(B)))))) # label(t33_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3705 (all A all B B = k3_card_3(k2_funcop_1(k1_tarski(A),B))) # label(t17_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3706 (all A all B all C r1_tarski(k4_xboole_0(k5_card_3(B,A),k5_card_3(B,C)),k5_card_3(B,k4_xboole_0(A,C)))) # label(t29_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3707 f1_s3_card_3 != k1_xboole_0 & (all A all B all C (p1_s3_card_3(A,B) & p1_s3_card_3(B,C) -> p1_s3_card_3(A,C))) & (all A all B (p1_s3_card_3(B,A) | p1_s3_card_3(A,B))) -> (exists A (r2_hidden(A,f1_s3_card_3) & (all B (r2_hidden(B,f1_s3_card_3) -> p1_s3_card_3(A,B))))) # label(s3_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3708 (all A (v1_funct_1(A) & v1_card_3(A) & v1_relat_1(A) -> v1_card_1(k7_card_3(A)))) # label(dt_k7_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3709 (exists A (v1_relat_1(A) & v1_funct_1(A) & f1_s4_card_3 = k1_relat_1(A) & (all B (r2_hidden(B,f1_s4_card_3) -> (all C (r2_hidden(C,f2_s4_card_3(B)) & p1_s4_card_3(B,C) <-> r2_hidden(C,k1_funct_1(A,B)))))))) # label(s4_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3710 (all A all B k2_zfmisc_1(B,A) = k3_card_3(k2_card_3(k2_funcop_1(A,B)))) # label(t36_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3711 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,B) -> r1_tarski(k3_card_3(A),k3_card_3(B))))))) # label(t35_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3712 (all A (v1_finset_1(A) -> r2_hidden(k1_card_1(A),k1_card_1(k5_ordinal2)))) # label(t58_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3713 (exists A (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) & k1_relat_1(A) = f1_s1_card_3 & (all B (r2_hidden(B,f1_s1_card_3) -> f2_s1_card_3(B) = k1_funct_1(A,B))))) # label(s1_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3714 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (k4_card_3(A) = B <-> (all C (r2_hidden(C,B) <-> (exists D (v1_relat_1(D) & C = D & (all E (r2_hidden(E,k1_relat_1(A)) -> r2_hidden(k1_funct_1(D,E),k1_funct_1(A,E)))) & k1_relat_1(A) = k1_relat_1(D) & v1_funct_1(D))))))))) # label(d5_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3715 $T # label(t21_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3716 (all A (v1_relat_1(A) & v1_card_3(A) & v1_funct_1(A) -> k7_card_3(A) = k1_card_1(k4_card_3(A)))) # label(d8_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3717 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) -> A = k1_card_3(A))) # label(t8_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3718 (all A (v1_funct_1(A) & v1_card_3(A) & v1_relat_1(A) -> (all B (r2_hidden(B,k1_relat_1(A)) -> k1_funct_1(A,B) = k1_card_1(k1_funct_1(A,B)))))) # label(t39_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3719 (all A (v3_ordinal1(A) -> (all B (v1_card_1(B) -> (r2_hidden(k1_card_1(A),B) -> r2_hidden(A,B)))))) # label(t60_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3720 (all A (v1_funct_1(A) & v1_card_3(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_card_3(B) -> (r1_tarski(A,B) -> r2_hidden(np__0,k2_relat_1(B)) | r1_tarski(k7_card_3(A),k7_card_3(B))))))) # label(t47_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3721 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,B) -> r1_tarski(k2_card_3(A),k2_card_3(B))))))) # label(t34_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3722 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_fraenkel(k4_card_3(A)))) # label(fc3_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3723 (all A all B (p1_s2_card_3(A,B) & p1_s2_card_3(B,A) -> A = B)) & (all A all B all C (p1_s2_card_3(A,B) & p1_s2_card_3(B,C) -> p1_s2_card_3(A,C))) & f1_s2_card_3 != k1_xboole_0 -> (exists A (r2_hidden(A,f1_s2_card_3) & (all B -(r2_hidden(B,f1_s2_card_3) & B != A & p1_s2_card_3(B,A))))) # label(s2_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3724 (all A (v1_card_1(A) -> k7_card_3(k2_funcop_1(k1_xboole_0,A)) = np__1)) # label(t49_card_3) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3725 (all A all B (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(B,A) -> k3_tarski(B) = k3_classes2(A,B))) # label(redefinition_k3_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3726 (all A (v2_classes1(A) -> v4_ordinal1(k1_card_1(A)))) # label(t20_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3727 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> k5_classes2(A,B,C) = k5_classes2(A,C,B))) # label(commutativity_k5_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3728 (all A v2_classes1(k4_classes1(k1_card_1(k1_classes1(A))))) # label(t40_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3729 (all A all B (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(B,A) -> m1_subset_1(k1_classes2(A,B),A))) # label(dt_k1_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3730 (all A (v3_ordinal1(A) -> (all B -((all C -(k6_classes1(C) = A & r2_hidden(C,B))) & r2_hidden(A,k6_classes1(B)) & v1_ordinal1(B))))) # label(t41_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3731 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) -> (v4_ordinal1(A) & k1_relat_1(B) = A & (all C (v3_ordinal1(C) -> (r2_hidden(C,A) -> k1_funct_1(B,C) = k16_classes2(C)))) -> k1_xboole_0 = A | k16_classes2(A) = k15_classes2(k3_card_3(B))))))) # label(t78_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3732 (all A all B (r2_hidden(B,A) & v1_ordinal1(B) & v2_classes1(A) -> r2_hidden(B,k4_classes1(k1_card_1(A))))) # label(t43_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3733 (all A (v1_ordinal1(A) -> v1_ordinal1(k1_classes1(A)) & v2_classes1(k1_classes1(A)) & v1_classes2(k1_classes1(A)) & v1_classes1(k1_classes1(A)) & -v1_xboole_0(k1_classes1(A)))) # label(fc6_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3734 (all A (v1_classes2(A) & -v1_xboole_0(A) -> -v1_xboole_0(k1_classes1(A)) & v1_classes2(k1_classes1(A)))) # label(t52_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3735 $T # label(t68_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3736 (all A (v2_classes1(A) -> r1_tarski(k4_classes1(k1_card_1(A)),A))) # label(t28_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3737 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (-v1_xboole_0(B) & v1_classes2(B) -> (all C (v1_classes2(C) & -v1_xboole_0(C) -> (r2_hidden(A,B) & r2_hidden(B,C) -> r2_hidden(A,C)))))))) # label(t59_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3738 (all A all B (v1_classes2(B) & -v1_xboole_0(B) -> (r1_tarski(A,B) & (all C (-v1_xboole_0(C) & v1_classes2(C) -> (r1_tarski(A,C) -> r1_tarski(B,C)))) <-> B = k15_classes2(A)))) # label(d4_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3739 (all A all B (v1_classes2(A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k1_zfmisc_1(B) = k2_classes2(A,B))) # label(redefinition_k2_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3740 (all A (v1_card_1(A) -> (all B (r2_hidden(A,k1_card_1(k1_classes1(B))) -> r2_hidden(A,k1_classes1(B)))))) # label(t17_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3741 (all A (v3_ordinal1(A) -> (all B (r2_hidden(A,k2_ordinal2(k1_classes1(B))) -> r2_hidden(k4_classes1(A),k1_classes1(B)) & r2_hidden(k1_card_1(k4_classes1(A)),k1_card_1(k1_classes1(B))))))) # label(t27_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3742 (all A (v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> (v4_ordinal1(k1_relat_1(A)) & (all B (v3_ordinal1(B) -> (r2_hidden(B,k1_relat_1(A)) -> k4_classes1(B) = k1_funct_1(A,B)))) -> k4_classes1(k1_relat_1(A)) = k3_card_3(A)))) # label(t25_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3743 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (-v1_xboole_0(B) & v1_classes2(B) -> -(-r2_hidden(A,B) & A != B & -r2_hidden(B,A)))))) # label(t56_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3744 (all A all B all C (r2_hidden(B,A) & r2_hidden(C,A) & v2_classes1(A) -> r2_hidden(k1_tarski(B),A) & r2_hidden(k2_tarski(B,C),A))) # label(t3_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3745 (all A all B (v1_ordinal1(A) & r2_hidden(A,k1_classes1(B)) -> r1_tarski(A,k1_classes1(B)))) # label(t9_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3746 (all A all B all C (r2_hidden(B,A) & r2_hidden(C,A) & v2_classes1(A) -> r2_hidden(k4_tarski(B,C),A))) # label(t4_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3747 (all A all B (v2_classes1(A) & r2_hidden(B,A) -> r1_tarski(k1_classes1(B),A))) # label(t5_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3748 (all A (v3_ordinal1(A) -> (all B (r2_hidden(A,B) & v2_classes1(B) -> r2_hidden(k1_ordinal1(A),B) & r1_tarski(A,B))))) # label(t6_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3749 (all A all B all C (v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k12_classes2(A,B,C) = k1_funct_2(B,C))) # label(redefinition_k12_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3750 (all A (v1_classes2(A) & -v1_xboole_0(A) -> v3_ordinal1(k2_ordinal2(A)))) # label(t50_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3751 (all A (v1_classes1(k1_classes1(A)) & v2_classes1(k1_classes1(A)) & -v1_xboole_0(k1_classes1(A)))) # label(fc1_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3752 $T # label(t49_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3753 (all A all B all C (v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> m1_subset_1(k8_classes2(A,B,C),A))) # label(dt_k8_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3754 (all A (v2_classes1(A) & v1_ordinal1(A) -> r1_tarski(A,k4_classes1(k1_card_1(A))))) # label(t31_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3755 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & v1_classes2(A) -> k3_xboole_0(B,C) = k8_classes2(A,B,C))) # label(redefinition_k8_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3756 (all A all B (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(B,A) -> m1_subset_1(k3_classes2(A,B),A))) # label(dt_k3_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3757 (all A (v1_ordinal1(A) -> r1_tarski(k1_card_1(k6_classes1(A)),k1_card_1(A)))) # label(t42_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3758 (all A (v3_ordinal1(A) -> (all B (v2_classes1(B) & r2_hidden(A,k2_ordinal2(B)) -> r1_tarski(k1_card_1(k4_classes1(A)),k1_card_1(B)))))) # label(t33_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3759 (all A all B (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(B,A) -> m1_subset_1(k4_classes2(A,B),A))) # label(dt_k4_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3760 $T # label(t48_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3761 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(A,B) <-> r2_hidden(k16_classes2(A),k16_classes2(B))))))) # label(t80_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3762 (all A (v3_ordinal1(A) -> v1_classes2(k1_classes1(A)))) # label(t53_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3763 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> m1_subset_1(k12_classes2(A,B,C),A))) # label(dt_k12_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3764 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (exists B (-v1_xboole_0(B) & m1_subset_1(B,A))))) # label(rc2_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3765 (all A (v1_classes2(A) & -v1_xboole_0(A) -> v4_ordinal1(k2_ordinal2(A)) & k1_xboole_0 != k2_ordinal2(A))) # label(t55_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3766 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & v1_classes2(A) & -v1_xboole_0(A) -> k11_classes2(A,B,C) = k2_zfmisc_1(B,C))) # label(redefinition_k11_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3767 (all A all B all C (m1_subset_1(C,A) & m1_subset_1(B,A) & v1_classes2(A) & -v1_xboole_0(A) -> m1_subset_1(k10_classes2(A,B,C),A))) # label(dt_k10_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3768 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & v1_classes2(A) -> m1_subset_1(k9_classes2(A,B,C),A))) # label(dt_k9_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3769 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> k7_classes2(A,C,B) = k7_classes2(A,B,C))) # label(commutativity_k7_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3770 (all A (v1_classes2(A) & -v1_xboole_0(A) -> -v1_xboole_0(k1_classes1(A)) & v1_classes1(k1_classes1(A)) & v1_classes2(k1_classes1(A)) & v2_classes1(k1_classes1(A)) & v1_ordinal1(k1_classes1(A)))) # label(fc3_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3771 (all A (v2_classes1(A) -> v2_classes1(k4_classes1(k1_card_1(A))))) # label(t39_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3772 (all A (v3_ordinal1(A) -> k16_classes2(k1_ordinal1(A)) = k1_classes1(k16_classes2(A)))) # label(t76_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3773 $T # label(t60_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3774 (all A (v3_ordinal1(A) -> v1_ordinal1(k1_classes1(A)) & v1_classes2(k1_classes1(A)) & v2_classes1(k1_classes1(A)) & v1_classes1(k1_classes1(A)) & -v1_xboole_0(k1_classes1(A)))) # label(fc4_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3775 (all A v1_ordinal1(k5_classes1(A))) # label(fc5_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3776 (all A r1_tarski(k4_classes1(k1_card_1(k1_classes1(A))),k1_classes1(A))) # label(t29_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3777 (all A (v1_card_1(A) -> (all B (r2_hidden(A,k1_card_1(B)) & v2_classes1(B) -> r2_hidden(A,B))))) # label(t16_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3778 (all A all B (r2_hidden(B,A) & v1_classes1(A) -> r2_hidden(k1_card_1(B),k1_card_1(A)) & -r2_wellord2(B,A))) # label(t1_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3779 (all A all B (r2_hidden(A,k1_classes1(B)) -> r2_hidden(k1_card_1(A),k1_classes1(B)))) # label(t13_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3780 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & v1_classes2(A) -> m1_subset_1(k6_classes2(A,B,C),A))) # label(dt_k6_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3781 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & v1_classes2(A) & -v1_xboole_0(A) -> B = k7_classes2(A,B,B))) # label(idempotence_k7_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3782 (all A (-v1_xboole_0(A) & v1_classes2(A) -> v1_ordinal1(k2_ordinal2(A)) & v3_ordinal1(k2_ordinal2(A)) & v2_ordinal1(k2_ordinal2(A)))) # label(fc2_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3783 (all A (v3_ordinal1(A) -> (all B (B = k16_classes2(A) <-> (exists C (v1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> k15_classes2(k3_card_3(k2_ordinal1(C,D))) = k1_funct_1(C,D) | D = k1_xboole_0))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = k1_classes1(k1_funct_1(C,D))))) & k1_funct_1(C,k1_xboole_0) = k13_classes2 & k1_relat_1(C) = k1_ordinal1(A) & k1_ordinal2(C) = B & v5_ordinal1(C) & v1_funct_1(C))))))) # label(d5_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3784 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & v1_classes2(A) -> m1_subset_1(k7_classes2(A,B,C),A))) # label(dt_k7_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3785 (all A all B -(-r2_hidden(A,k4_classes1(k1_card_1(k1_classes1(B)))) & -r2_wellord2(A,k4_classes1(k1_card_1(k1_classes1(B)))) & r1_tarski(A,k4_classes1(k1_card_1(k1_classes1(B)))))) # label(t38_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3786 $T # label(t73_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3787 (all A all B all C (v1_classes2(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k2_tarski(B,C) = k5_classes2(A,B,C))) # label(redefinition_k5_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3788 (all A (v2_classes1(A) & v1_ordinal1(A) -> v1_classes2(A))) # label(cc3_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3789 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> m1_subset_1(k5_classes2(A,B,C),A))) # label(dt_k5_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3790 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (v1_classes2(B) & -v1_xboole_0(B) -> -v1_xboole_0(k2_xboole_0(A,B)) & -v1_xboole_0(k3_xboole_0(A,B)) & v1_classes2(k3_xboole_0(A,B)) & v1_classes2(k2_xboole_0(A,B)))))) # label(t61_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3791 (all A all B (r2_hidden(B,A) & v2_classes1(A) -> r2_hidden(k1_card_1(B),A))) # label(t12_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3792 (all A (v1_classes2(A) & -v1_xboole_0(A) -> r2_hidden(k1_xboole_0,A))) # label(t62_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3793 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & v1_classes2(A) -> k5_xboole_0(B,C) = k10_classes2(A,B,C))) # label(redefinition_k10_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3794 (all A (-v1_xboole_0(k15_classes2(A)) & v1_classes2(k15_classes2(A)))) # label(dt_k15_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3795 (all A (v2_classes1(A) -> k1_card_1(A) != np__0 & v4_ordinal1(k1_card_1(A)) & k1_xboole_0 != k1_card_1(A) | k1_xboole_0 = A)) # label(t21_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3796 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) & v1_classes2(A) -> k4_classes2(A,B) = k1_setfam_1(B))) # label(redefinition_k4_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3797 (all A (v1_classes2(A) & -v1_xboole_0(A) -> r1_tarski(k13_classes2,A) & r1_tarski(k1_classes1(k1_xboole_0),A) & r1_tarski(k16_classes2(k1_xboole_0),A))) # label(t79_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3798 (all A (v2_classes1(A) & v1_ordinal1(A) -> k4_classes1(k1_card_1(A)) = A)) # label(t32_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3799 (all A all B all C (v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k4_tarski(B,C) = k6_classes2(A,B,C))) # label(redefinition_k6_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3800 $T # label(t2_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3801 (all A (v2_classes1(A) -> k1_card_1(A) = k1_card_1(k4_classes1(k1_card_1(A))))) # label(t35_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3802 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (-v1_xboole_0(B) & v1_classes2(B) -> r1_tarski(A,B) | r2_hidden(B,A))))) # label(t57_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3803 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> m1_subset_1(k11_classes2(A,B,C),A))) # label(dt_k11_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3804 (all A all B (v2_classes1(A) & r2_hidden(B,A) & v1_ordinal1(A) -> r2_hidden(k6_classes1(B),A))) # label(t30_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3805 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (v1_classes2(B) & -v1_xboole_0(B) -> r3_xboole_0(A,B))))) # label(t58_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3806 (all A all B all C (-v1_xboole_0(C) & v1_classes2(C) -> (r2_hidden(B,C) & r2_hidden(A,C) -> r2_hidden(k2_zfmisc_1(A,B),C) & r2_hidden(k1_funct_2(A,B),C)))) # label(t67_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3807 $T # label(t72_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3808 (all A all B (v1_classes1(A) & v1_ordinal1(B) & r2_hidden(B,A) -> r1_tarski(B,A))) # label(t8_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3809 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & v1_classes2(A) & -v1_xboole_0(A) -> k8_classes2(A,B,B) = B)) # label(idempotence_k8_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3810 (exists A (v1_classes1(A) & v1_classes2(A) & v2_classes1(A) & -v1_xboole_0(A) & v1_ordinal1(A))) # label(rc1_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3811 (all A all B (r2_hidden(B,k1_card_1(A)) & v2_classes1(A) -> r2_hidden(B,A))) # label(t14_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3812 (all A (k1_card_1(k1_classes1(A)) != np__0 & k1_card_1(k1_classes1(A)) != k1_xboole_0 & v4_ordinal1(k1_card_1(k1_classes1(A))))) # label(t22_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3813 (all A all B (-v1_xboole_0(B) & v1_classes2(B) -> (r2_hidden(A,B) -> r2_hidden(k3_tarski(A),B) & r2_hidden(k1_setfam_1(A),B) & r2_hidden(k1_zfmisc_1(A),B)))) # label(t65_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3814 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> k9_classes2(A,B,C) = k4_xboole_0(B,C))) # label(redefinition_k9_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3815 (all A (v3_ordinal1(A) -> (all B (v2_classes1(B) & r2_hidden(A,k2_ordinal2(B)) -> r2_hidden(k1_card_1(k4_classes1(A)),k1_card_1(B)) & r2_hidden(k4_classes1(A),B))))) # label(t26_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3816 (all A all B all C (v1_classes2(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k8_classes2(A,B,C) = k8_classes2(A,C,B))) # label(commutativity_k8_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3817 (all A (v2_classes1(A) -> k1_card_1(A) = k2_ordinal2(A))) # label(t10_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3818 (all A (v1_ordinal1(A) -> k4_classes1(k1_card_1(k1_classes1(A))) = k1_classes1(A))) # label(t46_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3819 (all A all B (v2_classes1(A) -> r1_tarski(k1_funct_2(B,A),A) | -(r2_hidden(B,A) & v1_ordinal1(A)) & -(r2_hidden(B,A) & r1_tarski(B,A)) & -(r1_tarski(B,A) & r2_hidden(k1_card_1(B),k1_card_1(A))))) # label(t23_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3820 (all A all B (-v1_xboole_0(B) & v1_classes2(B) -> (r2_hidden(A,B) -> r2_hidden(k1_tarski(A),B)))) # label(t63_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3821 (all A (v1_card_1(A) -> (all B (r2_hidden(A,B) & v2_classes1(B) -> r1_tarski(A,B))))) # label(t18_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3822 (all A (v3_ordinal1(A) -> v1_ordinal1(k4_classes1(A)))) # label(fc7_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3823 $T # label(t47_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3824 (all A all B (r2_hidden(A,k1_classes1(B)) & v1_ordinal1(A) -> r2_hidden(A,k4_classes1(k1_card_1(k1_classes1(B)))))) # label(t44_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3825 (all A (v3_ordinal1(A) -> v1_classes1(k16_classes2(A)) & v2_classes1(k16_classes2(A)) & v1_classes2(k16_classes2(A)) & -v1_xboole_0(k16_classes2(A)) & v1_ordinal1(k16_classes2(A)))) # label(fc8_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3826 (all A (v3_ordinal1(A) -> (all B (r2_hidden(A,k2_ordinal2(k1_classes1(B))) -> r1_tarski(k1_card_1(k4_classes1(A)),k1_card_1(k1_classes1(B))))))) # label(t34_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3827 (all A all B (v1_classes2(A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k1_classes2(A,B) = k1_tarski(B))) # label(redefinition_k1_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3828 (all A all B -(v2_classes1(A) & -r2_hidden(B,k4_classes1(k1_card_1(A))) & -r2_wellord2(B,k4_classes1(k1_card_1(A))) & r1_tarski(B,k4_classes1(k1_card_1(A))))) # label(t37_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3829 (all A (v2_classes1(A) -> v1_classes1(A))) # label(cc1_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3830 (all A (v1_ordinal1(A) -> v1_classes2(k1_classes1(A)))) # label(t51_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3831 (all A (v1_classes2(A) -> v1_ordinal1(A) & v1_classes1(A) & v2_classes1(A))) # label(cc2_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3832 (all A k2_ordinal2(k1_classes1(A)) = k1_card_1(k1_classes1(A))) # label(t11_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3833 (all A k1_card_1(k4_classes1(k1_card_1(k1_classes1(A)))) = k1_card_1(k1_classes1(A))) # label(t36_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3834 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> k7_classes2(A,B,C) = k2_xboole_0(B,C))) # label(redefinition_k7_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3835 (all A all B all C (v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k10_classes2(A,C,B) = k10_classes2(A,B,C))) # label(commutativity_k10_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3836 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (k16_classes2(A) = k16_classes2(B) -> A = B))))) # label(t81_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3837 (all A all B (r2_hidden(A,k1_card_1(k1_classes1(B))) -> r2_hidden(A,k1_classes1(B)))) # label(t15_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3838 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r1_tarski(k16_classes2(A),k16_classes2(B)) <-> r1_ordinal1(A,B)))))) # label(t82_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3839 (all A all B all C (-v1_xboole_0(C) & v1_classes2(C) -> (r2_hidden(A,C) & r2_hidden(B,C) -> r2_hidden(k3_xboole_0(A,B),C) & r2_hidden(k4_xboole_0(A,B),C) & r2_hidden(k5_xboole_0(A,B),C) & r2_hidden(k2_xboole_0(A,B),C)))) # label(t66_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3840 (all A (v3_ordinal1(A) -> (all B (r2_hidden(A,k1_classes1(B)) -> r1_tarski(A,k1_classes1(B)) & r2_hidden(k1_ordinal1(A),k1_classes1(B)))))) # label(t7_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3841 (all A (v1_ordinal1(A) -> r1_classes1(A,k4_classes1(k1_card_1(k1_classes1(A)))))) # label(t45_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3842 (all A all B (-(-(r1_tarski(A,k1_classes1(B)) & r2_hidden(A,k1_classes1(B))) & -(r1_tarski(A,k1_classes1(B)) & r2_hidden(k1_card_1(A),k1_card_1(k1_classes1(B)))) & -(r2_hidden(A,k1_classes1(B)) & v1_ordinal1(B))) -> r1_tarski(k1_funct_2(A,k1_classes1(B)),k1_classes1(B)))) # label(t24_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3843 (all A (v1_ordinal1(A) & v2_classes1(A) <-> v1_classes2(A))) # label(d1_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3844 (all A all B (v1_classes2(A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> m1_subset_1(k2_classes2(A,B),A) & -v1_xboole_0(k2_classes2(A,B)))) # label(dt_k2_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3845 (all A all B all C (v1_classes2(C) & -v1_xboole_0(C) -> (r2_hidden(B,C) & r2_hidden(A,C) -> r2_hidden(k4_tarski(A,B),C) & r2_hidden(k2_tarski(A,B),C)))) # label(t64_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3846 $T # label(t74_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3847 (all A (-v1_xboole_0(A) & v1_classes2(A) -> k4_classes1(k2_ordinal2(A)) = A)) # label(t54_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3848 (all A (v1_card_1(A) -> (all B (r2_hidden(A,k1_classes1(B)) -> r1_tarski(A,k1_classes1(B)))))) # label(t19_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3849 $T # label(dt_k16_classes2) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3850 (all A (m1_subset_1(A,k5_numbers) -> (exists B m1_qc_lang1(B,A)))) # label(existence_m1_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3851 (all A (m1_subset_1(A,k5_numbers) -> -v1_xboole_0(k7_qc_lang1(A)))) # label(fc6_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3852 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k7_finseq_1(k7_finseq_1(k9_finseq_1(k4_tarski(np__2,np__0)),k10_qc_lang1(A)),k10_qc_lang1(B)) = k13_qc_lang1(A,B))))) # label(d15_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3853 $T # label(dt_k1_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3854 $T # label(t32_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3855 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang1(A) -> (all B (m2_finseq_1(B,k1_qc_lang1) -> (k16_qc_lang1(A) = B <-> (exists C ((exists D (m2_subset_1(D,k5_qc_lang1,k7_qc_lang1(C)) & (exists E (B = E & k9_qc_lang1(D,E) = A & m1_qc_lang1(E,C))))) & m2_subset_1(C,k1_numbers,k5_numbers))))))))) # label(d22_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3856 $T # label(t29_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3857 $T # label(t30_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3858 (all A (m1_subset_1(A,k5_qc_lang1) -> (all B (m2_finseq_1(B,k1_qc_lang1) -> (k3_finseq_1(B) = k6_qc_lang1(A) -> k9_qc_lang1(A,B) = k7_finseq_1(k12_finseq_1(k5_qc_lang1,A),B)))))) # label(d11_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3859 (all A (-v1_xboole_0(A) -> (all B all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> r1_tarski(k2_zfmisc_1(k1_enumset1(C,D,E),B),k2_zfmisc_1(A,B)))))))))) # label(t2_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.53 3860 $T # label(t25_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.54 3861 (all A (m1_subset_1(A,k8_qc_lang1) -> m2_subset_1(k20_qc_lang1(A),k1_qc_lang1,k2_qc_lang1))) # label(dt_k20_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.54 3862 (all A (m1_subset_1(A,k8_qc_lang1) -> -(r1_xreal_0(k3_finseq_1(k10_qc_lang1(A)),k3_finseq_1(k10_qc_lang1(k17_qc_lang1(A)))) & v3_qc_lang1(A)))) # label(t45_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.54 3863 (all A (m1_subset_1(A,k8_qc_lang1) -> (v5_qc_lang1(A) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> ((exists C (m1_subset_1(C,k8_qc_lang1) & k14_qc_lang1(B,C) = A)) <-> k20_qc_lang1(A) = B)))))) # label(d26_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.54 3864 $T # label(t38_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.54 3865 (all A (m2_finseq_1(A,k1_qc_lang1) -> a_1_1_qc_lang1(A) = k22_qc_lang1(A))) # label(d28_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.54 3866 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (k18_qc_lang1(A) = B <-> (exists C (k13_qc_lang1(B,C) = A & m1_subset_1(C,k8_qc_lang1))))))))) # label(d24_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.54 3867 (all A all B (m2_finseq_1(B,k1_qc_lang1) -> (r2_hidden(A,a_1_1_qc_lang1(B)) <-> (exists C (r1_xreal_0(C,k3_finseq_1(B)) & r2_hidden(k1_funct_1(B,C),k2_qc_lang1) & r1_xreal_0(np__1,C) & A = k1_funct_1(B,C) & m2_subset_1(C,k1_numbers,k5_numbers)))))) # label(fraenkel_a_1_1_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.54 3868 $T # label(t40_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.54 3869 $T # label(dt_k5_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.54 3870 $T # label(t42_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.54 3871 (all A (m1_subset_1(A,k2_qc_lang1) -> k1_tarski(A) = k23_qc_lang1(A))) # label(redefinition_k23_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.54 3872 $T # label(t28_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.54 3873 $T # label(t44_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.54 3874 (all A all B (m1_finseq_1(B,k1_qc_lang1) & m1_subset_1(A,k5_qc_lang1) -> m1_subset_1(k9_qc_lang1(A,B),k8_qc_lang1))) # label(dt_k9_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.54 3875 (all A (m1_subset_1(A,k8_qc_lang1) -> m2_finseq_1(k16_qc_lang1(A),k1_qc_lang1))) # label(dt_k16_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.54 3876 $T # label(t8_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.54 3877 $T # label(t18_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.54 3878 (all A (m1_subset_1(A,k1_zfmisc_1(k13_finseq_1(k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)))) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(B)) -> (all D (m1_qc_lang1(D,B) -> r2_hidden(k7_finseq_1(k12_finseq_1(k7_qc_lang1(B),C),D),A))))))) & (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_finseq_1(C,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) -> (r2_hidden(C,A) -> r2_hidden(k7_finseq_1(k7_finseq_1(k9_finseq_1(k4_tarski(np__3,np__0)),k12_finseq_1(k2_qc_lang1,B)),C),A)))))) & (all B (m2_finseq_1(B,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) -> (all C (m2_finseq_1(C,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) -> (r2_hidden(C,A) & r2_hidden(B,A) -> r2_hidden(k7_finseq_1(k7_finseq_1(k9_finseq_1(k4_tarski(np__2,np__0)),B),C),A)))))) & (all B (m2_finseq_1(B,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) -> (r2_hidden(B,A) -> r2_hidden(k7_finseq_1(k9_finseq_1(k4_tarski(np__1,np__0)),B),A)))) & r2_hidden(k9_finseq_1(k4_tarski(np__0,np__0)),A) <-> v1_qc_lang1(A))) # label(d9_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.54 3879 $T # label(t15_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.54 3880 $T # label(t5_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.54 3881 $T # label(t17_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 14.93/14.54 3882 $T # label(t39_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3883 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k7_qc_lang1(A) = a_1_0_qc_lang1(A))) # label(d7_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3884 (all A (m1_subset_1(A,k8_qc_lang1) -> -(v5_qc_lang1(A) & r1_xreal_0(k3_finseq_1(k10_qc_lang1(A)),k3_finseq_1(k10_qc_lang1(k21_qc_lang1(A))))))) # label(t47_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3885 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang1(A) <-> (exists B ((exists C (m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(B)) & (exists D (A = k9_qc_lang1(C,D) & m1_qc_lang1(D,B))))) & m2_subset_1(B,k1_numbers,k5_numbers)))))) # label(d17_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3886 $T # label(t6_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3887 (all A (m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k18_qc_lang1(A),k8_qc_lang1))) # label(dt_k18_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3888 (all A (m1_finseq_1(A,k1_qc_lang1) -> m1_subset_1(k22_qc_lang1(A),k1_zfmisc_1(k2_qc_lang1)))) # label(dt_k22_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3889 (all A (m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k21_qc_lang1(A),k8_qc_lang1))) # label(dt_k21_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3890 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang1(A) -> (all B (m1_subset_1(B,k5_qc_lang1) -> ((exists C (m2_subset_1(C,k1_numbers,k5_numbers) & (exists D (m1_qc_lang1(D,C) & (exists E (k9_qc_lang1(E,D) = A & B = E & m2_subset_1(E,k5_qc_lang1,k7_qc_lang1(C)))))))) <-> k15_qc_lang1(A) = B)))))) # label(d21_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3891 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) -> (all B (m1_subset_1(B,k8_qc_lang1) -> ((exists C (m1_subset_1(C,k8_qc_lang1) & A = k13_qc_lang1(C,B))) <-> B = k19_qc_lang1(A))))))) # label(d25_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3892 p1_s1_qc_lang1(k11_qc_lang1) & (all A (m1_subset_1(A,k8_qc_lang1) -> (p1_s1_qc_lang1(A) -> p1_s1_qc_lang1(k12_qc_lang1(A))))) & (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (p1_s1_qc_lang1(A) & p1_s1_qc_lang1(B) -> p1_s1_qc_lang1(k13_qc_lang1(A,B))))))) & (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (p1_s1_qc_lang1(B) -> p1_s1_qc_lang1(k14_qc_lang1(A,B))))))) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A)) -> (all C (m1_qc_lang1(C,A) -> p1_s1_qc_lang1(k9_qc_lang1(B,C)))))))) -> (all A (m1_subset_1(A,k8_qc_lang1) -> p1_s1_qc_lang1(A))) # label(s1_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3893 (all A (m1_subset_1(A,k5_numbers) -> m1_subset_1(k7_qc_lang1(A),k1_zfmisc_1(k5_qc_lang1)))) # label(dt_k7_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3894 $T # label(t41_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3895 (all A (r2_hidden(A,a_0_0_qc_lang1) <-> (exists B exists C (m2_subset_1(B,k1_numbers,k5_numbers) & k4_tarski(B,C) = A & r1_xreal_0(np__7,B) & m2_subset_1(C,k1_numbers,k5_numbers))))) # label(fraenkel_a_0_0_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3896 (exists A (f2_s3_qc_lang1 = k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,k11_qc_lang1) & (all B (m1_subset_1(B,k8_qc_lang1) -> (v2_qc_lang1(B) -> f3_s3_qc_lang1(B) = k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,B)) & (v5_qc_lang1(B) -> k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,B) = f6_s3_qc_lang1(B,k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,k21_qc_lang1(B)))) & (v4_qc_lang1(B) -> f5_s3_qc_lang1(k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,k18_qc_lang1(B)),k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,k19_qc_lang1(B))) = k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,B)) & (v3_qc_lang1(B) -> f4_s3_qc_lang1(k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,k17_qc_lang1(B))) = k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,B)))) & m2_relset_1(A,k8_qc_lang1,f1_s3_qc_lang1) & v1_funct_2(A,k8_qc_lang1,f1_s3_qc_lang1) & v1_funct_1(A))) # label(s3_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3897 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A)) -> k6_qc_lang1(B) = A)))) # label(t35_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3898 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (k7_finseq_1(k10_qc_lang1(B),C) = k10_qc_lang1(A) -> k10_qc_lang1(B) = k10_qc_lang1(A)))))))) # label(t37_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3899 (all A all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(A,a_1_0_qc_lang1(B)) <-> (exists C (A = C & B = k6_qc_lang1(C) & m1_subset_1(C,k5_qc_lang1)))))) # label(fraenkel_a_1_0_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3900 $T # label(t14_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3901 $T # label(t11_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3902 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) -> -r1_xreal_0(k3_finseq_1(k10_qc_lang1(A)),k3_finseq_1(k10_qc_lang1(k18_qc_lang1(A)))) & -r1_xreal_0(k3_finseq_1(k10_qc_lang1(A)),k3_finseq_1(k10_qc_lang1(k19_qc_lang1(A))))))) # label(t46_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3903 (all A (-v1_xboole_0(A) -> (all B all C (m1_subset_1(C,A) -> r1_tarski(k2_zfmisc_1(k1_tarski(C),B),k2_zfmisc_1(A,B)))))) # label(t1_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3904 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k7_finseq_1(k7_finseq_1(k9_finseq_1(k4_tarski(np__3,np__0)),k12_finseq_1(k2_qc_lang1,A)),k10_qc_lang1(B)) = k14_qc_lang1(A,B))))) # label(d16_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3905 (all A (-v1_xboole_0(A) -> (v1_qc_lang1(A) & (all B (-v1_xboole_0(B) -> (v1_qc_lang1(B) -> r1_tarski(A,B)))) <-> k8_qc_lang1 = A))) # label(d10_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3906 (all A (m1_subset_1(A,k8_qc_lang1) -> -(A != k11_qc_lang1 & -v2_qc_lang1(A) & -v4_qc_lang1(A) & -v5_qc_lang1(A) & -v3_qc_lang1(A)))) # label(t33_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3907 (all A (m1_subset_1(A,k8_qc_lang1) -> (v6_qc_lang1(A) <-> k1_xboole_0 = k24_qc_lang1(A)))) # label(d30_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3908 $T # label(t3_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3909 (all A (m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k17_qc_lang1(A),k8_qc_lang1))) # label(dt_k17_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3910 $T # label(t27_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3911 (all A (m1_subset_1(A,k8_qc_lang1) -> (v3_qc_lang1(A) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (k17_qc_lang1(A) = B <-> k12_qc_lang1(B) = A)))))) # label(d23_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3912 (all A (m1_subset_1(A,k5_qc_lang1) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k1_mcart_1(A) = k1_nat_1(np__7,B) <-> B = k6_qc_lang1(A)))))) # label(d6_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3913 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A)) -> (all C (m1_qc_lang1(C,A) -> k7_finseq_1(k12_finseq_1(k7_qc_lang1(A),B),C) = k9_qc_lang1(B,C))))))) # label(t23_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3914 (all A (m1_subset_1(A,k2_qc_lang1) -> m1_subset_1(k23_qc_lang1(A),k1_zfmisc_1(k2_qc_lang1)))) # label(dt_k23_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3915 (all A (m1_subset_1(A,k8_qc_lang1) -> ((exists B (m1_subset_1(B,k8_qc_lang1) & (exists C (k13_qc_lang1(B,C) = A & m1_subset_1(C,k8_qc_lang1))))) <-> v4_qc_lang1(A)))) # label(d19_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3916 (all A (m1_subset_1(A,k5_numbers) -> (all B (m1_qc_lang1(B,A) -> m2_finseq_1(B,k1_qc_lang1))))) # label(dt_m1_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3917 $T # label(t20_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3918 (all A (m1_subset_1(A,k8_qc_lang1) -> k1_mcart_1(k1_funct_1(k10_qc_lang1(k11_qc_lang1),np__1)) = np__0 & -((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> -m2_subset_1(k1_funct_1(k10_qc_lang1(A),np__1),k5_qc_lang1,k7_qc_lang1(B)))) & v2_qc_lang1(A)) & (v3_qc_lang1(A) -> np__1 = k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1))) & (v5_qc_lang1(A) -> np__3 = k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1))) & (v4_qc_lang1(A) -> np__2 = k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1))))) # label(t49_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3919 (all A (m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k15_qc_lang1(A),k5_qc_lang1))) # label(dt_k15_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3920 $T # label(t7_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3921 (all A all B (m1_subset_1(B,k8_qc_lang1) & m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k13_qc_lang1(A,B),k8_qc_lang1))) # label(dt_k13_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3922 (all A all B (m1_subset_1(A,k2_qc_lang1) & m1_subset_1(B,k8_qc_lang1) -> m1_subset_1(k14_qc_lang1(A,B),k8_qc_lang1))) # label(dt_k14_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3923 (all A (m1_subset_1(A,k8_qc_lang1) -> (v5_qc_lang1(A) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (k21_qc_lang1(A) = B <-> (exists C (A = k14_qc_lang1(C,B) & m2_subset_1(C,k1_qc_lang1,k2_qc_lang1))))))))) # label(d27_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3924 $T # label(t19_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3925 (all A (m1_subset_1(A,k8_qc_lang1) -> k10_qc_lang1(A) = A)) # label(d12_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3926 $T # label(t12_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3927 $T # label(t24_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3928 $T # label(t26_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3929 (all A (m1_subset_1(A,k8_qc_lang1) -> k7_finseq_1(k9_finseq_1(k4_tarski(np__1,np__0)),k10_qc_lang1(A)) = k12_qc_lang1(A))) # label(d14_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3930 (all A all B (m1_subset_1(B,k8_qc_lang1) -> ((exists C (m2_subset_1(C,k1_numbers,k5_numbers) & r2_hidden(k1_funct_1(k16_qc_lang1(B),C),k2_qc_lang1) & r1_xreal_0(C,k3_finseq_1(k16_qc_lang1(B))) & r1_xreal_0(np__1,C) & k1_funct_1(k16_qc_lang1(B),C) = A)) <-> r2_hidden(A,a_1_2_qc_lang1(B))))) # label(fraenkel_a_1_2_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3931 $T # label(t16_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3932 (all A (m1_subset_1(A,k8_qc_lang1) -> (k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) = np__1 -> v3_qc_lang1(A)) & (k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) = np__3 -> v5_qc_lang1(A)) & ((exists B (m2_subset_1(B,k1_numbers,k5_numbers) & m2_subset_1(k1_funct_1(k10_qc_lang1(A),np__1),k5_qc_lang1,k7_qc_lang1(B)))) -> v2_qc_lang1(A)) & (k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) = np__2 -> v4_qc_lang1(A)) & (k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) = np__0 -> A = k11_qc_lang1))) # label(t36_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3933 (all A (m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k24_qc_lang1(A),k1_zfmisc_1(k2_qc_lang1)))) # label(dt_k24_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3934 $T # label(t9_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3935 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang1(A) -> k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) != np__0 & np__1 != k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) & np__3 != k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) & np__2 != k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1))))) # label(t50_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3936 (all A (m1_subset_1(A,k8_qc_lang1) -> m2_finseq_1(k10_qc_lang1(A),k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)))) # label(dt_k10_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3937 (all A (m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k19_qc_lang1(A),k8_qc_lang1))) # label(dt_k19_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3938 (all A (m1_subset_1(A,k8_qc_lang1) -> (v3_qc_lang1(A) <-> (exists B (k12_qc_lang1(B) = A & m1_subset_1(B,k8_qc_lang1)))))) # label(d18_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3939 $T # label(t31_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3940 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k1_zfmisc_1(k2_qc_lang1)) -> ((exists C (v1_funct_2(C,k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1)) & m2_relset_1(C,k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1)) & (all D (m1_subset_1(D,k8_qc_lang1) -> k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,k11_qc_lang1) = k1_xboole_0 & (v5_qc_lang1(D) -> k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,D) = k6_subset_1(k2_qc_lang1,k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,k21_qc_lang1(D)),k23_qc_lang1(k20_qc_lang1(D)))) & (v4_qc_lang1(D) -> k4_subset_1(k2_qc_lang1,k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,k18_qc_lang1(D)),k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,k19_qc_lang1(D))) = k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,D)) & (v3_qc_lang1(D) -> k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,D) = k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,k17_qc_lang1(D))) & (v2_qc_lang1(D) -> k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,D) = a_1_2_qc_lang1(D)))) & B = k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,A) & v1_funct_1(C))) <-> k24_qc_lang1(A) = B))))) # label(d29_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3941 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_finseq_1(B,k1_qc_lang1) -> (m1_qc_lang1(B,A) <-> A = k3_finseq_1(B)))))) # label(d8_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3942 (all A (m1_subset_1(A,k8_qc_lang1) -> r1_xreal_0(np__1,k3_finseq_1(k10_qc_lang1(A))))) # label(t34_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3943 (all A (m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k12_qc_lang1(A),k8_qc_lang1))) # label(dt_k12_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3944 (all A (m1_subset_1(A,k8_qc_lang1) -> (v5_qc_lang1(A) <-> (exists B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) & (exists C (A = k14_qc_lang1(B,C) & m1_subset_1(C,k8_qc_lang1)))))))) # label(d20_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3945 (all A (m1_subset_1(A,k5_qc_lang1) -> m2_subset_1(k6_qc_lang1(A),k1_numbers,k5_numbers))) # label(dt_k6_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3946 $T # label(t43_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3947 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang1(A) -> p1_s2_qc_lang1(A)) & (v5_qc_lang1(A) & p1_s2_qc_lang1(k21_qc_lang1(A)) -> p1_s2_qc_lang1(A)) & (p1_s2_qc_lang1(k19_qc_lang1(A)) & p1_s2_qc_lang1(k18_qc_lang1(A)) & v4_qc_lang1(A) -> p1_s2_qc_lang1(A)) & (p1_s2_qc_lang1(k17_qc_lang1(A)) & v3_qc_lang1(A) -> p1_s2_qc_lang1(A)) & p1_s2_qc_lang1(k11_qc_lang1))) -> (all A (m1_subset_1(A,k8_qc_lang1) -> p1_s2_qc_lang1(A))) # label(s2_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3948 $T # label(t22_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3949 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A)) -> np__0 != k1_mcart_1(B) & k1_mcart_1(B) != np__1 & np__3 != k1_mcart_1(B) & k1_mcart_1(B) != np__2)))) # label(t48_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3950 $T # label(t13_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3951 (all A (m1_subset_1(A,k8_qc_lang1) -> -(v2_qc_lang1(A) & v4_qc_lang1(A)) & -(v3_qc_lang1(A) & v4_qc_lang1(A)) & -(v5_qc_lang1(A) & v3_qc_lang1(A)) & -(v4_qc_lang1(A) & v5_qc_lang1(A)) & -(v5_qc_lang1(A) & v2_qc_lang1(A)) & -(v2_qc_lang1(A) & v3_qc_lang1(A)))) # label(t51_qc_lang1_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3952 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (r2_qc_lang2(A,B) <-> r3_qc_lang2(A,k14_qc_lang1(C,B))))))))) # label(t91_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3953 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k12_qc_lang1(k13_qc_lang1(k12_qc_lang1(A),k12_qc_lang1(B))) = k3_qc_lang2(A,B))))) # label(d3_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3954 (all A (m1_subset_1(A,k8_qc_lang1) -> (r2_qc_lang2(A,k1_qc_lang2) <-> A = k11_qc_lang1 | A = k1_qc_lang2))) # label(t101_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3955 (all A (m1_subset_1(A,k8_qc_lang1) -> (v5_qc_lang1(A) -> k2_xboole_0(k15_qc_lang2(k21_qc_lang1(A)),k1_tarski(A)) = k15_qc_lang2(A)))) # label(t119_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3956 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) -> k2_xboole_0(k2_xboole_0(k15_qc_lang2(k18_qc_lang1(A)),k15_qc_lang2(k19_qc_lang1(A))),k1_tarski(A)) = k15_qc_lang2(A)))) # label(t118_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3957 (all A all B all C (m1_subset_1(A,k2_qc_lang1) & m1_subset_1(C,k8_qc_lang1) & m1_subset_1(B,k2_qc_lang1) -> m1_subset_1(k6_qc_lang2(A,B,C),k8_qc_lang1))) # label(dt_k6_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3958 $T # label(t70_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3959 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k12_qc_lang1(k13_qc_lang1(A,k12_qc_lang1(B))) = k2_qc_lang2(A,B))))) # label(d2_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3960 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (all E (m1_subset_1(E,k8_qc_lang1) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (k14_qc_lang1(F,E) = k8_qc_lang2(A,B,C,D) -> E = k6_qc_lang2(B,C,D) & A = F))))))))))))) # label(t28_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3961 $T # label(t41_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3962 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> r3_qc_lang2(k12_qc_lang1(B),k2_qc_lang2(A,B)) & r3_qc_lang2(B,k2_qc_lang2(A,B)) & r3_qc_lang2(A,k2_qc_lang2(A,B)) & r3_qc_lang2(k13_qc_lang1(A,k12_qc_lang1(B)),k2_qc_lang2(A,B)))))) # label(t93_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3963 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r2_qc_lang2(A,B) -> r1_tarski(k15_qc_lang2(A),k15_qc_lang2(B))))))) # label(t104_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3964 (all A all B all C all D (m1_subset_1(A,k2_qc_lang1) & m1_subset_1(B,k2_qc_lang1) & m1_subset_1(D,k8_qc_lang1) & m1_subset_1(C,k2_qc_lang1) -> m1_subset_1(k9_qc_lang2(A,B,C,D),k8_qc_lang1))) # label(dt_k9_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3965 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v5_qc_lang1(A) -> (r1_qc_lang2(B,A) <-> B = k21_qc_lang1(A))))))) # label(t67_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3966 $T # label(t37_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3967 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r2_hidden(A,k15_qc_lang2(B)) -> r2_qc_lang2(A,B)))))) # label(t103_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3968 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (r2_hidden(B,k15_qc_lang2(C)) -> r2_hidden(A,k15_qc_lang2(C)) | -r1_qc_lang2(A,B) & -r3_qc_lang2(A,B) & -r2_qc_lang2(A,B)))))))) # label(t120_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3969 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r2_qc_lang2(A,B) <-> (exists C ((exists D (k3_finseq_1(D) = C & B = k1_funct_1(D,C) & (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> -(-r1_xreal_0(C,E) & (all F (m1_subset_1(F,k8_qc_lang1) -> (all G (m1_subset_1(G,k8_qc_lang1) -> -(k1_funct_1(D,E) = F & k1_funct_1(D,k1_nat_1(E,np__1)) = G & r1_qc_lang2(F,G)))))) & r1_xreal_0(np__1,E)))) & A = k1_funct_1(D,np__1) & r1_xreal_0(np__1,C) & v1_finseq_1(D) & v1_funct_1(D) & v1_relat_1(D))) & m2_subset_1(C,k1_numbers,k5_numbers)))))))) # label(d21_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3970 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m2_subset_1(D,k1_qc_lang1,k2_qc_lang1) -> (all E (m2_subset_1(E,k1_qc_lang1,k2_qc_lang1) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_qc_lang1,k2_qc_lang1) -> (all H (m2_subset_1(H,k1_qc_lang1,k2_qc_lang1) -> (k9_qc_lang2(D,F,H,B) = k9_qc_lang2(C,E,G,A) -> D = C & G = H & A = B & F = E))))))))))))))))) # label(t30_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3971 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (r3_qc_lang2(B,C) & r3_qc_lang2(A,B) -> r3_qc_lang2(A,C)))))))) # label(t76_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3972 $T # label(t15_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3973 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r2_hidden(A,k15_qc_lang2(B)) -> r1_tarski(k15_qc_lang2(A),k15_qc_lang2(B))))))) # label(t105_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3974 (all A (m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k12_qc_lang2(A),k8_qc_lang1))) # label(dt_k12_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3975 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> k14_qc_lang1(A,k6_qc_lang2(B,C,D)) = k8_qc_lang2(A,B,C,D))))))))) # label(d8_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3976 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> r3_qc_lang2(k13_qc_lang1(k12_qc_lang1(A),k12_qc_lang1(B)),k3_qc_lang2(A,B)) & r3_qc_lang2(k12_qc_lang1(A),k3_qc_lang2(A,B)) & r3_qc_lang2(B,k3_qc_lang2(A,B)) & r3_qc_lang2(A,k3_qc_lang2(A,B)) & r3_qc_lang2(k12_qc_lang1(B),k3_qc_lang2(A,B)))))) # label(t94_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3977 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang2(A) -> k5_qc_lang2(k20_qc_lang1(k17_qc_lang1(A)),k17_qc_lang1(k21_qc_lang1(k17_qc_lang1(A)))) = A))) # label(t56_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3978 $T # label(d17_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3979 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (k2_qc_lang2(C,D) = k2_qc_lang2(A,B) -> C = A & B = D))))))))) # label(t17_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3980 (all A (m1_subset_1(A,k8_qc_lang1) -> (v3_qc_lang2(A) -> v2_qc_lang2(k19_qc_lang1(A)) & v2_qc_lang2(k18_qc_lang1(A)) & v4_qc_lang1(A)))) # label(t51_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3981 (all A (m1_subset_1(A,k8_qc_lang1) -> -r3_qc_lang2(A,k11_qc_lang1))) # label(t84_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3982 $T # label(t102_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3983 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r3_qc_lang2(A,B) & r1_xreal_0(k3_finseq_1(k10_qc_lang1(B)),k3_finseq_1(k10_qc_lang1(A)))))))) # label(t74_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3984 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r2_qc_lang2(k12_qc_lang1(A),B) -> r3_qc_lang2(A,B)))))) # label(t87_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3985 (all A (m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k11_qc_lang2(A),k8_qc_lang1))) # label(dt_k11_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3986 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (k12_qc_lang1(B) = k12_qc_lang1(A) -> A = B))))) # label(t1_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3987 (all A (m1_subset_1(A,k8_qc_lang1) -> k13_qc_lang2(A) = k12_qc_lang2(k18_qc_lang1(A)))) # label(d18_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3988 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> k9_qc_lang2(A,B,C,D) = k5_qc_lang2(A,k7_qc_lang2(B,C,D)) & k14_qc_lang1(A,k6_qc_lang2(B,C,D)) = k8_qc_lang2(A,B,C,D))))))))) # label(t26_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3989 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (r2_qc_lang2(k13_qc_lang1(A,B),C) -> r3_qc_lang2(A,C) & r3_qc_lang2(B,C)))))))) # label(t90_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3990 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (all E (m1_subset_1(E,k8_qc_lang1) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (k9_qc_lang2(A,B,C,D) = k5_qc_lang2(F,E) -> E = k7_qc_lang2(B,C,D) & A = F))))))))))))) # label(t31_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3991 $T # label(t40_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3992 (all A all B all C (m1_subset_1(A,k2_qc_lang1) & m1_subset_1(C,k8_qc_lang1) & m1_subset_1(B,k2_qc_lang1) -> m1_subset_1(k7_qc_lang2(A,B,C),k8_qc_lang1))) # label(dt_k7_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3993 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r1_qc_lang2(A,B) & r1_xreal_0(k3_finseq_1(k10_qc_lang1(B)),k3_finseq_1(k10_qc_lang1(A)))))))) # label(t71_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3994 $T # label(t44_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3995 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r2_qc_lang2(A,B) & B != A <-> r3_qc_lang2(A,B)))))) # label(d22_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3996 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang2(A) <-> (exists B ((exists C (m1_subset_1(C,k8_qc_lang1) & k2_qc_lang2(B,C) = A)) & m1_subset_1(B,k8_qc_lang1)))))) # label(d11_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3997 (all A (m1_subset_1(A,k8_qc_lang1) -> (A = k11_qc_lang1 <-> r1_qc_lang2(A,k1_qc_lang2)))) # label(t61_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3998 $T # label(t39_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 3999 (all A (m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k13_qc_lang2(A),k8_qc_lang1))) # label(dt_k13_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4000 (all A all B (m1_subset_1(A,k8_qc_lang1) & m1_subset_1(B,k8_qc_lang1) -> m1_subset_1(k4_qc_lang2(A,B),k8_qc_lang1))) # label(dt_k4_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4001 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r1_qc_lang2(A,B) <-> -(k12_qc_lang1(A) != B & (all C (m1_subset_1(C,k8_qc_lang1) -> k13_qc_lang1(C,A) != B & B != k13_qc_lang1(A,C))) & (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> k14_qc_lang1(C,A) != B)))))))) # label(d20_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4002 $T # label(t68_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4003 $T # label(t36_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4004 $T # label(t42_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4005 $T # label(t9_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4006 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m2_subset_1(D,k1_qc_lang1,k2_qc_lang1) -> (all E (m2_subset_1(E,k1_qc_lang1,k2_qc_lang1) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_qc_lang1,k2_qc_lang1) -> (all H (m2_subset_1(H,k1_qc_lang1,k2_qc_lang1) -> (k8_qc_lang2(C,E,G,A) = k8_qc_lang2(D,F,H,B) -> C = D & E = F & B = A & G = H))))))))))))))))) # label(t27_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4007 $T # label(t35_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4008 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> A = k13_qc_lang2(k4_qc_lang2(A,B)) & B = k14_qc_lang2(k4_qc_lang2(A,B)) & k2_qc_lang2(A,B) = k18_qc_lang1(k4_qc_lang2(A,B)) & k19_qc_lang1(k4_qc_lang2(A,B)) = k2_qc_lang2(B,A))))) # label(t47_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4009 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (r1_qc_lang2(A,k14_qc_lang1(C,B)) <-> A = B))))))) # label(t63_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4010 (all A all B (m1_subset_1(A,k8_qc_lang1) & m1_subset_1(B,k8_qc_lang1) -> m1_subset_1(k2_qc_lang2(A,B),k8_qc_lang1))) # label(dt_k2_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4011 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k12_qc_lang1(k14_qc_lang1(A,k12_qc_lang1(B))) = k5_qc_lang2(A,B))))) # label(d5_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4012 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> k7_qc_lang2(A,B,C) = k5_qc_lang2(A,k5_qc_lang2(B,C)))))))) # label(d7_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4013 $T # label(t11_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4014 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (k5_qc_lang2(B,D) = k5_qc_lang2(A,C) -> C = D & A = B))))))))) # label(t19_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4015 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (k3_qc_lang2(C,D) = k3_qc_lang2(A,B) -> C = A & D = B))))))))) # label(t16_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4016 (all A (m1_subset_1(A,k8_qc_lang1) -> (k11_qc_lang1 = A | v2_qc_lang1(A) <-> k1_tarski(A) = k15_qc_lang2(A)))) # label(t116_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4017 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> k14_qc_lang1(A,k14_qc_lang1(B,C)) = k6_qc_lang2(A,B,C) & k5_qc_lang2(A,k5_qc_lang2(B,C)) = k7_qc_lang2(A,B,C))))))) # label(t20_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4018 (all A (m1_subset_1(A,k8_qc_lang1) -> k14_qc_lang2(A) = k11_qc_lang2(k18_qc_lang1(A)))) # label(d19_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4019 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> v5_qc_lang1(k8_qc_lang2(A,B,C,D)) & A = k20_qc_lang1(k8_qc_lang2(A,B,C,D)) & k21_qc_lang1(k8_qc_lang2(A,B,C,D)) = k6_qc_lang2(B,C,D))))))))) # label(t33_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4020 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(B)) -> (all D (m1_qc_lang1(D,B) -> (r2_qc_lang2(A,k9_qc_lang1(C,D)) <-> A = k9_qc_lang1(C,D)))))))))) # label(t100_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4021 (all A (m1_subset_1(A,k8_qc_lang1) -> k17_qc_lang1(k18_qc_lang1(k17_qc_lang1(A))) = k10_qc_lang2(A))) # label(d14_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4022 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r1_qc_lang2(A,B) -> r3_qc_lang2(A,B)))))) # label(t73_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4023 (all A (m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k10_qc_lang2(A),k8_qc_lang1))) # label(dt_k10_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4024 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) -> A = k13_qc_lang1(k18_qc_lang1(A),k19_qc_lang1(A))))) # label(t4_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4025 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v3_qc_lang1(A) -> (k17_qc_lang1(A) = B <-> r1_qc_lang2(B,A))))))) # label(t65_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4026 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r1_qc_lang2(B,A) & r3_qc_lang2(A,B)))))) # label(t82_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4027 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k17_qc_lang1(k5_qc_lang2(A,B)) = k14_qc_lang1(A,k12_qc_lang1(B)))))) # label(t48_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4028 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k13_qc_lang1(k2_qc_lang2(A,B),k2_qc_lang2(B,A)) = k4_qc_lang2(A,B))))) # label(d4_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4029 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (all E (m1_subset_1(E,k8_qc_lang1) -> (k6_qc_lang2(A,B,D) = k14_qc_lang1(C,E) -> A = C & k14_qc_lang1(B,D) = E))))))))))) # label(t22_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4030 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (all E (m1_subset_1(E,k8_qc_lang1) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_qc_lang1,k2_qc_lang1) -> (k9_qc_lang2(A,B,C,D) = k7_qc_lang2(F,G,E) -> F = A & E = k5_qc_lang2(C,D) & B = G))))))))))))))) # label(t32_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4031 (all A all B all C all D (m1_subset_1(C,k2_qc_lang1) & m1_subset_1(D,k8_qc_lang1) & m1_subset_1(B,k2_qc_lang1) & m1_subset_1(A,k2_qc_lang1) -> m1_subset_1(k8_qc_lang2(A,B,C,D),k8_qc_lang1))) # label(dt_k8_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4032 (all A (m1_subset_1(A,k8_qc_lang1) -> (v3_qc_lang2(A) -> A = k4_qc_lang2(k13_qc_lang2(A),k14_qc_lang2(A))))) # label(t55_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4033 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k12_qc_lang2(k2_qc_lang2(A,B)) = A & B = k11_qc_lang2(k2_qc_lang2(A,B)) & k13_qc_lang1(A,k12_qc_lang1(B)) = k17_qc_lang1(k2_qc_lang2(A,B)))))) # label(t46_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4034 $T # label(dt_k15_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4035 (all A (m1_subset_1(A,k8_qc_lang1) -> (v3_qc_lang1(A) -> r3_qc_lang2(k17_qc_lang1(A),A)))) # label(t96_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4036 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> v5_qc_lang1(k6_qc_lang2(A,B,C)) & k21_qc_lang1(k6_qc_lang2(A,B,C)) = k14_qc_lang1(B,C) & A = k20_qc_lang1(k6_qc_lang2(A,B,C)))))))) # label(t25_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4037 (all A (m1_subset_1(A,k8_qc_lang1) -> k11_qc_lang2(A) = k17_qc_lang1(k19_qc_lang1(k17_qc_lang1(A))))) # label(d15_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4038 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (all E (m1_subset_1(E,k8_qc_lang1) -> (k7_qc_lang2(A,B,D) = k5_qc_lang2(C,E) -> k5_qc_lang2(B,D) = E & C = A))))))))))) # label(t24_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4039 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r1_qc_lang2(A,B) -> r2_qc_lang2(A,B)))))) # label(t72_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4040 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m2_subset_1(D,k1_qc_lang1,k2_qc_lang1) -> (all E (m2_subset_1(E,k1_qc_lang1,k2_qc_lang1) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (k7_qc_lang2(D,F,B) = k7_qc_lang2(C,E,A) -> C = D & B = A & E = F))))))))))))) # label(t23_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4041 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k2_qc_lang2(k12_qc_lang1(A),B) = k3_qc_lang2(A,B))))) # label(t14_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4042 (all A (m1_subset_1(A,k8_qc_lang1) -> (v5_qc_lang1(A) -> r3_qc_lang2(k21_qc_lang1(A),A)))) # label(t98_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4043 (all A all B (m1_subset_1(B,k8_qc_lang1) & m1_subset_1(A,k2_qc_lang1) -> m1_subset_1(k5_qc_lang2(A,B),k8_qc_lang1))) # label(dt_k5_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4044 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (r2_qc_lang2(A,C) | r2_qc_lang2(A,B) <-> r3_qc_lang2(A,k13_qc_lang1(B,C))))))))) # label(t89_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4045 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A)) -> (all C (m1_qc_lang1(C,A) -> k1_tarski(k9_qc_lang1(B,C)) = k15_qc_lang2(k9_qc_lang1(B,C)))))))) # label(t108_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4046 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k15_qc_lang2(k13_qc_lang1(A,B)) = k2_xboole_0(k2_xboole_0(k15_qc_lang2(A),k15_qc_lang2(B)),k1_tarski(k13_qc_lang1(A,B))))))) # label(t111_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4047 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(B)) -> (all D (m1_qc_lang1(D,B) -> -r1_qc_lang2(A,k9_qc_lang1(C,D)))))))))) # label(t59_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4048 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(v2_qc_lang1(A) & r1_qc_lang2(B,A)))))) # label(t64_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4049 (all A all B (m1_subset_1(B,k8_qc_lang1) & m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k3_qc_lang2(A,B),k8_qc_lang1))) # label(dt_k3_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4050 (all A all B (m1_subset_1(B,k8_qc_lang1) & m1_subset_1(A,k8_qc_lang1) -> r2_qc_lang2(A,A))) # label(reflexivity_r2_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4051 (all A (m1_subset_1(A,k8_qc_lang1) -> k2_xboole_0(k15_qc_lang2(A),k1_tarski(k12_qc_lang1(A))) = k15_qc_lang2(k12_qc_lang1(A)))) # label(t110_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4052 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m2_subset_1(D,k1_qc_lang1,k2_qc_lang1) -> (all E (m2_subset_1(E,k1_qc_lang1,k2_qc_lang1) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (k6_qc_lang2(D,F,B) = k6_qc_lang2(C,E,A) -> C = D & A = B & F = E))))))))))))) # label(t21_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4053 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k2_xboole_0(k2_xboole_0(k15_qc_lang2(A),k15_qc_lang2(B)),k1_enumset1(k12_qc_lang1(B),k13_qc_lang1(A,k12_qc_lang1(B)),k2_qc_lang2(A,B))) = k15_qc_lang2(k2_qc_lang2(A,B)))))) # label(t113_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4054 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r3_qc_lang2(A,k12_qc_lang1(B)) <-> r2_qc_lang2(A,B)))))) # label(t86_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4055 (all A all B (m1_subset_1(B,k8_qc_lang1) & m1_subset_1(A,k8_qc_lang1) -> -r3_qc_lang2(A,A))) # label(irreflexivity_r3_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4056 (all A (m1_subset_1(A,k8_qc_lang1) -> (v1_qc_lang2(A) -> v3_qc_lang1(A) & v4_qc_lang1(k17_qc_lang1(A)) & v3_qc_lang1(k18_qc_lang1(k17_qc_lang1(A))) & v3_qc_lang1(k19_qc_lang1(k17_qc_lang1(A))) & v2_qc_lang2(A)))) # label(t49_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4057 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r2_qc_lang2(B,A) & r3_qc_lang2(A,B)))))) # label(t79_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4058 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k17_qc_lang1(k3_qc_lang2(A,B)) = k13_qc_lang1(k12_qc_lang1(A),k12_qc_lang1(B)) & B = k11_qc_lang2(k3_qc_lang2(A,B)) & k10_qc_lang2(k3_qc_lang2(A,B)) = A)))) # label(t45_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4059 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (k13_qc_lang1(A,B) = k13_qc_lang1(C,D) -> B = D & A = C))))))))) # label(t3_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4060 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (all E (m1_subset_1(E,k8_qc_lang1) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_qc_lang1,k2_qc_lang1) -> (k8_qc_lang2(A,B,C,D) = k6_qc_lang2(F,G,E) -> F = A & k14_qc_lang1(C,D) = E & G = B))))))))))))))) # label(t29_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4061 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k15_qc_lang2(k4_qc_lang2(A,B)) = k2_xboole_0(k2_xboole_0(k15_qc_lang2(A),k15_qc_lang2(B)),k5_enumset1(k12_qc_lang1(B),k13_qc_lang1(A,k12_qc_lang1(B)),k2_qc_lang2(A,B),k12_qc_lang1(A),k13_qc_lang1(B,k12_qc_lang1(A)),k2_qc_lang2(B,A),k4_qc_lang2(A,B))))))) # label(t115_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4062 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang2(A) -> v3_qc_lang1(A) & v3_qc_lang1(k21_qc_lang1(k17_qc_lang1(A))) & v5_qc_lang1(k17_qc_lang1(A))))) # label(t52_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4063 $T # label(t10_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4064 (all A (m1_subset_1(A,k8_qc_lang1) -> (r3_qc_lang2(A,k1_qc_lang2) <-> r2_qc_lang2(A,k11_qc_lang1)))) # label(t88_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4065 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B ((all C (r2_hidden(C,B) <-> (exists D (m1_subset_1(D,k8_qc_lang1) & r2_qc_lang2(D,A) & D = C)))) <-> B = k15_qc_lang2(A))))) # label(d23_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4066 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (A = B | C = A <-> r1_qc_lang2(A,k13_qc_lang1(B,C))))))))) # label(t62_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4067 (all A (m1_subset_1(A,k8_qc_lang1) -> (v1_qc_lang2(A) -> k3_qc_lang2(k10_qc_lang2(A),k11_qc_lang2(A)) = A))) # label(t53_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4068 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r2_qc_lang2(B,A) & r2_qc_lang2(A,B) -> A = B))))) # label(t78_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4069 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -((all C (m1_subset_1(C,k8_qc_lang1) -> -r1_qc_lang2(C,B))) & r3_qc_lang2(A,B)))))) # label(t75_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4070 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(B)) -> (all D (m1_qc_lang1(D,B) -> -r3_qc_lang2(A,k9_qc_lang1(C,D)))))))))) # label(t85_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4071 (all A (m1_subset_1(A,k8_qc_lang1) -> ((exists B (m1_subset_1(B,k8_qc_lang1) & (exists C (A = k4_qc_lang2(B,C) & m1_subset_1(C,k8_qc_lang1))))) <-> v3_qc_lang2(A)))) # label(d12_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.55 4072 $T # label(t69_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4073 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v4_qc_lang1(A) -> (r1_qc_lang2(B,A) <-> k19_qc_lang1(A) = B | B = k18_qc_lang1(A))))))) # label(t66_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4074 (all A (m1_subset_1(A,k8_qc_lang1) -> (v1_qc_lang2(A) <-> (exists B ((exists C (k3_qc_lang2(B,C) = A & m1_subset_1(C,k8_qc_lang1))) & m1_subset_1(B,k8_qc_lang1)))))) # label(d10_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4075 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (k4_qc_lang2(C,D) = k4_qc_lang2(A,B) -> B = D & C = A))))))))) # label(t18_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4076 (all A (m1_subset_1(A,k8_qc_lang1) -> (A = k11_qc_lang1 <-> r2_qc_lang2(A,k11_qc_lang1)))) # label(t99_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4077 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> k2_xboole_0(k15_qc_lang2(A),k1_tarski(k14_qc_lang1(B,A))) = k15_qc_lang2(k14_qc_lang1(B,A)))))) # label(t112_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4078 $T # label(t43_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4079 $T # label(t12_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4080 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (r2_qc_lang2(B,C) & r2_qc_lang2(A,B) -> r2_qc_lang2(A,C)))))))) # label(t77_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4081 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r3_qc_lang2(B,A) & r3_qc_lang2(A,B)))))) # label(t80_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4082 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> k14_qc_lang1(A,k14_qc_lang1(B,C)) = k6_qc_lang2(A,B,C))))))) # label(d6_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4083 $T # label(t34_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4084 (all A (m1_subset_1(A,k8_qc_lang1) -> (v3_qc_lang1(A) -> k2_xboole_0(k15_qc_lang2(k17_qc_lang1(A)),k1_tarski(A)) = k15_qc_lang2(A)))) # label(t117_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4085 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (-(-(r3_qc_lang2(B,C) & r2_qc_lang2(A,B)) & -(r2_qc_lang2(A,B) & r1_qc_lang2(B,C)) & -(r3_qc_lang2(A,B) & r1_qc_lang2(B,C)) & -(r1_qc_lang2(A,B) & r3_qc_lang2(B,C)) & -(r2_qc_lang2(B,C) & r1_qc_lang2(A,B)) & -(r2_qc_lang2(B,C) & r3_qc_lang2(A,B))) -> r3_qc_lang2(A,C)))))))) # label(t83_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4086 $T # label(t57_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4087 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (k14_qc_lang1(B,D) = k14_qc_lang1(A,C) -> D = C & A = B))))))))) # label(t6_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4088 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang2(A) -> k2_qc_lang2(k12_qc_lang2(A),k11_qc_lang2(A)) = A))) # label(t54_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4089 (all A (m1_subset_1(A,k8_qc_lang1) -> A = k17_qc_lang1(k12_qc_lang1(A)))) # label(t2_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4090 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> A = k20_qc_lang1(k14_qc_lang1(A,B)) & B = k21_qc_lang1(k14_qc_lang1(A,B)))))) # label(t8_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4091 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r3_qc_lang2(B,A) & v2_qc_lang1(A)))))) # label(t95_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4092 (all A (m1_subset_1(A,k8_qc_lang1) -> -r1_qc_lang2(A,k11_qc_lang1))) # label(t58_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4093 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (r2_qc_lang2(k14_qc_lang1(C,A),B) -> r3_qc_lang2(A,B)))))))) # label(t92_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4094 $T # label(t106_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4095 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang2(A) -> v3_qc_lang1(A) & v4_qc_lang1(k17_qc_lang1(A)) & v3_qc_lang1(k19_qc_lang1(k17_qc_lang1(A)))))) # label(t50_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4096 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) -> r3_qc_lang2(k19_qc_lang1(A),A) & r3_qc_lang2(k18_qc_lang1(A),A)))) # label(t97_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4097 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k15_qc_lang2(k3_qc_lang2(A,B)) = k2_xboole_0(k2_xboole_0(k15_qc_lang2(A),k15_qc_lang2(B)),k2_enumset1(k12_qc_lang1(B),k12_qc_lang1(A),k13_qc_lang1(k12_qc_lang1(A),k12_qc_lang1(B)),k3_qc_lang2(A,B))))))) # label(t114_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4098 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (A = B <-> r1_qc_lang2(A,k12_qc_lang1(B))))))) # label(t60_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4099 (all A (m1_subset_1(A,k8_qc_lang1) -> (v5_qc_lang1(A) -> k14_qc_lang1(k20_qc_lang1(A),k21_qc_lang1(A)) = A))) # label(t7_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4100 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> k9_qc_lang2(A,B,C,D) = k5_qc_lang2(A,k7_qc_lang2(B,C,D)))))))))) # label(d9_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4101 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r2_qc_lang2(A,B) & r1_qc_lang2(B,A)))))) # label(t81_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4102 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> v4_qc_lang2(k7_qc_lang2(A,B,D)) & v4_qc_lang2(k9_qc_lang2(A,B,C,D)))))))))) # label(t38_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4103 (all A (m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k14_qc_lang2(A),k8_qc_lang1))) # label(dt_k14_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4104 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang2(A) <-> (exists B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) & (exists C (k5_qc_lang2(B,C) = A & m1_subset_1(C,k8_qc_lang1)))))))) # label(d13_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4105 (all A (m1_subset_1(A,k8_qc_lang1) -> k18_qc_lang1(k17_qc_lang1(A)) = k12_qc_lang2(A))) # label(d16_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4106 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k18_qc_lang1(k13_qc_lang1(A,B)) = A & B = k19_qc_lang1(k13_qc_lang1(A,B)))))) # label(t5_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4107 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v3_qc_lang1(B) -> k17_cqc_lang(B,A) = k12_qc_lang1(k17_cqc_lang(k17_qc_lang1(B),A))))))) # label(t31_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4108 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (v1_cqc_lang(E,D) & m1_qc_lang1(E,D) -> (all F (m2_subset_1(F,k5_qc_lang1,k7_qc_lang1(D)) -> k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,k8_cqc_lang(D,F,E)) = f5_s3_cqc_lang(D,F,E) & f6_s3_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,A)) = k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,k10_cqc_lang(A)) & k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,k15_cqc_lang(C,A)) = f8_s3_cqc_lang(C,k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,A)) & f7_s3_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,A),k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,B)) = k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,k11_cqc_lang(A,B)))))))))))))) & (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (m1_qc_lang1(E,D) & v1_cqc_lang(E,D) -> (all F (m2_subset_1(F,k5_qc_lang1,k7_qc_lang1(D)) -> k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,k15_cqc_lang(C,A)) = f8_s3_cqc_lang(C,k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,A)) & f7_s3_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,A),k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,B)) = k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,k11_cqc_lang(A,B)) & k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,k10_cqc_lang(A)) = f6_s3_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,A)) & k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,k8_cqc_lang(D,F,E)) = f5_s3_cqc_lang(D,F,E))))))))))))) & k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,k9_cqc_lang) = f4_s3_cqc_lang & f4_s3_cqc_lang = k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,k9_cqc_lang) -> f3_s3_cqc_lang = f2_s3_cqc_lang # label(s3_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4109 (all A all B all C k1_binop_1(k9_funct_2(A,B,C),A,B) = C) # label(t43_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4110 $T # label(dt_k3_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4111 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k4_qc_lang1) -> m2_relset_1(k3_cqc_lang(B,A),k4_qc_lang1,k1_qc_lang1) & v1_funct_1(k3_cqc_lang(B,A)))))) # label(t10_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4112 $T # label(t3_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4113 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m1_subset_1(B,f1_s9_cqc_lang) -> (B = f2_s9_cqc_lang(A) <-> (exists C (v1_funct_1(C) & v1_funct_2(C,k7_cqc_lang,f1_s9_cqc_lang) & m2_relset_1(C,k7_cqc_lang,f1_s9_cqc_lang) & k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k9_cqc_lang) = f3_s9_cqc_lang & (all D (m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) -> (all E (m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (all H (m1_qc_lang1(H,G) & v1_cqc_lang(H,G) -> (all I (m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G)) -> f7_s9_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,D)) = k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k15_cqc_lang(F,D)) & f6_s9_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,E)) = k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k11_cqc_lang(D,E)) & f5_s9_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,D)) = k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k10_cqc_lang(D)) & k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s9_cqc_lang(G,I,H))))))))))))) & k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,A) = B))))))) -> f2_s9_cqc_lang(k15_cqc_lang(f8_s9_cqc_lang,f9_s9_cqc_lang)) = f7_s9_cqc_lang(f8_s9_cqc_lang,f2_s9_cqc_lang(f9_s9_cqc_lang)) # label(s9_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4114 (all A (m1_subset_1(A,f1_s4_cqc_lang) -> (all B (m1_subset_1(B,f1_s4_cqc_lang) -> -((exists C (v1_funct_1(C) & v1_funct_2(C,k7_cqc_lang,f1_s4_cqc_lang) & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,f2_s4_cqc_lang) = A & (all D (m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) -> (all E (m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (all H (v1_cqc_lang(H,G) & m1_qc_lang1(H,G) -> (all I (m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G)) -> f6_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,E)) = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k11_cqc_lang(D,E)) & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k15_cqc_lang(F,D)) = f7_s4_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D)) & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k10_cqc_lang(D)) = f5_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D)) & f4_s4_cqc_lang(G,I,H) = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k8_cqc_lang(G,I,H)))))))))))))) & f3_s4_cqc_lang = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k9_cqc_lang) & m2_relset_1(C,k7_cqc_lang,f1_s4_cqc_lang))) & A != B & (exists C (f3_s4_cqc_lang = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k9_cqc_lang) & (all D (m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) -> (all E (m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (all H (v1_cqc_lang(H,G) & m1_qc_lang1(H,G) -> (all I (m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G)) -> f4_s4_cqc_lang(G,I,H) = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k8_cqc_lang(G,I,H)) & f7_s4_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D)) = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k15_cqc_lang(F,D)) & f6_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,E)) = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k11_cqc_lang(D,E)) & f5_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D)) = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k10_cqc_lang(D)))))))))))))) & B = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,f2_s4_cqc_lang) & m2_relset_1(C,k7_cqc_lang,f1_s4_cqc_lang) & v1_funct_2(C,k7_cqc_lang,f1_s4_cqc_lang) & v1_funct_1(C)))))))) # label(s4_cqc_lang_AndLHS) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4115 (exists A ((exists B (v1_funct_2(B,k7_cqc_lang,f1_s4_cqc_lang) & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,k9_cqc_lang) = f3_s4_cqc_lang & (all C (m2_subset_1(C,k8_qc_lang1,k7_cqc_lang) -> (all D (m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) -> (all E (m2_subset_1(E,k1_qc_lang1,k2_qc_lang1) -> (all F (m2_subset_1(F,k1_numbers,k5_numbers) -> (all G (v1_cqc_lang(G,F) & m1_qc_lang1(G,F) -> (all H (m2_subset_1(H,k5_qc_lang1,k7_qc_lang1(F)) -> k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,k8_cqc_lang(F,H,G)) = f4_s4_cqc_lang(F,H,G) & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,k10_cqc_lang(C)) = f5_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,C)) & f6_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,C),k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,D)) = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,k11_cqc_lang(C,D)) & f7_s4_cqc_lang(E,k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,C)) = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,k15_cqc_lang(E,C)))))))))))))) & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,f2_s4_cqc_lang) = A & m2_relset_1(B,k7_cqc_lang,f1_s4_cqc_lang) & v1_funct_1(B))) & m1_subset_1(A,f1_s4_cqc_lang))) # label(s4_cqc_lang_AndRHS) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4116 (all A ((exists B (B = A & k5_qc_lang3(B) = k1_xboole_0 & k1_xboole_0 = k6_qc_lang3(B) & m1_subset_1(B,k8_qc_lang1))) <-> r2_hidden(A,a_0_0_cqc_lang))) # label(fraenkel_a_0_0_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4117 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> m2_subset_1(k5_qc_lang2(A,B),k8_qc_lang1,k7_cqc_lang))))) # label(t24_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4118 (all A all B all C (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k7_qc_lang1(A)) & m1_qc_lang1(C,A) & v1_cqc_lang(C,A) -> k8_cqc_lang(A,B,C) = k9_qc_lang1(B,C))) # label(redefinition_k8_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4119 (all A all B (v1_funct_1(k3_cqc_lang(A,B)) & v1_relat_1(k3_cqc_lang(A,B)))) # label(fc1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4120 $T # label(t8_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4121 (all A all B all C k9_funct_2(A,B,C) = k3_cqc_lang(k4_tarski(A,B),C)) # label(t42_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4122 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v2_qc_lang1(B) -> k9_qc_lang1(k15_qc_lang1(B),k4_cqc_lang(k16_qc_lang1(B),k6_cqc_lang(k3_qc_lang3(np__0),A))) = k17_cqc_lang(B,A)))))) # label(t29_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4123 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> k17_cqc_lang(B,A) = B)))) # label(t40_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4124 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m1_subset_1(B,f1_s5_cqc_lang) -> ((exists C (v1_funct_1(C) & m2_relset_1(C,k7_cqc_lang,f1_s5_cqc_lang) & (all D (m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) -> (all E (m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (all H (m1_qc_lang1(H,G) & v1_cqc_lang(H,G) -> (all I (m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G)) -> k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k11_cqc_lang(D,E)) = f6_s5_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,E)) & f7_s5_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,D)) = k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k15_cqc_lang(F,D)) & f5_s5_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,D)) = k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k10_cqc_lang(D)) & k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s5_cqc_lang(G,I,H))))))))))))) & k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k9_cqc_lang) = f3_s5_cqc_lang & k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,A) = B & v1_funct_2(C,k7_cqc_lang,f1_s5_cqc_lang))) <-> B = f2_s5_cqc_lang(A)))))) -> f2_s5_cqc_lang(k9_cqc_lang) = f3_s5_cqc_lang # label(s5_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4125 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> m2_subset_1(k4_qc_lang2(A,B),k8_qc_lang1,k7_cqc_lang))))) # label(t22_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4126 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (B != A -> k17_cqc_lang(k14_qc_lang1(A,C),B) = k14_qc_lang1(A,k17_cqc_lang(C,B))))))))) # label(t38_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4127 (all A all B (m1_subset_1(A,k7_cqc_lang) & m1_subset_1(B,k7_cqc_lang) -> m2_subset_1(k12_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang))) # label(dt_k12_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4128 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m1_subset_1(B,f1_s6_cqc_lang) -> ((exists C (m2_relset_1(C,k7_cqc_lang,f1_s6_cqc_lang) & B = k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,A) & f2_s6_cqc_lang = k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k9_cqc_lang) & (all D (m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) -> (all E (m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (all H (m1_qc_lang1(H,G) & v1_cqc_lang(H,G) -> (all I (m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G)) -> f4_s6_cqc_lang(G,I,H) = k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k8_cqc_lang(G,I,H)) & k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k10_cqc_lang(D)) = f8_s6_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,D)) & k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k15_cqc_lang(F,D)) = f10_s6_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,D)) & f9_s6_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,E)) = k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k11_cqc_lang(D,E)))))))))))))) & v1_funct_2(C,k7_cqc_lang,f1_s6_cqc_lang) & v1_funct_1(C))) <-> B = f3_s6_cqc_lang(A)))))) -> f4_s6_cqc_lang(f5_s6_cqc_lang,f6_s6_cqc_lang,f7_s6_cqc_lang) = f3_s6_cqc_lang(k8_cqc_lang(f5_s6_cqc_lang,f6_s6_cqc_lang,f7_s6_cqc_lang)) # label(s6_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4129 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> m2_subset_1(k3_qc_lang2(A,B),k8_qc_lang1,k7_cqc_lang))))) # label(t21_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4130 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> ((exists D ((all E (m1_subset_1(E,k8_qc_lang1) -> (v4_qc_lang1(E) -> k13_qc_lang1(k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,k18_qc_lang1(E)),k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,k19_qc_lang1(E))) = k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,E)) & (v5_qc_lang1(E) -> k2_cqc_lang(k8_qc_lang1,k20_qc_lang1(E),B,E,k14_qc_lang1(k20_qc_lang1(E),k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,k21_qc_lang1(E)))) = k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,E)) & (v3_qc_lang1(E) -> k12_qc_lang1(k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,k17_qc_lang1(E))) = k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,E)) & (v2_qc_lang1(E) -> k9_qc_lang1(k15_qc_lang1(E),k4_cqc_lang(k16_qc_lang1(E),k6_cqc_lang(k3_qc_lang3(np__0),B))) = k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,E)) & k9_cqc_lang = k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,k9_cqc_lang))) & k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,A) = C & m2_relset_1(D,k8_qc_lang1,k8_qc_lang1) & v1_funct_2(D,k8_qc_lang1,k8_qc_lang1) & v1_funct_1(D))) <-> k17_cqc_lang(A,B) = C))))))) # label(d6_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4131 (all A all B all C (m1_subset_1(A,k5_numbers) & m1_qc_lang1(B,A) & v1_funct_1(C) & m1_relset_1(C,k4_qc_lang1,k1_qc_lang1) -> m1_qc_lang1(k5_cqc_lang(A,B,C),A))) # label(dt_k5_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4132 (all A all B (m1_subset_1(A,k7_cqc_lang) & m1_subset_1(B,k7_cqc_lang) -> k12_cqc_lang(A,B) = k2_qc_lang2(A,B))) # label(redefinition_k12_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4133 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m1_subset_1(B,f1_s8_cqc_lang) -> (f2_s8_cqc_lang(A) = B <-> (exists C (v1_funct_1(C) & v1_funct_2(C,k7_cqc_lang,f1_s8_cqc_lang) & m2_relset_1(C,k7_cqc_lang,f1_s8_cqc_lang) & (all D (m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) -> (all E (m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (all H (v1_cqc_lang(H,G) & m1_qc_lang1(H,G) -> (all I (m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G)) -> k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k10_cqc_lang(D)) = f5_s8_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,D)) & f6_s8_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,E)) = k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k11_cqc_lang(D,E)) & k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k15_cqc_lang(F,D)) = f9_s8_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,D)) & f4_s8_cqc_lang(G,I,H) = k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k8_cqc_lang(G,I,H)))))))))))))) & f3_s8_cqc_lang = k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k9_cqc_lang) & B = k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,A)))))))) -> f2_s8_cqc_lang(k11_cqc_lang(f7_s8_cqc_lang,f8_s8_cqc_lang)) = f6_s8_cqc_lang(f2_s8_cqc_lang(f7_s8_cqc_lang),f2_s8_cqc_lang(f8_s8_cqc_lang)) # label(s8_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4134 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (k1_xboole_0 = k5_qc_lang3(B) -> k17_cqc_lang(B,A) = B))))) # label(t39_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4135 (all A all B (m1_subset_1(A,k2_qc_lang1) & m1_subset_1(B,k7_cqc_lang) -> m2_subset_1(k16_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang))) # label(dt_k16_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4136 (all A all B (v1_funct_1(B) & m1_relset_1(B,k4_qc_lang1,k1_qc_lang1) & m1_finseq_1(A,k1_qc_lang1) -> m2_finseq_1(k4_cqc_lang(A,B),k1_qc_lang1))) # label(dt_k4_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4137 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(A)) -> (all D (m1_qc_lang1(D,A) -> k9_qc_lang1(C,k5_cqc_lang(A,D,k6_cqc_lang(k3_qc_lang3(np__0),B))) = k17_cqc_lang(k9_qc_lang1(C,D),B))))))))) # label(t30_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4138 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v5_qc_lang1(B) -> k14_qc_lang1(k20_qc_lang1(B),k17_cqc_lang(k21_qc_lang1(B),A)) = k17_cqc_lang(B,A) | A = k20_qc_lang1(B)))))) # label(t36_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4139 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (m2_subset_1(k13_qc_lang1(A,B),k8_qc_lang1,k7_cqc_lang) <-> m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) & m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)))))) # label(t19_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4140 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v4_qc_lang1(B) -> k17_cqc_lang(B,A) = k13_qc_lang1(k17_cqc_lang(k18_qc_lang1(B),A),k17_cqc_lang(k19_qc_lang1(B),A))))))) # label(t33_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4141 (all A (m1_subset_1(A,k7_cqc_lang) -> m2_subset_1(k10_cqc_lang(A),k8_qc_lang1,k7_cqc_lang))) # label(dt_k10_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4142 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (v1_cqc_lang(E,D) & m1_qc_lang1(E,D) -> (all F (m2_subset_1(F,k5_qc_lang1,k7_qc_lang1(D)) -> p1_s1_cqc_lang(k8_cqc_lang(D,F,E)) & (p1_s1_cqc_lang(A) & p1_s1_cqc_lang(B) -> p1_s1_cqc_lang(k11_cqc_lang(A,B))) & (p1_s1_cqc_lang(A) -> p1_s1_cqc_lang(k15_cqc_lang(C,A))) & (p1_s1_cqc_lang(A) -> p1_s1_cqc_lang(k10_cqc_lang(A))) & p1_s1_cqc_lang(k9_cqc_lang))))))))))))) -> (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> p1_s1_cqc_lang(A))) # label(s1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4143 (all A all B (m1_subset_1(B,k7_cqc_lang) & m1_subset_1(A,k7_cqc_lang) -> k13_cqc_lang(A,B) = k3_qc_lang2(A,B))) # label(redefinition_k13_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4144 (all A (r2_hidden(A,k1_qc_lang1) <-> -(-r2_hidden(A,k3_qc_lang1) & -r2_hidden(A,k4_qc_lang1) & -r2_hidden(A,k2_qc_lang1)))) # label(t7_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4145 (all A all B (m1_subset_1(A,k2_qc_lang1) & m1_subset_1(B,k7_cqc_lang) -> k16_cqc_lang(A,B) = k5_qc_lang2(A,B))) # label(redefinition_k16_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4146 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m1_qc_lang1(B,A) -> (v1_cqc_lang(B,A) & m1_qc_lang1(B,A) <-> a_2_0_cqc_lang(A,B) = k1_xboole_0 & a_2_1_cqc_lang(A,B) = k1_xboole_0))))) # label(t15_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4147 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k14_qc_lang1(A,B) = k17_cqc_lang(k14_qc_lang1(A,B),A))))) # label(t37_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4148 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> k13_qc_lang1(k17_cqc_lang(B,A),k17_cqc_lang(C,A)) = k17_cqc_lang(k13_qc_lang1(B,C),A))))))) # label(t34_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4149 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (m2_subset_1(k14_qc_lang1(A,B),k8_qc_lang1,k7_cqc_lang) <-> m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)))))) # label(t23_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4150 (all A all B (m1_subset_1(B,k7_cqc_lang) & m1_subset_1(A,k7_cqc_lang) -> m2_subset_1(k11_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang))) # label(dt_k11_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4151 (all A all B k2_funcop_1(k1_tarski(A),B) = k3_cqc_lang(A,B)) # label(d2_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4152 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k4_qc_lang1) -> (all D (m2_finseq_1(D,k1_qc_lang1) -> (all E (m2_finseq_1(E,k1_qc_lang1) -> (all F (v1_funct_1(F) & m2_relset_1(F,k4_qc_lang1,k1_qc_lang1) -> (F = k6_cqc_lang(C,B) & D = k4_cqc_lang(E,F) & r1_xreal_0(A,k3_finseq_1(E)) & r1_xreal_0(np__1,A) -> (C = k1_funct_1(E,A) -> k1_funct_1(D,A) = B) & (k1_funct_1(E,A) != C -> k1_funct_1(E,A) = k1_funct_1(D,A))))))))))))))) # label(t11_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4153 (all A all B (m1_subset_1(A,k7_cqc_lang) & m1_subset_1(B,k7_cqc_lang) -> k4_qc_lang2(A,B) = k14_cqc_lang(A,B))) # label(redefinition_k14_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4154 (all A all B all C all D ((A = B -> k1_cqc_lang(A,B,C,D) = C) & (A != B -> D = k1_cqc_lang(A,B,C,D)))) # label(d1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4155 (all A all B (m1_subset_1(A,k2_qc_lang1) & m1_subset_1(B,k7_cqc_lang) -> m2_subset_1(k15_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang))) # label(dt_k15_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4156 (all A (m2_finseq_1(A,k1_qc_lang1) -> (all B (v1_funct_1(B) & m2_relset_1(B,k4_qc_lang1,k1_qc_lang1) -> (all C (m2_finseq_1(C,k1_qc_lang1) -> (C = k4_cqc_lang(A,B) <-> k3_finseq_1(C) = k3_finseq_1(A) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r1_xreal_0(D,k3_finseq_1(A)) & r1_xreal_0(np__1,D) -> (-r2_hidden(k1_funct_1(A,D),k1_relat_1(B)) -> k1_funct_1(A,D) = k1_funct_1(C,D)) & (r2_hidden(k1_funct_1(A,D),k1_relat_1(B)) -> k1_funct_1(C,D) = k1_funct_1(B,k1_funct_1(A,D))))))))))))) # label(d3_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4157 (all A all B k1_funct_1(k3_cqc_lang(A,B),A) = B) # label(t6_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4158 (all A all B (m1_subset_1(B,k7_cqc_lang) & m1_subset_1(A,k7_cqc_lang) -> m2_subset_1(k13_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang))) # label(dt_k13_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4159 (all A all B (m1_subset_1(A,k8_qc_lang1) & m1_subset_1(B,k2_qc_lang1) -> m1_subset_1(k17_cqc_lang(A,B),k8_qc_lang1))) # label(dt_k17_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4160 (all A (m1_subset_1(A,k8_qc_lang1) -> (m2_subset_1(k12_qc_lang1(A),k8_qc_lang1,k7_cqc_lang) <-> m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)))) # label(t18_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4161 (all A (m1_subset_1(A,k7_cqc_lang) -> k10_cqc_lang(A) = k12_qc_lang1(A))) # label(redefinition_k10_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4162 $T # label(t14_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4163 $T # label(t27_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4164 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> m2_subset_1(k2_qc_lang2(A,B),k8_qc_lang1,k7_cqc_lang))))) # label(t20_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4165 $T # label(t4_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4166 (all A all B all C all D all E (m1_subset_1(D,A) & m1_subset_1(E,A) & -v1_xboole_0(A) -> m1_subset_1(k2_cqc_lang(A,B,C,D,E),A))) # label(dt_k2_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4167 (all A all B (m1_subset_1(B,k7_cqc_lang) & m1_subset_1(A,k7_cqc_lang) -> m2_subset_1(k14_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang))) # label(dt_k14_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4168 (all A all B (m1_subset_1(B,k7_cqc_lang) & m1_subset_1(A,k7_cqc_lang) -> k13_qc_lang1(A,B) = k11_cqc_lang(A,B))) # label(redefinition_k11_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4169 (all A all B all C (m1_qc_lang1(C,B) & m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(A,a_2_0_cqc_lang(B,C)) <-> (exists D (A = k1_funct_1(C,D) & r1_xreal_0(D,k3_finseq_1(C)) & r2_hidden(k1_funct_1(C,D),k4_qc_lang1) & r1_xreal_0(np__1,D) & m2_subset_1(D,k1_numbers,k5_numbers)))))) # label(fraenkel_a_2_0_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4170 (all A all B (m1_subset_1(B,k2_qc_lang1) & m1_subset_1(A,k4_qc_lang1) -> k3_cqc_lang(A,B) = k6_cqc_lang(A,B))) # label(redefinition_k6_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.01/14.56 4171 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k6_qc_lang3(B) = k6_qc_lang3(k17_cqc_lang(B,A)))))) # label(t41_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4172 (all A all B all C (m2_subset_1(B,k1_numbers,k5_numbers) & m1_qc_lang1(C,B) -> ((exists D (k1_funct_1(C,D) = A & r1_xreal_0(np__1,D) & r1_xreal_0(D,k3_finseq_1(C)) & r2_hidden(k1_funct_1(C,D),k3_qc_lang1) & m2_subset_1(D,k1_numbers,k5_numbers))) <-> r2_hidden(A,a_2_1_cqc_lang(B,C))))) # label(fraenkel_a_2_1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4173 $T # label(t9_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4174 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> k17_cqc_lang(k9_cqc_lang,A) = k9_cqc_lang)) # label(t28_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4175 $T # label(t1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4176 $T # label(dt_k1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4177 (all A all B (k2_relat_1(k3_cqc_lang(A,B)) = k1_tarski(B) & k1_relat_1(k3_cqc_lang(A,B)) = k1_tarski(A))) # label(t5_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4178 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m1_subset_1(B,f1_s7_cqc_lang) -> (f2_s7_cqc_lang(A) = B <-> (exists C (v1_funct_1(C) & v1_funct_2(C,k7_cqc_lang,f1_s7_cqc_lang) & k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,A) = B & k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k9_cqc_lang) = f3_s7_cqc_lang & (all D (m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) -> (all E (m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (all H (m1_qc_lang1(H,G) & v1_cqc_lang(H,G) -> (all I (m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G)) -> k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s7_cqc_lang(G,I,H) & f5_s7_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,D)) = k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k10_cqc_lang(D)) & k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k11_cqc_lang(D,E)) = f7_s7_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,E)) & k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k15_cqc_lang(F,D)) = f8_s7_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,D)))))))))))))) & m2_relset_1(C,k7_cqc_lang,f1_s7_cqc_lang)))))))) -> f5_s7_cqc_lang(f2_s7_cqc_lang(f6_s7_cqc_lang)) = f2_s7_cqc_lang(k10_cqc_lang(f6_s7_cqc_lang)) # label(s7_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4179 (all A all B (m1_subset_1(A,k4_qc_lang1) & m1_subset_1(B,k2_qc_lang1) -> m2_relset_1(k6_cqc_lang(A,B),k4_qc_lang1,k1_qc_lang1) & v1_funct_1(k6_cqc_lang(A,B)))) # label(dt_k6_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4180 $T # label(t25_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4181 (all A (m1_subset_1(A,k8_qc_lang1) -> (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) <-> k5_qc_lang3(A) = k1_xboole_0 & k1_xboole_0 = k6_qc_lang3(A)))) # label(t13_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4182 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A)) -> (all C (m1_qc_lang1(C,A) -> (k1_xboole_0 = a_2_0_cqc_lang(A,C) & k1_xboole_0 = a_2_1_cqc_lang(A,C) <-> m2_subset_1(k9_qc_lang1(B,C),k8_qc_lang1,k7_cqc_lang)))))))) # label(t17_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4183 (exists A (v1_funct_1(A) & k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k9_cqc_lang) = f2_s2_cqc_lang & (all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> (all C (m2_subset_1(C,k8_qc_lang1,k7_cqc_lang) -> (all D (m2_subset_1(D,k1_qc_lang1,k2_qc_lang1) -> (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (all F (v1_cqc_lang(F,E) & m1_qc_lang1(F,E) -> (all G (m2_subset_1(G,k5_qc_lang1,k7_qc_lang1(E)) -> k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k8_cqc_lang(E,G,F)) = f3_s2_cqc_lang(E,G,F) & k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k10_cqc_lang(B)) = f4_s2_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,B)) & k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k11_cqc_lang(B,C)) = f5_s2_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,B),k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,C)) & f6_s2_cqc_lang(D,k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,B)) = k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k15_cqc_lang(D,B)))))))))))))) & m2_relset_1(A,k7_cqc_lang,f1_s2_cqc_lang) & v1_funct_2(A,k7_cqc_lang,f1_s2_cqc_lang))) # label(s2_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4184 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k12_qc_lang1(k17_cqc_lang(B,A)) = k17_cqc_lang(k12_qc_lang1(B),A))))) # label(t32_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4185 $T # label(t12_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4186 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m1_qc_lang1(B,A) -> (r1_tarski(k2_relat_1(B),k2_qc_lang1) <-> v1_cqc_lang(B,A)))))) # label(d5_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4187 $T # label(t2_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4188 (all A all B (m1_subset_1(A,k2_qc_lang1) & m1_subset_1(B,k7_cqc_lang) -> k14_qc_lang1(A,B) = k15_cqc_lang(A,B))) # label(redefinition_k15_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4189 (all A all B all C (m1_subset_1(A,k5_numbers) & m1_qc_lang1(C,A) & v1_cqc_lang(C,A) & m1_subset_1(B,k7_qc_lang1(A)) -> m2_subset_1(k8_cqc_lang(A,B,C),k8_qc_lang1,k7_cqc_lang))) # label(dt_k8_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4190 (all A all B all C (m1_qc_lang1(B,A) & m1_relset_1(C,k4_qc_lang1,k1_qc_lang1) & v1_funct_1(C) & m1_subset_1(A,k5_numbers) -> k5_cqc_lang(A,B,C) = k4_cqc_lang(B,C))) # label(redefinition_k5_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4191 $T # label(t26_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4192 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v5_qc_lang1(B) & A = k20_qc_lang1(B) -> B = k17_cqc_lang(B,A)))))) # label(t35_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4193 (all A all B all C all D all E (m1_subset_1(D,A) & m1_subset_1(E,A) & -v1_xboole_0(A) -> k2_cqc_lang(A,B,C,D,E) = k1_cqc_lang(B,C,D,E))) # label(redefinition_k2_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4194 (all A (m1_subset_1(A,k5_numbers) -> (exists B (v1_finseq_1(B) & v1_cqc_lang(B,A) & v1_funct_1(B) & v1_relat_1(B) & m1_qc_lang1(B,A))))) # label(rc1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4195 (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]. 15.04/14.57 4196 (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]. 15.04/14.57 4197 (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]. 15.04/14.57 4198 (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]. 15.04/14.57 4199 (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]. 15.04/14.57 4200 (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]. 15.04/14.57 4201 (all A exists B m1_pboole(B,A)) # label(existence_m1_pboole) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4202 (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]. 15.04/14.57 4203 (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]. 15.04/14.57 4204 (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]. 15.04/14.57 4205 (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]. 15.04/14.57 4206 (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]. 15.04/14.57 4207 (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]. 15.04/14.57 4208 (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]. 15.04/14.57 4209 (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]. 15.04/14.57 4210 (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]. 15.04/14.57 4211 (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]. 15.04/14.57 4212 (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]. 15.04/14.57 4213 (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]. 15.04/14.57 4214 (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]. 15.04/14.57 4215 (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]. 15.04/14.57 4216 (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]. 15.04/14.57 4217 (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]. 15.04/14.57 4218 $T # label(t31_pboole) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4219 $T # label(d1_pboole) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4220 (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]. 15.04/14.57 4221 (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]. 15.04/14.57 4222 (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]. 15.04/14.57 4223 (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]. 15.04/14.57 4224 $T # label(t93_pboole) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4225 (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]. 15.04/14.57 4226 (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]. 15.04/14.57 4227 (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]. 15.04/14.57 4228 (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]. 15.04/14.57 4229 (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]. 15.04/14.57 4230 (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]. 15.04/14.57 4231 (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]. 15.04/14.57 4232 (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]. 15.04/14.57 4233 (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]. 15.04/14.57 4234 (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]. 15.04/14.57 4235 (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]. 15.04/14.57 4236 (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]. 15.04/14.57 4237 (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]. 15.04/14.57 4238 (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]. 15.04/14.57 4239 (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]. 15.04/14.57 4240 $T # label(t14_pboole) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4241 (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]. 15.04/14.57 4242 (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]. 15.04/14.57 4243 (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]. 15.04/14.57 4244 (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]. 15.04/14.57 4245 (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]. 15.04/14.57 4246 (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]. 15.04/14.57 4247 (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]. 15.04/14.57 4248 (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]. 15.04/14.57 4249 (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]. 15.04/14.57 4250 (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]. 15.04/14.57 4251 (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]. 15.04/14.57 4252 (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]. 15.04/14.57 4253 (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]. 15.04/14.57 4254 (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]. 15.04/14.57 4255 (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]. 15.04/14.57 4256 (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]. 15.04/14.57 4257 (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]. 15.04/14.57 4258 (exists A (v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A))) # label(rc1_pboole) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4259 (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]. 15.04/14.57 4260 (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]. 15.04/14.57 4261 (all A all B k1_xboole_0 = k1_funct_1(k1_pboole(B),A)) # label(t5_pboole) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4262 (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]. 15.04/14.57 4263 (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]. 15.04/14.57 4264 (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]. 15.04/14.57 4265 (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]. 15.04/14.57 4266 (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]. 15.04/14.57 4267 (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]. 15.04/14.57 4268 (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]. 15.04/14.57 4269 (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]. 15.04/14.57 4270 $T # label(t125_pboole) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4271 (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]. 15.04/14.57 4272 (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]. 15.04/14.57 4273 (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]. 15.04/14.57 4274 (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]. 15.04/14.57 4275 (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]. 15.04/14.57 4276 (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]. 15.04/14.57 4277 $T # label(t117_pboole) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4278 (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]. 15.04/14.57 4279 (all A all B k2_funcop_1(A,B) = k10_pboole(A,B)) # label(redefinition_k10_pboole) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4280 (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]. 15.04/14.57 4281 (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]. 15.04/14.57 4282 (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]. 15.04/14.57 4283 (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]. 15.04/14.57 4284 (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]. 15.04/14.57 4285 (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]. 15.04/14.57 4286 (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]. 15.04/14.57 4287 (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]. 15.04/14.57 4288 (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]. 15.04/14.57 4289 (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]. 15.04/14.57 4290 (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]. 15.04/14.57 4291 (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]. 15.04/14.57 4292 (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]. 15.04/14.57 4293 (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]. 15.04/14.57 4294 (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]. 15.04/14.57 4295 (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]. 15.04/14.57 4296 (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]. 15.04/14.57 4297 (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]. 15.04/14.57 4298 (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]. 15.04/14.57 4299 (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]. 15.04/14.57 4300 (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]. 15.04/14.57 4301 (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]. 15.04/14.57 4302 (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]. 15.04/14.57 4303 (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]. 15.04/14.57 4304 (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]. 15.04/14.57 4305 (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]. 15.04/14.57 4306 (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]. 15.04/14.57 4307 (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]. 15.04/14.57 4308 (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]. 15.04/14.57 4309 (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]. 15.04/14.57 4310 (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]. 15.04/14.57 4311 (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]. 15.04/14.57 4312 (all A all B (m1_pboole(B,A) -> r2_pboole(A,k1_pboole(A),B))) # label(t49_pboole) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4313 (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]. 15.04/14.57 4314 (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]. 15.04/14.57 4315 (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]. 15.04/14.57 4316 (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]. 15.04/14.57 4317 (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]. 15.04/14.57 4318 (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]. 15.04/14.57 4319 (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]. 15.04/14.57 4320 (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]. 15.04/14.57 4321 (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]. 15.04/14.57 4322 (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]. 15.04/14.57 4323 (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]. 15.04/14.57 4324 (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]. 15.04/14.57 4325 (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]. 15.04/14.57 4326 (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]. 15.04/14.57 4327 (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]. 15.04/14.57 4328 (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]. 15.04/14.57 4329 (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]. 15.04/14.57 4330 (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]. 15.04/14.57 4331 (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]. 15.04/14.57 4332 (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]. 15.04/14.57 4333 (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]. 15.04/14.57 4334 (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]. 15.04/14.57 4335 (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]. 15.04/14.57 4336 (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]. 15.04/14.57 4337 (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]. 15.04/14.57 4338 (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]. 15.04/14.57 4339 (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]. 15.04/14.57 4340 (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]. 15.04/14.57 4341 (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]. 15.04/14.57 4342 (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]. 15.04/14.57 4343 (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]. 15.04/14.57 4344 (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]. 15.04/14.57 4345 (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]. 15.04/14.57 4346 $T # label(t13_pboole) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4347 (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]. 15.04/14.57 4348 (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]. 15.04/14.57 4349 (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]. 15.04/14.57 4350 (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]. 15.04/14.57 4351 (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]. 15.04/14.57 4352 (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]. 15.04/14.57 4353 (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]. 15.04/14.57 4354 $T # label(t30_pboole) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4355 (all A k2_funcop_1(A,k1_xboole_0) = k1_pboole(A)) # label(d6_pboole) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4356 (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]. 15.04/14.57 4357 (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]. 15.04/14.57 4358 (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]. 15.04/14.57 4359 (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]. 15.04/14.57 4360 (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]. 15.04/14.57 4361 (all A m1_pboole(k1_pboole(A),A)) # label(dt_k1_pboole) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4362 (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]. 15.04/14.57 4363 (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]. 15.04/14.57 4364 $T # label(t90_pboole) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4365 $T # label(t32_pboole) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4366 (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]. 15.04/14.57 4367 (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]. 15.04/14.57 4368 (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]. 15.04/14.57 4369 (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]. 15.04/14.57 4370 (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]. 15.04/14.57 4371 (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]. 15.04/14.57 4372 (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]. 15.04/14.57 4373 (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]. 15.04/14.57 4374 (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]. 15.04/14.57 4375 (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]. 15.04/14.57 4376 (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]. 15.04/14.57 4377 (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]. 15.04/14.57 4378 (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]. 15.04/14.57 4379 (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]. 15.04/14.57 4380 (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]. 15.04/14.57 4381 (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]. 15.04/14.57 4382 $T # label(t33_pboole) # label(axiom) # label(non_clause). [assumption]. 15.04/14.57 4383 (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]. 15.04/14.57 4384 (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]. 15.04/14.57 4385 (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]. 15.04/14.57 4386 (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]. 15.04/14.57 4387 (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]. 15.04/14.57 4388 (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]. 15.04/14.57 4389 (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]. 15.04/14.57 4390 (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]. 15.04/14.57 4391 (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]. 15.04/14.57 4392 (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]. 15.04/14.57 4393 (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]. 15.04/14.57 4394 (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]. 15.04/14.57 4395 (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]. 15.04/14.57 4396 (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]. 15.04/14.58 4397 (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]. 15.04/14.58 4398 (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]. 15.04/14.58 4399 (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]. 15.04/14.58 4400 $T # label(t131_pboole) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4401 (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]. 15.04/14.58 4402 (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]. 15.04/14.58 4403 (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]. 15.04/14.58 4404 (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]. 15.04/14.58 4405 (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]. 15.04/14.58 4406 (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]. 15.04/14.58 4407 (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]. 15.04/14.58 4408 (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]. 15.04/14.58 4409 (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]. 15.04/14.58 4410 (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]. 15.04/14.58 4411 (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]. 15.04/14.58 4412 (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]. 15.04/14.58 4413 (all A (m1_pboole(A,k1_xboole_0) -> k1_xboole_0 = A)) # label(t134_pboole) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4414 (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]. 15.04/14.58 4415 (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]. 15.04/14.58 4416 (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]. 15.04/14.58 4417 (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]. 15.04/14.58 4418 (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]. 15.04/14.58 4419 (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]. 15.04/14.58 4420 $T # label(d2_pboole) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4421 (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]. 15.04/14.58 4422 (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]. 15.04/14.58 4423 (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]. 15.04/14.58 4424 (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]. 15.04/14.58 4425 (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]. 15.04/14.58 4426 $T # label(t107_pboole) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4427 (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]. 15.04/14.58 4428 (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]. 15.04/14.58 4429 (all A all B all C all D all E all F all G all H (-v1_xboole_0(C) & -v1_xboole_0(D) & v1_funct_1(E) & v1_funct_2(E,k3_zfmisc_1(A,B,C),D) & m1_subset_1(F,A) & m1_subset_1(H,C) & m1_subset_1(G,B) & m1_relset_1(E,k3_zfmisc_1(A,B,C),D) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k2_multop_1(A,B,C,D,E,F,G,H) = k1_multop_1(E,F,G,H))) # label(redefinition_k2_multop_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4430 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_2(E,k3_zfmisc_1(A,B,C),D) & m2_relset_1(E,k3_zfmisc_1(A,B,C),D) & v1_funct_1(E) -> (all F (v1_funct_1(F) & v1_funct_2(F,k3_zfmisc_1(A,B,C),D) & m2_relset_1(F,k3_zfmisc_1(A,B,C),D) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> k8_funct_2(k3_zfmisc_1(A,B,C),D,F,k4_domain_1(A,B,C,G,H,I)) = k8_funct_2(k3_zfmisc_1(A,B,C),D,E,k4_domain_1(A,B,C,G,H,I)))))))) -> E = F))))))))))))) # label(t3_multop_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4431 $T # label(dt_k3_multop_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4432 (all A (m1_subset_1(A,f1_s2_multop_1) -> (all B (m1_subset_1(B,f1_s2_multop_1) -> (all C (m1_subset_1(C,f1_s2_multop_1) -> (exists D (p1_s2_multop_1(A,B,C,D) & m1_subset_1(D,f1_s2_multop_1))))))))) -> (exists A (v1_funct_1(A) & (all B (m1_subset_1(B,f1_s2_multop_1) -> (all C (m1_subset_1(C,f1_s2_multop_1) -> (all D (m1_subset_1(D,f1_s2_multop_1) -> p1_s2_multop_1(B,C,D,k2_multop_1(f1_s2_multop_1,f1_s2_multop_1,f1_s2_multop_1,f1_s2_multop_1,A,B,C,D)))))))) & m2_relset_1(A,k3_zfmisc_1(f1_s2_multop_1,f1_s2_multop_1,f1_s2_multop_1),f1_s2_multop_1) & v1_funct_2(A,k3_zfmisc_1(f1_s2_multop_1,f1_s2_multop_1,f1_s2_multop_1),f1_s2_multop_1))) # label(s2_multop_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4433 (all A (m1_subset_1(A,f1_s5_multop_1) -> (all B (m1_subset_1(B,f2_s5_multop_1) -> (all C (m1_subset_1(C,f3_s5_multop_1) -> (all D (m1_subset_1(D,f4_s5_multop_1) -> (exists E (m1_subset_1(E,f5_s5_multop_1) & p1_s5_multop_1(A,B,C,D,E))))))))))) -> (exists A (v1_funct_2(A,k4_zfmisc_1(f1_s5_multop_1,f2_s5_multop_1,f3_s5_multop_1,f4_s5_multop_1),f5_s5_multop_1) & (all B (m1_subset_1(B,f1_s5_multop_1) -> (all C (m1_subset_1(C,f2_s5_multop_1) -> (all D (m1_subset_1(D,f3_s5_multop_1) -> (all E (m1_subset_1(E,f4_s5_multop_1) -> p1_s5_multop_1(B,C,D,E,k8_funct_2(k4_zfmisc_1(f1_s5_multop_1,f2_s5_multop_1,f3_s5_multop_1,f4_s5_multop_1),f5_s5_multop_1,A,k5_domain_1(f1_s5_multop_1,f2_s5_multop_1,f3_s5_multop_1,f4_s5_multop_1,B,C,D,E))))))))))) & m2_relset_1(A,k4_zfmisc_1(f1_s5_multop_1,f2_s5_multop_1,f3_s5_multop_1,f4_s5_multop_1),f5_s5_multop_1) & v1_funct_1(A))) # label(s5_multop_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4434 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C all D all E k3_multop_1(A,B,C,D,E) = k1_funct_1(A,k4_mcart_1(B,C,D,E))))) # label(d2_multop_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4435 (all A (m1_subset_1(A,f1_s6_multop_1) -> (all B (m1_subset_1(B,f1_s6_multop_1) -> (all C (m1_subset_1(C,f1_s6_multop_1) -> (all D (m1_subset_1(D,f1_s6_multop_1) -> (exists E (p1_s6_multop_1(A,B,C,D,E) & m1_subset_1(E,f1_s6_multop_1))))))))))) -> (exists A (v1_funct_1(A) & m2_relset_1(A,k4_zfmisc_1(f1_s6_multop_1,f1_s6_multop_1,f1_s6_multop_1,f1_s6_multop_1),f1_s6_multop_1) & (all B (m1_subset_1(B,f1_s6_multop_1) -> (all C (m1_subset_1(C,f1_s6_multop_1) -> (all D (m1_subset_1(D,f1_s6_multop_1) -> (all E (m1_subset_1(E,f1_s6_multop_1) -> p1_s6_multop_1(B,C,D,E,k4_multop_1(f1_s6_multop_1,f1_s6_multop_1,f1_s6_multop_1,f1_s6_multop_1,f1_s6_multop_1,A,B,C,D,E)))))))))) & v1_funct_2(A,k4_zfmisc_1(f1_s6_multop_1,f1_s6_multop_1,f1_s6_multop_1,f1_s6_multop_1),f1_s6_multop_1))) # label(s6_multop_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4436 $T # label(t5_multop_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4437 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (m2_relset_1(F,k4_zfmisc_1(A,B,C,D),E) & v1_funct_2(F,k4_zfmisc_1(A,B,C,D),E) & v1_funct_1(F) -> (all G (v1_funct_1(G) & v1_funct_2(G,k4_zfmisc_1(A,B,C,D),E) & m2_relset_1(G,k4_zfmisc_1(A,B,C,D),E) -> ((all H (m1_subset_1(H,A) -> (all I (m1_subset_1(I,B) -> (all J (m1_subset_1(J,C) -> (all K (m1_subset_1(K,D) -> k4_multop_1(A,B,C,D,E,F,H,I,J,K) = k4_multop_1(A,B,C,D,E,G,H,I,J,K))))))))) -> F = G))))))))))))))) # label(t8_multop_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4438 $T # label(t1_multop_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4439 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (v1_funct_1(F) & v1_funct_2(F,k4_zfmisc_1(A,B,C,D),E) & m2_relset_1(F,k4_zfmisc_1(A,B,C,D),E) -> (all G (v1_funct_1(G) & m2_relset_1(G,k4_zfmisc_1(A,B,C,D),E) & v1_funct_2(G,k4_zfmisc_1(A,B,C,D),E) -> ((all H (m1_subset_1(H,A) -> (all I (m1_subset_1(I,B) -> (all J (m1_subset_1(J,C) -> (all K (m1_subset_1(K,D) -> k8_funct_2(k4_zfmisc_1(A,B,C,D),E,F,k5_domain_1(A,B,C,D,H,I,J,K)) = k8_funct_2(k4_zfmisc_1(A,B,C,D),E,G,k5_domain_1(A,B,C,D,H,I,J,K)))))))))) -> G = F))))))))))))))) # label(t7_multop_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4440 (all A (-v1_xboole_0(A) -> (all B all C all D all E all F (v1_funct_2(F,k4_zfmisc_1(B,C,D,E),A) & m2_relset_1(F,k4_zfmisc_1(B,C,D,E),A) & v1_funct_1(F) -> (all G (m2_relset_1(G,k4_zfmisc_1(B,C,D,E),A) & v1_funct_2(G,k4_zfmisc_1(B,C,D,E),A) & v1_funct_1(G) -> ((all H all I all J all K (r2_hidden(H,B) & r2_hidden(K,E) & r2_hidden(J,D) & r2_hidden(I,C) -> k1_funct_1(F,k4_mcart_1(H,I,J,K)) = k1_funct_1(G,k4_mcart_1(H,I,J,K)))) -> G = F))))))) # label(t6_multop_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4441 (all A all B all C all D all E all F all G all H all I all J (-v1_xboole_0(C) & m1_subset_1(G,A) & m1_subset_1(H,B) & m1_subset_1(J,D) & m1_subset_1(I,C) & m1_relset_1(F,k4_zfmisc_1(A,B,C,D),E) & v1_funct_2(F,k4_zfmisc_1(A,B,C,D),E) & v1_funct_1(F) & -v1_xboole_0(E) & -v1_xboole_0(D) & -v1_xboole_0(B) & -v1_xboole_0(A) -> m1_subset_1(k4_multop_1(A,B,C,D,E,F,G,H,I,J),E))) # label(dt_k4_multop_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4442 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C all D k1_multop_1(A,B,C,D) = k1_funct_1(A,k3_mcart_1(B,C,D))))) # label(d1_multop_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4443 (all A all B all C all D all E all F all G all H (-v1_xboole_0(B) & -v1_xboole_0(C) & m1_relset_1(E,k3_zfmisc_1(A,B,C),D) & m1_subset_1(F,A) & m1_subset_1(H,C) & m1_subset_1(G,B) & v1_funct_2(E,k3_zfmisc_1(A,B,C),D) & v1_funct_1(E) & -v1_xboole_0(D) & -v1_xboole_0(A) -> m1_subset_1(k2_multop_1(A,B,C,D,E,F,G,H),D))) # label(dt_k2_multop_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4444 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,k3_zfmisc_1(A,B,C),D) & m2_relset_1(E,k3_zfmisc_1(A,B,C),D) -> (all F (m2_relset_1(F,k3_zfmisc_1(A,B,C),D) & v1_funct_2(F,k3_zfmisc_1(A,B,C),D) & v1_funct_1(F) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> k2_multop_1(A,B,C,D,E,G,H,I) = k2_multop_1(A,B,C,D,F,G,H,I))))))) -> E = F))))))))))))) # label(t4_multop_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4445 (all A (-v1_xboole_0(A) -> (all B all C all D all E (m2_relset_1(E,k3_zfmisc_1(B,C,D),A) & v1_funct_2(E,k3_zfmisc_1(B,C,D),A) & v1_funct_1(E) -> (all F (m2_relset_1(F,k3_zfmisc_1(B,C,D),A) & v1_funct_2(F,k3_zfmisc_1(B,C,D),A) & v1_funct_1(F) -> ((all G all H all I (r2_hidden(G,B) & r2_hidden(H,C) & r2_hidden(I,D) -> k1_funct_1(F,k3_mcart_1(G,H,I)) = k1_funct_1(E,k3_mcart_1(G,H,I)))) -> F = E))))))) # label(t2_multop_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4446 (all A (m1_subset_1(A,f1_s1_multop_1) -> (all B (m1_subset_1(B,f2_s1_multop_1) -> (all C (m1_subset_1(C,f3_s1_multop_1) -> (exists D (p1_s1_multop_1(A,B,C,D) & m1_subset_1(D,f4_s1_multop_1))))))))) -> (exists A (v1_funct_1(A) & (all B (m1_subset_1(B,f1_s1_multop_1) -> (all C (m1_subset_1(C,f2_s1_multop_1) -> (all D (m1_subset_1(D,f3_s1_multop_1) -> p1_s1_multop_1(B,C,D,k8_funct_2(k3_zfmisc_1(f1_s1_multop_1,f2_s1_multop_1,f3_s1_multop_1),f4_s1_multop_1,A,k4_domain_1(f1_s1_multop_1,f2_s1_multop_1,f3_s1_multop_1,B,C,D))))))))) & m2_relset_1(A,k3_zfmisc_1(f1_s1_multop_1,f2_s1_multop_1,f3_s1_multop_1),f4_s1_multop_1) & v1_funct_2(A,k3_zfmisc_1(f1_s1_multop_1,f2_s1_multop_1,f3_s1_multop_1),f4_s1_multop_1))) # label(s1_multop_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4447 (exists A (v1_funct_1(A) & v1_funct_2(A,k4_zfmisc_1(f1_s7_multop_1,f2_s7_multop_1,f3_s7_multop_1,f4_s7_multop_1),f5_s7_multop_1) & m2_relset_1(A,k4_zfmisc_1(f1_s7_multop_1,f2_s7_multop_1,f3_s7_multop_1,f4_s7_multop_1),f5_s7_multop_1) & (all B (m1_subset_1(B,f1_s7_multop_1) -> (all C (m1_subset_1(C,f2_s7_multop_1) -> (all D (m1_subset_1(D,f3_s7_multop_1) -> (all E (m1_subset_1(E,f4_s7_multop_1) -> f6_s7_multop_1(B,C,D,E) = k8_funct_2(k4_zfmisc_1(f1_s7_multop_1,f2_s7_multop_1,f3_s7_multop_1,f4_s7_multop_1),f5_s7_multop_1,A,k5_domain_1(f1_s7_multop_1,f2_s7_multop_1,f3_s7_multop_1,f4_s7_multop_1,B,C,D,E)))))))))))) # label(s7_multop_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4448 (exists A (v1_funct_1(A) & m2_relset_1(A,k3_zfmisc_1(f1_s3_multop_1,f2_s3_multop_1,f3_s3_multop_1),f4_s3_multop_1) & (all B (m1_subset_1(B,f1_s3_multop_1) -> (all C (m1_subset_1(C,f2_s3_multop_1) -> (all D (m1_subset_1(D,f3_s3_multop_1) -> f5_s3_multop_1(B,C,D) = k8_funct_2(k3_zfmisc_1(f1_s3_multop_1,f2_s3_multop_1,f3_s3_multop_1),f4_s3_multop_1,A,k4_domain_1(f1_s3_multop_1,f2_s3_multop_1,f3_s3_multop_1,B,C,D)))))))) & v1_funct_2(A,k3_zfmisc_1(f1_s3_multop_1,f2_s3_multop_1,f3_s3_multop_1),f4_s3_multop_1))) # label(s3_multop_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4449 $T # label(dt_k1_multop_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4450 (exists A (v1_funct_1(A) & m2_relset_1(A,k3_zfmisc_1(f1_s4_multop_1,f2_s4_multop_1,f3_s4_multop_1),f4_s4_multop_1) & (all B (m1_subset_1(B,f1_s4_multop_1) -> (all C (m1_subset_1(C,f2_s4_multop_1) -> (all D (m1_subset_1(D,f3_s4_multop_1) -> f5_s4_multop_1(B,C,D) = k2_multop_1(f1_s4_multop_1,f2_s4_multop_1,f3_s4_multop_1,f4_s4_multop_1,A,B,C,D))))))) & v1_funct_2(A,k3_zfmisc_1(f1_s4_multop_1,f2_s4_multop_1,f3_s4_multop_1),f4_s4_multop_1))) # label(s4_multop_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4451 (all A all B all C all D all E all F all G all H all I all J (-v1_xboole_0(A) & -v1_xboole_0(D) & -v1_xboole_0(E) & v1_funct_1(F) & v1_funct_2(F,k4_zfmisc_1(A,B,C,D),E) & m1_subset_1(H,B) & m1_subset_1(J,D) & m1_subset_1(I,C) & m1_subset_1(G,A) & m1_relset_1(F,k4_zfmisc_1(A,B,C,D),E) & -v1_xboole_0(C) & -v1_xboole_0(B) -> k4_multop_1(A,B,C,D,E,F,G,H,I,J) = k3_multop_1(F,G,H,I,J))) # label(redefinition_k4_multop_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4452 (exists A (v1_funct_1(A) & v1_funct_2(A,k4_zfmisc_1(f1_s8_multop_1,f1_s8_multop_1,f1_s8_multop_1,f1_s8_multop_1),f1_s8_multop_1) & (all B (m1_subset_1(B,f1_s8_multop_1) -> (all C (m1_subset_1(C,f1_s8_multop_1) -> (all D (m1_subset_1(D,f1_s8_multop_1) -> (all E (m1_subset_1(E,f1_s8_multop_1) -> f2_s8_multop_1(B,C,D,E) = k4_multop_1(f1_s8_multop_1,f1_s8_multop_1,f1_s8_multop_1,f1_s8_multop_1,f1_s8_multop_1,A,B,C,D,E))))))))) & m2_relset_1(A,k4_zfmisc_1(f1_s8_multop_1,f1_s8_multop_1,f1_s8_multop_1,f1_s8_multop_1),f1_s8_multop_1))) # label(s8_multop_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4453 (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]. 15.04/14.58 4454 (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]. 15.04/14.58 4455 (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]. 15.04/14.58 4456 (exists A (l1_struct_0(A) & v1_struct_0(A))) # label(rc1_struct_0) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4457 (exists A (-v3_struct_0(A) & l2_struct_0(A))) # label(rc4_struct_0) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4458 (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]. 15.04/14.58 4459 (exists A (l2_struct_0(A) & v2_struct_0(A))) # label(rc2_struct_0) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4460 (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]. 15.04/14.58 4461 (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]. 15.04/14.58 4462 (exists A (-v3_struct_0(A) & l1_struct_0(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4463 (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]. 15.04/14.58 4464 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4465 (all A (l2_struct_0(A) -> l1_struct_0(A))) # label(dt_l2_struct_0) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4466 (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]. 15.04/14.58 4467 (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]. 15.04/14.58 4468 (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]. 15.04/14.58 4469 (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]. 15.04/14.58 4470 (exists A l1_struct_0(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4471 (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]. 15.04/14.58 4472 (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]. 15.04/14.58 4473 (exists A l2_struct_0(A)) # label(existence_l2_struct_0) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4474 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4475 (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]. 15.04/14.58 4476 (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]. 15.04/14.58 4477 (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]. 15.04/14.58 4478 (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]. 15.04/14.58 4479 (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]. 15.04/14.58 4480 (all A (l1_cat_1(A) -> v1_funct_1(u4_cat_1(A)) & m2_relset_1(u4_cat_1(A),u2_cat_1(A),u1_cat_1(A)) & v1_funct_2(u4_cat_1(A),u2_cat_1(A),u1_cat_1(A)))) # label(dt_u4_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4481 (all A all B all C all D all E (v2_cat_1(B) & v2_cat_1(C) & m2_cat_1(D,A,B) & m2_cat_1(E,B,C) & l1_cat_1(C) & l1_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> m2_cat_1(k14_cat_1(A,B,C,D,E),A,C))) # label(dt_k14_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4482 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> v4_cat_1(k10_cat_1(A,B),A))))) # label(t69_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4483 $T # label(t17_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4484 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,B,C) -> (all F (m1_cat_1(F,A,C,D) -> (v4_cat_1(k9_cat_1(A,B,C,D,E,F),A) -> k1_xboole_0 = k6_cat_1(A,B,C) | k6_cat_1(A,C,D) = k1_xboole_0 | v4_cat_1(F,A)))))))))))))) # label(t67_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4485 $T # label(t120_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4486 (all A all B (l1_cat_1(A) & m1_subset_1(B,u2_cat_1(A)) -> m1_subset_1(k2_cat_1(A,B),u1_cat_1(A)))) # label(dt_k2_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4487 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,B,C) -> (all F (m1_cat_1(F,A,C,D) -> (v3_cat_1(k9_cat_1(A,B,C,D,E,F),A) -> k6_cat_1(A,B,C) = k1_xboole_0 | v3_cat_1(E,A) | k1_xboole_0 = k6_cat_1(A,C,D)))))))))))))) # label(t62_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4488 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (v7_cat_1(B,A) -> (all C (m1_cat_1(C,A,B,B) -> C = k10_cat_1(A,B)))))))) # label(t83_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4489 (all A all B all C all D (l1_cat_1(A) & l1_cat_1(B) & m2_cat_1(C,A,B) & m1_subset_1(D,u1_cat_1(A)) & v2_cat_1(B) & v2_cat_1(A) -> m1_subset_1(k13_cat_1(A,B,C,D),u1_cat_1(B)))) # label(dt_k13_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4490 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)) = k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),k2_cat_1(A,D)) & k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)) = k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),k3_cat_1(A,D)))))))))) # label(t105_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4491 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (k6_cat_1(A,D,E) != k1_xboole_0 -> (all F (m1_cat_1(F,A,D,E) -> m1_cat_1(k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,F),B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E))))))))))))))) # label(t125_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4492 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> k6_cat_1(A,B,C) = a_3_0_cat_1(A,B,C))))))) # label(d6_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4493 (all A (l1_cat_1(A) & v2_cat_1(A) -> m2_cat_1(k15_cat_1(A),A,A))) # label(dt_k15_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4494 $T # label(t31_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4495 $T # label(t121_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4496 $T # label(t11_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4497 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (B = k3_cat_1(A,C) -> C = k4_cat_1(A,C,k5_cat_1(A,B))))))))) # label(t46_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4498 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,B,C) -> (v10_cat_1(D,A,B) & v10_cat_1(E,B,C) -> v10_cat_1(k14_cat_1(A,B,C,D,E),A,C)))))))))))) # label(t128_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4499 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> k13_cat_1(A,B,C,D) = k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D))))))))) # label(d20_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4500 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (v6_cat_1(B,A) & r1_cat_1(A,C,B) -> v6_cat_1(C,A)))))))) # label(t89_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4501 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (r2_hidden(D,k6_cat_1(A,B,C)) <-> k2_cat_1(A,D) = B & k3_cat_1(A,D) = C))))))))) # label(t18_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4502 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,B,C) -> (all F (m1_subset_1(F,u1_cat_1(A)) -> k8_funct_2(u1_cat_1(B),u1_cat_1(C),k12_cat_1(B,C,E),k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,D),F)) = k8_funct_2(u1_cat_1(A),u1_cat_1(C),k12_cat_1(A,C,k14_cat_1(A,B,C,D,E)),F))))))))))))) # label(t112_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4503 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (k1_xboole_0 != k6_cat_1(A,B,C) -> k9_cat_1(A,B,B,C,k10_cat_1(A,B),D) = D))))))))) # label(t58_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4504 (all A all B all C (v1_funct_1(k1_cat_1(A,B,C)) & m2_relset_1(k1_cat_1(A,B,C),k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)))) # label(dt_k1_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4505 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> r1_cat_1(A,B,B))))) # label(t91_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4506 (all A all B all C (m1_subset_1(C,u1_cat_1(k8_cat_1(A,B))) -> (all D (m1_subset_1(D,u1_cat_1(k8_cat_1(A,B))) -> (all E (m1_subset_1(E,u2_cat_1(k8_cat_1(A,B))) -> m1_cat_1(E,k8_cat_1(A,B),C,D))))))) # label(t37_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4507 (all A all B all C (l1_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) & m1_subset_1(C,u1_cat_1(A)) -> (exists D m1_cat_1(D,A,B,C)))) # label(existence_m1_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4508 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (k1_xboole_0 != k6_cat_1(A,B,C) -> D = k9_cat_1(A,B,C,C,D,k10_cat_1(A,C))))))))))) # label(t57_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4509 $T # label(t53_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4510 $T # label(dt_l1_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4511 (all A (l1_cat_1(A) -> v1_funct_1(u5_cat_1(A)) & m2_relset_1(u5_cat_1(A),k2_zfmisc_1(u2_cat_1(A),u2_cat_1(A)),u2_cat_1(A)))) # label(dt_u5_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4512 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (r2_hidden(D,k6_cat_1(A,B,C)) -> m1_cat_1(D,A,B,C))))))))) # label(t21_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4513 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (k3_cat_1(A,C) = k2_cat_1(A,B) <-> r2_hidden(k4_tarski(B,C),k1_relat_1(u5_cat_1(A)))))))))) # label(t40_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4514 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,B,C) -> (all F (m1_cat_1(F,A,C,D) -> (v5_cat_1(E,A) & v5_cat_1(F,A) -> k6_cat_1(A,C,D) = k1_xboole_0 | k9_cat_1(A,D,C,B,k11_cat_1(A,C,D,F),k11_cat_1(A,B,C,E)) = k11_cat_1(A,B,D,k9_cat_1(A,B,C,D,E,F)) | k6_cat_1(A,B,C) = k1_xboole_0))))))))))))) # label(t77_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4515 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k3_cat_1(A,D))) = k10_cat_1(B,k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) & k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k2_cat_1(A,D))) = k10_cat_1(B,k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))))))))))) # label(t98_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4516 $T # label(t2_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4517 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (r2_hidden(F,k6_cat_1(A,D,E)) -> r2_hidden(k1_funct_1(C,F),k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E))))))))))))))) # label(t123_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.04/14.58 4518 (all A all B all C (k1_relat_1(k1_cat_1(A,B,C)) = k1_tarski(k4_tarski(A,B)) & k2_zfmisc_1(k1_tarski(A),k1_tarski(B)) = k1_relat_1(k1_cat_1(A,B,C)))) # label(t7_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4519 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> k5_cat_1(A,B) = k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B))))) # label(d5_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4520 (all A all B m1_subset_1(A,u2_cat_1(k8_cat_1(B,A)))) # label(t33_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4521 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> ((all E (m1_cat_1(E,A,B,C) -> E = D)) -> k6_cat_1(A,B,C) = k1_xboole_0 | k1_tarski(D) = k6_cat_1(A,B,C)))))))))) # label(t26_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4522 (all A (l1_cat_1(A) -> ((all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (r2_hidden(k4_tarski(C,B),k1_relat_1(u5_cat_1(A))) <-> k3_cat_1(A,B) = k2_cat_1(A,C)))))) & (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (k2_cat_1(A,C) = k3_cat_1(A,B) -> k3_cat_1(A,k4_cat_1(A,B,C)) = k3_cat_1(A,C) & k2_cat_1(A,k4_cat_1(A,B,C)) = k2_cat_1(A,B)))))) & (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (k2_cat_1(A,C) = k3_cat_1(A,B) & k2_cat_1(A,D) = k3_cat_1(A,C) -> k4_cat_1(A,k4_cat_1(A,B,C),D) = k4_cat_1(A,B,k4_cat_1(A,C,D))))))))) & (all B (m1_subset_1(B,u1_cat_1(A)) -> B = k2_cat_1(A,k5_cat_1(A,B)) & k3_cat_1(A,k5_cat_1(A,B)) = B & (all C (m1_subset_1(C,u2_cat_1(A)) -> (B = k2_cat_1(A,C) -> C = k4_cat_1(A,k5_cat_1(A,B),C)))) & (all C (m1_subset_1(C,u2_cat_1(A)) -> (k3_cat_1(A,C) = B -> C = k4_cat_1(A,C,k5_cat_1(A,B))))))) -> v2_cat_1(A)))) # label(t29_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4523 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,u1_cat_1(A),u1_cat_1(B)) & m2_relset_1(D,u1_cat_1(A),u1_cat_1(B)) -> ((all E (m1_subset_1(E,u2_cat_1(A)) -> (all F (m1_subset_1(F,u2_cat_1(A)) -> (k2_cat_1(A,F) = k3_cat_1(A,E) -> k4_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,F)) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k4_cat_1(A,E,F))))))) & (all E (m1_subset_1(E,u2_cat_1(A)) -> k8_funct_2(u1_cat_1(A),u1_cat_1(B),D,k3_cat_1(A,E)) = k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)) & k8_funct_2(u1_cat_1(A),u1_cat_1(B),D,k2_cat_1(A,E)) = k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)))) & (all E (m1_subset_1(E,u1_cat_1(A)) -> k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,E)) = k10_cat_1(B,k8_funct_2(u1_cat_1(A),u1_cat_1(B),D,E)))) -> m2_cat_1(C,A,B)))))))))) # label(t100_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4524 (all A all B all C all D (-v1_xboole_0(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,D) & m2_relset_1(E,A,D) -> (r1_tarski(k2_funct_2(A,D,E,B),C) & r1_tarski(B,A) -> v1_funct_1(k2_partfun1(A,D,E,B)) & m2_relset_1(k2_partfun1(A,D,E,B),B,C) & v1_funct_2(k2_partfun1(A,D,E,B),B,C)))))) # label(t4_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4525 (all A (l1_cat_1(A) -> -v1_xboole_0(u1_cat_1(A)))) # label(dt_u1_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4526 (all A (l1_cat_1(A) & v2_cat_1(A) -> k6_partfun1(u1_cat_1(A)) = k12_cat_1(A,A,k15_cat_1(A)))) # label(t117_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4527 (all A (l1_cat_1(A) & v2_cat_1(A) -> m2_cat_1(k6_partfun1(u2_cat_1(A)),A,A))) # label(t111_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4528 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> v3_cat_1(k10_cat_1(A,B),A))))) # label(t64_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4529 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> k2_cat_1(A,B) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),B))))) # label(d2_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4530 (all A all B all C all D (m1_subset_1(D,k1_tarski(A)) -> (all E (m1_subset_1(E,k1_tarski(B)) -> k1_funct_1(k1_cat_1(A,B,C),k4_tarski(D,E)) = C)))) # label(t9_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4531 $T # label(t5_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4532 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,B,C) -> (v9_cat_1(E,B,C) & v9_cat_1(D,A,B) -> v9_cat_1(k14_cat_1(A,B,C,D,E),A,C)))))))))))) # label(t127_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4533 $T # label(t78_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4534 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (r1_cat_1(A,B,C) -> r1_cat_1(A,C,B)))))))) # label(t92_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4535 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> ((all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)) != k1_xboole_0 -> (all F (m1_cat_1(F,B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)) -> (exists G (F = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,G) & m1_cat_1(G,A,D,E))) & k6_cat_1(A,D,E) != k1_xboole_0))))))) <-> v9_cat_1(C,A,B)))))))) # label(d23_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4536 (all A all B all C all D all E (l1_cat_1(A) & l1_cat_1(C) & m2_cat_1(E,B,C) & m2_cat_1(D,A,B) & v2_cat_1(C) & l1_cat_1(B) & v2_cat_1(B) & v2_cat_1(A) -> k14_cat_1(A,B,C,D,E) = k5_relat_1(D,E))) # label(redefinition_k14_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4537 $T # label(t130_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4538 $T # label(t49_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4539 (all A all B all C all D all E all F (-v1_xboole_0(B) & v1_funct_1(C) & m1_relset_1(C,B,A) & v1_funct_1(D) & v1_funct_2(D,B,A) & m1_relset_1(D,B,A) & m1_relset_1(E,k2_zfmisc_1(B,B),B) & v1_funct_2(F,A,B) & m1_relset_1(F,A,B) & v1_funct_1(F) & v1_funct_1(E) & v1_funct_2(C,B,A) & -v1_xboole_0(A) -> l1_cat_1(g1_cat_1(A,B,C,D,E,F)) & v1_cat_1(g1_cat_1(A,B,C,D,E,F)))) # label(dt_g1_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4540 $T # label(t20_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4541 $T # label(t95_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4542 (all A all B (v1_cat_1(k8_cat_1(A,B)) & v2_cat_1(k8_cat_1(A,B)) & l1_cat_1(k8_cat_1(A,B)))) # label(dt_k8_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4543 (all A all B all C (m1_subset_1(C,u1_cat_1(k8_cat_1(A,B))) -> (all D (m1_subset_1(D,u1_cat_1(k8_cat_1(A,B))) -> (all E (m1_subset_1(E,u1_cat_1(k8_cat_1(A,B))) -> (all F (m1_subset_1(F,u1_cat_1(k8_cat_1(A,B))) -> (all G (m1_cat_1(G,k8_cat_1(A,B),C,D) -> (all H (m1_cat_1(H,k8_cat_1(A,B),E,F) -> H = G)))))))))))) # label(t39_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4544 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) -> (m2_cat_1(C,A,B) <-> (all D (m1_subset_1(D,u2_cat_1(A)) -> (all E (m1_subset_1(E,u2_cat_1(A)) -> (r2_hidden(k4_tarski(E,D),k1_relat_1(u5_cat_1(A))) -> k1_funct_1(u5_cat_1(B),k4_tarski(k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) = k1_funct_1(C,k1_funct_1(u5_cat_1(A),k4_tarski(E,D)))))))) & (all D (m1_subset_1(D,u2_cat_1(A)) -> k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),D))) = k8_funct_2(u1_cat_1(B),u2_cat_1(B),u6_cat_1(B),k8_funct_2(u2_cat_1(B),u1_cat_1(B),u4_cat_1(B),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) & k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),D))) = k8_funct_2(u1_cat_1(B),u2_cat_1(B),u6_cat_1(B),k8_funct_2(u2_cat_1(B),u1_cat_1(B),u3_cat_1(B),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))))) & (all D (m1_subset_1(D,u1_cat_1(A)) -> (exists E (m1_subset_1(E,u1_cat_1(B)) & k8_funct_2(u1_cat_1(B),u2_cat_1(B),u6_cat_1(B),E) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),D))))))))))))) # label(d18_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4545 (all A all B all C (m1_subset_1(B,u1_cat_1(A)) & m1_subset_1(C,u1_cat_1(A)) & l1_cat_1(A) -> m1_subset_1(k6_cat_1(A,B,C),k1_zfmisc_1(u2_cat_1(A))))) # label(dt_k6_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4546 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (k1_xboole_0 != k6_cat_1(A,B,C) -> (v5_cat_1(D,A) <-> k1_xboole_0 != k6_cat_1(A,C,B) & (exists E (k9_cat_1(A,B,C,B,D,E) = k10_cat_1(A,B) & k9_cat_1(A,C,B,C,E,D) = k10_cat_1(A,C) & m1_cat_1(E,A,C,B))))))))))))) # label(t70_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4547 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> k13_cat_1(A,B,C,k3_cat_1(A,D)) = k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)) & k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)) = k13_cat_1(A,B,C,k2_cat_1(A,D)))))))))) # label(t109_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4548 $T # label(t72_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4549 $T # label(t14_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4550 (all A all B all C k1_cat_1(A,B,C) = k3_cqc_lang(k4_tarski(A,B),C)) # label(d1_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4551 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) -> ((all D (m1_subset_1(D,u1_cat_1(A)) -> (exists E (m1_subset_1(E,u1_cat_1(B)) & k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,E))))) & (all D (m1_subset_1(D,u2_cat_1(A)) -> (all E (m1_subset_1(E,u2_cat_1(A)) -> (k3_cat_1(A,D) = k2_cat_1(A,E) -> k4_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k4_cat_1(A,D,E))))))) & (all D (m1_subset_1(D,u2_cat_1(A)) -> k10_cat_1(B,k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k3_cat_1(A,D))) & k10_cat_1(B,k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k2_cat_1(A,D))))) -> m2_cat_1(C,A,B)))))))) # label(t96_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4552 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> k2_partfun1(u2_cat_1(A),u2_cat_1(B),C,k6_cat_1(A,D,E)) = k16_cat_1(A,B,C,D,E))))))))))) # label(d25_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4553 $T # label(t13_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4554 (all A all B all C (l1_cat_1(A) & m1_subset_1(C,u2_cat_1(A)) & m1_subset_1(B,u2_cat_1(A)) -> m1_subset_1(k4_cat_1(A,B,C),u2_cat_1(A)))) # label(dt_k4_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4555 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (v6_cat_1(B,A) -> v3_cat_1(D,A) | k6_cat_1(A,B,C) = k1_xboole_0))))))))) # label(t90_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4556 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (k3_cat_1(A,B) = k2_cat_1(A,C) -> k3_cat_1(A,k4_cat_1(A,B,C)) = k3_cat_1(A,C) & k2_cat_1(A,B) = k2_cat_1(A,k4_cat_1(A,B,C))))))))) # label(t42_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4557 (all A all B all C all D (v2_cat_1(A) & l1_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) & m1_cat_1(D,A,B,C) & m1_subset_1(C,u1_cat_1(A)) -> m1_cat_1(k11_cat_1(A,B,C,D),A,C,B))) # label(dt_k11_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4558 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> (k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,E) -> k13_cat_1(A,B,C,D) = E))))))))))) # label(t107_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4559 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (r1_cat_1(A,B,C) <-> (exists D (v5_cat_1(D,A) & m1_cat_1(D,A,B,C))) & k6_cat_1(A,B,C) != k1_xboole_0))))))) # label(d17_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4560 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (v6_cat_1(B,A) <-> (all C (m1_subset_1(C,u1_cat_1(A)) -> k6_cat_1(A,C,B) != k1_xboole_0 & (exists D ((all E (m1_cat_1(E,A,C,B) -> E = D)) & m1_cat_1(D,A,C,B)))))))))) # label(d15_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4561 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> ((all C (m1_subset_1(C,u1_cat_1(A)) -> k6_cat_1(A,B,C) != k1_xboole_0 & (exists D ((all E (m1_cat_1(E,A,B,C) -> D = E)) & m1_cat_1(D,A,B,C))))) <-> v7_cat_1(B,A)))))) # label(d16_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4562 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> m1_cat_1(B,A,k2_cat_1(A,B),k3_cat_1(A,B)))))) # label(t22_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4563 (all A all B k8_cat_1(A,B) = g1_cat_1(k1_tarski(A),k1_tarski(B),k7_cat_1(B,A),k7_cat_1(B,A),k1_cat_1(B,B,B),k7_cat_1(A,B))) # label(d9_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4564 $T # label(t6_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4565 (exists A l1_cat_1(A)) # label(existence_l1_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4566 (all A all B (m1_subset_1(B,u2_cat_1(A)) & l1_cat_1(A) -> m1_subset_1(k3_cat_1(A,B),u1_cat_1(A)))) # label(dt_k3_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4567 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (k2_cat_1(A,B) = k3_cat_1(A,C) -> k4_cat_1(A,C,B) = k1_funct_1(u5_cat_1(A),k4_tarski(B,C))))))))) # label(t41_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4568 $T # label(t15_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4569 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> k9_cat_1(A,B,B,B,k10_cat_1(A,B),k10_cat_1(A,B)) = k10_cat_1(A,B))))) # label(t59_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4570 (all A all B (v1_funct_1(k7_cat_1(A,B)) & m2_relset_1(k7_cat_1(A,B),k1_tarski(A),k1_tarski(B)) & v1_funct_2(k7_cat_1(A,B),k1_tarski(A),k1_tarski(B)))) # label(dt_k7_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4571 $T # label(t106_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4572 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (k2_cat_1(A,C) = B -> C = k4_cat_1(A,k5_cat_1(A,B),C)))))))) # label(t47_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4573 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (k5_cat_1(A,B) = k5_cat_1(A,C) -> C = B))))))) # label(t45_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4574 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (r1_cat_1(A,B,C) & v7_cat_1(B,A) -> v7_cat_1(C,A)))))))) # label(t85_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4575 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (all E (m1_cat_1(E,A,C,B) -> (k9_cat_1(A,C,B,C,E,D) = k10_cat_1(A,C) -> v4_cat_1(D,A) | k1_xboole_0 = k6_cat_1(A,C,B) | k1_xboole_0 = k6_cat_1(A,B,C)))))))))))) # label(t68_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4576 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> v5_cat_1(k10_cat_1(A,B),A))))) # label(t74_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4577 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,B,C) -> (all F (m1_cat_1(F,A,C,D) -> (v5_cat_1(E,A) & v5_cat_1(F,A) -> k1_xboole_0 = k6_cat_1(A,C,D) | v5_cat_1(k9_cat_1(A,B,C,D,E,F),A) | k6_cat_1(A,B,C) = k1_xboole_0))))))))))))) # label(t75_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4578 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> ((all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> k2_relat_1(k16_cat_1(A,B,C,D,E)) = k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)))))) <-> v9_cat_1(C,A,B)))))))) # label(t132_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4579 (exists A (v2_cat_1(A) & l1_cat_1(A))) # label(rc2_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4580 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (all E (m1_cat_1(E,A,C,B) -> (k10_cat_1(A,C) = k9_cat_1(A,C,B,C,E,D) -> k1_xboole_0 = k6_cat_1(A,C,B) | v3_cat_1(E,A) | k6_cat_1(A,B,C) = k1_xboole_0))))))))))) # label(t63_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4581 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_1(C) -> ((all D (m1_subset_1(D,u1_cat_1(A)) -> (exists E (k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,E) & m1_subset_1(E,u1_cat_1(B)))))) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> (k10_cat_1(B,E) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) -> k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D) = E)))))))))))) # label(t102_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4582 (all A all B (l1_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) -> m1_subset_1(k5_cat_1(A,B),u2_cat_1(A)))) # label(dt_k5_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4583 $T # label(t94_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4584 (all A all B all C (v2_cat_1(A) & v1_funct_1(C) & m1_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & l1_cat_1(B) & v2_cat_1(B) & l1_cat_1(A) -> v1_funct_1(k12_cat_1(A,B,C)) & v1_funct_2(k12_cat_1(A,B,C),u1_cat_1(A),u1_cat_1(B)) & m2_relset_1(k12_cat_1(A,B,C),u1_cat_1(A),u1_cat_1(B)))) # label(dt_k12_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4585 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (v7_cat_1(C,A) & v7_cat_1(B,A) -> r1_cat_1(A,B,C)))))))) # label(t84_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4586 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (v6_cat_1(B,A) -> (all C (m1_cat_1(C,A,B,B) -> C = k10_cat_1(A,B)))))))) # label(t87_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4587 (all A (l1_cat_1(A) -> v1_funct_1(u6_cat_1(A)) & v1_funct_2(u6_cat_1(A),u1_cat_1(A),u2_cat_1(A)) & m2_relset_1(u6_cat_1(A),u1_cat_1(A),u2_cat_1(A)))) # label(dt_u6_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4588 $T # label(t101_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4589 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (v10_cat_1(C,A,B) <-> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> v2_funct_1(k16_cat_1(A,B,C,D,E))))))))))))) # label(t133_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4590 (all A all B all C (m1_subset_1(C,u1_cat_1(k8_cat_1(A,B))) -> (all D (m1_subset_1(D,u1_cat_1(k8_cat_1(A,B))) -> (all E (m1_subset_1(E,u2_cat_1(k8_cat_1(A,B))) -> r2_hidden(E,k6_cat_1(k8_cat_1(A,B),C,D)))))))) # label(t36_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4591 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> ((all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (k1_xboole_0 != k6_cat_1(A,D,E) -> (all F (m1_cat_1(F,A,D,E) -> (all G (m1_cat_1(G,A,D,E) -> (k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,G) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,F) -> F = G)))))))))) <-> v10_cat_1(C,A,B)))))))) # label(d24_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4592 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_cat_1(F,A,B,C) -> (all G (m1_cat_1(G,A,C,D) -> (all H (m1_cat_1(H,A,D,E) -> -(k1_xboole_0 != k6_cat_1(A,B,C) & k9_cat_1(A,B,C,E,F,k9_cat_1(A,C,D,E,G,H)) != k9_cat_1(A,B,D,E,k9_cat_1(A,B,C,D,F,G),H) & k1_xboole_0 != k6_cat_1(A,D,E) & k1_xboole_0 != k6_cat_1(A,C,D)))))))))))))))))) # label(t54_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4593 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> r1_tarski(k2_funct_2(u2_cat_1(A),u2_cat_1(B),C,k6_cat_1(A,D,E)),k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E))))))))))))) # label(t129_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4594 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> -(k1_xboole_0 = k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)) & k6_cat_1(A,D,E) != k1_xboole_0))))))))))) # label(t126_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4595 (all A (l1_cat_1(A) & v2_cat_1(A) -> v8_cat_1(k15_cat_1(A),A,A))) # label(t122_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4596 $T # label(t10_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4597 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (k1_xboole_0 != k6_cat_1(A,D,E) -> (all F (m1_cat_1(F,A,D,E) -> k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,F) = k1_funct_1(k16_cat_1(A,B,C,D,E),F)))))))))))))) # label(t131_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4598 (all A (v2_cat_1(A) & l1_cat_1(A) -> k6_partfun1(u2_cat_1(A)) = k15_cat_1(A))) # label(d21_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4599 $T # label(t30_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4600 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (v5_cat_1(D,A) -> v4_cat_1(D,A) & v3_cat_1(D,A) | k6_cat_1(A,B,C) = k1_xboole_0))))))))) # label(t73_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4601 (all A all B all C all D (m1_subset_1(C,u1_cat_1(B)) & m1_subset_1(D,u1_cat_1(B)) & l1_cat_1(B) -> (r2_hidden(A,a_3_0_cat_1(B,C,D)) <-> (exists E (k2_cat_1(B,E) = C & D = k3_cat_1(B,E) & E = A & m1_subset_1(E,u2_cat_1(B))))))) # label(fraenkel_a_3_0_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4602 (all A all B all C (m1_subset_1(C,u1_cat_1(k8_cat_1(A,B))) -> A = C)) # label(t34_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4603 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,B,C) -> m2_cat_1(k7_funct_2(u2_cat_1(A),u2_cat_1(B),u2_cat_1(C),D,E),A,C))))))))))) # label(t110_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4604 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_1(C) -> ((all D (m1_subset_1(D,u1_cat_1(A)) -> (exists E (k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),D)) = k8_funct_2(u1_cat_1(B),u2_cat_1(B),u6_cat_1(B),E) & m1_subset_1(E,u1_cat_1(B)))))) -> (all D (v1_funct_1(D) & m2_relset_1(D,u1_cat_1(A),u1_cat_1(B)) & v1_funct_2(D,u1_cat_1(A),u1_cat_1(B)) -> ((all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_subset_1(F,u1_cat_1(B)) -> (k8_funct_2(u1_cat_1(B),u2_cat_1(B),u6_cat_1(B),F) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),E)) -> k8_funct_2(u1_cat_1(A),u1_cat_1(B),D,E) = F))))) <-> k12_cat_1(A,B,C) = D)))))))))) # label(d19_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4605 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> k8_funct_2(u1_cat_1(A),u1_cat_1(A),k12_cat_1(A,A,k15_cat_1(A)),B) = B)))) # label(t116_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4606 (all A all B all C (m1_subset_1(C,u2_cat_1(k8_cat_1(A,B))) -> B = C)) # label(t35_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4607 (all A all B (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) -> (exists C m2_cat_1(C,A,B)))) # label(existence_m2_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4608 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> ((all C (m1_subset_1(C,u1_cat_1(A)) -> (exists D (k1_tarski(D) = k6_cat_1(A,B,C) & m1_cat_1(D,A,B,C))))) <-> v7_cat_1(B,A)))))) # label(t82_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4609 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (k3_cat_1(A,B) = k2_cat_1(A,C) & k2_cat_1(A,D) = k3_cat_1(A,C) -> k4_cat_1(A,k4_cat_1(A,B,C),D) = k4_cat_1(A,B,k4_cat_1(A,C,D))))))))))) # label(t43_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4610 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (v5_cat_1(D,A) -> k1_xboole_0 = k6_cat_1(A,B,C) | (all E (m1_cat_1(E,A,C,B) -> (E = k11_cat_1(A,B,C,D) <-> k9_cat_1(A,C,B,C,E,D) = k10_cat_1(A,C) & k10_cat_1(A,B) = k9_cat_1(A,B,C,B,D,E))))))))))))) # label(d14_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4611 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> ((exists C (m1_subset_1(C,u2_cat_1(A)) & k2_cat_1(A,B) = k3_cat_1(A,C) & k5_cat_1(A,k2_cat_1(A,B)) = k4_cat_1(A,B,C) & k4_cat_1(A,C,B) = k5_cat_1(A,k3_cat_1(A,B)) & k2_cat_1(A,C) = k3_cat_1(A,B))) <-> v5_cat_1(B,A)))))) # label(d12_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4612 $T # label(t50_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4613 (all A all B (l1_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) & v2_cat_1(A) -> m1_cat_1(k10_cat_1(A,B),A,B,B))) # label(dt_k10_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4614 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> (k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,E) -> k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D) = E))))))))))) # label(t103_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4615 $T # label(t12_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4616 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> k6_cat_1(A,k2_cat_1(A,B),k3_cat_1(A,B)) != k1_xboole_0)))) # label(t19_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4617 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> -(k6_cat_1(A,C,B) != k1_xboole_0 & (exists E ((exists F (k10_cat_1(A,B) = k9_cat_1(A,B,C,B,D,F) & F != E & k9_cat_1(A,C,B,C,E,D) = k10_cat_1(A,C) & m1_cat_1(F,A,C,B))) & m1_cat_1(E,A,C,B))) & k1_xboole_0 != k6_cat_1(A,B,C)))))))))) # label(t71_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4618 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,B,C) -> (all F (m1_cat_1(F,A,C,D) -> -(k6_cat_1(A,C,D) != k1_xboole_0 & -r2_hidden(k4_cat_1(A,E,F),k6_cat_1(A,B,D)) & k6_cat_1(A,B,C) != k1_xboole_0))))))))))))) # label(t51_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4619 (all A all B all C k1_funct_1(k1_cat_1(A,B,C),k4_tarski(A,B)) = C) # label(t8_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4620 (all A all B all C all D all E all F (l1_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) & m1_cat_1(F,A,C,D) & m1_cat_1(E,A,B,C) & m1_subset_1(D,u1_cat_1(A)) & m1_subset_1(C,u1_cat_1(A)) & v2_cat_1(A) -> m1_cat_1(k9_cat_1(A,B,C,D,E,F),A,B,D))) # label(dt_k9_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4621 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (exists E (k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,E) & m1_subset_1(E,u1_cat_1(B)))))))))))) # label(t97_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4622 (all A (l1_cat_1(A) -> v1_funct_2(u3_cat_1(A),u2_cat_1(A),u1_cat_1(A)) & m2_relset_1(u3_cat_1(A),u2_cat_1(A),u1_cat_1(A)) & v1_funct_1(u3_cat_1(A)))) # label(dt_u3_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4623 (all A (l1_cat_1(A) -> -v1_xboole_0(u2_cat_1(A)))) # label(dt_u2_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4624 $T # label(t16_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4625 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (k1_xboole_0 != k6_cat_1(A,B,C) -> B = k2_cat_1(A,D) & C = k3_cat_1(A,D)))))))))) # label(t23_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4626 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> -(k1_xboole_0 = k6_cat_1(A,B,D) & k6_cat_1(A,C,D) != k1_xboole_0 & k1_xboole_0 != k6_cat_1(A,B,C)))))))))) # label(t52_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4627 $T # label(t3_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4628 (all A all B all C all D all E all F (-v1_xboole_0(A) & m1_relset_1(C,B,A) & v1_funct_1(D) & v1_funct_1(E) & m1_relset_1(F,A,B) & v1_funct_2(F,A,B) & v1_funct_1(F) & m1_relset_1(E,k2_zfmisc_1(B,B),B) & m1_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_2(C,B,A) & v1_funct_1(C) & -v1_xboole_0(B) -> (all G all H all I all J all K all L (g1_cat_1(A,B,C,D,E,F) = g1_cat_1(G,H,I,J,K,L) -> A = G & C = I & D = J & L = F & E = K & H = B)))) # label(free_g1_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4629 (all A all B all C all D all E (v2_cat_1(B) & m2_cat_1(C,A,B) & m1_subset_1(E,u1_cat_1(A)) & m1_subset_1(D,u1_cat_1(A)) & l1_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> m2_relset_1(k16_cat_1(A,B,C,D,E),k6_cat_1(A,D,E),k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E))) & v1_funct_2(k16_cat_1(A,B,C,D,E),k6_cat_1(A,D,E),k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E))) & v1_funct_1(k16_cat_1(A,B,C,D,E)))) # label(dt_k16_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4630 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> k6_cat_1(A,B,B) != k1_xboole_0)))) # label(t56_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4631 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (k6_cat_1(A,B,C) != k1_xboole_0 -> (v4_cat_1(D,A) <-> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_cat_1(F,A,C,E) -> (all G (m1_cat_1(G,A,C,E) -> (k9_cat_1(A,B,C,E,D,F) = k9_cat_1(A,B,C,E,D,G) -> k1_xboole_0 = k6_cat_1(A,C,E) | G = F))))))))))))))))) # label(t65_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.66 4632 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (k1_xboole_0 != k6_cat_1(A,D,E) -> (all F (m1_cat_1(F,A,D,E) -> r2_hidden(k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,F),k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)))))))))))))))) # label(t124_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.67 4633 (all A all B all C (m1_subset_1(C,u1_cat_1(k8_cat_1(A,B))) -> (all D (m1_subset_1(D,u1_cat_1(k8_cat_1(A,B))) -> k1_xboole_0 != k6_cat_1(k8_cat_1(A,B),C,D))))) # label(t38_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.67 4634 $T # label(t119_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.67 4635 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D)))))))))) # label(t104_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.67 4636 $T # label(t28_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.67 4637 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,B,C) -> (all F (m1_cat_1(F,A,C,D) -> (v4_cat_1(F,A) & v4_cat_1(E,A) -> k1_xboole_0 = k6_cat_1(A,B,C) | k6_cat_1(A,C,D) = k1_xboole_0 | v4_cat_1(k9_cat_1(A,B,C,D,E,F),A)))))))))))))) # label(t66_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.67 4638 (all A all B (v2_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) & l1_cat_1(A) -> k5_cat_1(A,B) = k10_cat_1(A,B))) # label(redefinition_k10_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.67 4639 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,B,C) -> (all F (m1_cat_1(F,A,C,D) -> (v3_cat_1(E,A) & v3_cat_1(F,A) -> k1_xboole_0 = k6_cat_1(A,B,C) | v3_cat_1(k9_cat_1(A,B,C,D,E,F),A) | k6_cat_1(A,C,D) = k1_xboole_0))))))))))))) # label(t61_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.67 4640 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),B) = k3_cat_1(A,B))))) # label(d3_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.67 4641 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_cat_1(F,A,B,C) -> -(r2_tarski(k6_cat_1(A,B,C),k6_cat_1(A,D,E)) & k6_cat_1(A,B,C) = k1_tarski(F) & (all G (m1_cat_1(G,A,D,E) -> k1_tarski(G) != k6_cat_1(A,D,E)))))))))))))))) # label(t27_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.67 4642 (exists A (v1_cat_1(A) & v2_cat_1(A) & l1_cat_1(A))) # label(rc3_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.67 4643 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> r2_hidden(k5_cat_1(A,B),k6_cat_1(A,B,B)))))) # label(t55_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.67 4644 $T # label(t79_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.67 4645 (all A all B (l1_cat_1(A) & l1_cat_1(B) & v2_cat_1(B) & v2_cat_1(A) -> (all C (m2_cat_1(C,A,B) -> v1_funct_1(C) & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)))))) # label(dt_m2_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.67 4646 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> ((all C (m1_subset_1(C,u1_cat_1(A)) -> (exists D (m1_cat_1(D,A,C,B) & k1_tarski(D) = k6_cat_1(A,C,B))))) <-> v6_cat_1(B,A)))))) # label(t86_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.67 4647 (all A all B k3_cqc_lang(A,B) = k7_cat_1(A,B)) # label(redefinition_k7_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.67 4648 (exists A (v1_cat_1(A) & l1_cat_1(A))) # label(rc1_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.67 4649 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (r1_cat_1(A,B,C) & r1_cat_1(A,C,D) -> r1_cat_1(A,B,D)))))))))) # label(t93_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.12/14.67 4650 (all A all B m1_subset_1(A,u1_cat_1(k8_cat_1(A,B)))) # label(t32_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.24/14.85 4651 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (k6_cat_1(A,B,C) != k1_xboole_0 -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (m1_cat_1(D,A,B,C) <-> r2_hidden(D,k6_cat_1(A,B,C)))))))))))) # label(d7_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.24/14.85 4652 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (k6_cat_1(A,B,C) = k1_tarski(D) -> (all E (m1_cat_1(E,A,B,C) -> E = D))))))))))) # label(t25_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.24/14.85 4653 (all A (l1_cat_1(A) -> ((all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (r2_hidden(k4_tarski(C,B),k1_relat_1(u5_cat_1(A))) <-> k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),B)))))) & (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),B) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C) -> k1_funct_1(u3_cat_1(A),k1_funct_1(u5_cat_1(A),k4_tarski(C,B))) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),B) & k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C) = k1_funct_1(u4_cat_1(A),k1_funct_1(u5_cat_1(A),k4_tarski(C,B)))))))) & (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C) = B -> k1_funct_1(u5_cat_1(A),k4_tarski(k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B),C)) = C))) & (all C (m1_subset_1(C,u2_cat_1(A)) -> (B = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C) -> k1_funct_1(u5_cat_1(A),k4_tarski(C,k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B))) = C))) & k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B)) = B & k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B)) = B)) & (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),D) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C) & k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),B) -> k1_funct_1(u5_cat_1(A),k4_tarski(k1_funct_1(u5_cat_1(A),k4_tarski(D,C)),B)) = k1_funct_1(u5_cat_1(A),k4_tarski(D,k1_funct_1(u5_cat_1(A),k4_tarski(C,B))))))))))) <-> v2_cat_1(A)))) # label(d8_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.24/14.85 4654 (all A all B all C (m1_subset_1(B,u1_cat_1(A)) & m1_subset_1(C,u1_cat_1(A)) & l1_cat_1(A) -> (all D (m1_cat_1(D,A,B,C) -> m1_subset_1(D,u2_cat_1(A)))))) # label(dt_m1_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.24/14.85 4655 $T # label(t114_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.24/14.85 4656 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_cat_1(F,A,B,C) -> (all G (m1_cat_1(G,A,D,E) -> (G = F -> E = C & D = B | k1_xboole_0 = k6_cat_1(A,D,E) | k6_cat_1(A,B,C) = k1_xboole_0))))))))))))))) # label(t24_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.24/14.85 4657 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,B,C) -> (all F (m1_cat_1(F,A,C,D) -> -(k1_xboole_0 != k6_cat_1(A,B,C) & k6_cat_1(A,C,D) != k1_xboole_0 & k9_cat_1(A,B,C,D,E,F) != k4_cat_1(A,E,F)))))))))))))) # label(d13_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.24/14.85 4658 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (v3_cat_1(B,A) <-> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (k3_cat_1(A,C) = k2_cat_1(A,B) & k2_cat_1(A,B) = k3_cat_1(A,D) & k4_cat_1(A,C,B) = k4_cat_1(A,D,B) & k2_cat_1(A,C) = k2_cat_1(A,D) -> D = C)))))))))) # label(d10_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.24/14.85 4659 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> k8_funct_2(u2_cat_1(A),u2_cat_1(A),k15_cat_1(A),B) = B)))) # label(t115_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.24/14.85 4660 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (v2_funct_1(C) & u2_cat_1(B) = k2_relat_1(C) & k2_relat_1(k12_cat_1(A,B,C)) = u1_cat_1(B) <-> v8_cat_1(C,A,B)))))))) # label(d22_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.24/14.85 4661 $T # label(t1_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.24/14.85 4662 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> ((all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (k3_cat_1(A,B) = k2_cat_1(A,C) & k4_cat_1(A,B,C) = k4_cat_1(A,B,D) & k3_cat_1(A,C) = k3_cat_1(A,D) & k2_cat_1(A,D) = k3_cat_1(A,B) -> C = D))))) <-> v4_cat_1(B,A)))))) # label(d11_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.24/14.85 4663 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,k13_cat_1(A,B,C,D)))))))))) # label(t108_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.24/14.85 4664 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (v5_cat_1(D,A) -> v5_cat_1(k11_cat_1(A,B,C,D),A) | k1_xboole_0 = k6_cat_1(A,B,C)))))))))) # label(t76_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.24/14.85 4665 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,B,C) -> (all F (m1_subset_1(F,u1_cat_1(A)) -> k13_cat_1(B,C,E,k13_cat_1(A,B,D,F)) = k13_cat_1(A,C,k14_cat_1(A,B,C,D,E),F))))))))))))) # label(t113_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.24/14.85 4666 $T # label(t48_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.24/14.85 4667 (all A (l1_cat_1(A) -> (v1_cat_1(A) -> g1_cat_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A)) = A))) # label(abstractness_v1_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.24/14.85 4668 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (k1_xboole_0 != k6_cat_1(A,B,C) & (exists D ((exists E (k10_cat_1(A,C) = k9_cat_1(A,C,B,C,E,D) & k9_cat_1(A,B,C,B,D,E) = k10_cat_1(A,B) & m1_cat_1(E,A,C,B))) & m1_cat_1(D,A,B,C))) & k6_cat_1(A,C,B) != k1_xboole_0 <-> r1_cat_1(A,B,C)))))))) # label(t81_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.24/14.85 4669 $T # label(t80_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.24/14.85 4670 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (v6_cat_1(C,A) & v6_cat_1(B,A) -> r1_cat_1(A,B,C)))))))) # label(t88_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.24/14.85 4671 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> k3_cat_1(A,k5_cat_1(A,B)) = B & B = k2_cat_1(A,k5_cat_1(A,B)))))) # label(t44_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.24/14.85 4672 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (all E (m1_subset_1(E,u2_cat_1(A)) -> (k2_cat_1(A,E) = k3_cat_1(A,D) -> k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k4_cat_1(A,D,E)) = k4_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)) & k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)) = k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))))))))))))) # label(t99_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.24/14.85 4673 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (r2_hidden(k4_tarski(C,B),k1_relat_1(u5_cat_1(A))) -> k1_funct_1(u5_cat_1(A),k4_tarski(C,B)) = k4_cat_1(A,B,C)))))))) # label(d4_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.24/14.85 4674 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> B = k13_cat_1(A,A,k15_cat_1(A),B))))) # label(t118_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.24/14.85 4675 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (k6_cat_1(A,B,C) != k1_xboole_0 -> ((all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_cat_1(F,A,E,B) -> (all G (m1_cat_1(G,A,E,B) -> (k9_cat_1(A,E,B,C,G,D) = k9_cat_1(A,E,B,C,F,D) -> k6_cat_1(A,E,B) = k1_xboole_0 | F = G))))))) <-> v3_cat_1(D,A))))))))))) # label(t60_cat_1) # label(axiom) # label(non_clause). [assumption]. 15.24/14.85 4676 (exists A l1_lattices(A)) # label(existence_l1_lattices) # label(axiom) # label(non_clause). [assumption]. 15.24/14.85 4677 (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]. 15.24/14.85 4678 (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]. 15.24/14.85 4679 (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]. 15.24/14.85 4680 (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]. 15.24/14.85 4681 (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]. 15.24/14.85 4682 (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]. 15.24/14.85 4683 (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]. 15.24/14.85 4684 (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]. 15.24/14.85 4685 (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]. 15.24/14.85 4686 (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]. 15.24/14.85 4687 (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]. 15.24/14.85 4688 (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]. 15.24/14.85 4689 (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]. 15.24/14.85 4690 (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]. 15.24/14.85 4691 $T # label(t46_lattices) # label(axiom) # label(non_clause). [assumption]. 15.24/14.85 4692 (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]. 15.24/14.85 4693 (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]. 15.24/14.85 4694 $T # label(t13_lattices) # label(axiom) # label(non_clause). [assumption]. 15.24/14.85 4695 (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]. 15.24/14.85 4696 (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]. 15.24/14.85 4697 (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]. 15.24/14.85 4698 $T # label(t37_lattices) # label(axiom) # label(non_clause). [assumption]. 15.24/14.85 4699 (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]. 15.24/14.85 4700 (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]. 15.24/14.85 4701 $T # label(t14_lattices) # label(axiom) # label(non_clause). [assumption]. 15.24/14.85 4702 (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]. 15.24/14.85 4703 (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]. 15.24/14.85 4704 (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]. 15.24/14.85 4705 $T # label(t6_lattices) # label(axiom) # label(non_clause). [assumption]. 15.24/14.85 4706 (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]. 15.24/14.86 4707 (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]. 15.24/14.86 4708 (all A (l3_lattices(A) -> l1_lattices(A) & l2_lattices(A))) # label(dt_l3_lattices) # label(axiom) # label(non_clause). [assumption]. 15.24/14.86 4709 (exists A l2_lattices(A)) # label(existence_l2_lattices) # label(axiom) # label(non_clause). [assumption]. 15.24/14.86 4710 (exists A (l1_lattices(A) & v1_lattices(A))) # label(rc1_lattices) # label(axiom) # label(non_clause). [assumption]. 15.24/14.86 4711 (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]. 15.24/14.86 4712 (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]. 15.24/14.86 4713 (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]. 15.24/14.86 4714 (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]. 15.24/14.86 4715 (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]. 15.24/14.86 4716 (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]. 15.24/14.86 4717 (all A (l2_lattices(A) -> l1_struct_0(A))) # label(dt_l2_lattices) # label(axiom) # label(non_clause). [assumption]. 15.24/14.86 4718 $T # label(t4_lattices) # label(axiom) # label(non_clause). [assumption]. 15.24/14.86 4719 (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]. 15.24/14.86 4720 (exists A (-v3_struct_0(A) & v3_lattices(A) & l3_lattices(A))) # label(rc6_lattices) # label(axiom) # label(non_clause). [assumption]. 15.24/14.86 4721 (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]. 15.24/14.86 4722 (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]. 15.24/14.86 4723 $T # label(t24_lattices) # label(axiom) # label(non_clause). [assumption]. 15.24/14.86 4724 (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]. 15.24/14.86 4725 $T # label(t10_lattices) # label(axiom) # label(non_clause). [assumption]. 15.24/14.86 4726 $T # label(t8_lattices) # label(axiom) # label(non_clause). [assumption]. 15.24/14.86 4727 (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]. 15.24/14.86 4728 (exists A (l3_lattices(A) & v3_lattices(A))) # label(rc3_lattices) # label(axiom) # label(non_clause). [assumption]. 15.24/14.86 4729 (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]. 15.24/14.86 4730 $T # label(t16_lattices) # label(axiom) # label(non_clause). [assumption]. 15.24/14.86 4731 $T # label(t1_lattices) # label(axiom) # label(non_clause). [assumption]. 15.24/14.86 4732 (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]. 15.24/14.86 4733 (exists A (l1_lattices(A) & v1_lattices(A) & -v3_struct_0(A))) # label(rc5_lattices) # label(axiom) # label(non_clause). [assumption]. 15.24/14.86 4734 (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]. 15.24/14.86 4735 (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]. 15.24/14.86 4736 (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]. 15.24/14.86 4737 (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]. 15.24/14.86 4738 (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]. 15.24/14.86 4739 (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]. 15.24/14.86 4740 (exists A (l2_lattices(A) & v2_lattices(A))) # label(rc2_lattices) # label(axiom) # label(non_clause). [assumption]. 15.24/14.86 4741 (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]. 15.24/14.86 4742 (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]. 15.24/14.86 4743 (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]. 15.24/14.86 4744 $T # label(t28_lattices) # label(axiom) # label(non_clause). [assumption]. 15.24/14.86 4745 (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]. 15.24/14.86 4746 (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]. 15.33/14.86 4747 (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]. 15.33/14.86 4748 (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]. 15.33/14.86 4749 (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]. 15.33/14.86 4750 (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]. 15.33/14.86 4751 (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]. 15.33/14.86 4752 $T # label(t20_lattices) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4753 (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]. 15.33/14.86 4754 (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]. 15.33/14.86 4755 $T # label(t3_lattices) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4756 (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]. 15.33/14.86 4757 (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]. 15.33/14.86 4758 (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]. 15.33/14.86 4759 (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]. 15.33/14.86 4760 (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]. 15.33/14.86 4761 (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]. 15.33/14.86 4762 $T # label(t11_lattices) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4763 (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]. 15.33/14.86 4764 (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]. 15.33/14.86 4765 (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]. 15.33/14.86 4766 (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]. 15.33/14.86 4767 (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]. 15.33/14.86 4768 (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]. 15.33/14.86 4769 (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]. 15.33/14.86 4770 (exists A (l2_lattices(A) & v2_lattices(A) & -v3_struct_0(A))) # label(rc4_lattices) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4771 (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]. 15.33/14.86 4772 (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]. 15.33/14.86 4773 $T # label(t38_lattices) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4774 (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]. 15.33/14.86 4775 (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]. 15.33/14.86 4776 $T # label(t33_lattices) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4777 (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]. 15.33/14.86 4778 (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]. 15.33/14.86 4779 (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]. 15.33/14.86 4780 $T # label(t42_lattices) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4781 (exists A l3_lattices(A)) # label(existence_l3_lattices) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4782 $T # label(t36_lattices) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4783 (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]. 15.33/14.86 4784 (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]. 15.33/14.86 4785 $T # label(t7_lattices) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4786 $T # label(t5_lattices) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4787 $T # label(t35_lattices) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4788 $T # label(t15_lattices) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4789 (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]. 15.33/14.86 4790 (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]. 15.33/14.86 4791 $T # label(t9_lattices) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4792 (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]. 15.33/14.86 4793 (all A (l1_lattices(A) -> l1_struct_0(A))) # label(dt_l1_lattices) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4794 $T # label(t12_lattices) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4795 (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]. 15.33/14.86 4796 (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]. 15.33/14.86 4797 (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]. 15.33/14.86 4798 $T # label(t2_lattices) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4799 (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]. 15.33/14.86 4800 $T # label(t30_lattices) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4801 (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]. 15.33/14.86 4802 (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]. 15.33/14.86 4803 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (D = C -> k3_xboole_0(k6_pre_topc(A,C),k2_pre_topc(B)) = k6_pre_topc(B,D)))))))))) # label(t47_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4804 $T # label(t38_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4805 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,u1_pre_topc(A)) <-> v3_pre_topc(B,A)))))) # label(d5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4806 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C all D (g1_pre_topc(A,B) = g1_pre_topc(C,D) -> B = D & C = A)))) # label(free_g1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4807 $T # label(t29_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4808 $T # label(t7_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4809 (all A (l1_struct_0(A) -> m1_subset_1(k1_pre_topc(A),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4810 $T # label(t37_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4811 $T # label(t11_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4812 (all A (l1_struct_0(A) -> m1_subset_1(k2_pre_topc(A),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4813 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> v2_pre_topc(B))))) # label(cc1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4814 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> r2_hidden(k1_xboole_0,u1_pre_topc(A)))) # label(t5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4815 $T # label(t1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4816 (all A all B all C all D (l1_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)) & l1_struct_0(B) -> m1_subset_1(k4_pre_topc(A,B,C,D),k1_zfmisc_1(u1_struct_0(B))))) # label(dt_k4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4817 (all A all B all C all D (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) & l1_struct_0(A) -> m1_subset_1(k5_pre_topc(A,B,C,D),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4818 $T # label(t10_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4819 (exists A l1_pre_topc(A)) # label(existence_l1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4820 (all A all B all C all D (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) -> k9_relat_1(C,D) = k4_pre_topc(A,B,C,D))) # label(redefinition_k4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4821 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_pre_topc(C,A) & v1_pre_topc(C) -> (k3_pre_topc(A,B) = C <-> B = k2_pre_topc(C)))))))) # label(d10_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4822 (all A (l1_struct_0(A) -> u1_struct_0(A) = k2_pre_topc(A))) # label(t12_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4823 $T # label(t32_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4824 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,C)),k5_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,C))))))))) # label(t51_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4825 $T # label(t36_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4826 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(B,k6_pre_topc(A,B)))))) # label(t48_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4827 $T # label(d7_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4828 $T # label(t28_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4829 (all A (l1_struct_0(A) -> k2_pre_topc(A) = u1_struct_0(A))) # label(d3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4830 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> B = k6_subset_1(u1_struct_0(A),k2_pre_topc(A),k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B)))))) # label(t22_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4831 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> l1_pre_topc(B))))) # label(dt_m1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4832 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (k2_pre_topc(A) = k4_subset_1(u1_struct_0(A),B,C) & r1_xboole_0(B,C) -> C = k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B)))))))) # label(t25_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4833 (all A (-v3_struct_0(A) & l1_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r2_hidden(B,k2_pre_topc(A)))))) # label(t13_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4834 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc6_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4835 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(B != k1_pre_topc(A) & (all C (m1_subset_1(C,u1_struct_0(A)) -> -r2_hidden(C,B)))))))) # label(t41_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4836 $T # label(t2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4837 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> ((exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D,A) & k3_xboole_0(D,k2_pre_topc(B)) = C)) <-> v4_pre_topc(C,B)))))))) # label(t43_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4838 $T # label(d4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4839 $T # label(t34_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4840 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k4_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,C)) = k6_pre_topc(A,k4_subset_1(u1_struct_0(A),B,C)))))))) # label(t50_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4841 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> v4_pre_topc(k2_pre_topc(A),A))) # label(fc5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4842 $T # label(t19_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4843 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(B,k2_pre_topc(A)))))) # label(t14_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4844 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(B != k2_pre_topc(A) & k1_xboole_0 = k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B)) & -(k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) != k1_xboole_0 & k2_pre_topc(A) = B))))) # label(t23_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4845 (all A (-v3_struct_0(A) & l1_struct_0(A) -> -v1_xboole_0(k2_pre_topc(A)))) # label(fc2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4846 $T # label(t35_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4847 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> v4_pre_topc(k2_pre_topc(A),A))) # label(t42_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4848 (exists A (l1_pre_topc(A) & v1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A))) # label(rc2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4849 (all A (l1_pre_topc(A) -> (v2_pre_topc(A) <-> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(B,u1_pre_topc(A)) -> r2_hidden(k5_setfam_1(u1_struct_0(A),B),u1_pre_topc(A))))) & (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,u1_pre_topc(A)) & r2_hidden(C,u1_pre_topc(A)) -> r2_hidden(k5_subset_1(u1_struct_0(A),B,C),u1_pre_topc(A))))))) & r2_hidden(u1_struct_0(A),u1_pre_topc(A))))) # label(d1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4850 $T # label(t6_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4851 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (C = k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) -> k4_subset_1(u1_struct_0(A),B,C) = k2_pre_topc(A)))))))) # label(t24_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4852 $T # label(t9_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4853 $T # label(t30_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4854 (all A (l1_struct_0(A) -> k1_pre_topc(A) = k1_xboole_0)) # label(d2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4855 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k2_pre_topc(A) = k4_subset_1(u1_struct_0(A),B,k3_subset_1(u1_struct_0(A),B)))))) # label(t18_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4856 $T # label(t40_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4857 (all A (l1_pre_topc(A) -> (v1_pre_topc(A) -> g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = A))) # label(abstractness_v1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4858 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> l1_pre_topc(g1_pre_topc(A,B)) & v1_pre_topc(g1_pre_topc(A,B)))) # label(dt_g1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4859 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (C = k6_pre_topc(A,B) <-> (all D (r2_hidden(D,u1_struct_0(A)) -> (r2_hidden(D,C) <-> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(E,A) & r1_xboole_0(B,E) & r2_hidden(D,E)))))))))))))) # label(d13_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4860 (all A (l1_pre_topc(A) -> l1_struct_0(A))) # label(dt_l1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4861 (all A (l1_struct_0(A) -> k3_subset_1(u1_struct_0(A),k1_pre_topc(A)) = k2_pre_topc(A))) # label(t27_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4862 (all A (l1_struct_0(A) -> v1_xboole_0(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)))) # label(fc1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4863 $T # label(t31_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4864 (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)))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> v4_pre_topc(C,A)))) -> v4_pre_topc(k6_setfam_1(u1_struct_0(A),B),A)))))) # label(t44_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4865 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B),A) <-> v4_pre_topc(B,A)))))) # label(d6_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4866 (all A (l1_pre_topc(A) -> (exists B (m1_pre_topc(B,A) & v1_pre_topc(B))))) # label(rc3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4867 $T # label(t3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4868 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_pre_topc(A,B) <-> k2_pre_topc(A) = k5_setfam_1(u1_struct_0(A),B)))))) # label(d8_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4869 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,C) -> r1_tarski(k6_pre_topc(A,B),k6_pre_topc(A,C))))))))) # label(t49_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4870 $T # label(d11_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4871 $T # label(t33_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4872 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (m1_pre_topc(B,A) & v1_pre_topc(B) & v2_pre_topc(B))))) # label(rc5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4873 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))))))))) # label(t39_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4874 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (m1_pre_topc(B,A) <-> r1_tarski(k2_pre_topc(B),k2_pre_topc(A)) & (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> ((exists D (k3_xboole_0(D,k2_pre_topc(B)) = C & r2_hidden(D,u1_pre_topc(A)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))))) <-> r2_hidden(C,u1_pre_topc(B)))))))))) # label(d9_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4875 (all A all B (l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> m1_subset_1(k6_pre_topc(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k6_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4876 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,k6_pre_topc(A,B)) <-> -v3_struct_0(A) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_hidden(C,D) & r1_xboole_0(B,D) & v3_pre_topc(D,A))))))))))) # label(t54_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4877 (all A all B (v2_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> v2_pre_topc(k3_pre_topc(A,B)) & v1_pre_topc(k3_pre_topc(A,B)))) # label(fc4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4878 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(B,A) & -v1_xboole_0(B))))) # label(rc7_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4879 (all A (l1_pre_topc(A) -> (exists B m1_pre_topc(B,A)))) # label(existence_m1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4880 (all A all B all C all D (l1_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_struct_0(A) -> k10_relat_1(C,D) = k5_pre_topc(A,B,C,D))) # label(redefinition_k5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4881 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_pre_topc(A) & k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) = k6_pre_topc(A,k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B)) -> v3_pre_topc(B,A)) & (v3_pre_topc(B,A) -> k6_pre_topc(A,k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B)) = k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B)))))) # label(t53_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4882 (all A all B (-v3_struct_0(A) & l1_pre_topc(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v1_pre_topc(k3_pre_topc(A,B)) & -v3_struct_0(k3_pre_topc(A,B)))) # label(fc3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4883 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (r2_hidden(C,u1_struct_0(A)) -> (r2_hidden(C,k6_pre_topc(A,B)) <-> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,D) & v4_pre_topc(D,A) -> r2_hidden(C,D))))))))))) # label(t45_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4884 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (exists C ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(D,C) <-> v4_pre_topc(D,A) & r1_tarski(B,D)))) & k6_setfam_1(u1_struct_0(A),C) = k6_pre_topc(A,B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))))))) # label(t46_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4885 (all A (l1_struct_0(A) -> (all B (r1_tarski(B,k2_pre_topc(A)) -> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(t16_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4886 $T # label(t8_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4887 $T # label(t21_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4888 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) -> B = k6_pre_topc(A,B)) & (B = k6_pre_topc(A,B) & v2_pre_topc(A) -> v4_pre_topc(B,A)))))) # label(t52_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4889 (exists A (l1_pre_topc(A) & v1_pre_topc(A))) # label(rc1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4890 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (exists B (-v3_struct_0(B) & v1_pre_topc(B) & m1_pre_topc(B,A))))) # label(rc4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4891 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> m1_pre_topc(k3_pre_topc(A,B),A) & v1_pre_topc(k3_pre_topc(A,B)))) # label(dt_k3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4892 $T # label(t4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4893 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> B = k5_subset_1(u1_struct_0(A),B,k2_pre_topc(A)))))) # label(t15_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4894 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) = k3_subset_1(u1_struct_0(A),B))))) # label(t17_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4895 $T # label(t20_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4896 $T # label(t26_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4897 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v4_pre_topc(D,B) -> v4_pre_topc(k5_pre_topc(A,B,C,D),A)))) <-> v5_pre_topc(C,A,B)))))))) # label(d12_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4898 (all A (l1_pre_topc(A) -> m1_subset_1(u1_pre_topc(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))) # label(dt_u1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4899 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) -> v3_tops_1(k2_tops_1(A,B),A)))))) # label(t96_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4900 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> v4_pre_topc(k2_pre_topc(A),A) & v3_pre_topc(k2_pre_topc(A),A))) # label(fc8_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4901 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v5_tops_1(B,A) -> r1_tarski(k2_tops_1(A,B),k6_pre_topc(A,k1_tops_1(A,B)))))))) # label(t103_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4902 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k1_tops_1(A,k6_subset_1(u1_struct_0(A),B,C)),k6_subset_1(u1_struct_0(A),k1_tops_1(A,B),k1_tops_1(A,C))))))))) # label(t50_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.86 4903 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_tops_1(B,A) -> k1_tops_1(A,k2_tops_1(A,B)) = k1_xboole_0))))) # label(t110_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4904 $T # label(t16_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4905 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,C))) = k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,C))))))))) # label(t41_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4906 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,C) & v3_pre_topc(B,A) -> r1_tarski(B,k1_tops_1(A,C))))))))) # label(t56_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4907 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,B))) = k6_pre_topc(A,B)))))) # label(t59_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4908 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> m1_subset_1(k1_tops_1(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k1_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4909 (all A all B (l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(B,A) & v2_pre_topc(A) -> v3_tops_1(k2_tops_1(A,B),A) & v2_tops_1(k2_tops_1(A,B),A))) # label(fc12_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4910 $T # label(t24_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4911 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v6_tops_1(C,A) & v6_tops_1(B,A) -> v6_tops_1(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t109_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4912 $T # label(t60_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4913 (all A all B (v3_tops_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) & v2_pre_topc(A) -> v1_tops_1(k3_subset_1(u1_struct_0(A),B),A))) # label(fc11_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4914 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tops_1(B,A) <-> k1_xboole_0 = k1_tops_1(A,B)))))) # label(t84_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4915 $T # label(t78_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4916 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v6_tops_1(B,A) -> k2_tops_1(A,k6_pre_topc(A,B)) = k6_subset_1(u1_struct_0(A),k6_pre_topc(A,B),B) & k2_tops_1(A,k6_pre_topc(A,B)) = k2_tops_1(A,B)))))) # label(t104_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4917 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v3_pre_topc(k1_tops_1(A,B),A))))) # label(t51_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4918 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> v3_pre_topc(k1_pre_topc(A),A))) # label(t52_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4919 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k2_tops_1(A,k5_subset_1(u1_struct_0(A),B,C)),k4_subset_1(u1_struct_0(A),k2_tops_1(A,B),k2_tops_1(A,C))))))))) # label(t66_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4920 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k6_pre_topc(A,k1_tops_1(A,B)) = k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,k1_tops_1(A,B)))))))) # label(t58_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4921 $T # label(t1_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4922 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> k1_tops_1(A,k2_pre_topc(A)) = k2_pre_topc(A))) # label(t43_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4923 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> v3_tops_1(k2_tops_1(A,B),A)))))) # label(t95_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4924 $T # label(t14_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4925 (all A (l1_pre_topc(A) -> v1_xboole_0(k1_tops_1(A,k1_pre_topc(A))) & v3_membered(k1_tops_1(A,k1_pre_topc(A))) & v5_membered(k1_tops_1(A,k1_pre_topc(A))) & v4_membered(k1_tops_1(A,k1_pre_topc(A))) & v2_membered(k1_tops_1(A,k1_pre_topc(A))) & v1_membered(k1_tops_1(A,k1_pre_topc(A))))) # label(fc5_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4926 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k2_tops_1(A,k2_tops_1(A,B)),k2_tops_1(A,B)))))) # label(t68_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4927 $T # label(t18_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4928 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_xboole_0(k1_tops_1(A,B),k2_tops_1(A,B)))))) # label(t73_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4929 $T # label(t7_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4930 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) & v3_pre_topc(C,A) -> v3_pre_topc(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t38_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4931 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(C,A) & v4_pre_topc(B,A) -> v4_pre_topc(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t35_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4932 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_hidden(C,D) & r1_xboole_0(B,D) & v3_pre_topc(D,A)))) <-> r2_hidden(C,k6_pre_topc(A,B))))))))) # label(t39_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4933 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k1_tops_1(A,B) = k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B))))))) # label(d1_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4934 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) & v4_pre_topc(C,A) -> v4_pre_topc(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t36_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4935 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,k2_tops_1(A,B)) <-> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(D,A) & r2_hidden(C,D) -> -r1_xboole_0(k3_subset_1(u1_struct_0(A),B),D) & -r1_xboole_0(B,D))))))))))) # label(t61_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4936 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_tops_1(B,A) <-> r1_tarski(B,k6_pre_topc(A,k1_tops_1(A,B))) & r1_tarski(k1_tops_1(A,k6_pre_topc(A,B)),B)))))) # label(d6_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4937 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(C != k1_xboole_0 & v3_pre_topc(C,A) & r1_xboole_0(B,C)))) <-> v1_tops_1(B,A)))))) # label(t80_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4938 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k4_subset_1(u1_struct_0(A),k1_tops_1(A,B),k1_tops_1(A,C)),k1_tops_1(A,k4_subset_1(u1_struct_0(A),B,C))))))))) # label(t49_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4939 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k1_tops_1(A,k1_tops_1(A,B)) = k1_tops_1(A,B))))) # label(t45_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4940 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(B,A) -> v2_tops_1(B,A)))))) # label(t92_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4941 $T # label(t25_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4942 $T # label(t23_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4943 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v3_pre_topc(D,B) -> k1_tops_1(B,D) = D) & (C = k1_tops_1(A,C) -> v3_pre_topc(C,A)))))))))) # label(t55_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4944 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tops_1(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(C,B) & v3_pre_topc(C,A) -> C = k1_xboole_0)))))))) # label(t86_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4945 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k1_tops_1(A,B) = k6_subset_1(u1_struct_0(A),B,k2_tops_1(A,B)))))) # label(t74_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4946 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) & v2_tops_1(B,A) -> v3_tops_1(B,A)))))) # label(t93_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4947 $T # label(t6_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4948 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,C) & v1_tops_1(B,A) -> v1_tops_1(C,A)))))))) # label(t79_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4949 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) & v4_pre_topc(C,A) -> k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,C)) = k5_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,C))))))))) # label(t34_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4950 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),k2_tops_1(A,k4_subset_1(u1_struct_0(A),B,C)),k2_tops_1(A,k5_subset_1(u1_struct_0(A),B,C))),k5_subset_1(u1_struct_0(A),k2_tops_1(A,B),k2_tops_1(A,C))) = k4_subset_1(u1_struct_0(A),k2_tops_1(A,B),k2_tops_1(A,C)))))))) # label(t70_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4951 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(B,A) -> v1_tops_1(k3_subset_1(u1_struct_0(A),B),A)))))) # label(t91_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4952 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k4_subset_1(u1_struct_0(A),B,k2_pre_topc(A)) = k2_pre_topc(A))))) # label(t2_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4953 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) & v3_tops_1(B,A) -> k1_xboole_0 = B))))) # label(t97_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4954 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) -> r1_tarski(k2_tops_1(A,B),B)))))) # label(t69_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4955 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_xboole_0(B) -> v2_tops_1(B,A)))))) # label(cc2_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4956 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_xboole_0(B) -> v4_pre_topc(B,A) & v3_pre_topc(B,A)))))) # label(cc1_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4957 $T # label(t28_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4958 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k6_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,C)),k6_pre_topc(A,k6_subset_1(u1_struct_0(A),B,C))))))))) # label(t32_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4959 (all A (l1_pre_topc(A) -> v1_tops_1(k2_pre_topc(A),A))) # label(fc9_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4960 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k2_tops_1(A,B) = k2_tops_1(A,k3_subset_1(u1_struct_0(A),B)))))) # label(t62_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4961 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k2_tops_1(A,k6_pre_topc(A,B)),k2_tops_1(A,B)))))) # label(t72_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4962 (all A (l1_pre_topc(A) -> k2_pre_topc(A) = k6_pre_topc(A,k2_pre_topc(A)))) # label(t27_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4963 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k2_tops_1(A,k1_tops_1(A,B)),k2_tops_1(A,B)))))) # label(t71_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4964 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(C,A) -> k6_pre_topc(A,C) = k6_pre_topc(A,k5_subset_1(u1_struct_0(A),C,B)))))))))) # label(t81_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4965 (all A (l1_struct_0(A) -> k1_pre_topc(A) = k3_subset_1(u1_struct_0(A),k2_pre_topc(A)))) # label(t8_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4966 $T # label(t9_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4967 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tops_1(B,A) <-> r1_tarski(B,k2_tops_1(A,B))))))) # label(t88_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4968 $T # label(t5_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4969 $T # label(t3_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4970 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) -> (v2_tops_1(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(C != k1_xboole_0 & v3_pre_topc(C,A) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_tarski(D,C) & k1_xboole_0 != D & r1_xboole_0(B,D) & v3_pre_topc(D,A))))))))))))) # label(t87_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4971 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v5_tops_1(B,A) <-> B = k6_pre_topc(A,k1_tops_1(A,B))))))) # label(d7_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4972 $T # label(t42_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4973 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k1_tops_1(A,B),B))))) # label(t44_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4974 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_1(B,A) & v3_pre_topc(C,A) & v1_tops_1(C,A) -> v1_tops_1(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t82_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4975 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k4_subset_1(u1_struct_0(A),B,k2_tops_1(A,B)) = k6_pre_topc(A,B))))) # label(t65_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4976 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> v3_pre_topc(k2_pre_topc(A),A))) # label(t53_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4977 $T # label(t10_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4978 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_tops_1(B,A) -> v4_tops_1(k6_pre_topc(A,B),A) & v4_tops_1(k1_tops_1(A,B),A)))))) # label(t111_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4979 (all A all B (v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v3_pre_topc(k1_tops_1(A,B),A))) # label(fc6_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4980 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tops_1(B,A) & v4_pre_topc(C,A) & v2_tops_1(C,A) -> v2_tops_1(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t85_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4981 $T # label(t100_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4982 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) -> (v3_tops_1(B,A) <-> k2_tops_1(A,B) = B)))))) # label(t94_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4983 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tops_1(k6_pre_topc(A,B),A) <-> v3_tops_1(B,A)))))) # label(d5_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4984 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) & v2_tops_1(B,A) -> v3_tops_1(B,A) & v2_tops_1(B,A)))))) # label(cc5_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4985 (all A all B (v2_pre_topc(A) & l1_pre_topc(A) & v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v3_pre_topc(k3_subset_1(u1_struct_0(A),B),A))) # label(fc3_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4986 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (v3_pre_topc(B,A) & v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc2_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4987 $T # label(t13_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4988 (all A all B (v3_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) & v2_pre_topc(A) -> v4_pre_topc(k3_subset_1(u1_struct_0(A),B),A))) # label(fc4_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4989 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (k3_subset_1(u1_struct_0(A),C) = k3_subset_1(u1_struct_0(A),B) -> B = C))))))) # label(t21_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4990 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (v3_pre_topc(B,A) & v4_pre_topc(B,A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc3_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4991 $T # label(t89_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4992 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v5_tops_1(B,A) & v5_tops_1(C,A) -> v5_tops_1(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t108_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4993 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v5_tops_1(B,A) -> k2_tops_1(A,k1_tops_1(A,B)) = k2_tops_1(A,B)))))) # label(t102_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4994 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(C,B) & v4_pre_topc(B,A) -> r1_tarski(k6_pre_topc(A,C),B)))))))) # label(t31_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4995 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> r1_tarski(k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,C)),k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,C)))))))))) # label(t40_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4996 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k2_tops_1(A,k4_subset_1(u1_struct_0(A),B,C)),k4_subset_1(u1_struct_0(A),k2_tops_1(A,B),k2_tops_1(A,C))))))))) # label(t67_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4997 (all A all B (l1_pre_topc(A) & v2_tops_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v1_xboole_0(k1_tops_1(A,B)) & v1_membered(k1_tops_1(A,B)) & v4_membered(k1_tops_1(A,B)) & v5_membered(k1_tops_1(A,B)) & v2_tops_1(k1_tops_1(A,B),A) & v3_membered(k1_tops_1(A,B)) & v2_membered(k1_tops_1(A,B)))) # label(fc10_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4998 $T # label(t4_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 4999 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(B,A) & l1_pre_topc(A) & v2_pre_topc(A) -> v3_tops_1(k2_tops_1(A,B),A) & v2_tops_1(k2_tops_1(A,B),A))) # label(fc13_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5000 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> v1_xboole_0(k1_pre_topc(A)) & v3_pre_topc(k1_pre_topc(A),A) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v4_pre_topc(k1_pre_topc(A),A))) # label(fc7_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5001 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(B,A) & v3_tops_1(C,A) -> v3_tops_1(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t90_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5002 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v5_tops_1(k3_subset_1(u1_struct_0(A),B),A) <-> v6_tops_1(B,A)))))) # label(t101_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5003 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v4_pre_topc(D,B) & v4_tops_1(D,B) -> v5_tops_1(D,B)) & (v5_tops_1(C,A) -> v4_tops_1(C,A) & v4_pre_topc(C,A)))))))))) # label(t106_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5004 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) <-> (all C ((exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & r2_hidden(C,D) & r1_tarski(D,B) & v3_pre_topc(D,A))) <-> r2_hidden(C,B)))))))) # label(t57_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5005 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k6_pre_topc(A,B) = k6_pre_topc(A,k6_pre_topc(A,B)))))) # label(t26_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5006 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> m1_subset_1(k2_tops_1(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k2_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5007 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) <-> v4_pre_topc(k3_subset_1(u1_struct_0(A),B),A)))))) # label(t30_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5008 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_xboole_0(B,k3_subset_1(u1_struct_0(A),C)) <-> r1_tarski(B,C)))))))) # label(t20_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5009 (all A all B (l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v2_pre_topc(A) -> v4_pre_topc(k6_pre_topc(A,B),A))) # label(fc2_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5010 $T # label(t15_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5011 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k5_subset_1(u1_struct_0(A),k1_tops_1(A,B),k1_tops_1(A,C)) = k1_tops_1(A,k5_subset_1(u1_struct_0(A),B,C)))))))) # label(t46_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5012 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k2_tops_1(A,B),k6_pre_topc(A,B)))))) # label(t63_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5013 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k2_tops_1(A,B) = k5_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B))))))) # label(d2_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5014 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> v4_pre_topc(k1_pre_topc(A),A))) # label(t22_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5015 $T # label(t98_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5016 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> v1_xboole_0(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v4_pre_topc(k1_pre_topc(A),A))) # label(fc1_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5017 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k2_tops_1(A,k2_tops_1(A,k2_tops_1(A,B))) = k2_tops_1(A,k2_tops_1(A,B)))))) # label(t75_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5018 (all A (l1_pre_topc(A) -> k1_tops_1(A,k1_pre_topc(A)) = k1_pre_topc(A))) # label(t47_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5019 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(C,A) & v3_pre_topc(B,A) -> v3_pre_topc(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t37_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5020 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v6_tops_1(C,A) -> v3_pre_topc(C,A) & v4_tops_1(C,A)) & (v3_pre_topc(D,B) & v4_tops_1(D,B) -> v6_tops_1(D,B)))))))))) # label(t107_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5021 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(B,A) -> v2_tops_1(B,A)))))) # label(cc4_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5022 $T # label(t33_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5023 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) & v4_pre_topc(B,A) -> (v6_tops_1(B,A) <-> v5_tops_1(B,A))))))) # label(t105_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5024 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tops_1(B,A) <-> v1_tops_1(k3_subset_1(u1_struct_0(A),B),A)))))) # label(d4_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5025 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (exists B (v3_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc1_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5026 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_1(B,A) <-> k2_pre_topc(A) = k6_pre_topc(A,B)))))) # label(d3_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5027 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) <-> k2_tops_1(A,B) = k6_subset_1(u1_struct_0(A),B,k1_tops_1(A,B))))))) # label(t77_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5028 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B,A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v5_membered(B) & v3_tops_1(B,A) & v2_tops_1(B,A) & v4_membered(B) & v4_pre_topc(B,A))))) # label(rc5_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5029 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k4_subset_1(u1_struct_0(A),k5_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B)),B),k6_subset_1(u1_struct_0(A),k6_pre_topc(A,B),B)) = k2_tops_1(A,B))))) # label(t64_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5030 $T # label(t17_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5031 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,C) -> r1_tarski(k1_tops_1(A,B),k1_tops_1(A,C))))))))) # label(t48_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5032 $T # label(t83_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5033 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (B = k1_tops_1(A,k6_pre_topc(A,B)) <-> v6_tops_1(B,A)))))) # label(d8_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5034 $T # label(t19_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5035 (all A (l1_pre_topc(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v2_tops_1(B,A) & v5_membered(B) & v4_membered(B) & v3_membered(B) & v2_membered(B) & v1_membered(B) & v1_xboole_0(B))))) # label(rc4_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5036 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_xboole_0(B) -> v3_tops_1(B,A)))))) # label(cc3_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5037 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) <-> k2_tops_1(A,B) = k6_subset_1(u1_struct_0(A),k6_pre_topc(A,B),B)))))) # label(t76_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5038 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) <-> v3_pre_topc(k3_subset_1(u1_struct_0(A),B),A)))))) # label(t29_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5039 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((exists D (r1_tarski(D,C) & r2_hidden(B,D) & v3_pre_topc(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))))) <-> r2_hidden(B,k1_tops_1(A,C))))))) # label(t54_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5040 $T # label(t11_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5041 $T # label(t99_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5042 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(B,A) & v3_pre_topc(B,A) -> v1_xboole_0(B) & v1_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v3_tops_1(B,A) & v2_tops_1(B,A) & v2_membered(B) & v4_pre_topc(B,A) & v3_pre_topc(B,A)))))) # label(cc6_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5043 $T # label(t12_tops_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5044 $T # label(t1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5045 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k5_rlvect_1(A,C) = k5_rlvect_1(A,B) -> B = C))))))) # label(t31_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5046 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k5_rlvect_1(A,k5_rlvect_1(A,B)) = B)))) # label(t30_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5047 (all A all B all C (l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & -v3_struct_0(A) -> k7_rlvect_1(A,B,C) = k10_finseq_1(B,C))) # label(redefinition_k7_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 15.33/14.87 5048 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k6_rlvect_1(A,B,C) = k9_rlvect_1(A,k7_rlvect_1(A,B,k5_rlvect_1(A,C))))))))) # label(t77_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5049 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_rlvect_1(A,B,C) = k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A),u1_rlvect_1(A),k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C)))))))) # label(d3_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5050 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (C = k2_rlvect_1(A,B,D) & m1_subset_1(D,u1_struct_0(A)))))))))) # label(t20_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5051 (all A (v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_rlvect_1(A) = k2_rlvect_1(A,B,k5_rlvect_1(A,B)) & k2_rlvect_1(A,k5_rlvect_1(A,B),B) = k1_rlvect_1(A))))) # label(t16_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5052 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_rlvect_1(A) = k9_rlvect_1(A,k7_rlvect_1(A,B,k5_rlvect_1(A,B))) & k1_rlvect_1(A) = k9_rlvect_1(A,k7_rlvect_1(A,k5_rlvect_1(A,B),B)))))) # label(t76_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5053 (all A (l2_rlvect_1(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,k2_rlvect_1(A,B,C),D) = k2_rlvect_1(A,B,k2_rlvect_1(A,C,D)))))))) & (all B (m1_subset_1(B,u1_struct_0(A)) -> (exists C (k1_rlvect_1(A) = k2_rlvect_1(A,B,C) & m1_subset_1(C,u1_struct_0(A)))))) & (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k3_rlvect_1(A,D,k3_real_1(B,C)) = k2_rlvect_1(A,k3_rlvect_1(A,D,B),k3_rlvect_1(A,D,C)))))))) & (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k3_rlvect_1(A,B,np__1))) & (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k3_rlvect_1(A,k3_rlvect_1(A,D,C),B) = k3_rlvect_1(A,D,k4_real_1(B,C)))))))) & (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,k3_rlvect_1(A,C,B),k3_rlvect_1(A,D,B)) = k3_rlvect_1(A,k2_rlvect_1(A,C,D),B))))))) & (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k2_rlvect_1(A,B,k1_rlvect_1(A)))) & (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_rlvect_1(A,C,B) = k2_rlvect_1(A,B,C))))) -> v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(A)))) # label(t7_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5054 (exists A (l1_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v1_rlvect_1(A) & -v3_struct_0(A))) # label(rc5_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5055 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> k9_rlvect_1(A,k6_finseq_1(u1_struct_0(A))) = k1_rlvect_1(A))) # label(t60_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5056 (all A all B all C all D (m1_subset_1(B,A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A) & v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A) & v1_funct_1(D) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> l2_rlvect_1(g2_rlvect_1(A,B,C,D)) & v2_rlvect_1(g2_rlvect_1(A,B,C,D)))) # label(dt_g2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5057 (all A all B all C (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & m1_subset_1(C,A) -> (all D all E all F (g1_rlvect_1(D,E,F) = g1_rlvect_1(A,B,C) -> E = B & F = C & D = A)))) # label(free_g1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5058 $T # label(t13_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5059 $T # label(t15_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5060 $T # label(t12_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5061 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> (v2_funct_1(C) & v2_funct_1(B) & k2_relat_1(B) = k2_relat_1(C) -> k9_rlvect_1(A,C) = k9_rlvect_1(A,B)))))))) # label(t59_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5062 (exists A (l1_rlvect_1(A) & v1_rlvect_1(A))) # label(rc1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5063 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)) = k9_rlvect_1(A,k8_rlvect_1(A,D,B,C)))))))))) # label(t89_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5064 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_rlvect_1(A,B,C) = k9_rlvect_1(A,k7_rlvect_1(A,B,C)))))))) # label(t62_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5065 (all A (v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,k9_rlvect_1(A,k7_rlvect_1(A,B,C)),D) = k9_rlvect_1(A,k8_rlvect_1(A,B,C,D)))))))))) # label(t82_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5066 (all A (v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_rlvect_1(A,k5_rlvect_1(A,C),k5_rlvect_1(A,B)) = k5_rlvect_1(A,k2_rlvect_1(A,B,C)))))))) # label(t45_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5067 (all A (-v3_struct_0(A) & l2_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v8_rlvect_1(B,A) <-> B != k1_rlvect_1(A)))))) # label(d13_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5068 (all A all B all C (-v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> m2_finseq_1(k7_rlvect_1(A,B,C),u1_struct_0(A)))) # label(dt_k7_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5069 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k5_rlvect_1(A,B) = k6_rlvect_1(A,k1_rlvect_1(A),B))))) # label(t27_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5070 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (np__0 = k3_finseq_1(B) -> k9_rlvect_1(A,B) = k1_rlvect_1(A)))))) # label(t94_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5071 (all A (l2_rlvect_1(A) -> v1_funct_1(u2_rlvect_1(A)) & v1_funct_2(u2_rlvect_1(A),k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A)) & m2_relset_1(u2_rlvect_1(A),k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A)))) # label(dt_u2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5072 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k6_rlvect_1(A,B,C) = k1_rlvect_1(A) -> B = C))))))) # label(t35_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5073 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k2_rlvect_1(A,k1_rlvect_1(A),B) = B & B = k2_rlvect_1(A,B,k1_rlvect_1(A)))))) # label(t10_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5074 $T # label(t65_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5075 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_rlvect_1(A,B,k1_rlvect_1(A)) = B)))) # label(t26_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5076 (all A (v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k9_rlvect_1(A,k8_rlvect_1(A,k1_rlvect_1(A),k1_rlvect_1(A),B)) & B = k9_rlvect_1(A,k8_rlvect_1(A,B,k1_rlvect_1(A),k1_rlvect_1(A))) & B = k9_rlvect_1(A,k8_rlvect_1(A,k1_rlvect_1(A),B,k1_rlvect_1(A))))))) # label(t91_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5077 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k9_rlvect_1(A,k7_rlvect_1(A,k5_rlvect_1(A,B),k5_rlvect_1(A,C))) = k5_rlvect_1(A,k2_rlvect_1(A,C,B)))))))) # label(t78_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5078 (all A (v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,k2_rlvect_1(A,k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),B)),k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),C))),k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),D))) = k9_rlvect_1(A,k8_rlvect_1(A,B,C,D)))))))))) # label(t81_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5079 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> ((exists D ((all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (all F (m1_subset_1(F,u1_struct_0(A)) -> (k1_funct_1(B,k1_nat_1(E,np__1)) = F -> k8_funct_2(k5_numbers,u1_struct_0(A),D,k1_nat_1(E,np__1)) = k2_rlvect_1(A,k8_funct_2(k5_numbers,u1_struct_0(A),D,E),F) | r1_xreal_0(k3_finseq_1(B),E)))))) & k8_funct_2(k5_numbers,u1_struct_0(A),D,np__0) = k1_rlvect_1(A) & C = k8_funct_2(k5_numbers,u1_struct_0(A),D,k3_finseq_1(B)) & m2_relset_1(D,k5_numbers,u1_struct_0(A)) & v1_funct_2(D,k5_numbers,u1_struct_0(A)) & v1_funct_1(D))) <-> k9_rlvect_1(A,B) = C))))))) # label(d12_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5080 $T # label(t11_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5081 (all A all B all C all D (-v3_struct_0(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_struct_0(A) -> m2_finseq_1(k8_rlvect_1(A,B,C,D),u1_struct_0(A)))) # label(dt_k8_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5082 (exists A (l2_rlvect_1(A) & -v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & v2_rlvect_1(A))) # label(rc6_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5083 (all A all B all C (l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & v3_rlvect_1(A) & -v3_struct_0(A) -> k2_rlvect_1(A,B,C) = k4_rlvect_1(A,B,C))) # label(redefinition_k4_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5084 $T # label(t14_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5085 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (B = k5_rlvect_1(A,B) -> B = k1_rlvect_1(A)))))) # label(t33_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5086 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k3_finseq_1(B) = k1_nat_1(k3_finseq_1(C),np__1) & D = k1_funct_1(B,k3_finseq_1(B)) & k7_relat_1(B,k4_finseq_1(C)) = C -> k9_rlvect_1(A,B) = k2_rlvect_1(A,k9_rlvect_1(A,C),D)))))))))) # label(t55_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5087 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> ((all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (E = k1_funct_1(C,D) & r2_hidden(D,k4_finseq_1(B)) -> k5_rlvect_1(A,E) = k1_funct_1(B,D)))))) & k3_finseq_1(B) = k3_finseq_1(C) -> k9_rlvect_1(A,B) = k5_rlvect_1(A,k9_rlvect_1(A,C))))))))) # label(t57_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5088 (all A all B all C all D (l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & -v3_struct_0(A) -> k8_rlvect_1(A,B,C,D) = k11_finseq_1(B,C,D))) # label(redefinition_k8_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5089 (all A (-v3_struct_0(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k9_rlvect_1(A,k7_rlvect_1(A,B,B)) = k3_rlvect_1(A,B,np__2))))) # label(t79_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5090 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) -> k5_rlvect_1(A,k9_rlvect_1(A,k6_finseq_1(u1_struct_0(A)))) = k1_rlvect_1(A))) # label(t68_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5091 (all A (l1_rlvect_1(A) -> v1_funct_1(u1_rlvect_1(A)) & m2_relset_1(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_2(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)))) # label(dt_u1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5092 (all A (v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k3_rlvect_1(A,B,k1_real_1(np__1)) = k5_rlvect_1(A,B))))) # label(t29_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5093 (all A (l2_rlvect_1(A) -> l1_rlvect_1(A))) # label(dt_l2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5094 $T # label(t6_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5095 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k9_rlvect_1(A,k8_rlvect_1(A,B,B,B)) = k3_rlvect_1(A,B,np__3))))) # label(t93_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5096 (all A all B (-v3_struct_0(A) & l1_rlvect_1(A) & m1_finseq_1(B,u1_struct_0(A)) -> m1_subset_1(k9_rlvect_1(A,B),u1_struct_0(A)))) # label(dt_k9_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5097 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k9_rlvect_1(A,k8_rlvect_1(A,B,C,D)) = k2_rlvect_1(A,k2_rlvect_1(A,B,C),D))))))))) # label(t63_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5098 (all A (v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_rlvect_1(A,B,C) = k9_rlvect_1(A,k8_rlvect_1(A,k1_rlvect_1(A),B,C)) & k9_rlvect_1(A,k8_rlvect_1(A,B,C,k1_rlvect_1(A))) = k2_rlvect_1(A,B,C) & k9_rlvect_1(A,k8_rlvect_1(A,B,k1_rlvect_1(A),C)) = k2_rlvect_1(A,B,C))))))) # label(t92_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5099 (all A all B all C (-v3_struct_0(A) & v3_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_rlvect_1(A) -> k4_rlvect_1(A,C,B) = k4_rlvect_1(A,B,C))) # label(commutativity_k4_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5100 (all A all B all C (-v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,k1_numbers) & l2_rlvect_1(A) -> m1_subset_1(k3_rlvect_1(A,B,C),u1_struct_0(A)))) # label(dt_k3_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5101 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_rlvect_1(A,B,B) = k1_rlvect_1(A))))) # label(t28_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5102 (all A (l1_rlvect_1(A) -> (v1_rlvect_1(A) -> A = g1_rlvect_1(u1_struct_0(A),u1_rlvect_1(A),u2_struct_0(A))))) # label(abstractness_v1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5103 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k5_rlvect_1(A,k6_rlvect_1(A,B,C)) = k2_rlvect_1(A,C,k5_rlvect_1(A,B)))))))) # label(t47_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5104 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_rlvect_1(A),B,C) = k2_rlvect_1(A,B,C))))))) # label(t5_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5105 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (C = k1_funct_1(B,np__1) & k1_funct_1(B,np__2) = D & E = k1_funct_1(B,np__3) & k3_finseq_1(B) = np__3 -> k9_rlvect_1(A,B) = k2_rlvect_1(A,k2_rlvect_1(A,C,D),E)))))))))))) # label(t97_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5106 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,C,B),k3_rlvect_1(A,D,B)),k3_rlvect_1(A,E,B)) = k3_rlvect_1(A,k9_rlvect_1(A,k8_rlvect_1(A,C,D,E)),B))))))))))) # label(t67_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5107 (exists A (l2_rlvect_1(A) & -v3_struct_0(A))) # label(rc3_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5108 $T # label(t17_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5109 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k1_funct_1(B,np__2) = D & k1_funct_1(B,np__1) = C & np__2 = k3_finseq_1(B) -> k2_rlvect_1(A,C,D) = k9_rlvect_1(A,B)))))))))) # label(t96_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5110 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_rlvect_1(A) = k2_rlvect_1(A,B,C) -> B = k5_rlvect_1(A,C)))))))) # label(t19_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5111 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(C,k2_finseq_1(D)) & D = k3_finseq_1(B) -> m1_subset_1(k1_funct_1(B,C),u1_struct_0(A))))))))))) # label(t54_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5112 (all A all B all C (-v3_struct_0(A) & l1_rlvect_1(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) -> m1_subset_1(k6_rlvect_1(A,B,C),u1_struct_0(A)))) # label(dt_k6_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5113 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (v4_rlvect_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,k2_rlvect_1(A,B,C),D) = k2_rlvect_1(A,B,k2_rlvect_1(A,C,D))))))))))) # label(d6_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5114 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (exists C (m1_subset_1(C,u1_struct_0(A)) & k1_rlvect_1(A) = k2_rlvect_1(A,B,C))))) <-> v6_rlvect_1(A)))) # label(d8_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5115 (all A (v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k5_rlvect_1(A,k2_rlvect_1(A,B,C)) = k6_rlvect_1(A,k5_rlvect_1(A,C),B))))))) # label(t44_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5116 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (-v3_struct_0(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v7_rlvect_1(C) & l2_rlvect_1(C) & v4_rlvect_1(C) & v3_rlvect_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k3_rlvect_1(C,D,k5_real_1(A,B)) = k6_rlvect_1(C,k3_rlvect_1(C,D,A),k3_rlvect_1(C,D,B)))))))))) # label(t49_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5117 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> k2_rlvect_1(A,k9_rlvect_1(A,B),k9_rlvect_1(A,C)) = k9_rlvect_1(A,k8_finseq_1(u1_struct_0(A),B,C)))))))) # label(t58_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5118 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k9_rlvect_1(A,k8_rlvect_1(A,B,D,C)) = k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)))))))))) # label(t87_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5119 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k5_rlvect_1(A,B) = k5_rlvect_1(A,k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),B))))))) # label(t69_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5120 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> k1_rlvect_1(A) = k5_rlvect_1(A,k1_rlvect_1(A)))) # label(t25_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5121 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (k3_finseq_1(B) = np__1 -> k1_funct_1(B,np__1) = k9_rlvect_1(A,B)))))) # label(t95_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5122 (all A (v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k9_rlvect_1(A,k7_rlvect_1(A,B,k1_rlvect_1(A))) = B & B = k9_rlvect_1(A,k7_rlvect_1(A,k1_rlvect_1(A),B)))))) # label(t75_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5123 (all A (m1_subset_1(A,k1_numbers) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & l2_rlvect_1(B) & v7_rlvect_1(B) & v6_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k3_rlvect_1(B,C,A) = k3_rlvect_1(B,k5_rlvect_1(B,C),k1_real_1(A)))))))) # label(t40_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5124 (all A (m1_subset_1(A,k1_numbers) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> -(A != np__0 & k1_rlvect_1(B) != C & k1_rlvect_1(B) = k3_rlvect_1(B,C,A)))))))) # label(t24_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5125 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k9_rlvect_1(A,k7_rlvect_1(A,B,C)) = k2_rlvect_1(A,k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),B)),k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),C))))))))) # label(t73_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5126 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k4_rlvect_1(A,k9_rlvect_1(A,k7_rlvect_1(A,C,D)),B) = k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)))))))))) # label(t84_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5127 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k9_rlvect_1(A,k8_rlvect_1(A,C,D,B)) = k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)))))))))) # label(t85_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5128 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)) = k9_rlvect_1(A,k8_rlvect_1(A,B,C,D)))))))))) # label(t86_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5129 $T # label(t88_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5130 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k6_rlvect_1(A,k5_rlvect_1(A,B),C) = k5_rlvect_1(A,k9_rlvect_1(A,k7_rlvect_1(A,B,C))))))))) # label(t70_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5131 (exists A (v2_rlvect_1(A) & l2_rlvect_1(A))) # label(rc2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5132 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (k2_rlvect_1(A,B,D) = k2_rlvect_1(A,B,E) | k2_rlvect_1(A,D,B) = k2_rlvect_1(A,E,B) -> E = D))))))))))) # label(t21_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5133 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_rlvect_1(A,B,k5_rlvect_1(A,C)) = k6_rlvect_1(A,B,C))))))) # label(d11_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5134 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k6_rlvect_1(A,k5_rlvect_1(A,B),C) = k6_rlvect_1(A,k5_rlvect_1(A,C),B))))))) # label(t46_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5135 $T # label(t32_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5136 (all A (l2_struct_0(A) -> k1_rlvect_1(A) = u2_struct_0(A))) # label(d2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5137 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> k2_rlvect_1(A,B,k1_rlvect_1(A)) = B)) <-> v5_rlvect_1(A)))) # label(d7_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5138 (all A (l2_rlvect_1(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,k3_rlvect_1(A,C,B),k3_rlvect_1(A,D,B)) = k3_rlvect_1(A,k2_rlvect_1(A,C,D),B))))))) & (all B (m1_subset_1(B,u1_struct_0(A)) -> k3_rlvect_1(A,B,np__1) = B)) & (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k3_rlvect_1(A,D,k4_real_1(B,C)) = k3_rlvect_1(A,k3_rlvect_1(A,D,C),B))))))) & (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k3_rlvect_1(A,D,k3_real_1(B,C)) = k2_rlvect_1(A,k3_rlvect_1(A,D,B),k3_rlvect_1(A,D,C)))))))) <-> v7_rlvect_1(A)))) # label(d9_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5139 (all A (v4_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,B,k6_rlvect_1(A,C,D)) = k6_rlvect_1(A,k2_rlvect_1(A,B,C),D))))))))) # label(t42_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5140 $T # label(t2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5141 (all A all B all C all D (m1_subset_1(B,A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A) & m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all E all F all G all H (g2_rlvect_1(A,B,C,D) = g2_rlvect_1(E,F,G,H) -> A = E & D = H & C = G & B = F)))) # label(free_g2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5142 (all A all B all C all D (-v1_xboole_0(A) & m1_subset_1(B,A) & v1_funct_1(C) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A) & m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A) & v1_funct_1(D) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> v2_rlvect_1(g2_rlvect_1(A,B,C,D)) & -v3_struct_0(g2_rlvect_1(A,B,C,D)))) # label(fc1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5143 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),B)) = B)))) # label(t61_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5144 (all A (m1_subset_1(A,k1_numbers) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l2_rlvect_1(B) & v7_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k3_rlvect_1(B,k6_rlvect_1(B,C,D),A) = k6_rlvect_1(B,k3_rlvect_1(B,C,A),k3_rlvect_1(B,D,A)))))))))) # label(t48_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5145 (all A all B all C (-v3_struct_0(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & v3_rlvect_1(A) -> m1_subset_1(k4_rlvect_1(A,B,C),u1_struct_0(A)))) # label(dt_k4_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5146 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k5_rlvect_1(A,B) = C <-> k2_rlvect_1(A,B,C) = k1_rlvect_1(A))))))))) # label(d10_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5147 $T # label(t8_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5148 $T # label(t4_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5149 (all A (v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> k1_rlvect_1(A) = k9_rlvect_1(A,k7_rlvect_1(A,k1_rlvect_1(A),k1_rlvect_1(A))))) # label(t74_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5150 $T # label(t9_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5151 (all A (l2_rlvect_1(A) -> (v2_rlvect_1(A) -> g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A)) = A))) # label(abstractness_v2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5152 (all A all B (-v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & l1_rlvect_1(A) -> m1_subset_1(k5_rlvect_1(A,B),u1_struct_0(A)))) # label(dt_k5_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5153 (exists A l2_rlvect_1(A)) # label(existence_l2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5154 (all A (-v3_struct_0(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k9_rlvect_1(A,k7_rlvect_1(A,k5_rlvect_1(A,B),k5_rlvect_1(A,B))) = k3_rlvect_1(A,B,k1_real_1(np__2)))))) # label(t80_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5155 (all A (l2_struct_0(A) -> m1_subset_1(k1_rlvect_1(A),u1_struct_0(A)))) # label(dt_k1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5156 (all A (m1_subset_1(A,k1_numbers) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k3_rlvect_1(B,k5_rlvect_1(B,C),A) = k3_rlvect_1(B,C,k1_real_1(A)))))))) # label(t38_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5157 (all A (v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k1_rlvect_1(A) = k4_rlvect_1(A,B,B) -> B = k1_rlvect_1(A)))))) # label(t34_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5158 (all A all B all C (v1_funct_1(B) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & m1_subset_1(C,A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> l1_rlvect_1(g1_rlvect_1(A,B,C)) & v1_rlvect_1(g1_rlvect_1(A,B,C)))) # label(dt_g1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.70 5159 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (v5_rlvect_1(C) & v6_rlvect_1(C) & v7_rlvect_1(C) & l2_rlvect_1(C) & v4_rlvect_1(C) & v3_rlvect_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (k3_rlvect_1(C,D,B) = k3_rlvect_1(C,D,A) -> k1_rlvect_1(C) = D | A = B))))))))) # label(t51_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5160 (all A (l1_struct_0(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_rlvect_1(A,B))))) # label(t3_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5161 (exists A l1_rlvect_1(A)) # label(existence_l1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5162 $T # label(t18_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5163 (all A all B all C (l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & -v3_struct_0(A) -> m1_subset_1(k2_rlvect_1(A,B,C),u1_struct_0(A)))) # label(dt_k2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5164 (all A (l1_struct_0(A) -> (all B (r1_rlvect_1(A,B) <-> r2_hidden(B,u1_struct_0(A)))))) # label(d1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5165 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_numbers) -> k3_rlvect_1(A,k9_rlvect_1(A,k6_finseq_1(u1_struct_0(A))),B) = k1_rlvect_1(A))))) # label(t64_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5166 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k6_rlvect_1(A,B,D) = k6_rlvect_1(A,B,C) -> D = C))))))))) # label(t37_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5167 (all A (m1_subset_1(A,k1_numbers) -> (all B (v7_rlvect_1(B) & l2_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (k1_rlvect_1(B) = C | np__0 = A -> k3_rlvect_1(B,C,A) = k1_rlvect_1(B)))))))) # label(t23_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5168 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)) = k4_rlvect_1(A,k9_rlvect_1(A,k7_rlvect_1(A,B,D)),C))))))))) # label(t83_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5169 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k4_rlvect_1(A,k3_rlvect_1(A,C,B),k3_rlvect_1(A,D,B)) = k3_rlvect_1(A,k9_rlvect_1(A,k7_rlvect_1(A,C,D)),B))))))))) # label(t66_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5170 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k9_rlvect_1(A,k7_rlvect_1(A,C,B)) = k9_rlvect_1(A,k7_rlvect_1(A,B,C)))))))) # label(t72_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5171 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_rlvect_1(A,C,B) = k2_rlvect_1(A,B,C))))) <-> v3_rlvect_1(A)))) # label(d5_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5172 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k2_rlvect_1(A,B,C) = B | k2_rlvect_1(A,C,B) = B -> C = k1_rlvect_1(A)))))))) # label(t22_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5173 (exists A (l1_rlvect_1(A) & v1_rlvect_1(A) & -v3_struct_0(A))) # label(rc4_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5174 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> k9_rlvect_1(A,k8_rlvect_1(A,k1_rlvect_1(A),k1_rlvect_1(A),k1_rlvect_1(A))) = k1_rlvect_1(A))) # label(t90_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5175 (all A (l1_rlvect_1(A) -> l2_struct_0(A))) # label(dt_l1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5176 (all A (m1_subset_1(A,k1_numbers) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & l2_rlvect_1(B) & v7_rlvect_1(B) & v6_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (k3_rlvect_1(B,D,A) = k3_rlvect_1(B,C,A) -> C = D | A = np__0))))))))) # label(t50_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5177 $T # label(t53_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5178 (all A (m1_subset_1(A,k1_numbers) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & l2_rlvect_1(B) & v7_rlvect_1(B) & v6_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k3_rlvect_1(B,k5_rlvect_1(B,C),A) = k5_rlvect_1(B,k3_rlvect_1(B,C,A)))))))) # label(t39_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5179 (all A (v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (B = k6_rlvect_1(A,C,D) & m1_subset_1(D,u1_struct_0(A)))))))))) # label(t36_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5180 (all A (v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k4_rlvect_1(A,k6_rlvect_1(A,B,C),D) = k6_rlvect_1(A,B,k6_rlvect_1(A,C,D)))))))))) # label(t43_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5181 (all A (l2_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_numbers) -> k3_rlvect_1(A,B,C) = k8_funct_2(k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A),u2_rlvect_1(A),k1_domain_1(k1_numbers,u1_struct_0(A),C,B)))))))) # label(d4_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5182 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k5_rlvect_1(A,k9_rlvect_1(A,k8_rlvect_1(A,B,C,D))) = k6_rlvect_1(A,k6_rlvect_1(A,k5_rlvect_1(A,B),C),D))))))))) # label(t71_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5183 (all A (m1_subset_1(A,k1_numbers) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l2_rlvect_1(B) & v7_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m2_finseq_1(C,u1_struct_0(B)) -> (all D (m2_finseq_1(D,u1_struct_0(B)) -> ((all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> (r2_hidden(E,k4_finseq_1(C)) & F = k1_funct_1(D,E) -> k3_rlvect_1(B,F,A) = k1_funct_1(C,E)))))) & k3_finseq_1(C) = k3_finseq_1(D) -> k9_rlvect_1(B,C) = k3_rlvect_1(B,k9_rlvect_1(B,D),A)))))))))) # label(t56_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5184 (all A (v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k6_rlvect_1(A,k6_rlvect_1(A,B,D),C) = k6_rlvect_1(A,B,k2_rlvect_1(A,C,D)))))))))) # label(t41_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5185 $T # label(t52_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5186 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k2_group_1(A) = k3_group_1(A,B) -> k2_group_1(A) = B))))) # label(t18_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5187 $T # label(t39_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5188 (all A (-v3_struct_0(A) & l1_group_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (m1_subset_1(D,u1_struct_0(A)) & C = k1_group_1(A,D,B))) & (exists D (m1_subset_1(D,u1_struct_0(A)) & k1_group_1(A,B,D) = C)))))) & (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_group_1(A,B,k1_group_1(A,C,D)) = k1_group_1(A,k1_group_1(A,B,C),D))))))) -> v4_group_1(A) & v3_group_1(A)))) # label(t6_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5189 (all A (v1_int_1(A) -> (all B (v3_group_1(B) & l1_group_1(B) & v4_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (r1_xreal_0(np__0,A) -> k6_group_1(B,A,C) = k6_group_1(B,k1_int_2(A),C)))))))) # label(t55_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5190 (all A (-v3_struct_0(A) & l1_group_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_group_1(A,B,k1_group_1(A,C,D)) = k1_group_1(A,k1_group_1(A,B,C),D))))))) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> -(all C (m1_subset_1(C,u1_struct_0(A)) -> C = k1_group_1(A,B,C) & (exists D (m1_subset_1(D,u1_struct_0(A)) & k1_group_1(A,C,D) = B & k1_group_1(A,D,C) = B)) & C = k1_group_1(A,C,B))))) | l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A)))) # label(t5_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5191 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k6_group_1(A,B,C) = k2_binop_1(u1_struct_0(A),k5_numbers,u1_struct_0(A),k5_group_1(A),C,B))))))) # label(d10_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5192 $T # label(t4_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5193 (exists A l1_group_1(A)) # label(existence_l1_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5194 (all A (v1_int_1(A) -> (all B (v4_group_1(B) & l1_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (A = np__0 -> k2_group_1(B) = k6_group_1(B,A,C)))))))) # label(t59_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5195 $T # label(t89_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5196 (all A (v1_int_1(A) -> (all B (-v3_struct_0(B) & v3_group_1(B) & l1_group_1(B) & v4_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k6_group_1(B,k4_xcmplx_0(A),C) = k3_group_1(B,k6_group_1(B,A,C)))))))) # label(t70_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5197 (all A (l1_group_1(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_group_1(A,k1_group_1(A,B,C),D) = k1_group_1(A,B,k1_group_1(A,C,D)))))))) <-> v4_group_1(A)))) # label(d4_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5198 $T # label(t11_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5199 $T # label(t57_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5200 (all A (-v3_struct_0(A) & l1_group_1(A) -> m1_subset_1(k2_group_1(A),u1_struct_0(A)))) # label(dt_k2_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5201 (all A (l1_group_1(A) & -v3_struct_0(A) -> v1_funct_1(k5_group_1(A)) & m2_relset_1(k5_group_1(A),k2_zfmisc_1(u1_struct_0(A),k5_numbers),u1_struct_0(A)) & v1_funct_2(k5_group_1(A),k2_zfmisc_1(u1_struct_0(A),k5_numbers),u1_struct_0(A)))) # label(dt_k5_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5202 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (v3_group_1(C) & l1_group_1(C) & v4_group_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (all E (m1_subset_1(E,u1_struct_0(C)) -> (k1_group_1(C,E,D) = k1_group_1(C,D,E) -> k1_group_1(C,k6_group_1(C,B,E),k6_group_1(C,A,D)) = k1_group_1(C,k6_group_1(C,A,D),k6_group_1(C,B,E))))))))))))) # label(t53_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5203 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_group_1(A,B,C) = k2_group_1(A) & k2_group_1(A) = k1_group_1(A,C,B) <-> k3_group_1(A,B) = C))))))) # label(d6_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5204 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v3_struct_0(B) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (k6_group_1(B,A,C) = k2_group_1(B) -> r1_nat_1(k7_group_1(B,C),A)))))))) # label(t86_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5205 (all A (l1_group_1(A) -> (-v3_struct_0(A) & v3_group_1(A) -> v2_group_1(A) & -v3_struct_0(A)))) # label(cc1_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5206 (all A (l1_struct_0(A) -> (v6_group_1(A) <-> v1_finset_1(u1_struct_0(A))))) # label(d14_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5207 (all A (l1_group_1(A) -> v1_funct_1(u1_group_1(A)) & m2_relset_1(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_2(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)))) # label(dt_u1_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5208 (all A (l1_group_1(A) & -v3_struct_0(A) -> (v2_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (B = k2_group_1(A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,B,C) = C & k1_group_1(A,C,B) = C)))))))) # label(d5_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5209 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (v3_group_1(C) & l1_group_1(C) & v4_group_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k1_group_1(C,k6_group_1(C,B,D),k6_group_1(C,A,D)) = k6_group_1(C,k2_xcmplx_0(B,A),D))))))))) # label(t65_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5210 (all A all B all C (v1_funct_1(B) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & m1_subset_1(C,A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & -v1_xboole_0(A) -> -v3_struct_0(g1_rlvect_1(A,B,C)) & v1_rlvect_1(g1_rlvect_1(A,B,C)))) # label(fc2_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5211 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> np__1 = k7_group_1(A,k2_group_1(A)))) # label(t84_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5212 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> (B = k4_group_1(A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> k3_group_1(A,C) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C)))))))) # label(d7_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5213 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (k1_group_1(A,B,D) = C & m1_subset_1(D,u1_struct_0(A)))))))))) # label(t23_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5214 (all A all B (m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & -v1_xboole_0(A) -> v1_group_1(g1_group_1(A,B)) & -v3_struct_0(g1_group_1(A,B)))) # label(fc1_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5215 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (l1_group_1(C) & v4_group_1(C) & v3_group_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (all E (m1_subset_1(E,u1_struct_0(C)) -> (k1_group_1(C,D,E) = k1_group_1(C,E,D) -> k1_group_1(C,k6_group_1(C,A,D),k6_group_1(C,B,E)) = k1_group_1(C,k6_group_1(C,B,E),k6_group_1(C,A,D))))))))))))) # label(t75_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5216 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> v1_funct_1(k4_group_1(A)) & v1_funct_2(k4_group_1(A),u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(k4_group_1(A),u1_struct_0(A),u1_struct_0(A)))) # label(dt_k4_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5217 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (-v3_struct_0(C) & l1_group_1(C) & v4_group_1(C) & v3_group_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k6_group_1(C,k1_nat_1(A,B),D) = k1_group_1(C,k6_group_1(C,A,D),k6_group_1(C,B,D)))))))))) # label(t48_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5218 (all A (l1_group_1(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,C,B) = k1_group_1(A,B,C))))) <-> v7_group_1(A)))) # label(d16_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5219 $T # label(t9_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5220 $T # label(t88_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5221 $T # label(t83_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5222 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> k8_group_1(A) = k1_card_1(u1_struct_0(A)))) # label(d13_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5223 (all A (l1_group_1(A) -> (v1_group_1(A) -> A = g1_group_1(u1_struct_0(A),u1_group_1(A))))) # label(abstractness_v1_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5224 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v7_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k3_group_1(A,k10_group_1(A,B,C)) = k10_group_1(A,k3_group_1(A,B),k3_group_1(A,C)))))))) # label(t94_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5225 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> v1_card_1(k8_group_1(A)))) # label(dt_k8_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5226 $T # label(t93_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5227 $T # label(t78_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5228 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (v3_group_1(C) & l1_group_1(C) & v4_group_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k6_group_1(C,k2_nat_1(A,B),D) = k6_group_1(C,B,k6_group_1(C,A,D)))))))))) # label(t50_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5229 (all A all B all C (-v3_struct_0(A) & l1_group_1(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & v7_group_1(A) -> k10_group_1(A,B,C) = k1_group_1(A,B,C))) # label(redefinition_k10_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5230 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_group_1(A,C,B) = k1_group_1(A,B,C) <-> k1_group_1(A,k3_group_1(A,C),k3_group_1(A,B)) = k1_group_1(A,k3_group_1(A,B),k3_group_1(A,C))))))))) # label(t27_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5231 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k1_group_1(A,C,B) = k1_group_1(A,D,B) | k1_group_1(A,B,D) = k1_group_1(A,B,C) -> D = C))))))))) # label(t14_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5232 (all A all B (v3_group_1(A) & l1_group_1(A) & m1_subset_1(B,u1_struct_0(A)) & v4_group_1(A) & -v3_struct_0(A) -> m1_subset_1(k3_group_1(A,B),u1_struct_0(A)))) # label(dt_k3_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5233 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (k2_group_1(A) = k6_group_1(A,C,B) -> C = np__0))) <-> v5_group_1(B,A)))))) # label(d11_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5234 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (v5_group_1(B,A) -> (C = k7_group_1(A,B) <-> C = np__0)) & (-v5_group_1(B,A) -> (C != np__0 & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (k2_group_1(A) = k6_group_1(A,D,B) -> r1_xreal_0(C,D) | D = np__0))) & k6_group_1(A,C,B) = k2_group_1(A) <-> C = k7_group_1(A,B))))))))) # label(d12_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5235 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C all D (g1_group_1(C,D) = g1_group_1(A,B) -> C = A & D = B)))) # label(free_g1_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5236 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k3_group_1(A,B) = k3_group_1(A,C) -> C = B))))))) # label(t17_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5237 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (B = k1_group_1(A,B,C) | B = k1_group_1(A,C,B) -> k2_group_1(A) = C))))))) # label(t15_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5238 $T # label(t81_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5239 $T # label(t3_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5240 (all A (v1_int_1(A) -> (all B (-v3_struct_0(B) & l1_group_1(B) & v4_group_1(B) & v3_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k6_group_1(B,k2_xcmplx_0(A,np__1),C) = k1_group_1(B,C,k6_group_1(B,A,C)) & k1_group_1(B,k6_group_1(B,A,C),C) = k6_group_1(B,k2_xcmplx_0(A,np__1),C))))))) # label(t66_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5241 (all A (-v3_struct_0(A) & l1_group_1(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),k5_numbers),u1_struct_0(A)) & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),k5_numbers),u1_struct_0(A)) -> (k5_group_1(A) = B <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_group_1(A) = k2_binop_1(u1_struct_0(A),k5_numbers,u1_struct_0(A),B,C,np__0) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> k2_binop_1(u1_struct_0(A),k5_numbers,u1_struct_0(A),B,C,k1_nat_1(D,np__1)) = k1_group_1(A,k2_binop_1(u1_struct_0(A),k5_numbers,u1_struct_0(A),B,C,D),C)))))))))) # label(d8_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5242 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) -> v2_binop_1(u1_group_1(A),u1_struct_0(A)))) # label(t31_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5243 $T # label(t80_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5244 $T # label(t76_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5245 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k2_group_1(A) = k1_group_1(A,B,C) & k2_group_1(A) = k1_group_1(A,C,B) -> C = k3_group_1(A,B)))))))) # label(t12_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5246 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_group_1(A,k7_binop_2(np__1),B) = k3_group_1(A,B))))) # label(t62_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5247 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> v1_finseqop(u1_group_1(A),u1_struct_0(A)))) # label(t36_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5248 (all A all B (v1_funct_1(B) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> l1_group_1(g1_group_1(A,B)) & v1_group_1(g1_group_1(A,B)))) # label(dt_g1_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5249 $T # label(t1_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5250 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_group_1(A,np__0,B) = k2_group_1(A))))) # label(t43_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5251 (all A (v1_int_1(A) -> (all B (v4_group_1(B) & l1_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (r1_xreal_0(A,np__0) -> k3_group_1(B,k6_group_1(B,k1_int_2(A),C)) = k6_group_1(B,A,C)))))))) # label(t60_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5252 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_group_1(A,B,B) = k6_group_1(A,np__2,B))))) # label(t45_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5253 (all A (v1_int_1(A) -> (all B (-v3_struct_0(B) & v4_group_1(B) & l1_group_1(B) & v7_group_1(B) & v3_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k6_group_1(B,A,k10_group_1(B,C,D)) = k10_group_1(B,k6_group_1(B,A,C),k6_group_1(B,A,D)))))))))) # label(t96_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5254 (all A (v1_int_1(A) -> (all B (v4_group_1(B) & l1_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (k1_group_1(B,D,C) = k1_group_1(B,C,D) -> k1_group_1(B,C,k6_group_1(B,A,D)) = k1_group_1(B,k6_group_1(B,A,D),C)))))))))) # label(t77_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5255 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (-v3_struct_0(C) & l1_group_1(C) & v4_group_1(C) & v3_group_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (all E (m1_subset_1(E,u1_struct_0(C)) -> (k1_group_1(C,E,D) = k1_group_1(C,D,E) -> k1_group_1(C,k6_group_1(C,A,D),k6_group_1(C,B,E)) = k1_group_1(C,k6_group_1(C,B,E),k6_group_1(C,A,D))))))))))))) # label(t74_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5256 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k3_group_1(A,k1_group_1(A,B,C)) = k1_group_1(A,k3_group_1(A,B),k3_group_1(A,C)) <-> k1_group_1(A,B,C) = k1_group_1(A,C,B)))))))) # label(t26_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5257 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v3_struct_0(B) & v4_group_1(B) & l1_group_1(B) & v3_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (k1_group_1(B,D,C) = k1_group_1(B,C,D) -> k1_group_1(B,k6_group_1(B,A,C),k6_group_1(B,A,D)) = k6_group_1(B,A,k1_group_1(B,C,D))))))))))) # label(t54_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5258 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k3_group_1(A,k3_group_1(A,B)))))) # label(t19_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5259 (exists A (l1_group_1(A) & -v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & v2_group_1(A) & v1_group_1(A))) # label(rc3_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5260 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (-v3_struct_0(C) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k6_group_1(C,k3_xcmplx_0(A,B),D) = k6_group_1(C,B,k6_group_1(C,A,D)))))))))) # label(t68_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5261 (all A (-v3_struct_0(A) & l1_group_1(A) -> ((exists B (m1_subset_1(B,u1_struct_0(A)) & (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,C,B) = C & C = k1_group_1(A,B,C))))) <-> v2_group_1(A)))) # label(d2_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5262 $T # label(t41_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5263 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (l1_group_1(B) & v7_group_1(B) & v4_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k6_group_1(B,A,k10_group_1(B,C,D)) = k10_group_1(B,k6_group_1(B,A,C),k6_group_1(B,A,D)))))))))) # label(t95_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5264 (all A (l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,B,C) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_group_1(A),B,C))))))) # label(d1_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5265 (all A (v1_int_1(A) -> (all B (l1_group_1(B) & v4_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> k2_group_1(B) = k6_group_1(B,A,k2_group_1(B)))))) # label(t61_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5266 (all A (v7_group_1(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> v4_rlvect_1(g1_rlvect_1(u1_struct_0(A),u1_group_1(A),k2_group_1(A))) & v6_rlvect_1(g1_rlvect_1(u1_struct_0(A),u1_group_1(A),k2_group_1(A))) & v5_rlvect_1(g1_rlvect_1(u1_struct_0(A),u1_group_1(A),k2_group_1(A))) & v3_rlvect_1(g1_rlvect_1(u1_struct_0(A),u1_group_1(A),k2_group_1(A))))) # label(t97_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5267 (exists A (v1_group_1(A) & l1_group_1(A))) # label(rc1_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5268 $T # label(t38_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5269 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> k2_group_1(A) = k3_group_1(A,k2_group_1(A)))) # label(t16_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5270 (all A all B (-v3_struct_0(A) & l1_group_1(A) & m1_subset_1(B,u1_struct_0(A)) & v4_group_1(A) & v3_group_1(A) -> m2_subset_1(k7_group_1(A,B),k1_numbers,k5_numbers))) # label(dt_k7_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5271 $T # label(t8_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5272 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (B = k3_group_1(A,B) <-> k2_group_1(A) = k6_group_1(A,np__2,B)))))) # label(t47_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5273 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k2_group_1(A) = k6_group_1(A,k7_group_1(A,B),B))))) # label(t82_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5274 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (D = k1_group_1(A,B,C) <-> k1_group_1(A,k3_group_1(A,B),D) = C))))))))) # label(t21_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5275 (all A (v1_int_1(A) -> (all B (l1_group_1(B) & v4_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (k1_group_1(B,C,D) = k1_group_1(B,D,C) -> k6_group_1(B,A,k1_group_1(B,C,D)) = k1_group_1(B,k6_group_1(B,A,C),k6_group_1(B,A,D))))))))))) # label(t73_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5276 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,k3_group_1(A,C),k3_group_1(A,B)) = k3_group_1(A,k1_group_1(A,B,C)))))))) # label(t25_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5277 (all A (l1_group_1(A) -> l1_struct_0(A))) # label(dt_l1_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5278 (all A all B all C (-v3_struct_0(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_group_1(A) -> m1_subset_1(k1_group_1(A,B,C),u1_struct_0(A)))) # label(dt_k1_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5279 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_group_1(A,C,B) = k1_group_1(A,B,C) <-> k1_group_1(A,k3_group_1(A,C),B) = k1_group_1(A,B,k3_group_1(A,C))))))))) # label(t28_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5280 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v3_struct_0(B) & v3_group_1(B) & l1_group_1(B) & v4_group_1(B) -> k2_group_1(B) = k6_group_1(B,A,k2_group_1(B)))))) # label(t42_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5281 (exists A (-v3_struct_0(A) & v1_group_1(A) & l1_group_1(A))) # label(rc2_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5282 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (np__1 = k7_group_1(A,B) -> k2_group_1(A) = B))))) # label(t85_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5283 $T # label(t87_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5284 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (v1_int_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (-r1_xreal_0(np__0,B) -> k6_group_1(A,B,C) = k3_group_1(A,k2_binop_1(u1_struct_0(A),k5_numbers,u1_struct_0(A),k5_group_1(A),C,k1_int_2(B)))) & (r1_xreal_0(np__0,B) -> k6_group_1(A,B,C) = k2_binop_1(u1_struct_0(A),k5_numbers,u1_struct_0(A),k5_group_1(A),C,k1_int_2(B))))))))) # label(d9_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5285 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> -v5_group_1(k2_group_1(A),A))) # label(t79_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5286 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> C = k1_group_1(A,B,C) & k1_group_1(A,C,B) = C)) -> B = k2_group_1(A)))))) # label(t10_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5287 (all A (l1_group_1(A) & v2_group_1(A) & -v3_struct_0(A) -> r3_binop_1(u1_struct_0(A),k2_group_1(A),u1_group_1(A)))) # label(t32_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5288 $T # label(t58_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5289 $T # label(t29_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5290 (all A (l1_group_1(A) & -v3_struct_0(A) -> (v3_group_1(A) <-> (exists B (m1_subset_1(B,u1_struct_0(A)) & (all C (m1_subset_1(C,u1_struct_0(A)) -> C = k1_group_1(A,C,B) & (exists D (B = k1_group_1(A,C,D) & B = k1_group_1(A,D,C) & m1_subset_1(D,u1_struct_0(A)))) & k1_group_1(A,B,C) = C))))))) # label(d3_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5291 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (v3_group_1(C) & l1_group_1(C) & v4_group_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k6_group_1(C,k2_xcmplx_0(A,B),D) = k1_group_1(C,k6_group_1(C,A,D),k6_group_1(C,B,D)))))))))) # label(t64_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5292 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k6_group_1(C,k2_xcmplx_0(A,B),D) = k1_group_1(C,k6_group_1(C,A,D),k6_group_1(C,B,D)))))))))) # label(t63_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5293 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k2_group_1(A) = k1_group_1(A,B,C) | k1_group_1(A,C,B) = k2_group_1(A) -> B = k3_group_1(A,C) & C = k3_group_1(A,B)))))))) # label(t20_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5294 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (v6_group_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> ((exists C (v1_finset_1(C) & C = u1_struct_0(A) & k4_card_1(C) = B)) <-> k9_group_1(A) = B)))))) # label(d15_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5295 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_group_1(A,np__3,B) = k1_group_1(A,k1_group_1(A,B,B),B))))) # label(t46_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5296 $T # label(t30_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5297 (all A (l1_group_1(A) & v2_group_1(A) & -v3_struct_0(A) -> k2_group_1(A) = k3_binop_1(u1_struct_0(A),u1_group_1(A)))) # label(t33_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5298 $T # label(t13_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5299 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v3_struct_0(B) & v3_group_1(B) & l1_group_1(B) & v4_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k6_group_1(B,A,k3_group_1(B,C)) = k3_group_1(B,k6_group_1(B,A,C)))))))) # label(t51_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5300 (all A all B all C (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(C,u1_struct_0(A)) & v1_int_1(B) & -v3_struct_0(A) -> m1_subset_1(k6_group_1(A,B,C),u1_struct_0(A)))) # label(dt_k6_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5301 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> m2_subset_1(k9_group_1(A),k1_numbers,k5_numbers))) # label(dt_k9_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5302 (all A (-v3_struct_0(A) & l1_group_1(A) & v2_group_1(A) -> v1_setwiseo(u1_group_1(A),u1_struct_0(A)))) # label(t34_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5303 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k6_group_1(A,np__1,B))))) # label(t44_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5304 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v4_group_1(C) & l1_group_1(C) & v3_group_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k6_group_1(C,B,k6_group_1(C,A,D)) = k6_group_1(C,k3_xcmplx_0(A,B),D))))))))) # label(t67_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5305 (all A (v1_int_1(A) -> (all B (-v3_struct_0(B) & v4_group_1(B) & l1_group_1(B) & v3_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (-r1_xreal_0(np__0,A) -> k3_group_1(B,k6_group_1(B,k1_int_2(A),C)) = k6_group_1(B,A,C)))))))) # label(t56_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5306 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (l1_group_1(B) & v4_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k6_group_1(B,k1_nat_1(A,np__1),C) = k1_group_1(B,C,k6_group_1(B,A,C)) & k1_group_1(B,k6_group_1(B,A,C),C) = k6_group_1(B,k1_nat_1(A,np__1),C))))))) # label(t49_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5307 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v3_struct_0(B) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k3_group_1(B,k6_group_1(B,A,C)) = k6_group_1(B,k7_binop_2(A),C))))))) # label(t71_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5308 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> r1_finseqop(u1_struct_0(A),k4_group_1(A),u1_group_1(A)))) # label(t35_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5309 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (B = k1_group_1(A,D,k3_group_1(A,C)) <-> k1_group_1(A,B,C) = D))))))))) # label(t22_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5310 $T # label(t91_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5311 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v3_struct_0(B) & l1_group_1(B) & v4_group_1(B) & v3_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (k1_group_1(B,C,D) = k1_group_1(B,D,C) -> k1_group_1(B,C,k6_group_1(B,A,D)) = k1_group_1(B,k6_group_1(B,A,D),C)))))))))) # label(t52_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5312 (all A all B all C (v7_group_1(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_group_1(A) & -v3_struct_0(A) -> k10_group_1(A,B,C) = k10_group_1(A,C,B))) # label(commutativity_k10_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5313 (exists A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & v7_group_1(A) & v2_group_1(A) & v1_group_1(A) & l1_group_1(A))) # label(rc4_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5314 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> k6_finseqop(u1_struct_0(A),u1_group_1(A)) = k4_group_1(A))) # label(t37_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5315 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (C = k1_group_1(A,D,B) & m1_subset_1(D,u1_struct_0(A)))))))))) # label(t24_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5316 $T # label(t2_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5317 $T # label(t40_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5318 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (v6_group_1(A) -> r1_xreal_0(np__1,k9_group_1(A))))) # label(t90_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5319 (all A (v1_int_1(A) -> (all B (-v3_struct_0(B) & l1_group_1(B) & v4_group_1(B) & v3_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k3_group_1(B,k6_group_1(B,A,C)) = k6_group_1(B,A,k3_group_1(B,C)))))))) # label(t72_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5320 (all A all B all C (-v3_struct_0(A) & l1_group_1(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & v7_group_1(A) -> m1_subset_1(k10_group_1(A,B,C),u1_struct_0(A)))) # label(dt_k10_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5321 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k6_group_1(C,A,k6_group_1(C,B,D)) = k6_group_1(C,k3_xcmplx_0(B,A),D))))))))) # label(t69_group_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5322 (all A (l1_vectsp_1(A) -> (v2_group_1(A) & -v3_struct_0(A) -> v6_vectsp_1(A) & v8_vectsp_1(A) & -v3_struct_0(A)))) # label(cc3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5323 (all A (-v3_struct_0(A) & l3_vectsp_1(A) -> (v5_vectsp_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,k1_group_1(A,C,B),k1_group_1(A,D,B)) = k1_group_1(A,k2_rlvect_1(A,C,D),B)))))))))) # label(d12_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5324 $T # label(t16_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5325 (all A all B all C (m1_relset_1(B,k2_zfmisc_1(A,A),A) & m1_subset_1(C,A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> l1_vectsp_1(g1_vectsp_1(A,B,C)) & v1_vectsp_1(g1_vectsp_1(A,B,C)))) # label(dt_g1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5326 (all A (v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k5_rlvect_1(A,k6_rlvect_1(A,C,D)) = k2_rlvect_1(A,D,k5_rlvect_1(A,C)) & k6_rlvect_1(A,B,k2_rlvect_1(A,D,C)) = k6_rlvect_1(A,k6_rlvect_1(A,B,C),D) & k5_rlvect_1(A,k6_rlvect_1(A,k5_rlvect_1(A,C),D)) = k2_rlvect_1(A,D,C) & k6_rlvect_1(A,C,D) = k5_rlvect_1(A,k2_rlvect_1(A,D,k5_rlvect_1(A,C))) & k5_rlvect_1(A,k2_rlvect_1(A,C,D)) = k6_rlvect_1(A,k5_rlvect_1(A,D),C))))))))) # label(t64_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5327 (all A (-v3_struct_0(A) & v4_group_1(A) & v7_group_1(A) & l3_vectsp_1(A) & v9_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (B != k1_rlvect_1(A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k2_group_1(A) = k10_group_1(A,B,C) <-> C = k4_vectsp_1(A,B))))))))) # label(d22_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5328 $T # label(d4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5329 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l3_vectsp_1(A) & v5_vectsp_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k5_rlvect_1(A,k1_group_1(A,B,C)) = k1_group_1(A,k5_rlvect_1(A,B),C))))))) # label(t41_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5330 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (exists B (l4_vectsp_1(B,A) & v3_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & v11_vectsp_1(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B))))) # label(rc13_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5331 $T # label(t83_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5332 $T # label(t71_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5333 $T # label(t24_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5334 $T # label(t31_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5335 (all A all B (l4_vectsp_1(B,A) & l1_struct_0(A) -> m2_relset_1(u2_vectsp_1(A,B),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B)) & v1_funct_2(u2_vectsp_1(A,B),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B)) & v1_funct_1(u2_vectsp_1(A,B)))) # label(dt_u2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5336 (all A (l1_struct_0(A) -> (exists B (l4_vectsp_1(B,A) & -v3_struct_0(B) & v11_vectsp_1(B,A))))) # label(rc12_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5337 $T # label(d10_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5338 (exists A l2_vectsp_1(A)) # label(existence_l2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5339 (all A (l1_struct_0(A) -> (exists B (l4_vectsp_1(B,A) & v11_vectsp_1(B,A))))) # label(rc11_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5340 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,C,B) = k2_rlvect_1(A,B,C) & k2_rlvect_1(A,B,k2_rlvect_1(A,C,D)) = k2_rlvect_1(A,k2_rlvect_1(A,B,C),D) & (exists E (k2_rlvect_1(A,B,E) = k1_rlvect_1(A) & m1_subset_1(E,u1_struct_0(A)))) & B = k2_rlvect_1(A,B,k1_rlvect_1(A)))))))) <-> v3_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A)))) # label(t7_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5341 $T # label(t76_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5342 $T # label(t55_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5343 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_rlvect_1(A,k5_rlvect_1(A,C),B) = k5_rlvect_1(A,k2_rlvect_1(A,k5_rlvect_1(A,B),C)))))))) # label(t92_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5344 $T # label(t2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5345 $T # label(t11_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5346 $T # label(t1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5347 $T # label(t17_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5348 $T # label(t9_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5349 $T # label(t75_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.71 5350 $T # label(t91_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5351 $T # label(d1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5352 (all A all B (v8_vectsp_1(A) & l3_vectsp_1(A) & m1_subset_1(B,u1_struct_0(A)) & v9_vectsp_1(A) & v7_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> m1_subset_1(k4_vectsp_1(A,B),u1_struct_0(A)))) # label(dt_k4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5353 (all A (l1_struct_0(A) -> (all B (l4_vectsp_1(B,A) -> l1_rlvect_1(B))))) # label(dt_l4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5354 $T # label(t8_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5355 (all A (-v3_struct_0(A) & l3_vectsp_1(A) -> (v7_vectsp_1(A) & l3_vectsp_1(A) & v9_vectsp_1(A) & -v3_struct_0(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,k1_group_1(A,B,C),k1_group_1(A,B,D)) = k1_group_1(A,B,k2_rlvect_1(A,C,D)) & k2_rlvect_1(A,k1_group_1(A,C,B),k1_group_1(A,D,B)) = k1_group_1(A,k2_rlvect_1(A,C,D),B) & -(B != k1_rlvect_1(A) & (all E (m1_subset_1(E,u1_struct_0(A)) -> k1_group_1(A,B,E) != k2_group_1(A))))))))))))) # label(t22_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5356 (all A (-v3_struct_0(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k5_rlvect_1(A,k6_rlvect_1(A,B,C)) = k6_rlvect_1(A,C,B))))))) # label(t81_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5357 $T # label(t37_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5358 (all A all B all C all D all E (l1_struct_0(A) & -v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m1_relset_1(C,k2_zfmisc_1(B,B),B) & m1_subset_1(D,B) & v1_funct_1(E) & m1_relset_1(E,k2_zfmisc_1(u1_struct_0(A),B),B) & v1_funct_2(E,k2_zfmisc_1(u1_struct_0(A),B),B) -> -v3_struct_0(g4_vectsp_1(A,B,C,D,E)) & v11_vectsp_1(g4_vectsp_1(A,B,C,D,E),A))) # label(fc6_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5359 $T # label(t35_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5360 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v5_vectsp_1(A) & l3_vectsp_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_rlvect_1(A) = k1_group_1(A,k1_rlvect_1(A),B))))) # label(t39_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5361 (all A (l1_vectsp_1(A) -> m1_subset_1(u1_vectsp_1(A),u1_struct_0(A)))) # label(dt_u1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5362 (all A (-v3_struct_0(A) & l3_vectsp_1(A) -> (all B (-v3_struct_0(B) & l4_vectsp_1(B,A) -> (v12_vectsp_1(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> E = k6_vectsp_1(A,B,k2_group_1(A),E) & k6_vectsp_1(A,B,C,k6_vectsp_1(A,B,D,E)) = k6_vectsp_1(A,B,k1_group_1(A,C,D),E) & k6_vectsp_1(A,B,k2_rlvect_1(A,C,D),E) = k2_rlvect_1(B,k6_vectsp_1(A,B,C,E),k6_vectsp_1(A,B,D,E)) & k6_vectsp_1(A,B,C,k2_rlvect_1(B,E,F)) = k2_rlvect_1(B,k6_vectsp_1(A,B,C,E),k6_vectsp_1(A,B,C,F))))))))))))))) # label(d26_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5363 (exists A (l1_vectsp_1(A) & -v3_struct_0(A) & v1_vectsp_1(A))) # label(rc3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5364 (all A all B all C all D all E (l1_struct_0(A) & v1_funct_1(C) & m1_relset_1(C,k2_zfmisc_1(B,B),B) & m1_subset_1(D,B) & v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(u1_struct_0(A),B),B) & m1_relset_1(E,k2_zfmisc_1(u1_struct_0(A),B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all F all G all H all I all J (g4_vectsp_1(A,B,C,D,E) = g4_vectsp_1(F,G,H,I,J) -> C = H & J = E & D = I & B = G & F = A)))) # label(free_g4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5365 $T # label(t10_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5366 $T # label(t27_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5367 (all A (-v3_struct_0(A) & l2_vectsp_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> -(B != k1_rlvect_1(A) & (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,B,C) != k2_group_1(A)))))) <-> v9_vectsp_1(A)))) # label(d20_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5368 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_vectsp_1(A) & l3_vectsp_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k5_rlvect_1(A,k1_group_1(A,B,C)) = k1_group_1(A,B,k5_rlvect_1(A,C)))))))) # label(t40_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5369 $T # label(t15_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5370 $T # label(t53_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5371 $T # label(d7_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5372 $T # label(t56_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5373 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> k6_vectsp_1(A,B,k5_rlvect_1(A,C),D) = k5_rlvect_1(B,k6_vectsp_1(A,B,C,D)) & k6_rlvect_1(B,E,k6_vectsp_1(A,B,C,D)) = k2_rlvect_1(B,E,k6_vectsp_1(A,B,k5_rlvect_1(A,C),D)))))))))))) # label(t68_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5374 $T # label(t82_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5375 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v8_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k1_rlvect_1(A) != B -> k1_rlvect_1(A) != k4_vectsp_1(A,B) & k1_rlvect_1(A) != k5_rlvect_1(A,k4_vectsp_1(A,B))))))) # label(t74_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5376 (all A (l1_struct_0(A) & -v3_struct_0(A) -> (all B (l4_vectsp_1(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k2_binop_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u2_vectsp_1(A,B),C,D) = k6_vectsp_1(A,B,C,D))))))))) # label(d24_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5377 $T # label(t18_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5378 (all A (l3_vectsp_1(A) -> (-v3_struct_0(A) & v5_vectsp_1(A) & v4_vectsp_1(A) -> v7_vectsp_1(A) & -v3_struct_0(A)))) # label(cc2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5379 $T # label(d5_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5380 (all A (l2_vectsp_1(A) -> l1_vectsp_1(A) & l2_struct_0(A))) # label(dt_l2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5381 $T # label(t29_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5382 (all A (l3_vectsp_1(A) -> l2_vectsp_1(A) & l1_rlvect_1(A))) # label(dt_l3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5383 (all A all B all C all D all E (v1_funct_1(B) & m1_subset_1(D,A) & m1_subset_1(E,A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> l3_vectsp_1(g3_vectsp_1(A,B,C,D,E)) & v3_vectsp_1(g3_vectsp_1(A,B,C,D,E)))) # label(dt_g3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5384 (all A (v4_group_1(A) & v7_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (B != k1_rlvect_1(A) -> B = k4_vectsp_1(A,k4_vectsp_1(A,B))))))) # label(t73_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5385 $T # label(t32_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5386 (all A all B all C (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & m1_subset_1(C,A) -> (all D all E all F (g1_vectsp_1(D,E,F) = g1_vectsp_1(A,B,C) -> A = D & E = B & C = F)))) # label(free_g1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5387 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v7_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (B = k1_rlvect_1(A) | C = k1_rlvect_1(A) <-> k10_group_1(A,B,C) = k1_rlvect_1(A)))))))) # label(t44_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5388 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v5_vectsp_1(A) & l3_vectsp_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_group_1(A,k6_rlvect_1(A,B,C),D) = k6_rlvect_1(A,k1_group_1(A,B,D),k1_group_1(A,C,D)))))))))) # label(t45_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5389 (exists A (l2_vectsp_1(A) & -v3_struct_0(A) & v2_vectsp_1(A))) # label(rc5_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5390 $T # label(t48_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5391 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_rlvect_1(A) = k2_rlvect_1(A,B,k5_rlvect_1(A,C)) -> B = C) & (k6_rlvect_1(A,B,C) = k1_rlvect_1(A) -> B = C) & (C = B -> k6_rlvect_1(A,B,C) = k1_rlvect_1(A)) & (C = B -> k2_rlvect_1(A,B,k5_rlvect_1(A,C)) = k1_rlvect_1(A)))))))) # label(t66_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5392 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k6_vectsp_1(A,B,C,k5_rlvect_1(B,D)) = k5_rlvect_1(B,k6_vectsp_1(A,B,C,D)))))))))) # label(t69_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5393 (all A (v4_vectsp_1(A) & l3_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k6_rlvect_1(A,k1_group_1(A,B,C),k1_group_1(A,B,D)) = k1_group_1(A,B,k6_rlvect_1(A,C,D)))))))))) # label(t43_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5394 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k6_rlvect_1(A,k2_rlvect_1(A,C,B),k2_rlvect_1(A,D,B)) = k6_rlvect_1(A,C,D))))))))) # label(t90_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5395 $T # label(t19_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5396 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v6_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,B,C) = k1_group_1(A,k5_rlvect_1(A,B),k5_rlvect_1(A,C)))))))) # label(t42_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5397 (all A (l1_vectsp_1(A) -> (v7_group_1(A) & v8_vectsp_1(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v6_vectsp_1(A)))) # label(cc5_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5398 (all A (l1_vectsp_1(A) -> m1_subset_1(k2_vectsp_1(A),u1_struct_0(A)))) # label(dt_k2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5399 (all A all B all C (-v3_struct_0(A) & v7_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l3_vectsp_1(A) & v9_vectsp_1(A) & v4_group_1(A) -> m1_subset_1(k5_vectsp_1(A,B,C),u1_struct_0(A)))) # label(dt_k5_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5400 (exists A (-v3_struct_0(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & v2_group_1(A) & l1_vectsp_1(A))) # label(rc9_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5401 $T # label(t26_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5402 $T # label(t54_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5403 (all A all B all C all D all E (l1_struct_0(A) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(E) & m1_relset_1(E,k2_zfmisc_1(u1_struct_0(A),B),B) & v1_funct_2(E,k2_zfmisc_1(u1_struct_0(A),B),B) & m1_subset_1(D,B) & m1_relset_1(C,k2_zfmisc_1(B,B),B) -> v11_vectsp_1(g4_vectsp_1(A,B,C,D,E),A) & l4_vectsp_1(g4_vectsp_1(A,B,C,D,E),A))) # label(dt_g4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5404 (all A (-v3_struct_0(A) & l3_vectsp_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,k1_group_1(A,B,C),k1_group_1(A,B,D)) = k1_group_1(A,B,k2_rlvect_1(A,C,D)))))))) <-> v4_vectsp_1(A)))) # label(d11_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5405 $T # label(t38_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5406 (all A (l1_vectsp_1(A) -> (v1_vectsp_1(A) -> g1_vectsp_1(u1_struct_0(A),u1_group_1(A),u1_vectsp_1(A)) = A))) # label(abstractness_v1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5407 (all A all B (l4_vectsp_1(B,A) & l1_struct_0(A) -> (v11_vectsp_1(B,A) -> g4_vectsp_1(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u2_vectsp_1(A,B)) = B))) # label(abstractness_v11_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5408 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> v1_funct_2(k7_vectsp_1(A),u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(k7_vectsp_1(A),u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(k7_vectsp_1(A)))) # label(dt_k7_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5409 $T # label(t77_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5410 (all A (-v3_struct_0(A) & l1_vectsp_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> k1_group_1(A,B,k2_group_1(A)) = B)) <-> v6_vectsp_1(A)))) # label(d13_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5411 $T # label(d17_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5412 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> -v3_struct_0(g1_group_1(u1_struct_0(A),u1_rlvect_1(A))) & v4_group_1(g1_group_1(u1_struct_0(A),u1_rlvect_1(A))) & l1_group_1(g1_group_1(u1_struct_0(A),u1_rlvect_1(A))) & v7_group_1(g1_group_1(u1_struct_0(A),u1_rlvect_1(A))) & v3_group_1(g1_group_1(u1_struct_0(A),u1_rlvect_1(A))))) # label(t94_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5413 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v9_vectsp_1(A) & v8_vectsp_1(A) & v7_group_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v3_struct_0(C) & v5_rlvect_1(C) & v12_vectsp_1(C,A) & l4_vectsp_1(C,A) & v6_rlvect_1(C) & v4_rlvect_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (B != k1_rlvect_1(A) -> k6_vectsp_1(A,C,k4_vectsp_1(A,B),k6_vectsp_1(A,C,B,D)) = D))))))))) # label(t67_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5414 (all A (l1_vectsp_1(A) -> u1_vectsp_1(A) = k2_vectsp_1(A))) # label(d9_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5415 (exists A (v1_vectsp_1(A) & l1_vectsp_1(A))) # label(rc2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5416 $T # label(t47_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5417 $T # label(d3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5418 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> k5_rlvect_1(A,C) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C))) <-> B = k7_vectsp_1(A)))))) # label(d25_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5419 (all A (l1_vectsp_1(A) & -v3_struct_0(A) -> (v8_vectsp_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k1_group_1(A,k2_group_1(A),B)))))) # label(d19_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5420 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_rlvect_1(A,B,C) = k5_rlvect_1(A,k2_rlvect_1(A,k5_rlvect_1(A,C),k5_rlvect_1(A,B))))))))) # label(t89_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5421 $T # label(t14_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5422 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v7_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (k2_rlvect_1(A,k2_group_1(A),k2_group_1(A)) != k1_rlvect_1(A) <-> v13_vectsp_1(A)))) # label(d29_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5423 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v6_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v3_struct_0(C) & v5_rlvect_1(C) & l4_vectsp_1(C,A) & v12_vectsp_1(C,A) & v6_rlvect_1(C) & v4_rlvect_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (k1_rlvect_1(A) = B | k1_rlvect_1(C) = D <-> k1_rlvect_1(C) = k6_vectsp_1(A,C,B,D)))))))))) # label(t60_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5424 (all A (l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k5_rlvect_1(A,B) = k1_rlvect_1(A) -> B = k1_rlvect_1(A)))))) # label(t86_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5425 $T # label(t85_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5426 (all A (v4_group_1(A) & v7_group_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k5_vectsp_1(A,B,C) = k10_group_1(A,B,k4_vectsp_1(A,C)))))))) # label(d23_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5427 (exists A l1_vectsp_1(A)) # label(existence_l1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5428 (all A (l3_vectsp_1(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,k1_group_1(A,B,C),k1_group_1(A,B,D)) = k1_group_1(A,B,k2_rlvect_1(A,C,D)) & k2_rlvect_1(A,k1_group_1(A,C,B),k1_group_1(A,D,B)) = k1_group_1(A,k2_rlvect_1(A,C,D),B))))))) <-> v7_vectsp_1(A)))) # label(d18_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5429 $T # label(t30_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5430 (all A (l3_vectsp_1(A) -> (v3_vectsp_1(A) -> A = g3_vectsp_1(u1_struct_0(A),u1_rlvect_1(A),u1_group_1(A),u1_vectsp_1(A),u2_struct_0(A))))) # label(abstractness_v3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5431 (all A (m1_subset_1(A,u1_struct_0(k3_vectsp_1)) -> (all B (m1_subset_1(B,u1_struct_0(k3_vectsp_1)) -> (all C (m1_subset_1(C,u1_struct_0(k3_vectsp_1)) -> k4_rlvect_1(k3_vectsp_1,A,B) = k4_rlvect_1(k3_vectsp_1,B,A) & k4_rlvect_1(k3_vectsp_1,A,k4_rlvect_1(k3_vectsp_1,B,C)) = k4_rlvect_1(k3_vectsp_1,k4_rlvect_1(k3_vectsp_1,A,B),C) & k4_rlvect_1(k3_vectsp_1,A,k1_rlvect_1(k3_vectsp_1)) = A & k1_rlvect_1(k3_vectsp_1) = k4_rlvect_1(k3_vectsp_1,A,k5_rlvect_1(k3_vectsp_1,A)) & -(A != k1_rlvect_1(k3_vectsp_1) & (all D (m1_subset_1(D,u1_struct_0(k3_vectsp_1)) -> k10_group_1(k3_vectsp_1,A,D) != k2_group_1(k3_vectsp_1)))) & k10_group_1(k3_vectsp_1,k4_rlvect_1(k3_vectsp_1,B,C),A) = k4_rlvect_1(k3_vectsp_1,k10_group_1(k3_vectsp_1,B,A),k10_group_1(k3_vectsp_1,C,A)) & k4_rlvect_1(k3_vectsp_1,k10_group_1(k3_vectsp_1,A,B),k10_group_1(k3_vectsp_1,A,C)) = k10_group_1(k3_vectsp_1,A,k4_rlvect_1(k3_vectsp_1,B,C)) & k10_group_1(k3_vectsp_1,k2_group_1(k3_vectsp_1),A) = A & k10_group_1(k3_vectsp_1,A,k10_group_1(k3_vectsp_1,B,C)) = k10_group_1(k3_vectsp_1,k10_group_1(k3_vectsp_1,A,B),C) & k10_group_1(k3_vectsp_1,B,A) = k10_group_1(k3_vectsp_1,A,B))))))) # label(t21_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5432 (all A (l1_vectsp_1(A) -> (-v3_struct_0(A) & v8_vectsp_1(A) & v6_vectsp_1(A) -> -v3_struct_0(A) & v2_group_1(A)))) # label(cc4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5433 (exists A (l3_vectsp_1(A) & v3_vectsp_1(A))) # label(rc6_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5434 (exists A (l2_vectsp_1(A) & v2_vectsp_1(A))) # label(rc4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5435 (all A (m1_subset_1(A,u1_struct_0(k1_vectsp_1)) -> (all B (m1_subset_1(B,u1_struct_0(k1_vectsp_1)) -> (all C (m1_subset_1(C,u1_struct_0(k1_vectsp_1)) -> k4_rlvect_1(k1_vectsp_1,B,A) = k4_rlvect_1(k1_vectsp_1,A,B) & k1_rlvect_1(k1_vectsp_1) = k4_rlvect_1(k1_vectsp_1,A,k5_rlvect_1(k1_vectsp_1,A)) & A = k4_rlvect_1(k1_vectsp_1,A,k1_rlvect_1(k1_vectsp_1)) & k4_rlvect_1(k1_vectsp_1,A,k4_rlvect_1(k1_vectsp_1,B,C)) = k4_rlvect_1(k1_vectsp_1,k4_rlvect_1(k1_vectsp_1,A,B),C))))))) # label(t6_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5436 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (v13_vectsp_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k2_rlvect_1(A,B,B) = k1_rlvect_1(A) -> k1_rlvect_1(A) = B)))))) # label(d28_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5437 $T # label(t51_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5438 (exists A (l1_rlvect_1(A) & -v3_struct_0(A) & v13_vectsp_1(A))) # label(rc14_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5439 $T # label(t62_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5440 $T # label(t58_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5441 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k6_rlvect_1(A,C,k10_group_1(A,D,B)) = k1_rlvect_1(A) -> B = k1_rlvect_1(A) | k10_group_1(A,C,k4_vectsp_1(A,B)) = D) & (k6_rlvect_1(A,k10_group_1(A,B,D),C) = k1_rlvect_1(A) -> B = k1_rlvect_1(A) | k10_group_1(A,C,k4_vectsp_1(A,B)) = D))))))))) # label(t88_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5442 $T # label(t13_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5443 $T # label(d8_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5444 $T # label(t28_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5445 (exists A (l1_group_1(A) & -v3_struct_0(A) & v4_group_1(A) & v7_group_1(A))) # label(rc8_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5446 $T # label(t4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5447 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k6_rlvect_1(A,B,C) = k1_rlvect_1(A) -> k1_rlvect_1(A) = k6_rlvect_1(A,C,B)))))))) # label(t87_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5448 $T # label(t49_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5449 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v12_vectsp_1(C,A) & l4_vectsp_1(C,A) & v6_rlvect_1(C) & v5_rlvect_1(C) & v4_rlvect_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k1_rlvect_1(C) = k6_vectsp_1(A,C,k1_rlvect_1(A),D) & k6_vectsp_1(A,C,k5_rlvect_1(A,k2_group_1(A)),D) = k5_rlvect_1(C,D) & k1_rlvect_1(C) = k6_vectsp_1(A,C,B,k1_rlvect_1(C)))))))))) # label(t59_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5450 $T # label(t50_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5451 $T # label(t3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5452 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k5_rlvect_1(A,B) = k6_rlvect_1(A,k1_rlvect_1(A),B) & B = k6_rlvect_1(A,B,k1_rlvect_1(A)))))) # label(t65_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5453 (all A (l1_vectsp_1(A) -> l1_group_1(A))) # label(dt_l1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5454 $T # label(d27_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5455 (all A all B all C all D (-v3_struct_0(A) & l1_struct_0(A) & l4_vectsp_1(B,A) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(C,u1_struct_0(A)) & -v3_struct_0(B) -> m1_subset_1(k6_vectsp_1(A,B,C,D),u1_struct_0(B)))) # label(dt_k6_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5456 $T # label(t25_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5457 (exists A l3_vectsp_1(A)) # label(existence_l3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5458 (all A (l2_vectsp_1(A) -> (v2_vectsp_1(A) -> A = g2_vectsp_1(u1_struct_0(A),u1_group_1(A),u1_vectsp_1(A),u2_struct_0(A))))) # label(abstractness_v2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5459 (all A all B all C all D (m1_subset_1(C,A) & m1_subset_1(D,A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> l2_vectsp_1(g2_vectsp_1(A,B,C,D)) & v2_vectsp_1(g2_vectsp_1(A,B,C,D)))) # label(dt_g2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5460 $T # label(d14_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5461 $T # label(t57_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5462 $T # label(d2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5463 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k6_rlvect_1(A,k6_rlvect_1(A,B,C),D) = k6_rlvect_1(A,k6_rlvect_1(A,B,D),C))))))))) # label(t93_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5464 $T # label(t12_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5465 $T # label(t46_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5466 (all A (l2_vectsp_1(A) & -v3_struct_0(A) -> (k1_rlvect_1(A) = k2_group_1(A) <-> v10_vectsp_1(A)))) # label(d21_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5467 (exists A (l1_rlvect_1(A) & -v3_struct_0(A) & v1_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A))) # label(rc1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5468 (all A (l1_struct_0(A) -> (exists B l4_vectsp_1(B,A)))) # label(existence_l4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5469 $T # label(d16_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5470 $T # label(t79_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5471 $T # label(t52_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5472 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & l3_vectsp_1(A) & v4_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_rlvect_1(A) = k1_group_1(A,B,k1_rlvect_1(A)))))) # label(t36_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5473 (all A all B all C all D all E (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_subset_1(D,A) & m1_subset_1(E,A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all F all G all H all I all J (g3_vectsp_1(F,G,H,I,J) = g3_vectsp_1(A,B,C,D,E) -> G = B & I = D & E = J & C = H & A = F)))) # label(free_g3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5474 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k5_rlvect_1(A,B) = C <-> k1_rlvect_1(A) = k2_rlvect_1(A,B,C)))))))) # label(t63_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5475 (all A all B all C all D (m1_subset_1(C,A) & m1_subset_1(D,A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all E all F all G all H (g2_vectsp_1(E,F,G,H) = g2_vectsp_1(A,B,C,D) -> F = B & C = G & D = H & E = A)))) # label(free_g2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5476 (exists A (l3_vectsp_1(A) & v2_group_1(A) & v4_group_1(A) & v7_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v6_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v3_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A))) # label(rc10_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5477 (all A (v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_rlvect_1(A) = k6_rlvect_1(A,B,C) -> B = C))))))) # label(t84_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5478 $T # label(t34_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5479 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> k6_rlvect_1(B,k6_vectsp_1(A,B,C,D),k6_vectsp_1(A,B,C,E)) = k6_vectsp_1(A,B,C,k6_rlvect_1(B,D,E)))))))))))) # label(t70_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5480 $T # label(t5_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5481 $T # label(t23_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5482 (exists A (v3_vectsp_1(A) & -v3_struct_0(A) & l3_vectsp_1(A))) # label(rc7_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5483 (all A (v4_group_1(A) & v7_group_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k10_group_1(A,B,D) = k10_group_1(A,B,C) -> D = C | B = k1_rlvect_1(A)))))))))) # label(t33_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5484 $T # label(t80_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5485 $T # label(t72_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5486 $T # label(t61_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5487 (all A (l3_vectsp_1(A) -> (-v3_struct_0(A) & v7_vectsp_1(A) -> v4_vectsp_1(A) & v5_vectsp_1(A) & -v3_struct_0(A)))) # label(cc1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5488 (exists A (l3_vectsp_1(A) & -v3_struct_0(A) & v5_rlvect_1(A) & v2_group_1(A) & v4_group_1(A) & v7_group_1(A) & v7_vectsp_1(A) & -v10_vectsp_1(A) & v13_vectsp_1(A) & v9_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v5_vectsp_1(A) & v4_vectsp_1(A) & v3_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A))) # label(rc15_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5489 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (l1_pre_topc(C) & -v3_struct_0(C) -> (all D (m2_relset_1(D,u1_struct_0(A),u1_struct_0(C)) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(C)) & v1_funct_1(D) -> (v6_compts_1(B,A) & k2_pre_topc(C) = k2_relat_1(D) & v5_pre_topc(D,A,C) -> v6_compts_1(k4_pre_topc(A,C,D,B),C)))))))))) # label(t24_compts_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5490 (all A ((all B -(v1_finset_1(B) & k1_setfam_1(B) = k1_xboole_0 & r1_tarski(B,A) & B != k1_xboole_0)) & k1_xboole_0 != A <-> v1_compts_1(A))) # label(d2_compts_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5491 (all A (l1_pre_topc(A) -> v6_compts_1(k1_pre_topc(A),A))) # label(t9_compts_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5492 $T # label(t2_compts_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5493 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v6_compts_1(B,A) & v6_compts_1(C,A) & v3_compts_1(A) -> v6_compts_1(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t20_compts_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5494 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) & v2_compts_1(A) -> v6_compts_1(B,A)))))) # label(t17_compts_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5495 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (v2_compts_1(A) <-> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(k6_setfam_1(u1_struct_0(A),B) = k1_xboole_0 & v2_tops_2(B,A) & v1_compts_1(B))))))) # label(t13_compts_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5496 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v6_compts_1(B,A) & v6_compts_1(C,A) -> v6_compts_1(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t19_compts_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5497 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (v2_compts_1(A) & v3_compts_1(A) -> v4_compts_1(A)))) # label(t21_compts_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5498 $T # label(t3_compts_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5499 (all A (l1_pre_topc(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -(C != B & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(D,A) & v3_pre_topc(E,A) & r2_hidden(B,D) & r2_hidden(C,E) & r1_xboole_0(D,E))))))))))) <-> v3_compts_1(A)))) # label(d4_compts_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5500 $T # label(t4_compts_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5501 (all A (l1_pre_topc(A) -> (v2_compts_1(A) <-> v6_compts_1(k2_pre_topc(A),A)))) # label(t10_compts_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5502 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) -> (all C (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_compts_1(B) & k2_pre_topc(A) = k1_relat_1(C) & v2_funct_1(C) & v5_pre_topc(C,A,B) & k2_pre_topc(B) = k2_relat_1(C) & v2_compts_1(A) -> v3_tops_2(C,A,B)))))))) # label(t26_compts_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5503 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (v2_compts_1(A) <-> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(v2_tops_2(B,A) & (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(r1_tarski(C,B) & k1_xboole_0 = k6_setfam_1(u1_struct_0(A),C) & v1_finset_1(C) & C != k1_xboole_0))) & k1_xboole_0 = k6_setfam_1(u1_struct_0(A),B) & B != k1_xboole_0)))))) # label(t14_compts_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5504 $T # label(t5_compts_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5505 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(C,k2_pre_topc(B)) -> (v6_compts_1(C,A) <-> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (D = C -> v6_compts_1(D,B)))))))))))) # label(t11_compts_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5506 $T # label(t1_compts_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5507 (all A (l1_pre_topc(A) -> (v4_compts_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(v4_pre_topc(C,A) & r2_hidden(B,k3_subset_1(u1_struct_0(A),C)) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(D,A) & v3_pre_topc(E,A) & r2_hidden(B,D) & r1_xboole_0(D,E) & r1_tarski(C,E)))))) & C != k1_xboole_0)))))))) # label(d5_compts_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5508 (all A (l1_pre_topc(A) -> (all B (-v3_struct_0(B) & l1_pre_topc(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v2_compts_1(A) & k2_relat_1(C) = k2_pre_topc(B) & v5_pre_topc(C,A,B) -> v2_compts_1(B)))))))) # label(t23_compts_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5509 $T # label(t8_compts_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5510 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(C,B) & v4_pre_topc(C,A) & v6_compts_1(B,A) -> v6_compts_1(C,A)))))))) # label(t18_compts_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5511 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (v3_compts_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v6_compts_1(B,A) -> B = k1_xboole_0 | (all C (m1_subset_1(C,u1_struct_0(A)) -> -(r2_hidden(C,k3_subset_1(u1_struct_0(A),B)) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(E,A) & r2_hidden(C,D) & r1_tarski(B,E) & r1_xboole_0(D,E) & v3_pre_topc(D,A))))))))))))))) # label(t15_compts_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5512 (all A (l1_pre_topc(A) -> (v2_compts_1(A) <-> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(r1_pre_topc(A,B) & v1_tops_2(B,A) & (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(r1_tarski(C,B) & r1_pre_topc(A,C) & v1_finset_1(C)))))))))) # label(d3_compts_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5513 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(C,k5_setfam_1(u1_struct_0(A),B)) <-> r1_compts_1(A,B,C)))))))) # label(d1_compts_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5514 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_compts_1(A) & v6_compts_1(B,A) -> v4_pre_topc(B,A)))))) # label(t16_compts_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5515 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_pre_topc(A) -> (v2_compts_1(k3_pre_topc(A,B)) <-> v6_compts_1(B,A)) | k1_xboole_0 = B) & (B = k1_xboole_0 -> (v2_compts_1(k3_pre_topc(A,B)) <-> v6_compts_1(B,A))))))) # label(t12_compts_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5516 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (v3_compts_1(B) & v5_pre_topc(C,A,B) & k2_pre_topc(B) = k2_relat_1(C) & v2_compts_1(A) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(D,A) -> v4_pre_topc(k4_pre_topc(A,B,C,D),B))))))))))) # label(t25_compts_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5517 (all A (l1_pre_topc(A) -> (v5_compts_1(A) <-> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(B != k1_xboole_0 & C != k1_xboole_0 & v4_pre_topc(C,A) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_tarski(B,D) & r1_tarski(C,E) & r1_xboole_0(D,E) & v3_pre_topc(E,A) & v3_pre_topc(D,A)))))) & r1_xboole_0(B,C) & v4_pre_topc(B,A))))))))) # label(d6_compts_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5518 $T # label(t6_compts_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5519 $T # label(t7_compts_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5520 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (v3_compts_1(A) & v2_compts_1(A) -> v5_compts_1(A)))) # label(t22_compts_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5521 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v6_compts_1(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(r1_compts_1(A,C,B) & (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(r1_tarski(D,C) & v1_finset_1(D) & r1_compts_1(A,D,B)))) & v1_tops_2(C,A))))))))) # label(d7_compts_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5522 (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]. 116.12/115.72 5523 (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]. 116.12/115.72 5524 $T # label(t74_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5525 $T # label(d1_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5526 (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]. 116.12/115.72 5527 $T # label(t19_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5528 $T # label(t98_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.72 5529 $T # label(t118_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5530 $T # label(t75_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5531 $T # label(t105_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5532 $T # label(t111_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5533 (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]. 116.12/115.73 5534 $T # label(t106_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5535 $T # label(t101_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5536 $T # label(t122_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5537 $T # label(t131_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5538 $T # label(t104_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5539 $T # label(t141_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5540 $T # label(t147_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5541 (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]. 116.12/115.73 5542 (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]. 116.12/115.73 5543 (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]. 116.12/115.73 5544 (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]. 116.12/115.73 5545 $T # label(t144_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5546 $T # label(t23_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5547 (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]. 116.12/115.73 5548 (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]. 116.12/115.73 5549 (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]. 116.12/115.73 5550 $T # label(t20_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5551 (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]. 116.12/115.73 5552 (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]. 116.12/115.73 5553 (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]. 116.12/115.73 5554 (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]. 116.12/115.73 5555 (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]. 116.12/115.73 5556 (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]. 116.12/115.73 5557 (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]. 116.12/115.73 5558 $T # label(t54_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5559 $T # label(t130_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5560 (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]. 116.12/115.73 5561 $T # label(t22_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5562 $T # label(t113_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5563 $T # label(t149_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5564 (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]. 116.12/115.73 5565 (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]. 116.12/115.73 5566 $T # label(t155_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5567 $T # label(t91_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5568 (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]. 116.12/115.73 5569 (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]. 116.12/115.73 5570 $T # label(t34_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5571 (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]. 116.12/115.73 5572 (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]. 116.12/115.73 5573 $T # label(t140_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5574 $T # label(t41_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5575 (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]. 116.12/115.73 5576 $T # label(t8_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5577 (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]. 116.12/115.73 5578 (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]. 116.12/115.73 5579 (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]. 116.12/115.73 5580 (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]. 116.12/115.73 5581 $T # label(t150_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5582 (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]. 116.12/115.73 5583 (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]. 116.12/115.73 5584 $T # label(t120_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5585 (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]. 116.12/115.73 5586 $T # label(t16_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5587 (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]. 116.12/115.73 5588 $T # label(t129_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5589 $T # label(t93_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5590 (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]. 116.12/115.73 5591 $T # label(t138_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5592 (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]. 116.12/115.73 5593 (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]. 116.12/115.73 5594 $T # label(t4_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5595 $T # label(t115_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5596 (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]. 116.12/115.73 5597 (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]. 116.12/115.73 5598 $T # label(t132_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5599 (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]. 116.12/115.73 5600 $T # label(t114_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5601 (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]. 116.12/115.73 5602 $T # label(t21_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5603 $T # label(t154_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5604 (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]. 116.12/115.73 5605 (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]. 116.12/115.73 5606 (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]. 116.12/115.73 5607 (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]. 116.12/115.73 5608 $T # label(t102_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5609 (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]. 116.12/115.73 5610 (exists A (v1_orders_2(A) & l1_orders_2(A))) # label(rc1_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5611 (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]. 116.12/115.73 5612 (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]. 116.12/115.73 5613 (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]. 116.12/115.73 5614 (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]. 116.12/115.73 5615 (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]. 116.12/115.73 5616 $T # label(t121_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5617 $T # label(t92_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5618 (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]. 116.12/115.73 5619 $T # label(t90_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5620 $T # label(t95_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5621 (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]. 116.12/115.73 5622 $T # label(t151_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5623 $T # label(t139_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5624 (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]. 116.12/115.73 5625 $T # label(t119_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5626 (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]. 116.12/115.73 5627 (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]. 116.12/115.73 5628 (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]. 116.12/115.73 5629 $T # label(t33_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5630 $T # label(t148_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5631 $T # label(t146_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5632 $T # label(t15_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5633 $T # label(dt_k4_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5634 (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]. 116.12/115.73 5635 $T # label(t86_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5636 $T # label(t58_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5637 $T # label(t100_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5638 $T # label(t12_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5639 $T # label(t14_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5640 (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]. 116.12/115.73 5641 $T # label(t153_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5642 $T # label(t17_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5643 $T # label(t134_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5644 $T # label(t127_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5645 (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]. 116.12/115.73 5646 (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]. 116.12/115.73 5647 $T # label(t152_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5648 (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]. 116.12/115.73 5649 (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]. 116.12/115.73 5650 (all A (l1_orders_2(A) -> l1_struct_0(A))) # label(dt_l1_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5651 $T # label(t94_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5652 $T # label(t63_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5653 (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]. 116.12/115.73 5654 $T # label(t13_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5655 (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]. 116.12/115.73 5656 $T # label(t9_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5657 $T # label(d2_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5658 $T # label(t125_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5659 $T # label(t53_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5660 $T # label(d8_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5661 $T # label(t5_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5662 (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]. 116.12/115.73 5663 $T # label(t42_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5664 (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]. 116.12/115.73 5665 (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]. 116.12/115.73 5666 $T # label(t116_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5667 $T # label(t11_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5668 $T # label(t96_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5669 (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]. 116.12/115.73 5670 $T # label(t112_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5671 $T # label(t2_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5672 (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]. 116.12/115.73 5673 $T # label(t117_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5674 $T # label(d7_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5675 (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]. 116.12/115.73 5676 $T # label(t6_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5677 (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]. 116.12/115.73 5678 (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]. 116.12/115.73 5679 (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]. 116.12/115.73 5680 $T # label(t76_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5681 $T # label(d3_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5682 $T # label(t85_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5683 $T # label(t99_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5684 $T # label(t110_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5685 (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]. 116.12/115.73 5686 (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]. 116.12/115.73 5687 (exists A l1_orders_2(A)) # label(existence_l1_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5688 (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]. 116.12/115.73 5689 $T # label(t103_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5690 $T # label(t137_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5691 (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]. 116.12/115.73 5692 $T # label(t126_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5693 (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]. 116.12/115.73 5694 $T # label(t55_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5695 $T # label(t145_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5696 $T # label(t124_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5697 (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]. 116.12/115.73 5698 $T # label(t27_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5699 (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]. 116.12/115.73 5700 $T # label(t1_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5701 (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]. 116.12/115.73 5702 (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]. 116.12/115.73 5703 (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]. 116.12/115.73 5704 (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]. 116.12/115.73 5705 (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]. 116.12/115.73 5706 (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]. 116.12/115.73 5707 (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]. 116.12/115.73 5708 $T # label(t3_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5709 (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]. 116.12/115.73 5710 $T # label(t97_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5711 $T # label(t59_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5712 $T # label(t133_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5713 $T # label(t128_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5714 (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]. 116.12/115.73 5715 $T # label(t157_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5716 $T # label(t10_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5717 $T # label(t143_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5718 $T # label(t77_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5719 $T # label(t18_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5720 $T # label(t142_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5721 $T # label(t123_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5722 $T # label(t156_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5723 (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]. 116.12/115.73 5724 $T # label(t66_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5725 $T # label(t31_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5726 (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]. 116.12/115.73 5727 (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]. 116.12/115.73 5728 $T # label(t7_orders_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5729 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_metric_1(A,B,C) = k1_metric_1(u1_struct_0(A),u1_struct_0(A),u1_metric_1(A),B,C))))))) # label(d1_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5730 (all A (l1_metric_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k2_metric_1(A,B,C) = np__0 -> B = C))))) <-> v7_metric_1(A)))) # label(t2_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5731 (exists A l1_metric_1(A)) # label(existence_l1_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5732 (all A (l1_metric_1(k6_metric_1(A)) & v1_metric_1(k6_metric_1(A)))) # label(dt_k6_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5733 (all A all B all C all D (v1_xreal_0(B) & -v3_struct_0(C) & l1_metric_1(C) & m1_subset_1(D,u1_struct_0(C)) -> ((exists E (A = E & k2_metric_1(C,D,E) = B & m1_subset_1(E,u1_struct_0(C)))) <-> r2_hidden(A,a_3_2_metric_1(B,C,D))))) # label(fraenkel_a_3_2_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5734 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v1_xreal_0(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (-v3_struct_0(A) -> (D = k9_metric_1(A,B,C) <-> (exists E (-v3_struct_0(E) & (exists F (A = E & a_3_0_metric_1(C,E,F) = D & F = B & m1_subset_1(F,u1_struct_0(E)))) & l1_metric_1(E))))) & (v3_struct_0(A) -> (k9_metric_1(A,B,C) = D <-> v1_xboole_0(D))))))))))) # label(d15_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5735 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v1_xreal_0(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (-v3_struct_0(A) -> (k10_metric_1(A,B,C) = D <-> (exists E (l1_metric_1(E) & (exists F (F = B & a_3_1_metric_1(C,E,F) = D & A = E & m1_subset_1(F,u1_struct_0(E)))) & -v3_struct_0(E))))) & (v3_struct_0(A) -> (v1_xboole_0(D) <-> D = k10_metric_1(A,B,C))))))))))) # label(d16_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5736 (all A (l1_metric_1(A) -> (v7_metric_1(A) <-> v3_metric_1(u1_metric_1(A),u1_struct_0(A))))) # label(d8_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5737 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_1(B) -> (v5_metric_1(B,A) <-> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> r1_xreal_0(k1_metric_1(A,A,B,C,E),k3_real_1(k1_metric_1(A,A,B,C,D),k1_metric_1(A,A,B,D,E)))))))))))) # label(d6_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5738 (all A all B all C all D all E (m1_relset_1(C,k2_zfmisc_1(A,B),k1_numbers) & m1_subset_1(D,A) & m1_subset_1(E,B) & v1_funct_1(C) -> k1_binop_1(C,D,E) = k1_metric_1(A,B,C,D,E))) # label(redefinition_k1_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5739 (all A (v1_xreal_0(A) -> (all B (l1_metric_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k10_metric_1(B,C,A) = a_3_1_metric_1(A,B,C))))))) # label(t19_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5740 (exists A (v1_metric_1(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & v7_metric_1(A) & -v3_struct_0(A) & l1_metric_1(A))) # label(rc3_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5741 (all A all B all C (m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_metric_1(A) -> m1_subset_1(k2_metric_1(A,B,C),k1_numbers))) # label(dt_k2_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5742 (all A (v1_metric_1(k6_metric_1(A)) & v6_metric_1(k6_metric_1(A)) & v7_metric_1(k6_metric_1(A)) & v9_metric_1(k6_metric_1(A)) & v8_metric_1(k6_metric_1(A)))) # label(fc2_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5743 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers) & m1_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_1(B) -> l1_metric_1(g1_metric_1(A,B)) & v1_metric_1(g1_metric_1(A,B)))) # label(dt_g1_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5744 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> k1_metric_1(k1_numbers,k1_numbers,k7_metric_1,A,B) = k1_metric_1(k1_numbers,k1_numbers,k7_metric_1,B,A))))) # label(t10_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5745 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> r1_xreal_0(k1_metric_1(k1_numbers,k1_numbers,k7_metric_1,A,B),k3_real_1(k1_metric_1(k1_numbers,k1_numbers,k7_metric_1,A,C),k1_metric_1(k1_numbers,k1_numbers,k7_metric_1,C,B))))))))) # label(t11_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5746 (all A (v1_xreal_0(A) -> (all B (l1_metric_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k9_metric_1(B,C,A) = a_3_0_metric_1(A,B,C))))))) # label(t18_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5747 (all A (l1_metric_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> np__0 = k2_metric_1(A,B,B))) <-> v6_metric_1(A)))) # label(t1_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5748 (all A (v1_xreal_0(A) -> (all B (l1_metric_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (-v3_struct_0(B) & A = k2_metric_1(B,C,D) <-> r2_hidden(D,k11_metric_1(B,C,A))))))))))) # label(t14_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5749 (all A (l1_metric_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_metric_1(A,C,B) = k2_metric_1(A,B,C) & r1_xreal_0(k2_metric_1(A,B,D),k3_real_1(k2_metric_1(A,B,C),k2_metric_1(A,C,D))) & (B = C -> np__0 = k2_metric_1(A,B,C)) & (k2_metric_1(A,B,C) = np__0 -> C = B))))))) -> v8_metric_1(A) & l1_metric_1(A) & v9_metric_1(A) & v7_metric_1(A) & v6_metric_1(A)))) # label(t6_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5750 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_1(B) -> ((all C (m1_subset_1(C,A) -> np__0 = k1_metric_1(A,A,B,C,C))) <-> v2_metric_1(B,A)))) # label(d3_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5751 (all A all B all C (v8_metric_1(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_metric_1(A) -> k2_metric_1(A,B,C) = k4_metric_1(A,B,C))) # label(redefinition_k4_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5752 (all A (l1_metric_1(A) -> (v5_metric_1(u1_metric_1(A),u1_struct_0(A)) <-> v9_metric_1(A)))) # label(d10_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5753 (all A (l1_metric_1(A) -> l1_struct_0(A))) # label(dt_l1_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5754 (all A all B all C all D all E (v1_funct_1(C) & m1_relset_1(C,k2_zfmisc_1(A,B),k1_numbers) & m1_subset_1(E,B) & m1_subset_1(D,A) -> m1_subset_1(k1_metric_1(A,B,C,D,E),k1_numbers))) # label(dt_k1_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5755 (all A (l1_metric_1(A) -> (v9_metric_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> r1_xreal_0(k2_metric_1(A,B,D),k3_real_1(k2_metric_1(A,B,C),k2_metric_1(A,C,D)))))))))))) # label(t4_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5756 (all A all B all C all D (v1_xreal_0(B) & l1_metric_1(C) & m1_subset_1(D,u1_struct_0(C)) & -v3_struct_0(C) -> (r2_hidden(A,a_3_0_metric_1(B,C,D)) <-> (exists E (A = E & -r1_xreal_0(B,k2_metric_1(C,D,E)) & m1_subset_1(E,u1_struct_0(C))))))) # label(fraenkel_a_3_0_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5757 (all A (v1_xreal_0(A) -> (all B (l1_metric_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> r1_tarski(k9_metric_1(B,C,A),k10_metric_1(B,C,A)))))))) # label(t15_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5758 (all A (l1_metric_1(A) -> v1_funct_2(u1_metric_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_numbers) & m2_relset_1(u1_metric_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_numbers) & v1_funct_1(u1_metric_1(A)))) # label(dt_u1_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5759 (all A all B all C (m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_metric_1(A) & v8_metric_1(A) -> m1_subset_1(k4_metric_1(A,B,C),k1_numbers))) # label(dt_k4_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5760 $T # label(t7_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5761 (all A all B all C (m1_subset_1(B,u1_struct_0(A)) & v1_xreal_0(C) & l1_metric_1(A) -> m1_subset_1(k10_metric_1(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k10_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5762 (all A (v1_xreal_0(A) -> (all B (l1_metric_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (r2_hidden(D,k10_metric_1(B,C,A)) <-> r1_xreal_0(k2_metric_1(B,C,D),A) & -v3_struct_0(B)))))))))) # label(t13_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5763 (all A (l1_metric_1(A) & v9_metric_1(A) & v8_metric_1(A) & v6_metric_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r1_xreal_0(np__0,k4_metric_1(A,B,C)))))))) # label(t5_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5764 (all A (v1_xreal_0(A) -> (all B (l1_metric_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k4_subset_1(u1_struct_0(B),k11_metric_1(B,C,A),k9_metric_1(B,C,A)) = k10_metric_1(B,C,A))))))) # label(t17_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5765 (all A (l1_metric_1(A) -> (v1_metric_1(A) -> g1_metric_1(u1_struct_0(A),u1_metric_1(A)) = A))) # label(abstractness_v1_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5766 (all A all B all C (v1_xreal_0(C) & m1_subset_1(B,u1_struct_0(A)) & l1_metric_1(A) -> m1_subset_1(k11_metric_1(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k11_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5767 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (B = A <-> k1_metric_1(k1_numbers,k1_numbers,k7_metric_1,A,B) = np__0))))) # label(t9_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.73 5768 $T # label(t8_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5769 (all A (v1_xreal_0(A) -> (all B (l1_metric_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k11_metric_1(B,C,A) = a_3_2_metric_1(A,B,C))))))) # label(t20_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5770 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers) & m1_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_1(B) -> (all C all D (g1_metric_1(A,B) = g1_metric_1(C,D) -> D = B & A = C)))) # label(free_g1_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5771 (exists A (l1_metric_1(A) & v1_metric_1(A))) # label(rc1_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5772 (all A (v1_funct_1(k5_metric_1(A)) & m2_relset_1(k5_metric_1(A),k2_zfmisc_1(A,A),k1_numbers) & v1_funct_2(k5_metric_1(A),k2_zfmisc_1(A,A),k1_numbers))) # label(dt_k5_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5773 (all A all B all C (l1_metric_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & v8_metric_1(A) -> k4_metric_1(A,B,C) = k4_metric_1(A,C,B))) # label(commutativity_k4_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5774 (all A k6_metric_1(A) = g1_metric_1(A,k5_metric_1(A))) # label(d12_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5775 (all A (v1_xreal_0(A) -> (all B (l1_metric_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> r1_tarski(k11_metric_1(B,C,A),k10_metric_1(B,C,A)))))))) # label(t16_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5776 (all A (l1_metric_1(A) -> (v6_metric_1(A) <-> v2_metric_1(u1_metric_1(A),u1_struct_0(A))))) # label(d7_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5777 (all A (v1_xreal_0(A) -> (all B (l1_metric_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (-r1_xreal_0(A,k2_metric_1(B,C,D)) & -v3_struct_0(B) <-> r2_hidden(D,k9_metric_1(B,C,A))))))))))) # label(t12_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5778 (all A (v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) -> (k7_metric_1 = A <-> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> k1_metric_1(k1_numbers,k1_numbers,A,B,C) = k18_complex1(k5_real_1(B,C))))))))) # label(d13_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5779 (all A all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers) -> ((all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> np__0 = k1_metric_1(A,A,B,C,C) & (D != C -> np__1 = k1_metric_1(A,A,B,C,D)))))) <-> k5_metric_1(A) = B))) # label(d11_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5780 (all A all B all C all D (-v3_struct_0(C) & l1_metric_1(C) & m1_subset_1(D,u1_struct_0(C)) & v1_xreal_0(B) -> ((exists E (m1_subset_1(E,u1_struct_0(C)) & A = E & r1_xreal_0(k2_metric_1(C,D,E),B))) <-> r2_hidden(A,a_3_1_metric_1(B,C,D))))) # label(fraenkel_a_3_1_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5781 (all A all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) -> (v3_metric_1(B,A) <-> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (k1_metric_1(A,A,B,C,D) = np__0 -> C = D)))))))) # label(d4_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5782 (all A (-v1_xboole_0(A) -> -v3_struct_0(k6_metric_1(A)) & v1_metric_1(k6_metric_1(A)))) # label(fc1_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5783 (all A all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) -> (v4_metric_1(B,A) <-> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> k1_metric_1(A,A,B,D,C) = k1_metric_1(A,A,B,C,D)))))))) # label(d5_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5784 (exists A (l1_metric_1(A) & -v3_struct_0(A) & v1_metric_1(A))) # label(rc2_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5785 (all A all B all C (m1_subset_1(B,u1_struct_0(A)) & v1_xreal_0(C) & l1_metric_1(A) -> m1_subset_1(k9_metric_1(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k9_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5786 (all A (l1_metric_1(A) -> (v4_metric_1(u1_metric_1(A),u1_struct_0(A)) <-> v8_metric_1(A)))) # label(d9_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5787 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v1_xreal_0(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (-v3_struct_0(A) -> ((exists E (-v3_struct_0(E) & (exists F (B = F & D = a_3_2_metric_1(C,E,F) & A = E & m1_subset_1(F,u1_struct_0(E)))) & l1_metric_1(E))) <-> D = k11_metric_1(A,B,C))) & (v3_struct_0(A) -> (v1_xboole_0(D) <-> D = k11_metric_1(A,B,C))))))))))) # label(d17_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5788 (all A (l1_metric_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_metric_1(A,C,B) = k2_metric_1(A,B,C))))) <-> v8_metric_1(A)))) # label(t3_metric_1) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5789 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(k11_cat_2(A,B))) -> (exists D (m1_subset_1(D,u1_cat_1(A)) & (exists E (m1_subset_1(E,u1_cat_1(B)) & k12_cat_2(A,B,D,E) = C)))))))))) # label(t35_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5790 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> (all F (m1_subset_1(F,u2_cat_1(A)) -> k8_funct_2(u2_cat_1(A),u2_cat_1(C),k15_cat_2(A,B,C,D,E),F) = k8_funct_2(u2_cat_1(k11_cat_2(A,B)),u2_cat_1(C),D,k13_cat_2(A,B,F,k10_cat_1(B,E))))))))))))))) # label(t50_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5791 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> C = k8_funct_2(u1_cat_1(k11_cat_2(A,B)),u1_cat_1(A),k12_cat_1(k11_cat_2(A,B),A,k16_cat_2(A,B)),k12_cat_2(A,B,C,D)))))))))) # label(t59_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5792 $T # label(t49_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5793 (all A all B all C all D (-v1_xboole_0(A) & v1_funct_1(C) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & m1_relset_1(D,k2_zfmisc_1(B,B),B) & v1_funct_1(D) & -v1_xboole_0(B) -> v1_funct_1(k10_cat_2(A,B,C,D)) & m2_relset_1(k10_cat_2(A,B,C,D),k2_zfmisc_1(k2_zfmisc_1(A,B),k2_zfmisc_1(A,B)),k2_zfmisc_1(A,B)))) # label(dt_k10_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5794 $T # label(t26_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5795 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u2_cat_1(k11_cat_2(A,B))) -> (exists D ((exists E (C = k13_cat_2(A,B,D,E) & m1_subset_1(E,u2_cat_1(B)))) & m1_subset_1(D,u2_cat_1(A)))))))))) # label(t37_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5796 (all A all B (v2_cat_1(A) & l1_cat_1(A) & m3_cat_2(B,A) -> m2_cat_1(k8_cat_2(A,B),B,A))) # label(dt_k8_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5797 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> k14_cat_2(A,B,C,D,E) = k1_funct_1(k3_funct_5(D),k10_cat_1(A,E)))))))))))) # label(d8_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5798 (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(B,A),C) & m2_relset_1(D,k2_zfmisc_1(B,A),C) & v1_funct_1(D) -> v1_funct_1(k5_funct_5(D)) & m2_relset_1(k5_funct_5(D),A,k1_fraenkel(B,C)) & v1_funct_2(k5_funct_5(D),A,k1_fraenkel(B,C)))))))))) # label(t2_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5799 (all A all B all C all D (v2_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m1_subset_1(D,u2_cat_1(B)) & m1_subset_1(C,u2_cat_1(A)) & l1_cat_1(A) -> k13_cat_2(A,B,C,D) = k4_tarski(C,D))) # label(redefinition_k13_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5800 (all A all B (l1_cat_1(B) & v2_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> k5_cat_2(A,B) = k7_cat_2(A,B))) # label(redefinition_k7_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5801 $T # label(t9_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5802 (all A all B all C all D all E (v2_cat_1(A) & v2_cat_1(B) & m2_cat_1(E,A,C) & m2_cat_1(D,A,B) & l1_cat_1(C) & v2_cat_1(C) & l1_cat_1(B) & l1_cat_1(A) -> k13_funct_3(D,E) = k18_cat_2(A,B,C,D,E))) # label(redefinition_k18_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5803 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) & -v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (k3_tarski(a_2_0_cat_2(A,B)) = C -> v1_funct_1(k2_partfun1(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C)) & v1_funct_1(k2_partfun1(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C)) & v1_funct_2(k2_partfun1(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C),C,B) & v1_funct_1(k1_realset1(u5_cat_1(A),C)) & m2_relset_1(k1_realset1(u5_cat_1(A),C),k2_zfmisc_1(C,C),C) & v1_funct_1(k2_partfun1(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B)) & v1_funct_2(k2_partfun1(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B),B,C) & m2_relset_1(k2_partfun1(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B),B,C) & m2_relset_1(k2_partfun1(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C),C,B) & m2_relset_1(k2_partfun1(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C),C,B) & v1_funct_2(k2_partfun1(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C),C,B)))))))) # label(t29_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5804 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> (all C (m1_subset_1(C,u2_cat_1(B)) -> m1_subset_1(C,u2_cat_1(A)))))))) # label(t14_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5805 (all A all B all C all D all E (v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(C) & l1_cat_1(C) & m2_cat_1(D,k11_cat_2(A,B),C) & m1_subset_1(E,u1_cat_1(B)) & l1_cat_1(A) & v2_cat_1(A) -> m2_cat_1(k15_cat_2(A,B,C,D,E),A,C))) # label(dt_k15_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5806 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> k10_funct_3(u2_cat_1(A),u2_cat_1(B)) = k17_cat_2(A,B))))) # label(d11_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5807 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(B)) -> k2_cat_1(k11_cat_2(A,B),k13_cat_2(A,B,C,D)) = k12_cat_2(A,B,k2_cat_1(A,C),k2_cat_1(B,D)) & k3_cat_1(k11_cat_2(A,B),k13_cat_2(A,B,C,D)) = k12_cat_2(A,B,k3_cat_1(A,C),k3_cat_1(B,D)))))))))) # label(t38_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5808 (all A all B all C all D (v2_cat_1(A) & v2_cat_1(B) & m1_subset_1(C,u1_cat_1(A)) & m1_subset_1(D,u1_cat_1(B)) & l1_cat_1(B) & l1_cat_1(A) -> m1_subset_1(k12_cat_2(A,B,C,D),u1_cat_1(k11_cat_2(A,B))))) # label(dt_k12_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5809 (all A all B all C all D all E all F (-v1_xboole_0(C) & v1_funct_1(E) & m1_relset_1(E,A,D) & m1_subset_1(F,A) & v1_funct_2(E,A,D) & m1_fraenkel(D,B,C) & -v1_xboole_0(A) -> k1_funct_1(E,F) = k1_cat_2(A,B,C,D,E,F))) # label(redefinition_k1_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5810 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (v2_cat_1(D) & l1_cat_1(D) -> (all E (m2_cat_1(E,A,B) -> (all F (m2_cat_1(F,C,D) -> m2_cat_1(k9_cat_2(u2_cat_1(A),u2_cat_1(C),u2_cat_1(B),u2_cat_1(D),E,F),k11_cat_2(A,C),k11_cat_2(B,D)))))))))))))) # label(t65_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5811 (all A all B all C all D all E all F (-v1_xboole_0(D) & v1_funct_1(E) & m1_relset_1(E,A,C) & v1_funct_1(F) & m1_relset_1(F,B,D) & v1_funct_2(F,B,D) & v1_funct_2(E,A,C) & -v1_xboole_0(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k15_funct_3(E,F) = k9_cat_2(A,B,C,D,E,F))) # label(redefinition_k9_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5812 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> k9_cat_2(u2_cat_1(A),u2_cat_1(B),u1_cat_1(A),u1_cat_1(B),u3_cat_1(A),u3_cat_1(B)) = u3_cat_1(k11_cat_2(A,B)) & k10_cat_2(u2_cat_1(A),u2_cat_1(B),u5_cat_1(A),u5_cat_1(B)) = u5_cat_1(k11_cat_2(A,B)) & u6_cat_1(k11_cat_2(A,B)) = k9_cat_2(u1_cat_1(A),u1_cat_1(B),u2_cat_1(A),u2_cat_1(B),u6_cat_1(A),u6_cat_1(B)) & k9_cat_2(u2_cat_1(A),u2_cat_1(B),u1_cat_1(A),u1_cat_1(B),u4_cat_1(A),u4_cat_1(B)) = u4_cat_1(k11_cat_2(A,B)) & k2_zfmisc_1(u2_cat_1(A),u2_cat_1(B)) = u2_cat_1(k11_cat_2(A,B)) & u1_cat_1(k11_cat_2(A,B)) = k2_zfmisc_1(u1_cat_1(A),u1_cat_1(B)))))) # label(t33_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5813 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) & -v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,C,B) & v1_funct_2(D,C,B) -> (all E (v1_funct_1(E) & m2_relset_1(E,C,B) & v1_funct_2(E,C,B) -> (all F (v1_funct_1(F) & m2_relset_1(F,k2_zfmisc_1(C,C),C) -> (all G (m2_relset_1(G,B,C) & v1_funct_2(G,B,C) & v1_funct_1(G) -> (C = k3_tarski(a_2_0_cat_2(A,B)) & k2_partfun1(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C) = D & k1_realset1(u5_cat_1(A),C) = F & k2_partfun1(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B) = G & E = k2_partfun1(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C) -> r1_cat_2(g1_cat_1(B,C,D,E,F,G),A)))))))))))))))) # label(t30_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5814 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> k10_cat_1(k11_cat_2(A,B),k12_cat_2(A,B,C,D)) = k13_cat_2(A,B,k10_cat_1(A,C),k10_cat_1(B,D)))))))))) # label(t41_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5815 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_subset_1(F,u1_cat_1(B)) -> k8_funct_2(u1_cat_1(A),u1_cat_1(C),k12_cat_1(A,C,k15_cat_2(A,B,C,D,F)),E) = k8_funct_2(u1_cat_1(k11_cat_2(A,B)),u1_cat_1(C),k12_cat_1(k11_cat_2(A,B),C,D),k12_cat_2(A,B,E,F)))))))))))))) # label(t51_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5816 (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) -> v1_funct_1(k3_funct_5(D)) & v1_funct_2(k3_funct_5(D),A,k1_fraenkel(B,C)) & m2_relset_1(k3_funct_5(D),A,k1_fraenkel(B,C)))))))))) # label(t1_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5817 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) -> -v1_xboole_0(k3_tarski(a_2_0_cat_2(A,B))) & m1_subset_1(k3_tarski(a_2_0_cat_2(A,B)),k1_zfmisc_1(u2_cat_1(A))))))) # label(t28_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5818 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,u1_cat_1(A),k7_cat_2(B,C)) & m2_relset_1(D,u1_cat_1(A),k7_cat_2(B,C)) -> (all E (v1_funct_2(E,u1_cat_1(B),k7_cat_2(A,C)) & m2_relset_1(E,u1_cat_1(B),k7_cat_2(A,C)) & v1_funct_1(E) -> ((exists F ((all G (m1_subset_1(G,u1_cat_1(A)) -> (all H (m1_subset_1(H,u1_cat_1(B)) -> k6_cat_2(u1_cat_1(A),B,C,k7_cat_2(B,C),D,G) = k15_cat_2(B,A,C,F,G) & k14_cat_2(B,A,C,F,H) = k6_cat_2(u1_cat_1(B),A,C,k7_cat_2(A,C),E,H))))) & m2_cat_1(F,k11_cat_2(B,A),C))) -> (all F (m1_subset_1(F,u2_cat_1(B)) -> (all G (m1_subset_1(G,u2_cat_1(A)) -> k4_cat_1(C,k8_funct_2(u2_cat_1(A),u2_cat_1(C),k6_cat_2(u1_cat_1(B),A,C,k7_cat_2(A,C),E,k2_cat_1(B,F)),G),k8_funct_2(u2_cat_1(B),u2_cat_1(C),k6_cat_2(u1_cat_1(A),B,C,k7_cat_2(B,C),D,k3_cat_1(A,G)),F)) = k4_cat_1(C,k8_funct_2(u2_cat_1(B),u2_cat_1(C),k6_cat_2(u1_cat_1(A),B,C,k7_cat_2(B,C),D,k2_cat_1(A,G)),F),k8_funct_2(u2_cat_1(A),u2_cat_1(C),k6_cat_2(u1_cat_1(B),A,C,k7_cat_2(A,C),E,k3_cat_1(B,F)),G))))))))))))))))) # label(t53_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5819 (all A all B all C all D all E all F (v2_cat_1(A) & l1_cat_1(B) & v2_cat_1(C) & v2_cat_1(D) & l1_cat_1(D) & m2_cat_1(F,B,D) & m2_cat_1(E,A,C) & l1_cat_1(C) & v2_cat_1(B) & l1_cat_1(A) -> m2_cat_1(k19_cat_2(A,B,C,D,E,F),k11_cat_2(A,B),k11_cat_2(C,D)))) # label(dt_k19_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5820 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) & -v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_2(D,C,B) & m2_relset_1(D,C,B) & v1_funct_1(D) -> (all E (m2_relset_1(E,C,B) & v1_funct_2(E,C,B) & v1_funct_1(E) -> (all F (v1_funct_1(F) & m2_relset_1(F,k2_zfmisc_1(C,C),C) -> (all G (m2_relset_1(G,B,C) & v1_funct_2(G,B,C) & v1_funct_1(G) -> (r1_cat_2(g1_cat_1(B,C,D,E,F,G),A) -> C = k3_tarski(a_2_0_cat_2(A,B)) & k2_partfun1(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C) = D & E = k2_partfun1(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C) & k2_partfun1(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B) = G & F = k1_realset1(u5_cat_1(A),C)))))))))))))))) # label(t31_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5821 $T # label(t57_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5822 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> (all F (m1_subset_1(F,u1_cat_1(B)) -> k2_zfmisc_1(k6_cat_1(A,C,D),k6_cat_1(B,E,F)) = k6_cat_1(k11_cat_2(A,B),k12_cat_2(A,B,C,E),k12_cat_2(A,B,D,F)))))))))))))) # label(t42_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5823 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(B)) -> C = k8_funct_2(u2_cat_1(k11_cat_2(A,B)),u2_cat_1(A),k16_cat_2(A,B),k13_cat_2(A,B,C,D)))))))))) # label(t58_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5824 (all A all B all C all D (-v1_xboole_0(B) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) & -v1_xboole_0(C) & -v1_xboole_0(A) -> k5_funct_5(D) = k3_cat_2(A,B,C,D))) # label(redefinition_k3_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5825 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(B)) -> k10_cat_1(A,C) = k8_funct_2(u2_cat_1(B),u2_cat_1(A),k4_cat_2(B,A,C),D))))))))) # label(t6_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5826 (all A all B all C all D all E all F (-v1_xboole_0(A) & -v1_xboole_0(C) & v1_funct_2(E,A,D) & m1_subset_1(F,A) & m1_relset_1(E,A,D) & v1_funct_1(E) & m1_fraenkel(D,B,C) -> m2_fraenkel(k1_cat_2(A,B,C,D,E,F),B,C,D))) # label(dt_k1_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5827 (all A (l1_cat_1(A) & v2_cat_1(A) -> m3_cat_2(A,A))) # label(t18_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5828 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(B)) -> k8_funct_2(u2_cat_1(k11_cat_2(A,B)),u2_cat_1(B),k17_cat_2(A,B),k13_cat_2(A,B,C,D)) = D)))))))) # label(t60_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5829 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (v2_cat_1(D) & l1_cat_1(D) -> (all E (m2_cat_1(E,A,B) -> (all F (m2_cat_1(F,C,D) -> k18_cat_2(k11_cat_2(A,C),B,D,k14_cat_1(k11_cat_2(A,C),A,B,k16_cat_2(A,C),E),k14_cat_1(k11_cat_2(A,C),C,D,k17_cat_2(A,C),F)) = k9_cat_2(u2_cat_1(A),u2_cat_1(C),u2_cat_1(B),u2_cat_1(D),E,F))))))))))))) # label(t64_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5830 $T # label(t56_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5831 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,C) -> m2_cat_1(k14_funct_3(u2_cat_1(A),u2_cat_1(B),u2_cat_1(C),D,E),A,k11_cat_2(B,C)))))))))))) # label(t62_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5832 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(C) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & -v1_xboole_0(B) -> v1_funct_1(k3_cat_2(A,B,C,D)) & v1_funct_2(k3_cat_2(A,B,C,D),B,k1_fraenkel(A,C)) & m2_relset_1(k3_cat_2(A,B,C,D),B,k1_fraenkel(A,C)))) # label(dt_k3_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5833 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (k5_cat_2(A,B) = C <-> (all D (m2_cat_1(D,A,B) <-> r2_hidden(D,C))))))))) # label(d2_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5834 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> (v9_cat_1(k8_cat_2(A,B),B,A) <-> (all C (m1_subset_1(C,u1_cat_1(B)) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_subset_1(F,u1_cat_1(A)) -> (F = D & E = C -> k6_cat_1(A,E,F) = k6_cat_1(B,C,D))))))))))))))) # label(t25_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5835 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & -v1_xboole_0(C) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m1_relset_1(D,k2_zfmisc_1(A,B),C) -> v1_funct_1(k2_cat_2(A,B,C,D)) & v1_funct_2(k2_cat_2(A,B,C,D),A,k1_fraenkel(B,C)) & m2_relset_1(k2_cat_2(A,B,C,D),A,k1_fraenkel(B,C)))) # label(dt_k2_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5836 (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) -> k8_funct_2(B,C,k1_cat_2(A,B,C,k1_fraenkel(B,C),k2_cat_2(A,B,C,F),D),E) = k8_funct_2(k2_zfmisc_1(A,B),C,F,k1_domain_1(A,B,D,E)))))))))))))) # label(t3_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5837 $T # label(t8_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5838 $T # label(t11_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5839 (all A all B all C all D (-v1_xboole_0(A) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) & -v1_xboole_0(C) & -v1_xboole_0(B) -> k2_cat_2(A,B,C,D) = k3_funct_5(D))) # label(redefinition_k2_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5840 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> m2_cat_1(k9_funct_3(u2_cat_1(A),u2_cat_1(B)),k11_cat_2(A,B),A))))) # label(t54_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5841 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (all E (m1_subset_1(E,u2_cat_1(B)) -> (all F (m1_subset_1(F,u2_cat_1(B)) -> (k3_cat_1(k11_cat_2(A,B),k13_cat_2(A,B,C,E)) = k2_cat_1(k11_cat_2(A,B),k13_cat_2(A,B,D,F)) -> k4_cat_1(k11_cat_2(A,B),k13_cat_2(A,B,C,E),k13_cat_2(A,B,D,F)) = k13_cat_2(A,B,k4_cat_1(A,C,D),k4_cat_1(B,E,F))))))))))))))) # label(t40_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5842 (all A (l1_cat_1(A) & v2_cat_1(A) -> (exists B m3_cat_2(B,A)))) # label(existence_m3_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5843 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (-v1_xboole_0(C) -> ((all D (m1_subset_1(D,C) -> m2_cat_1(D,A,B))) <-> m1_cat_2(C,A,B)))))))) # label(d3_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5844 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,u1_cat_1(A),k7_cat_2(B,C)) & v1_funct_2(D,u1_cat_1(A),k7_cat_2(B,C)) -> (all E (v1_funct_1(E) & m2_relset_1(E,u1_cat_1(B),k7_cat_2(A,C)) & v1_funct_2(E,u1_cat_1(B),k7_cat_2(A,C)) -> -((all F (m1_subset_1(F,u2_cat_1(B)) -> (all G (m1_subset_1(G,u2_cat_1(A)) -> k4_cat_1(C,k8_funct_2(u2_cat_1(A),u2_cat_1(C),k6_cat_2(u1_cat_1(B),A,C,k7_cat_2(A,C),E,k2_cat_1(B,F)),G),k8_funct_2(u2_cat_1(B),u2_cat_1(C),k6_cat_2(u1_cat_1(A),B,C,k7_cat_2(B,C),D,k3_cat_1(A,G)),F)) = k4_cat_1(C,k8_funct_2(u2_cat_1(B),u2_cat_1(C),k6_cat_2(u1_cat_1(A),B,C,k7_cat_2(B,C),D,k2_cat_1(A,G)),F),k8_funct_2(u2_cat_1(A),u2_cat_1(C),k6_cat_2(u1_cat_1(B),A,C,k7_cat_2(A,C),E,k3_cat_1(B,F)),G)))))) & (all F (m2_cat_1(F,k11_cat_2(B,A),C) -> -(all G (m1_subset_1(G,u2_cat_1(B)) -> (all H (m1_subset_1(H,u2_cat_1(A)) -> k8_funct_2(u2_cat_1(k11_cat_2(B,A)),u2_cat_1(C),F,k13_cat_2(B,A,G,H)) = k4_cat_1(C,k8_funct_2(u2_cat_1(A),u2_cat_1(C),k6_cat_2(u1_cat_1(B),A,C,k7_cat_2(A,C),E,k2_cat_1(B,G)),H),k8_funct_2(u2_cat_1(B),u2_cat_1(C),k6_cat_2(u1_cat_1(A),B,C,k7_cat_2(B,C),D,k3_cat_1(A,H)),G)))))))) & (all F (m1_subset_1(F,u1_cat_1(A)) -> (all G (m1_subset_1(G,u1_cat_1(B)) -> k8_funct_2(u2_cat_1(B),u2_cat_1(C),k6_cat_2(u1_cat_1(A),B,C,k7_cat_2(B,C),D,F),k10_cat_1(B,G)) = k8_funct_2(u2_cat_1(A),u2_cat_1(C),k6_cat_2(u1_cat_1(B),A,C,k7_cat_2(A,C),E,G),k10_cat_1(A,F))))))))))))))))) # label(t52_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5845 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m3_cat_2(B,A) -> (all C (m1_subset_1(C,u2_cat_1(B)) -> C = k8_funct_2(u2_cat_1(B),u2_cat_1(A),k8_cat_2(A,B),C))))))) # label(t21_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5846 (all A all B all C (l1_cat_1(A) & v2_cat_1(B) & m1_cat_2(C,A,B) & l1_cat_1(B) & v2_cat_1(A) -> (exists D m2_cat_2(D,A,B,C)))) # label(existence_m2_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5847 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m3_cat_2(B,A) -> m2_cat_1(k15_cat_1(B),B,A))))) # label(t19_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5848 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> k10_pboole(u2_cat_1(A),k10_cat_1(B,C)) = k4_cat_2(A,B,C))))))) # label(d1_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5849 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> m2_cat_1(k1_funct_1(k3_funct_5(D),k10_cat_1(A,E)),B,C))))))))))) # label(t44_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5850 $T # label(t20_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5851 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,C) -> (all F (m1_subset_1(F,u1_cat_1(A)) -> k8_funct_2(u1_cat_1(A),u1_cat_1(k11_cat_2(B,C)),k12_cat_1(A,k11_cat_2(B,C),k18_cat_2(A,B,C,D,E)),F) = k12_cat_2(B,C,k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,D),F),k8_funct_2(u1_cat_1(A),u1_cat_1(C),k12_cat_1(A,C,E),F)))))))))))))) # label(t63_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5852 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> g1_cat_1(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(B)),k2_zfmisc_1(u2_cat_1(A),u2_cat_1(B)),k9_cat_2(u2_cat_1(A),u2_cat_1(B),u1_cat_1(A),u1_cat_1(B),u3_cat_1(A),u3_cat_1(B)),k9_cat_2(u2_cat_1(A),u2_cat_1(B),u1_cat_1(A),u1_cat_1(B),u4_cat_1(A),u4_cat_1(B)),k10_cat_2(u2_cat_1(A),u2_cat_1(B),u5_cat_1(A),u5_cat_1(B)),k9_cat_2(u1_cat_1(A),u1_cat_1(B),u2_cat_1(A),u2_cat_1(B),u6_cat_1(A),u6_cat_1(B))) = k11_cat_2(A,B))))) # label(d7_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5853 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> k13_cat_1(B,A,k8_cat_2(A,B),C) = C)))))) # label(t23_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5854 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (all E (m1_subset_1(E,u2_cat_1(B)) -> (all F (m1_subset_1(F,u2_cat_1(B)) -> (k2_cat_1(A,D) = k3_cat_1(A,C) & k2_cat_1(B,F) = k3_cat_1(B,E) -> k13_cat_2(A,B,k4_cat_1(A,C,D),k4_cat_1(B,E,F)) = k4_cat_1(k11_cat_2(A,B),k13_cat_2(A,B,C,E),k13_cat_2(A,B,D,F))))))))))))))) # label(t39_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5855 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> k16_cat_2(A,B) = k9_funct_3(u2_cat_1(A),u2_cat_1(B)))))) # label(d10_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5856 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> m1_subset_1(C,u1_cat_1(A)))))))) # label(t12_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5857 (all A all B (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) -> (exists C m1_cat_2(C,A,B)))) # label(existence_m1_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5858 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> m2_cat_1(k1_funct_1(k5_funct_5(D),k10_cat_1(B,E)),A,C))))))))))) # label(t45_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5859 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> l1_cat_1(B) & v2_cat_1(B))))) # label(dt_m3_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5860 $T # label(t46_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5861 $T # label(t32_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5862 (all A all B (v2_cat_1(A) & l1_cat_1(B) & v2_cat_1(B) & l1_cat_1(A) -> -v1_xboole_0(k5_cat_2(A,B)))) # label(fc1_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5863 (all A all B (l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(A) -> l1_cat_1(k11_cat_2(A,B)) & v2_cat_1(k11_cat_2(A,B)))) # label(dt_k11_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5864 (all A all B (v2_cat_1(A) & l1_cat_1(B) & v2_cat_1(B) & l1_cat_1(A) -> m2_cat_1(k16_cat_2(A,B),k11_cat_2(A,B),A))) # label(dt_k16_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5865 (all A all B all C all D (-v1_xboole_0(A) & v1_funct_1(C) & m1_relset_1(D,k2_zfmisc_1(B,B),B) & v1_funct_1(D) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & -v1_xboole_0(B) -> k10_cat_2(A,B,C,D) = k3_funct_4(C,D))) # label(redefinition_k10_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5866 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (v2_cat_1(D) & l1_cat_1(D) -> (all E (m2_cat_1(E,A,B) -> (all F (m2_cat_1(F,C,D) -> (all G (m1_subset_1(G,u1_cat_1(A)) -> (all H (m1_subset_1(H,u1_cat_1(C)) -> k8_funct_2(u1_cat_1(k11_cat_2(A,C)),u1_cat_1(k11_cat_2(B,D)),k12_cat_1(k11_cat_2(A,C),k11_cat_2(B,D),k19_cat_2(A,C,B,D,E,F)),k12_cat_2(A,C,G,H)) = k12_cat_2(B,D,k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,E),G),k8_funct_2(u1_cat_1(C),u1_cat_1(D),k12_cat_1(C,D,F),H)))))))))))))))))) # label(t66_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5867 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> m1_subset_1(k1_domain_1(u1_cat_1(A),u1_cat_1(B),C,D),u1_cat_1(k11_cat_2(A,B))))))))))) # label(t34_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5868 (all A all B all C all D all E (l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & l1_cat_1(C) & m2_cat_1(E,A,C) & m2_cat_1(D,A,B) & v2_cat_1(C) & v2_cat_1(A) -> m2_cat_1(k18_cat_2(A,B,C,D,E),A,k11_cat_2(B,C)))) # label(dt_k18_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5869 $T # label(t5_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5870 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_subset_1(F,u1_cat_1(A)) -> (all G (m1_cat_1(G,B,C,D) -> (E = C & F = D -> m1_cat_1(G,A,E,F) | k6_cat_1(B,C,D) = k1_xboole_0))))))))))))))) # label(t16_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5871 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,C,D) -> (all F (m1_subset_1(F,u1_cat_1(B)) -> (all G (m1_subset_1(G,u1_cat_1(B)) -> (all H (m1_cat_1(H,B,F,G) -> -(-m1_cat_1(k13_cat_2(A,B,E,H),k11_cat_2(A,B),k12_cat_2(A,B,C,F),k12_cat_2(A,B,D,G)) & k1_xboole_0 != k6_cat_1(B,F,G) & k6_cat_1(A,C,D) != k1_xboole_0))))))))))))))))) # label(t43_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5872 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,B) -> (all F (v1_funct_1(F) & m2_relset_1(F,k2_zfmisc_1(A,B),C) & v1_funct_2(F,k2_zfmisc_1(A,B),C) -> k8_funct_2(k2_zfmisc_1(A,B),C,F,k1_domain_1(A,B,D,E)) = k8_funct_2(A,C,k1_cat_2(B,A,C,k1_fraenkel(A,C),k3_cat_2(A,B,C,F),E),D))))))))))))) # label(t4_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5873 (all A all B all C all D all E (l1_cat_1(A) & l1_cat_1(B) & v2_cat_1(C) & m2_cat_1(D,k11_cat_2(A,B),C) & m1_subset_1(E,u1_cat_1(A)) & l1_cat_1(C) & v2_cat_1(B) & v2_cat_1(A) -> m2_cat_1(k14_cat_2(A,B,C,D,E),B,C))) # label(dt_k14_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5874 (all A all B all C (l1_cat_1(B) & -v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_cat_1(B))) & v2_cat_1(B) -> (r2_hidden(A,a_2_0_cat_2(B,C)) <-> (exists D exists E (m1_subset_1(D,u1_cat_1(B)) & A = k6_cat_1(B,D,E) & r2_hidden(E,C) & r2_hidden(D,C) & m1_subset_1(E,u1_cat_1(B))))))) # label(fraenkel_a_2_0_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5875 (all A all B (v2_cat_1(A) & l1_cat_1(A) & l1_cat_1(B) & v2_cat_1(B) -> m2_cat_1(k17_cat_2(A,B),k11_cat_2(A,B),B))) # label(dt_k17_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5876 (all A all B all C all D all E all F (v2_cat_1(C) & m1_cat_2(D,B,C) & v1_funct_2(E,A,D) & m1_subset_1(F,A) & m1_relset_1(E,A,D) & v1_funct_1(E) & l1_cat_1(C) & l1_cat_1(B) & v2_cat_1(B) & -v1_xboole_0(A) -> m2_cat_2(k6_cat_2(A,B,C,D,E,F),B,C,D))) # label(dt_k6_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5877 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> k15_cat_1(B) = k8_cat_2(A,B))))) # label(d5_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5878 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (m3_cat_2(B,A) <-> r1_tarski(u5_cat_1(B),u5_cat_1(A)) & (all C (m1_subset_1(C,u1_cat_1(B)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (D = C -> k10_cat_1(A,D) = k10_cat_1(B,C)))))) & (all C (m1_subset_1(C,u1_cat_1(B)) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_subset_1(F,u1_cat_1(A)) -> (C = E & D = F -> r1_tarski(k6_cat_1(B,C,D),k6_cat_1(A,E,F))))))))))) & r1_tarski(u1_cat_1(B),u1_cat_1(A))))))) # label(d4_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5879 (all A all B all C all D (l1_cat_1(B) & m1_subset_1(C,u1_cat_1(A)) & m1_subset_1(D,u1_cat_1(B)) & v2_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> k4_tarski(C,D) = k12_cat_2(A,B,C,D))) # label(redefinition_k12_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5880 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> k15_cat_2(A,B,C,D,E) = k1_funct_1(k5_funct_5(D),k10_cat_1(B,E)))))))))))) # label(d9_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5881 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_subset_1(F,u1_cat_1(B)) -> k8_funct_2(u1_cat_1(k11_cat_2(A,B)),u1_cat_1(C),k12_cat_1(k11_cat_2(A,B),C,D),k12_cat_2(A,B,E,F)) = k8_funct_2(u1_cat_1(B),u1_cat_1(C),k12_cat_1(B,C,k14_cat_2(A,B,C,D,E)),F))))))))))))) # label(t48_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5882 (all A (l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> ((all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> (all F (m1_subset_1(F,u1_cat_1(B)) -> (D = F & C = E -> k6_cat_1(A,C,D) = k6_cat_1(B,E,F)))))))))) & m3_cat_2(A,B) <-> r1_cat_2(A,B)))))) # label(d6_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5883 (all A all B (v2_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & l1_cat_1(A) -> m1_cat_2(k7_cat_2(A,B),A,B))) # label(dt_k7_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5884 (all A all B all C all D all E all F (l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(F,B,D) & m2_cat_1(E,A,C) & l1_cat_1(D) & v2_cat_1(D) & l1_cat_1(C) & v2_cat_1(C) & v2_cat_1(A) -> k19_cat_2(A,B,C,D,E,F) = k15_funct_3(E,F))) # label(redefinition_k19_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5885 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> (all C (m1_subset_1(C,u2_cat_1(B)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (C = D -> k2_cat_1(A,D) = k2_cat_1(B,C) & k3_cat_1(A,D) = k3_cat_1(B,C)))))))))) # label(t15_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5886 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_subset_1(F,u2_cat_1(B)) -> k8_funct_2(u2_cat_1(k11_cat_2(A,B)),u2_cat_1(C),D,k13_cat_2(A,B,k10_cat_1(A,E),F)) = k8_funct_2(u2_cat_1(B),u2_cat_1(C),k14_cat_2(A,B,C,D,E),F))))))))))))) # label(t47_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5887 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m3_cat_2(B,A) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> k8_funct_2(u1_cat_1(B),u1_cat_1(A),k12_cat_1(B,A,k8_cat_2(A,B)),C) = C)))))) # label(t22_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5888 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> v10_cat_1(k8_cat_2(A,B),B,A))))) # label(t24_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5889 (all A all B all C all D all E all F (-v1_xboole_0(A) & v2_cat_1(B) & m1_cat_2(D,B,C) & v1_funct_1(E) & m1_subset_1(F,A) & m1_relset_1(E,A,D) & v1_funct_2(E,A,D) & l1_cat_1(C) & v2_cat_1(C) & l1_cat_1(B) -> k6_cat_2(A,B,C,D,E,F) = k1_funct_1(E,F))) # label(redefinition_k6_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5890 (all A all B all C (v2_cat_1(B) & l1_cat_1(B) & m1_subset_1(C,u1_cat_1(B)) & l1_cat_1(A) & v2_cat_1(A) -> m2_cat_1(k4_cat_2(A,B,C),A,B))) # label(dt_k4_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5891 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m3_cat_2(B,A) -> (v9_cat_1(k8_cat_2(A,B),B,A) <-> r1_cat_2(B,A)))))) # label(t27_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5892 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> m2_cat_1(k10_funct_3(u2_cat_1(A),u2_cat_1(B)),k11_cat_2(A,B),B))))) # label(t55_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5893 (all A all B all C (l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m1_cat_2(C,A,B) & v2_cat_1(A) -> (all D (m2_cat_2(D,A,B,C) -> m2_cat_1(D,A,B))))) # label(dt_m2_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5894 (all A all B all C (v2_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m1_cat_2(C,A,B) & l1_cat_1(A) -> (all D (m2_cat_2(D,A,B,C) <-> m1_subset_1(D,C))))) # label(redefinition_m2_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5895 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> k8_funct_2(u1_cat_1(k11_cat_2(A,B)),u1_cat_1(B),k12_cat_1(k11_cat_2(A,B),B,k17_cat_2(A,B)),k12_cat_2(A,B,C,D)) = D)))))))) # label(t61_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5896 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m3_cat_2(B,A) -> (all C (m1_subset_1(C,u2_cat_1(B)) -> (all D (m1_subset_1(D,u2_cat_1(B)) -> (all E (m1_subset_1(E,u2_cat_1(A)) -> (all F (m1_subset_1(F,u2_cat_1(A)) -> (E = C & F = D & k2_cat_1(B,D) = k3_cat_1(B,C) -> k4_cat_1(A,E,F) = k4_cat_1(B,C,D)))))))))))))) # label(t17_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5897 (all A (l1_cat_1(A) & v2_cat_1(A) -> (exists B (m3_cat_2(B,A) & v1_cat_1(B) & v2_cat_1(B))))) # label(rc1_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5898 $T # label(dt_k5_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5899 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> C = k8_funct_2(u1_cat_1(B),u1_cat_1(A),k12_cat_1(B,A,k4_cat_2(B,A,C)),D))))))))) # label(t7_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5900 (all A all B (l1_cat_1(A) & l1_cat_1(B) & v2_cat_1(B) & v2_cat_1(A) -> (all C (m1_cat_2(C,A,B) -> -v1_xboole_0(C))))) # label(dt_m1_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5901 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(B)) -> m1_subset_1(k1_domain_1(u2_cat_1(A),u2_cat_1(B),C,D),u2_cat_1(k11_cat_2(A,B))))))))))) # label(t36_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5902 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> r1_tarski(u2_cat_1(B),u2_cat_1(A)))))) # label(t13_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5903 $T # label(t10_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.74 5904 (all A all B all C all D all E all F (-v1_xboole_0(C) & v1_funct_1(F) & v1_funct_2(F,B,D) & m1_relset_1(F,B,D) & m1_relset_1(E,A,C) & v1_funct_2(E,A,C) & v1_funct_1(E) & -v1_xboole_0(D) & -v1_xboole_0(B) & -v1_xboole_0(A) -> v1_funct_1(k9_cat_2(A,B,C,D,E,F)) & m2_relset_1(k9_cat_2(A,B,C,D,E,F),k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) & v1_funct_2(k9_cat_2(A,B,C,D,E,F),k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)))) # label(dt_k9_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.75 5905 (all A all B all C all D (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & m1_subset_1(C,u2_cat_1(A)) & m1_subset_1(D,u2_cat_1(B)) & l1_cat_1(B) -> m1_subset_1(k13_cat_2(A,B,C,D),u2_cat_1(k11_cat_2(A,B))))) # label(dt_k13_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.75 5906 (all A all B (l1_cat_1(B) & v2_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> v2_cat_1(k11_cat_2(A,B)) & v1_cat_1(k11_cat_2(A,B)))) # label(fc2_cat_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.75 5907 (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]. 116.12/115.75 5908 (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]. 116.12/115.75 5909 (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]. 116.12/115.75 5910 (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]. 116.12/115.75 5911 (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]. 116.12/115.75 5912 (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]. 116.12/115.75 5913 (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]. 116.12/115.75 5914 (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]. 116.12/115.75 5915 (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]. 116.12/115.75 5916 (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]. 116.12/115.75 5917 (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]. 116.12/115.75 5918 (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]. 116.12/115.75 5919 (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]. 116.12/115.75 5920 (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]. 116.12/115.75 5921 (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]. 116.12/115.75 5922 (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]. 116.12/115.75 5923 (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]. 116.12/115.75 5924 (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]. 116.12/115.75 5925 (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]. 116.12/115.75 5926 (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]. 116.12/115.75 5927 (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]. 116.12/115.75 5928 (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]. 116.12/115.75 5929 (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]. 116.12/115.75 5930 $T # label(t21_filter_0) # label(axiom) # label(non_clause). [assumption]. 116.12/115.75 5931 (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]. 116.12/115.75 5932 (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]. 116.12/115.75 5933 $T # label(t33_filter_0) # label(axiom) # label(non_clause). [assumption]. 116.12/115.75 5934 (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]. 116.12/115.75 5935 (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]. 116.12/115.75 5936 (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]. 116.12/115.75 5937 (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]. 116.12/115.75 5938 (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]. 116.12/115.75 5939 (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]. 116.12/115.75 5940 (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]. 116.12/115.75 5941 (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]. 116.12/115.75 5942 $T # label(t16_filter_0) # label(axiom) # label(non_clause). [assumption]. 116.12/115.75 5943 (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]. 116.12/115.75 5944 (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]. 116.12/115.75 5945 (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]. 116.12/115.75 5946 (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]. 116.12/115.75 5947 $T # label(t17_filter_0) # label(axiom) # label(non_clause). [assumption]. 116.12/115.75 5948 (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]. 116.12/115.75 5949 (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]. 116.12/115.75 5950 $T # label(t61_filter_0) # label(axiom) # label(non_clause). [assumption]. 116.12/115.75 5951 (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]. 116.12/115.75 5952 (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]. 116.12/115.75 5953 (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]. 116.12/115.75 5954 (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]. 116.12/115.75 5955 $T # label(t79_filter_0) # label(axiom) # label(non_clause). [assumption]. 116.12/115.75 5956 (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]. 116.12/115.75 5957 (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]. 116.12/115.75 5958 (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]. 116.12/115.75 5959 $T # label(t25_filter_0) # label(axiom) # label(non_clause). [assumption]. 116.12/115.75 5960 (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]. 116.12/115.75 5961 (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]. 116.12/115.75 5962 (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]. 116.12/115.75 5963 (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]. 116.12/115.75 5964 (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]. 116.12/115.75 5965 (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]. 116.12/115.75 5966 (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]. 116.12/115.75 5967 (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]. 116.12/115.75 5968 (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]. 116.12/115.75 5969 (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]. 116.12/115.75 5970 (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]. 116.12/115.75 5971 (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]. 116.12/115.75 5972 (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]. 116.12/115.75 5973 (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]. 116.12/115.75 5974 (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]. 116.12/115.75 5975 (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]. 116.12/115.75 5976 (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]. 116.12/115.75 5977 (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]. 116.12/115.75 5978 $T # label(t86_filter_0) # label(axiom) # label(non_clause). [assumption]. 116.12/115.75 5979 (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]. 116.12/115.75 5980 (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]. 116.12/115.75 5981 (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]. 116.12/115.75 5982 (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]. 116.12/115.75 5983 $T # label(t43_filter_0) # label(axiom) # label(non_clause). [assumption]. 116.12/115.75 5984 (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]. 116.12/115.75 5985 (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]. 116.12/115.75 5986 (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]. 116.12/115.75 5987 (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]. 116.12/115.75 5988 (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]. 116.12/115.75 5989 (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]. 116.12/115.75 5990 (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]. 116.12/115.75 5991 $T # label(t8_filter_0) # label(axiom) # label(non_clause). [assumption]. 116.12/115.75 5992 (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]. 116.12/115.75 5993 (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]. 116.12/115.75 5994 (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]. 116.12/115.75 5995 (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]. 116.12/115.75 5996 (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]. 116.12/115.75 5997 $T # label(t36_filter_0) # label(axiom) # label(non_clause). [assumption]. 116.12/115.75 5998 (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]. 116.12/115.75 5999 (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]. 116.12/115.75 6000 (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]. 116.12/115.75 6001 (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]. 116.12/115.75 6002 (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]. 116.12/115.75 6003 (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]. 116.12/115.75 6004 (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]. 116.12/115.75 6005 (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]. 116.12/115.75 6006 (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]. 116.12/115.75 6007 (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]. 116.12/115.75 6008 (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]. 116.12/115.75 6009 (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]. 116.12/115.75 6010 (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]. 116.12/115.75 6011 (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]. 116.12/115.75 6012 (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]. 116.12/115.75 6013 $T # label(t76_filter_0) # label(axiom) # label(non_clause). [assumption]. 116.12/115.75 6014 (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]. 116.12/115.75 6015 (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]. 116.12/115.75 6016 (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]. 116.12/115.75 6017 (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]. 116.12/115.75 6018 (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]. 116.12/115.75 6019 (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]. 116.12/115.75 6020 (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]. 116.12/115.75 6021 (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]. 116.12/115.75 6022 (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]. 116.12/115.75 6023 (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]. 116.12/115.75 6024 (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]. 116.12/115.75 6025 (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]. 116.12/115.75 6026 (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]. 116.12/115.75 6027 (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]. 116.12/115.75 6028 (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]. 116.12/115.75 6029 (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]. 116.12/115.75 6030 (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]. 116.12/115.75 6031 $T # label(t28_filter_0) # label(axiom) # label(non_clause). [assumption]. 116.12/115.75 6032 $T # label(t35_filter_0) # label(axiom) # label(non_clause). [assumption]. 116.12/115.75 6033 (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]. 116.12/115.75 6034 (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]. 116.12/115.75 6035 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(C,A) & r2_hidden(B,C) & r1_tarski(C,k1_connsp_2(A,B)) & v3_pre_topc(C,A) -> C = k1_connsp_2(A,B)))))))) # label(t31_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.75 6036 $T # label(t1_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.75 6037 $T # label(t15_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.75 6038 $T # label(t17_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.75 6039 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,B) & v3_pre_topc(B,A) -> m1_connsp_2(B,A,C)))))))) # label(t5_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.76 6040 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,C) & r3_connsp_1(A,B) -> r4_connsp_1(A,C,B)))))))) # label(t13_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.76 6041 $T # label(t2_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.76 6042 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) & v2_pre_topc(A) -> (all C (m2_connsp_2(C,A,B) -> m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))))))) # label(dt_m2_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.76 6043 (all A all B (m1_subset_1(B,u1_struct_0(A)) & l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all C (m1_connsp_2(C,A,B) -> m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))))))) # label(dt_m1_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.76 6044 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (m1_connsp_2(D,A,B) & m1_connsp_2(C,A,B) <-> m1_connsp_2(k5_subset_1(u1_struct_0(A),C,D),A,B)))))))))) # label(t4_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.76 6045 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(k1_xboole_0 != B & C != k2_pre_topc(A) & r1_tarski(B,C) & v4_pre_topc(B,A) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(D,A) & r1_tarski(B,D) & r1_tarski(k6_pre_topc(A,D),C)))) & v3_pre_topc(C,A)))))) <-> v5_compts_1(A)))) # label(t26_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.76 6046 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(D,C) <-> v3_pre_topc(D,A) & v4_pre_topc(D,A) & r2_hidden(B,D)))) & C = k1_xboole_0))))))) # label(t28_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.76 6047 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (m1_connsp_2(C,A,B) <-> (exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D,A) & r2_hidden(B,D) & r1_tarski(D,C)))))))))) # label(t8_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.76 6048 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (v1_connsp_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,B)))) -> -(v2_connsp_1(C,k3_pre_topc(A,B)) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(D,A) & v2_connsp_1(D,A) & k5_subset_1(u1_struct_0(A),B,D) = C))) & v3_pre_topc(C,k3_pre_topc(A,B)))))))))) # label(t25_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.76 6049 (all A all B (l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) & v2_pre_topc(A) & -v3_struct_0(A) -> (exists C m1_connsp_2(C,A,B)))) # label(existence_m1_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.76 6050 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(D) -> -((all E (m1_subset_1(E,u1_struct_0(k3_pre_topc(A,D))) -> -(r1_connsp_2(k3_pre_topc(A,D),E) & C = E))) & D = B))) <-> r2_connsp_2(A,B,C)))))))) # label(d5_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.76 6051 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (v5_compts_1(A) & v1_connsp_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(B != k1_xboole_0 & k1_xboole_0 != C & v2_connsp_1(B,A) & v2_connsp_1(C,A) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(v2_connsp_1(D,A) & v2_connsp_1(E,A) & v3_pre_topc(D,A) & v3_pre_topc(E,A) & r1_tarski(B,D) & r1_xboole_0(D,E) & r1_tarski(C,E)))))) & r1_xboole_0(B,C) & v4_pre_topc(C,A) & v4_pre_topc(B,A))))))))) # label(t27_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.76 6052 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> -(r2_hidden(C,B) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_tarski(D,B) & m1_connsp_2(D,A,C))))))) <-> v3_pre_topc(B,A)))))) # label(t9_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.76 6053 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_connsp_2(k3_pre_topc(A,B)) <-> v2_connsp_2(B,A)))))) # label(d6_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.76 6054 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (m1_connsp_2(B,A,C) -> r2_hidden(C,B)))))))) # label(t6_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.76 6055 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,k1_tops_1(A,C)) <-> m1_connsp_2(C,A,B)))))))) # label(d1_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.76 6056 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (r1_connsp_2(A,B) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v2_connsp_1(D,A) & r1_tarski(D,C) & m1_connsp_2(D,A,B)))) & m1_connsp_2(C,A,B))))))))) # label(d3_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.76 6057 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,k1_tops_1(A,C)) <-> m2_connsp_2(C,A,B)))))))) # label(d2_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.76 6058 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(k3_pre_topc(A,B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,B)))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (all F (m1_subset_1(F,u1_struct_0(A)) -> (v3_pre_topc(B,A) & F = C & E = D & m1_connsp_2(D,k3_pre_topc(A,B),C) -> m1_connsp_2(E,A,F)))))))))))))) # label(t11_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.76 6059 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_tarski(k1_connsp_1(A,B),k1_connsp_2(A,B)))))) # label(t33_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.76 6060 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((exists D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & k6_setfam_1(u1_struct_0(A),D) = C & (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(E,D) <-> v4_pre_topc(E,A) & r2_hidden(B,E) & v3_pre_topc(E,A)))))) <-> C = k1_connsp_2(A,B)))))))) # label(d7_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.76 6061 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (v1_connsp_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r3_connsp_1(A,B) -> v3_pre_topc(B,A))))))) # label(t21_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.12/115.76 6062 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r2_hidden(B,k1_connsp_2(A,B)))))) # label(t30_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.23/115.76 6063 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (v1_connsp_2(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_connsp_2(A,B)))))) # label(d4_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.23/115.76 6064 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (v1_connsp_2(A) <-> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) & r4_connsp_1(A,B,C) -> v3_pre_topc(C,A))))))))) # label(t24_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.23/115.76 6065 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (v1_connsp_2(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> v2_connsp_2(B,A))))))) # label(t23_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.23/115.76 6066 $T # label(t18_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.23/115.76 6067 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(D) -> -(m1_connsp_2(D,A,B) & r1_tarski(D,C) & v3_pre_topc(D,A)))) & m1_connsp_2(C,A,B)))))))) # label(t7_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.23/115.76 6068 (all A all B (v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) & -v3_struct_0(A) -> m1_subset_1(k1_connsp_2(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k1_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.23/115.76 6069 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r4_connsp_1(A,C,D) & r2_hidden(B,D) & m1_connsp_2(C,A,B) -> m1_connsp_2(D,A,B)))))) <-> r1_connsp_2(A,B)))))) # label(t19_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.23/115.76 6070 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) -> -(v3_pre_topc(C,A) & (all D (m1_subset_1(D,u1_struct_0(k3_pre_topc(A,C))) -> -(D = B & r2_hidden(B,k1_tops_1(k3_pre_topc(A,C),k1_connsp_1(k3_pre_topc(A,C),D)))))) & r2_hidden(B,C)))) <-> r1_connsp_2(A,B)))))) # label(t20_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.23/115.76 6071 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(k3_pre_topc(A,B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,B)))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (all F (m1_subset_1(F,u1_struct_0(A)) -> (E = D & C = F & m1_connsp_2(E,A,F) -> m1_connsp_2(D,k3_pre_topc(A,B),C)))))))))))))) # label(t12_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.23/115.76 6072 $T # label(t29_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.23/115.76 6073 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (D = C -> r1_tarski(k1_connsp_1(B,D),k1_connsp_1(A,C))))))))))) # label(t14_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.23/115.76 6074 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (m2_connsp_2(C,A,k1_struct_0(A,B)) <-> m1_connsp_2(C,A,B)))))))) # label(t10_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.23/115.76 6075 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (m1_connsp_2(C,A,B) & m1_connsp_2(D,A,B) -> m1_connsp_2(k4_subset_1(u1_struct_0(A),C,D),A,B)))))))))) # label(t3_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.23/115.76 6076 (all A all B (v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (exists C m2_connsp_2(C,A,B)))) # label(existence_m2_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.23/115.76 6077 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (r1_connsp_2(A,B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) -> (v3_pre_topc(C,A) & r2_hidden(B,C) -> r2_connsp_2(A,C,B))))))))) # label(t22_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.23/115.76 6078 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> v4_pre_topc(k1_connsp_2(A,B),A))))) # label(t32_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.23/115.76 6079 $T # label(t16_connsp_2) # label(axiom) # label(non_clause). [assumption]. 116.23/115.76 6080 (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]. 116.23/115.76 6081 (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]. 116.23/115.76 6082 (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]. 116.23/115.76 6083 (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]. 116.23/115.76 6084 (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]. 116.23/115.76 6085 (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]. 116.23/115.76 6086 (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]. 116.23/115.76 6087 (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]. 116.23/115.76 6088 (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]. 116.23/115.76 6089 (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]. 116.23/115.76 6090 (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]. 116.23/115.76 6091 (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]. 116.23/115.76 6092 (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]. 116.23/115.76 6093 (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]. 116.23/115.76 6094 (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]. 116.23/115.76 6095 (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]. 116.23/115.76 6096 (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]. 116.23/115.76 6097 (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]. 116.23/115.76 6098 (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]. 116.23/115.76 6099 (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]. 116.23/115.76 6100 (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]. 116.23/115.76 6101 (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]. 116.23/115.76 6102 (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]. 116.23/115.76 6103 (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]. 116.23/115.76 6104 (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]. 116.23/115.76 6105 (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]. 116.23/115.76 6106 (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]. 116.23/115.76 6107 (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]. 116.23/115.76 6108 (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]. 116.23/115.76 6109 (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]. 116.23/115.76 6110 (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]. 116.23/115.76 6111 (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]. 116.23/115.76 6112 (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]. 116.23/115.76 6113 (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]. 116.23/115.76 6114 (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]. 116.23/115.76 6115 (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]. 116.23/115.76 6116 (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]. 116.23/115.76 6117 (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]. 116.23/115.76 6118 (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]. 116.23/115.76 6119 (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]. 116.23/115.76 6120 (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]. 116.23/115.76 6121 (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]. 116.23/115.76 6122 (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]. 116.23/115.76 6123 (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]. 116.23/115.76 6124 (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]. 116.23/115.76 6125 (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]. 116.23/115.76 6126 (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]. 116.23/115.76 6127 (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]. 116.23/115.76 6128 (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]. 116.23/115.76 6129 (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]. 116.23/115.76 6130 (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]. 116.23/115.76 6131 (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]. 116.23/115.76 6132 (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]. 116.23/115.76 6133 (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]. 116.23/115.76 6134 (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]. 116.23/115.76 6135 (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]. 116.23/115.76 6136 (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]. 116.23/115.76 6137 (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]. 116.23/115.76 6138 (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]. 116.23/115.76 6139 (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]. 116.23/115.76 6140 (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]. 116.23/115.76 6141 (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]. 116.23/115.76 6142 (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]. 116.23/115.76 6143 (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]. 116.23/115.76 6144 (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]. 116.23/115.76 6145 (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]. 116.23/115.76 6146 (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]. 116.23/115.76 6147 (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]. 116.23/115.76 6148 (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]. 116.23/115.76 6149 (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]. 116.23/115.76 6150 (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]. 116.23/115.76 6151 (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]. 116.23/115.76 6152 (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]. 116.23/115.76 6153 (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]. 116.23/115.76 6154 (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]. 116.23/115.76 6155 (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]. 116.23/115.76 6156 (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]. 116.23/115.76 6157 (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]. 116.23/115.76 6158 (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]. 116.23/115.76 6159 (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]. 116.23/115.76 6160 (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]. 116.23/115.76 6161 (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]. 116.23/115.77 6162 (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]. 116.23/115.77 6163 (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]. 116.23/115.77 6164 (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]. 116.23/115.77 6165 (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]. 116.23/115.77 6166 (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]. 116.23/115.77 6167 (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]. 116.23/115.77 6168 (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]. 116.23/115.77 6169 (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]. 116.23/115.77 6170 (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]. 116.23/115.77 6171 (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]. 116.23/115.77 6172 (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]. 116.23/115.77 6173 (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]. 116.23/115.77 6174 (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]. 116.23/115.77 6175 (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]. 116.23/115.77 6176 (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]. 116.23/115.77 6177 (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]. 116.23/115.77 6178 (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]. 116.23/115.77 6179 (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]. 116.23/115.77 6180 (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]. 116.23/115.77 6181 (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]. 116.23/115.77 6182 (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]. 116.23/115.77 6183 (all A k1_pcomps_1(A) = k1_zfmisc_1(A)) # label(redefinition_k1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6184 (all A (l1_metric_1(A) & -v3_struct_0(A) -> v2_pre_topc(k5_pcomps_1(A)) & v1_pre_topc(k5_pcomps_1(A)) & -v3_struct_0(k5_pcomps_1(A)))) # label(fc4_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6185 (all A all B (-v1_xboole_0(A) & m1_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_1(B) -> -v3_struct_0(k6_pcomps_1(A,B)) & v1_metric_1(k6_pcomps_1(A,B)) & v9_metric_1(k6_pcomps_1(A,B)) & l1_metric_1(k6_pcomps_1(A,B)) & v8_metric_1(k6_pcomps_1(A,B)) & v7_metric_1(k6_pcomps_1(A,B)) & v6_metric_1(k6_pcomps_1(A,B)))) # label(dt_k6_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6186 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_finset_1(B) -> k6_pre_topc(A,k5_setfam_1(u1_struct_0(A),B)) = k5_setfam_1(u1_struct_0(A),k3_pcomps_1(A,B))))))) # label(t19_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6187 (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)))) -> (k1_xboole_0 = B -> k3_pcomps_1(A,B) = k1_xboole_0))))) # label(t15_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6188 (all A (-v1_xboole_0(A) -> v1_pre_topc(k2_pcomps_1(A)) & v2_pre_topc(k2_pcomps_1(A)) & -v3_struct_0(k2_pcomps_1(A)))) # label(fc2_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6189 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (exists C (-r1_xreal_0(C,np__0) & r1_tarski(k9_metric_1(A,B,C),u1_struct_0(A)) & m1_subset_1(C,k1_numbers))))))) # label(t29_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6190 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_pcomps_1(B,A) -> k5_setfam_1(u1_struct_0(A),k3_pcomps_1(A,B)) = k6_pre_topc(A,k5_setfam_1(u1_struct_0(A),B))))))) # label(t23_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6191 (all A k2_pcomps_1(A) = g1_pre_topc(A,k1_pcomps_1(A))) # label(d1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6192 (all A (l1_metric_1(A) -> v2_pre_topc(g1_pre_topc(u1_struct_0(A),k4_pcomps_1(A))) & l1_pre_topc(g1_pre_topc(u1_struct_0(A),k4_pcomps_1(A))))) # label(t37_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6193 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v2_tops_2(B,A) & v1_pcomps_1(B,A) -> v4_pre_topc(k5_setfam_1(u1_struct_0(A),B),A)))))) # label(t24_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6194 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v3_compts_1(A) -> v4_pre_topc(k1_struct_0(A,B),A)))))) # label(t10_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6195 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (v2_pcomps_1(A) & v3_compts_1(A) -> v5_compts_1(A)))) # label(t28_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6196 (all A (l1_pre_topc(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(r1_pre_topc(A,B) & v1_tops_2(B,A) & (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(v1_tops_2(C,A) & v1_pcomps_1(C,A) & r1_setfam_1(C,B) & r1_pre_topc(A,C))))))) <-> v2_pcomps_1(A)))) # label(d4_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6197 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(a_3_1_pcomps_1(A,B,C),B))))))) # label(t11_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6198 (all A v2_compts_1(k2_pcomps_1(k1_tarski(A)))) # label(t9_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6199 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(k1_xboole_0 != B & k1_xboole_0 = k6_pre_topc(A,B)) & -(k1_xboole_0 = B & k1_xboole_0 != k6_pre_topc(A,B)))))) # label(t2_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6200 (exists A (l1_pre_topc(A) & v2_pre_topc(A) & v2_pcomps_1(A) & -v3_struct_0(A))) # label(rc1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6201 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v1_xreal_0(C) -> (v9_metric_1(A) -> r2_hidden(k9_metric_1(A,B,C),k4_pcomps_1(A))))))))) # label(t33_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6202 (all A (l1_metric_1(A) -> r2_hidden(u1_struct_0(A),k4_pcomps_1(A)))) # label(t34_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6203 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers) & m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) -> (r1_pcomps_1(A,B) <-> v7_metric_1(g1_metric_1(A,B)) & v9_metric_1(g1_metric_1(A,B)) & l1_metric_1(g1_metric_1(A,B)) & v8_metric_1(g1_metric_1(A,B)) & v6_metric_1(g1_metric_1(A,B))))) # label(t39_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6204 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_pcomps_1(B,A) -> v1_pcomps_1(k3_pcomps_1(A,B),A)))))) # label(t21_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6205 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (C = k1_tarski(B) -> k3_pcomps_1(A,C) = k1_tarski(k6_pre_topc(A,B))))))))) # label(t16_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6206 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & r2_hidden(C,D) & v3_pre_topc(D,A) & v1_finset_1(a_3_0_pcomps_1(A,B,D)))))) <-> v1_pcomps_1(B,A)))))) # label(d2_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6207 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (v3_pcomps_1(A) <-> (exists B (u1_pre_topc(A) = k4_pcomps_1(k6_pcomps_1(u1_struct_0(A),B)) & r1_pcomps_1(u1_struct_0(A),B) & m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_numbers) & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_numbers) & v1_funct_1(B)))))) # label(d9_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6208 (all A (l1_metric_1(A) -> v1_pre_topc(k5_pcomps_1(A)) & v2_pre_topc(k5_pcomps_1(A)))) # label(fc3_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6209 (all A (-v1_xboole_0(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers) & m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_1(B) -> (r1_pcomps_1(A,B) -> g1_metric_1(A,B) = k6_pcomps_1(A,B)))))) # label(d8_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6210 (all A (l1_metric_1(A) -> l1_pre_topc(k5_pcomps_1(A)))) # label(dt_k5_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6211 (all A (-v3_struct_0(A) & v7_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) & v8_metric_1(A) & v6_metric_1(A) -> v3_compts_1(k5_pcomps_1(A)))) # label(t38_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6212 (all A m1_subset_1(k1_pcomps_1(A),k1_zfmisc_1(k1_zfmisc_1(A)))) # label(dt_k1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6213 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(v4_pre_topc(B,A) & r1_xboole_0(B,C) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_tarski(B,D) & r1_tarski(C,E) & r1_xboole_0(D,E) & v3_pre_topc(E,A) & v3_pre_topc(D,A)))))) & (all D (m1_subset_1(D,u1_struct_0(A)) -> -((all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (all F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(E,A) & r1_tarski(B,E) & r1_xboole_0(E,F) & r2_hidden(D,F) & v3_pre_topc(F,A)))))) & r2_hidden(D,C)))) & v4_pre_topc(C,A) & v2_pcomps_1(A)))))))) # label(t26_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6214 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (v2_pcomps_1(A) & v3_compts_1(A) -> v4_compts_1(A)))) # label(t27_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6215 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (v1_xreal_0(D) -> -(v9_metric_1(A) & r2_hidden(B,k9_metric_1(A,C,D)) & (all E (m1_subset_1(E,k1_numbers) -> -(r1_tarski(k9_metric_1(A,B,E),k9_metric_1(A,C,D)) & -r1_xreal_0(E,np__0))))))))))))) # label(t30_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6216 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> r1_tarski(k5_setfam_1(u1_struct_0(A),B),k5_setfam_1(u1_struct_0(A),k3_pcomps_1(A,B))))))) # label(t22_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6217 (all A all B all C all D (v2_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & l1_pre_topc(B) & -v3_struct_0(B) -> ((exists E (E = A & r2_hidden(E,C) & -r1_xboole_0(E,D) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))))) <-> r2_hidden(A,a_3_1_pcomps_1(B,C,D))))) # label(fraenkel_a_3_1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6218 $T # label(t32_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6219 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> v2_tops_2(k3_pcomps_1(A,B),A))))) # label(t14_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6220 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_pre_topc(A,B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & r2_hidden(C,D) & r2_hidden(D,B)))))))))) # label(t5_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6221 (exists A (l1_pre_topc(A) & v2_pre_topc(A) & v3_pcomps_1(A) & v1_pre_topc(A) & -v3_struct_0(A))) # label(rc3_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6222 (all A (m1_subset_1(A,k1_zfmisc_1(u1_struct_0(f1_s1_pcomps_1))) -> (r2_hidden(A,f2_s1_pcomps_1) -> r2_hidden(f4_s1_pcomps_1(A),f3_s1_pcomps_1)))) -> (exists A (v1_funct_1(A) & v1_funct_2(A,f2_s1_pcomps_1,f3_s1_pcomps_1) & m2_relset_1(A,f2_s1_pcomps_1,f3_s1_pcomps_1) & (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s1_pcomps_1))) -> (r2_hidden(B,f2_s1_pcomps_1) -> f4_s1_pcomps_1(B) = k1_funct_1(A,B)))))) # label(s1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6223 (exists A (l1_pre_topc(A) & v1_pre_topc(A) & v3_compts_1(A) & v2_pre_topc(A) & -v3_struct_0(A))) # label(rc2_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6224 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(B,k4_pcomps_1(A)) -> r2_hidden(k5_setfam_1(u1_struct_0(A),B),k4_pcomps_1(A))))))) # label(t36_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6225 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (all F (m1_subset_1(F,u1_struct_0(A)) -> -(r2_hidden(D,k5_subset_1(u1_struct_0(A),k9_metric_1(A,E,B),k9_metric_1(A,F,C))) & (all G (m1_subset_1(G,k1_numbers) -> -(r1_tarski(k9_metric_1(A,D,G),k9_metric_1(A,E,B)) & r1_tarski(k9_metric_1(A,D,G),k9_metric_1(A,F,C))))) & v9_metric_1(A)))))))))))))) # label(t31_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6226 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (B = k4_pcomps_1(A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> -((all E (m1_subset_1(E,k1_numbers) -> -(-r1_xreal_0(E,np__0) & r1_tarski(k9_metric_1(A,D,E),C)))) & r2_hidden(D,C)))) <-> r2_hidden(C,B))))))))) # label(d5_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6227 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> r1_setfam_1(B,k3_pcomps_1(A,B)))))) # label(t20_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6228 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,k4_pcomps_1(A)) & r2_hidden(C,k4_pcomps_1(A)) -> r2_hidden(k5_subset_1(u1_struct_0(A),B,C),k4_pcomps_1(A))))))))) # label(t35_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6229 (all A l1_pre_topc(k2_pcomps_1(A))) # label(dt_k2_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6230 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & l1_pre_topc(A) -> m1_subset_1(k3_pcomps_1(A,B),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))) # label(dt_k3_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6231 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(D,C) <-> (exists E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & k6_pre_topc(A,E) = D & r2_hidden(E,B)))))) <-> C = k3_pcomps_1(A,B)))))))) # label(d3_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6232 (all A (l1_metric_1(A) -> k5_pcomps_1(A) = g1_pre_topc(u1_struct_0(A),k4_pcomps_1(A)))) # label(d6_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6233 (all A A = u1_struct_0(k2_pcomps_1(A))) # label(t8_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6234 (all A (l1_metric_1(A) -> m1_subset_1(k4_pcomps_1(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))) # label(dt_k4_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6235 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(B,C) -> r1_tarski(k3_pcomps_1(A,B),k3_pcomps_1(A,C))))))))) # label(t17_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6236 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (v2_compts_1(A) -> v2_pcomps_1(A)))) # label(t25_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6237 (all A all B all C all D (l1_pre_topc(B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) -> ((exists E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & E = A & -r1_xboole_0(E,D) & r2_hidden(E,C))) <-> r2_hidden(A,a_3_0_pcomps_1(B,C,D))))) # label(fraenkel_a_3_0_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6238 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers) & m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_1(B) -> (r1_pcomps_1(A,B) <-> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (C = D -> k1_metric_1(A,A,B,C,D) = np__0) & r1_xreal_0(k1_metric_1(A,A,B,C,E),k3_real_1(k1_metric_1(A,A,B,C,D),k1_metric_1(A,A,B,D,E))) & k1_metric_1(A,A,B,C,D) = k1_metric_1(A,A,B,D,C) & (k1_metric_1(A,A,B,C,D) = np__0 -> C = D)))))))))) # label(d7_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6239 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_finset_1(B) -> v1_pcomps_1(B,A)))))) # label(t13_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6240 (all A (v2_pre_topc(k2_pcomps_1(A)) & v1_pre_topc(k2_pcomps_1(A)))) # label(fc1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6241 $T # label(t3_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6242 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> k3_pcomps_1(A,k4_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C)) = k4_subset_1(k1_zfmisc_1(u1_struct_0(A)),k3_pcomps_1(A,B),k3_pcomps_1(A,C)))))))) # label(t18_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6243 $T # label(t4_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6244 (all A k1_pcomps_1(A) = u1_pre_topc(k2_pcomps_1(A))) # label(t7_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6245 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(B,C) & v1_pcomps_1(C,A) -> v1_pcomps_1(B,A)))))))) # label(t12_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6246 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(C,D) -> r1_tarski(k9_metric_1(A,B,C),k9_metric_1(A,B,D))))))))))) # label(t1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6247 $T # label(t6_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6248 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) & m1_eqrel_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(k16_borsuk_1(A,B))) -> (exists D (C = k8_funct_2(u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,B)),k17_borsuk_1(A,B),D) & m1_subset_1(D,u1_struct_0(A)))))))))) # label(t71_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6249 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v1_xboole_0(B) & m1_eqrel_1(B,u1_struct_0(A)) -> (m1_borsuk_1(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> (all D (m2_connsp_2(D,A,C) -> (exists E (v3_pre_topc(E,A) & r1_tarski(E,D) & (all F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(F,B) -> r1_xboole_0(F,E) | r1_tarski(F,E)))) & r1_tarski(C,E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))))))))))))))) # label(d13_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6250 (all A all B all C (l1_struct_0(A) & -v3_struct_0(B) & m1_subset_1(C,u1_struct_0(B)) & l1_struct_0(B) -> v1_funct_2(k3_borsuk_1(A,B,C),u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(k3_borsuk_1(A,B,C),u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(k3_borsuk_1(A,B,C)))) # label(dt_k3_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6251 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v1_xboole_0(C) & m1_eqrel_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(k8_funct_2(u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,k18_borsuk_1(A,B,C))),k17_borsuk_1(A,k18_borsuk_1(A,B,C)),D),u1_struct_0(k16_borsuk_1(B,C))) -> r2_hidden(D,u1_struct_0(B))))))))))) # label(t79_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6252 (all A all B all C all D (v1_funct_2(C,k1_pcomps_1(A),k1_pcomps_1(B)) & m1_relset_1(C,k1_pcomps_1(A),k1_pcomps_1(B)) & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) & v1_funct_1(C) -> m1_subset_1(k14_borsuk_1(A,B,C,D),k1_zfmisc_1(k1_zfmisc_1(B))))) # label(dt_k14_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6253 (all A all B all C (m1_subset_1(C,A) & -v1_xboole_0(A) -> v1_funct_1(k1_borsuk_1(A,B,C)) & v1_funct_2(k1_borsuk_1(A,B,C),B,A) & m2_relset_1(k1_borsuk_1(A,B,C),B,A))) # label(dt_k1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6254 (all A all B all C (-v3_struct_0(A) & l1_pre_topc(A) & -v3_struct_0(B) & m1_borsuk_1(C,B) & m1_pre_topc(B,A) & v1_borsuk_1(B,A) & v2_pre_topc(A) -> m1_borsuk_1(k19_borsuk_1(A,B,C),A))) # label(dt_k19_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6255 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k1_borsuk_1(u1_struct_0(B),u1_struct_0(A),C) = k3_borsuk_1(A,B,C))))))) # label(d3_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6256 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & v1_borsuk_1(B,A) & -v3_struct_0(B) -> (all C (v2_borsuk_1(C,B) & m1_borsuk_1(C,B) -> (r1_borsuk_1(A,B) -> r1_borsuk_1(k16_borsuk_1(A,k20_borsuk_1(A,B,C)),k21_borsuk_1(A,B,C))))))))) # label(t84_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6257 (all A all B (l1_pre_topc(A) & l1_pre_topc(B) & v2_pre_topc(B) & v2_pre_topc(A) -> l1_pre_topc(k6_borsuk_1(A,B)) & v2_pre_topc(k6_borsuk_1(A,B)) & v1_pre_topc(k6_borsuk_1(A,B)))) # label(dt_k6_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6258 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v1_xboole_0(C) & m1_eqrel_1(C,u1_struct_0(B)) -> (all D (r2_hidden(D,u1_struct_0(B)) -> r2_hidden(k1_funct_1(k17_borsuk_1(A,k18_borsuk_1(A,B,C)),D),u1_struct_0(k16_borsuk_1(B,C))))))))))) # label(t80_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6259 (all A all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) -> k2_funct_2(A,B,C,k5_setfam_1(A,D)) = k5_setfam_1(B,k2_funct_2(k1_zfmisc_1(A),k1_zfmisc_1(B),k2_funct_3(A,B,C),D)))))))) # label(t16_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6260 (all A all B all C (v2_pre_topc(B) & l1_pre_topc(B) & v2_pre_topc(C) & l1_pre_topc(C) -> ((exists D exists E (r2_hidden(E,u1_pre_topc(C)) & r2_hidden(D,u1_pre_topc(B)) & k12_mcart_1(u1_struct_0(B),u1_struct_0(C),D,E) = A & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))))) <-> r2_hidden(A,a_2_1_borsuk_1(B,C))))) # label(fraenkel_a_2_1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6261 (all A all B all C all D all E (-v3_struct_0(A) & v2_pre_topc(B) & l1_pre_topc(C) & v5_pre_topc(D,A,B) & m1_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C)) & v5_pre_topc(E,B,C) & m1_relset_1(E,u1_struct_0(B),u1_struct_0(C)) & v1_funct_1(E) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(D) & v2_pre_topc(C) & -v3_struct_0(C) & l1_pre_topc(B) & -v3_struct_0(B) & l1_pre_topc(A) & v2_pre_topc(A) -> v1_funct_1(k4_borsuk_1(A,B,C,D,E)) & v1_funct_2(k4_borsuk_1(A,B,C,D,E),u1_struct_0(A),u1_struct_0(C)) & v5_pre_topc(k4_borsuk_1(A,B,C,D,E),A,C) & m2_relset_1(k4_borsuk_1(A,B,C,D,E),u1_struct_0(A),u1_struct_0(C)))) # label(dt_k4_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6262 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(B)) -> (k1_xboole_0 != k12_mcart_1(A,B,C,D) -> k2_funct_2(k2_zfmisc_1(A,B),A,k9_funct_3(A,B),k12_mcart_1(A,B,C,D)) = C & k2_funct_2(k2_zfmisc_1(A,B),B,k10_funct_3(A,B),k12_mcart_1(A,B,C,D)) = D))))) # label(t12_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6263 (all A all B (v2_pre_topc(A) & l1_pre_topc(A) & m1_eqrel_1(B,u1_struct_0(A)) -> v2_pre_topc(k16_borsuk_1(A,B)) & l1_pre_topc(k16_borsuk_1(A,B)) & v1_pre_topc(k16_borsuk_1(A,B)))) # label(dt_k16_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6264 $T # label(t1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6265 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) & -v3_struct_0(B) -> k13_borsuk_1(A,B) = k2_funct_3(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B),k10_funct_3(u1_struct_0(A),u1_struct_0(B))))))) # label(d8_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6266 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (exists B (m1_pre_topc(B,A) & v2_pre_topc(B) & v1_borsuk_1(B,A) & v1_pre_topc(B) & -v3_struct_0(B))))) # label(rc4_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6267 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> m1_borsuk_1(k15_borsuk_1(A),A))) # label(t82_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6268 $T # label(t8_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6269 (all A all B all C all D all E (-v3_struct_0(A) & v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(C) & v2_pre_topc(C) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(D,A,B) & m1_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C)) & m1_relset_1(E,u1_struct_0(B),u1_struct_0(C)) & v5_pre_topc(E,B,C) & v1_funct_1(D) & l1_pre_topc(C) & -v3_struct_0(B) & l1_pre_topc(A) & v2_pre_topc(A) -> k4_borsuk_1(A,B,C,D,E) = k5_relat_1(D,E))) # label(redefinition_k4_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6270 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> k11_borsuk_1(A,B,C) = a_3_1_borsuk_1(A,B,C))))))) # label(d6_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6271 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_eqrel_1(C,u1_struct_0(B)) & -v1_xboole_0(C) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (-r2_hidden(D,u1_struct_0(B)) -> k8_funct_2(u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,k18_borsuk_1(A,B,C))),k17_borsuk_1(A,k18_borsuk_1(A,B,C)),D) = k1_struct_0(A,D)))))))))) # label(t77_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6272 (all A all B all C (v2_pre_topc(A) & m1_pre_topc(B,A) & -v1_xboole_0(C) & m1_eqrel_1(C,u1_struct_0(B)) & -v3_struct_0(B) & l1_pre_topc(A) & -v3_struct_0(A) -> m1_eqrel_1(k18_borsuk_1(A,B,C),u1_struct_0(A)) & -v1_xboole_0(k18_borsuk_1(A,B,C)))) # label(dt_k18_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6273 (all A all B (m1_eqrel_1(B,u1_struct_0(A)) & -v1_xboole_0(B) & l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> m2_relset_1(k17_borsuk_1(A,B),u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,B))) & v5_pre_topc(k17_borsuk_1(A,B),A,k16_borsuk_1(A,B)) & v1_funct_2(k17_borsuk_1(A,B),u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,B))) & v1_funct_1(k17_borsuk_1(A,B)))) # label(dt_k17_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6274 (all A (-v1_xboole_0(A) -> (all B (m1_eqrel_1(B,A) & -v1_xboole_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(B)) -> k3_tarski(C) = k3_funct_2(A,B,k2_borsuk_1(A,B),C))))))) # label(t31_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6275 (all A (-v3_struct_0(A) & l1_struct_0(A) -> v1_setfam_1(k15_borsuk_1(A)) & -v1_xboole_0(k15_borsuk_1(A)))) # label(fc3_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6276 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_connsp_2(E,A,C) -> (all F (m1_connsp_2(F,B,D) -> m1_connsp_2(k7_borsuk_1(A,B,E,F),k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D)))))))))))))) # label(t48_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6277 (all A all B (l1_pre_topc(A) & m1_eqrel_1(B,u1_struct_0(A)) & -v1_xboole_0(B) & v2_pre_topc(A) & -v3_struct_0(A) -> v1_pre_topc(k16_borsuk_1(A,B)) & v2_pre_topc(k16_borsuk_1(A,B)) & -v3_struct_0(k16_borsuk_1(A,B)))) # label(fc4_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6278 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_eqrel_1(B,u1_struct_0(A)) -> (all C (v2_pre_topc(C) & l1_pre_topc(C) & v1_pre_topc(C) -> (a_2_2_borsuk_1(A,B) = u1_pre_topc(C) & B = u1_struct_0(C) <-> C = k16_borsuk_1(A,B)))))))) # label(d10_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6279 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l1_pre_topc(B) & v2_pre_topc(B) -> k2_funct_3(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(A),k9_funct_3(u1_struct_0(A),u1_struct_0(B))) = k12_borsuk_1(A,B))))) # label(d7_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6280 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) -> -(r1_tarski(C,k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(A),k12_borsuk_1(A,B),D)) & (all E (m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) -> -(r1_tarski(E,D) & C = k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(A),k12_borsuk_1(A,B),E) & v1_finset_1(E)))) & v1_finset_1(C)))))))))) # label(t64_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6281 (all A all B all C (m1_eqrel_1(C,u1_struct_0(B)) & l1_pre_topc(B) & v2_pre_topc(B) -> (r2_hidden(A,a_2_2_borsuk_1(B,C)) <-> (exists D (m1_subset_1(D,k1_zfmisc_1(C)) & r2_hidden(k3_tarski(D),u1_pre_topc(B)) & D = A))))) # label(fraenkel_a_2_2_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6282 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(A,B)))) -> ((all E (r2_hidden(E,D) -> r1_tarski(E,C) & (exists F ((exists G (m1_subset_1(G,k1_zfmisc_1(B)) & k12_mcart_1(A,B,F,G) = E)) & m1_subset_1(F,k1_zfmisc_1(A)))))) -> r1_tarski(k2_zfmisc_1(k3_tarski(k9_relat_1(k1_funct_3(k9_funct_3(A,B)),D)),k1_setfam_1(k9_relat_1(k1_funct_3(k10_funct_3(A,B)),D))),C)))))) # label(t14_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6283 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> -v1_xboole_0(k8_eqrel_1(A,B)))))) # label(t28_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6284 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> k3_tarski(k5_setfam_1(A,B)) = k3_tarski(a_2_0_borsuk_1(A,B)))) # label(t17_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6285 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,C) -> k1_domain_1(B,C,k8_funct_2(A,B,D,E),F) = k8_funct_2(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C),k16_funct_3(A,C,B,C,D,k6_partfun1(C)),k1_domain_1(A,C,E,F)))))))))))))) # label(t21_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6286 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v3_pre_topc(D,B) & v3_pre_topc(C,A) -> v3_pre_topc(k7_borsuk_1(A,B,C,D),k6_borsuk_1(A,B))))))))))) # label(t46_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6287 (all A all B all C all D (v1_funct_2(C,k1_pcomps_1(A),k1_pcomps_1(B)) & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) & m1_relset_1(C,k1_pcomps_1(A),k1_pcomps_1(B)) & v1_funct_1(C) -> k14_borsuk_1(A,B,C,D) = k9_relat_1(C,D))) # label(redefinition_k14_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6288 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) -> (all D -((all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> -(k2_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B),k10_funct_3(u1_struct_0(A),u1_struct_0(B)),E) = D & r2_hidden(E,C)))) & r2_hidden(D,k2_funct_2(k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(B)),k13_borsuk_1(A,B),C)))))))))) # label(t58_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6289 $T # label(t2_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6290 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (exists B m1_borsuk_1(B,A)))) # label(existence_m1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6291 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) & m1_eqrel_1(B,u1_struct_0(A)) -> k2_borsuk_1(u1_struct_0(A),B) = k17_borsuk_1(A,B))))) # label(d11_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6292 (all A all B (v2_pre_topc(A) & l1_pre_topc(A) & v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) & -v3_struct_0(A) -> v1_funct_1(k13_borsuk_1(A,B)) & v1_funct_2(k13_borsuk_1(A,B),k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(B))) & m2_relset_1(k13_borsuk_1(A,B),k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(B))))) # label(dt_k13_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6293 $T # label(t43_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6294 (all A all B all C all D (v2_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & l1_pre_topc(B) & l1_pre_topc(A) & v2_pre_topc(A) -> m1_subset_1(k7_borsuk_1(A,B,C,D),k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))))) # label(dt_k7_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6295 (all A all B all C all D all E all F (l1_pre_topc(A) & -v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(B)) & m1_connsp_2(E,A,C) & m1_connsp_2(F,B,D) & v2_pre_topc(A) & -v3_struct_0(A) -> k9_borsuk_1(A,B,C,D,E,F) = k2_zfmisc_1(E,F))) # label(redefinition_k9_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6296 (all A all B (-v1_xboole_0(B) & m1_eqrel_1(B,A) & -v1_xboole_0(A) -> m2_relset_1(k2_borsuk_1(A,B),A,B) & v1_funct_2(k2_borsuk_1(A,B),A,B) & v1_funct_1(k2_borsuk_1(A,B)))) # label(dt_k2_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6297 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -((all C (m1_subset_1(C,u1_struct_0(A)) -> B != k1_struct_0(A,C))) & r2_hidden(B,k15_borsuk_1(A))))))) # label(t68_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6298 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) -> (r1_compts_1(k6_borsuk_1(A,B),C,k7_borsuk_1(A,B,D,E)) -> (k1_xboole_0 != D -> r1_compts_1(B,k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(B),k13_borsuk_1(A,B),C),E)) & (E != k1_xboole_0 -> r1_compts_1(A,k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(A),k12_borsuk_1(A,B),C),D))))))))))))) # label(t62_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6299 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(B) = C -> v4_pre_topc(C,A)))) <-> v1_borsuk_1(B,A)))))) # label(d14_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6300 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -((all E (m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(r1_tarski(E,C) & (all F -(r1_xboole_0(F,D) & r2_hidden(F,E))) & r1_compts_1(A,E,D)))) & r1_compts_1(A,C,D)))))))))) # label(t63_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6301 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,C) -> k12_mcart_1(A,C,k3_funct_2(A,B,D,k6_domain_1(B,E)),k6_domain_1(C,F)) = k3_funct_2(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C),k16_funct_3(A,C,B,C,D,k6_partfun1(C)),k6_domain_1(k2_zfmisc_1(B,C),k1_domain_1(B,C,E,F))))))))))))))) # label(t24_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6302 (all A (l1_struct_0(A) -> m1_eqrel_1(k15_borsuk_1(A),u1_struct_0(A)))) # label(dt_k15_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6303 (all A (l1_struct_0(A) -> k8_eqrel_1(u1_struct_0(A),k6_partfun1(u1_struct_0(A))) = k15_borsuk_1(A))) # label(d9_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6304 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) & -v3_struct_0(B) -> k1_funct_1(k13_borsuk_1(A,B),k1_xboole_0) = k1_xboole_0 & k1_xboole_0 = k1_funct_1(k12_borsuk_1(A,B),k1_xboole_0))))) # label(t66_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.77 6305 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> v1_tops_2(k11_borsuk_1(A,B,C),k6_borsuk_1(A,B)))))))) # label(t51_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6306 (all A (l1_pre_topc(A) -> (A = k22_borsuk_1 <-> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(k8_metric_1)))) -> (B = k1_rcomp_1(np__0,np__1) -> A = k3_pre_topc(k5_pcomps_1(k8_metric_1),B))))))) # label(d16_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6307 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (v1_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)) -> (r2_hidden(D,u1_struct_0(B)) -> k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D) = D))) <-> v3_borsuk_1(C,A,B)))))))) # label(d19_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6308 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(B)) -> (k1_xboole_0 != k12_mcart_1(A,B,C,D) -> D = k1_funct_1(k1_funct_3(k10_funct_3(A,B)),k12_mcart_1(A,B,C,D)) & C = k1_funct_1(k1_funct_3(k9_funct_3(A,B)),k12_mcart_1(A,B,C,D))))))) # label(t13_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6309 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_eqrel_1(B,u1_struct_0(A)) & -v1_xboole_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r2_hidden(C,k8_funct_2(u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,B)),k17_borsuk_1(A,B),C)))))))) # label(t70_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6310 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) -> (r2_hidden(A,a_2_0_borsuk_1(B,C)) <-> (exists D (m1_subset_1(D,k1_zfmisc_1(B)) & r2_hidden(D,C) & k3_tarski(D) = A))))) # label(fraenkel_a_2_0_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6311 (all A all B all C r1_tarski(k9_relat_1(k2_funcop_1(A,B),C),k1_tarski(B))) # label(t6_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6312 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> (v3_pre_topc(C,k6_borsuk_1(A,B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) -> (k2_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(A),k9_funct_3(u1_struct_0(A),u1_struct_0(B)),C) = D -> v3_pre_topc(D,A)) & (E = k2_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B),k10_funct_3(u1_struct_0(A),u1_struct_0(B)),C) -> v3_pre_topc(E,B))))))))))))) # label(t59_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6313 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_eqrel_1(B,u1_struct_0(A)) & -v1_xboole_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(B)) -> (r2_hidden(C,u1_pre_topc(k16_borsuk_1(A,B))) <-> r2_hidden(k3_tarski(C),u1_pre_topc(A))))))))) # label(t69_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6314 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_borsuk_1(B,A) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> v6_compts_1(C,A)))) <-> v2_borsuk_1(B,A)))))) # label(d15_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6315 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) & m1_eqrel_1(B,u1_struct_0(A)) -> k2_relat_1(k17_borsuk_1(A,B)) = u1_struct_0(k16_borsuk_1(A,B)))))) # label(t72_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6316 (all A all B all C (r1_tarski(A,k2_zfmisc_1(B,C)) -> k2_funct_2(k2_zfmisc_1(B,C),B,k9_funct_3(B,C),A) = k1_funct_1(k1_funct_3(k9_funct_3(B,C)),A))) # label(t9_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6317 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> ((exists C (v1_funct_1(C) & (all D (m1_subset_1(D,u1_struct_0(A)) -> k8_funct_2(u1_struct_0(k6_borsuk_1(A,k22_borsuk_1)),u1_struct_0(A),C,k8_borsuk_1(A,k22_borsuk_1,D,k23_borsuk_1)) = D & r2_hidden(k8_funct_2(u1_struct_0(k6_borsuk_1(A,k22_borsuk_1)),u1_struct_0(A),C,k8_borsuk_1(A,k22_borsuk_1,D,k24_borsuk_1)),u1_struct_0(B)) & (r2_hidden(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(k22_borsuk_1)) -> D = k8_funct_2(u1_struct_0(k6_borsuk_1(A,k22_borsuk_1)),u1_struct_0(A),C,k8_borsuk_1(A,k22_borsuk_1,D,E))))))) & m2_relset_1(C,u1_struct_0(k6_borsuk_1(A,k22_borsuk_1)),u1_struct_0(A)) & v5_pre_topc(C,k6_borsuk_1(A,k22_borsuk_1),A) & v1_funct_2(C,u1_struct_0(k6_borsuk_1(A,k22_borsuk_1)),u1_struct_0(A)))) <-> r2_borsuk_1(A,B)))))) # label(d21_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6318 (all A (-v1_xboole_0(A) -> (all B (m1_eqrel_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (k3_tarski(C) = D -> k3_subset_1(A,D) = k3_tarski(k3_subset_1(B,C))))))))))) # label(t27_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6319 (all A all B (v2_pre_topc(A) & v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) & l1_pre_topc(A) & -v3_struct_0(A) -> (exists C (m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_relat_1(C) & v1_partfun1(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) & -v1_xboole_0(C))))) # label(rc2_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6320 $T # label(t34_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6321 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m2_connsp_2(D,A,C) -> (r1_tarski(B,C) -> m2_connsp_2(D,A,B)))))))))) # label(t39_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6322 (all A all B all C all D (l1_pre_topc(A) & -v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(C,u1_struct_0(A)) & v2_pre_topc(A) & -v3_struct_0(A) -> m1_subset_1(k8_borsuk_1(A,B,C,D),u1_struct_0(k6_borsuk_1(A,B))))) # label(dt_k8_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6323 (all A all B all C (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(B) & m1_pre_topc(B,A) & m1_borsuk_1(C,B) & v2_borsuk_1(C,B) & v1_borsuk_1(B,A) & -v3_struct_0(A) -> k18_borsuk_1(A,B,C) = k20_borsuk_1(A,B,C))) # label(redefinition_k20_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6324 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v1_xboole_0(C) & m1_eqrel_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (-r2_hidden(D,u1_struct_0(B)) -> r2_hidden(k1_struct_0(A,D),k18_borsuk_1(A,B,C))))))))))) # label(t75_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6325 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(k6_borsuk_1(A,B))) -> (exists D (m1_subset_1(D,u1_struct_0(A)) & (exists E (m1_subset_1(E,u1_struct_0(B)) & C = k8_borsuk_1(A,B,D,E))))))))))) # label(t50_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6326 (all A all B (m1_eqrel_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(B)) -> k3_xboole_0(k3_tarski(C),k3_tarski(D)) = k3_tarski(k5_subset_1(B,C,D)))))))) # label(t26_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6327 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v5_pre_topc(D,B,A) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(D) -> (all E (m1_connsp_2(E,A,C) -> m2_connsp_2(k5_pre_topc(B,A,D,E),B,k5_pre_topc(B,A,D,k1_struct_0(A,C))))))))))))) # label(t38_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6328 $T # label(t22_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6329 (all A all B (-v3_struct_0(A) & l1_pre_topc(A) & -v3_struct_0(B) & l1_pre_topc(B) & v2_pre_topc(B) & v2_pre_topc(A) -> m2_relset_1(k12_borsuk_1(A,B),k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(A))) & v1_funct_2(k12_borsuk_1(A,B),k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(A))) & v1_funct_1(k12_borsuk_1(A,B)))) # label(dt_k12_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6330 (all A all B all C all D all E all F (v2_pre_topc(A) & l1_pre_topc(A) & l1_pre_topc(B) & m1_connsp_2(E,A,C) & m1_connsp_2(F,B,D) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(C,u1_struct_0(A)) & v2_pre_topc(B) & -v3_struct_0(B) & -v3_struct_0(A) -> m1_connsp_2(k9_borsuk_1(A,B,C,D,E,F),k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D)))) # label(dt_k9_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6331 (all A all B all C all D (v2_pre_topc(B) & v2_pre_topc(C) & l1_pre_topc(C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(B,C)))) & l1_pre_topc(B) -> ((exists E exists F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(C))) & v3_pre_topc(F,C) & v3_pre_topc(E,B) & r1_tarski(k7_borsuk_1(B,C,E,F),D) & A = k7_borsuk_1(B,C,E,F) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))))) <-> r2_hidden(A,a_3_1_borsuk_1(B,C,D))))) # label(fraenkel_a_3_1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6332 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (m1_pre_topc(B,A) & v1_pre_topc(B) & v2_pre_topc(B) & v1_borsuk_1(B,A))))) # label(rc3_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6333 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_2(E,A,C) & m2_relset_1(E,A,C) & v1_funct_1(E) -> -((all F (v1_funct_1(F) & v1_funct_2(F,B,C) & m2_relset_1(F,B,C) -> k7_funct_2(A,B,C,D,F) != E)) & (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,A) -> (k8_funct_2(A,B,D,G) = k8_funct_2(A,B,D,F) -> k8_funct_2(A,C,E,G) = k8_funct_2(A,C,E,F))))))))))))))))) # label(t19_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6334 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) -> (all D -((all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> -(r2_hidden(E,C) & k2_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(A),k9_funct_3(u1_struct_0(A),u1_struct_0(B)),E) = D))) & r2_hidden(D,k2_funct_2(k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(A)),k12_borsuk_1(A,B),C)))))))))) # label(t57_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6335 (all A all B all C all D (-v3_struct_0(A) & v2_pre_topc(A) & -v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(B)) & l1_pre_topc(A) -> k8_borsuk_1(A,B,C,D) = k4_tarski(C,D))) # label(redefinition_k8_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6336 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> r1_tarski(u1_struct_0(B),u1_struct_0(A)))))) # label(t35_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6337 (all A all B all C all D all E all F (-v3_struct_0(A) & l1_pre_topc(A) & -v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_connsp_2(F,B,D) & m2_connsp_2(E,A,C) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v2_pre_topc(A) -> k10_borsuk_1(A,B,C,D,E,F) = k2_zfmisc_1(E,F))) # label(redefinition_k10_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6338 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_eqrel_1(C,u1_struct_0(B)) & -v1_xboole_0(C) -> k2_xboole_0(C,a_2_3_borsuk_1(A,B)) = k18_borsuk_1(A,B,C))))))) # label(d12_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6339 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_borsuk_1(B,A) -> (all C (m1_subset_1(C,u1_struct_0(k16_borsuk_1(A,B))) -> (all D (m2_connsp_2(D,A,k5_pre_topc(A,k16_borsuk_1(A,B),k17_borsuk_1(A,B),k1_struct_0(k16_borsuk_1(A,B),C))) -> m1_connsp_2(k4_pre_topc(A,k16_borsuk_1(A,B),k17_borsuk_1(A,B),D),k16_borsuk_1(A,B),C))))))))) # label(t81_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6340 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k3_funct_2(A,A,k6_partfun1(A),B) = B)) # label(t4_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6341 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (m1_subset_1(E,k1_zfmisc_1(A)) -> (all F (m1_subset_1(F,k1_zfmisc_1(C)) -> k12_mcart_1(B,C,k2_funct_2(A,B,D,E),F) = k2_funct_2(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C),k16_funct_3(A,C,B,C,D,k6_partfun1(C)),k12_mcart_1(A,C,E,F)))))))))))))) # label(t23_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6342 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(B)) -> m1_subset_1(k3_tarski(C),k1_zfmisc_1(A)))))))) # label(t25_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6343 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v1_xboole_0(C) & m1_eqrel_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -((all E (m1_subset_1(E,u1_struct_0(A)) -> -(D = k1_struct_0(A,E) & -r2_hidden(E,k2_pre_topc(B))))) & -r2_hidden(D,C) & r2_hidden(D,k18_borsuk_1(A,B,C))))))))))) # label(t74_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6344 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & m1_eqrel_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m2_subset_1(D,k1_zfmisc_1(A),B) -> (r2_hidden(C,D) -> D = k8_funct_2(A,B,k2_borsuk_1(A,B),C)))))))))) # label(t29_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6345 $T # label(t40_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6346 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(A,B)))) -> ((all E (r2_hidden(E,D) -> (exists F (m1_subset_1(F,k1_zfmisc_1(A)) & (exists G (m1_subset_1(G,k1_zfmisc_1(B)) & E = k12_mcart_1(A,B,F,G))))) & r1_tarski(E,C))) -> r1_tarski(k2_zfmisc_1(k1_setfam_1(k9_relat_1(k1_funct_3(k9_funct_3(A,B)),D)),k3_tarski(k9_relat_1(k1_funct_3(k10_funct_3(A,B)),D))),C)))))) # label(t15_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6347 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) -> ((all E (r2_hidden(E,D) -> (exists F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) & (exists G (m1_subset_1(G,k1_zfmisc_1(u1_struct_0(B))) & E = k7_borsuk_1(A,B,F,G))))) & r1_tarski(E,C))) -> r1_tarski(k7_borsuk_1(A,B,k5_setfam_1(u1_struct_0(A),k2_funct_2(k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(A)),k12_borsuk_1(A,B),D)),k6_setfam_1(u1_struct_0(B),k2_funct_2(k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(B)),k13_borsuk_1(A,B),D))),C)))))))))) # label(t56_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6348 (all A all B (-v3_struct_0(A) & l1_pre_topc(B) & v2_pre_topc(B) & -v3_struct_0(B) & l1_pre_topc(A) & v2_pre_topc(A) -> v1_pre_topc(k6_borsuk_1(A,B)) & v2_pre_topc(k6_borsuk_1(A,B)) & -v3_struct_0(k6_borsuk_1(A,B)))) # label(fc2_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6349 $T # label(t7_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6350 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k5_setfam_1(A,B) = A -> (all C (m1_subset_1(C,k1_zfmisc_1(B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (k3_tarski(C) = D -> r1_tarski(k3_subset_1(A,D),k3_tarski(k3_subset_1(B,C))))))))))) # label(t18_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6351 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_eqrel_1(C,u1_struct_0(B)) & -v1_xboole_0(C) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (k8_funct_2(u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,k18_borsuk_1(A,B,C))),k17_borsuk_1(A,k18_borsuk_1(A,B,C)),D) = k8_funct_2(u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,k18_borsuk_1(A,B,C))),k17_borsuk_1(A,k18_borsuk_1(A,B,C)),E) -> E = D | r2_hidden(D,u1_struct_0(B))))))))))))) # label(t78_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6352 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (v1_pre_topc(C) & v2_pre_topc(C) & l1_pre_topc(C) -> (k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)) = u1_struct_0(C) & a_3_0_borsuk_1(A,B,C) = u1_pre_topc(C) <-> k6_borsuk_1(A,B) = C))))))) # label(d5_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6353 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v6_compts_1(D,B) -> (all E (m2_connsp_2(E,k6_borsuk_1(B,A),k7_borsuk_1(B,A,D,k1_struct_0(A,C))) -> (exists F ((exists G (m1_connsp_2(G,A,C) & r1_tarski(k10_borsuk_1(B,A,D,C,F,G),E))) & m2_connsp_2(F,B,D)))))))))))))) # label(t67_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6354 (all A all B all C (l1_pre_topc(A) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) & v2_pre_topc(B) & v2_pre_topc(A) -> m1_subset_1(k11_borsuk_1(A,B,C),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))))) # label(dt_k11_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6355 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> k7_borsuk_1(A,B,k1_tops_1(A,C),k1_tops_1(B,D)) = k1_tops_1(k6_borsuk_1(A,B),k7_borsuk_1(A,B,C,D)))))))))) # label(t47_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6356 $T # label(t11_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6357 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (D = C -> (v6_compts_1(D,B) <-> v6_compts_1(C,A))))))))))) # label(t42_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6358 (all A all B all C all D (v2_pre_topc(B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(B) & l1_pre_topc(A) & v2_pre_topc(A) -> k2_zfmisc_1(C,D) = k7_borsuk_1(A,B,C,D))) # label(redefinition_k7_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6359 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v1_xboole_0(C) & m1_eqrel_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,u1_struct_0(B)) -> k1_funct_1(k17_borsuk_1(B,C),D) = k8_funct_2(u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,k18_borsuk_1(A,B,C))),k17_borsuk_1(A,k18_borsuk_1(A,B,C)),D)))))))))) # label(t76_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6360 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & m1_eqrel_1(B,A) -> (all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> ((all D (m1_subset_1(D,A) -> r2_hidden(D,k8_funct_2(A,B,C,D)))) <-> k2_borsuk_1(A,B) = C))))))) # label(d1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6361 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & m1_eqrel_1(B,A) -> (all C (m2_subset_1(C,k1_zfmisc_1(A),B) -> k3_funct_2(A,B,k2_borsuk_1(A,B),k6_domain_1(B,C)) = C)))))) # label(t30_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6362 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (k1_xboole_0 != k7_borsuk_1(A,B,C,D) -> k8_funct_2(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(A)),k12_borsuk_1(A,B),k7_borsuk_1(A,B,C,D)) = C & k8_funct_2(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(B)),k13_borsuk_1(A,B),k7_borsuk_1(A,B,C,D)) = D))))))))) # label(t65_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6363 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> (r1_tarski(C,D) -> r1_tarski(k11_borsuk_1(A,B,C),k11_borsuk_1(A,B,D))))))))))) # label(t52_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6364 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (r1_borsuk_1(A,B) <-> (exists C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v3_borsuk_1(C,A,B) & v5_pre_topc(C,A,B)))))))) # label(d20_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6365 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> r1_tarski(k5_setfam_1(u1_struct_0(k6_borsuk_1(A,B)),k11_borsuk_1(A,B,C)),C))))))) # label(t53_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6366 (all A (-v1_xboole_0(A) -> (all B (m1_eqrel_1(B,A) & -v1_xboole_0(B) -> (all C (m2_subset_1(C,k1_zfmisc_1(A),B) -> (exists D (C = k8_funct_2(A,B,k2_borsuk_1(A,B),D) & m1_subset_1(D,A))))))))) # label(t32_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6367 (all A all B all C all D (v2_pre_topc(B) & v2_pre_topc(C) & l1_pre_topc(C) & v2_pre_topc(D) & l1_pre_topc(D) & v1_pre_topc(D) & l1_pre_topc(B) -> (r2_hidden(A,a_3_0_borsuk_1(B,C,D)) <-> (exists E (k5_setfam_1(u1_struct_0(D),E) = A & r1_tarski(E,a_2_1_borsuk_1(B,C)) & m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(D))))))))) # label(fraenkel_a_3_0_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6368 $T # label(t44_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6369 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) -> k2_funcop_1(B,C) = k1_borsuk_1(A,B,C))) # label(redefinition_k1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6370 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> k1_tops_1(k6_borsuk_1(A,B),C) = k5_setfam_1(u1_struct_0(k6_borsuk_1(A,B)),k11_borsuk_1(A,B,C)))))))) # label(t55_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6371 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> v6_compts_1(k1_struct_0(A,B),A))))) # label(t41_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6372 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> (v3_pre_topc(C,k6_borsuk_1(A,B)) -> k5_setfam_1(u1_struct_0(k6_borsuk_1(A,B)),k11_borsuk_1(A,B,C)) = C))))))) # label(t54_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6373 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> v5_pre_topc(k3_borsuk_1(B,A,C),B,A))))))) # label(t36_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6374 (all A all B all C all D all E (-v3_struct_0(A) & l1_pre_topc(A) & -v3_struct_0(B) & l1_pre_topc(B) & m1_subset_1(C,u1_struct_0(B)) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & m1_connsp_2(E,B,C) & v5_pre_topc(D,A,B) & v1_funct_1(D) & v2_pre_topc(B) & v2_pre_topc(A) -> k10_relat_1(D,E) = k5_borsuk_1(A,B,C,D,E))) # label(redefinition_k5_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6375 (all A all B all C (-v3_struct_0(A) & l1_pre_topc(A) & -v3_struct_0(B) & v1_borsuk_1(B,A) & m1_pre_topc(B,A) & v2_borsuk_1(C,B) & m1_borsuk_1(C,B) & v2_pre_topc(A) -> k21_borsuk_1(A,B,C) = k16_borsuk_1(B,C))) # label(redefinition_k21_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6376 (all A all B all C (-v3_struct_0(B) & m1_borsuk_1(C,B) & v2_borsuk_1(C,B) & m1_pre_topc(B,A) & v1_borsuk_1(B,A) & l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> v1_borsuk_1(k21_borsuk_1(A,B,C),k16_borsuk_1(A,k20_borsuk_1(A,B,C))) & m1_pre_topc(k21_borsuk_1(A,B,C),k16_borsuk_1(A,k20_borsuk_1(A,B,C))) & v1_pre_topc(k21_borsuk_1(A,B,C)))) # label(dt_k21_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6377 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (exists B (v1_setfam_1(B) & v2_borsuk_1(B,A) & -v1_xboole_0(B) & m1_borsuk_1(B,A))))) # label(rc5_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6378 (all A all B all C all D all E all F (-v3_struct_0(A) & l1_pre_topc(A) & -v3_struct_0(B) & m1_connsp_2(F,B,D) & m2_connsp_2(E,A,C) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(B) & v2_pre_topc(B) & v2_pre_topc(A) -> m2_connsp_2(k10_borsuk_1(A,B,C,D,E,F),k6_borsuk_1(A,B),k7_borsuk_1(A,B,C,k1_struct_0(B,D))))) # label(dt_k10_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6379 (all A all B all C (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(B) & v1_borsuk_1(B,A) & m1_pre_topc(B,A) & m1_borsuk_1(C,B) & -v3_struct_0(A) -> k18_borsuk_1(A,B,C) = k19_borsuk_1(A,B,C))) # label(redefinition_k19_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6380 (all A all B all C (r1_tarski(A,k2_zfmisc_1(B,C)) -> k2_funct_2(k2_zfmisc_1(B,C),C,k10_funct_3(B,C),A) = k1_funct_1(k1_funct_3(k10_funct_3(B,C)),A))) # label(t10_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6381 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v5_pre_topc(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> r1_tarski(k5_pre_topc(A,B,C,k1_tops_1(B,D)),k1_tops_1(A,k5_pre_topc(A,B,C,D))))))))))) # label(t37_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6382 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_borsuk_1(B,A) -> m1_eqrel_1(B,u1_struct_0(A)) & -v1_xboole_0(B))))) # label(dt_m1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6383 (all A (-v1_xboole_0(A) -> (all B (m1_eqrel_1(B,A) & -v1_xboole_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(D,B) -> r1_xboole_0(D,C) | r1_tarski(D,C)))) -> C = k3_funct_2(A,B,k2_borsuk_1(A,B),k2_funct_2(A,B,k2_borsuk_1(A,B),C))))))))) # label(t33_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6384 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,k10_relat_1(C,B)) -> r1_tarski(k9_relat_1(C,A),B)))) # label(t5_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6385 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) -> (k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(A),k12_borsuk_1(A,B),C) = k1_xboole_0 | k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(B),k13_borsuk_1(A,B),C) = k1_xboole_0 -> C = k1_xboole_0))))))) # label(t61_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6386 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> ((exists D (k5_setfam_1(u1_struct_0(k6_borsuk_1(A,B)),D) = C & (all E -((all F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) -> (all G (m1_subset_1(G,k1_zfmisc_1(u1_struct_0(B))) -> -(v3_pre_topc(F,A) & v3_pre_topc(G,B) & k12_mcart_1(u1_struct_0(A),u1_struct_0(B),F,G) = E))))) & r2_hidden(E,D))) & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))))) <-> v3_pre_topc(C,k6_borsuk_1(A,B))))))))) # label(t45_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6387 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v1_xboole_0(C) & m1_eqrel_1(C,u1_struct_0(B)) -> r1_tarski(C,k18_borsuk_1(A,B,C)))))))) # label(t73_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6388 (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_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (all F (v1_funct_1(F) & v1_funct_2(F,B,C) & m2_relset_1(F,B,C) -> r1_tarski(k3_funct_2(A,B,E,k6_domain_1(B,D)),k3_funct_2(A,C,k7_funct_2(A,B,C,E,F),k6_domain_1(C,k8_funct_2(B,C,F,D)))))))))))))))) # label(t20_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6389 (all A all B all C (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(B) & l1_pre_topc(B) & m1_subset_1(C,u1_struct_0(B)) & v2_pre_topc(B) & -v3_struct_0(A) -> -v1_xboole_0(k3_borsuk_1(A,B,C)) & v1_partfun1(k3_borsuk_1(A,B,C),u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(k3_borsuk_1(A,B,C),A,B) & v1_funct_2(k3_borsuk_1(A,B,C),u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(k3_borsuk_1(A,B,C)) & v1_relat_1(k3_borsuk_1(A,B,C)))) # label(fc1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6390 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) & v1_borsuk_1(B,A) -> (all C (v2_borsuk_1(C,B) & m1_borsuk_1(C,B) -> (r2_borsuk_1(A,B) -> r2_borsuk_1(k16_borsuk_1(A,k20_borsuk_1(A,B,C)),k21_borsuk_1(A,B,C))))))))) # label(t85_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6391 (all A (-v1_xboole_0(A) -> (exists B (m1_eqrel_1(B,A) & v1_setfam_1(B) & -v1_xboole_0(B))))) # label(rc1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6392 (all A all B all C (-v3_struct_0(B) & m1_pre_topc(B,A) & m1_borsuk_1(C,B) & v2_borsuk_1(C,B) & v1_borsuk_1(B,A) & l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> m1_borsuk_1(k20_borsuk_1(A,B,C),A) & v2_borsuk_1(k20_borsuk_1(A,B,C),A))) # label(dt_k20_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6393 $T # label(d4_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6394 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_connsp_2(E,B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D)) -> (exists F (m1_connsp_2(F,A,D) & r1_tarski(k4_pre_topc(A,B,C,F),E))))))) <-> v5_pre_topc(C,A,B)))))))) # label(d2_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6395 (all A all B all C (v2_pre_topc(B) & l1_pre_topc(B) & m1_pre_topc(C,B) & -v3_struct_0(C) & -v3_struct_0(B) -> (r2_hidden(A,a_2_3_borsuk_1(B,C)) <-> (exists D (m1_subset_1(D,u1_struct_0(B)) & -r2_hidden(D,u1_struct_0(C)) & k1_struct_0(B,D) = A))))) # label(fraenkel_a_2_3_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6396 (all A all B all C all D all E (v2_pre_topc(B) & m1_subset_1(C,u1_struct_0(B)) & v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(D,A,B) & m1_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & m1_connsp_2(E,B,C) & l1_pre_topc(B) & -v3_struct_0(B) & l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> m2_connsp_2(k5_borsuk_1(A,B,C,D,E),A,k5_pre_topc(A,B,D,k1_struct_0(B,C))))) # label(dt_k5_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6397 $T # label(t3_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6398 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) -> (v1_tops_2(C,k6_borsuk_1(A,B)) -> v1_tops_2(k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(A),k12_borsuk_1(A,B),C),A) & v1_tops_2(k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(B),k13_borsuk_1(A,B),C),B)))))))) # label(t60_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6399 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (all E (m2_connsp_2(E,A,C) -> (all F (m2_connsp_2(F,B,D) -> m2_connsp_2(k7_borsuk_1(A,B,E,F),k6_borsuk_1(A,B),k7_borsuk_1(A,B,C,D)))))))))))))) # label(t49_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6400 (all A (v3_grcat_1(A) & l1_grcat_1(A) -> (all B (v3_grcat_1(B) & l1_grcat_1(B) -> (k9_grcat_1(A) = k10_grcat_1(B) -> (all C (l1_grcat_1(C) & v3_grcat_1(C) & v2_grcat_1(C) -> ((all D (-v3_struct_0(D) & v4_rlvect_1(D) & v5_rlvect_1(D) & v6_rlvect_1(D) & l1_rlvect_1(D) -> (all E (-v3_struct_0(E) & v4_rlvect_1(E) & v5_rlvect_1(E) & l1_rlvect_1(E) & v6_rlvect_1(E) -> (all F (-v3_struct_0(F) & v6_rlvect_1(F) & l1_rlvect_1(F) & v5_rlvect_1(F) & v4_rlvect_1(F) -> (all G (v1_funct_2(G,u1_struct_0(E),u1_struct_0(F)) & m2_relset_1(G,u1_struct_0(E),u1_struct_0(F)) & v1_funct_1(G) -> (all H (v1_funct_2(H,u1_struct_0(D),u1_struct_0(E)) & m2_relset_1(H,u1_struct_0(D),u1_struct_0(E)) & v1_funct_1(H) -> (g1_grcat_1(u1_grcat_1(B),u2_grcat_1(B),u3_grcat_1(B)) = g1_grcat_1(D,E,H) & g1_grcat_1(u1_grcat_1(A),u2_grcat_1(A),u3_grcat_1(A)) = g1_grcat_1(E,F,G) -> C = g1_grcat_1(D,F,k7_funct_2(u1_struct_0(D),u1_struct_0(E),u1_struct_0(F),H,G))))))))))))) <-> C = k15_grcat_1(A,B))))))))) # label(d21_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6401 (all A all B (v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(B) & l1_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(A) & -v3_struct_0(A) -> (exists C (v2_grcat_1(C) & v3_grcat_1(C) & m1_grcat_1(C,A,B))))) # label(rc3_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6402 (all A ((all B (r2_hidden(B,A) -> -v3_struct_0(B) & v1_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(B))) <-> v4_grcat_1(A))) # label(d22_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6403 (all A (l1_grcat_1(A) -> k10_grcat_1(A) = u2_grcat_1(A))) # label(d15_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6404 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) -> k3_grcat_1(A,B) = k2_partfun1(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k1_grcat_1(A,B)))))) # label(d7_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6405 $T # label(t27_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6406 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & l1_rlvect_1(B) -> v1_grcat_1(k8_grcat_1(A,B),A,B))))) # label(t16_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6407 (exists A (-v1_xboole_0(A) & v4_grcat_1(A))) # label(rc4_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6408 (exists A (l1_grcat_1(A) & v3_grcat_1(A) & v2_grcat_1(A))) # label(rc2_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6409 (all A (-v1_xboole_0(A) & v1_classes2(A) -> -v1_xboole_0(k31_grcat_1(A)))) # label(fc14_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6410 $T # label(d2_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6411 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) -> k2_partfun1(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k1_grcat_1(A,B)) = k2_grcat_1(A,B))))) # label(d6_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6412 (all A (l1_grcat_1(A) -> (all B (v6_rlvect_1(B) & l1_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & l1_rlvect_1(C) & v6_rlvect_1(C) & v5_rlvect_1(C) & v4_rlvect_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C)) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) -> (g1_grcat_1(B,C,D) = A -> D = k11_grcat_1(A) & k10_grcat_1(A) = C & k9_grcat_1(A) = B))))))))) # label(t17_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6413 (all A all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) & l1_cat_1(A) & v2_cat_1(A) -> v1_funct_2(k3_grcat_1(A,B),k1_grcat_1(A,B),B) & m2_relset_1(k3_grcat_1(A,B),k1_grcat_1(A,B),B) & v1_funct_1(k3_grcat_1(A,B)))) # label(dt_k3_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6414 (all A (-v1_xboole_0(A) & v4_grcat_1(A) -> v1_funct_1(k24_grcat_1(A)) & v1_funct_2(k24_grcat_1(A),k20_grcat_1(A),A) & m2_relset_1(k24_grcat_1(A),k20_grcat_1(A),A))) # label(dt_k24_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6415 (all A (v4_grcat_1(A) & -v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & v5_grcat_1(B) -> ((all C ((exists D ((exists E (v2_grcat_1(C) & m1_grcat_1(C,D,E) & m2_grcat_1(E,A) & v1_rlvect_1(E))) & m2_grcat_1(D,A) & v1_rlvect_1(D))) <-> r2_hidden(C,B))) <-> B = k20_grcat_1(A)))))) # label(d30_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6416 (all A (l1_grcat_1(A) -> v5_rlvect_1(u2_grcat_1(A)) & v6_rlvect_1(u2_grcat_1(A)) & l1_rlvect_1(u2_grcat_1(A)) & v4_rlvect_1(u2_grcat_1(A)) & -v3_struct_0(u2_grcat_1(A)))) # label(dt_u2_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6417 (all A (-v1_xboole_0(A) & v4_grcat_1(A) -> (all B (m3_grcat_1(B,k20_grcat_1(A)) -> (all C (m3_grcat_1(C,k20_grcat_1(A)) -> (k22_grcat_1(A,C) = k21_grcat_1(A,B) -> r2_hidden(k15_grcat_1(B,C),k20_grcat_1(A))))))))) # label(t45_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6418 (all A (l1_grcat_1(A) -> k9_grcat_1(A) = u1_grcat_1(A))) # label(d14_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6419 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) & -v1_xboole_0(B) -> r1_cat_2(g1_cat_1(B,k1_grcat_1(A,B),k2_grcat_1(A,B),k3_grcat_1(A,B),k4_grcat_1(A,B),k5_grcat_1(A,B)),A))))) # label(t9_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6420 (all A all B all C (-v3_struct_0(A) & v5_rlvect_1(A) & m4_grcat_1(C,A,B) & l1_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all D (m7_grcat_1(D,A,B,C) -> m1_grcat_1(D,A,B))))) # label(dt_m7_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6421 (all A all B all C (v2_cat_1(B) & l1_cat_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_cat_1(B))) & -v1_xboole_0(C) -> ((exists D exists E (m1_subset_1(D,u1_cat_1(B)) & m1_subset_1(E,u1_cat_1(B)) & k6_cat_1(B,D,E) = A & r2_hidden(E,C) & r2_hidden(D,C))) <-> r2_hidden(A,a_2_0_grcat_1(B,C))))) # label(fraenkel_a_2_0_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6422 (all A all B all C (v5_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(B) & m4_grcat_1(C,A,B) & l1_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & l1_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (exists D m7_grcat_1(D,A,B,C)))) # label(existence_m7_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6423 $T # label(t1_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6424 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(B) & v4_rlvect_1(B) -> (all C (-v3_struct_0(C) & v5_rlvect_1(C) & l1_rlvect_1(C) & v6_rlvect_1(C) & v4_rlvect_1(C) -> (all D (m1_grcat_1(D,B,C) -> (all E (m1_grcat_1(E,A,B) -> (all F (v1_funct_1(F) & v1_funct_2(F,u1_struct_0(B),u1_struct_0(C)) & m2_relset_1(F,u1_struct_0(B),u1_struct_0(C)) -> (all G (v1_funct_1(G) & m2_relset_1(G,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(G,u1_struct_0(A),u1_struct_0(B)) -> (g1_grcat_1(B,C,F) = D & g1_grcat_1(A,B,G) = E -> g1_grcat_1(A,C,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),G,F)) = k16_grcat_1(A,B,C,D,E)))))))))))))))) # label(t29_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.78 6425 (all A (v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(B) -> (all C (m1_grcat_1(C,A,B) -> (exists 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_grcat_1(D,A,B) & g1_grcat_1(u1_grcat_1(C),u2_grcat_1(C),u3_grcat_1(C)) = g1_grcat_1(A,B,D) & v1_funct_1(D))))))))) # label(t22_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6426 (all A (m1_subset_1(A,u1_struct_0(k2_algstr_1)) -> (all B (m1_subset_1(B,u1_struct_0(k2_algstr_1)) -> k4_rlvect_1(k2_algstr_1,A,B) = k1_xboole_0)))) # label(t8_grcat_1_AndLHS) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6427 (all A (m1_subset_1(A,u1_struct_0(k2_algstr_1)) -> k5_rlvect_1(k2_algstr_1,A) = k1_xboole_0)) # label(t8_grcat_1_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6428 (all A (m1_subset_1(A,u1_struct_0(k2_algstr_1)) -> A = k1_xboole_0)) # label(t8_grcat_1_AndRHS_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6429 (all A (v1_classes2(A) & -v1_xboole_0(A) -> r2_hidden(k2_algstr_1,k31_grcat_1(A)))) # label(t54_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6430 (all A (-v1_xboole_0(A) & v1_classes2(A) -> m3_cat_2(k32_grcat_1(A),k30_grcat_1(A)))) # label(dt_k32_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6431 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (v5_rlvect_1(B) & l1_rlvect_1(B) & v6_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_grcat_1(C,A,B) & v2_grcat_1(C) -> m4_grcat_1(k1_tarski(C),A,B))))))) # label(t39_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6432 (all A all B (v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all C (m4_grcat_1(C,A,B) -> v5_grcat_1(C) & -v1_xboole_0(C))))) # label(dt_m4_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6433 (all A (v4_grcat_1(A) & -v1_xboole_0(A) -> (exists B m2_grcat_1(B,A)))) # label(existence_m2_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6434 (all A (-v1_xboole_0(A) & v1_classes2(A) -> v1_cat_1(k30_grcat_1(A)) & v2_cat_1(k30_grcat_1(A)))) # label(fc13_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6435 (all A all B (v4_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(B) & v5_rlvect_1(B) & l1_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> m1_grcat_1(k14_grcat_1(A,B),A,B) & v2_grcat_1(k14_grcat_1(A,B)))) # label(dt_k14_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6436 (all A all B (v4_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(B) & v5_rlvect_1(B) & -v3_struct_0(B) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> m4_grcat_1(k18_grcat_1(A,B),A,B))) # label(dt_k18_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6437 (all A all B (v2_cat_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) & -v1_xboole_0(B) & l1_cat_1(A) -> m3_cat_2(k6_grcat_1(A,B),A))) # label(dt_k6_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6438 (all A all B all C (l1_struct_0(A) & -v1_xboole_0(C) & m5_grcat_1(C,A,B) & l1_struct_0(B) & -v3_struct_0(B) -> (all D (m6_grcat_1(D,A,B,C) -> 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(dt_m6_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6439 (all A (-v1_xboole_0(A) & v4_grcat_1(A) -> (all B (m2_grcat_1(B,A) -> k23_grcat_1(A,B) = k13_grcat_1(B))))) # label(d31_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6440 $T # label(t36_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6441 (all A (-v1_xboole_0(A) & v1_classes2(A) -> r2_hidden(k1_tarski(k1_xboole_0),A) & r2_hidden(k7_vectsp_2,A) & r2_hidden(k2_midsp_1,A) & r2_hidden(k2_zfmisc_1(k1_tarski(k1_xboole_0),k1_tarski(k1_xboole_0)),A) & r2_hidden(k4_tarski(k1_tarski(k1_xboole_0),k1_tarski(k1_xboole_0)),A))) # label(t6_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6442 (all A (-v1_xboole_0(A) & v4_grcat_1(A) -> (all B (m3_grcat_1(B,k20_grcat_1(A)) -> (all C (m3_grcat_1(C,k20_grcat_1(A)) -> -(k21_grcat_1(A,B) = k22_grcat_1(A,C) & (all D (m2_grcat_1(D,A) & v1_rlvect_1(D) -> (all E (m2_grcat_1(E,A) & v1_rlvect_1(E) -> (all F (m2_grcat_1(F,A) & v1_rlvect_1(F) -> -(m1_grcat_1(B,E,F) & m1_grcat_1(C,D,E))))))))))))))) # label(t44_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6443 (all A all B (l1_struct_0(A) & -v3_struct_0(B) & l1_struct_0(B) -> (exists C (-v1_xboole_0(C) & m5_grcat_1(C,A,B))))) # label(rc8_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6444 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (exists B (r2_hidden(B,A) & r1_grcat_1(B,k2_algstr_1))))) # label(t41_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6445 (all A (v1_classes2(A) & -v1_xboole_0(A) -> v1_cat_1(k28_grcat_1(A)))) # label(fc10_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6446 (all A (v2_grcat_1(A) & l1_grcat_1(A) & v3_grcat_1(A) -> -v1_xboole_0(k1_tarski(A)) & v5_grcat_1(k1_tarski(A)))) # label(t37_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6447 (all A all B all C (r1_grcat_1(A,B) & r1_grcat_1(A,C) -> B = C)) # label(t40_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6448 (all A (-v1_xboole_0(A) & v1_classes2(A) -> m3_cat_2(k30_grcat_1(A),k28_grcat_1(A)))) # label(dt_k30_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6449 $T # label(dt_l1_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6450 (all A (-v1_xboole_0(A) & v1_classes2(A) -> k6_grcat_1(k28_grcat_1(A),k29_grcat_1(A)) = k30_grcat_1(A))) # label(d38_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6451 (all A (v1_classes2(A) & -v1_xboole_0(A) -> l1_cat_1(k28_grcat_1(A)))) # label(dt_k28_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6452 (all A all B (-v3_struct_0(B) & l1_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> v3_grcat_1(k12_grcat_1(A,B)) & v2_grcat_1(k12_grcat_1(A,B)))) # label(fc5_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6453 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l1_rlvect_1(B) -> (all C (l1_rlvect_1(C) & -v3_struct_0(C) -> (all D (v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(D) -> (all E (m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C)) & v1_funct_1(E) -> (v1_grcat_1(D,A,B) & v1_grcat_1(E,B,C) -> v1_grcat_1(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C)))))))))))) # label(t14_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6454 (all A (-v1_xboole_0(A) & v1_classes2(A) -> k28_grcat_1(A) = g1_cat_1(k19_grcat_1(A),k20_grcat_1(k19_grcat_1(A)),k24_grcat_1(k19_grcat_1(A)),k25_grcat_1(k19_grcat_1(A)),k27_grcat_1(k19_grcat_1(A)),k26_grcat_1(k19_grcat_1(A))))) # label(d36_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6455 (all A (l1_grcat_1(A) -> -v3_struct_0(k9_grcat_1(A)) & v4_rlvect_1(k9_grcat_1(A)) & l1_rlvect_1(k9_grcat_1(A)) & v6_rlvect_1(k9_grcat_1(A)) & v5_rlvect_1(k9_grcat_1(A)))) # label(dt_k9_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6456 (all A all B (l1_struct_0(B) & -v3_struct_0(B) & l1_struct_0(A) -> -v1_xboole_0(k17_grcat_1(A,B)))) # label(fc7_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6457 (all A all B all C (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & m4_grcat_1(C,A,B) & l1_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(A) -> (all D (m7_grcat_1(D,A,B,C) <-> m1_subset_1(D,C))))) # label(redefinition_m7_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6458 (all A (v1_classes2(A) & -v1_xboole_0(A) -> m1_subset_1(k29_grcat_1(A),k1_zfmisc_1(u1_cat_1(k28_grcat_1(A)))))) # label(dt_k29_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6459 (all A all B (-v1_xboole_0(B) & v1_classes2(B) -> (r2_hidden(A,a_1_0_grcat_1(B)) <-> (exists C (m1_subset_1(C,u1_cat_1(k28_grcat_1(B))) & (exists D (-v3_struct_0(D) & v4_rlvect_1(D) & v5_rlvect_1(D) & l1_rlvect_1(D) & C = D & v6_rlvect_1(D) & v3_rlvect_1(D))) & C = A))))) # label(fraenkel_a_1_0_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6460 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (v5_rlvect_1(B) & l1_rlvect_1(B) & v6_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (v4_rlvect_1(C) & v6_rlvect_1(C) & l1_rlvect_1(C) & v5_rlvect_1(C) & -v3_struct_0(C) -> (all D (-v3_struct_0(D) & v5_rlvect_1(D) & l1_rlvect_1(D) & v6_rlvect_1(D) & v4_rlvect_1(D) -> (all E (v2_grcat_1(E) & m1_grcat_1(E,A,B) -> (all F (v2_grcat_1(F) & m1_grcat_1(F,B,C) -> (all G (m1_grcat_1(G,C,D) & v2_grcat_1(G) -> k16_grcat_1(A,C,D,G,k16_grcat_1(A,B,C,F,E)) = k16_grcat_1(A,B,D,k16_grcat_1(B,C,D,G,F),E))))))))))))))) # label(t32_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6461 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) -> u1_cat_1(k6_grcat_1(A,B)) = B)))) # label(t10_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6462 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B all C (r2_hidden(B,C) & r2_hidden(C,A) -> r2_hidden(B,A))))) # label(t4_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6463 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (m1_subset_1(B,u2_cat_1(k28_grcat_1(A))) -> (all C (m3_grcat_1(C,k20_grcat_1(k19_grcat_1(A))) -> (all D (m1_subset_1(D,u1_cat_1(k28_grcat_1(A))) -> (all E (m2_grcat_1(E,k19_grcat_1(A)) -> v2_grcat_1(B) & m3_grcat_1(B,k20_grcat_1(k19_grcat_1(A))) & m1_subset_1(C,u2_cat_1(k28_grcat_1(A))) & v1_rlvect_1(D) & m1_subset_1(E,u1_cat_1(k28_grcat_1(A))) & m2_grcat_1(D,k19_grcat_1(A)))))))))))) # label(t47_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6464 (all A (-v1_xboole_0(A) & v1_classes2(A) -> -v1_xboole_0(k29_grcat_1(A)))) # label(fc12_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6465 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) -> (all B (v5_rlvect_1(B) & l1_rlvect_1(B) & v6_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (v2_grcat_1(C) & m1_grcat_1(C,A,B) -> (exists D (v1_funct_1(D) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & C = g1_grcat_1(A,B,D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)))))))))) # label(t23_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6466 (all A (v3_grcat_1(A) & l1_grcat_1(A) -> v1_grcat_1(u3_grcat_1(A),u1_grcat_1(A),u2_grcat_1(A)))) # label(t18_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6467 (all A (-v3_struct_0(A) & l2_struct_0(A) -> (all B (-v3_struct_0(B) & l1_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k8_funct_2(u1_struct_0(A),u1_struct_0(B),k8_grcat_1(A,B),C) = k1_rlvect_1(B))))))) # label(t15_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6468 (all A (v1_classes2(A) & -v1_xboole_0(A) -> u1_cat_1(k30_grcat_1(A)) = k29_grcat_1(A))) # label(t52_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6469 (all A all B all C all D -(r2_hidden(D,C) & r1_tarski(C,k2_zfmisc_1(A,B)) & (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> k4_tarski(E,F) != D)))))) # label(t2_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6470 (all A (l1_grcat_1(A) -> v1_funct_2(u3_grcat_1(A),u1_struct_0(u1_grcat_1(A)),u1_struct_0(u2_grcat_1(A))) & m2_relset_1(u3_grcat_1(A),u1_struct_0(u1_grcat_1(A)),u1_struct_0(u2_grcat_1(A))) & v1_funct_1(u3_grcat_1(A)))) # label(dt_u3_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6471 (all A all B all C all D all E (v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(B) & -v3_struct_0(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & m1_grcat_1(E,A,B) & m1_grcat_1(D,B,C) & l1_rlvect_1(C) & v4_rlvect_1(C) & -v3_struct_0(B) & v6_rlvect_1(A) & -v3_struct_0(A) -> k16_grcat_1(A,B,C,D,E) = k15_grcat_1(D,E))) # label(redefinition_k16_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6472 (all A (l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v6_rlvect_1(B) & l1_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (l1_grcat_1(C) & v3_grcat_1(C) -> (A = k9_grcat_1(C) & B = k10_grcat_1(C) <-> m1_grcat_1(C,A,B)))))))) # label(d19_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6473 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,k20_grcat_1(A)) & v4_grcat_1(A) -> v1_rlvect_1(k21_grcat_1(A,B)) & m2_grcat_1(k21_grcat_1(A,B),A))) # label(dt_k21_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6474 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (m1_subset_1(B,k19_grcat_1(A)) -> v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(B) & v1_rlvect_1(B) & -v3_struct_0(B))))) # label(t43_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6475 (all A (-v1_xboole_0(A) & v5_grcat_1(A) -> (exists B m3_grcat_1(B,A)))) # label(existence_m3_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6476 (all A all B (r1_grcat_1(A,B) <-> (exists C exists D exists E exists F (A = k4_mcart_1(C,D,E,F) & (exists G (-v3_struct_0(G) & v4_rlvect_1(G) & u1_rlvect_1(G) = D & k7_vectsp_1(G) = E & F = u2_struct_0(G) & C = u1_struct_0(G) & G = B & l1_rlvect_1(G) & v6_rlvect_1(G) & v5_rlvect_1(G) & v1_rlvect_1(G))))))) # label(d28_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6477 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (B = k19_grcat_1(A) <-> (all C (r2_hidden(C,B) <-> (exists D (r2_hidden(D,A) & r1_grcat_1(D,C))))))))) # label(d29_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6478 (exists A (-v1_xboole_0(A) & v5_grcat_1(A))) # label(rc6_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6479 (all A (v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (v2_grcat_1(B) & l1_grcat_1(B) & v3_grcat_1(B) -> (A = k10_grcat_1(B) -> k15_grcat_1(k13_grcat_1(A),B) = B))) & (all B (l1_grcat_1(B) & v3_grcat_1(B) & v2_grcat_1(B) -> (A = k9_grcat_1(B) -> k15_grcat_1(B,k13_grcat_1(A)) = B))) & A = k10_grcat_1(k13_grcat_1(A)) & A = k9_grcat_1(k13_grcat_1(A)))) # label(t34_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6480 (all A (v1_classes2(A) & -v1_xboole_0(A) -> m1_subset_1(k31_grcat_1(A),k1_zfmisc_1(u1_cat_1(k30_grcat_1(A)))))) # label(dt_k31_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6481 (all A (v4_grcat_1(A) & -v1_xboole_0(A) -> (all B (m2_grcat_1(B,A) -> v5_rlvect_1(B) & l1_rlvect_1(B) & v6_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B))))) # label(dt_m2_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6482 (all A all B (v2_cat_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) & -v1_xboole_0(B) & l1_cat_1(A) -> v1_funct_1(k4_grcat_1(A,B)) & m2_relset_1(k4_grcat_1(A,B),k12_mcart_1(u2_cat_1(A),u2_cat_1(A),k1_grcat_1(A,B),k1_grcat_1(A,B)),k1_grcat_1(A,B)))) # label(dt_k4_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6483 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> C = k1_partfun1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),k7_grcat_1(A),C) & C = k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),C,k7_grcat_1(B)))))))) # label(t12_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6484 (all A (v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> v3_grcat_1(k13_grcat_1(A)) & v2_grcat_1(k13_grcat_1(A)))) # label(fc6_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6485 (all A (-v1_xboole_0(A) -> (all B (v4_rlvect_1(B) & l1_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & l1_rlvect_1(C) & v6_rlvect_1(C) & v5_rlvect_1(C) & v4_rlvect_1(C) -> (m4_grcat_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> v2_grcat_1(D) & m1_grcat_1(D,B,C)))))))))) # label(t38_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6486 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(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)) -> (v1_grcat_1(C,A,B) -> v2_grcat_1(g1_grcat_1(A,B,C)) & m1_grcat_1(g1_grcat_1(A,B,C),A,B)))))))) # label(t20_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6487 (all A all B all C all D all E (v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(B) & v6_rlvect_1(B) & -v3_struct_0(C) & v5_rlvect_1(C) & m1_grcat_1(D,B,C) & m1_grcat_1(E,A,B) & l1_rlvect_1(C) & v6_rlvect_1(C) & v4_rlvect_1(C) & l1_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(A) & -v3_struct_0(A) -> m1_grcat_1(k16_grcat_1(A,B,C,D,E),A,C) & v2_grcat_1(k16_grcat_1(A,B,C,D,E)))) # label(dt_k16_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6488 (all A (v4_grcat_1(A) & -v1_xboole_0(A) -> (all B (m2_grcat_1(B,A) <-> m1_subset_1(B,A))))) # label(redefinition_m2_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6489 (all A all B (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(B) & l1_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & -v3_struct_0(B) & l1_rlvect_1(A) -> (exists C m1_grcat_1(C,A,B)))) # label(existence_m1_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6490 (all A all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) & l1_cat_1(A) & v2_cat_1(A) -> v2_cat_1(k6_grcat_1(A,B)) & v1_cat_1(k6_grcat_1(A,B)))) # label(fc3_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6491 $T # label(d1_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6492 $T # label(dt_k19_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6493 $T # label(t35_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6494 (all A all B all C (-v3_struct_0(B) & m5_grcat_1(C,A,B) & -v1_xboole_0(C) & l1_struct_0(B) & l1_struct_0(A) -> (exists D m6_grcat_1(D,A,B,C)))) # label(existence_m6_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6495 $T # label(d3_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6496 (all A all B all C (-v1_xboole_0(C) & m5_grcat_1(C,A,B) & l1_struct_0(B) & -v3_struct_0(B) & l1_struct_0(A) -> (all D (m1_subset_1(D,C) <-> m6_grcat_1(D,A,B,C))))) # label(redefinition_m6_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6497 (exists A (l1_grcat_1(A) & v2_grcat_1(A))) # label(rc1_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6498 (all A (v1_classes2(A) & -v1_xboole_0(A) -> u1_cat_1(k32_grcat_1(A)) = k31_grcat_1(A))) # label(t53_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6499 (all A (v4_grcat_1(A) & -v1_xboole_0(A) -> v1_funct_1(k25_grcat_1(A)) & m2_relset_1(k25_grcat_1(A),k20_grcat_1(A),A) & v1_funct_2(k25_grcat_1(A),k20_grcat_1(A),A))) # label(dt_k25_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6500 (all A (-v1_xboole_0(A) & v4_grcat_1(A) -> (exists B (-v3_struct_0(B) & v1_rlvect_1(B) & v4_rlvect_1(B) & v1_algstr_1(B) & v3_algstr_1(B) & v4_algstr_1(B) & v6_algstr_1(B) & v5_algstr_1(B) & v2_algstr_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & m1_subset_1(B,A))))) # label(rc5_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6501 (all A (v4_grcat_1(A) & -v1_xboole_0(A) -> (all B (m2_relset_1(B,A,k20_grcat_1(A)) & v1_funct_2(B,A,k20_grcat_1(A)) & v1_funct_1(B) -> ((all C (m2_grcat_1(C,A) -> k23_grcat_1(A,C) = k8_funct_2(A,k20_grcat_1(A),B,C))) <-> B = k26_grcat_1(A)))))) # label(d34_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6502 (all A all B (v4_grcat_1(A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> v2_grcat_1(k23_grcat_1(A,B)) & m3_grcat_1(k23_grcat_1(A,B),k20_grcat_1(A)))) # label(dt_k23_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6503 (all A (-v1_xboole_0(A) & v4_grcat_1(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k20_grcat_1(A),A) & m2_relset_1(B,k20_grcat_1(A),A) -> ((all C (m3_grcat_1(C,k20_grcat_1(A)) -> k21_grcat_1(A,C) = k8_funct_2(k20_grcat_1(A),A,B,C))) <-> B = k24_grcat_1(A)))))) # label(d32_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6504 (all A all B all C (v4_rlvect_1(A) & v5_rlvect_1(A) & v5_rlvect_1(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_rlvect_1(B) & v6_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) & l1_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> v2_grcat_1(g1_grcat_1(A,B,C)) & l1_grcat_1(g1_grcat_1(A,B,C)))) # label(dt_g1_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6505 (all A (v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l1_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (l1_rlvect_1(C) & v6_rlvect_1(C) & v5_rlvect_1(C) & v4_rlvect_1(C) & -v3_struct_0(C) -> (all D (m1_grcat_1(D,B,C) -> (all E (m1_grcat_1(E,A,B) -> m1_grcat_1(k15_grcat_1(D,E),A,C))))))))))) # label(t28_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6506 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(B) & -v3_struct_0(B) -> (all C (v5_grcat_1(C) & -v1_xboole_0(C) -> (m4_grcat_1(C,A,B) <-> (all D (m3_grcat_1(D,C) -> v2_grcat_1(D) & m1_grcat_1(D,A,B)))))))))) # label(d24_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6507 (all A all B (-v3_struct_0(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(B) & l1_rlvect_1(B) & v6_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) & v5_rlvect_1(A) & v4_rlvect_1(A) -> l1_grcat_1(k12_grcat_1(A,B)))) # label(dt_k12_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6508 (all A all B (v2_cat_1(A) & l1_cat_1(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) -> v1_funct_1(k2_grcat_1(A,B)) & v1_funct_2(k2_grcat_1(A,B),k1_grcat_1(A,B),B) & m2_relset_1(k2_grcat_1(A,B),k1_grcat_1(A,B),B))) # label(dt_k2_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6509 (all A (v5_grcat_1(A) <-> (all B (r2_hidden(B,A) -> v2_grcat_1(B) & v3_grcat_1(B) & l1_grcat_1(B))))) # label(d23_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6510 (all A all B (m1_subset_1(B,k20_grcat_1(A)) & v4_grcat_1(A) & -v1_xboole_0(A) -> k22_grcat_1(A,B) = k10_grcat_1(B))) # label(redefinition_k22_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6511 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) -> k1_funct_2(u1_struct_0(A),u1_struct_0(B)) = k17_grcat_1(A,B))))) # label(d26_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6512 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) -> (all C (m5_grcat_1(C,A,B) <-> (all D (r2_hidden(D,C) -> 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(d25_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6513 (all A (-v1_xboole_0(A) & v1_classes2(A) -> v1_cat_1(k32_grcat_1(A)) & v2_cat_1(k32_grcat_1(A)))) # label(fc15_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6514 (all A all B (v4_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all C (m1_grcat_1(C,A,B) -> l1_grcat_1(C) & v3_grcat_1(C))))) # label(dt_m1_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6515 (all A (v3_grcat_1(A) & l1_grcat_1(A) -> (exists B (-v3_struct_0(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & (exists C (-v3_struct_0(C) & l1_rlvect_1(C) & m1_grcat_1(A,B,C) & v6_rlvect_1(C) & v5_rlvect_1(C) & v4_rlvect_1(C))) & l1_rlvect_1(B) & v4_rlvect_1(B))))) # label(t24_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6516 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (m1_subset_1(B,u1_cat_1(k28_grcat_1(A))) -> (all C (m2_grcat_1(C,k19_grcat_1(A)) -> (B = C -> k23_grcat_1(k19_grcat_1(A),C) = k5_cat_1(k28_grcat_1(A),B)))))))) # label(t48_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6517 (all A all B (r2_hidden(A,f1_s1_grcat_1) & r2_hidden(B,f2_s1_grcat_1) & p1_s1_grcat_1(A,B) -> r2_hidden(f4_s1_grcat_1(A,B),f3_s1_grcat_1))) -> (exists A (v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(f1_s1_grcat_1,f2_s1_grcat_1),f3_s1_grcat_1) & (all B all C (r2_hidden(B,f1_s1_grcat_1) & p1_s1_grcat_1(B,C) & r2_hidden(C,f2_s1_grcat_1) <-> r2_hidden(k4_tarski(B,C),k1_relat_1(A)))) & (all B all C (r2_hidden(k4_tarski(B,C),k1_relat_1(A)) -> k1_funct_1(A,k4_tarski(B,C)) = f4_s1_grcat_1(B,C))))) # label(s1_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6518 (all A (-v3_struct_0(A) & l1_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k8_funct_2(u1_struct_0(A),u1_struct_0(A),k7_grcat_1(A),B) = B)))) # label(t11_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6519 (all A (l1_grcat_1(A) & v3_grcat_1(A) & v2_grcat_1(A) -> (all B (v2_grcat_1(B) & l1_grcat_1(B) & v3_grcat_1(B) -> (all C (v2_grcat_1(C) & l1_grcat_1(C) & v3_grcat_1(C) -> (k9_grcat_1(B) = k10_grcat_1(A) & k9_grcat_1(C) = k10_grcat_1(B) -> k15_grcat_1(C,k15_grcat_1(B,A)) = k15_grcat_1(k15_grcat_1(C,B),A)))))))) # label(t33_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6520 (all A (m1_subset_1(A,f1_s2_grcat_1) -> (all B (m1_subset_1(B,f2_s2_grcat_1) -> (p1_s2_grcat_1(A,B) -> r2_hidden(f4_s2_grcat_1(A,B),f3_s2_grcat_1)))))) -> (exists A (m2_relset_1(A,k2_zfmisc_1(f1_s2_grcat_1,f2_s2_grcat_1),f3_s2_grcat_1) & (all B (m1_subset_1(B,f1_s2_grcat_1) -> (all C (m1_subset_1(C,f2_s2_grcat_1) -> (r2_hidden(k4_tarski(B,C),k1_relat_1(A)) <-> p1_s2_grcat_1(B,C)))))) & (all B (m1_subset_1(B,f1_s2_grcat_1) -> (all C (m1_subset_1(C,f2_s2_grcat_1) -> (r2_hidden(k4_tarski(B,C),k1_relat_1(A)) -> f4_s2_grcat_1(B,C) = k1_funct_1(A,k4_tarski(B,C))))))) & v1_funct_1(A))) # label(s2_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6521 (all A (l1_struct_0(A) -> k7_grcat_1(A) = k6_partfun1(u1_struct_0(A)))) # label(d11_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6522 (all A all B (v4_grcat_1(A) & m1_subset_1(B,k20_grcat_1(A)) & -v1_xboole_0(A) -> m2_grcat_1(k22_grcat_1(A,B),A) & v1_rlvect_1(k22_grcat_1(A,B)))) # label(dt_k22_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6523 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) -> k1_realset1(u5_cat_1(A),k1_grcat_1(A,B)) = k4_grcat_1(A,B))))) # label(d8_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6524 (all A (-v1_xboole_0(A) & v4_grcat_1(A) -> m2_relset_1(k27_grcat_1(A),k2_zfmisc_1(k20_grcat_1(A),k20_grcat_1(A)),k20_grcat_1(A)) & v1_funct_1(k27_grcat_1(A)))) # label(dt_k27_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6525 (exists A l1_grcat_1(A)) # label(existence_l1_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6526 (all A (-v1_xboole_0(A) & v4_grcat_1(A) -> m2_relset_1(k26_grcat_1(A),A,k20_grcat_1(A)) & v1_funct_2(k26_grcat_1(A),A,k20_grcat_1(A)) & v1_funct_1(k26_grcat_1(A)))) # label(dt_k26_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6527 $T # label(d4_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6528 (all A (v3_grcat_1(A) & l1_grcat_1(A) & v2_grcat_1(A) -> (all B (v2_grcat_1(B) & v3_grcat_1(B) & l1_grcat_1(B) -> (k9_grcat_1(B) = k10_grcat_1(A) -> k9_grcat_1(A) = k9_grcat_1(k15_grcat_1(B,A)) & k10_grcat_1(k15_grcat_1(B,A)) = k10_grcat_1(B)))))) # label(t31_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6529 (all A all B (-v3_struct_0(A) & l2_struct_0(B) & -v3_struct_0(B) & l2_struct_0(A) -> m2_relset_1(k8_grcat_1(A,B),u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(k8_grcat_1(A,B),u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(k8_grcat_1(A,B)))) # label(dt_k8_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6530 (all A (v2_grcat_1(A) & l1_grcat_1(A) & v3_grcat_1(A) -> (all B (l1_grcat_1(B) & v3_grcat_1(B) & v2_grcat_1(B) -> -((all C (-v3_struct_0(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & l1_rlvect_1(C) & v6_rlvect_1(C) -> (all D (v4_rlvect_1(D) & v6_rlvect_1(D) & l1_rlvect_1(D) & v5_rlvect_1(D) & -v3_struct_0(D) -> (all E (v4_rlvect_1(E) & v5_rlvect_1(E) & l1_rlvect_1(E) & v6_rlvect_1(E) & -v3_struct_0(E) -> (all F (v1_funct_2(F,u1_struct_0(C),u1_struct_0(D)) & m2_relset_1(F,u1_struct_0(C),u1_struct_0(D)) & v1_funct_1(F) -> (all G (v1_funct_1(G) & v1_funct_2(G,u1_struct_0(D),u1_struct_0(E)) & m2_relset_1(G,u1_struct_0(D),u1_struct_0(E)) -> -(B = g1_grcat_1(D,E,G) & g1_grcat_1(C,E,k7_funct_2(u1_struct_0(C),u1_struct_0(D),u1_struct_0(E),F,G)) = k15_grcat_1(B,A) & g1_grcat_1(C,D,F) = A))))))))))) & k9_grcat_1(B) = k10_grcat_1(A)))))) # label(t30_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6531 (all A all B (l1_struct_0(B) & l1_struct_0(A) -> m5_grcat_1(k17_grcat_1(A,B),A,B))) # label(dt_k17_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6532 (all A (l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> m1_grcat_1(k13_grcat_1(A),A,A))) # label(dt_k13_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6533 (all A (l1_grcat_1(A) -> v1_funct_2(k11_grcat_1(A),u1_struct_0(k9_grcat_1(A)),u1_struct_0(k10_grcat_1(A))) & m2_relset_1(k11_grcat_1(A),u1_struct_0(k9_grcat_1(A)),u1_struct_0(k10_grcat_1(A))) & v1_funct_1(k11_grcat_1(A)))) # label(dt_k11_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6534 (all A (v1_classes2(A) & -v1_xboole_0(A) -> k6_grcat_1(k30_grcat_1(A),k31_grcat_1(A)) = k32_grcat_1(A))) # label(d40_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6535 (all A all B (v2_cat_1(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) & l1_cat_1(A) -> v1_funct_1(k5_grcat_1(A,B)) & m2_relset_1(k5_grcat_1(A,B),B,k1_grcat_1(A,B)) & v1_funct_2(k5_grcat_1(A,B),B,k1_grcat_1(A,B)))) # label(dt_k5_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6536 (all A all B (l1_grcat_1(B) & v3_grcat_1(B) & l1_grcat_1(A) & v3_grcat_1(A) -> v2_grcat_1(k15_grcat_1(A,B)) & v3_grcat_1(k15_grcat_1(A,B)) & l1_grcat_1(k15_grcat_1(A,B)))) # label(dt_k15_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6537 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (m1_subset_1(B,u2_cat_1(k28_grcat_1(A))) -> (all C (m3_grcat_1(C,k20_grcat_1(k19_grcat_1(A))) -> (C = B -> k2_cat_1(k28_grcat_1(A),B) = k21_grcat_1(k19_grcat_1(A),C) & k3_cat_1(k28_grcat_1(A),B) = k22_grcat_1(k19_grcat_1(A),C)))))))) # label(t49_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6538 (all A (-v1_xboole_0(A) & v5_grcat_1(A) -> (all B (m3_grcat_1(B,A) <-> m1_subset_1(B,A))))) # label(redefinition_m3_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6539 (all A (l1_grcat_1(A) & v3_grcat_1(A) -> (all B (l1_grcat_1(B) & v3_grcat_1(B) -> -((all C (-v3_struct_0(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & l1_rlvect_1(C) & v6_rlvect_1(C) -> (all D (-v3_struct_0(D) & v4_rlvect_1(D) & l1_rlvect_1(D) & v6_rlvect_1(D) & v5_rlvect_1(D) -> (all E (v5_rlvect_1(E) & l1_rlvect_1(E) & v6_rlvect_1(E) & v4_rlvect_1(E) & -v3_struct_0(E) -> -(m1_grcat_1(B,C,D) & m1_grcat_1(A,D,E)))))))) & k9_grcat_1(A) = k10_grcat_1(B)))))) # label(t26_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6540 (all A all B all C (l1_rlvect_1(A) & -v3_struct_0(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(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)) & v5_rlvect_1(B) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all D all E all F (g1_grcat_1(D,E,F) = g1_grcat_1(A,B,C) -> E = B & F = C & D = A)))) # label(free_g1_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6541 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v5_rlvect_1(B) & l1_rlvect_1(B) & v6_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m4_grcat_1(C,A,B) -> ((all D (m1_grcat_1(D,A,B) & v2_grcat_1(D) <-> r2_hidden(D,C))) <-> C = k18_grcat_1(A,B)))))))) # label(d27_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6542 (all A (l1_struct_0(A) -> m2_relset_1(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(k7_grcat_1(A)))) # label(dt_k7_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6543 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (m1_subset_1(B,u2_cat_1(k28_grcat_1(A))) -> (all C (m1_subset_1(C,u2_cat_1(k28_grcat_1(A))) -> (r2_hidden(k4_tarski(C,B),k1_relat_1(u5_cat_1(k28_grcat_1(A)))) <-> k2_cat_1(k28_grcat_1(A),C) = k3_cat_1(k28_grcat_1(A),B)))))))) # label(t46_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6544 (all A (l1_grcat_1(A) -> (v2_grcat_1(A) -> A = g1_grcat_1(u1_grcat_1(A),u2_grcat_1(A),u3_grcat_1(A))))) # label(abstractness_v2_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6545 (all A (l1_grcat_1(A) -> (v3_grcat_1(A) <-> v1_grcat_1(k11_grcat_1(A),k9_grcat_1(A),k10_grcat_1(A))))) # label(d18_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6546 (all A (l1_grcat_1(A) -> -v3_struct_0(k10_grcat_1(A)) & v6_rlvect_1(k10_grcat_1(A)) & l1_rlvect_1(k10_grcat_1(A)) & v5_rlvect_1(k10_grcat_1(A)) & v4_rlvect_1(k10_grcat_1(A)))) # label(dt_k10_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6547 (all A (-v1_xboole_0(A) & v1_classes2(A) -> k29_grcat_1(A) = a_1_0_grcat_1(A))) # label(d37_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6548 (all A (l1_grcat_1(A) -> l1_rlvect_1(u1_grcat_1(A)) & v6_rlvect_1(u1_grcat_1(A)) & v5_rlvect_1(u1_grcat_1(A)) & v4_rlvect_1(u1_grcat_1(A)) & -v3_struct_0(u1_grcat_1(A)))) # label(dt_u1_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6549 (all A (v3_grcat_1(A) & l1_grcat_1(A) & v2_grcat_1(A) -> (exists B (v5_rlvect_1(B) & l1_rlvect_1(B) & (exists C (-v3_struct_0(C) & v5_rlvect_1(C) & (exists D (v1_funct_1(D) & m1_grcat_1(A,B,C) & g1_grcat_1(B,C,D) = A & v1_grcat_1(D,B,C) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C)))) & l1_rlvect_1(C) & v6_rlvect_1(C) & v4_rlvect_1(C))) & v6_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B))))) # label(t25_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6550 (all A (-v1_xboole_0(A) & v5_grcat_1(A) -> (all B (m3_grcat_1(B,A) -> v3_grcat_1(B) & l1_grcat_1(B))))) # label(dt_m3_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6551 (all A (l2_struct_0(A) & -v3_struct_0(A) -> (all B (l2_struct_0(B) & -v3_struct_0(B) -> k2_funcop_1(u1_struct_0(A),k1_rlvect_1(B)) = k8_grcat_1(A,B))))) # label(d12_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6552 (all A all B (v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(B) & v5_rlvect_1(B) & -v3_struct_0(B) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> k14_grcat_1(A,B) = k12_grcat_1(A,B))) # label(redefinition_k14_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6553 (all A all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) & l1_cat_1(A) & v2_cat_1(A) -> m1_subset_1(k1_grcat_1(A,B),k1_zfmisc_1(u2_cat_1(A))))) # label(dt_k1_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6554 (all A (v4_grcat_1(A) & -v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(k20_grcat_1(A),k20_grcat_1(A)),k20_grcat_1(A)) -> (k27_grcat_1(A) = B <-> (all C (m3_grcat_1(C,k20_grcat_1(A)) -> (all D (m3_grcat_1(D,k20_grcat_1(A)) -> (k21_grcat_1(A,C) = k22_grcat_1(A,D) <-> r2_hidden(k4_tarski(C,D),k1_relat_1(B))))))) & (all C (m3_grcat_1(C,k20_grcat_1(A)) -> (all D (m3_grcat_1(D,k20_grcat_1(A)) -> (r2_hidden(k4_tarski(C,D),k1_relat_1(B)) -> k15_grcat_1(C,D) = k1_funct_1(B,k4_tarski(C,D)))))))))))) # label(d35_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6555 (all A (-v1_xboole_0(A) & v4_grcat_1(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k20_grcat_1(A),A) & v1_funct_2(B,k20_grcat_1(A),A) -> ((all C (m3_grcat_1(C,k20_grcat_1(A)) -> k8_funct_2(k20_grcat_1(A),A,B,C) = k22_grcat_1(A,C))) <-> k25_grcat_1(A) = B))))) # label(d33_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6556 (all A (-v1_xboole_0(A) & v1_classes2(A) -> v1_cat_1(k28_grcat_1(A)) & v2_cat_1(k28_grcat_1(A)))) # label(fc11_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6557 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) -> (all B (v5_rlvect_1(B) & l1_rlvect_1(B) & v6_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (l1_grcat_1(C) & v2_grcat_1(C) -> (k10_grcat_1(C) = B & v1_grcat_1(k11_grcat_1(C),k9_grcat_1(C),k10_grcat_1(C)) & k9_grcat_1(C) = A -> m1_grcat_1(C,A,B) & v2_grcat_1(C)))))))) # label(t19_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6558 (all A (v1_classes2(A) & -v1_xboole_0(A) -> -v1_xboole_0(k19_grcat_1(A)))) # label(fc8_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6559 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (m1_subset_1(B,u2_cat_1(k28_grcat_1(A))) -> (all C (m1_subset_1(C,u2_cat_1(k28_grcat_1(A))) -> (all D (m3_grcat_1(D,k20_grcat_1(k19_grcat_1(A))) -> (all E (m3_grcat_1(E,k20_grcat_1(k19_grcat_1(A))) -> (D = B & C = E -> (k2_cat_1(k28_grcat_1(A),C) = k3_cat_1(k28_grcat_1(A),B) -> k22_grcat_1(k19_grcat_1(A),D) = k21_grcat_1(k19_grcat_1(A),E)) & (r2_hidden(k4_tarski(E,D),k1_relat_1(k27_grcat_1(k19_grcat_1(A)))) -> k3_cat_1(k28_grcat_1(A),B) = k2_cat_1(k28_grcat_1(A),C)) & (k21_grcat_1(k19_grcat_1(A),D) = k21_grcat_1(k19_grcat_1(A),E) -> k2_cat_1(k28_grcat_1(A),B) = k2_cat_1(k28_grcat_1(A),C)) & (k22_grcat_1(k19_grcat_1(A),D) = k22_grcat_1(k19_grcat_1(A),E) -> k3_cat_1(k28_grcat_1(A),B) = k3_cat_1(k28_grcat_1(A),C)) & (k3_cat_1(k28_grcat_1(A),C) = k3_cat_1(k28_grcat_1(A),B) -> k22_grcat_1(k19_grcat_1(A),E) = k22_grcat_1(k19_grcat_1(A),D)) & (k2_cat_1(k28_grcat_1(A),B) = k2_cat_1(k28_grcat_1(A),C) -> k21_grcat_1(k19_grcat_1(A),D) = k21_grcat_1(k19_grcat_1(A),E)) & (k2_cat_1(k28_grcat_1(A),C) = k3_cat_1(k28_grcat_1(A),B) -> k4_cat_1(k28_grcat_1(A),B,C) = k15_grcat_1(E,D)) & (k2_cat_1(k28_grcat_1(A),C) = k3_cat_1(k28_grcat_1(A),B) -> r2_hidden(k4_tarski(E,D),k1_relat_1(k27_grcat_1(k19_grcat_1(A))))) & (k22_grcat_1(k19_grcat_1(A),D) = k21_grcat_1(k19_grcat_1(A),E) -> k3_cat_1(k28_grcat_1(A),B) = k2_cat_1(k28_grcat_1(A),C))))))))))))) # label(t50_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6560 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (all B (-v3_struct_0(B) & l1_rlvect_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k2_rlvect_1(A,D,E)) = k2_rlvect_1(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)))))) <-> v1_grcat_1(C,A,B)))))))) # label(d13_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6561 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) -> g1_cat_1(B,k1_grcat_1(A,B),k2_grcat_1(A,B),k3_grcat_1(A,B),k4_grcat_1(A,B),k5_grcat_1(A,B)) = k6_grcat_1(A,B))))) # label(d10_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6562 (all A (-v1_xboole_0(A) & v4_grcat_1(A) -> -v1_xboole_0(k20_grcat_1(A)) & v5_grcat_1(k20_grcat_1(A)))) # label(dt_k20_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6563 (all A all B (l1_struct_0(B) & l1_struct_0(A) -> (exists C m5_grcat_1(C,A,B)))) # label(existence_m5_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6564 (all A (v1_classes2(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) -> (all E (m1_subset_1(E,A) -> m1_subset_1(k3_mcart_1(B,C,D),A) & m1_subset_1(k4_mcart_1(B,C,D,E),A))))))))))) # label(t3_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6565 $T # label(dt_m5_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6566 (all A all B (m1_subset_1(B,k20_grcat_1(A)) & v4_grcat_1(A) & -v1_xboole_0(A) -> k21_grcat_1(A,B) = k9_grcat_1(B))) # label(redefinition_k21_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6567 (all A all B all C (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(B) & m4_grcat_1(C,A,B) & v4_rlvect_1(A) -> (exists D (m1_subset_1(D,C) & v3_grcat_1(D) & v2_grcat_1(D))))) # label(rc9_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.79 6568 (all A (-v1_xboole_0(A) & v1_classes2(A) -> v4_grcat_1(k19_grcat_1(A)) & -v1_xboole_0(k19_grcat_1(A)))) # label(fc9_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6569 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> v1_grcat_1(k7_grcat_1(A),A,A))) # label(t21_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6570 (all A (l1_grcat_1(A) -> k11_grcat_1(A) = u3_grcat_1(A))) # label(d16_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6571 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) & -v1_xboole_0(B) & l1_cat_1(A) & v2_cat_1(A) -> -v1_xboole_0(k1_grcat_1(A,B)))) # label(fc2_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6572 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> g1_grcat_1(A,A,k7_grcat_1(A)) = k13_grcat_1(A))) # label(d20_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6573 (all A all B (-v3_struct_0(A) & v4_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(B) & v6_rlvect_1(B) & l1_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(A) & v5_rlvect_1(A) -> v2_grcat_1(k12_grcat_1(A,B)))) # label(fc4_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6574 (all A (-v1_xboole_0(A) & v1_classes2(A) -> a_1_1_grcat_1(A) = k31_grcat_1(A))) # label(d39_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6575 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) -> k3_tarski(a_2_0_grcat_1(A,B)) = k1_grcat_1(A,B))))) # label(d5_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6576 (all A (v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & l1_rlvect_1(B) & v6_rlvect_1(B) -> k12_grcat_1(A,B) = g1_grcat_1(A,B,k8_grcat_1(A,B)))))) # label(d17_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6577 (all A (-v1_xboole_0(A) & v1_classes2(A) -> r2_hidden(k2_algstr_1,k19_grcat_1(A)))) # label(t42_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6578 (all A all B (-v1_xboole_0(B) & v1_classes2(B) -> (r2_hidden(A,a_1_1_grcat_1(B)) <-> (exists C (m1_subset_1(C,u1_cat_1(k30_grcat_1(B))) & C = A & (exists D (-v3_struct_0(D) & l1_rlvect_1(D) & D = C & v1_midsp_2(D) & v6_rlvect_1(D) & v5_rlvect_1(D) & v4_rlvect_1(D) & v3_rlvect_1(D)))))))) # label(fraenkel_a_1_1_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6579 (all A (-v1_xboole_0(A) & v5_grcat_1(A) -> (exists B (v2_grcat_1(B) & v3_grcat_1(B) & m1_subset_1(B,A))))) # label(rc7_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6580 (all A all B (-v3_struct_0(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(B) & l1_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (exists C m4_grcat_1(C,A,B)))) # label(existence_m4_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6581 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) -> k2_partfun1(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B) = k5_grcat_1(A,B))))) # label(d9_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6582 (all A (-v1_xboole_0(A) & v1_classes2(A) -> r2_hidden(k2_algstr_1,k29_grcat_1(A)))) # label(t51_grcat_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6583 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (k1_tsep_1(A,B,C) = A -> (r4_tsep_1(A,B,C) <-> -(-m1_pre_topc(C,B) & (all D (v1_borsuk_1(D,A) & m1_pre_topc(D,A) & -v3_struct_0(D) -> (all E (-v3_struct_0(E) & v1_borsuk_1(E,A) & m1_pre_topc(E,A) -> -(m1_pre_topc(D,B) & -((all F (v1_tsep_1(F,A) & m1_pre_topc(F,A) & -v3_struct_0(F) -> -(m1_pre_topc(F,k2_tsep_1(A,B,C)) & A = k1_tsep_1(A,k1_tsep_1(A,D,E),F)))) & A != k1_tsep_1(A,D,E)) & m1_pre_topc(E,C)))))) & -m1_pre_topc(B,C))) | r1_tsep_1(A,B,C)))))))) # label(t94_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6584 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & v1_tsep_1(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & v1_tsep_1(C,A) & m1_pre_topc(C,A) -> (-r1_tsep_1(A,B,C) -> v1_tsep_1(k2_tsep_1(A,B,C),A) & m1_pre_topc(k2_tsep_1(A,B,C),A)))))))) # label(t33_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6585 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (all D (-v3_struct_0(D) & m1_pre_topc(D,A) -> (r3_tsep_1(A,C,D) & r3_tsep_1(A,B,D) <-> r3_tsep_1(A,k1_tsep_1(A,B,C),D)))))))))) # label(t79_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6586 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> -((all C (v1_pre_topc(C) & v1_borsuk_1(C,A) & m1_pre_topc(C,A) & -v3_struct_0(C) -> u1_struct_0(C) != B)) & v4_pre_topc(B,A)))))) # label(t15_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6587 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) -> (m1_pre_topc(C,B) & m1_pre_topc(B,C) -> g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))))))))) # label(t6_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6588 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (all D (-v3_struct_0(D) & m1_pre_topc(D,A) -> k1_tsep_1(A,B,k1_tsep_1(A,C,D)) = k1_tsep_1(A,k1_tsep_1(A,B,C),D))))))))) # label(t21_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6589 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (all D (m1_pre_topc(D,A) & -v3_struct_0(D) -> (r4_tsep_1(A,C,D) & r4_tsep_1(A,B,D) -> r4_tsep_1(A,k1_tsep_1(A,B,C),D)) & (r4_tsep_1(A,D,C) & r4_tsep_1(A,D,B) -> r4_tsep_1(A,D,k1_tsep_1(A,B,C))))))))))) # label(t92_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6590 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (all D (-v3_struct_0(D) & m1_pre_topc(D,A) -> (r3_tsep_1(A,B,D) -> r1_tsep_1(A,B,C) | r3_tsep_1(A,k2_tsep_1(A,B,C),D)))))))))) # label(t78_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6591 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (k1_tsep_1(A,B,C) = g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) <-> m1_pre_topc(B,C)))))))) # label(t23_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6592 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(B) = C -> v3_pre_topc(C,A)))) <-> v1_tsep_1(B,A)))))) # label(d1_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6593 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (-r1_tsep_1(A,B,C) -> m1_pre_topc(k2_tsep_1(A,B,C),B) & m1_pre_topc(k2_tsep_1(A,B,C),C)))))))) # label(t30_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6594 (all A (l1_pre_topc(A) & v1_pre_topc(A) -> k3_pre_topc(A,k2_pre_topc(A)) = A)) # label(t3_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6595 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(B) = C -> (m1_pre_topc(B,A) & v1_borsuk_1(B,A) <-> v4_pre_topc(C,A))))))))) # label(t11_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6596 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & v1_tsep_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (C = D -> (v3_pre_topc(C,A) <-> v3_pre_topc(D,B))))))))))) # label(t17_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6597 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (-r1_tsep_1(A,B,C) -> (-(-m1_pre_topc(C,B) & (all D (-v3_struct_0(D) & v1_tsep_1(D,A) & m1_pre_topc(D,A) -> (all E (-v3_struct_0(E) & m1_pre_topc(E,A) & v1_tsep_1(E,A) -> -(m1_pre_topc(k2_tsep_1(A,D,k1_tsep_1(A,B,C)),B) & m1_pre_topc(k2_tsep_1(A,E,k1_tsep_1(A,B,C)),C) & -(-m1_pre_topc(k1_tsep_1(A,B,C),k1_tsep_1(A,D,E)) & (all F (v1_borsuk_1(F,A) & m1_pre_topc(F,A) & -v3_struct_0(F) -> -(m1_pre_topc(k2_tsep_1(A,F,k1_tsep_1(A,B,C)),k2_tsep_1(A,B,C)) & g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = k1_tsep_1(A,k1_tsep_1(A,D,E),F)))))))))) & -m1_pre_topc(B,C)) <-> r4_tsep_1(A,B,C))))))))) # label(t96_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6598 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & v1_tsep_1(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (r1_tarski(u1_struct_0(B),u1_struct_0(C)) -> m1_pre_topc(B,C) & v1_tsep_1(B,C)))))))) # label(t19_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6599 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> m1_subset_1(u1_struct_0(B),k1_zfmisc_1(u1_struct_0(A))))))) # label(t1_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6600 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & v1_borsuk_1(B,A) & -v3_struct_0(B) -> (all C (v1_borsuk_1(C,A) & m1_pre_topc(C,A) & -v3_struct_0(C) -> v1_borsuk_1(k1_tsep_1(A,B,C),A) & m1_pre_topc(k1_tsep_1(A,B,C),A))))))) # label(t24_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6601 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) & v3_pre_topc(C,A) -> r2_tsep_1(A,B,C)))))))) # label(t54_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6602 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_tsep_1(A,B,C) & -r1_tarski(C,B) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(D) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(E) -> -(-(-r1_tarski(k4_subset_1(u1_struct_0(A),B,C),k4_subset_1(u1_struct_0(A),D,E)) & (all F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(F) -> -(v3_pre_topc(F,A) & r1_tarski(k5_subset_1(u1_struct_0(A),F,k4_subset_1(u1_struct_0(A),B,C)),k5_subset_1(u1_struct_0(A),B,C)) & k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),D,E),F) = u1_struct_0(A))))) & r1_tarski(k5_subset_1(u1_struct_0(A),E,k4_subset_1(u1_struct_0(A),B,C)),C) & r1_tarski(k5_subset_1(u1_struct_0(A),D,k4_subset_1(u1_struct_0(A),B,C)),B) & v4_pre_topc(E,A) & v4_pre_topc(D,A)))))) & -r1_tarski(B,C)))))))) # label(t60_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6603 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & v1_borsuk_1(B,A) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & v1_borsuk_1(C,A) & m1_pre_topc(C,A) -> (r1_tsep_1(A,B,C) <-> r3_tsep_1(A,B,C)))))))) # label(t70_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6604 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & v1_borsuk_1(B,A) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (r1_tarski(u1_struct_0(B),u1_struct_0(C)) -> v1_borsuk_1(B,C) & m1_pre_topc(B,C) & -v3_struct_0(B)))))))) # label(t14_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6605 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> ((exists D (v1_tsep_1(D,A) & (exists E (v1_tsep_1(E,A) & m1_pre_topc(E,A) & m1_pre_topc(B,D) & (r1_tsep_1(A,k2_tsep_1(A,D,E),k1_tsep_1(A,B,C)) | r1_tsep_1(A,D,E)) & m1_pre_topc(C,E) & -v3_struct_0(E))) & m1_pre_topc(D,A) & -v3_struct_0(D))) <-> r3_tsep_1(A,B,C)))))))) # label(t83_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6606 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(u1_struct_0(A) = k4_subset_1(u1_struct_0(A),B,C) & r2_tsep_1(A,B,C) & -r1_tarski(B,C) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(D) -> (all E (-v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(D,A) & r1_tarski(D,B) & -((all F (-v1_xboole_0(F) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_tarski(F,k5_subset_1(u1_struct_0(A),B,C)) & v4_pre_topc(F,A) & k4_subset_1(u1_struct_0(A),B,C) = k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),D,E),F)))) & k4_subset_1(u1_struct_0(A),D,E) != k4_subset_1(u1_struct_0(A),B,C)) & r1_tarski(E,C) & v3_pre_topc(E,A)))))) & -r1_tarski(C,B)))))))) # label(t66_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6607 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (r1_tsep_1(A,B,C) & k1_tsep_1(A,B,C) = A -> (r4_tsep_1(A,B,C) <-> v1_tsep_1(B,A) & m1_pre_topc(C,A) & v1_tsep_1(C,A) & m1_pre_topc(B,A))))))))) # label(t98_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6608 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_connsp_1(A,B,C) <-> (exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & (exists E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & r1_tarski(C,E) & v3_pre_topc(E,A) & v3_pre_topc(D,A) & r1_xboole_0(E,B) & r1_xboole_0(D,C) & r1_tarski(B,D)))))))))))) # label(t48_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6609 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (exists B (m1_pre_topc(B,A) & v1_pre_topc(B) & v2_pre_topc(B) & v1_tsep_1(B,A) & -v3_struct_0(B))))) # label(rc2_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6610 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) & v4_pre_topc(C,A) -> (r1_xboole_0(B,C) <-> r1_connsp_1(A,B,C))))))))) # label(t38_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6611 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v1_tsep_1(B,A) & m1_pre_topc(B,A) -> (all C (v1_tsep_1(C,A) & m1_pre_topc(C,A) -> r4_tsep_1(A,B,C))))))) # label(t88_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6612 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(B) = D & u1_struct_0(C) = E -> r1_connsp_1(A,D,E)))))) <-> r3_tsep_1(A,B,C)))))))) # label(d8_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6613 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_tsep_1(A,C,D) & r2_tsep_1(A,B,D) -> r2_tsep_1(A,k4_subset_1(u1_struct_0(A),B,C),D)))))))))) # label(t58_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6614 $T # label(t50_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6615 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,C) -> r2_tsep_1(A,B,C)))))))) # label(t52_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6616 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_tsep_1(A,B,C) -> r2_tsep_1(A,k4_subset_1(u1_struct_0(A),B,D),k4_subset_1(u1_struct_0(A),C,D))))))))))) # label(t55_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6617 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) -> (u1_struct_0(C) = u1_struct_0(B) -> g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(C),u1_pre_topc(C))))))))) # label(t5_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6618 $T # label(t69_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6619 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (m1_pre_topc(B,C) -> r4_tsep_1(A,B,C)))))))) # label(t86_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6620 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(D,B) & r1_tarski(E,C) & r2_tsep_1(A,C,B) -> r2_tsep_1(A,k4_subset_1(u1_struct_0(A),C,D),k4_subset_1(u1_struct_0(A),B,E))))))))))))) # label(t56_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6621 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (r3_tsep_1(A,B,C) & m1_pre_topc(k1_tsep_1(A,B,C),A) & v1_tsep_1(k1_tsep_1(A,B,C),A) -> v1_tsep_1(B,A) & m1_pre_topc(B,A)))))))) # label(t75_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6622 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_connsp_1(A,k6_subset_1(u1_struct_0(A),B,C),k6_subset_1(u1_struct_0(A),C,B)) <-> r2_tsep_1(A,B,C)))))))) # label(d7_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6623 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (k1_tsep_1(A,B,C) = A & r3_tsep_1(A,B,C) -> v1_tsep_1(B,A) & m1_pre_topc(B,A)))))))) # label(t74_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6624 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(C,A) & v3_pre_topc(B,A) -> (r1_connsp_1(A,B,C) <-> r1_xboole_0(B,C))))))))) # label(t41_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6625 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> m1_pre_topc(B,k1_tsep_1(A,B,C)))))))) # label(t22_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6626 $T # label(t26_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6627 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (r3_tsep_1(A,B,C) -> r1_tsep_1(A,B,C)))))))) # label(t68_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6628 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_connsp_1(A,B,C) <-> (exists D ((exists E (r1_tarski(B,D) & r1_tarski(C,E) & v4_pre_topc(E,A) & v4_pre_topc(D,A) & r1_xboole_0(k5_subset_1(u1_struct_0(A),D,E),k4_subset_1(u1_struct_0(A),B,C)) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))))))))))) # label(t47_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6629 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r1_connsp_1(A,B,C) -> r1_connsp_1(A,k5_subset_1(u1_struct_0(A),B,D),k5_subset_1(u1_struct_0(A),C,D))))))))))) # label(t43_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6630 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (all D (m1_pre_topc(D,A) -> (all E (m1_pre_topc(E,A) -> (m1_pre_topc(D,B) & m1_pre_topc(E,C) & r3_tsep_1(A,B,C) -> r3_tsep_1(A,D,E)))))))))))) # label(t77_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6631 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (k4_subset_1(u1_struct_0(A),B,C) = u1_struct_0(A) -> ((exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & (exists E ((exists F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) & r1_tarski(E,C) & r1_tarski(F,k5_subset_1(u1_struct_0(A),B,C)) & v4_pre_topc(D,A) & v3_pre_topc(F,A) & v4_pre_topc(E,A) & r1_tarski(D,B) & k4_subset_1(u1_struct_0(A),B,C) = k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),D,E),F))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))))))) <-> r2_tsep_1(A,B,C))))))))) # label(t61_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6632 $T # label(t28_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6633 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (r3_tsep_1(A,B,C) <-> r1_tsep_1(A,B,C) & r4_tsep_1(A,B,C)))))))) # label(t85_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6634 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(k4_subset_1(u1_struct_0(A),B,C),A) & r1_connsp_1(A,B,C) -> v4_pre_topc(B,A) & v4_pre_topc(C,A)))))))) # label(t39_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6635 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (v1_borsuk_1(B,A) & m1_pre_topc(B,A) -> (all C (v1_borsuk_1(C,A) & m1_pre_topc(C,A) -> r4_tsep_1(A,B,C))))))) # label(t87_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6636 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_tsep_1(A,B,C) <-> (exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & (exists E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & (exists F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) & r1_tarski(k5_subset_1(u1_struct_0(A),F,k4_subset_1(u1_struct_0(A),B,C)),k5_subset_1(u1_struct_0(A),B,C)) & k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),D,E),F) = u1_struct_0(A) & v3_pre_topc(D,A) & v3_pre_topc(E,A) & v4_pre_topc(F,A) & r1_tarski(k5_subset_1(u1_struct_0(A),E,k4_subset_1(u1_struct_0(A),B,C)),C) & r1_tarski(k5_subset_1(u1_struct_0(A),D,k4_subset_1(u1_struct_0(A),B,C)),B)))))))))))))) # label(t63_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6637 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (k1_tsep_1(A,B,C) = A -> (r4_tsep_1(A,B,C) <-> -((all D (m1_pre_topc(D,A) & v1_tsep_1(D,A) & -v3_struct_0(D) -> (all E (v1_tsep_1(E,A) & m1_pre_topc(E,A) & -v3_struct_0(E) -> -(m1_pre_topc(E,C) & -(k1_tsep_1(A,D,E) != A & (all F (v1_borsuk_1(F,A) & m1_pre_topc(F,A) & -v3_struct_0(F) -> -(A = k1_tsep_1(A,k1_tsep_1(A,D,E),F) & m1_pre_topc(F,k2_tsep_1(A,B,C)))))) & m1_pre_topc(D,B)))))) & -m1_pre_topc(C,B) & -m1_pre_topc(B,C))) | r1_tsep_1(A,B,C)))))))) # label(t97_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6638 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (all D (m1_pre_topc(D,A) & -v3_struct_0(D) -> (-r1_tsep_1(A,B,C) -> k1_tsep_1(A,k2_tsep_1(A,B,C),D) = k2_tsep_1(A,k1_tsep_1(A,B,D),k1_tsep_1(A,C,D)) & k1_tsep_1(A,D,k2_tsep_1(A,B,C)) = k2_tsep_1(A,k1_tsep_1(A,D,B),k1_tsep_1(A,D,C))))))))))) # label(t36_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6639 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_tsep_1(A,C,D) & r2_tsep_1(A,B,D) -> r2_tsep_1(A,k5_subset_1(u1_struct_0(A),B,C),D)))))))))) # label(t57_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6640 $T # label(d4_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6641 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (r3_tsep_1(A,B,C) <-> (exists D (-v3_struct_0(D) & m1_pre_topc(D,A) & (exists E ((r1_tsep_1(A,D,E) | r1_tsep_1(A,k2_tsep_1(A,D,E),k1_tsep_1(A,B,C))) & m1_pre_topc(C,E) & m1_pre_topc(B,D) & r4_tsep_1(A,D,E) & m1_pre_topc(E,A) & -v3_struct_0(E)))))))))))) # label(t99_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6642 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(C,A) & v4_pre_topc(B,A) -> r2_tsep_1(A,B,C)))))))) # label(t53_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6643 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) -> (r1_tsep_1(A,B,C) <-> r1_xboole_0(u1_struct_0(B),u1_struct_0(C))))))))) # label(d3_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6644 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (exists C (-v3_struct_0(C) & v1_pre_topc(C) & u1_struct_0(C) = B & m1_pre_topc(C,A))))))) # label(t10_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6645 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r1_connsp_1(A,C,D) | r1_connsp_1(A,B,D) -> r1_connsp_1(A,k5_subset_1(u1_struct_0(A),B,C),D)))))))))) # label(t44_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6646 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (-r1_tsep_1(A,B,C) -> (m1_pre_topc(B,C) -> g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = k2_tsep_1(A,B,C)) & (m1_pre_topc(C,B) -> k2_tsep_1(A,B,C) = g1_pre_topc(u1_struct_0(C),u1_pre_topc(C))) & (k2_tsep_1(A,B,C) = g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) -> m1_pre_topc(C,B)) & (g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = k2_tsep_1(A,B,C) -> m1_pre_topc(B,C))))))))) # label(t31_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6647 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_tsep_1(A,B,C) <-> (exists D ((exists E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & (exists F (r1_tarski(k5_subset_1(u1_struct_0(A),E,k4_subset_1(u1_struct_0(A),B,C)),C) & v3_pre_topc(F,A) & v4_pre_topc(E,A) & v4_pre_topc(D,A) & k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),D,E),F) = u1_struct_0(A) & r1_tarski(k5_subset_1(u1_struct_0(A),F,k4_subset_1(u1_struct_0(A),B,C)),k5_subset_1(u1_struct_0(A),B,C)) & r1_tarski(k5_subset_1(u1_struct_0(A),D,k4_subset_1(u1_struct_0(A),B,C)),B) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))))))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))))))))))) # label(t59_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6648 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_connsp_1(A,B,C) <-> r1_xboole_0(B,C) & r2_tsep_1(A,B,C)))))))) # label(t51_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6649 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (all D (-v3_struct_0(D) & m1_pre_topc(D,A) -> (-r1_tsep_1(A,C,D) -> (r4_tsep_1(A,B,C) & r4_tsep_1(A,B,D) -> r4_tsep_1(A,B,k2_tsep_1(A,C,D))) & (r4_tsep_1(A,D,B) & r4_tsep_1(A,C,B) -> r4_tsep_1(A,k2_tsep_1(A,C,D),B))))))))))) # label(t91_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6650 (all A all B all C (m1_pre_topc(B,A) & m1_pre_topc(C,A) & l1_pre_topc(A) -> (r4_tsep_1(A,B,C) -> r4_tsep_1(A,C,B)))) # label(symmetry_r4_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6651 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (C = u1_struct_0(B) -> (v3_pre_topc(C,A) <-> v1_tsep_1(B,A) & m1_pre_topc(B,A))))))))) # label(t16_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6652 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_connsp_1(A,B,C) & v3_pre_topc(k4_subset_1(u1_struct_0(A),B,C),A) -> v3_pre_topc(B,A) & v3_pre_topc(C,A)))))))) # label(t42_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6653 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_connsp_1(A,B,C) <-> (exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & (exists E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & r1_tarski(B,D) & r1_tarski(C,E) & v3_pre_topc(D,A) & v3_pre_topc(E,A) & r1_xboole_0(k5_subset_1(u1_struct_0(A),D,E),k4_subset_1(u1_struct_0(A),B,C))))))))))))) # label(t49_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6654 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r1_connsp_1(A,k4_subset_1(u1_struct_0(A),B,C),D) <-> r1_connsp_1(A,B,D) & r1_connsp_1(A,C,D)))))))))) # label(t45_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6655 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (r1_tsep_1(A,B,C) & k1_tsep_1(A,B,C) = A -> (r4_tsep_1(A,B,C) <-> m1_pre_topc(B,A) & m1_pre_topc(C,A) & v1_borsuk_1(C,A) & v1_borsuk_1(B,A))))))))) # label(t95_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6656 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v1_borsuk_1(B,A) & m1_pre_topc(B,A) -> (all C (v1_borsuk_1(C,B) & m1_pre_topc(C,B) -> m1_pre_topc(C,A) & v1_borsuk_1(C,A))))))) # label(t13_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6657 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,B) -> m1_pre_topc(C,A))))))) # label(t7_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6658 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) -> (v4_pre_topc(C,A) & r1_tarski(D,C) & E = D & r1_tarski(C,u1_struct_0(B)) -> (v4_pre_topc(E,B) <-> v4_pre_topc(D,A))))))))))))) # label(t8_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6659 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & v1_tsep_1(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) & v1_tsep_1(C,A) -> v1_tsep_1(k1_tsep_1(A,B,C),A) & m1_pre_topc(k1_tsep_1(A,B,C),A))))))) # label(t25_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6660 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> ((exists D (-v3_struct_0(D) & m1_pre_topc(D,A) & (exists E (-v3_struct_0(E) & m1_pre_topc(C,E) & r1_tsep_1(A,D,C) & r1_tsep_1(A,E,B) & m1_pre_topc(B,D) & m1_pre_topc(E,A) & v1_borsuk_1(E,A))) & v1_borsuk_1(D,A))) <-> r3_tsep_1(A,B,C)))))))) # label(t80_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6661 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((exists D ((exists E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & r1_tarski(B,D) & r1_tarski(C,E) & r1_xboole_0(D,C) & v4_pre_topc(E,A) & v4_pre_topc(D,A) & r1_xboole_0(E,B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))))) <-> r1_connsp_1(A,B,C)))))))) # label(t46_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6662 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (all D (m1_pre_topc(D,A) & -v3_struct_0(D) -> -(-r1_tsep_1(A,B,D) & -r1_tsep_1(A,D,C) & -(k2_tsep_1(A,D,k1_tsep_1(A,B,C)) = k1_tsep_1(A,k2_tsep_1(A,D,B),k2_tsep_1(A,D,C)) & k1_tsep_1(A,k2_tsep_1(A,B,D),k2_tsep_1(A,C,D)) = k2_tsep_1(A,k1_tsep_1(A,B,C),D))))))))))) # label(t35_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6663 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (v1_borsuk_1(k1_tsep_1(A,B,C),A) & m1_pre_topc(k1_tsep_1(A,B,C),A) & r3_tsep_1(A,B,C) -> m1_pre_topc(B,A) & v1_borsuk_1(B,A)))))))) # label(t72_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6664 (all A (l1_pre_topc(A) -> m1_pre_topc(A,A))) # label(t2_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6665 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(-r1_tarski(B,C) & -r1_tarski(C,B) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(D) -> (all E (-v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_tarski(k5_subset_1(u1_struct_0(A),D,k4_subset_1(u1_struct_0(A),B,C)),B) & -((all F (-v1_xboole_0(F) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_tarski(k5_subset_1(u1_struct_0(A),F,k4_subset_1(u1_struct_0(A),B,C)),k5_subset_1(u1_struct_0(A),B,C)) & k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),D,E),F) = u1_struct_0(A) & v4_pre_topc(F,A)))) & -r1_tarski(k4_subset_1(u1_struct_0(A),B,C),k4_subset_1(u1_struct_0(A),D,E))) & r1_tarski(k5_subset_1(u1_struct_0(A),E,k4_subset_1(u1_struct_0(A),B,C)),C) & v3_pre_topc(E,A) & v3_pre_topc(D,A)))))) & r2_tsep_1(A,B,C)))))))) # label(t64_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6666 (all A all B all C (m1_pre_topc(B,A) & -v3_struct_0(C) & m1_pre_topc(C,A) & -v3_struct_0(B) & l1_pre_topc(A) & -v3_struct_0(A) -> m1_pre_topc(k1_tsep_1(A,B,C),A) & v1_pre_topc(k1_tsep_1(A,B,C)) & -v3_struct_0(k1_tsep_1(A,B,C)))) # label(dt_k1_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6667 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) -> (r4_tsep_1(A,B,C) <-> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (D = u1_struct_0(B) & E = u1_struct_0(C) -> r2_tsep_1(A,D,E))))))))))))) # label(d9_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6668 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_xboole_0(B,C) & v3_pre_topc(B,A) -> r1_xboole_0(B,k6_pre_topc(A,C))))))))) # label(t40_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6669 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (-r1_tsep_1(A,B,C) -> m1_pre_topc(k2_tsep_1(A,B,C),k1_tsep_1(A,B,C))))))))) # label(t34_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6670 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (all D (m1_pre_topc(D,A) & -v3_struct_0(D) -> (all E (-v3_struct_0(E) & m1_pre_topc(E,A) -> (r4_tsep_1(A,C,B) & m1_pre_topc(E,C) & m1_pre_topc(D,B) -> r4_tsep_1(A,k1_tsep_1(A,C,D),k1_tsep_1(A,B,E)) & r4_tsep_1(A,k1_tsep_1(A,D,C),k1_tsep_1(A,E,B))))))))))))) # label(t90_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6671 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (k1_tsep_1(A,B,C) = A & r3_tsep_1(A,B,C) -> m1_pre_topc(B,A) & v1_borsuk_1(B,A)))))))) # label(t71_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6672 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (exists B (m1_pre_topc(B,A) & v1_tsep_1(B,A) & v2_pre_topc(B) & v1_pre_topc(B))))) # label(rc1_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6673 (all A all B all C (l1_pre_topc(A) & m1_pre_topc(C,A) & m1_pre_topc(B,A) -> (r1_tsep_1(A,B,C) -> r1_tsep_1(A,C,B)))) # label(symmetry_r1_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6674 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> (r2_tsep_1(A,B,C) -> r2_tsep_1(A,C,B)))) # label(symmetry_r2_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.80 6675 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (all D (m1_pre_topc(D,A) & v1_pre_topc(D) & -v3_struct_0(D) -> (u1_struct_0(D) = k2_xboole_0(u1_struct_0(B),u1_struct_0(C)) <-> D = k1_tsep_1(A,B,C)))))))))) # label(d2_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.81 6676 (all A all B all C (-v3_struct_0(B) & -v3_struct_0(C) & m1_pre_topc(C,A) & m1_pre_topc(B,A) & l1_pre_topc(A) & -v3_struct_0(A) -> k1_tsep_1(A,C,B) = k1_tsep_1(A,B,C))) # label(commutativity_k1_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.81 6677 (all A all B all C (l1_pre_topc(A) & -v3_struct_0(B) & m1_pre_topc(B,A) & -v3_struct_0(C) & m1_pre_topc(C,A) & -v3_struct_0(A) -> v1_pre_topc(k2_tsep_1(A,B,C)) & m1_pre_topc(k2_tsep_1(A,B,C),A) & -v3_struct_0(k2_tsep_1(A,B,C)))) # label(dt_k2_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.81 6678 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (all D (-v3_struct_0(D) & m1_pre_topc(D,A) -> (-r1_tsep_1(A,B,C) -> k2_tsep_1(A,B,C) = k2_tsep_1(A,C,B)) & (-r1_tsep_1(A,k2_tsep_1(A,B,C),D) & -r1_tsep_1(A,B,C) | -r1_tsep_1(A,B,k2_tsep_1(A,C,D)) & -r1_tsep_1(A,C,D) -> k2_tsep_1(A,k2_tsep_1(A,B,C),D) = k2_tsep_1(A,B,k2_tsep_1(A,C,D))))))))))) # label(t29_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.81 6679 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v1_borsuk_1(B,A) & m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (C = D -> (v4_pre_topc(D,B) <-> v4_pre_topc(C,A))))))))))) # label(t12_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.81 6680 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (-r1_tsep_1(A,B,C) -> (all D (m1_pre_topc(D,A) & v1_pre_topc(D) & -v3_struct_0(D) -> (k2_tsep_1(A,B,C) = D <-> u1_struct_0(D) = k3_xboole_0(u1_struct_0(B),u1_struct_0(C)))))))))))) # label(d5_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.81 6681 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) -> (v3_pre_topc(C,A) & r1_tarski(D,C) & E = D & r1_tarski(C,u1_struct_0(B)) -> (v3_pre_topc(E,B) <-> v3_pre_topc(D,A))))))))))))) # label(t9_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.81 6682 $T # label(d6_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.81 6683 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(A) = k4_subset_1(u1_struct_0(A),B,C) -> (r2_tsep_1(A,B,C) <-> (exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & (exists E ((exists F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) & k4_subset_1(u1_struct_0(A),B,C) = k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),D,E),F) & r1_tarski(F,k5_subset_1(u1_struct_0(A),B,C)) & v3_pre_topc(D,A) & v4_pre_topc(F,A) & v3_pre_topc(E,A) & r1_tarski(E,C) & r1_tarski(D,B))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))))))))))))))) # label(t65_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.81 6684 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v1_tsep_1(B,A) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & v1_tsep_1(C,A) & m1_pre_topc(C,A) -> (r1_tsep_1(A,B,C) <-> r3_tsep_1(A,B,C)))))))) # label(t73_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.81 6685 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (all D (m1_pre_topc(D,A) & -v3_struct_0(D) -> (r3_tsep_1(A,C,D) -> r1_tsep_1(A,C,B) | r3_tsep_1(A,k2_tsep_1(A,C,B),k2_tsep_1(A,D,B)) & r3_tsep_1(A,k2_tsep_1(A,B,C),k2_tsep_1(A,B,D)) | r1_tsep_1(A,D,B)))))))))) # label(t76_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.81 6686 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> ((exists D (-v3_struct_0(D) & (exists E (-v3_struct_0(E) & m1_pre_topc(C,E) & r1_tsep_1(A,D,C) & r1_tsep_1(A,E,B) & m1_pre_topc(B,D) & m1_pre_topc(E,A) & v1_tsep_1(E,A))) & m1_pre_topc(D,A) & v1_tsep_1(D,A))) <-> r3_tsep_1(A,B,C)))))))) # label(t82_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.81 6687 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (-r1_tsep_1(A,B,C) -> (r4_tsep_1(A,B,C) <-> -(-m1_pre_topc(B,C) & (all D (-v3_struct_0(D) & v1_borsuk_1(D,A) & m1_pre_topc(D,A) -> (all E (m1_pre_topc(E,A) & v1_borsuk_1(E,A) & -v3_struct_0(E) -> -(m1_pre_topc(k2_tsep_1(A,D,k1_tsep_1(A,B,C)),B) & -((all F (v1_tsep_1(F,A) & m1_pre_topc(F,A) & -v3_struct_0(F) -> -(m1_pre_topc(k2_tsep_1(A,F,k1_tsep_1(A,B,C)),k2_tsep_1(A,B,C)) & k1_tsep_1(A,k1_tsep_1(A,D,E),F) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))))) & -m1_pre_topc(k1_tsep_1(A,B,C),k1_tsep_1(A,D,E))) & m1_pre_topc(k2_tsep_1(A,E,k1_tsep_1(A,B,C)),C)))))) & -m1_pre_topc(C,B)))))))))) # label(t93_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.81 6688 (all A all B all C (l1_pre_topc(A) & m1_pre_topc(B,A) & m1_pre_topc(C,A) -> (r3_tsep_1(A,B,C) -> r3_tsep_1(A,C,B)))) # label(symmetry_r3_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.81 6689 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & v1_tsep_1(B,A) -> (all C (m1_pre_topc(C,B) & v1_tsep_1(C,B) -> m1_pre_topc(C,A) & v1_tsep_1(C,A))))))) # label(t18_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.81 6690 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -((all C (-v3_struct_0(C) & v1_pre_topc(C) & m1_pre_topc(C,A) & v1_tsep_1(C,A) -> u1_struct_0(C) != B)) & v3_pre_topc(B,A)))))) # label(t20_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.81 6691 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> ((exists D (v1_borsuk_1(D,A) & (exists E (-v3_struct_0(E) & v1_borsuk_1(E,A) & m1_pre_topc(B,D) & (r1_tsep_1(A,k2_tsep_1(A,D,E),k1_tsep_1(A,B,C)) | r1_tsep_1(A,D,E)) & m1_pre_topc(C,E) & m1_pre_topc(E,A))) & m1_pre_topc(D,A) & -v3_struct_0(D))) <-> r3_tsep_1(A,B,C)))))))) # label(t81_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.23/115.81 6692 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(u1_struct_0(A) = k4_subset_1(u1_struct_0(A),B,C) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(D) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(E) -> -(v4_pre_topc(D,A) & v4_pre_topc(E,A) & r1_tarski(D,B) & -((all F (-v1_xboole_0(F) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_tarski(F,k5_subset_1(u1_struct_0(A),B,C)) & v3_pre_topc(F,A) & k4_subset_1(u1_struct_0(A),B,C) = k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),D,E),F)))) & k4_subset_1(u1_struct_0(A),B,C) != k4_subset_1(u1_struct_0(A),D,E)) & r1_tarski(E,C)))))) & -r1_tarski(C,B) & -r1_tarski(B,C) & r2_tsep_1(A,B,C)))))))) # label(t62_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.81 6693 $T # label(t84_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.81 6694 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) & v1_borsuk_1(B,A) -> (all C (m1_pre_topc(C,A) & v1_borsuk_1(C,A) & -v3_struct_0(C) -> (-r1_tsep_1(A,B,C) -> v1_borsuk_1(k2_tsep_1(A,B,C),A) & m1_pre_topc(k2_tsep_1(A,B,C),A)))))))) # label(t32_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.81 6695 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) -> (m1_pre_topc(B,C) <-> r1_tarski(u1_struct_0(B),u1_struct_0(C))))))))) # label(t4_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.81 6696 $T # label(t37_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.81 6697 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_connsp_1(A,B,C) <-> (exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & (exists E (r1_tarski(B,D) & r1_tarski(C,E) & r1_xboole_0(k5_subset_1(u1_struct_0(A),D,E),k4_subset_1(u1_struct_0(A),B,C)) & r2_tsep_1(A,D,E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))))))))))))) # label(t67_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.81 6698 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (all D (-v3_struct_0(D) & m1_pre_topc(D,A) -> (r4_tsep_1(A,B,C) -> r4_tsep_1(A,k1_tsep_1(A,B,D),k1_tsep_1(A,C,D))))))))))) # label(t89_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.81 6699 $T # label(t27_tsep_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.81 6700 (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]. 116.28/115.81 6701 (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]. 116.28/115.81 6702 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]. 116.28/115.81 6703 (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]. 116.28/115.81 6704 (all A (A = k6_lattices(k1_lattice3(A)) & v14_lattices(k1_lattice3(A)))) # label(t4_lattice3) # label(axiom) # label(non_clause). [assumption]. 116.28/115.81 6705 (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]. 116.28/115.81 6706 (all A v4_lattice3(k1_lattice3(A))) # label(t25_lattice3) # label(axiom) # label(non_clause). [assumption]. 116.28/115.81 6707 (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]. 116.28/115.81 6708 (all A (l1_orders_2(A) -> (v2_lattice3(k7_lattice3(A)) <-> v1_lattice3(A)))) # label(t10_lattice3) # label(axiom) # label(non_clause). [assumption]. 116.28/115.81 6709 (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]. 116.28/115.81 6710 (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]. 116.28/115.81 6711 (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]. 116.28/115.81 6712 (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]. 116.28/115.81 6713 (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]. 116.28/115.81 6714 (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]. 116.28/115.81 6715 (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]. 116.28/115.81 6716 (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]. 116.28/115.81 6717 (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]. 116.28/115.81 6718 (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]. 116.28/115.81 6719 (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]. 116.28/115.81 6720 (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]. 116.28/115.81 6721 (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]. 116.28/115.81 6722 (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]. 116.28/115.81 6723 (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]. 116.28/115.81 6724 (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]. 116.28/115.81 6725 (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]. 116.28/115.81 6726 (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]. 116.28/115.81 6727 (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]. 116.28/115.81 6728 (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]. 116.28/115.81 6729 (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]. 116.28/115.81 6730 (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]. 116.28/115.81 6731 (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]. 116.28/115.81 6732 (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]. 116.28/115.81 6733 (all A (v13_lattices(k1_lattice3(A)) & k1_xboole_0 = k5_lattices(k1_lattice3(A)))) # label(t3_lattice3) # label(axiom) # label(non_clause). [assumption]. 116.28/115.81 6734 (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]. 116.28/115.81 6735 (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]. 116.28/115.81 6736 (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]. 116.28/115.81 6737 (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]. 116.28/115.81 6738 (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]. 116.28/115.81 6739 (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]. 116.28/115.81 6740 (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]. 116.28/115.81 6741 (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]. 116.28/115.81 6742 (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]. 116.28/115.81 6743 (all A (v3_lattices(k1_lattice3(A)) & l3_lattices(k1_lattice3(A)))) # label(dt_k1_lattice3) # label(axiom) # label(non_clause). [assumption]. 116.28/115.81 6744 (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]. 116.28/115.81 6745 (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]. 116.28/115.81 6746 (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]. 116.28/115.81 6747 $T # label(t39_lattice3) # label(axiom) # label(non_clause). [assumption]. 116.28/115.81 6748 (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]. 116.28/115.81 6749 (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]. 116.28/115.81 6750 (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]. 116.28/115.81 6751 (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]. 116.28/115.81 6752 (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]. 116.28/115.81 6753 (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]. 116.28/115.81 6754 (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]. 116.28/115.81 6755 (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]. 116.28/115.81 6756 (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]. 116.28/115.81 6757 (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]. 116.28/115.81 6758 (all A (l1_orders_2(A) -> (v2_lattice3(A) -> -v3_struct_0(A)))) # label(cc2_lattice3) # label(axiom) # label(non_clause). [assumption]. 116.28/115.81 6759 (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]. 116.28/115.81 6760 (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]. 116.28/115.81 6761 (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]. 116.28/115.81 6762 (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]. 116.28/115.81 6763 (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]. 116.28/115.81 6764 (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]. 116.28/115.81 6765 (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]. 116.28/115.81 6766 (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]. 116.28/115.81 6767 (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]. 116.28/115.81 6768 (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]. 116.28/115.81 6769 (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]. 116.28/115.81 6770 (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]. 116.28/115.81 6771 (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]. 116.28/115.81 6772 (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]. 116.28/115.81 6773 (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]. 116.28/115.81 6774 (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]. 116.28/115.81 6775 (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]. 116.28/115.81 6776 (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]. 116.28/115.81 6777 (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]. 116.28/115.81 6778 (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]. 116.28/115.81 6779 (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]. 116.28/115.81 6780 (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]. 116.28/115.81 6781 (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]. 116.28/115.81 6782 (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]. 116.28/115.81 6783 (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]. 116.28/115.81 6784 (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]. 116.28/115.81 6785 (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]. 116.28/115.81 6786 (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]. 116.28/115.81 6787 (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]. 116.28/115.81 6788 (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]. 116.28/115.81 6789 (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]. 116.28/115.81 6790 (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]. 116.28/115.81 6791 (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]. 116.28/115.81 6792 (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]. 116.28/115.82 6793 (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]. 116.28/115.82 6794 (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]. 116.28/115.82 6795 (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]. 116.28/115.82 6796 (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]. 116.28/115.82 6797 (all A v6_lattice3(k1_lattice3(A))) # label(t27_lattice3) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6798 (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]. 116.28/115.82 6799 (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]. 116.28/115.82 6800 (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]. 116.28/115.82 6801 (all A (l1_orders_2(A) -> (v1_lattice3(A) -> -v3_struct_0(A)))) # label(cc1_lattice3) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6802 (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]. 116.28/115.82 6803 (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]. 116.28/115.82 6804 (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]. 116.28/115.82 6805 (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]. 116.28/115.82 6806 (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]. 116.28/115.82 6807 (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]. 116.28/115.82 6808 (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]. 116.28/115.82 6809 (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]. 116.28/115.82 6810 (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]. 116.28/115.82 6811 (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]. 116.28/115.82 6812 (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]. 116.28/115.82 6813 (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]. 116.28/115.82 6814 (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]. 116.28/115.82 6815 (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]. 116.28/115.82 6816 (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]. 116.28/115.82 6817 (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]. 116.28/115.82 6818 (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]. 116.28/115.82 6819 (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]. 116.28/115.82 6820 (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]. 116.28/115.82 6821 (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]. 116.28/115.82 6822 (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]. 116.28/115.82 6823 (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]. 116.28/115.82 6824 (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]. 116.28/115.82 6825 (all A v5_lattice3(k1_lattice3(A))) # label(t26_lattice3) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6826 (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]. 116.28/115.82 6827 (all A (v3_lattices(k1_lattice3(A)) & -v3_struct_0(k1_lattice3(A)))) # label(fc1_lattice3) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6828 (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]. 116.28/115.82 6829 (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]. 116.28/115.82 6830 (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]. 116.28/115.82 6831 (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]. 116.28/115.82 6832 (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]. 116.28/115.82 6833 (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]. 116.28/115.82 6834 (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]. 116.28/115.82 6835 (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]. 116.28/115.82 6836 (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]. 116.28/115.82 6837 (all A all B (m1_subset_1(B,k4_partfun1(k13_finseq_1(A),A)) & -v1_xboole_0(A) -> m2_finseq_1(k1_unialg_1(A,B),k4_partfun1(k13_finseq_1(A),A)))) # label(dt_k1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6838 (exists A (-v3_struct_0(A) & v7_unialg_1(A) & v8_unialg_1(A) & v6_unialg_1(A) & v3_unialg_1(A) & l1_unialg_1(A))) # label(rc5_unialg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6839 (exists A (v3_unialg_1(A) & -v3_struct_0(A) & l1_unialg_1(A))) # label(rc3_unialg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6840 (exists A l1_unialg_1(A)) # label(existence_l1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6841 (all A (l1_unialg_1(A) -> (v4_unialg_1(u1_unialg_1(A),u1_struct_0(A)) <-> v6_unialg_1(A)))) # label(d7_unialg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6842 (all A (-v3_struct_0(A) & v6_unialg_1(A) & l1_unialg_1(A) & v8_unialg_1(A) -> m2_finseq_1(k3_unialg_1(A),k5_numbers))) # label(dt_k3_unialg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6843 (all A (-v3_struct_0(A) & l1_unialg_1(A) & v8_unialg_1(A) & v6_unialg_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(B,k4_finseq_1(u1_unialg_1(A))) -> v1_funct_1(k1_funct_1(u1_unialg_1(A),B)) & m2_relset_1(k1_funct_1(u1_unialg_1(A),B),k13_finseq_1(u1_struct_0(A)),u1_struct_0(A))))))) # label(t5_unialg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6844 (all A all B (m1_finseq_1(B,k4_partfun1(k13_finseq_1(A),A)) & -v1_xboole_0(A) -> v3_unialg_1(g1_unialg_1(A,B)) & -v3_struct_0(g1_unialg_1(A,B)))) # label(fc1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6845 $T # label(d6_unialg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6846 (all A all B (v1_funct_1(B) & m2_relset_1(B,k13_finseq_1(A),A) -> ((all C (m2_finseq_1(C,A) -> (all D (m2_finseq_1(D,A) -> (r2_hidden(C,k1_relat_1(B)) & k3_finseq_1(D) = k3_finseq_1(C) -> r2_hidden(D,k1_relat_1(B))))))) <-> v2_unialg_1(B,A)))) # label(d2_unialg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6847 (all A (v6_unialg_1(A) & l1_unialg_1(A) & v8_unialg_1(A) & -v3_struct_0(A) -> (all B (m2_finseq_1(B,k5_numbers) -> (k3_finseq_1(B) = k3_finseq_1(u1_unialg_1(A)) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(C,k4_finseq_1(B)) -> (all D (v1_unialg_1(D,u1_struct_0(A)) & m2_relset_1(D,k13_finseq_1(u1_struct_0(A)),u1_struct_0(A)) & v1_funct_1(D) & -v1_xboole_0(D) -> (D = k1_funct_1(u1_unialg_1(A),C) -> k1_funct_1(B,C) = k2_unialg_1(u1_struct_0(A),D))))))) <-> B = k3_unialg_1(A)))))) # label(d11_unialg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6848 (exists A (v3_unialg_1(A) & l1_unialg_1(A))) # label(rc2_unialg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6849 (all A (-v1_xboole_0(A) -> (exists B (-v1_xboole_0(B) & v2_unialg_1(B,A) & v1_unialg_1(B,A) & v1_funct_1(B) & v1_relat_1(B) & m1_relset_1(B,k13_finseq_1(A),A))))) # label(rc1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6850 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> v2_unialg_1(k2_funcop_1(k1_tarski(k6_finseq_1(A)),B),A) & m2_relset_1(k2_funcop_1(k1_tarski(k6_finseq_1(A)),B),k13_finseq_1(A),A) & v1_unialg_1(k2_funcop_1(k1_tarski(k6_finseq_1(A)),B),A) & v1_funct_1(k2_funcop_1(k1_tarski(k6_finseq_1(A)),B)) & -v1_xboole_0(k2_funcop_1(k1_tarski(k6_finseq_1(A)),B)))))) # label(t2_unialg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6851 (all A (l1_unialg_1(A) -> l1_struct_0(A))) # label(dt_l1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6852 (all A (v6_unialg_1(A) & l1_unialg_1(A) -> v1_relat_1(u1_unialg_1(A)) & v1_funct_1(u1_unialg_1(A)) & v4_unialg_1(u1_unialg_1(A),u1_struct_0(A)) & v1_finseq_1(u1_unialg_1(A)))) # label(fc2_unialg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6853 (all A all B (m1_finseq_1(B,k4_partfun1(k13_finseq_1(A),A)) -> l1_unialg_1(g1_unialg_1(A,B)) & v3_unialg_1(g1_unialg_1(A,B)))) # label(dt_g1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6854 (all A all B (m2_finseq_1(B,k4_partfun1(k13_finseq_1(A),A)) -> (v5_unialg_1(B,A) <-> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_relset_1(D,k13_finseq_1(A),A) & v1_funct_1(D) -> (r2_hidden(C,k4_finseq_1(B)) & D = k1_funct_1(B,C) -> v2_unialg_1(D,A))))))))) # label(d5_unialg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6855 (all A (l1_unialg_1(A) -> m2_finseq_1(u1_unialg_1(A),k4_partfun1(k13_finseq_1(u1_struct_0(A)),u1_struct_0(A))))) # label(dt_u1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6856 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k13_finseq_1(A),A) & v1_unialg_1(B,A) & -v1_xboole_0(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> ((all D (m2_finseq_1(D,A) -> (r2_hidden(D,k1_relat_1(B)) -> k3_finseq_1(D) = C))) <-> C = k2_unialg_1(A,B)))))))) # label(d10_unialg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6857 (all A (l1_unialg_1(A) & v7_unialg_1(A) -> v1_funct_1(u1_unialg_1(A)) & v1_finseq_1(u1_unialg_1(A)) & v5_unialg_1(u1_unialg_1(A),u1_struct_0(A)) & v1_relat_1(u1_unialg_1(A)))) # label(fc3_unialg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6858 (all A all B (m2_relset_1(B,k13_finseq_1(A),A) & v1_funct_1(B) -> (v1_unialg_1(B,A) <-> (all C (m2_finseq_1(C,A) -> (all D (m2_finseq_1(D,A) -> (r2_hidden(C,k1_relat_1(B)) & r2_hidden(D,k1_relat_1(B)) -> k3_finseq_1(D) = k3_finseq_1(C))))))))) # label(d1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6859 (all A all B (m1_finseq_1(B,k4_partfun1(k13_finseq_1(A),A)) -> (all C all D (g1_unialg_1(C,D) = g1_unialg_1(A,B) -> A = C & D = B)))) # label(free_g1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6860 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_relset_1(B,k13_finseq_1(A),A) & v1_unialg_1(B,A) & v1_funct_1(B) -> m2_subset_1(k2_unialg_1(A,B),k1_numbers,k5_numbers))) # label(dt_k2_unialg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6861 (all A all B (m2_finseq_1(B,k4_partfun1(k13_finseq_1(A),A)) -> (v4_unialg_1(B,A) <-> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (v1_funct_1(D) & m2_relset_1(D,k13_finseq_1(A),A) -> (D = k1_funct_1(B,C) & r2_hidden(C,k4_finseq_1(B)) -> v1_unialg_1(D,A))))))))) # label(d4_unialg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6862 (all A (l1_unialg_1(A) -> (v3_unialg_1(A) -> A = g1_unialg_1(u1_struct_0(A),u1_unialg_1(A))))) # label(abstractness_v3_unialg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6863 (all A (l1_unialg_1(A) -> (v2_relat_1(u1_unialg_1(A)) & k1_xboole_0 != u1_unialg_1(A) <-> v8_unialg_1(A)))) # label(d9_unialg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6864 (all A all B (m1_subset_1(B,k4_partfun1(k13_finseq_1(A),A)) & -v1_xboole_0(A) -> k1_unialg_1(A,B) = k5_finseq_1(B))) # label(redefinition_k1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6865 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> m1_subset_1(k2_funcop_1(k1_tarski(k6_finseq_1(A)),B),k4_partfun1(k13_finseq_1(A),A)))))) # label(t3_unialg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6866 $T # label(d3_unialg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6867 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,k4_partfun1(k13_finseq_1(A),A)) -> (C = k2_funcop_1(k1_tarski(k6_finseq_1(A)),B) -> v2_relat_1(k1_unialg_1(A,C)) & v5_unialg_1(k1_unialg_1(A,C),A) & v4_unialg_1(k1_unialg_1(A,C),A)))))))) # label(t4_unialg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6868 (all A all B (m2_relset_1(B,k13_finseq_1(A),A) & v1_funct_1(B) -> -(-v1_xboole_0(B) & k1_xboole_0 = k1_relat_1(B)) & -(v1_xboole_0(B) & k1_xboole_0 != k1_relat_1(B)))) # label(t1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6869 (all A (l1_unialg_1(A) & v8_unialg_1(A) -> -v1_xboole_0(u1_unialg_1(A)) & v2_relat_1(u1_unialg_1(A)) & v1_finseq_1(u1_unialg_1(A)) & v1_funct_1(u1_unialg_1(A)) & v1_relat_1(u1_unialg_1(A)))) # label(fc4_unialg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6870 (all A (-v1_xboole_0(A) -> (exists B (v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B) & v5_unialg_1(B,A) & v4_unialg_1(B,A) & v1_finseq_1(B) & m1_finseq_1(B,k4_partfun1(k13_finseq_1(A),A)))))) # label(rc4_unialg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6871 (all A (l1_unialg_1(A) -> (v5_unialg_1(u1_unialg_1(A),u1_struct_0(A)) <-> v7_unialg_1(A)))) # label(d8_unialg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6872 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B (r2_hidden(B,k1_relat_1(A)) -> v6_unialg_1(k1_funct_1(A,B)) & l1_unialg_1(k1_funct_1(A,B)) & v8_unialg_1(k1_funct_1(A,B)) & v7_unialg_1(k1_funct_1(A,B)) & -v3_struct_0(k1_funct_1(A,B)))) <-> v1_pralg_1(A)))) # label(d10_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6873 (all A all B all C (v2_relat_1(B) & v4_pralg_1(C) & m1_pralg_1(C,A,B) & m1_pboole(B,A) & -v1_xboole_0(A) -> v1_funct_1(k22_pralg_1(A,B,C)) & v1_unialg_1(k22_pralg_1(A,B,C),k4_card_3(B)) & m2_relset_1(k22_pralg_1(A,B,C),k3_finseq_2(k4_card_3(B)),k4_card_3(B)) & v2_unialg_1(k22_pralg_1(A,B,C),k4_card_3(B)) & -v1_xboole_0(k22_pralg_1(A,B,C)))) # label(dt_k22_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6874 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_pralg_1(A) -> v1_funct_1(A) & v2_pralg_1(A) & v1_relat_1(A))) # label(cc1_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6875 (all A (-v1_xboole_0(A) -> (exists B (m1_subset_1(B,k3_finseq_2(A)) & v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) & -v1_xboole_0(B))))) # label(rc2_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6876 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) & v3_pralg_1(B) & v1_pralg_1(B) -> (all C (m2_finseq_1(C,k4_partfun1(k13_finseq_1(k4_card_3(k12_pralg_1(A,B))),k4_card_3(k12_pralg_1(A,B)))) -> (k3_finseq_1(k13_pralg_1(A,B)) = k3_finseq_1(C) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(C)) -> k22_pralg_1(A,k12_pralg_1(A,B),k23_pralg_1(A,B,D)) = k1_funct_1(C,D)))) <-> C = k24_pralg_1(A,B)))))))) # label(d23_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6877 (all A all B (m1_pboole(B,A) & v2_relat_1(B) & -v1_xboole_0(A) -> (exists C m1_pralg_1(C,A,B)))) # label(existence_m1_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6878 (all A (v4_ordinal2(A) -> -v1_xboole_0(k7_pralg_1(A)) & v1_relat_1(k7_pralg_1(A)) & v1_funct_1(k7_pralg_1(A)) & v1_unialg_1(k7_pralg_1(A),k1_tarski(k1_xboole_0)) & v2_unialg_1(k7_pralg_1(A),k1_tarski(k1_xboole_0)))) # label(fc1_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6879 (all A all B all C (-v1_xboole_0(A) & m1_finseq_1(C,k4_card_3(B)) & m1_pboole(B,A) & v2_relat_1(B) -> k4_funct_5(C) = k17_pralg_1(A,B,C))) # label(redefinition_k17_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6880 (all A (-v3_struct_0(A) & v7_unialg_1(A) & v8_unialg_1(A) & l1_unialg_1(A) & v6_unialg_1(A) -> (all B (v8_unialg_1(B) & l1_unialg_1(B) & v7_unialg_1(B) & v6_unialg_1(B) & -v3_struct_0(B) -> (r1_unialg_2(A,B) -> v3_unialg_1(g1_unialg_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k4_pralg_1(A,B))) & v7_unialg_1(g1_unialg_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k4_pralg_1(A,B))) & v8_unialg_1(g1_unialg_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k4_pralg_1(A,B))) & l1_unialg_1(g1_unialg_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k4_pralg_1(A,B))) & v6_unialg_1(g1_unialg_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k4_pralg_1(A,B))) & -v3_struct_0(g1_unialg_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k4_pralg_1(A,B)))))))) # label(t2_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6881 (all A (-v1_xboole_0(A) -> (all B (v2_relat_1(B) & m1_pboole(B,A) -> (all C (m1_pralg_1(C,A,B) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> k2_unialg_1(k1_funct_1(B,E),k14_pralg_1(A,B,C,E)) = k2_unialg_1(k1_funct_1(B,D),k14_pralg_1(A,B,C,D)))))) <-> v4_pralg_1(C)))))))) # label(t12_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6882 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) & v3_pralg_1(B) & v1_pralg_1(B) -> (all C (v4_ordinal2(C) -> (r2_hidden(C,k4_finseq_1(k13_pralg_1(A,B))) -> (all D (v4_pralg_1(D) & m1_pralg_1(D,A,k12_pralg_1(A,B)) -> (D = k23_pralg_1(A,B,C) <-> (all E (m1_subset_1(E,A) -> (all F (m2_unialg_2(F,u1_struct_0(k11_pralg_1(A,B,E)),k1_unialg_2(k11_pralg_1(A,B,E))) -> (F = k1_funct_1(u1_unialg_1(k11_pralg_1(A,B,E)),C) -> F = k14_pralg_1(A,k12_pralg_1(A,B),D,E)))))))))))))))) # label(d22_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6883 (all A (m1_finseq_1(A,k5_numbers) -> m2_finseq_1(k8_pralg_1(A),k4_partfun1(k13_finseq_1(k1_tarski(k1_xboole_0)),k1_tarski(k1_xboole_0))))) # label(dt_k8_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6884 (all A all B (-v1_xboole_0(A) & v2_relat_1(B) & m1_pboole(B,A) -> (all C (m1_pralg_1(C,A,B) -> m1_pboole(C,A) & v1_funcop_1(C))))) # label(dt_m1_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6885 (all A all B all C (v1_pralg_1(B) & m1_pboole(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k1_funct_1(B,C) = k11_pralg_1(A,B,C))) # label(redefinition_k11_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6886 (all A all B (-v1_xboole_0(A) & m1_pboole(B,A) & v2_relat_1(B) -> (exists C (v1_funcop_1(C) & v4_pralg_1(C) & v1_funct_1(C) & v1_relat_1(C) & m1_pralg_1(C,A,B))))) # label(rc6_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6887 (all A all B all C all D (-v1_xboole_0(A) & v2_relat_1(B) & m1_pboole(B,A) & m1_subset_1(D,A) & m1_pralg_1(C,A,B) -> k1_funct_1(C,D) = k14_pralg_1(A,B,C,D))) # label(redefinition_k14_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6888 (all A all B (-v1_xboole_0(A) & m1_pboole(B,A) & v3_pralg_1(B) & v1_pralg_1(B) -> m2_finseq_1(k13_pralg_1(A,B),k5_numbers))) # label(dt_k13_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6889 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) & v1_funct_1(C) & v2_unialg_1(C,A) & m2_relset_1(C,k3_finseq_2(A),A) & v1_unialg_1(C,A) -> (all D (-v1_xboole_0(D) & v1_unialg_1(D,B) & m2_relset_1(D,k3_finseq_2(B),B) & v2_unialg_1(D,B) & v1_funct_1(D) -> (k2_unialg_1(B,D) = k2_unialg_1(A,C) -> (all E (v1_funct_1(E) & v2_unialg_1(E,k2_zfmisc_1(A,B)) & m2_relset_1(E,k3_finseq_2(k2_zfmisc_1(A,B)),k2_zfmisc_1(A,B)) & v1_unialg_1(E,k2_zfmisc_1(A,B)) & -v1_xboole_0(E) -> ((all F (m2_finseq_1(F,k2_zfmisc_1(A,B)) -> (r2_hidden(F,k1_relat_1(E)) -> k1_funct_1(E,F) = k4_tarski(k1_funct_1(C,k1_pralg_1(A,B,F)),k1_funct_1(D,k2_pralg_1(A,B,F)))))) & k4_finseq_2(k2_unialg_1(A,C),k2_zfmisc_1(A,B)) = k1_relat_1(E) <-> E = k3_pralg_1(A,B,C,D))))))))))))) # label(d3_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6890 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) & v2_relat_1(B) -> (all C (m1_pboole(C,A) & v1_funcop_1(C) -> (m1_pralg_1(C,A,B) <-> (all D (m1_subset_1(D,A) -> -v1_xboole_0(k1_funct_1(C,D)) & v1_funct_1(k1_funct_1(C,D)) & m2_relset_1(k1_funct_1(C,D),k3_finseq_2(k1_funct_1(B,D)),k1_funct_1(B,D)) & v2_unialg_1(k1_funct_1(C,D),k1_funct_1(B,D)) & v1_unialg_1(k1_funct_1(C,D),k1_funct_1(B,D))))))))))) # label(d15_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6891 (all A (m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k4_partfun1(k13_finseq_1(k1_tarski(k1_xboole_0)),k1_tarski(k1_xboole_0))) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(C,k4_finseq_1(B)) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (k1_funct_1(A,C) = D -> k7_pralg_1(D) = k1_funct_1(B,C))))))) & k3_finseq_1(B) = k3_finseq_1(A) <-> k8_pralg_1(A) = B))))) # label(d8_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6892 (exists A (v1_funct_1(A) & v1_pralg_1(A) & v1_relat_1(A))) # label(rc3_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6893 (all A all B all C all D (v2_relat_1(B) & m1_pralg_1(C,A,B) & m1_subset_1(D,A) & m1_pboole(B,A) & -v1_xboole_0(A) -> -v1_xboole_0(k14_pralg_1(A,B,C,D)) & v1_funct_1(k14_pralg_1(A,B,C,D)) & m2_relset_1(k14_pralg_1(A,B,C,D),k3_finseq_2(k1_funct_1(B,D)),k1_funct_1(B,D)) & v2_unialg_1(k14_pralg_1(A,B,C,D),k1_funct_1(B,D)) & v1_unialg_1(k14_pralg_1(A,B,C,D),k1_funct_1(B,D)))) # label(dt_k14_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6894 (all A all B (m1_pboole(B,A) & v2_pralg_1(B) -> (all C (m1_pboole(C,A) -> (C = k12_pralg_1(A,B) <-> (all D -(r2_hidden(D,A) & (all E (l1_struct_0(E) -> -(E = k1_funct_1(B,D) & k1_funct_1(C,D) = u1_struct_0(E))))))))))) # label(d13_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6895 (all A all B all C (m1_finseq_1(C,k2_zfmisc_1(A,B)) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k1_pralg_1(A,B,C) = k15_mcart_1(C))) # label(redefinition_k1_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6896 (all A all B all C (-v1_xboole_0(B) & m1_pboole(C,k2_zfmisc_1(A,B)) -> m1_pboole(k19_pralg_1(A,B,C),A))) # label(dt_k19_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6897 (all A (-v1_xboole_0(A) -> (exists B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) & -v1_xboole_0(B) & m1_finseq_1(B,A))))) # label(rc1_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6898 (all A (-v3_struct_0(A) & v8_unialg_1(A) & l1_unialg_1(A) & v7_unialg_1(A) & v6_unialg_1(A) -> (all B (v7_unialg_1(B) & l1_unialg_1(B) & v8_unialg_1(B) & v6_unialg_1(B) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & v7_unialg_1(C) & v8_unialg_1(C) & l1_unialg_1(C) & v6_unialg_1(C) -> (all D (v6_unialg_1(D) & v8_unialg_1(D) & l1_unialg_1(D) & v7_unialg_1(D) & -v3_struct_0(D) -> (m3_unialg_2(A,B) & r1_unialg_2(B,D) & m3_unialg_2(C,D) -> m3_unialg_2(k5_pralg_1(A,C),k5_pralg_1(B,D))))))))))) # label(t8_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6899 (all A all B (v3_pralg_1(B) & m1_pboole(B,A) & v1_pralg_1(B) & -v1_xboole_0(A) -> -v3_struct_0(k25_pralg_1(A,B)) & v3_unialg_1(k25_pralg_1(A,B)) & v6_unialg_1(k25_pralg_1(A,B)) & v7_unialg_1(k25_pralg_1(A,B)) & l1_unialg_1(k25_pralg_1(A,B)) & v8_unialg_1(k25_pralg_1(A,B)))) # label(dt_k25_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6900 (all A all B all C (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_finseq_1(C,k2_zfmisc_1(A,B)) -> m2_finseq_1(k2_pralg_1(A,B,C),B))) # label(dt_k2_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6901 (all A (v1_relat_1(A) & v1_funcop_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) -> (k15_pralg_1(A,B) = C <-> k1_relat_1(C) = k1_relat_1(A) & (all D (r2_hidden(D,k1_relat_1(A)) -> k1_funct_1(k1_funct_1(A,D),k1_funct_1(B,D)) = k1_funct_1(C,D)))))))))) # label(d17_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6902 (all A all B all C (m1_pboole(C,k2_zfmisc_1(A,B)) -> m1_pboole(k18_pralg_1(A,B,C),k2_zfmisc_1(B,A)))) # label(dt_k18_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6903 (all A all B all C (-v1_xboole_0(A) & m1_pboole(B,A) & m1_subset_1(C,A) & v2_pralg_1(B) -> l1_struct_0(k10_pralg_1(A,B,C)))) # label(dt_k10_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6904 (all A all B all C (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_finseq_1(C,k2_zfmisc_1(A,B)) -> m2_finseq_1(k1_pralg_1(A,B,C),A))) # label(dt_k1_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6905 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_1(C,k2_zfmisc_1(A,B)) -> (all D (m2_finseq_1(D,B) -> ((all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (r2_hidden(E,k4_finseq_1(D)) -> k1_funct_1(D,E) = k2_mcart_1(k1_funct_1(C,E))))) & k3_finseq_1(C) = k3_finseq_1(D) <-> k2_pralg_1(A,B,C) = D))))))))) # label(d2_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6906 (all A all B all C (m1_pboole(C,k2_zfmisc_1(A,B)) -> k2_funct_4(C) = k18_pralg_1(A,B,C))) # label(redefinition_k18_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6907 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> v1_funct_1(k6_pralg_1(A,B)) & v1_funct_2(k6_pralg_1(A,B),k2_zfmisc_1(A,B),k2_zfmisc_1(B,A)) & m2_relset_1(k6_pralg_1(A,B),k2_zfmisc_1(A,B),k2_zfmisc_1(B,A)))) # label(dt_k6_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6908 (all A all B all C (v2_pralg_1(B) & m1_pboole(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k10_pralg_1(A,B,C) = k1_funct_1(B,C))) # label(redefinition_k10_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6909 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) & v2_relat_1(B) -> (all C (v4_pralg_1(C) & m1_pralg_1(C,A,B) -> (all D (v1_funct_1(D) & v1_unialg_1(D,k4_card_3(B)) & v2_unialg_1(D,k4_card_3(B)) & m2_relset_1(D,k3_finseq_2(k4_card_3(B)),k4_card_3(B)) & -v1_xboole_0(D) -> (k1_relat_1(D) = k4_finseq_2(k20_pralg_1(A,B,C),k4_card_3(B)) & (all E (m2_finseq_2(E,k4_card_3(B),k3_finseq_2(k4_card_3(B))) -> (r2_hidden(E,k1_relat_1(D)) -> (k4_finseq_1(E) != k1_xboole_0 -> (all F (-v1_xboole_0(F) -> (all G (m1_pboole(G,k2_zfmisc_1(A,F)) -> (G = k18_pralg_1(k4_finseq_1(E),A,k17_pralg_1(A,B,E)) & k4_finseq_1(E) = F -> k16_pralg_1(A,C,k19_pralg_1(A,F,G)) = k1_funct_1(D,E))))))) & (k1_xboole_0 = k4_finseq_1(E) -> k1_funct_1(D,E) = k16_pralg_1(A,C,k21_pralg_1(A,B)))))) <-> D = k22_pralg_1(A,B,C)))))))))) # label(d21_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6910 (all A (-v3_struct_0(A) & v6_unialg_1(A) & v8_unialg_1(A) & l1_unialg_1(A) & v7_unialg_1(A) -> (all B (v7_unialg_1(B) & v8_unialg_1(B) & l1_unialg_1(B) & v6_unialg_1(B) & -v3_struct_0(B) -> (r1_unialg_2(A,B) -> (all C (m2_unialg_2(C,u1_struct_0(A),k1_unialg_2(A)) -> (all D (m2_unialg_2(D,u1_struct_0(B),k1_unialg_2(B)) -> (all E (m2_unialg_2(E,u1_struct_0(k5_pralg_1(A,B)),k1_unialg_2(k5_pralg_1(A,B))) -> (all F (m2_subset_1(F,k1_numbers,k5_numbers) -> (k1_funct_1(u1_unialg_1(k5_pralg_1(A,B)),F) = E & r2_hidden(F,k4_finseq_1(u1_unialg_1(A))) & k1_funct_1(u1_unialg_1(B),F) = D & C = k1_funct_1(u1_unialg_1(A),F) -> E = k3_pralg_1(u1_struct_0(A),u1_struct_0(B),C,D) & k2_unialg_1(u1_struct_0(B),D) = k2_unialg_1(u1_struct_0(k5_pralg_1(A,B)),E) & k2_unialg_1(u1_struct_0(k5_pralg_1(A,B)),E) = k2_unialg_1(u1_struct_0(A),C))))))))))))))) # label(t6_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6911 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v3_pralg_1(A) <-> (all B all C (r2_hidden(C,k1_relat_1(A)) & r2_hidden(B,k1_relat_1(A)) -> (all D (l1_unialg_1(D) & v8_unialg_1(D) & v7_unialg_1(D) & v6_unialg_1(D) & -v3_struct_0(D) -> (all E (v7_unialg_1(E) & l1_unialg_1(E) & v8_unialg_1(E) & v6_unialg_1(E) & -v3_struct_0(E) -> (k1_funct_1(A,B) = D & E = k1_funct_1(A,C) -> k3_unialg_1(D) = k3_unialg_1(E))))))))))) # label(d12_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6912 (all A (m2_finseq_1(A,k5_numbers) -> v5_unialg_1(k8_pralg_1(A),k1_tarski(k1_xboole_0)) & v2_relat_1(k8_pralg_1(A)) & v4_unialg_1(k8_pralg_1(A),k1_tarski(k1_xboole_0)))) # label(t10_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6913 (all A (-v1_xboole_0(A) -> (all B (v3_pralg_1(B) & m1_pboole(B,A) & v1_pralg_1(B) -> (all C (m2_finseq_1(C,k5_numbers) -> (k13_pralg_1(A,B) = C <-> (all D (m1_subset_1(D,A) -> C = k3_unialg_1(k11_pralg_1(A,B,D))))))))))) # label(d14_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6914 (all A (-v1_xboole_0(A) -> (exists B (v1_relat_1(B) & v1_funct_1(B) & v1_pralg_1(B) & v3_pralg_1(B) & v2_pralg_1(B) & m1_pboole(B,A))))) # label(rc5_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6915 (all A (v7_unialg_1(A) & v8_unialg_1(A) & l1_unialg_1(A) & v6_unialg_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v6_unialg_1(B) & v8_unialg_1(B) & l1_unialg_1(B) & v7_unialg_1(B) -> (r1_unialg_2(A,B) -> r1_unialg_2(k5_pralg_1(A,B),A)))))) # label(t7_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6916 (all A (-v1_xboole_0(A) -> (all B (v3_pralg_1(B) & m1_pboole(B,A) & v1_pralg_1(B) -> g1_unialg_1(k4_card_3(k12_pralg_1(A,B)),k24_pralg_1(A,B)) = k25_pralg_1(A,B))))) # label(d24_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6917 (all A all B all C (m1_pboole(C,k2_zfmisc_1(A,B)) & -v1_xboole_0(B) -> k3_funct_5(C) = k19_pralg_1(A,B,C))) # label(redefinition_k19_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6918 (all A all B (m1_pboole(B,A) -> m1_pboole(k21_pralg_1(A,B),A))) # label(dt_k21_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6919 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> k9_funcop_1(k2_zfmisc_1(A,B),B,A,k6_pralg_1(A,B)) = k2_zfmisc_1(B,A))))) # label(t3_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6920 (all A (m2_finseq_1(A,k5_numbers) -> (A != k1_xboole_0 -> -v3_struct_0(g1_unialg_1(k1_tarski(k1_xboole_0),k8_pralg_1(A))) & v3_unialg_1(g1_unialg_1(k1_tarski(k1_xboole_0),k8_pralg_1(A))) & v6_unialg_1(g1_unialg_1(k1_tarski(k1_xboole_0),k8_pralg_1(A))) & v7_unialg_1(g1_unialg_1(k1_tarski(k1_xboole_0),k8_pralg_1(A))) & l1_unialg_1(g1_unialg_1(k1_tarski(k1_xboole_0),k8_pralg_1(A))) & v8_unialg_1(g1_unialg_1(k1_tarski(k1_xboole_0),k8_pralg_1(A)))))) # label(t11_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6921 (all A (v4_ordinal2(A) -> (all B (m2_relset_1(B,k3_finseq_2(k1_tarski(k1_xboole_0)),k1_tarski(k1_xboole_0)) & v1_funct_1(B) -> (k1_tarski(k2_finseq_2(A,k1_xboole_0)) = k1_relat_1(B) & k2_relat_1(B) = k1_tarski(k1_xboole_0) <-> k7_pralg_1(A) = B))))) # label(d7_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6922 (all A all B (v1_funct_1(A) & v1_funcop_1(A) & v1_funct_1(B) & v1_relat_1(B) & v1_relat_1(A) -> v1_relat_1(k15_pralg_1(A,B)) & v1_funct_1(k15_pralg_1(A,B)))) # label(dt_k15_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6923 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) & v2_relat_1(B) -> (all C (v4_pralg_1(C) & m1_pralg_1(C,A,B) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (k20_pralg_1(A,B,C) = D <-> (all E (m1_subset_1(E,A) -> k2_unialg_1(k1_funct_1(B,E),k14_pralg_1(A,B,C,E)) = D))))))))))) # label(d19_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6924 (all A (-v3_struct_0(A) & v6_unialg_1(A) & v8_unialg_1(A) & l1_unialg_1(A) & v7_unialg_1(A) -> (all B (v6_unialg_1(B) & v8_unialg_1(B) & l1_unialg_1(B) & v7_unialg_1(B) & -v3_struct_0(B) -> (r1_unialg_2(A,B) -> g1_unialg_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k4_pralg_1(A,B)) = k5_pralg_1(A,B)))))) # label(d5_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6925 (all A all B all C (-v1_xboole_0(A) & m1_finseq_1(C,k2_zfmisc_1(A,B)) & -v1_xboole_0(B) -> k16_mcart_1(C) = k2_pralg_1(A,B,C))) # label(redefinition_k2_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6926 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> v2_funct_1(k6_pralg_1(A,B)))))) # label(t4_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6927 (all A (m2_finseq_1(A,k5_numbers) & -v1_xboole_0(A) -> k9_pralg_1(A) = g1_unialg_1(k1_tarski(k1_xboole_0),k8_pralg_1(A)))) # label(d9_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6928 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_1(C,k2_zfmisc_1(A,B)) -> (all D (m2_finseq_1(D,A) -> (k3_finseq_1(C) = k3_finseq_1(D) & (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (r2_hidden(E,k4_finseq_1(D)) -> k1_funct_1(D,E) = k1_mcart_1(k1_funct_1(C,E))))) <-> k1_pralg_1(A,B,C) = D))))))))) # label(d1_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6929 (all A (v4_ordinal2(A) -> m2_relset_1(k7_pralg_1(A),k3_finseq_2(k1_tarski(k1_xboole_0)),k1_tarski(k1_xboole_0)) & v1_funct_1(k7_pralg_1(A)))) # label(dt_k7_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6930 (all A (m1_finseq_1(A,k5_numbers) & -v1_xboole_0(A) -> v3_unialg_1(k9_pralg_1(A)) & v6_unialg_1(k9_pralg_1(A)) & v7_unialg_1(k9_pralg_1(A)) & l1_unialg_1(k9_pralg_1(A)) & v8_unialg_1(k9_pralg_1(A)) & -v3_struct_0(k9_pralg_1(A)))) # label(dt_k9_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.82 6931 (all A all B all C all D (-v1_xboole_0(C) & v1_funct_1(C) & v1_unialg_1(C,A) & -v1_xboole_0(D) & v1_unialg_1(D,B) & v2_unialg_1(D,B) & m1_relset_1(D,k3_finseq_2(B),B) & v1_funct_1(D) & m1_relset_1(C,k3_finseq_2(A),A) & v2_unialg_1(C,A) & -v1_xboole_0(B) & -v1_xboole_0(A) -> v1_unialg_1(k3_pralg_1(A,B,C,D),k2_zfmisc_1(A,B)) & m2_relset_1(k3_pralg_1(A,B,C,D),k3_finseq_2(k2_zfmisc_1(A,B)),k2_zfmisc_1(A,B)) & v2_unialg_1(k3_pralg_1(A,B,C,D),k2_zfmisc_1(A,B)) & v1_funct_1(k3_pralg_1(A,B,C,D)) & -v1_xboole_0(k3_pralg_1(A,B,C,D)))) # label(dt_k3_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6932 (all A exists B (m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v2_pralg_1(B))) # label(rc4_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6933 (all A (v4_ordinal2(A) -> k2_unialg_1(k1_tarski(k1_xboole_0),k7_pralg_1(A)) = A)) # label(t9_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6934 (all A (-v3_struct_0(A) & l1_unialg_1(A) & v8_unialg_1(A) & v7_unialg_1(A) & v6_unialg_1(A) -> (all B (v6_unialg_1(B) & l1_unialg_1(B) & v8_unialg_1(B) & v7_unialg_1(B) & -v3_struct_0(B) -> (r1_unialg_2(A,B) -> v1_funct_1(k6_pralg_1(u1_struct_0(A),u1_struct_0(B))) & v1_funct_2(k6_pralg_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k5_pralg_1(A,B)),u1_struct_0(k5_pralg_1(B,A))) & m2_relset_1(k6_pralg_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k5_pralg_1(A,B)),u1_struct_0(k5_pralg_1(B,A)))))))) # label(t5_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6935 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v4_pralg_1(A) <-> (all B all C (r2_hidden(C,k1_relat_1(A)) & r2_hidden(B,k1_relat_1(A)) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (all E (v1_relat_1(E) & v1_funct_1(E) -> (E = k1_funct_1(A,C) & k1_funct_1(A,B) = D -> (all F (m2_subset_1(F,k1_numbers,k5_numbers) -> (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (all H (-v1_xboole_0(H) -> (all I (-v1_xboole_0(I) -> (k1_relat_1(E) = k4_finseq_2(G,I) & k4_finseq_2(F,H) = k1_relat_1(D) -> (all J (v1_funct_1(J) & v1_unialg_1(J,H) & m2_relset_1(J,k3_finseq_2(H),H) & v2_unialg_1(J,H) & -v1_xboole_0(J) -> (all K (v1_unialg_1(K,I) & v2_unialg_1(K,I) & m2_relset_1(K,k3_finseq_2(I),I) & v1_funct_1(K) & -v1_xboole_0(K) -> (E = K & J = D -> k2_unialg_1(H,J) = k2_unialg_1(I,K))))))))))))))))))))))))) # label(d16_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6936 (all A all B all C (-v1_xboole_0(A) & v2_relat_1(B) & v4_pralg_1(C) & m1_pralg_1(C,A,B) & m1_pboole(B,A) -> m2_subset_1(k20_pralg_1(A,B,C),k1_numbers,k5_numbers))) # label(dt_k20_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6937 (all A all B (-v1_xboole_0(A) & m1_pboole(B,A) & v1_pralg_1(B) -> v2_relat_1(k12_pralg_1(A,B)) & -v3_relat_1(k12_pralg_1(A,B)) & v1_funct_1(k12_pralg_1(A,B)) & v1_relat_1(k12_pralg_1(A,B)))) # label(fc2_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6938 (all A all B all C (-v1_xboole_0(A) & v1_pralg_1(B) & v3_pralg_1(B) & v4_ordinal2(C) & m1_pboole(B,A) -> m1_pralg_1(k23_pralg_1(A,B,C),A,k12_pralg_1(A,B)) & v4_pralg_1(k23_pralg_1(A,B,C)))) # label(dt_k23_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6939 (all A all B (-v1_xboole_0(A) & m1_pboole(B,A) & v2_relat_1(B) -> v1_fraenkel(k4_card_3(B)) & -v1_xboole_0(k4_card_3(B)))) # label(fc3_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6940 (all A all B all C (v1_funcop_1(B) & m1_pboole(C,A) & m1_pboole(B,A) -> m1_pboole(k16_pralg_1(A,B,C),A))) # label(dt_k16_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6941 (all A all B all C (v1_funcop_1(B) & m1_pboole(B,A) & m1_pboole(C,A) -> k15_pralg_1(B,C) = k16_pralg_1(A,B,C))) # label(redefinition_k16_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6942 (all A all B all C (-v1_xboole_0(A) & m1_finseq_1(C,k4_card_3(B)) & m1_pboole(B,A) & v2_relat_1(B) -> m1_pboole(k17_pralg_1(A,B,C),k2_zfmisc_1(k4_finseq_1(C),A)))) # label(dt_k17_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6943 (all A (-v3_struct_0(A) & v6_unialg_1(A) & v8_unialg_1(A) & l1_unialg_1(A) & v7_unialg_1(A) -> (all B (v6_unialg_1(B) & v7_unialg_1(B) & v8_unialg_1(B) & l1_unialg_1(B) & -v3_struct_0(B) -> (r1_unialg_2(A,B) -> (all C (m2_finseq_1(C,k4_partfun1(k13_finseq_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) -> ((all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(C)) -> (all E (-v1_xboole_0(E) & v1_funct_1(E) & v1_unialg_1(E,u1_struct_0(A)) & v2_unialg_1(E,u1_struct_0(A)) & m2_relset_1(E,k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)) -> (all F (v1_funct_1(F) & v1_unialg_1(F,u1_struct_0(B)) & m2_relset_1(F,k3_finseq_2(u1_struct_0(B)),u1_struct_0(B)) & v2_unialg_1(F,u1_struct_0(B)) & -v1_xboole_0(F) -> (k1_funct_1(u1_unialg_1(A),D) = E & F = k1_funct_1(u1_unialg_1(B),D) -> k3_pralg_1(u1_struct_0(A),u1_struct_0(B),E,F) = k1_funct_1(C,D))))))))) & k3_finseq_1(u1_unialg_1(A)) = k3_finseq_1(C) <-> k4_pralg_1(A,B) = C)))))))) # label(d4_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6944 (all A all B (m1_pboole(B,A) & v1_funcop_1(B) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (k16_pralg_1(A,B,C) = D <-> (all E (r2_hidden(E,A) -> (all F (v1_relat_1(F) & v1_funct_1(F) -> (k1_funct_1(B,E) = F -> k1_funct_1(D,E) = k1_funct_1(F,k1_funct_1(C,E)))))))))))))) # label(d18_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6945 (all A all B (-v1_xboole_0(A) & v1_pralg_1(B) & v3_pralg_1(B) & m1_pboole(B,A) -> m2_finseq_1(k24_pralg_1(A,B),k4_partfun1(k13_finseq_1(k4_card_3(k12_pralg_1(A,B))),k4_card_3(k12_pralg_1(A,B)))))) # label(dt_k24_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6946 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_pboole(B,A) & v1_pralg_1(B) -> v7_unialg_1(k11_pralg_1(A,B,C)) & l1_unialg_1(k11_pralg_1(A,B,C)) & v8_unialg_1(k11_pralg_1(A,B,C)) & v6_unialg_1(k11_pralg_1(A,B,C)) & -v3_struct_0(k11_pralg_1(A,B,C)))) # label(dt_k11_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6947 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_pralg_1(A) <-> (all B (r2_hidden(B,k1_relat_1(A)) -> l1_struct_0(k1_funct_1(A,B))))))) # label(d11_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6948 (all A all B (m1_pboole(B,A) & v2_pralg_1(B) -> m1_pboole(k12_pralg_1(A,B),A))) # label(dt_k12_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6949 (all A all B (l1_unialg_1(A) & v7_unialg_1(B) & l1_unialg_1(B) & v8_unialg_1(B) & v6_unialg_1(B) & -v3_struct_0(B) & v8_unialg_1(A) & v7_unialg_1(A) & v6_unialg_1(A) & -v3_struct_0(A) -> -v3_struct_0(k5_pralg_1(A,B)) & v6_unialg_1(k5_pralg_1(A,B)) & v7_unialg_1(k5_pralg_1(A,B)) & l1_unialg_1(k5_pralg_1(A,B)) & v8_unialg_1(k5_pralg_1(A,B)) & v3_unialg_1(k5_pralg_1(A,B)))) # label(dt_k5_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6950 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (k4_finseq_2(C,A) = k4_finseq_2(D,B) -> C = D))))))))) # label(t1_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6951 (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,B),k2_zfmisc_1(B,A)) & m2_relset_1(C,k2_zfmisc_1(A,B),k2_zfmisc_1(B,A)) -> ((all D (m1_subset_1(D,k2_zfmisc_1(A,B)) -> k8_funct_2(k2_zfmisc_1(A,B),k2_zfmisc_1(B,A),C,D) = k1_domain_1(B,A,k3_domain_1(A,B,D),k2_domain_1(A,B,D)))) <-> C = k6_pralg_1(A,B)))))))) # label(d6_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6952 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (C = k21_pralg_1(A,B) <-> (all D (r2_hidden(D,A) -> k1_funct_1(C,D) = k1_subset_1(k1_funct_1(B,D))))))))) # label(d20_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6953 (all A all B (-v3_struct_0(A) & v6_unialg_1(A) & -v3_struct_0(B) & l1_unialg_1(B) & v8_unialg_1(B) & v7_unialg_1(B) & v6_unialg_1(B) & l1_unialg_1(A) & v8_unialg_1(A) & v7_unialg_1(A) -> m2_finseq_1(k4_pralg_1(A,B),k4_partfun1(k13_finseq_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))))) # label(dt_k4_pralg_1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6954 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> k3_t_0topsp(A) = k16_borsuk_1(A,k2_t_0topsp(A)))) # label(d5_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6955 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (k8_funct_2(A,B,C,E) = k8_funct_2(A,B,C,F) & r2_hidden(E,D) -> r2_hidden(F,D)))))) -> k3_funct_2(A,B,C,k2_funct_2(A,B,C,D)) = D))))))))) # label(t2_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6956 (exists A (l1_pre_topc(A) & -v3_struct_0(A) & v2_t_0topsp(A) & v2_pre_topc(A))) # label(rc1_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6957 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> u1_pre_topc(k3_t_0topsp(A)) = a_1_0_t_0topsp(A) & k2_t_0topsp(A) = u1_struct_0(k3_t_0topsp(A)))) # label(t5_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6958 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) -> ((exists C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k3_t_0topsp(B)),u1_struct_0(k3_t_0topsp(A))) & m2_relset_1(C,u1_struct_0(k3_t_0topsp(B)),u1_struct_0(k3_t_0topsp(A))) & v3_tops_2(C,k3_t_0topsp(B),k3_t_0topsp(A)) & r1_rfinseq(k4_t_0topsp(A),k7_funct_2(u1_struct_0(B),u1_struct_0(k3_t_0topsp(B)),u1_struct_0(k3_t_0topsp(A)),k4_t_0topsp(B),C)))) -> r1_t_0topsp(A,B)))))) # label(t14_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6959 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> l1_pre_topc(k3_t_0topsp(A)) & v2_pre_topc(k3_t_0topsp(A)))) # label(dt_k3_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6960 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & v2_t_0topsp(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r2_hidden(k8_borsuk_1(A,A,D,E),k1_t_0topsp(A)) -> k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E) = k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D)))))))))))) # label(t15_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6961 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> k4_t_0topsp(A) = k17_borsuk_1(A,k2_t_0topsp(A)))) # label(d6_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6962 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> -v3_struct_0(k3_t_0topsp(A)) & v2_t_0topsp(k3_t_0topsp(A)) & l1_pre_topc(k3_t_0topsp(A)) & v2_pre_topc(k3_t_0topsp(A)))) # label(t13_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6963 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> v1_t_0topsp(k4_t_0topsp(A),A,k3_t_0topsp(A)))) # label(t12_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6964 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> k2_t_0topsp(A) = k8_eqrel_1(u1_struct_0(A),k1_t_0topsp(A)))) # label(d4_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6965 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> -v1_xboole_0(k2_t_0topsp(A)) & m1_eqrel_1(k2_t_0topsp(A),u1_struct_0(A)))) # label(dt_k2_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6966 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> ((exists C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v3_tops_2(C,A,B) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)))) <-> r1_t_0topsp(A,B)))))) # label(d1_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6967 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(D,A) -> v3_pre_topc(k4_pre_topc(A,B,C,D),B)))) <-> v1_t_0topsp(C,A,B)))))))) # label(d2_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6968 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> -v3_struct_0(k3_t_0topsp(A)) & v2_pre_topc(k3_t_0topsp(A)))) # label(fc1_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6969 (all A (l1_pre_topc(A) -> (v3_struct_0(A) | (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -(C != B & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -((-r2_hidden(B,D) & r2_hidden(C,D) | -r2_hidden(C,D) & r2_hidden(B,D)) & v3_pre_topc(D,A))))))))) <-> v2_t_0topsp(A)))) # label(d7_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6970 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k8_funct_2(u1_struct_0(A),u1_struct_0(k3_t_0topsp(A)),k4_t_0topsp(A),B) = k8_funct_2(u1_struct_0(A),u1_struct_0(k3_t_0topsp(A)),k4_t_0topsp(A),C) <-> r2_hidden(k8_borsuk_1(A,A,C,B),k1_t_0topsp(A))))))))) # label(t9_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6971 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,k2_t_0topsp(A)) -> r1_xboole_0(C,B) | r1_tarski(C,B))))))))) # label(t11_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6972 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(k3_t_0topsp(A))) <-> (exists C (k6_eqrel_1(u1_struct_0(A),k1_t_0topsp(A),C) = B & m1_subset_1(C,u1_struct_0(A)))))))) # label(t7_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6973 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_eqrel_1(u1_struct_0(A),k1_t_0topsp(A),B) = k8_funct_2(u1_struct_0(A),u1_struct_0(k3_t_0topsp(A)),k4_t_0topsp(A),B))))) # label(t8_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6974 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (v2_pre_topc(B) & v2_t_0topsp(B) & l1_pre_topc(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k4_pre_topc(A,B,C,k6_eqrel_1(u1_struct_0(A),k1_t_0topsp(A),D)) = k1_struct_0(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D)))))))))) # label(t16_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6975 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) -> ((all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> (r2_hidden(k4_tarski(E,F),D) <-> r2_hidden(k4_tarski(E,F),C)))))) -> D = C))))))))) # label(t1_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6976 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> v3_relat_2(k1_t_0topsp(A)) & m2_relset_1(k1_t_0topsp(A),u1_struct_0(A),u1_struct_0(A)) & v1_partfun1(k1_t_0topsp(A),u1_struct_0(A),u1_struct_0(A)) & v8_relat_2(k1_t_0topsp(A)))) # label(dt_k1_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6977 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & v2_t_0topsp(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (exists D (v1_funct_1(D) & m2_relset_1(D,u1_struct_0(k3_t_0topsp(A)),u1_struct_0(B)) & k4_borsuk_1(A,k3_t_0topsp(A),B,k4_t_0topsp(A),D) = C & v5_pre_topc(D,k3_t_0topsp(A),B) & v1_funct_2(D,u1_struct_0(k3_t_0topsp(A)),u1_struct_0(B)))))))))) # label(t17_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6978 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r2_hidden(B,k8_funct_2(u1_struct_0(A),u1_struct_0(k3_t_0topsp(A)),k4_t_0topsp(A),B)))))) # label(t3_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6979 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> k1_relat_1(k4_t_0topsp(A)) = u1_struct_0(A) & r1_tarski(k2_relat_1(k4_t_0topsp(A)),u1_struct_0(k3_t_0topsp(A))))) # label(t4_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6980 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(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,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> ((all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(E,A) -> (r2_hidden(C,E) <-> r2_hidden(D,E))))) <-> r2_hidden(k4_tarski(C,D),B)))))) <-> B = k1_t_0topsp(A)))))) # label(d3_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6981 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_t_0topsp(A)))) -> (v3_pre_topc(B,k3_t_0topsp(A)) <-> r2_hidden(k3_tarski(B),u1_pre_topc(A))))))) # label(t6_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6982 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(C,B) & k8_funct_2(u1_struct_0(A),u1_struct_0(k3_t_0topsp(A)),k4_t_0topsp(A),C) = k8_funct_2(u1_struct_0(A),u1_struct_0(k3_t_0topsp(A)),k4_t_0topsp(A),D) -> r2_hidden(D,B))))))))))) # label(t10_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6983 (all A all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> ((exists C (C = A & r2_hidden(k3_tarski(C),u1_pre_topc(B)) & m1_subset_1(C,k1_zfmisc_1(k2_t_0topsp(B))))) <-> r2_hidden(A,a_1_0_t_0topsp(B))))) # label(fraenkel_a_1_0_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6984 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> v1_funct_1(k4_t_0topsp(A)) & v5_pre_topc(k4_t_0topsp(A),A,k3_t_0topsp(A)) & m2_relset_1(k4_t_0topsp(A),u1_struct_0(A),u1_struct_0(k3_t_0topsp(A))) & v1_funct_2(k4_t_0topsp(A),u1_struct_0(A),u1_struct_0(k3_t_0topsp(A))))) # label(dt_k4_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6985 (all A all B all C all D (-v3_struct_0(B) & l1_quantal1(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) -> (r2_hidden(A,a_3_6_quantal1(B,C,D)) <-> (exists E (A = E & r1_lattices(B,k4_monoid_0(B,E,C),D) & m1_subset_1(E,u1_struct_0(B))))))) # label(fraenkel_a_3_6_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6986 (all A (-v3_struct_0(A) & l3_quantal1(A) -> (v20_quantal1(A) <-> v18_quantal1(u1_quantal1(A),A)))) # label(d19_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6987 (all A (-v3_struct_0(A) & v7_quantal1(A) & v8_quantal1(A) & l1_quantal1(A) & v4_lattice3(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)) -> k3_lattices(A,k4_monoid_0(A,D,B),k4_monoid_0(A,D,C)) = k4_monoid_0(A,D,k3_lattices(A,B,C)) & k3_lattices(A,k4_monoid_0(A,B,D),k4_monoid_0(A,C,D)) = k4_monoid_0(A,k3_lattices(A,B,C),D))))))))) # label(t6_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6988 (all A all B all C all D (l1_quantal1(B) & m1_subset_1(C,u1_struct_0(B)) & -v3_struct_0(B) -> (r2_hidden(A,a_3_1_quantal1(B,C,D)) <-> (exists E (A = k4_monoid_0(B,E,C) & r2_hidden(E,D) & m1_subset_1(E,u1_struct_0(B))))))) # label(fraenkel_a_3_1_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6989 (all A (-v3_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & v4_group_1(A) & v7_quantal1(A) & v8_quantal1(A) & l1_quantal1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v17_quantal1(B,A) -> v2_group_1(A) & k3_binop_1(u1_struct_0(A),u1_group_1(A)) = k2_quantal1(A,B,B) & k3_binop_1(u1_struct_0(A),u1_group_1(A)) = k1_quantal1(A,B,B)))))) # label(t19_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6990 (all A (l1_group_1(A) -> (v4_quantal1(A) & v5_quantal1(A) & -v3_struct_0(A) -> v6_quantal1(A) & -v3_struct_0(A)))) # label(cc2_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6991 (all A ((exists B (A = k15_lattice3(f1_s3_quantal1,a_1_0_quantal1(B)) & r2_hidden(B,f3_s3_quantal1) & m1_subset_1(B,u1_struct_0(f1_s3_quantal1)))) <-> r2_hidden(A,a_0_4_quantal1))) # label(fraenkel_a_0_4_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6992 (all A all B (m1_subset_1(B,u1_struct_0(A)) & l3_quantal1(A) & -v3_struct_0(A) -> m1_subset_1(k5_quantal1(A,B),u1_struct_0(A)))) # label(dt_k5_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6993 (all A (v10_lattices(A) & l3_lattices(A) & v4_lattice3(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)) -> (v14_quantal1(B,A) -> (v15_quantal1(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k15_lattice3(A,a_3_5_quantal1(A,B,C)) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,k15_lattice3(A,C)))))))))) # label(t10_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6994 (all A (-v3_struct_0(A) & l1_quantal1(A) -> (k1_lattice3(k1_xboole_0) = g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) -> v4_group_1(A) & v6_quantal1(A) & v10_lattices(A) & v8_quantal1(A) & v7_quantal1(A) & v4_lattice3(A) & v2_group_1(A) & v7_group_1(A)))) # label(t4_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6995 (all A (l1_quantal1(A) & -v3_struct_0(A) -> (v7_quantal1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C k15_lattice3(A,a_3_0_quantal1(A,B,C)) = k4_monoid_0(A,B,k15_lattice3(A,C)))))))) # label(d5_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6996 (all A (l3_lattices(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)) -> (v13_quantal1(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> r1_lattices(A,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),C)))))))) # label(d11_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6997 (all A (l3_lattices(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 (r1_lattices(A,k15_lattice3(A,C),D) & r2_hidden(D,B) & m1_subset_1(D,u1_struct_0(A)))))) <-> v1_quantal1(B,A)))))) # label(d1_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6998 (all A (-v3_struct_0(A) & v4_group_1(A) & v7_quantal1(A) & l3_quantal1(A) & v21_quantal1(A) & v20_quantal1(A) & v8_quantal1(A) & v2_group_1(A) & v4_lattice3(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (k16_lattice3(A,a_3_11_quantal1(A,B,C)) = k9_quantal1(A,k16_lattice3(A,C),B) & k4_monoid_0(A,k15_lattice3(A,C),B) = k15_lattice3(A,a_3_10_quantal1(A,B,C)))))))) # label(t28_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 6999 (all A (l3_lattices(A) & -v3_struct_0(A) -> (all B (v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattices(A,C,D) -> r1_lattices(A,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D))))))) <-> v14_quantal1(B,A)))))) # label(d12_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7000 (all A all B all C all D (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(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)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & v4_lattice3(B) -> (r2_hidden(A,a_3_5_quantal1(B,C,D)) <-> (exists E (m1_subset_1(E,u1_struct_0(B)) & r2_hidden(E,D) & k8_funct_2(u1_struct_0(B),u1_struct_0(B),C,E) = A))))) # label(fraenkel_a_3_5_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7001 (all A (-v3_struct_0(A) & l1_quantal1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> k2_quantal1(A,k1_quantal1(A,C,B),B) = C & C = k1_quantal1(A,k2_quantal1(A,C,B),B))) <-> v17_quantal1(B,A)))))) # label(d17_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7002 (all A (l3_quantal1(A) & -v3_struct_0(A) -> (v17_quantal1(u1_quantal1(A),A) <-> v21_quantal1(A)))) # label(d20_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7003 (all A (v10_lattices(A) & v4_lattice3(A) & v4_group_1(A) & v7_quantal1(A) & l1_quantal1(A) & v8_quantal1(A) & -v3_struct_0(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)) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> k8_funct_2(u1_struct_0(A),u1_struct_0(A),C,D) = k1_quantal1(A,k1_quantal1(A,D,B),B))) -> v14_quantal1(C,A)))))))) # label(t14_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7004 (all A all B all C (-v3_struct_0(B) & v10_lattices(B) & v2_group_1(B) & v4_group_1(B) & v7_quantal1(B) & v8_quantal1(B) & v20_quantal1(B) & v21_quantal1(B) & l3_quantal1(B) & v4_lattice3(B) -> (r2_hidden(A,a_2_0_quantal1(B,C)) <-> (exists D (k5_quantal1(B,D) = A & r2_hidden(D,C) & m1_subset_1(D,u1_struct_0(B))))))) # label(fraenkel_a_2_0_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7005 (all A (l1_group_1(A) -> (-v3_struct_0(A) & v6_quantal1(A) -> v5_quantal1(A) & v4_quantal1(A) & -v3_struct_0(A)))) # label(cc1_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7006 (all A (v10_lattices(A) & v4_lattice3(A) & v2_group_1(A) & v4_group_1(A) & v7_quantal1(A) & v20_quantal1(A) & l3_quantal1(A) & v21_quantal1(A) & v8_quantal1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (k4_monoid_0(A,B,k15_lattice3(A,C)) = k15_lattice3(A,a_3_8_quantal1(A,B,C)) & k16_lattice3(A,a_3_9_quantal1(A,B,C)) = k9_quantal1(A,B,k16_lattice3(A,C)))))))) # label(t27_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7007 (exists A (l3_quantal1(A) & v7_lattices(A) & v4_lattice3(A) & v2_group_1(A) & v8_quantal1(A) & v9_quantal1(A) & v19_quantal1(A) & v21_quantal1(A) & v20_quantal1(A) & v10_quantal1(A) & v7_quantal1(A) & v7_group_1(A) & v4_group_1(A) & v10_lattices(A) & v9_lattices(A) & v8_lattices(A) & v6_lattices(A) & v5_lattices(A) & v4_lattices(A) & -v3_struct_0(A))) # label(rc12_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7008 (all A (v10_lattices(A) & v4_lattice3(A) & v4_group_1(A) & v7_quantal1(A) & v8_quantal1(A) & v20_quantal1(A) & l3_quantal1(A) & v21_quantal1(A) & v2_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k5_quantal1(A,k4_monoid_0(A,k5_quantal1(A,B),k5_quantal1(A,C))) = k9_quantal1(A,B,C))))))) # label(d27_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7009 (all A (l2_quantal1(A) & v2_group_1(A) & -v3_struct_0(A) -> (-v3_struct_0(A) & v4_group_1(A) & v7_quantal1(A) & l1_quantal1(A) & v8_quantal1(A) & v4_lattice3(A) & v10_lattices(A) -> -v3_struct_0(A) & v2_group_1(A) & v4_group_1(A) & v4_quantal1(A) & v9_quantal1(A) & l2_quantal1(A) & v10_quantal1(A) & v6_quantal1(A) & v4_lattice3(A) & v10_lattices(A)))) # label(t7_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7010 (all A all B all C all D (-v3_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & v7_quantal1(B) & v8_quantal1(B) & l1_quantal1(B) -> ((exists E exists F (m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & r2_hidden(E,C) & r2_hidden(F,D) & k4_monoid_0(B,E,F) = A)) <-> r2_hidden(A,a_3_3_quantal1(B,C,D))))) # label(fraenkel_a_3_3_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7011 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (exists B (m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & -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)) & v14_quantal1(B,A) & v13_quantal1(B,A) & v12_quantal1(B,A) & v1_funct_1(B) & v1_relat_1(B))))) # label(rc9_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7012 (all A (v10_lattices(A) & v20_quantal1(A) & l3_quantal1(A) & v21_quantal1(A) & v8_quantal1(A) & v7_quantal1(A) & v4_group_1(A) & v2_group_1(A) & v4_lattice3(A) & -v3_struct_0(A) -> (all B k15_lattice3(A,a_2_0_quantal1(A,B)) = k5_quantal1(A,k16_lattice3(A,B))))) # label(t25_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7013 (all A all B all C all D all E all F (m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & m1_subset_1(F,A) & m1_subset_1(E,A) & m1_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & -v1_xboole_0(A) -> -v3_struct_0(g3_quantal1(A,B,C,D,E,F)) & v19_quantal1(g3_quantal1(A,B,C,D,E,F)))) # label(fc3_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7014 (exists A (v3_quantal1(A) & l2_quantal1(A))) # label(rc3_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7015 (all A (-v3_struct_0(A) & l1_quantal1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> k2_quantal1(A,C,B) = k1_quantal1(A,C,B))) <-> v18_quantal1(B,A)))))) # label(d18_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7016 (all A (l1_quantal1(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v1_quantal1(B,A) & v1_quantal1(C,A) -> k4_monoid_0(A,k15_lattice3(A,B),k15_lattice3(A,C)) = k15_lattice3(A,a_3_2_quantal1(A,B,C))))))) <-> v10_quantal1(A)))) # label(d8_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7017 (exists A l3_quantal1(A)) # label(existence_l3_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7018 (all A (l3_quantal1(A) -> m1_subset_1(u1_quantal1(A),u1_struct_0(A)))) # label(dt_u1_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7019 (all A (-v3_struct_0(A) & l3_lattices(A) -> (all B (-v3_struct_0(B) & l3_lattices(B) -> (g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) = g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(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)) -> (D = F & C = E -> k1_lattices(B,E,F) = k1_lattices(A,C,D) & (r1_lattices(B,E,F) -> r1_lattices(A,C,D)) & (r1_lattices(A,C,D) -> r1_lattices(B,E,F)) & k2_lattices(A,C,D) = k2_lattices(B,E,F))))))))))))))) # label(t1_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7020 (all A (l1_quantal1(A) & -v3_struct_0(A) -> (v9_quantal1(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_monoid_0(A,D,k1_lattices(A,B,C)) = k1_lattices(A,k4_monoid_0(A,D,B),k4_monoid_0(A,D,C)) & k1_lattices(A,k4_monoid_0(A,B,D),k4_monoid_0(A,C,D)) = k4_monoid_0(A,k1_lattices(A,B,C),D)))))))))) # label(d7_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7021 (all A (r2_hidden(A,a_0_0_quantal1) <-> (exists B (m1_subset_1(B,f2_s1_quantal1) & A = f3_s1_quantal1(B) & r2_hidden(B,a_0_1_quantal1))))) # label(fraenkel_a_0_0_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7022 (all A all B all C all D (-v3_struct_0(B) & l1_quantal1(B) & m1_subset_1(C,u1_struct_0(B)) -> ((exists E (m1_subset_1(E,u1_struct_0(B)) & r2_hidden(E,D) & k4_monoid_0(B,C,E) = A)) <-> r2_hidden(A,a_3_0_quantal1(B,C,D))))) # label(fraenkel_a_3_0_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7023 (exists A (-v3_struct_0(A) & v9_lattices(A) & v10_lattices(A) & v2_group_1(A) & v7_group_1(A) & v4_quantal1(A) & v6_quantal1(A) & v7_quantal1(A) & v8_quantal1(A) & v5_quantal1(A) & v4_group_1(A) & v4_lattice3(A) & v8_lattices(A) & v7_lattices(A) & v6_lattices(A) & v5_lattices(A) & v4_lattices(A) & l1_quantal1(A))) # label(rc6_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7024 (all A all B (-v3_struct_0(A) & v1_funct_1(B) & m1_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & l3_quantal1(A) -> m2_relset_1(k8_quantal1(A,B),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_2(k8_quantal1(A,B),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_1(k8_quantal1(A,B)))) # label(dt_k8_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7025 (all A all B all C all D (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_1(D) & m1_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> v2_quantal1(g1_quantal1(A,B,C,D)) & l1_quantal1(g1_quantal1(A,B,C,D)))) # label(dt_g1_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7026 (all A (-v3_struct_0(A) & v4_group_1(A) & v20_quantal1(A) & v21_quantal1(A) & l3_quantal1(A) & v8_quantal1(A) & v7_quantal1(A) & v2_group_1(A) & v4_lattice3(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k9_quantal1(A,k3_quantal1(A),B) = B & B = k9_quantal1(A,B,k3_quantal1(A)))))) # label(t33_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7027 (all A all B all C (-v3_struct_0(A) & l1_quantal1(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) -> m1_subset_1(k2_quantal1(A,B,C),u1_struct_0(A)))) # label(dt_k2_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7028 (exists A (-v3_struct_0(A) & l3_quantal1(A))) # label(rc11_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7029 (all A (v10_lattices(A) & v4_group_1(A) & l1_quantal1(A) & v8_quantal1(A) & v7_quantal1(A) & v4_lattice3(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_monoid_0(A,B,D),k4_monoid_0(A,C,E))))))))))))) # label(t9_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7030 (all A (r2_hidden(A,a_0_1_quantal1) <-> (exists B (m1_subset_1(B,f1_s1_quantal1) & A = f4_s1_quantal1(B) & p1_s1_quantal1(B))))) # label(fraenkel_a_0_1_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7031 (all A (v10_lattices(A) & l1_quantal1(A) & v8_quantal1(A) & v7_quantal1(A) & v4_group_1(A) & v4_lattice3(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)) -> (v18_quantal1(B,A) -> r3_lattices(A,C,k2_quantal1(A,k2_quantal1(A,C,B),B)) & r3_lattices(A,C,k1_quantal1(A,k1_quantal1(A,C,B),B))))))))) # label(t16_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7032 (all A (l1_quantal1(A) -> l3_lattices(A) & l1_group_1(A))) # label(dt_l1_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7033 (exists A l2_quantal1(A)) # label(existence_l2_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7034 (all A (v2_group_1(A) & v8_quantal1(A) & l3_quantal1(A) & v21_quantal1(A) & v20_quantal1(A) & v7_quantal1(A) & v4_group_1(A) & v4_lattice3(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,B,C) -> r3_lattices(A,k5_quantal1(A,C),k5_quantal1(A,B))))))))) # label(t23_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7035 (all A (-v3_struct_0(A) & l1_group_1(A) -> ((exists B (m1_subset_1(B,u1_struct_0(A)) & (all C (m1_subset_1(C,u1_struct_0(A)) -> B = k1_group_1(A,C,B))))) <-> v5_quantal1(A)))) # label(d3_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7036 (all A (v4_lattice3(A) & v7_quantal1(A) & v8_quantal1(A) & v20_quantal1(A) & v21_quantal1(A) & l3_quantal1(A) & v4_group_1(A) & v2_group_1(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k4_monoid_0(A,B,k4_quantal1(A)) = B & B = k4_monoid_0(A,k4_quantal1(A),B))))) # label(t32_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7037 (all A all B all C all D all E (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) & m1_relset_1(D,k2_zfmisc_1(A,A),A) & m1_subset_1(E,A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) -> (all F all G all H all I all J (g2_quantal1(F,G,H,I,J) = g2_quantal1(A,B,C,D,E) -> C = H & J = E & I = D & B = G & A = F)))) # label(free_g2_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7038 (all A all B all C all D all E all F (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_funct_2(D,k2_zfmisc_1(A,A),A) & m1_subset_1(E,A) & m1_subset_1(F,A) & m1_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) -> (all G all H all I all J all K all L (g3_quantal1(A,B,C,D,E,F) = g3_quantal1(G,H,I,J,K,L) -> J = D & F = L & E = K & C = I & B = H & G = A)))) # label(free_g3_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7039 (all A (l2_quantal1(A) -> (v4_lattice3(A) & v7_quantal1(A) & v8_quantal1(A) & v10_lattices(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v10_lattices(A) & v10_quantal1(A) & v9_quantal1(A) & v4_lattice3(A) & v9_lattices(A) & v4_lattices(A)))) # label(cc3_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7040 (all A (v10_lattices(A) & v4_group_1(A) & v7_quantal1(A) & l1_quantal1(A) & v8_quantal1(A) & v4_lattice3(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)) -> (v18_quantal1(B,A) -> r3_lattices(A,k4_monoid_0(A,k1_quantal1(A,k1_quantal1(A,C,B),B),k1_quantal1(A,k1_quantal1(A,D,B),B)),k1_quantal1(A,k1_quantal1(A,k4_monoid_0(A,C,D),B),B))))))))))) # label(t18_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7041 (all A (-v3_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & v2_group_1(A) & v8_quantal1(A) & v21_quantal1(A) & l3_quantal1(A) & v20_quantal1(A) & v7_quantal1(A) & v4_group_1(A) -> (all B k16_lattice3(A,a_2_0_quantal1(A,B)) = k5_quantal1(A,k15_lattice3(A,B))))) # label(t24_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7042 (all A all B all C all D (v2_group_1(B) & v4_group_1(B) & v8_quantal1(B) & m1_subset_1(C,u1_struct_0(B)) & l3_quantal1(B) & v21_quantal1(B) & v20_quantal1(B) & v7_quantal1(B) & v4_lattice3(B) & v10_lattices(B) & -v3_struct_0(B) -> ((exists E (m1_subset_1(E,u1_struct_0(B)) & r2_hidden(E,D) & k9_quantal1(B,C,E) = A)) <-> r2_hidden(A,a_3_9_quantal1(B,C,D))))) # label(fraenkel_a_3_9_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7043 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v11_quantal1(A) <-> k5_relat_1(A,A) = A))) # label(d9_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7044 (all A (l3_quantal1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k5_quantal1(A,B) = k1_quantal1(A,B,k3_quantal1(A)))))) # label(d23_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7045 (all A (v10_lattices(A) & v4_lattice3(A) & v4_group_1(A) & v20_quantal1(A) & l3_quantal1(A) & v21_quantal1(A) & v8_quantal1(A) & v7_quantal1(A) & v2_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r3_lattices(A,D,E) & r3_lattices(A,B,C) -> r3_lattices(A,k9_quantal1(A,B,D),k9_quantal1(A,C,E))))))))))))) # label(t30_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7046 (all A (r2_hidden(A,a_0_5_quantal1) <-> (exists B exists C (A = f2_s3_quantal1(B,C) & r2_hidden(C,f4_s3_quantal1) & r2_hidden(B,f3_s3_quantal1) & m1_subset_1(C,u1_struct_0(f1_s3_quantal1)) & m1_subset_1(B,u1_struct_0(f1_s3_quantal1)))))) # label(fraenkel_a_0_5_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7047 (all A (m1_subset_1(A,f1_s2_quantal1) -> -p1_s2_quantal1(A))) -> k1_xboole_0 = a_0_3_quantal1 # label(s2_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7048 (all A all B all C all D (m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) & l1_quantal1(B) & -v3_struct_0(B) -> (r2_hidden(A,a_3_7_quantal1(B,C,D)) <-> (exists E (m1_subset_1(E,u1_struct_0(B)) & A = E & r1_lattices(B,k4_monoid_0(B,C,E),D)))))) # label(fraenkel_a_3_7_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7049 (all A (-v3_struct_0(A) & l3_quantal1(A) -> k1_quantal1(A,k3_quantal1(A),k3_quantal1(A)) = k4_quantal1(A))) # label(d22_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.83 7050 (all A all B all C all D all E (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & m1_subset_1(E,A) & m1_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) -> l2_quantal1(g2_quantal1(A,B,C,D,E)) & v3_quantal1(g2_quantal1(A,B,C,D,E)))) # label(dt_g2_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7051 (all A (r2_hidden(A,a_0_2_quantal1) <-> (exists B (m1_subset_1(B,f1_s1_quantal1) & A = f3_s1_quantal1(f4_s1_quantal1(B)) & p1_s1_quantal1(B))))) # label(fraenkel_a_0_2_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7052 (exists A l1_quantal1(A)) # label(existence_l1_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7053 (all A (l3_lattices(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) -> (v15_quantal1(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_lattices(A,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,k15_lattice3(A,C)),k15_lattice3(A,a_3_4_quantal1(A,B,C)))))))))) # label(d13_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7054 (exists A (l1_quantal1(A) & v2_quantal1(A))) # label(rc1_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7055 (all A (-v3_struct_0(A) & v10_lattices(A) & v2_group_1(A) & v7_quantal1(A) & v8_quantal1(A) & v21_quantal1(A) & l3_quantal1(A) & v20_quantal1(A) & v4_group_1(A) & v4_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)) -> k4_lattices(A,k9_quantal1(A,B,C),k9_quantal1(A,B,D)) = k9_quantal1(A,B,k4_lattices(A,C,D)) & k4_lattices(A,k9_quantal1(A,C,B),k9_quantal1(A,D,B)) = k9_quantal1(A,k4_lattices(A,C,D),B))))))))) # label(t29_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7056 (all A all B all C all D all E all F (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) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & m1_subset_1(F,A) & m1_subset_1(E,A) & m1_relset_1(D,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> l3_quantal1(g3_quantal1(A,B,C,D,E,F)) & v19_quantal1(g3_quantal1(A,B,C,D,E,F)))) # label(dt_g3_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7057 (all A (l3_quantal1(A) & -v3_struct_0(A) -> m1_subset_1(k4_quantal1(A),u1_struct_0(A)))) # label(dt_k4_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7058 (all A all B all C all D (-v3_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & v2_group_1(B) & v4_group_1(B) & m1_subset_1(C,u1_struct_0(B)) & l3_quantal1(B) & v21_quantal1(B) & v20_quantal1(B) & v8_quantal1(B) & v7_quantal1(B) -> ((exists E (m1_subset_1(E,u1_struct_0(B)) & r2_hidden(E,D) & A = k4_monoid_0(B,C,E))) <-> r2_hidden(A,a_3_8_quantal1(B,C,D))))) # label(fraenkel_a_3_8_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7059 (all A all B all C all D (v10_lattices(B) & v2_group_1(B) & v4_group_1(B) & v7_quantal1(B) & v20_quantal1(B) & v21_quantal1(B) & l3_quantal1(B) & m1_subset_1(C,u1_struct_0(B)) & v8_quantal1(B) & v4_lattice3(B) & -v3_struct_0(B) -> (r2_hidden(A,a_3_11_quantal1(B,C,D)) <-> (exists E (m1_subset_1(E,u1_struct_0(B)) & k9_quantal1(B,E,C) = A & r2_hidden(E,D)))))) # label(fraenkel_a_3_11_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7060 (all A ((exists B (m1_subset_1(B,f1_s2_quantal1) & p1_s2_quantal1(B) & A = f2_s2_quantal1(B))) <-> r2_hidden(A,a_0_3_quantal1))) # label(fraenkel_a_0_3_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7061 (all A all B (m1_subset_1(B,u1_struct_0(f1_s3_quantal1)) -> ((exists C (m1_subset_1(C,u1_struct_0(f1_s3_quantal1)) & r2_hidden(C,f4_s3_quantal1) & f2_s3_quantal1(B,C) = A)) <-> r2_hidden(A,a_1_0_quantal1(B))))) # label(fraenkel_a_1_0_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7062 (all A all B (-v3_struct_0(A) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) & l3_quantal1(A) -> v1_funct_1(k7_quantal1(A,B)) & m2_relset_1(k7_quantal1(A,B),u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(k7_quantal1(A,B),u1_struct_0(A),u1_struct_0(A)))) # label(dt_k7_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7063 (all A all B all C all D (v1_funct_2(C,u1_struct_0(B),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & v1_funct_1(C) & l3_lattices(B) & -v3_struct_0(B) -> (r2_hidden(A,a_3_4_quantal1(B,C,D)) <-> (exists E (m1_subset_1(E,u1_struct_0(B)) & A = k8_funct_2(u1_struct_0(B),u1_struct_0(B),C,E) & r2_hidden(E,D)))))) # label(fraenkel_a_3_4_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7064 (all A (v2_group_1(A) & v7_quantal1(A) & v20_quantal1(A) & l3_quantal1(A) & v21_quantal1(A) & v8_quantal1(A) & v4_group_1(A) & v4_lattice3(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)) -> k5_quantal1(A,k4_lattices(A,B,C)) = k3_lattices(A,k5_quantal1(A,B),k5_quantal1(A,C)) & k5_quantal1(A,k3_lattices(A,B,C)) = k4_lattices(A,k5_quantal1(A,B),k5_quantal1(A,C)))))))) # label(t26_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7065 (all A (-v3_struct_0(A) & l3_lattices(A) -> (all B (l3_lattices(B) & -v3_struct_0(B) -> (g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (C = D -> (r4_lattice3(A,C,E) -> r4_lattice3(B,D,E)) & (r4_lattice3(B,D,E) -> r4_lattice3(A,C,E)) & (r3_lattice3(B,D,E) -> r3_lattice3(A,C,E)) & (r3_lattice3(A,C,E) -> r3_lattice3(B,D,E))))))))))))) # label(t2_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7066 (all A all B all C all D all E (m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & m1_subset_1(E,A) & m1_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & -v1_xboole_0(A) -> v3_quantal1(g2_quantal1(A,B,C,D,E)) & -v3_struct_0(g2_quantal1(A,B,C,D,E)))) # label(fc2_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7067 (all A (l3_quantal1(A) -> l2_quantal1(A))) # label(dt_l3_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7068 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_quantal1(A) & v8_quantal1(A) & v7_quantal1(A) & v4_lattice3(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v18_quantal1(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,k4_monoid_0(A,C,D),B) -> r3_lattices(A,k4_monoid_0(A,D,C),B))))))))))) # label(t15_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7069 (all A (-v3_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & v7_quantal1(A) & l1_quantal1(A) & v8_quantal1(A) -> (all B all C k15_lattice3(A,a_3_3_quantal1(A,B,C)) = k4_monoid_0(A,k15_lattice3(A,B),k15_lattice3(A,C))))) # label(t5_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7070 (exists A (l1_quantal1(A) & -v3_struct_0(A))) # label(rc2_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7071 (all A (l3_quantal1(A) -> k3_quantal1(A) = u1_quantal1(A))) # label(d21_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7072 (all A (l3_quantal1(A) -> (v19_quantal1(A) -> A = g3_quantal1(u1_struct_0(A),u2_lattices(A),u1_lattices(A),u1_group_1(A),u1_vectsp_1(A),u1_quantal1(A))))) # label(abstractness_v19_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7073 (all A (-v3_struct_0(A) & l3_lattices(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)) -> (v12_quantal1(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> r1_lattices(A,C,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C))))))))) # label(d10_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7074 (all A all B all C (v8_quantal1(A) & v20_quantal1(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l3_quantal1(A) & v21_quantal1(A) & v7_quantal1(A) & v4_group_1(A) & v2_group_1(A) & v4_lattice3(A) & v10_lattices(A) & -v3_struct_0(A) -> m1_subset_1(k9_quantal1(A,B,C),u1_struct_0(A)))) # label(dt_k9_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7075 (all A (-v3_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & v4_group_1(A) & l1_quantal1(A) & v8_quantal1(A) & v7_quantal1(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)) -> (v17_quantal1(B,A) -> k1_quantal1(A,C,D) = k1_quantal1(A,k4_monoid_0(A,C,k2_quantal1(A,D,B)),B) & k2_quantal1(A,C,D) = k2_quantal1(A,k4_monoid_0(A,k1_quantal1(A,D,B),C),B)))))))))) # label(t20_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7076 (all A (l1_quantal1(A) & -v3_struct_0(A) -> (v8_quantal1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C k4_monoid_0(A,k15_lattice3(A,C),B) = k15_lattice3(A,a_3_1_quantal1(A,B,C)))))))) # label(d6_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7077 (all A (-v3_struct_0(A) & v10_lattices(A) & v7_quantal1(A) & l1_quantal1(A) & v8_quantal1(A) & v4_group_1(A) & v4_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)) -> (r3_lattices(A,B,C) -> r3_lattices(A,k4_monoid_0(A,B,D),k4_monoid_0(A,C,D)) & r3_lattices(A,k4_monoid_0(A,D,B),k4_monoid_0(A,D,C))))))))))) # label(t8_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7078 (exists A (-v3_struct_0(A) & l2_quantal1(A))) # label(rc4_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7079 (all A (-v3_struct_0(A) & l1_quantal1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_quantal1(A,B,C) = k15_lattice3(A,a_3_7_quantal1(A,B,C)))))))) # label(d16_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7080 (all A all B all C all D (-v1_xboole_0(A) & 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(D,k2_zfmisc_1(A,A),A) & m1_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> -v3_struct_0(g1_quantal1(A,B,C,D)) & v2_quantal1(g1_quantal1(A,B,C,D)))) # label(fc1_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7081 (all A all B all C all D (-v3_struct_0(B) & l1_quantal1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (r2_hidden(A,a_3_2_quantal1(B,C,D)) <-> (exists E exists F (m1_subset_1(F,u1_struct_0(B)) & A = k4_monoid_0(B,E,F) & r2_hidden(F,D) & r2_hidden(E,C) & m1_subset_1(E,u1_struct_0(B))))))) # label(fraenkel_a_3_2_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7082 (all A (-v3_struct_0(A) & v2_group_1(A) & v4_group_1(A) & v7_quantal1(A) & v8_quantal1(A) & v20_quantal1(A) & v21_quantal1(A) & l3_quantal1(A) & v4_lattice3(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)) -> k9_quantal1(A,B,k9_quantal1(A,C,D)) = k9_quantal1(A,k9_quantal1(A,B,C),D))))))))) # label(t31_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7083 (all A (l1_group_1(A) & -v3_struct_0(A) -> (v6_quantal1(A) <-> v5_quantal1(A) & v4_quantal1(A)))) # label(d4_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7084 (all A all B all C (l1_quantal1(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & -v3_struct_0(A) -> m1_subset_1(k1_quantal1(A,B,C),u1_struct_0(A)))) # label(dt_k1_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7085 (exists A (l2_quantal1(A) & -v3_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v8_lattices(A) & v10_lattices(A) & v4_lattice3(A) & v9_lattices(A) & v7_lattices(A) & v6_lattices(A))) # label(rc7_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7086 (all A (l1_quantal1(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_quantal1(A,B,C) = k15_lattice3(A,a_3_6_quantal1(A,B,C)))))))) # label(d15_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7087 (all A (-v3_struct_0(A) & l3_lattices(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(v1_quantal1(B,A) & v1_xboole_0(B)))))) # label(t3_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7088 (exists A (l3_quantal1(A) & v19_quantal1(A))) # label(rc10_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7089 (all A (v4_lattice3(A) & v4_group_1(A) & v7_quantal1(A) & l1_quantal1(A) & v8_quantal1(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,C,D) -> r3_lattices(A,k1_quantal1(A,D,B),k1_quantal1(A,C,B)) & r3_lattices(A,k2_quantal1(A,D,B),k2_quantal1(A,C,B))))))))))) # label(t13_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7090 (all A (l3_quantal1(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,u1_struct_0(A)) -> k5_quantal1(A,C) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C))) <-> k6_quantal1(A) = B))))) # label(d24_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7091 (all A (-v3_struct_0(A) & l1_group_1(A) -> (v4_quantal1(A) <-> (exists B (m1_subset_1(B,u1_struct_0(A)) & (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,B,C) = B))))))) # label(d2_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7092 (all A (-v3_struct_0(A) & l3_quantal1(A) -> (g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = k1_lattice3(k1_xboole_0) -> v21_quantal1(A) & v20_quantal1(A)))) # label(t21_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7093 (all A (l1_quantal1(A) -> (v2_quantal1(A) -> g1_quantal1(u1_struct_0(A),u2_lattices(A),u1_lattices(A),u1_group_1(A)) = A))) # label(abstractness_v2_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7094 (all A (v4_lattice3(A) & v4_group_1(A) & v7_quantal1(A) & v8_quantal1(A) & l1_quantal1(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_monoid_0(A,B,C),D) <-> r3_lattices(A,B,k1_quantal1(A,C,D))))))))))) # label(t12_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7095 (all A (-v3_struct_0(A) & l3_quantal1(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_1(B) -> k7_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A),u1_struct_0(A),B,k6_quantal1(A)) = k8_quantal1(A,B))))) # label(d26_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7096 (all A (l2_quantal1(A) -> (v3_quantal1(A) -> A = g2_quantal1(u1_struct_0(A),u2_lattices(A),u1_lattices(A),u1_group_1(A),u1_vectsp_1(A))))) # label(abstractness_v3_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7097 (all A (l3_quantal1(A) -> m1_subset_1(k3_quantal1(A),u1_struct_0(A)))) # label(dt_k3_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7098 (all A all B all C all D (-v3_struct_0(B) & v10_lattices(B) & v2_group_1(B) & v7_quantal1(B) & v8_quantal1(B) & v20_quantal1(B) & l3_quantal1(B) & m1_subset_1(C,u1_struct_0(B)) & v21_quantal1(B) & v4_group_1(B) & v4_lattice3(B) -> ((exists E (k4_monoid_0(B,E,C) = A & r2_hidden(E,D) & m1_subset_1(E,u1_struct_0(B)))) <-> r2_hidden(A,a_3_10_quantal1(B,C,D))))) # label(fraenkel_a_3_10_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7099 (all A (v10_lattices(A) & v4_group_1(A) & v8_quantal1(A) & v20_quantal1(A) & v21_quantal1(A) & l3_quantal1(A) & v7_quantal1(A) & v2_group_1(A) & v4_lattice3(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k5_quantal1(A,k5_quantal1(A,B)))))) # label(t22_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7100 (all A all B all C all D (v1_funct_1(B) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & m1_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all E all F all G all H (g1_quantal1(A,B,C,D) = g1_quantal1(E,F,G,H) -> D = H & G = C & B = F & A = E)))) # label(free_g1_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7101 (all A (v10_lattices(A) & v4_group_1(A) & v7_quantal1(A) & v8_quantal1(A) & l1_quantal1(A) & v4_lattice3(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_monoid_0(A,B,C),D) <-> r3_lattices(A,C,k2_quantal1(A,B,D))))))))))) # label(t11_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7102 (all A (l3_quantal1(A) & -v3_struct_0(A) -> v1_funct_2(k6_quantal1(A),u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(k6_quantal1(A),u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(k6_quantal1(A)))) # label(dt_k6_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7103 (exists A (l1_group_1(A) & -v3_struct_0(A) & v4_quantal1(A) & v5_quantal1(A) & v6_quantal1(A))) # label(rc5_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7104 (exists A (l2_quantal1(A) & v4_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v4_lattice3(A) & v4_group_1(A) & v4_quantal1(A) & v6_quantal1(A) & v8_quantal1(A) & v9_quantal1(A) & v10_quantal1(A) & v7_quantal1(A) & v5_quantal1(A) & v7_group_1(A) & v2_group_1(A) & v5_lattices(A) & -v3_struct_0(A))) # label(rc8_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7105 (all A (l2_quantal1(A) -> l1_quantal1(A) & l1_vectsp_1(A))) # label(dt_l2_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7106 (all A (v10_lattices(A) & v4_lattice3(A) & v4_group_1(A) & v7_quantal1(A) & l1_quantal1(A) & v8_quantal1(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)) -> (v18_quantal1(B,A) -> k1_quantal1(A,C,B) = k1_quantal1(A,k1_quantal1(A,k1_quantal1(A,C,B),B),B) & k2_quantal1(A,C,B) = k2_quantal1(A,k2_quantal1(A,k2_quantal1(A,C,B),B),B)))))))) # label(t17_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7107 (all A (v4_lattice3(A) & v4_group_1(A) & l1_quantal1(A) & v8_quantal1(A) & v7_quantal1(A) & v10_lattices(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) -> -(v11_quantal1(B) & v15_quantal1(B,A) & (all C (-v3_struct_0(C) & v10_lattices(C) & l3_lattices(C) & v4_lattice3(C) -> -((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) -> k15_lattice3(C,D) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,k15_lattice3(A,D)))) & u1_struct_0(C) = k2_relat_1(B)))) & v14_quantal1(B,A)))))) # label(t34_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7108 (all A (l3_quantal1(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)) -> k2_monoid_0(u1_struct_0(A),B,k6_quantal1(A)) = k7_quantal1(A,B))))) # label(d25_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7109 (all A (-v3_struct_0(A) & l1_quantal1(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) -> (v16_quantal1(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> r1_lattices(A,k4_monoid_0(A,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D)),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,k4_monoid_0(A,C,D)))))))))))) # label(d14_quantal1) # label(axiom) # label(non_clause). [assumption]. 116.28/115.84 7110 (all A (-v1_xboole_0(A) & v2_cat_5(A) -> (all B (-v1_xboole_0(B) -> (all C (v3_cat_5(C) & l1_cat_1(C) & v2_cat_1(C) & v1_cat_1(C) -> (all D (v1_cat_1(D) & v2_cat_1(D) & l1_cat_1(D) & v3_cat_5(D) -> (A = u1_cat_1(D) & (all E (m1_cat_5(E,A) -> (all F (m1_cat_5(F,A) -> (all G (m2_cat_1(G,E,F) -> (r2_hidden(G,B) <-> m1_subset_1(k1_domain_1(k2_zfmisc_1(A,A),k1_zfmisc_1(k2_zfmisc_1(u2_cat_1(E),u2_cat_1(F))),k1_domain_1(A,A,E,F),G),u2_cat_1(D))))))))) & (all E (m1_cat_5(E,A) -> (all F (m1_cat_5(F,A) -> (all G (m2_cat_1(G,E,F) -> (r2_hidden(G,B) <-> m1_subset_1(k1_domain_1(k2_zfmisc_1(A,A),k1_zfmisc_1(k2_zfmisc_1(u2_cat_1(E),u2_cat_1(F))),k1_domain_1(A,A,E,F),G),u2_cat_1(C))))))))) & A = u1_cat_1(C) -> D = C))))))))) # label(t18_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.85 7111 (all A ((all B (r2_hidden(B,A) -> v2_cat_1(B) & l1_cat_1(B))) <-> v2_cat_5(A))) # label(d4_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.85 7112 (all A (v2_cat_5(A) & -v1_xboole_0(A) -> (all B (m1_cat_5(B,A) -> v2_cat_1(B) & l1_cat_1(B))))) # label(dt_m1_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.85 7113 (all A all B all C (m1_subset_1(C,u2_cat_1(k15_cat_5(A,B))) & m1_subset_1(B,u1_cat_1(A)) & l1_cat_1(A) & v2_cat_1(A) -> k19_cat_5(A,B,C) = k2_mcart_1(C))) # label(redefinition_k19_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.85 7114 (all A all B all C (m1_subset_1(C,u2_cat_1(k14_cat_5(A,B))) & m1_subset_1(B,u1_cat_1(A)) & l1_cat_1(A) & v2_cat_1(A) -> m2_subset_1(k18_cat_5(A,B,C),u2_cat_1(A),k12_cat_5(A,B)))) # label(dt_k18_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.85 7115 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m2_subset_1(C,u2_cat_1(A),k12_cat_5(A,B)) -> (all D (m1_subset_1(D,u1_cat_1(k14_cat_5(A,B))) -> (C = D -> k1_domain_1(u1_cat_1(k11_cat_2(k14_cat_5(A,B),k14_cat_5(A,B))),u2_cat_1(A),k12_cat_2(k14_cat_5(A,B),k14_cat_5(A,B),D,D),k10_cat_1(A,k2_cat_1(A,C))) = k10_cat_1(k14_cat_5(A,B),D)))))))))) # label(t30_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.85 7116 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,k2_zfmisc_1(A,B)) & -v1_xboole_0(B) -> k2_mcart_1(C) = k3_cat_5(A,B,C))) # label(redefinition_k3_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.85 7117 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m2_cat_1(C,k15_cat_5(A,k3_cat_1(A,B)),k15_cat_5(A,k2_cat_1(A,B))) -> ((all D (m1_subset_1(D,u2_cat_1(k15_cat_5(A,k3_cat_1(A,B)))) -> k8_funct_2(u2_cat_1(k15_cat_5(A,k3_cat_1(A,B))),u2_cat_1(k15_cat_5(A,k2_cat_1(A,B))),C,D) = k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,k4_cat_1(A,B,k20_cat_5(A,k3_cat_1(A,B),D)),k4_cat_1(A,B,k21_cat_5(A,k3_cat_1(A,B),D))),k19_cat_5(A,k3_cat_1(A,B),D)))) <-> k23_cat_5(A,B) = C))))))) # label(d14_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.85 7118 (all A all B (m1_subset_1(B,u2_cat_1(A)) & l1_cat_1(A) & v3_cat_5(A) & v2_cat_1(A) -> v2_cat_1(k8_cat_5(A,B)) & l1_cat_1(k8_cat_5(A,B)))) # label(dt_k8_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.85 7119 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(k15_cat_5(A,B))) -> k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,k20_cat_5(A,B,C),k21_cat_5(A,B,C)),k19_cat_5(A,B,C)) = C & k2_cat_1(A,k19_cat_5(A,B,C)) = k3_cat_1(A,k20_cat_5(A,B,C)) & k4_cat_1(A,k20_cat_5(A,B,C),k19_cat_5(A,B,C)) = k21_cat_5(A,B,C) & k20_cat_5(A,B,C) = k2_cat_1(k15_cat_5(A,B),C) & k3_cat_1(k15_cat_5(A,B),C) = k21_cat_5(A,B,C))))))) # label(t31_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.85 7120 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> k6_cat_1(A,B,C) = k5_subset_1(u2_cat_1(A),k13_cat_5(A,B),k12_cat_5(A,C)))))))) # label(t25_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.85 7121 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (l1_cat_1(C) & v1_cat_5(C) & v2_cat_1(C) & v1_cat_1(C) -> (C = k14_cat_5(A,B) <-> u1_cat_1(C) = k12_cat_5(A,B) & (all D (m2_subset_1(D,u2_cat_1(A),k12_cat_5(A,B)) -> (all E (m2_subset_1(E,u2_cat_1(A),k12_cat_5(A,B)) -> (all F (m1_subset_1(F,u2_cat_1(A)) -> (k2_cat_1(A,E) = k3_cat_1(A,F) & D = k4_cat_1(A,F,E) -> m1_subset_1(k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,D,E),F),u2_cat_1(C))))))))) & (all D (m1_subset_1(D,u2_cat_1(C)) -> (all E (m1_subset_1(E,u2_cat_1(C)) -> (all F (m2_subset_1(F,u2_cat_1(A),k12_cat_5(A,B)) -> (all G (m2_subset_1(G,u2_cat_1(A),k12_cat_5(A,B)) -> (all H (m2_subset_1(H,u2_cat_1(A),k12_cat_5(A,B)) -> (all I (m1_subset_1(I,u2_cat_1(A)) -> (all J (m1_subset_1(J,u2_cat_1(A)) -> (E = k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,G,H),J) & D = k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,F,G),I) -> k4_cat_1(C,D,E) = k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,F,H),k4_cat_1(A,I,J))))))))))))))))) & (all D (m1_subset_1(D,u2_cat_1(C)) -> (exists E ((exists F (m2_subset_1(F,u2_cat_1(A),k12_cat_5(A,B)) & (exists G (k2_cat_1(A,F) = k3_cat_1(A,G) & k4_cat_1(A,G,F) = E & D = k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,E,F),G) & m1_subset_1(G,u2_cat_1(A)))))) & m2_subset_1(E,u2_cat_1(A),k12_cat_5(A,B))))))))))))) # label(d11_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.85 7122 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m3_cat_2(D,B) & v1_cat_1(D) -> (u1_cat_1(D) = k2_relat_1(k12_cat_1(A,B,C)) & (all E (m3_cat_2(E,B) -> (r1_tarski(k2_relat_1(C),u2_cat_1(E)) & u1_cat_1(E) = k2_relat_1(k12_cat_1(A,B,C)) -> m3_cat_2(D,E)))) & r1_tarski(k2_relat_1(C),u2_cat_1(D)) <-> k7_cat_5(A,B,C) = D))))))))) # label(d3_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.85 7123 (all A (v2_cat_1(A) & l1_cat_1(A) -> v3_cat_5(k8_cat_1(A,k4_tarski(k4_tarski(A,A),k15_cat_1(A)))))) # label(t11_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.85 7124 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (k2_cat_1(A,C) = k3_cat_1(A,B) -> k22_cat_5(A,k4_cat_1(A,B,C)) = k1_partfun1(u2_cat_1(k14_cat_5(A,k2_cat_1(A,B))),u2_cat_1(k14_cat_5(A,k3_cat_1(A,B))),u2_cat_1(k14_cat_5(A,k2_cat_1(A,C))),u2_cat_1(k14_cat_5(A,k3_cat_1(A,C))),k22_cat_5(A,B),k22_cat_5(A,C))))))))) # label(t33_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.85 7125 (all A all B (l1_cat_1(A) & m1_subset_1(B,u2_cat_1(A)) & v3_cat_5(A) & v2_cat_1(A) -> k9_cat_5(A,B) = k18_mcart_1(B))) # label(redefinition_k9_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.85 7126 (all A (l1_cat_1(A) & v3_cat_5(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & v3_cat_5(B) & l1_cat_1(B) -> (u1_cat_1(A) = u1_cat_1(B) & u2_cat_1(A) = u2_cat_1(B) -> g1_cat_1(u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),u5_cat_1(B),u6_cat_1(B)) = g1_cat_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))))))) # label(t14_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.85 7127 (all A all B (v1_cat_5(A) & l1_cat_1(A) & m1_subset_1(B,u2_cat_1(A)) -> k17_mcart_1(B) = k4_cat_5(A,B))) # label(redefinition_k4_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.85 7128 (exists A (l1_cat_1(A) & v1_cat_5(A) & v3_cat_5(A) & v2_cat_1(A) & v1_cat_1(A))) # label(rc3_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.85 7129 (all A all B (v1_cat_5(A) & l1_cat_1(A) & m1_subset_1(B,u2_cat_1(A)) -> m1_subset_1(k5_cat_5(A,B),u1_cat_1(A)))) # label(dt_k5_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.85 7130 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m2_subset_1(C,u2_cat_1(A),k12_cat_5(A,k2_cat_1(A,B))) -> r2_hidden(k4_cat_1(A,C,B),k12_cat_5(A,k3_cat_1(A,B))))))))) # label(t27_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.85 7131 (all A (l1_cat_1(A) -> ((all B (m1_subset_1(B,u2_cat_1(A)) -> (exists C B = k4_tarski(k1_domain_1(u1_cat_1(A),u1_cat_1(A),k2_cat_1(A,B),k3_cat_1(A,B)),C)))) <-> v1_cat_5(A)))) # label(d1_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.85 7132 (all A (v2_cat_1(k10_cat_5(A)) & l1_cat_1(k10_cat_5(A)))) # label(dt_k10_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.85 7133 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> m2_cat_1(C,A,k7_cat_5(A,B,C)))))))) # label(t8_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.85 7134 (all A all B (v2_cat_1(A) & v3_cat_5(A) & m1_subset_1(B,u2_cat_1(A)) & l1_cat_1(A) -> l1_cat_1(k9_cat_5(A,B)) & v2_cat_1(k9_cat_5(A,B)))) # label(dt_k9_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.90 7135 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(C) & m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) & -v1_xboole_0(B) -> k18_mcart_1(D) = k2_cat_5(A,B,C,D))) # label(redefinition_k2_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.90 7136 (all A all B (v2_cat_1(A) & v3_cat_5(A) & m1_subset_1(B,u2_cat_1(A)) & l1_cat_1(A) -> m2_cat_1(k11_cat_5(A,B),k10_cat_5(k2_cat_1(A,B)),k10_cat_5(k3_cat_1(A,B))))) # label(dt_k11_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.90 7137 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) & -v1_xboole_0(A) -> m1_subset_1(k1_cat_5(A,B,C,D),A))) # label(dt_k1_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.90 7138 (exists A (-v1_xboole_0(A) & v2_cat_5(A))) # label(rc2_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.90 7139 (all A all B all C (v2_cat_1(A) & l1_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) & m1_subset_1(C,u2_cat_1(k15_cat_5(A,B))) -> m1_subset_1(k19_cat_5(A,B,C),u2_cat_1(A)))) # label(dt_k19_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.90 7140 (all A all B (v2_cat_1(A) & l1_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) -> v2_cat_1(k15_cat_5(A,B)) & v1_cat_5(k15_cat_5(A,B)) & l1_cat_1(k15_cat_5(A,B)) & v1_cat_1(k15_cat_5(A,B)))) # label(dt_k15_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.90 7141 (all A all B all C (v2_cat_1(B) & m2_cat_1(C,A,B) & l1_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> v1_cat_1(k7_cat_5(A,B,C)) & m3_cat_2(k7_cat_5(A,B,C),B))) # label(dt_k7_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.90 7142 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m3_cat_2(B,A) -> (all C (m3_cat_2(C,A) -> (-r2_subset_1(u1_cat_1(B),u1_cat_1(C)) -> m3_cat_2(k6_cat_5(B,C),B) & m3_cat_2(k6_cat_5(B,C),C)))))))) # label(t6_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.90 7143 (all A (v2_cat_5(A) & -v1_xboole_0(A) -> (all B (m1_cat_5(B,A) <-> m1_subset_1(B,A))))) # label(redefinition_m1_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.90 7144 (all A all B (v2_cat_1(A) & l1_cat_1(A) & m1_subset_1(B,u2_cat_1(A)) & v3_cat_5(A) -> k2_mcart_1(B) = k11_cat_5(A,B))) # label(redefinition_k11_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.90 7145 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(k14_cat_5(A,B))) -> k3_cat_1(A,k16_cat_5(A,B,C)) = k2_cat_1(A,k18_cat_5(A,B,C)) & k18_cat_5(A,B,C) = k3_cat_1(k14_cat_5(A,B),C) & k17_cat_5(A,B,C) = k2_cat_1(k14_cat_5(A,B),C) & k4_cat_1(A,k16_cat_5(A,B,C),k18_cat_5(A,B,C)) = k17_cat_5(A,B,C) & k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,k17_cat_5(A,B,C),k18_cat_5(A,B,C)),k16_cat_5(A,B,C)) = C)))))) # label(t29_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.90 7146 (all A (v2_cat_1(A) & v3_cat_5(A) & l1_cat_1(A) & v4_cat_5(A) -> (all B (v2_cat_1(B) & v3_cat_5(B) & l1_cat_1(B) & v4_cat_5(B) -> (u1_cat_1(B) = u1_cat_1(A) -> g1_cat_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A)) = g1_cat_1(u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),u5_cat_1(B),u6_cat_1(B))))))) # label(t19_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.90 7147 (all A (l1_cat_1(A) & v2_cat_1(A) -> ((all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (l1_cat_1(D) & v2_cat_1(D) -> (all E (l1_cat_1(E) & v2_cat_1(E) -> (all F (v2_cat_1(F) & l1_cat_1(F) -> (all G (m2_cat_1(G,D,E) -> (all H (m2_cat_1(H,E,F) -> (k4_tarski(k4_tarski(E,F),H) = C & k4_tarski(k4_tarski(D,E),G) = B -> k4_tarski(k4_tarski(D,F),k14_cat_1(D,E,F,G,H)) = k4_cat_1(A,B,C)))))))))))))))) & (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (l1_cat_1(D) & v2_cat_1(D) -> -((all E (m2_cat_1(E,C,D) -> B != k4_tarski(k4_tarski(C,D),E))) & k3_cat_1(A,B) = D & C = k2_cat_1(A,B)))))))) & (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (C = B -> k10_cat_1(A,B) = k4_tarski(k4_tarski(C,C),k15_cat_1(C))))))) & v2_cat_5(u1_cat_1(A)) <-> v3_cat_5(A)))) # label(d6_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.90 7148 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (B = k3_cat_1(A,C) <-> r2_hidden(C,k12_cat_5(A,B))))))))) # label(t23_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.90 7149 (all A all B all C (m1_subset_1(B,u1_cat_1(A)) & m1_subset_1(C,u2_cat_1(k14_cat_5(A,B))) & l1_cat_1(A) & v2_cat_1(A) -> m2_subset_1(k17_cat_5(A,B,C),u2_cat_1(A),k12_cat_5(A,B)))) # label(dt_k17_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.90 7150 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (r2_hidden(C,k13_cat_5(A,B)) <-> k2_cat_1(A,C) = B))))))) # label(t24_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.90 7151 (all A all B (m1_subset_1(B,u2_cat_1(A)) & l1_cat_1(A) & v1_cat_5(A) -> m1_subset_1(k4_cat_5(A,B),u1_cat_1(A)))) # label(dt_k4_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.90 7152 (exists A (v1_cat_1(A) & v2_cat_1(A) & v1_cat_5(A) & v3_cat_5(A) & v4_cat_5(A) & l1_cat_1(A))) # label(rc4_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.90 7153 (all A all B all C all D (-v1_xboole_0(A) & m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) & -v1_xboole_0(C) & -v1_xboole_0(B) -> m1_subset_1(k2_cat_5(A,B,C,D),B))) # label(dt_k2_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.90 7154 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> k12_cat_5(A,B) = k3_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k6_domain_1(u1_cat_1(A),B)))))) # label(d9_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.90 7155 (all A all B (v1_cat_5(A) & m1_subset_1(B,u2_cat_1(A)) & l1_cat_1(A) -> k5_cat_5(A,B) = k18_mcart_1(B))) # label(redefinition_k5_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.90 7156 (all A (l1_cat_1(A) & v3_cat_5(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) & v3_cat_5(B) -> (r1_tarski(u2_cat_1(A),u2_cat_1(B)) -> m3_cat_2(A,B)))))) # label(t15_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.90 7157 (all A all B (m1_subset_1(B,u1_cat_1(A)) & l1_cat_1(A) & v2_cat_1(A) -> v1_cat_5(k14_cat_5(A,B)) & l1_cat_1(k14_cat_5(A,B)) & v2_cat_1(k14_cat_5(A,B)) & v1_cat_1(k14_cat_5(A,B)))) # label(dt_k14_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.90 7158 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (k3_cat_1(A,B) = k2_cat_1(A,C) -> k1_partfun1(u2_cat_1(k15_cat_5(A,k3_cat_1(A,C))),u2_cat_1(k15_cat_5(A,k2_cat_1(A,C))),u2_cat_1(k15_cat_5(A,k3_cat_1(A,B))),u2_cat_1(k15_cat_5(A,k2_cat_1(A,B))),k23_cat_5(A,C),k23_cat_5(A,B)) = k23_cat_5(A,k4_cat_1(A,B,C))))))))) # label(t34_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.90 7159 (all A (l1_cat_1(A) -> (v3_cat_5(A) & v2_cat_1(A) -> v1_cat_5(A) & v2_cat_1(A)))) # label(cc1_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.90 7160 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m3_cat_2(B,A) -> (m3_cat_2(A,B) -> g1_cat_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A)) = g1_cat_1(u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),u5_cat_1(B),u6_cat_1(B))))))) # label(t3_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.90 7161 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m3_cat_2(B,A) -> (all C (m3_cat_2(C,A) -> (-r2_subset_1(u1_cat_1(B),u1_cat_1(C)) -> k6_cat_5(B,C) = k6_cat_5(C,B)))))))) # label(t5_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.90 7162 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> v2_cat_1(B) & l1_cat_1(B))) <-> v2_cat_5(A)))) # label(d5_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.90 7163 (all A (l1_cat_1(A) & v3_cat_5(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> v2_cat_1(B) & l1_cat_1(B))))) # label(t12_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.90 7164 (all A (v2_cat_5(A) & -v1_xboole_0(A) -> (exists B (v2_cat_1(B) & l1_cat_1(B) & A = u1_cat_1(B) & v4_cat_5(B) & v3_cat_5(B) & v1_cat_1(B))))) # label(t20_cat_5) # label(axiom) # label(non_clause). [assumption]. 116.33/115.90 7165 (all A all B all C (v2_cat_1(A) & l1_cat_1(A) & m1_subset_1(C,u2_cat_1(k15_cat_5(A,B))) & m1_subset_1(B,u1_cat_1(A)) -> m2_subset_1(k21_cat_5(A,B,C),u2_cat_1(A),k13_cat_5(A,B)))) # label(dt_k21_cat_5) # label(axiom) # label(non_clause). [assumption]. 120.18/119.73 7166 (all A (l1_cat_1(A) & v3_cat_5(A) & v2_cat_1(A) -> ((all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (m1_subset_1(B,u1_cat_1(A)) & m1_subset_1(C,u1_cat_1(A)) -> (all D (m2_cat_1(D,B,C) -> m1_subset_1(k4_tarski(k4_tarski(B,C),D),u2_cat_1(A))))))))) <-> v4_cat_5(A)))) # label(d8_cat_5) # label(axiom) # label(non_clause). [assumption]. 120.18/119.73 7167 (all A (m1_subset_1(A,f1_s1_cat_5) -> (exists B (p1_s1_cat_5(A,A,B) & (all C (m1_subset_1(C,f1_s1_cat_5) -> (all D (m1_subset_1(D,f2_s1_cat_5) -> (p1_s1_cat_5(A,C,D) -> f3_s1_cat_5(D,B) = D) & (p1_s1_cat_5(C,A,D) -> D = f3_s1_cat_5(B,D)))))) & m1_subset_1(B,f2_s1_cat_5))))) & (all A (m1_subset_1(A,f1_s1_cat_5) -> (all B (m1_subset_1(B,f1_s1_cat_5) -> (all C (m1_subset_1(C,f1_s1_cat_5) -> (all D (m1_subset_1(D,f1_s1_cat_5) -> (all E (m1_subset_1(E,f2_s1_cat_5) -> (all F (m1_subset_1(F,f2_s1_cat_5) -> (all G (m1_subset_1(G,f2_s1_cat_5) -> (p1_s1_cat_5(B,C,F) & p1_s1_cat_5(C,D,G) & p1_s1_cat_5(A,B,E) -> f3_s1_cat_5(G,f3_s1_cat_5(F,E)) = f3_s1_cat_5(f3_s1_cat_5(G,F),E)))))))))))))))) & (all A (m1_subset_1(A,f1_s1_cat_5) -> (all B (m1_subset_1(B,f1_s1_cat_5) -> (all C (m1_subset_1(C,f1_s1_cat_5) -> (all D (m1_subset_1(D,f2_s1_cat_5) -> (all E (m1_subset_1(E,f2_s1_cat_5) -> (p1_s1_cat_5(A,B,D) & p1_s1_cat_5(B,C,E) -> p1_s1_cat_5(A,C,f3_s1_cat_5(E,D)) & r2_hidden(f3_s1_cat_5(E,D),f2_s1_cat_5)))))))))))) -> (exists A ((all B (m1_subset_1(B,u2_cat_1(A)) -> (exists C (m1_subset_1(C,f1_s1_cat_5) & (exists D ((exists E (p1_s1_cat_5(C,D,E) & k1_domain_1(k2_zfmisc_1(f1_s1_cat_5,f1_s1_cat_5),f2_s1_cat_5,k1_domain_1(f1_s1_cat_5,f1_s1_cat_5,C,D),E) = B & m1_subset_1(E,f2_s1_cat_5))) & m1_subset_1(D,f1_s1_cat_5))))))) & (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,f1_s1_cat_5) -> (all E (m1_subset_1(E,f1_s1_cat_5) -> (all F (m1_subset_1(F,f1_s1_cat_5) -> (all G (m1_subset_1(G,f2_s1_cat_5) -> (all H (m1_subset_1(H,f2_s1_cat_5) -> (C = k1_domain_1(k2_zfmisc_1(f1_s1_cat_5,f1_s1_cat_5),f2_s1_cat_5,k1_domain_1(f1_s1_cat_5,f1_s1_cat_5,E,F),H) & B = k1_domain_1(k2_zfmisc_1(f1_s1_cat_5,f1_s1_cat_5),f2_s1_cat_5,k1_domain_1(f1_s1_cat_5,f1_s1_cat_5,D,E),G) -> k4_tarski(k1_domain_1(f1_s1_cat_5,f1_s1_cat_5,D,F),f3_s1_cat_5(H,G)) = k4_cat_1(A,B,C)))))))))))))))) & (all B (m1_subset_1(B,f1_s1_cat_5) -> (all C (m1_subset_1(C,f1_s1_cat_5) -> (all D (m1_subset_1(D,f2_s1_cat_5) -> (p1_s1_cat_5(B,C,D) -> m1_subset_1(k1_domain_1(k2_zfmisc_1(f1_s1_cat_5,f1_s1_cat_5),f2_s1_cat_5,k1_domain_1(f1_s1_cat_5,f1_s1_cat_5,B,C),D),u2_cat_1(A))))))))) & u1_cat_1(A) = f1_s1_cat_5 & l1_cat_1(A) & v1_cat_5(A) & v2_cat_1(A) & v1_cat_1(A))) # label(s1_cat_5) # label(axiom) # label(non_clause). [assumption]. 120.18/119.73 7168 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m3_cat_2(C,B) -> (all D (m2_cat_1(D,A,B) -> (r1_tarski(k2_relat_1(D),u2_cat_1(C)) -> m2_cat_1(D,A,C)))))))))) # label(t7_cat_5) # label(axiom) # label(non_clause). [assumption]. 120.18/119.73 7169 (all A all B all C (m1_subset_1(B,u1_cat_1(A)) & m1_subset_1(C,u2_cat_1(k14_cat_5(A,B))) & l1_cat_1(A) & v2_cat_1(A) -> k16_cat_5(A,B,C) = k2_mcart_1(C))) # label(redefinition_k16_cat_5) # label(axiom) # label(non_clause). [assumption]. 120.18/119.73 7170 (all A all B all C (m1_subset_1(B,u1_cat_1(A)) & m1_subset_1(C,u2_cat_1(k15_cat_5(A,B))) & l1_cat_1(A) & v2_cat_1(A) -> k20_cat_5(A,B,C) = k17_mcart_1(C))) # label(redefinition_k20_cat_5) # label(axiom) # label(non_clause). [assumption]. 120.18/119.73 7171 (all A (v3_cat_5(A) & l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> k10_cat_5(B) = B)))) # label(t16_cat_5) # label(axiom) # label(non_clause). [assumption]. 120.18/119.73 7172 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> r2_hidden(B,k12_cat_5(A,k3_cat_1(A,B))) & r2_hidden(B,k13_cat_5(A,k2_cat_1(A,B))))))) # label(t26_cat_5) # label(axiom) # label(non_clause). [assumption]. 120.18/119.74 7173 (all A all B all C (v2_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) & m1_subset_1(C,u2_cat_1(k15_cat_5(A,B))) & l1_cat_1(A) -> m2_subset_1(k20_cat_5(A,B,C),u2_cat_1(A),k13_cat_5(A,B)))) # label(dt_k20_cat_5) # label(axiom) # label(non_clause). [assumption]. 120.18/119.74 7174 (all A all B all C (m1_subset_1(B,u1_cat_1(A)) & m1_subset_1(C,u2_cat_1(k14_cat_5(A,B))) & l1_cat_1(A) & v2_cat_1(A) -> k18_mcart_1(C) = k18_cat_5(A,B,C))) # label(redefinition_k18_cat_5) # label(axiom) # label(non_clause). [assumption]. 120.18/119.74 7175 (all A (v3_cat_5(A) & l1_cat_1(A) & v2_cat_1(A) -> (all B (m3_cat_2(B,A) -> v3_cat_5(B))))) # label(cc2_cat_5) # label(axiom) # label(non_clause). [assumption]. 120.18/119.74 7176 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> (all C (m3_cat_2(C,B) -> m3_cat_2(C,A))))))) # label(t4_cat_5) # label(axiom) # label(non_clause). [assumption]. 120.18/119.74 7177 (all A all B all C (v2_cat_1(A) & m1_subset_1(C,u2_cat_1(k14_cat_5(A,B))) & m1_subset_1(B,u1_cat_1(A)) & l1_cat_1(A) -> k17_cat_5(A,B,C) = k17_mcart_1(C))) # label(redefinition_k17_cat_5) # label(axiom) # label(non_clause). [assumption]. 120.18/119.74 7178 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m2_subset_1(C,u2_cat_1(A),k13_cat_5(A,B)) -> (all D (m1_subset_1(D,u1_cat_1(k15_cat_5(A,B))) -> (C = D -> k1_domain_1(u1_cat_1(k11_cat_2(k15_cat_5(A,B),k15_cat_5(A,B))),u2_cat_1(A),k12_cat_2(k15_cat_5(A,B),k15_cat_5(A,B),D,D),k10_cat_1(A,k3_cat_1(A,C))) = k10_cat_1(k15_cat_5(A,B),D)))))))))) # label(t32_cat_5) # label(axiom) # label(non_clause). [assumption]. 120.18/119.74 7179 (all A all B (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) -> v1_cat_1(k6_cat_5(A,B)) & v2_cat_1(k6_cat_5(A,B)) & l1_cat_1(k6_cat_5(A,B)))) # label(dt_k6_cat_5) # label(axiom) # label(non_clause). [assumption]. 120.18/119.74 7180 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> k3_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k6_domain_1(u1_cat_1(A),B)) = k13_cat_5(A,B))))) # label(d10_cat_5) # label(axiom) # label(non_clause). [assumption]. 120.18/119.74 7181 (all A (l1_cat_1(A) & v1_cat_5(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> k2_cat_1(A,B) = k17_mcart_1(B) & k18_mcart_1(B) = k3_cat_1(A,B) & k4_tarski(k1_domain_1(u1_cat_1(A),u1_cat_1(A),k2_cat_1(A,B),k3_cat_1(A,B)),k2_mcart_1(B)) = B)))) # label(t2_cat_5) # label(axiom) # label(non_clause). [assumption]. 120.18/119.74 7182 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (g1_cat_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A)) = g1_cat_1(u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),u5_cat_1(B),u6_cat_1(B)) & v3_cat_5(A) -> v3_cat_5(B)))))) # label(t10_cat_5) # label(axiom) # label(non_clause). [assumption]. 120.18/119.74 7183 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,k2_zfmisc_1(A,B)) & -v1_xboole_0(B) -> m1_subset_1(k3_cat_5(A,B,C),B))) # label(dt_k3_cat_5) # label(axiom) # label(non_clause). [assumption]. 120.18/119.74 7184 (all A (l1_cat_1(A) -> (all B (l1_cat_1(B) -> (g1_cat_1(u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),u5_cat_1(B),u6_cat_1(B)) = g1_cat_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A)) & v2_cat_1(A) -> v2_cat_1(B)))))) # label(t1_cat_5) # label(axiom) # label(non_clause). [assumption]. 120.18/119.74 7185 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) & -v1_xboole_0(C) -> k17_mcart_1(D) = k1_cat_5(A,B,C,D))) # label(redefinition_k1_cat_5) # label(axiom) # label(non_clause). [assumption]. 120.18/119.74 7186 (all A (m1_subset_1(A,u2_cat_1(f1_s3_cat_5)) -> (all B (m1_subset_1(B,u2_cat_1(f1_s3_cat_5)) -> (all C (m1_subset_1(C,u2_cat_1(f2_s3_cat_5)) -> (all D (m1_subset_1(D,u2_cat_1(f2_s3_cat_5)) -> (C = f4_s3_cat_5(A) & D = f4_s3_cat_5(B) & k2_cat_1(f1_s3_cat_5,B) = k3_cat_1(f1_s3_cat_5,A) -> f4_s3_cat_5(k4_cat_1(f1_s3_cat_5,A,B)) = k4_cat_1(f2_s3_cat_5,C,D)))))))))) & (all A (m1_subset_1(A,u1_cat_1(f1_s3_cat_5)) -> f4_s3_cat_5(k10_cat_1(f1_s3_cat_5,A)) = k10_cat_1(f2_s3_cat_5,f3_s3_cat_5(A)))) & (all A (m1_subset_1(A,u2_cat_1(f1_s3_cat_5)) -> (all B (m1_subset_1(B,u2_cat_1(f2_s3_cat_5)) -> (f4_s3_cat_5(A) = B -> k2_cat_1(f2_s3_cat_5,B) = f3_s3_cat_5(k2_cat_1(f1_s3_cat_5,A)) & f3_s3_cat_5(k3_cat_1(f1_s3_cat_5,A)) = k3_cat_1(f2_s3_cat_5,B)))) & m1_subset_1(f4_s3_cat_5(A),u2_cat_1(f2_s3_cat_5)))) -> (exists A ((all B (m1_subset_1(B,u2_cat_1(f1_s3_cat_5)) -> f4_s3_cat_5(B) = k8_funct_2(u2_cat_1(f1_s3_cat_5),u2_cat_1(f2_s3_cat_5),A,B))) & m2_cat_1(A,f1_s3_cat_5,f2_s3_cat_5))) # label(s3_cat_5) # label(axiom) # label(non_clause). [assumption]. 120.18/119.74 7187 (all A all B (l1_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) & v2_cat_1(A) -> m1_subset_1(k12_cat_5(A,B),k1_zfmisc_1(u2_cat_1(A))))) # label(dt_k12_cat_5) # label(axiom) # label(non_clause). [assumption]. 120.18/119.74 7188 (all A all B (v2_cat_1(A) & l1_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) -> -v1_xboole_0(k13_cat_5(A,B)))) # label(fc2_cat_5) # label(axiom) # label(non_clause). [assumption]. 120.18/119.74 7189 (all A (l1_cat_1(A) & v2_cat_1(A) -> k10_cat_5(A) = A)) # label(d7_cat_5) # label(axiom) # label(non_clause). [assumption]. 120.18/119.74 7190 (all A (l1_cat_1(A) & v3_cat_5(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> k3_cat_1(A,B) = k5_cat_5(A,B) & k2_cat_1(A,B) = k4_cat_5(A,B))))) # label(t13_cat_5) # label(axiom) # label(non_clause). [assumption]. 120.18/119.74 7191 (exists A (v1_cat_1(A) & v1_cat_5(A) & v2_cat_1(A) & l1_cat_1(A))) # label(rc1_cat_5) # label(axiom) # label(non_clause). [assumption]. 120.18/119.74 7192 (all A (v2_cat_1(A) & v3_cat_5(A) & l1_cat_1(A) -> (all B (v3_cat_5(B) & v4_cat_5(B) & l1_cat_1(B) & v2_cat_1(B) -> (r1_tarski(u1_cat_1(A),u1_cat_1(B)) -> m3_cat_2(A,B)))))) # label(t21_cat_5) # label(axiom) # label(non_clause). [assumption]. 120.18/119.74 7193 (all A all B all C (m1_subset_1(B,u1_cat_1(A)) & m1_subset_1(C,u2_cat_1(k14_cat_5(A,B))) & l1_cat_1(A) & v2_cat_1(A) -> m1_subset_1(k16_cat_5(A,B,C),u2_cat_1(A)))) # label(dt_k16_cat_5) # label(axiom) # label(non_clause). [assumption]. 120.18/119.74 7194 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> -((exists C (v2_cat_1(C) & l1_cat_1(C) & m3_cat_2(B,C) & m3_cat_2(A,C))) & (exists C (m1_subset_1(C,u1_cat_1(A)) & m1_subset_1(C,u1_cat_1(B)))) & -(all C (v1_cat_1(C) & v2_cat_1(C) & l1_cat_1(C) -> (C = k6_cat_5(A,B) <-> k3_xboole_0(u1_cat_1(A),u1_cat_1(B)) = u1_cat_1(C) & u3_cat_1(C) = k2_partfun1(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),u2_cat_1(B)) & k2_partfun1(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),u2_cat_1(B)) = u4_cat_1(C) & u5_cat_1(C) = k1_realset1(u5_cat_1(A),u2_cat_1(B)) & u6_cat_1(C) = k2_partfun1(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),u1_cat_1(B)) & k3_xboole_0(u2_cat_1(A),u2_cat_1(B)) = u2_cat_1(C))))))))) # label(d2_cat_5) # label(axiom) # label(non_clause). [assumption]. 120.18/119.74 7195 (all A all B (v2_cat_1(A) & l1_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) -> -v1_xboole_0(k12_cat_5(A,B)))) # label(fc1_cat_5) # label(axiom) # label(non_clause). [assumption]. 120.18/119.74 7196 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) & v3_cat_5(B) -> (all C (v2_cat_1(C) & v3_cat_5(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,C) -> (E = D -> k7_cat_5(A,C,E) = k7_cat_5(A,B,D)))))))))))) # label(t22_cat_5) # label(axiom) # label(non_clause). [assumption]. 120.18/119.74 7197 (all A all B (v3_cat_5(A) & m1_subset_1(B,u2_cat_1(A)) & l1_cat_1(A) & v2_cat_1(A) -> k17_mcart_1(B) = k8_cat_5(A,B))) # label(redefinition_k8_cat_5) # label(axiom) # label(non_clause). [assumption]. 120.18/119.74 7198 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m2_subset_1(C,u2_cat_1(A),k13_cat_5(A,k3_cat_1(A,B))) -> r2_hidden(k4_cat_1(A,B,C),k13_cat_5(A,k2_cat_1(A,B))))))))) # label(t28_cat_5) # label(axiom) # label(non_clause). [assumption]. 120.18/119.74 7199 (all A (v2_cat_5(A) & -v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> -((all C (m1_cat_5(C,A) -> (all D (m1_cat_5(D,A) -> (all E (m1_cat_5(E,A) -> (all F (m2_cat_1(F,C,D) -> (all G (m2_cat_1(G,D,E) -> (r2_hidden(F,B) & r2_hidden(G,B) -> r2_hidden(k14_cat_1(C,D,E,F,G),B)))))))))))) & (all C (m1_cat_5(C,A) -> r2_hidden(k15_cat_1(C),B))) & (all C (v3_cat_5(C) & l1_cat_1(C) & v2_cat_1(C) & v1_cat_1(C) -> -((all D (m1_cat_5(D,A) -> (all E (m1_cat_5(E,A) -> (all F (m2_cat_1(F,D,E) -> (m1_subset_1(k1_domain_1(k2_zfmAlarm clock 180.50/180.02 Prover9 interrupted 180.50/180.02 EOF