0.04/0.15 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.04/0.15 % Command : tptp2X_and_run_prover9 %d %s 0.13/0.37 % Computer : n014.cluster.edu 0.13/0.37 % Model : x86_64 x86_64 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.37 % Memory : 8042.1875MB 0.13/0.37 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.37 % CPULimit : 960 0.13/0.37 % DateTime : Thu Jul 2 14:47:42 EDT 2020 0.13/0.38 % CPUTime : 56.07/55.05 ============================== Prover9 =============================== 56.07/55.05 Prover9 (32) version 2009-11A, November 2009. 56.07/55.05 Process 7173 was started by sandbox on n014.cluster.edu, 56.07/55.05 Thu Jul 2 14:48:30 2020 56.07/55.05 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 960 -f /tmp/Prover9_7003_n014.cluster.edu". 56.07/55.05 ============================== end of head =========================== 56.07/55.05 56.07/55.05 ============================== INPUT ================================= 56.07/55.05 56.07/55.05 % Reading from file /tmp/Prover9_7003_n014.cluster.edu 56.07/55.05 56.07/55.05 set(prolog_style_variables). 56.07/55.05 set(auto2). 56.07/55.05 % set(auto2) -> set(auto). 56.07/55.05 % set(auto) -> set(auto_inference). 56.07/55.05 % set(auto) -> set(auto_setup). 56.07/55.05 % set(auto_setup) -> set(predicate_elim). 56.07/55.05 % set(auto_setup) -> assign(eq_defs, unfold). 56.07/55.05 % set(auto) -> set(auto_limits). 56.07/55.05 % set(auto_limits) -> assign(max_weight, "100.000"). 56.07/55.05 % set(auto_limits) -> assign(sos_limit, 20000). 56.07/55.05 % set(auto) -> set(auto_denials). 56.07/55.05 % set(auto) -> set(auto_process). 56.07/55.05 % set(auto2) -> assign(new_constants, 1). 56.07/55.05 % set(auto2) -> assign(fold_denial_max, 3). 56.07/55.05 % set(auto2) -> assign(max_weight, "200.000"). 56.07/55.05 % set(auto2) -> assign(max_hours, 1). 56.07/55.05 % assign(max_hours, 1) -> assign(max_seconds, 3600). 56.07/55.05 % set(auto2) -> assign(max_seconds, 0). 56.07/55.05 % set(auto2) -> assign(max_minutes, 5). 56.07/55.05 % assign(max_minutes, 5) -> assign(max_seconds, 300). 56.07/55.05 % set(auto2) -> set(sort_initial_sos). 56.07/55.05 % set(auto2) -> assign(sos_limit, -1). 56.07/55.05 % set(auto2) -> assign(lrs_ticks, 3000). 56.07/55.05 % set(auto2) -> assign(max_megs, 400). 56.07/55.05 % set(auto2) -> assign(stats, some). 56.07/55.05 % set(auto2) -> clear(echo_input). 56.07/55.05 % set(auto2) -> set(quiet). 56.07/55.05 % set(auto2) -> clear(print_initial_clauses). 56.07/55.05 % set(auto2) -> clear(print_given). 56.07/55.05 assign(lrs_ticks,-1). 56.07/55.05 assign(sos_limit,10000). 56.07/55.05 assign(order,kbo). 56.07/55.05 set(lex_order_vars). 56.07/55.05 clear(print_given). 56.07/55.05 56.07/55.05 % formulas(sos). % not echoed (19321 formulas) 56.07/55.05 56.07/55.05 ============================== end of input ========================== 56.07/55.05 56.07/55.05 % From the command line: assign(max_seconds, 960). 56.07/55.05 56.07/55.05 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 56.07/55.05 56.07/55.05 % Formulas that are not ordinary clauses: 56.07/55.05 1 (all A all B (r2_hidden(A,B) -> -r2_hidden(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption]. 56.07/55.05 2 $T # label(t4_tarski) # label(axiom) # label(non_clause). [assumption]. 56.07/55.05 3 $T # label(t8_tarski) # label(axiom) # label(non_clause). [assumption]. 56.07/55.05 4 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption]. 56.07/55.05 5 (all A all B ((all C ((exists D (r2_hidden(C,D) & r2_hidden(D,A))) <-> r2_hidden(C,B))) <-> B = k3_tarski(A))) # label(d4_tarski) # label(axiom) # label(non_clause). [assumption]. 56.07/55.05 6 (all A all B all C (C = k2_tarski(A,B) <-> (all D (D = A | D = B <-> r2_hidden(D,C))))) # label(d2_tarski) # label(axiom) # label(non_clause). [assumption]. 56.07/55.05 7 (all A all B k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A))) # label(d5_tarski) # label(axiom) # label(non_clause). [assumption]. 56.07/55.05 8 $T # label(t5_tarski) # label(axiom) # label(non_clause). [assumption]. 56.07/55.05 9 (all A all B all C (p1_s1_tarski(A,C) & p1_s1_tarski(A,B) -> B = C)) -> (exists A all B ((exists C (p1_s1_tarski(C,B) & r2_hidden(C,f1_s1_tarski))) <-> r2_hidden(B,A))) # label(s1_tarski) # label(axiom) # label(non_clause). [assumption]. 56.07/55.05 10 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption]. 56.07/55.05 11 $T # label(t6_tarski) # label(axiom) # label(non_clause). [assumption]. 56.07/55.05 12 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 56.07/55.05 13 (all A all B ((all C (r2_hidden(C,B) <-> r2_hidden(C,A))) -> B = A)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption]. 56.07/55.05 14 (all A all B k2_tarski(B,A) = k2_tarski(A,B)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 56.07/55.05 15 $T # label(dt_k3_tarski) # label(axiom) # label(non_clause). [assumption]. 56.07/55.05 16 $T # label(t1_tarski) # label(axiom) # label(non_clause). [assumption]. 56.07/55.05 17 (all A all B (r2_tarski(A,B) <-> (exists C ((all D -((all E -(r2_hidden(E,A) & r2_hidden(k4_tarski(E,D),C))) & r2_hidden(D,B))) & (all D all E all F all G (r2_hidden(k4_tarski(F,G),C) & r2_hidden(k4_tarski(D,E),C) -> (G = E <-> F = D))) & (all D -((all E -(r2_hidden(k4_tarski(D,E),C) & r2_hidden(E,B))) & r2_hidden(D,A))))))) # label(d6_tarski) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 18 $T # label(t3_tarski) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 19 (all A all B (k1_tarski(A) = B <-> (all C (r2_hidden(C,B) <-> A = C)))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 20 (all A all B -((all C -((all D -(r2_hidden(D,C) & r2_hidden(D,B))) & r2_hidden(C,B))) & r2_hidden(A,B))) # label(t7_tarski) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 21 (all A all B r1_tarski(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 22 (all A all B (r1_tarski(A,B) <-> (all C (r2_hidden(C,A) -> r2_hidden(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 23 (all A exists B (r2_hidden(A,B) & (all C -(r2_hidden(C,B) & (all D -(r2_hidden(D,B) & (all E (r1_tarski(E,C) -> r2_hidden(E,D))))))) & (all C all D (r1_tarski(D,C) & r2_hidden(C,B) -> r2_hidden(D,B))) & (all C -(r1_tarski(C,B) & -r2_tarski(C,B) & -r2_hidden(C,B))))) # label(t9_tarski) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 24 (all A all B all C -(r2_hidden(C,k2_xboole_0(A,B)) & -(r2_hidden(C,B) & -r2_hidden(C,A)) & r1_xboole_0(A,B) & -(r2_hidden(C,A) & -r2_hidden(C,B)))) # label(t5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 25 (all A all B (r1_tarski(B,A) & r1_tarski(A,B) <-> A = B)) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 26 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 27 (all A (k1_xboole_0 = A <-> (all B -r2_hidden(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 28 (all A all B all C ((all D (-r2_hidden(D,B) & r2_hidden(D,A) <-> r2_hidden(D,C))) <-> k4_xboole_0(A,B) = C)) # label(d4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 29 (exists A v1_xboole_0(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 30 (all A all B all C ((all D ((r2_hidden(D,B) <-> r2_hidden(D,C)) <-> -r2_hidden(D,A))) -> k5_xboole_0(B,C) = A)) # label(t2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 31 (all A all B all C (-(r2_hidden(A,B) <-> r2_hidden(A,C)) <-> r2_hidden(A,k5_xboole_0(B,C)))) # label(t1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 32 (all A all B all C (C = k3_xboole_0(A,B) <-> (all D (r2_hidden(D,C) <-> r2_hidden(D,A) & r2_hidden(D,B))))) # label(d3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 33 (all A all B (r1_xboole_0(A,B) <-> k3_xboole_0(A,B) = k1_xboole_0)) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 34 (all A all B all C ((all D (r2_hidden(D,A) | r2_hidden(D,B) <-> r2_hidden(D,C))) <-> C = k2_xboole_0(A,B))) # label(d2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 35 (all A all B r3_xboole_0(A,A)) # label(reflexivity_r3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 36 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 37 (exists A all B (r2_hidden(B,A) <-> r2_hidden(B,f1_s1_xboole_0) & p1_s1_xboole_0(B))) # label(s1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 38 (all A all B (r3_xboole_0(A,B) <-> r1_tarski(B,A) | r1_tarski(A,B))) # label(d9_xboole_0) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 39 (all A all B -r2_xboole_0(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 40 (all A all B k5_xboole_0(B,A) = k5_xboole_0(A,B)) # label(commutativity_k5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 41 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 42 (all A (p1_s2_xboole_0(A) <-> r2_hidden(A,f2_s2_xboole_0))) & (all A (p1_s2_xboole_0(A) <-> r2_hidden(A,f1_s2_xboole_0))) -> f2_s2_xboole_0 = f1_s2_xboole_0 # label(s2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 43 (all A all B (r1_xboole_0(A,B) -> r1_xboole_0(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 44 (all A all B (r2_xboole_0(A,B) <-> B != A & r1_tarski(A,B))) # label(d8_xboole_0) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 45 (all A all B A = k3_xboole_0(A,A)) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 46 (all A all B (-(-r1_xboole_0(A,B) & (all C -r2_hidden(C,k3_xboole_0(A,B)))) & -(r1_xboole_0(A,B) & (exists C r2_hidden(C,k3_xboole_0(A,B)))))) # label(t4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 47 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 48 (all A all B ((all C (p1_s3_xboole_0(C) <-> r2_hidden(C,A))) & (all C (p1_s3_xboole_0(C) <-> r2_hidden(C,B))) -> A = B)) # label(s3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 49 (all A all B (r3_xboole_0(A,B) -> r3_xboole_0(B,A))) # label(symmetry_r3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 50 (all A all B k2_xboole_0(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 51 (all A all B (r2_xboole_0(A,B) -> -r2_xboole_0(B,A))) # label(antisymmetry_r2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 52 (all A all B k3_xboole_0(A,B) = k3_xboole_0(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 53 (all A all B k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(B,A)) = k5_xboole_0(A,B)) # label(d6_xboole_0) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 54 (all A all B k2_xboole_0(B,A) = k2_xboole_0(A,B)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 55 (all A all B (-((exists C (r2_hidden(C,B) & r2_hidden(C,A))) & r1_xboole_0(A,B)) & -((all C -(r2_hidden(C,A) & r2_hidden(C,B))) & -r1_xboole_0(A,B)))) # label(t3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 56 $T # label(dt_k5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 57 (all A (v1_xboole_0(A) <-> A = k1_xboole_0)) # label(d5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 58 (all A all B (-v1_xboole_0(A) -> -v1_xboole_0(k2_xboole_0(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 59 (exists A -v1_xboole_0(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 60 (all A all B (-v1_xboole_0(A) -> -v1_xboole_0(k2_xboole_0(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 61 (all A all B -(v1_xboole_0(B) & B != A & v1_xboole_0(A))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 62 (all A all B -(r2_hidden(A,B) & v1_xboole_0(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 63 (all A k1_xboole_0 = k3_xboole_0(A,k1_xboole_0)) # label(t2_boole) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 64 (all A k2_xboole_0(A,k1_xboole_0) = A) # label(t1_boole) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 65 (all A A = k5_xboole_0(A,k1_xboole_0)) # label(t5_boole) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 66 (all A k1_xboole_0 = k4_xboole_0(k1_xboole_0,A)) # label(t4_boole) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 67 (all A k4_xboole_0(A,k1_xboole_0) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 68 (all A (v1_xboole_0(A) -> A = k1_xboole_0)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 69 (all A all B all C all D (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k4_xboole_0(A,D),k4_xboole_0(B,C)))) # label(t35_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 70 (all A all B all C k4_xboole_0(A,k5_xboole_0(B,C)) = k2_xboole_0(k4_xboole_0(A,k2_xboole_0(B,C)),k3_xboole_0(k3_xboole_0(A,B),C))) # label(t102_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 71 (all A all B all C k2_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(k2_xboole_0(A,C),k2_xboole_0(B,C))) # label(t5_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 72 (all A all B r1_xboole_0(k3_xboole_0(A,B),k4_xboole_0(A,B))) # label(t89_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 73 (all A (r1_tarski(A,k1_xboole_0) -> k1_xboole_0 = A)) # label(t3_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 74 (all A all B k2_xboole_0(A,k4_xboole_0(B,A)) = k2_xboole_0(A,B)) # label(t39_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 75 (all A all B all C (r1_tarski(k2_xboole_0(A,B),C) -> r1_tarski(A,C))) # label(t11_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 76 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k3_xboole_0(A,C),k3_xboole_0(B,C)))) # label(t26_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 77 (all A all B all C (r1_tarski(k4_xboole_0(A,B),C) & r1_tarski(k4_xboole_0(B,A),C) -> r1_tarski(k5_xboole_0(A,B),C))) # label(t97_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 78 (all A all B all C k4_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(k4_xboole_0(A,C),k4_xboole_0(B,C))) # label(t42_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 79 (all A all B all C k4_xboole_0(k5_xboole_0(A,B),C) = k2_xboole_0(k4_xboole_0(A,k2_xboole_0(B,C)),k4_xboole_0(B,k2_xboole_0(A,C)))) # label(t99_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 80 (all A all B all C (r1_tarski(A,B) & r1_tarski(C,B) -> r1_tarski(k2_xboole_0(A,C),B))) # label(t8_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 81 (all A all B all C (r1_tarski(A,k2_xboole_0(B,C)) -> r1_tarski(k4_xboole_0(A,B),C))) # label(t43_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 82 (all A all B r1_tarski(k4_xboole_0(A,B),A)) # label(t36_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 83 (all A all B k4_xboole_0(A,k3_xboole_0(A,B)) = k4_xboole_0(A,B)) # label(t47_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 84 (all A all B all C all D (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,D)))) # label(t13_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 85 (all A all B r1_tarski(k4_xboole_0(A,B),k5_xboole_0(A,B))) # label(t96_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 86 (all A all B all C k3_xboole_0(A,k4_xboole_0(B,C)) = k4_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C))) # label(t50_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 87 (all A all B all C (r1_tarski(A,k4_xboole_0(B,C)) -> r1_xboole_0(A,C) & r1_tarski(A,B))) # label(t106_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 88 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,C)))) # label(t9_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 89 (all A all B all C all D (r1_xboole_0(D,B) & r1_xboole_0(C,A) & k2_xboole_0(A,B) = k2_xboole_0(C,D) -> B = C)) # label(t72_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 90 (all A all B r1_tarski(A,k2_xboole_0(A,B))) # label(t7_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 91 (all A all B all C (r1_tarski(C,B) & r1_tarski(A,B) -> r1_tarski(k5_xboole_0(A,C),B))) # label(t110_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 92 (all A all B all C ((all D (r1_tarski(D,B) & r1_tarski(D,C) -> r1_tarski(D,A))) & r1_tarski(A,C) & r1_tarski(A,B) -> k3_xboole_0(B,C) = A)) # label(t20_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 93 (all A all B -(r2_xboole_0(B,A) & r2_xboole_0(A,B))) # label(t57_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 94 (all A all B all C (r1_tarski(A,B) & r1_xboole_0(A,C) -> r1_tarski(A,k4_xboole_0(B,C)))) # label(t86_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 95 (all A all B k2_xboole_0(A,B) = k2_xboole_0(k5_xboole_0(A,B),k3_xboole_0(A,B))) # label(t93_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 96 (all A all B all C r1_tarski(k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C)),k2_xboole_0(B,C))) # label(t31_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 97 (all A all B r1_xboole_0(k4_xboole_0(A,k3_xboole_0(A,B)),B)) # label(t90_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 98 (all A all B all C (r1_xboole_0(B,C) & r1_tarski(A,B) -> r1_xboole_0(A,C))) # label(t63_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 99 (all A all B k1_xboole_0 = k4_xboole_0(A,k2_xboole_0(A,B))) # label(t46_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 100 (all A all B all C (r1_tarski(A,B) -> r1_xboole_0(A,k4_xboole_0(C,B)))) # label(t85_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 101 (all A all B all C k3_xboole_0(k5_xboole_0(A,C),B) = k5_xboole_0(k3_xboole_0(A,B),k3_xboole_0(C,B))) # label(t112_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 102 (all A all B all C (r1_tarski(B,C) & r2_xboole_0(A,B) -> r2_xboole_0(A,C))) # label(t58_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 103 (all A all B all C (r2_xboole_0(A,B) & r2_xboole_0(B,C) -> r2_xboole_0(A,C))) # label(t56_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 104 (all A all B all C (r1_tarski(A,k5_xboole_0(B,C)) <-> r1_tarski(A,k2_xboole_0(B,C)) & r1_xboole_0(A,k3_xboole_0(B,C)))) # label(t107_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 105 (all A all B all C all D (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k3_xboole_0(A,C),k3_xboole_0(B,D)))) # label(t27_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 106 (all A all B all C (r1_xboole_0(A,k4_xboole_0(B,C)) -> r1_xboole_0(B,k4_xboole_0(A,C)))) # label(t81_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 107 (all A all B all C (-(-r1_xboole_0(A,k2_xboole_0(B,C)) & r1_xboole_0(A,C) & r1_xboole_0(A,B)) & -(r1_xboole_0(A,k2_xboole_0(B,C)) & -(r1_xboole_0(A,C) & r1_xboole_0(A,B))))) # label(t70_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 108 (all A all B all C (r1_xboole_0(A,B) -> r1_xboole_0(k3_xboole_0(C,A),k3_xboole_0(C,B)))) # label(t76_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 109 (all A all B k5_xboole_0(A,B) = k4_xboole_0(k2_xboole_0(A,B),k3_xboole_0(A,B))) # label(t101_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 110 (all A all B all C r1_tarski(k3_xboole_0(A,B),k2_xboole_0(A,C))) # label(t29_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 111 (all A all B k5_xboole_0(k5_xboole_0(A,B),k2_xboole_0(A,B)) = k3_xboole_0(A,B)) # label(t95_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 112 (all A k1_xboole_0 = k5_xboole_0(A,A)) # label(t92_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 113 (all A all B r1_xboole_0(k4_xboole_0(A,B),B)) # label(t79_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 114 (all A all B (r1_xboole_0(A,B) <-> k4_xboole_0(A,B) = A)) # label(t83_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 115 (all A all B all C (r1_xboole_0(A,B) -> r1_xboole_0(A,k4_xboole_0(B,C)))) # label(t80_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 116 (all A all B -(r1_tarski(A,B) & r2_xboole_0(B,A))) # label(t60_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 117 (all A all B all C -(-r1_xboole_0(A,B) & r1_tarski(A,C) & r1_xboole_0(A,k3_xboole_0(B,C)))) # label(t77_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 118 (all A all B all C k4_xboole_0(A,k2_xboole_0(B,C)) = k4_xboole_0(k4_xboole_0(A,B),C)) # label(t41_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 119 (all A all B all C (-v1_xboole_0(C) -> -(r1_xboole_0(A,B) & r1_tarski(C,B) & r1_tarski(C,A)))) # label(t68_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 120 (all A all B all C (r1_tarski(A,B) -> k3_xboole_0(k2_xboole_0(A,C),B) = k2_xboole_0(A,k3_xboole_0(C,B)))) # label(t30_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 121 (all A all B k3_xboole_0(A,B) = k4_xboole_0(A,k4_xboole_0(A,B))) # label(t48_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 122 (all A all B all C all D (r1_xboole_0(A,D) & r1_xboole_0(C,D) & r1_xboole_0(B,D) -> r1_xboole_0(k2_xboole_0(k2_xboole_0(A,B),C),D))) # label(t114_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 123 (all A all B all C (r1_xboole_0(A,B) -> k3_xboole_0(A,k2_xboole_0(B,C)) = k3_xboole_0(A,C))) # label(t78_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 124 (all A all B k2_xboole_0(A,B) = k5_xboole_0(A,k4_xboole_0(B,A))) # label(t98_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 125 (all A all B all C (r1_xboole_0(A,C) & r1_tarski(A,k2_xboole_0(B,C)) -> r1_tarski(A,B))) # label(t73_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 126 (all A all B all C (r1_tarski(C,B) & (all D (r1_tarski(C,D) & r1_tarski(A,D) -> r1_tarski(B,D))) & r1_tarski(A,B) -> B = k2_xboole_0(A,C))) # label(t14_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 127 (all A all B -(r2_xboole_0(A,B) & k1_xboole_0 = k4_xboole_0(B,A))) # label(t105_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 128 (all A all B (k4_xboole_0(A,B) = k4_xboole_0(B,A) -> B = A)) # label(t32_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 129 (all A all B k2_xboole_0(A,k2_xboole_0(A,B)) = k2_xboole_0(A,B)) # label(t6_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 130 (all A all B (r1_xboole_0(A,B) -> A = k4_xboole_0(k2_xboole_0(A,B),B))) # label(t88_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 131 (all A all B all C (r1_tarski(A,B) & r1_tarski(B,C) -> r1_tarski(A,C))) # label(t1_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 132 (all A all B all C (r1_tarski(A,B) & r1_tarski(A,C) -> r1_tarski(A,k3_xboole_0(B,C)))) # label(t19_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 133 (all A all B all C k3_xboole_0(k3_xboole_0(k2_xboole_0(A,B),k2_xboole_0(B,C)),k2_xboole_0(C,A)) = k2_xboole_0(k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(B,C)),k3_xboole_0(C,A))) # label(t25_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 134 (all A all B k4_xboole_0(A,B) = k4_xboole_0(k2_xboole_0(A,B),B)) # label(t40_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 135 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k4_xboole_0(A,C),B))) # label(t109_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 136 (all A r1_xboole_0(A,k1_xboole_0)) # label(t65_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 137 (all A all B (k2_xboole_0(A,B) = k1_xboole_0 -> k1_xboole_0 = A)) # label(t15_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 138 (all A (k1_xboole_0 != A -> r2_xboole_0(k1_xboole_0,A))) # label(t61_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 139 (all A all B all C k5_xboole_0(k5_xboole_0(A,B),C) = k5_xboole_0(A,k5_xboole_0(B,C))) # label(t91_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 140 (all A all B k4_xboole_0(k2_xboole_0(A,B),k3_xboole_0(A,B)) = k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(B,A))) # label(t55_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 141 (all A all B all C (r1_tarski(A,B) -> r1_tarski(A,k2_xboole_0(C,B)))) # label(t10_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 142 (all A all B all C all D (r1_tarski(A,B) & r1_xboole_0(B,D) & r1_tarski(C,D) -> r1_xboole_0(A,C))) # label(t64_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 143 (all A all B all C all D k2_xboole_0(A,k2_xboole_0(k2_xboole_0(B,C),D)) = k2_xboole_0(k2_xboole_0(k2_xboole_0(A,B),C),D)) # label(t113_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 144 (all A all B k3_xboole_0(A,k2_xboole_0(A,B)) = A) # label(t21_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 145 (all A (-(A != k1_xboole_0 & r1_xboole_0(A,A)) & -(-r1_xboole_0(A,A) & k1_xboole_0 = A))) # label(t66_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 146 (all A all B A = k2_xboole_0(k3_xboole_0(A,B),k4_xboole_0(A,B))) # label(t51_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 147 (all A all B all C -(r1_xboole_0(A,C) & r1_xboole_0(A,k4_xboole_0(B,C)) & -r1_xboole_0(A,B))) # label(t84_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 148 (all A all B all C (r1_tarski(A,C) & r1_tarski(A,B) & r1_xboole_0(B,C) -> A = k1_xboole_0)) # label(t67_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 149 (all A all B (r1_tarski(A,k4_xboole_0(B,A)) -> A = k1_xboole_0)) # label(t38_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 150 (all A all B all C (r1_xboole_0(A,B) -> k2_xboole_0(k4_xboole_0(C,A),B) = k4_xboole_0(k2_xboole_0(C,B),A))) # label(t87_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 151 (all A all B all C (r1_tarski(k4_xboole_0(A,B),C) -> r1_tarski(A,k2_xboole_0(B,C)))) # label(t44_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 152 (all A all B all C -(r1_xboole_0(A,B) & -r1_xboole_0(A,k3_xboole_0(B,C)))) # label(t74_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 153 (all A all B k2_xboole_0(A,B) = k5_xboole_0(k5_xboole_0(A,B),k3_xboole_0(A,B))) # label(t94_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 154 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k4_xboole_0(C,B),k4_xboole_0(C,A)))) # label(t34_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 155 (all A all B all C k3_xboole_0(k2_xboole_0(A,B),k2_xboole_0(A,C)) = k2_xboole_0(A,k3_xboole_0(B,C))) # label(t24_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 156 (all A all B (r1_tarski(A,B) -> k2_xboole_0(A,B) = B)) # label(t12_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 157 (all A all B all C k2_xboole_0(k4_xboole_0(A,B),k3_xboole_0(A,C)) = k4_xboole_0(A,k4_xboole_0(B,C))) # label(t52_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 158 (all A all B all C (r1_tarski(A,k3_xboole_0(B,C)) -> r1_tarski(A,B))) # label(t18_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 159 (all A all B (r1_tarski(A,B) -> k2_xboole_0(A,k4_xboole_0(B,A)) = B)) # label(t45_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 160 (all A all B all C k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(A,C)) = k4_xboole_0(A,k3_xboole_0(B,C))) # label(t54_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 161 (all A all B all C k2_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(A,k2_xboole_0(B,C))) # label(t4_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 162 (all A all B all C k4_xboole_0(k3_xboole_0(A,B),k3_xboole_0(C,B)) = k3_xboole_0(k4_xboole_0(A,C),B)) # label(t111_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 163 (all A all B r1_xboole_0(k3_xboole_0(A,B),k5_xboole_0(A,B))) # label(t103_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 164 (all A all B r1_xboole_0(k4_xboole_0(A,B),k4_xboole_0(B,A))) # label(t82_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 165 (all A all B (-v1_xboole_0(B) -> -(r1_xboole_0(B,A) & r1_tarski(B,A)))) # label(t69_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 166 (all A all B -(r1_xboole_0(k3_xboole_0(A,B),B) & -r1_xboole_0(A,B))) # label(t75_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 167 (all A all B (k1_xboole_0 = k4_xboole_0(A,B) <-> r1_tarski(A,B))) # label(t37_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 168 (all A all B k4_xboole_0(A,B) = k5_xboole_0(A,k3_xboole_0(A,B))) # label(t100_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 169 (all A -r2_xboole_0(A,k1_xboole_0)) # label(t62_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 170 (all A all B all C (r1_tarski(A,B) & r2_xboole_0(B,C) -> r2_xboole_0(A,C))) # label(t59_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 171 (all A r1_tarski(k1_xboole_0,A)) # label(t2_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 172 (all A all B all C k3_xboole_0(k3_xboole_0(A,B),C) = k3_xboole_0(A,k3_xboole_0(B,C))) # label(t16_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 173 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k3_xboole_0(A,C),B))) # label(t108_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 174 (all A all B k2_xboole_0(A,k3_xboole_0(A,B)) = A) # label(t22_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 175 (all A all B all C k3_xboole_0(A,k2_xboole_0(B,C)) = k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C))) # label(t23_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.06 176 (all A all B (-(-r2_xboole_0(A,B) & B != A & -r2_xboole_0(B,A)) <-> r3_xboole_0(A,B))) # label(t104_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 177 (all A all B all C k4_xboole_0(A,k2_xboole_0(B,C)) = k3_xboole_0(k4_xboole_0(A,B),k4_xboole_0(A,C))) # label(t53_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 178 (all A all B all C (r1_xboole_0(C,B) & k2_xboole_0(A,B) = k2_xboole_0(C,B) & r1_xboole_0(A,B) -> C = A)) # label(t71_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 179 (all A all B all C k3_xboole_0(A,k4_xboole_0(B,C)) = k4_xboole_0(k3_xboole_0(A,B),C)) # label(t49_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 180 (all A all B r1_tarski(k3_xboole_0(A,B),A)) # label(t17_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 181 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k4_xboole_0(A,C),k4_xboole_0(B,C)))) # label(t33_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 182 (all A all B (r1_tarski(A,B) -> A = k3_xboole_0(A,B))) # label(t28_xboole_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 183 $T # label(t16_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 184 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(B,C,A,D)) # label(t110_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 185 (all A all B all C all D all E ((all F (-(B != F & D != F & F != A & C != F) <-> r2_hidden(F,E))) <-> E = k2_enumset1(A,B,C,D))) # label(d2_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 186 (all A all B all C all D all E k6_enumset1(A,A,A,A,B,C,D,E) = k3_enumset1(A,B,C,D,E)) # label(t86_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 187 $T # label(t30_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 188 $T # label(t19_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 189 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(A,D,C,B)) # label(t107_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 190 (all A all B all C all D all E all F all G k5_enumset1(A,B,C,D,E,F,G) = k2_xboole_0(k2_enumset1(A,B,C,D),k1_enumset1(E,F,G))) # label(t59_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 191 $T # label(t29_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 192 $T # label(t33_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 193 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(D,C,B,A)) # label(t125_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 194 (all A all B all C all D all E all F all G k2_xboole_0(k3_enumset1(A,B,C,D,E),k2_tarski(F,G)) = k5_enumset1(A,B,C,D,E,F,G)) # label(t60_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 195 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(A,C,D,B)) # label(t105_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 196 (all A all B all C all D all E all F all G all H k6_enumset1(A,B,C,D,E,F,G,H) = k2_xboole_0(k3_enumset1(A,B,C,D,E),k1_enumset1(F,G,H))) # label(t66_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 197 (all A all B all C all D (k1_enumset1(A,B,C) = D <-> (all E (-(E != B & A != E & C != E) <-> r2_hidden(E,D))))) # label(d1_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 198 $T # label(t15_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 199 (all A all B all C all D all E all F all G all H k6_enumset1(A,B,C,D,E,F,G,H) = k2_xboole_0(k1_tarski(A),k5_enumset1(B,C,D,E,F,G,H))) # label(t62_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 200 (all A all B all C k1_enumset1(A,B,C) = k1_enumset1(C,B,A)) # label(t102_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 201 $T # label(t101_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 202 (all A k5_enumset1(A,A,A,A,A,A,A) = k1_tarski(A)) # label(t94_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 203 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(A,B,D,C)) # label(t103_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 204 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(C,B,A,D)) # label(t116_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 205 $T # label(t106_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 206 $T # label(t27_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 207 $T # label(t24_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 208 (all A all B all C all D all E all F k4_enumset1(A,B,C,D,E,F) = k2_xboole_0(k1_tarski(A),k3_enumset1(B,C,D,E,F))) # label(t51_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 209 (all A all B k3_enumset1(A,A,A,A,B) = k2_tarski(A,B)) # label(t83_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 210 (all A k1_enumset1(A,A,A) = k1_tarski(A)) # label(t76_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 211 $T # label(t17_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 212 (all A all B all C all D k2_enumset1(A,C,B,D) = k2_enumset1(A,B,C,D)) # label(t104_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 213 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(C,D,B,A)) # label(t119_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 214 $T # label(t7_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 215 (all A all B all C all D all E k3_enumset1(A,B,C,D,E) = k2_xboole_0(k1_tarski(A),k2_enumset1(B,C,D,E))) # label(t47_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 216 $T # label(dt_k4_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 217 (all A all B all C all D k2_enumset1(C,D,A,B) = k2_enumset1(A,B,C,D)) # label(t118_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 218 $T # label(t3_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 219 (all A all B all C all D k2_enumset1(A,B,C,D) = k4_enumset1(A,A,A,B,C,D)) # label(t79_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 220 (all A k1_tarski(A) = k4_enumset1(A,A,A,A,A,A)) # label(t91_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 221 $T # label(t22_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 222 $T # label(t20_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 223 (all A all B all C k1_enumset1(A,B,C) = k4_enumset1(A,A,A,A,B,C)) # label(t84_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 224 $T # label(t124_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 225 (all A all B all C all D all E all F all G all H k2_xboole_0(k1_enumset1(A,B,C),k3_enumset1(D,E,F,G,H)) = k6_enumset1(A,B,C,D,E,F,G,H)) # label(t64_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 226 (all A all B all C all D all E all F k4_enumset1(A,B,C,D,E,F) = k5_enumset1(A,A,B,C,D,E,F)) # label(t74_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 227 (all A all B all C all D all E all F all G all H all I (I = k6_enumset1(A,B,C,D,E,F,G,H) <-> (all J (r2_hidden(J,I) <-> -(J != G & H != J & F != J & J != A & C != J & J != D & E != J & B != J))))) # label(d6_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 228 (all A all B all C k5_enumset1(A,A,A,A,A,B,C) = k1_enumset1(A,B,C)) # label(t89_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 229 $T # label(t11_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 230 (all A all B all C all D all E all F k2_xboole_0(k2_enumset1(A,B,C,D),k2_tarski(E,F)) = k4_enumset1(A,B,C,D,E,F)) # label(t54_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 231 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_xboole_0(k2_tarski(A,B),k2_tarski(C,D))) # label(t45_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 232 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(C,B,D,A)) # label(t117_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 233 (all A all B all C all D all E all F k2_xboole_0(k3_enumset1(A,B,C,D,E),k1_tarski(F)) = k4_enumset1(A,B,C,D,E,F)) # label(t55_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 234 (all A all B all C k1_enumset1(B,A,C) = k1_enumset1(A,B,C)) # label(t99_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 235 (all A all B all C all D all E k3_enumset1(A,B,C,D,E) = k2_xboole_0(k2_tarski(A,B),k1_enumset1(C,D,E))) # label(t48_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 236 $T # label(t37_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 237 $T # label(t25_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 238 (all A all B all C all D all E all F (k3_enumset1(A,B,C,D,E) = F <-> (all G (-(G != D & G != A & G != C & G != E & B != G) <-> r2_hidden(G,F))))) # label(d3_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 239 (all A all B all C all D all E k2_xboole_0(k1_enumset1(A,B,C),k2_tarski(D,E)) = k3_enumset1(A,B,C,D,E)) # label(t49_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 240 (all A all B all C all D all E all F all G k2_xboole_0(k1_enumset1(A,B,C),k2_enumset1(D,E,F,G)) = k5_enumset1(A,B,C,D,E,F,G)) # label(t58_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 241 $T # label(dt_k5_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 242 (all A all B k2_tarski(A,B) = k4_enumset1(A,A,A,A,A,B)) # label(t88_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 243 (all A all B k2_xboole_0(k1_tarski(A),k1_tarski(B)) = k2_tarski(A,B)) # label(t41_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 244 (all A all B all C all D all E all F all G all H k2_xboole_0(k2_enumset1(A,B,C,D),k2_enumset1(E,F,G,H)) = k6_enumset1(A,B,C,D,E,F,G,H)) # label(t65_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 245 $T # label(t6_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 246 (all A all B all C all D all E all F all G all H (H = k5_enumset1(A,B,C,D,E,F,G) <-> (all I (r2_hidden(I,H) <-> -(A != I & I != B & C != I & I != D & F != I & I != G & I != E))))) # label(d5_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 247 (all A all B all C all D all E all F all G (G = k4_enumset1(A,B,C,D,E,F) <-> (all H (-(H != A & H != F & H != B & H != C & D != H & E != H) <-> r2_hidden(H,G))))) # label(d4_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 248 (all A all B all C all D all E all F all G all H k2_xboole_0(k2_tarski(A,B),k4_enumset1(C,D,E,F,G,H)) = k6_enumset1(A,B,C,D,E,F,G,H)) # label(t63_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 249 $T # label(t18_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 250 $T # label(dt_k6_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 251 (all A k2_enumset1(A,A,A,A) = k1_tarski(A)) # label(t82_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 252 $T # label(t28_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 253 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(B,D,A,C)) # label(t112_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 254 (all A k6_enumset1(A,A,A,A,A,A,A,A) = k1_tarski(A)) # label(t96_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 255 (all A all B all C all D k2_enumset1(B,A,D,C) = k2_enumset1(A,B,C,D)) # label(t109_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 256 $T # label(t31_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 257 (all A k3_enumset1(A,A,A,A,A) = k1_tarski(A)) # label(t87_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 258 $T # label(t8_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 259 $T # label(t115_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 260 (all A all B all C all D k2_enumset1(B,D,C,A) = k2_enumset1(A,B,C,D)) # label(t113_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 261 (all A k1_tarski(A) = k2_tarski(A,A)) # label(t69_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 262 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(B,A,C,D)) # label(t108_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 263 (all A all B all C all D all E all F k4_enumset1(A,B,C,D,E,F) = k2_xboole_0(k2_tarski(A,B),k2_enumset1(C,D,E,F))) # label(t52_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 264 $T # label(t5_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 265 $T # label(t26_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 266 $T # label(t38_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 267 $T # label(t120_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 268 $T # label(dt_k2_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 269 (all A all B k1_enumset1(A,A,B) = k2_tarski(A,B)) # label(t70_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 270 $T # label(t1_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 271 $T # label(t10_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 272 $T # label(t34_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 273 (all A all B all C k1_enumset1(A,B,C) = k2_enumset1(A,A,B,C)) # label(t71_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 274 $T # label(t35_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 275 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_xboole_0(k1_enumset1(A,B,C),k1_tarski(D))) # label(t46_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 276 $T # label(t40_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 277 (all A all B all C k1_enumset1(A,B,C) = k1_enumset1(B,C,A)) # label(t100_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 278 (all A all B all C k2_xboole_0(k2_tarski(A,B),k1_tarski(C)) = k1_enumset1(A,B,C)) # label(t43_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 279 $T # label(t21_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 280 $T # label(t121_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 281 (all A all B k2_enumset1(A,A,A,B) = k2_tarski(A,B)) # label(t77_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 282 $T # label(t9_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 283 $T # label(dt_k1_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 284 (all A all B all C all D all E all F all G all H k6_enumset1(A,B,C,D,E,F,G,H) = k2_xboole_0(k4_enumset1(A,B,C,D,E,F),k2_tarski(G,H))) # label(t67_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 285 $T # label(t32_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 286 $T # label(t36_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 287 $T # label(t122_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 288 (all A all B all C all D all E all F k6_enumset1(A,A,A,B,C,D,E,F) = k4_enumset1(A,B,C,D,E,F)) # label(t81_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 289 $T # label(dt_k3_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 290 (all A all B all C all D k6_enumset1(A,A,A,A,A,B,C,D) = k2_enumset1(A,B,C,D)) # label(t90_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 291 (all A all B all C k6_enumset1(A,A,A,A,A,A,B,C) = k1_enumset1(A,B,C)) # label(t93_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 292 (all A all B all C all D k2_enumset1(B,C,D,A) = k2_enumset1(A,B,C,D)) # label(t111_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 293 (all A all B k6_enumset1(A,A,A,A,A,A,A,B) = k2_tarski(A,B)) # label(t95_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 294 $T # label(t12_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 295 (all A all B all C all D k2_enumset1(A,B,C,D) = k3_enumset1(A,A,B,C,D)) # label(t72_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 296 $T # label(t23_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 297 $T # label(t14_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 298 $T # label(t4_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 299 (all A all B all C all D all E k3_enumset1(A,B,C,D,E) = k5_enumset1(A,A,A,B,C,D,E)) # label(t80_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 300 $T # label(t2_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 301 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(D,B,C,A)) # label(t123_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 302 (all A all B all C k1_enumset1(A,B,C) = k2_xboole_0(k1_tarski(A),k2_tarski(B,C))) # label(t42_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 303 (all A all B all C all D all E all F all G k5_enumset1(A,B,C,D,E,F,G) = k2_xboole_0(k1_tarski(A),k4_enumset1(B,C,D,E,F,G))) # label(t56_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 304 (all A all B all C all D all E all F all G k2_xboole_0(k4_enumset1(A,B,C,D,E,F),k1_tarski(G)) = k5_enumset1(A,B,C,D,E,F,G)) # label(t61_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 305 (all A all B all C all D all E all F all G k5_enumset1(A,B,C,D,E,F,G) = k6_enumset1(A,A,B,C,D,E,F,G)) # label(t75_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 306 (all A all B k2_tarski(A,B) = k5_enumset1(A,A,A,A,A,A,B)) # label(t92_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 307 (all A all B all C k1_enumset1(A,B,C) = k3_enumset1(A,A,A,B,C)) # label(t78_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 308 $T # label(t39_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 309 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_xboole_0(k1_tarski(A),k1_enumset1(B,C,D))) # label(t44_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 310 (all A all B all C all D all E all F k4_enumset1(A,B,C,D,E,F) = k2_xboole_0(k1_enumset1(A,B,C),k1_enumset1(D,E,F))) # label(t53_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 311 (all A all B all C k1_enumset1(A,B,C) = k1_enumset1(A,C,B)) # label(t98_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 312 $T # label(t114_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 313 (all A all B all C all D all E k4_enumset1(A,A,B,C,D,E) = k3_enumset1(A,B,C,D,E)) # label(t73_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 314 (all A all B all C all D all E all F all G k5_enumset1(A,B,C,D,E,F,G) = k2_xboole_0(k2_tarski(A,B),k3_enumset1(C,D,E,F,G))) # label(t57_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 315 (all A all B all C all D k2_enumset1(A,B,C,D) = k5_enumset1(A,A,A,A,B,C,D)) # label(t85_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 316 $T # label(t97_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 317 (all A all B all C all D all E all F all G all H k2_xboole_0(k5_enumset1(A,B,C,D,E,F,G),k1_tarski(H)) = k6_enumset1(A,B,C,D,E,F,G,H)) # label(t68_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 318 (all A all B all C all D all E k3_enumset1(A,B,C,D,E) = k2_xboole_0(k2_enumset1(A,B,C,D),k1_tarski(E))) # label(t50_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 319 $T # label(t13_enumset1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 320 (all A all B -(k1_xboole_0 != A & k1_tarski(B) != A & k4_xboole_0(A,k1_tarski(B)) = k1_xboole_0)) # label(t66_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 321 $T # label(t85_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 322 (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]. 56.07/55.07 323 (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]. 56.07/55.07 324 $T # label(t76_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 325 (all A all B all C -(-(k1_tarski(A) = C & B = k1_xboole_0) & -(B = k1_tarski(A) & k1_xboole_0 = C) & -(B = k1_tarski(A) & C = k1_tarski(A)) & k2_xboole_0(B,C) = k1_tarski(A))) # label(t43_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 326 (all A all B (k4_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_xboole_0 -> A = B)) # label(t21_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 327 (all A all B all C (r1_tarski(k2_tarski(A,B),C) <-> r2_hidden(B,C) & r2_hidden(A,C))) # label(t38_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 328 (all A all B all C -(-r1_xboole_0(k2_tarski(A,C),B) & -r2_hidden(A,B) & -r2_hidden(C,B))) # label(t57_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 329 (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]. 56.07/55.07 330 (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]. 56.07/55.07 331 (all A all B all C all D (r1_xboole_0(A,B) | r1_xboole_0(C,D) -> r1_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)))) # label(t127_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 332 (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]. 56.07/55.07 333 (all A all B all C (k2_zfmisc_1(k4_xboole_0(A,B),C) = k4_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)) & k4_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) = k2_zfmisc_1(C,k4_xboole_0(A,B)))) # label(t125_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 334 (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]. 56.07/55.07 335 $T # label(dt_k3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 336 (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]. 56.07/55.07 337 $T # label(t62_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 338 (all A all B all C (r1_tarski(k2_tarski(A,B),k1_tarski(C)) -> k1_tarski(C) = k2_tarski(A,B))) # label(t27_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 339 $T # label(t4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 340 (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]. 56.07/55.07 341 (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]. 56.07/55.07 342 (all A all B (k2_zfmisc_1(A,A) = k2_zfmisc_1(B,B) -> A = B)) # label(t115_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 343 $T # label(t71_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 344 (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]. 56.07/55.07 345 $T # label(t3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 346 (all A all B all C all D all E all F (r1_tarski(A,k2_zfmisc_1(B,C)) & (all G all H (r2_hidden(k4_tarski(G,H),D) <-> r2_hidden(k4_tarski(G,H),A))) & r1_tarski(D,k2_zfmisc_1(E,F)) -> D = A)) # label(t110_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 347 (all A all B (B != A -> r1_xboole_0(k1_tarski(A),k1_tarski(B)))) # label(t17_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 348 (all A all B all C all D (r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) -> k2_zfmisc_1(A,B) = k1_xboole_0 | r1_tarski(A,C) & r1_tarski(B,D))) # label(t138_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 349 (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]. 56.07/55.07 350 (all A all B k2_tarski(A,B) = k3_tarski(k2_tarski(k1_tarski(A),k1_tarski(B)))) # label(t32_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 351 (all A all B (r2_hidden(A,B) -> r1_tarski(A,k3_tarski(B)))) # label(t92_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 352 $T # label(t7_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 353 $T # label(t61_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.07 354 (all A all B all C (k2_zfmisc_1(C,k3_xboole_0(A,B)) = k3_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) & k3_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)) = k2_zfmisc_1(k3_xboole_0(A,B),C))) # label(t122_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 355 (all A A = k3_tarski(k1_tarski(A))) # label(t31_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 356 (all A (r1_tarski(A,k2_zfmisc_1(A,A)) -> k1_xboole_0 = A)) # label(t116_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 357 (all A all B (k3_xboole_0(A,k1_tarski(B)) = k1_tarski(B) -> r2_hidden(B,A))) # label(t51_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 358 (all A all B all C all D (k4_tarski(C,D) = k4_tarski(A,B) -> A = C & B = D)) # label(t33_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 359 (all A all B k3_tarski(k2_tarski(A,B)) = k2_xboole_0(A,B)) # label(t93_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 360 (all A exists B ((all C all D (r2_hidden(C,B) & r1_tarski(D,C) -> r2_hidden(D,B))) & (all C -(-r2_tarski(C,B) & r1_tarski(C,B) & -r2_hidden(C,B))) & (all C (r2_hidden(C,B) -> r2_hidden(k1_zfmisc_1(C),B))) & r2_hidden(A,B))) # label(t136_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 361 (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]. 56.07/55.08 362 (all A all B all C (k1_xboole_0 = k4_xboole_0(k2_tarski(A,B),C) <-> r2_hidden(B,C) & r2_hidden(A,C))) # label(t73_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 363 (all A all B all C all D (r1_tarski(A,B) & r1_tarski(C,D) -> k3_xboole_0(k2_zfmisc_1(A,D),k2_zfmisc_1(B,C)) = k2_zfmisc_1(A,C))) # label(t124_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 364 (all A all B all C all D -(A != D & A != C & k2_tarski(A,B) = k2_tarski(C,D))) # label(t10_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 365 (all A A = k3_tarski(k1_zfmisc_1(A))) # label(t99_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 366 (all A all B (k1_xboole_0 = k4_xboole_0(k1_tarski(A),B) <-> r2_hidden(A,B))) # label(t68_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 367 (all A all B k2_xboole_0(k3_tarski(A),k3_tarski(B)) = k3_tarski(k2_xboole_0(A,B))) # label(t96_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 368 (all A all B all C (r1_tarski(k2_tarski(A,B),k1_tarski(C)) -> A = C)) # label(t26_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 369 (all A all B all C (r1_tarski(A,k2_tarski(B,C)) <-> -(k1_tarski(C) != A & A != k1_tarski(B) & A != k1_xboole_0 & k2_tarski(B,C) != A))) # label(t42_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 370 (all A all B (-r2_hidden(A,B) -> k4_xboole_0(k2_xboole_0(B,k1_tarski(A)),k1_tarski(A)) = B)) # label(t141_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 371 (all A all B (A != B -> k5_xboole_0(k1_tarski(A),k1_tarski(B)) = k2_tarski(A,B))) # label(t29_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 372 (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]. 56.07/55.08 373 (all A all B all C all D -(A != C & A != D & r1_tarski(k2_tarski(A,B),k2_tarski(C,D)))) # label(t28_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 374 (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]. 56.07/55.08 375 (all A all B all C (k1_tarski(A) = k2_tarski(B,C) -> A = B)) # label(t8_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 376 (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]. 56.07/55.08 377 (all A all B all C all D -(r2_hidden(D,A) & (all E all F -(r2_hidden(E,B) & r2_hidden(F,C) & k4_tarski(E,F) = D)) & r1_tarski(A,k2_zfmisc_1(B,C)))) # label(t103_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 378 (all A all B (k1_xboole_0 = A | k1_xboole_0 = B <-> k2_zfmisc_1(A,B) = k1_xboole_0)) # label(t113_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 379 (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]. 56.07/55.08 380 (all A all B (r1_tarski(k1_tarski(A),k1_tarski(B)) -> B = A)) # label(t6_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 381 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 382 (all A all B all C k2_zfmisc_1(k2_zfmisc_1(A,B),C) = k3_zfmisc_1(A,B,C)) # label(d3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 383 $T # label(t5_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 384 (all A all B all C all D (r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D)) <-> r2_hidden(B,D) & r2_hidden(A,C))) # label(t106_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 385 (all A all B ((all C all D (r2_hidden(k4_tarski(C,D),A) -> r2_hidden(k4_tarski(C,D),B))) & (all C -((all D all E C != k4_tarski(D,E)) & r2_hidden(C,A))) -> r1_tarski(A,B))) # label(t111_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 386 (all A all B all C (r2_hidden(A,B) -> k3_xboole_0(k2_tarski(A,C),B) = k1_tarski(A) | C != A & r2_hidden(C,B))) # label(t60_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 387 (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]. 56.07/55.08 388 (all A all B ((all C all D (r2_hidden(D,k2_xboole_0(A,B)) & r2_hidden(C,k2_xboole_0(A,B)) -> r1_xboole_0(C,D) | C = D)) -> k3_tarski(k3_xboole_0(A,B)) = k3_xboole_0(k3_tarski(A),k3_tarski(B)))) # label(t101_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 389 (all A all B all C (-r2_hidden(A,C) & -r2_hidden(B,C) <-> k2_tarski(A,B) = k4_xboole_0(k2_tarski(A,B),C))) # label(t72_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 390 $T # label(dt_k4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 391 (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]. 56.07/55.08 392 (all A all B -(A = B & r1_xboole_0(k1_tarski(A),k1_tarski(B)))) # label(t16_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 393 $T # label(t91_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 394 (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]. 56.07/55.08 395 (all A all B all C (-(A != k2_tarski(B,C) & A != k1_tarski(C) & k1_tarski(B) != A & A != k1_xboole_0) <-> k4_xboole_0(A,k2_tarski(B,C)) = k1_xboole_0)) # label(t75_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 396 (all A all B (r1_tarski(k1_tarski(A),k1_tarski(B)) -> B = A)) # label(t24_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 397 (all A all B (k1_tarski(A) = k2_xboole_0(k1_tarski(A),k1_tarski(B)) -> A = B)) # label(t13_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 398 $T # label(t15_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 399 (all A all B all C all D all E -(r2_hidden(A,k3_xboole_0(k2_zfmisc_1(B,C),k2_zfmisc_1(D,E))) & (all F all G -(r2_hidden(F,k3_xboole_0(B,D)) & r2_hidden(G,k3_xboole_0(C,E)) & A = k4_tarski(F,G))))) # label(t104_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 400 $T # label(t133_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 401 (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]. 56.07/55.08 402 (all A all B all C all D (B = D & r2_hidden(A,C) <-> r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,k1_tarski(D))))) # label(t129_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 403 $T # label(t89_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 404 (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]. 56.07/55.08 405 (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]. 56.07/55.08 406 $T # label(t78_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 407 (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]. 56.07/55.08 408 (all A all B all C (k2_tarski(k4_tarski(A,B),k4_tarski(A,C)) = k2_zfmisc_1(k1_tarski(A),k2_tarski(B,C)) & k2_zfmisc_1(k2_tarski(A,B),k1_tarski(C)) = k2_tarski(k4_tarski(A,C),k4_tarski(B,C)))) # label(t36_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 409 (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]. 56.07/55.08 410 (all A all B -(k1_tarski(B) != A & (all C -(r2_hidden(C,A) & C != B)) & k1_xboole_0 != A)) # label(t41_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 411 (all A all B (B != A -> k4_xboole_0(k2_tarski(A,B),k1_tarski(B)) = k1_tarski(A))) # label(t23_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 412 (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]. 56.07/55.08 413 $T # label(t87_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 414 (all A all B (k1_zfmisc_1(A) = B <-> (all C (r2_hidden(C,B) <-> r1_tarski(C,A))))) # label(d1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 415 (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]. 56.07/55.08 416 (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]. 56.07/55.08 417 (all A all B (k2_zfmisc_1(B,A) = k2_zfmisc_1(A,B) -> B = A | B = k1_xboole_0 | A = k1_xboole_0)) # label(t114_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 418 (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]. 56.07/55.08 419 (all A all B -v1_xboole_0(k4_tarski(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 420 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 421 (all A all B all C all D k4_zfmisc_1(A,B,C,D) = k2_zfmisc_1(k3_zfmisc_1(A,B,C),D)) # label(d4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 422 (all A all B all C all D (r2_hidden(k4_tarski(A,B),k2_zfmisc_1(k1_tarski(C),D)) <-> r2_hidden(B,D) & C = A)) # label(t128_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 423 (all A all B (k1_xboole_0 != A -> k2_zfmisc_1(k1_tarski(B),A) != k1_xboole_0 & k2_zfmisc_1(A,k1_tarski(B)) != k1_xboole_0)) # label(t130_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 424 (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]. 56.07/55.08 425 (all A all B all C -(A != B & r1_tarski(k1_tarski(A),k2_tarski(B,C)) & A != C)) # label(t25_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 426 (all A all B all C (r2_hidden(A,B) & r2_hidden(C,B) -> k3_xboole_0(k2_tarski(A,C),B) = k2_tarski(A,C))) # label(t53_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 427 (all A all B r1_tarski(k1_tarski(A),k2_tarski(A,B))) # label(t12_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 428 (all A all B all C all D (r2_hidden(k4_tarski(A,B),k2_zfmisc_1(k1_tarski(C),k1_tarski(D))) <-> D = B & A = C)) # label(t34_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 429 $T # label(t88_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 430 (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]. 56.07/55.08 431 (all A all B all C -((r1_tarski(k2_zfmisc_1(B,A),k2_zfmisc_1(C,A)) | r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(A,C))) & A != k1_xboole_0 & -r1_tarski(B,C))) # label(t117_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 432 $T # label(t90_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 433 (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]. 56.07/55.08 434 (all A all B all C -(k4_xboole_0(k2_tarski(A,B),C) != k1_tarski(A) & k1_tarski(B) != k4_xboole_0(k2_tarski(A,B),C) & k4_xboole_0(k2_tarski(A,B),C) != k1_xboole_0 & k4_xboole_0(k2_tarski(A,B),C) != k2_tarski(A,B))) # label(t74_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 435 (all A all B all C (k2_xboole_0(k2_zfmisc_1(C,k1_tarski(A)),k2_zfmisc_1(C,k1_tarski(B))) = k2_zfmisc_1(C,k2_tarski(A,B)) & k2_xboole_0(k2_zfmisc_1(k1_tarski(A),C),k2_zfmisc_1(k1_tarski(B),C)) = k2_zfmisc_1(k2_tarski(A,B),C))) # label(t132_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 436 (all A all B all C -((all D all E k4_tarski(D,E) != A) & r2_hidden(A,k2_zfmisc_1(B,C)))) # label(t102_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 437 (all A all B all C -(r1_xboole_0(k2_tarski(A,B),C) & r2_hidden(A,C))) # label(t55_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 438 (all A all B (r1_tarski(A,k1_tarski(B)) <-> A = k1_tarski(B) | k1_xboole_0 = A)) # label(t39_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 439 (all A all B (r1_xboole_0(k1_tarski(A),B) | k1_tarski(A) = k3_xboole_0(k1_tarski(A),B))) # label(t58_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 440 (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]. 56.07/55.08 441 (all A r1_tarski(A,k1_zfmisc_1(k3_tarski(A)))) # label(t100_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 442 (all A all B -(r1_xboole_0(k1_tarski(A),B) & r2_hidden(A,B))) # label(t54_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 443 (all A all B (r2_hidden(A,B) <-> r1_tarski(k1_tarski(A),B))) # label(t37_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 444 (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]. 56.07/55.08 445 (all A all B k2_zfmisc_1(k1_tarski(A),k1_tarski(B)) = k1_tarski(k4_tarski(A,B))) # label(t35_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 446 (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]. 56.07/55.08 447 (all A all B all C (k1_tarski(A) = k2_tarski(B,C) -> B = C)) # label(t9_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 448 (all A all B (r2_hidden(A,B) -> k2_xboole_0(k4_xboole_0(B,k1_tarski(A)),k1_tarski(A)) = B)) # label(t140_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 449 (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]. 56.07/55.08 450 (all A all B all C ((all D (r2_hidden(D,C) <-> (exists E exists F (r2_hidden(E,A) & k4_tarski(E,F) = D & r2_hidden(F,B))))) <-> C = k2_zfmisc_1(A,B))) # label(d2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 451 (all A all B (k4_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_tarski(A) <-> A != B)) # label(t20_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 452 (all A r1_tarski(k1_tarski(A),k1_zfmisc_1(A))) # label(t80_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 453 (all A all B (k1_tarski(A) = k3_xboole_0(k1_tarski(A),k1_tarski(B)) -> A = B)) # label(t18_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 454 (all A all B k1_tarski(A) = k3_xboole_0(k1_tarski(A),k2_tarski(A,B))) # label(t19_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 455 (all A all B all C all D k3_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) = k2_zfmisc_1(k3_xboole_0(A,B),k3_xboole_0(C,D))) # label(t123_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 456 (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]. 56.07/55.08 457 (all A all B all C -(k1_tarski(A) = k2_xboole_0(B,C) & B != C & k1_xboole_0 != B & C != k1_xboole_0)) # label(t44_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 458 (all A all B k1_zfmisc_1(k3_xboole_0(A,B)) = k3_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B))) # label(t83_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 459 (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]. 56.07/55.08 460 (all A all B all C -(r2_hidden(B,C) & k3_xboole_0(k2_tarski(A,B),C) = k1_tarski(A) & A != B)) # label(t59_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 461 (all A (-v1_xboole_0(A) -> (all B all C all D (r1_tarski(k2_zfmisc_1(B,A),k2_zfmisc_1(D,C)) | r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) -> r1_tarski(B,D))))) # label(t139_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 462 (all A all B ((all C all D (r2_hidden(k4_tarski(C,D),A) <-> r2_hidden(k4_tarski(C,D),B))) & (all C -(r2_hidden(C,A) & (all D all E k4_tarski(D,E) != C))) & (all C -(r2_hidden(C,B) & (all D all E C != k4_tarski(D,E)))) -> A = B)) # label(t112_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 463 (all A all B k1_xboole_0 != k2_xboole_0(k1_tarski(A),B)) # label(t49_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 464 $T # label(t11_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 465 (all A all B all C all D (k2_zfmisc_1(A,B) = k2_zfmisc_1(C,D) -> B = D & C = A | k1_xboole_0 = B | k1_xboole_0 = A)) # label(t134_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 466 (all A all B (k4_xboole_0(A,k1_tarski(B)) = A <-> -r2_hidden(B,A))) # label(t65_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 467 $T # label(t77_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 468 $T # label(t19_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 469 (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]. 56.07/55.08 470 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> (-r2_hidden(D,B) <-> r2_hidden(D,C)))) -> B = k3_subset_1(A,C)))))) # label(t52_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 471 (all A (k1_xboole_0 != A -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,A) -> (-r2_hidden(C,B) -> r2_hidden(C,k3_subset_1(A,B))))))))) # label(t50_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 472 (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]. 56.07/55.08 473 (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]. 56.07/55.08 474 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k3_subset_1(A,k6_subset_1(A,B,C)) = k4_subset_1(A,k3_subset_1(A,B),C))))) # label(t33_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 475 $T # label(t5_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 476 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> m1_subset_1(k4_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 477 (all A all B all C all D (-v1_xboole_0(C) & -v1_xboole_0(D) & -v1_xboole_0(B) & -v1_xboole_0(A) -> -v1_xboole_0(k4_zfmisc_1(A,B,C,D)))) # label(fc6_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 478 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(A) & -v1_xboole_0(B) -> (all C (m1_subset_1(C,B) <-> m2_subset_1(C,A,B))))) # label(redefinition_m2_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 479 (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]. 56.07/55.08 480 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,B) <-> -r2_hidden(E,D) & r2_hidden(E,C)))) -> k6_subset_1(A,C,D) = B))))))) # label(t17_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 481 (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]. 56.07/55.08 482 $T # label(t1_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 483 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> m1_subset_1(k5_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 484 (all A k3_subset_1(A,k1_subset_1(A)) = k2_subset_1(A)) # label(t22_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 485 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,A) -> (k1_xboole_0 != A -> m1_subset_1(k4_enumset1(B,C,D,E,F,G),k1_zfmisc_1(A))))))))))))))) # label(t60_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 486 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k6_subset_1(A,B,C) = k4_xboole_0(B,C))) # label(redefinition_k6_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 487 (all A exists B (m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 488 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k6_subset_1(A,B,C) = k5_subset_1(A,B,k3_subset_1(A,C)))))) # label(t32_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 489 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> (r1_subset_1(A,B) -> r1_subset_1(B,A)))) # label(symmetry_r1_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 490 (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]. 56.07/55.08 491 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> -v1_xboole_0(k2_zfmisc_1(A,B)))) # label(fc4_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 492 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 493 (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]. 56.07/55.08 494 $T # label(t23_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 495 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k3_subset_1(A,k7_subset_1(A,B,C)) = k4_subset_1(A,k5_subset_1(A,B,C),k5_subset_1(A,k3_subset_1(A,B),k3_subset_1(A,C))))))) # label(t34_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.08 496 (all A all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(A) -> (exists C m2_subset_1(C,A,B)))) # label(existence_m2_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 497 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,B) <-> r2_hidden(E,D) & r2_hidden(E,C)))) -> B = k5_subset_1(A,C,D)))))))) # label(t16_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 498 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (r1_tarski(k3_subset_1(A,B),B) <-> k2_subset_1(A) = B))) # label(t39_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 499 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> -r2_subset_1(A,A))) # label(irreflexivity_r2_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 500 $T # label(t27_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 501 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> k2_xboole_0(B,C) = k4_subset_1(A,B,C))) # label(redefinition_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 502 (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]. 56.07/55.09 503 (all A A = k2_subset_1(A)) # label(d4_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 504 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,B) <-> -(r2_hidden(E,C) <-> r2_hidden(E,D))))) -> B = k7_subset_1(A,C,D)))))))) # label(t18_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 505 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,A) -> (all I (m1_subset_1(I,A) -> (k1_xboole_0 != A -> m1_subset_1(k6_enumset1(B,C,D,E,F,G,H,I),k1_zfmisc_1(A))))))))))))))))))) # label(t62_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 506 (all A all B ((-v1_xboole_0(A) -> (r2_hidden(B,A) <-> m1_subset_1(B,A))) & (v1_xboole_0(A) -> (m1_subset_1(B,A) <-> v1_xboole_0(B))))) # label(d2_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 507 $T # label(t11_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 508 $T # label(d1_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 509 $T # label(t45_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 510 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,A) -> (A != k1_xboole_0 -> m1_subset_1(k5_enumset1(B,C,D,E,F,G,H),k1_zfmisc_1(A))))))))))))))))) # label(t61_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 511 (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]. 56.07/55.09 512 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k4_subset_1(A,C,B) = k4_subset_1(A,B,C))) # label(commutativity_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 513 (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]. 56.07/55.09 514 (all A (m1_subset_1(A,k1_zfmisc_1(f1_s2_subset_1)) -> (all B (m1_subset_1(B,k1_zfmisc_1(f1_s2_subset_1)) -> ((all C (m1_subset_1(C,f1_s2_subset_1) -> (p1_s2_subset_1(C) <-> r2_hidden(C,B)))) & (all C (m1_subset_1(C,f1_s2_subset_1) -> (p1_s2_subset_1(C) <-> r2_hidden(C,A)))) -> B = A))))) # label(s2_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 515 (all A -v1_xboole_0(k1_tarski(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 516 $T # label(t12_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 517 (all A k1_subset_1(A) = k3_subset_1(A,k2_subset_1(A))) # label(t21_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 518 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> k4_subset_1(A,B,B) = B)) # label(idempotence_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 519 (all A k1_subset_1(A) = k1_xboole_0) # label(d3_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 520 (all A m1_subset_1(k2_subset_1(A),k1_zfmisc_1(A))) # label(dt_k2_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 521 (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]. 56.07/55.09 522 $T # label(t2_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 523 (all A (-$T -> (all B (m1_subset_1(B,A) -> B = k8_subset_1(A))))) # label(d6_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 524 (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]. 56.07/55.09 525 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> -((all C (m1_subset_1(C,A) -> -r2_hidden(C,B))) & B != k1_xboole_0))) # label(t10_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 526 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (A != k1_xboole_0 -> m1_subset_1(k2_enumset1(B,C,D,E),k1_zfmisc_1(A))))))))))) # label(t58_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 527 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> ((all C (m1_subset_1(C,A) -> r2_hidden(C,B))) -> A = B))) # label(t49_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 528 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_xboole_0(k3_subset_1(A,B),k3_subset_1(A,C)) & r1_xboole_0(B,C) -> B = k3_subset_1(A,C)))))) # label(t46_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 529 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> m1_subset_1(k7_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k7_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 530 (all A all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(A) -> (all C (m2_subset_1(C,A,B) -> m1_subset_1(C,A))))) # label(dt_m2_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 531 $T # label(t37_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 532 (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]. 56.07/55.09 533 $T # label(t13_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 534 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(B,k3_subset_1(A,C)) & r1_tarski(B,C) -> k1_xboole_0 = B))) # label(t40_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 535 (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]. 56.07/55.09 536 (all A m1_subset_1(k8_subset_1(A),A)) # label(dt_k8_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 537 (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]. 56.07/55.09 538 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k7_subset_1(A,B,C) = k7_subset_1(A,C,B))) # label(commutativity_k7_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 539 (all A all B all C (-v1_xboole_0(A) & -v1_xboole_0(C) & -v1_xboole_0(B) -> -v1_xboole_0(k3_zfmisc_1(A,B,C)))) # label(fc5_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 540 (all A exists B m1_subset_1(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 541 $T # label(t20_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 542 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (k1_xboole_0 != A -> m1_subset_1(k3_enumset1(B,C,D,E,F),k1_zfmisc_1(A))))))))))))) # label(t59_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 543 (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]. 56.07/55.09 544 $T # label(t6_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 545 (all A m1_subset_1(k1_xboole_0,k1_zfmisc_1(A))) # label(t4_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 546 (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]. 56.07/55.09 547 (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]. 56.07/55.09 548 (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]. 56.07/55.09 549 (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]. 56.07/55.09 550 (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]. 56.07/55.09 551 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k4_subset_1(A,B,k3_subset_1(A,B)) = k2_subset_1(A))) # label(t25_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 552 (all A all B -v1_xboole_0(k2_tarski(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 553 (exists A ((all B (p1_s1_subset_1(B) & r2_hidden(B,f1_s1_subset_1) <-> r2_hidden(B,A))) & m1_subset_1(A,k1_zfmisc_1(f1_s1_subset_1)))) # label(s1_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 554 $T # label(t24_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 555 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> (r2_subset_1(A,B) <-> r1_xboole_0(A,B)))) # label(redefinition_r2_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 556 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,D) | r2_hidden(E,C) <-> r2_hidden(E,B)))) -> B = k4_subset_1(A,C,D)))))))) # label(t15_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 557 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k4_xboole_0(A,B) = k3_subset_1(A,B))) # label(d5_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 558 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> -(r2_hidden(D,B) <-> r2_hidden(D,C)))) -> B = k3_subset_1(A,C)))))) # label(t53_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 559 (all A all B (m1_subset_1(B,A) -> (k1_xboole_0 != A -> m1_subset_1(k1_tarski(B),k1_zfmisc_1(A))))) # label(t55_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 560 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k5_subset_1(A,k3_subset_1(A,B),k3_subset_1(A,C)) = k3_subset_1(A,k4_subset_1(A,B,C)))))) # label(t29_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 561 (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]. 56.07/55.09 562 (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]. 56.07/55.09 563 $T # label(t14_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 564 (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]. 56.07/55.09 565 (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]. 56.07/55.09 566 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k3_xboole_0(B,C) = k5_subset_1(A,B,C))) # label(redefinition_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 567 $T # label(t9_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 568 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k5_subset_1(A,B,B) = B)) # label(idempotence_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 569 (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]. 56.07/55.09 570 (all A -v1_xboole_0(k1_zfmisc_1(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 571 (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]. 56.07/55.09 572 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(B,k3_subset_1(A,C)) <-> r1_xboole_0(B,C)))))) # label(t43_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 573 $T # label(t3_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 574 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (B = k1_subset_1(A) <-> r1_tarski(B,k3_subset_1(A,B))))) # label(t38_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 575 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k5_subset_1(A,B,C) = k5_subset_1(A,C,B))) # label(commutativity_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 576 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> (r2_hidden(D,C) <-> r2_hidden(D,B)))) -> B = C))))) # label(t8_subset_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 577 (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]. 56.07/55.09 578 (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]. 56.07/55.09 579 (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]. 56.07/55.09 580 $T # label(t1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 581 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> k5_setfam_1(A,B) = k3_tarski(B))) # label(redefinition_k5_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 582 (all A all B ((all C (r2_hidden(C,A) -> r1_tarski(B,C))) -> A = k1_xboole_0 | r1_tarski(B,k1_setfam_1(A)))) # label(t6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 583 $T # label(t14_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 584 (all A all B (k1_xboole_0 != B -> k4_xboole_0(A,k3_tarski(B)) = k1_setfam_1(k4_setfam_1(k1_tarski(A),B)))) # label(t37_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 585 (all A all B all C (r1_setfam_1(B,C) & r1_setfam_1(A,B) -> r1_setfam_1(A,C))) # label(t23_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 586 (all A (r1_setfam_1(A,k1_xboole_0) -> A = k1_xboole_0)) # label(t21_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 587 $T # label(t16_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 588 (all A r1_setfam_1(k4_setfam_1(A,A),A)) # label(t31_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 589 (all A all B (k1_xboole_0 != B -> 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]. 56.07/55.09 590 $T # label(t42_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 591 (all A (-v2_setfam_1(A) -> -v1_xboole_0(A))) # label(cc2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 592 (all A all B (r1_setfam_1(A,B) <-> (all C -((all D -(r2_hidden(D,B) & r1_tarski(C,D))) & r2_hidden(C,A))))) # label(d2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 593 (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]. 56.07/55.09 594 (exists A (-v1_xboole_0(A) & v1_setfam_1(A))) # label(rc1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 595 $T # label(t32_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 596 $T # label(t45_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 597 $T # label(t33_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 598 (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]. 56.07/55.09 599 (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]. 56.07/55.09 600 $T # label(dt_k1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 601 $T # label(t22_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 602 (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]. 56.07/55.09 603 (all A all B r1_setfam_1(A,A)) # label(reflexivity_r1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 604 $T # label(dt_k3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 605 (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) -> C = B))))) # label(t53_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 606 (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]. 56.07/55.09 607 $T # label(t28_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 608 (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]. 56.07/55.09 609 $T # label(dt_k2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 610 (all A all B all C ((all D (r2_hidden(D,B) -> r1_xboole_0(D,C))) & r1_tarski(C,k3_tarski(k2_xboole_0(A,B))) -> r1_tarski(C,k3_tarski(A)))) # label(t57_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 611 (all A r1_tarski(k1_setfam_1(A),k3_tarski(A))) # label(t3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 612 (all A (v1_setfam_1(A) & -v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> -v1_xboole_0(B))))) # label(cc1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 613 (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]. 56.07/55.09 614 (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]. 56.07/55.09 615 $T # label(t50_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 616 (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]. 56.07/55.09 617 (all A all B (r2_setfam_1(A,B) <-> (all C -(r2_hidden(C,B) & (all D -(r1_tarski(D,C) & r2_hidden(D,A))))))) # label(d3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 618 $T # label(d7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 619 (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]. 56.07/55.09 620 (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]. 56.07/55.09 621 (all A all B all C ((all D ((exists E exists F (r2_hidden(F,B) & r2_hidden(E,A) & k4_xboole_0(E,F) = D)) <-> r2_hidden(D,C))) <-> k4_setfam_1(A,B) = C)) # label(d6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 622 (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]. 56.07/55.09 623 $T # label(t15_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 624 (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]. 56.07/55.09 625 (all A all B all C (r1_xboole_0(A,C) & r2_hidden(A,B) -> r1_xboole_0(k1_setfam_1(B),C))) # label(t9_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 626 (all A r1_setfam_1(k3_setfam_1(A,A),A)) # label(t30_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 627 (all A all B ((A = k1_xboole_0 -> (k1_xboole_0 = B <-> k1_setfam_1(A) = B)) & (k1_xboole_0 != A -> ((all C (r2_hidden(C,B) <-> (all D (r2_hidden(D,A) -> r2_hidden(C,D))))) <-> k1_setfam_1(A) = B)))) # label(d1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 628 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> -(B != k1_xboole_0 & k1_xboole_0 = k7_setfam_1(A,B)))) # label(t46_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 629 (all A all B (r1_tarski(A,B) -> r1_setfam_1(A,B))) # label(t17_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 630 (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]. 56.07/55.09 631 (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]. 56.07/55.09 632 (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]. 56.07/55.09 633 (all A all B all C (r1_setfam_1(C,k2_tarski(A,B)) -> (all D -(r2_hidden(D,C) & -r1_tarski(D,B) & -r1_tarski(D,A))))) # label(t25_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 634 (all A all B -(k1_xboole_0 != A & -r1_tarski(k2_xboole_0(k1_setfam_1(A),k1_setfam_1(B)),k1_setfam_1(k2_setfam_1(A,B))) & B != k1_xboole_0)) # label(t40_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 635 (all A all B r2_setfam_1(B,B)) # label(reflexivity_r2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 636 (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,k7_setfam_1(A,C)) <-> r1_tarski(k7_setfam_1(A,B),C)))))) # label(t52_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 637 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> k1_setfam_1(B) = k6_setfam_1(A,B))) # label(redefinition_k6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 638 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r2_hidden(B,A) -> (r2_hidden(B,k8_setfam_1(A,C)) <-> (all D (r2_hidden(D,C) -> r2_hidden(B,D))))))) # label(t58_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 639 (all A all B all C ((all D ((exists E exists F (D = k3_xboole_0(E,F) & r2_hidden(F,B) & r2_hidden(E,A))) <-> r2_hidden(D,C))) <-> C = k3_setfam_1(A,B))) # label(d5_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 640 $T # label(dt_k4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 641 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k1_xboole_0 = B -> A = k8_setfam_1(A,B)) & (k1_xboole_0 != B -> k8_setfam_1(A,B) = k6_setfam_1(A,B)))) # label(d10_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 642 (all A all B (v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> v1_xboole_0(k7_setfam_1(A,B)))) # label(fc1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 643 (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]. 56.07/55.09 644 (all A all B all C (k2_setfam_1(A,B) = C <-> (all D (r2_hidden(D,C) <-> (exists E exists F (k2_xboole_0(E,F) = D & r2_hidden(F,B) & r2_hidden(E,A))))))) # label(d4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 645 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> k7_setfam_1(A,k7_setfam_1(A,B)) = B)) # label(involutiveness_k7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 646 $T # label(t43_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 647 (all A r1_setfam_1(k1_xboole_0,A)) # label(t20_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 648 (all A all B k3_tarski(k3_setfam_1(k1_tarski(A),B)) = k3_xboole_0(A,k3_tarski(B))) # label(t36_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 649 (all A all B (v1_setfam_1(B) & v1_setfam_1(A) -> v1_setfam_1(k2_xboole_0(A,B)))) # label(fc4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 650 (all A all B k3_setfam_1(A,B) = k3_setfam_1(B,A)) # label(commutativity_k3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 651 $T # label(t13_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 652 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (B != k1_xboole_0 -> k6_subset_1(A,k2_subset_1(A),k6_setfam_1(A,B)) = k5_setfam_1(A,k7_setfam_1(A,B))))) # label(t48_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 653 $T # label(t27_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 654 (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]. 56.07/55.09 655 (all A all B -(k1_xboole_0 != A & k1_xboole_0 != B & k3_xboole_0(k1_setfam_1(A),k1_setfam_1(B)) != k1_setfam_1(k2_xboole_0(A,B)))) # label(t10_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 656 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k1_tarski(A) = B -> k7_setfam_1(A,B) = k1_tarski(k1_xboole_0)))) # label(t55_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 657 (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]. 56.07/55.09 658 $T # label(t26_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 659 (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))) -> k4_subset_1(k1_zfmisc_1(A),k7_setfam_1(A,B),k7_setfam_1(A,C)) = k7_setfam_1(A,k4_subset_1(k1_zfmisc_1(A),B,C)))))) # label(t54_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 660 (all A all B (B != k1_xboole_0 -> k3_tarski(k4_setfam_1(k1_tarski(A),B)) = k4_xboole_0(A,k1_setfam_1(B)))) # label(t38_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.09 661 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k7_setfam_1(A,B) = C <-> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(k3_subset_1(A,D),B) <-> r2_hidden(D,C))))))))) # label(d8_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 662 (all A r1_setfam_1(A,k2_setfam_1(A,A))) # label(t29_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 663 (all A all B (r2_setfam_1(B,A) -> r1_tarski(k1_setfam_1(B),k1_setfam_1(A)) | A = k1_xboole_0)) # label(t19_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 664 (all A (-r2_hidden(k1_xboole_0,A) <-> v1_setfam_1(A))) # label(d9_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 665 (all A A = k1_setfam_1(k1_tarski(A))) # label(t11_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 666 (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]. 56.07/55.10 667 (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]. 56.07/55.10 668 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k1_xboole_0 != B -> k6_setfam_1(A,k7_setfam_1(A,B)) = k6_subset_1(A,k2_subset_1(A),k5_setfam_1(A,B))))) # label(t47_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 669 (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]. 56.07/55.10 670 (exists A -v2_setfam_1(A)) # label(rc2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 671 (all A all B (m1_subset_1(A,B) -> r2_hidden(A,B) | v1_xboole_0(B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 672 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(C)) & r2_hidden(A,B) -> m1_subset_1(A,C))) # label(t4_subset) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 673 (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]. 56.07/55.10 674 (all A all B (r2_hidden(A,B) -> m1_subset_1(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 675 (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]. 56.07/55.10 676 $T # label(t57_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 677 (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]. 56.07/55.10 678 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k4_relat_1(k3_xboole_0(A,B)) = k3_xboole_0(k4_relat_1(A),k4_relat_1(B)))))) # label(t39_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 679 (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]. 56.07/55.10 680 (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]. 56.07/55.10 681 (exists A (v1_relat_1(A) & -v1_xboole_0(A))) # label(rc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 682 (all A all B (v1_relat_1(B) -> k8_relat_1(A,B) = k5_relat_1(B,k6_relat_1(A)))) # label(t123_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 683 (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]. 56.07/55.10 684 $T # label(t17_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 685 (all A all B (v1_relat_1(B) -> -(k9_relat_1(B,A) = k1_xboole_0 & r1_tarski(A,k1_relat_1(B)) & A != k1_xboole_0))) # label(t152_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 686 $T # label(t83_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 687 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(k7_relat_1(C,B))) <-> r2_hidden(A,B) & r2_hidden(A,k1_relat_1(C))))) # label(t86_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 688 (all A k9_relat_1(k1_xboole_0,A) = k1_xboole_0) # label(t150_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 689 (all A (v1_relat_1(A) -> k7_relat_1(A,k1_xboole_0) = k1_xboole_0)) # label(t110_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 690 $T # label(t68_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 691 (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]. 56.07/55.10 692 $T # label(t70_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 693 (all A (v1_relat_1(A) & -v1_xboole_0(A) -> -v1_xboole_0(k2_relat_1(A)))) # label(fc6_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 694 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> ((all D all E ((exists F (r2_hidden(k4_tarski(D,F),A) & r2_hidden(k4_tarski(F,E),B))) <-> r2_hidden(k4_tarski(D,E),C))) <-> k5_relat_1(A,B) = C))))))) # label(d8_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 695 (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]. 56.07/55.10 696 (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]. 56.07/55.10 697 (all A all B all C all D all E (v1_relat_1(E) -> (E = k2_tarski(k4_tarski(A,B),k4_tarski(C,D)) -> k1_relat_1(E) = k2_tarski(A,C) & k2_tarski(B,D) = k2_relat_1(E)))) # label(t24_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 698 (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]. 56.07/55.10 699 (all A (v1_relat_1(A) -> (k1_relat_1(A) = k1_xboole_0 <-> k1_xboole_0 = k2_relat_1(A)))) # label(t65_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 700 (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]. 56.07/55.10 701 $T # label(t7_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 702 (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]. 56.07/55.10 703 (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]. 56.07/55.10 704 (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]. 56.07/55.10 705 (all A (v1_xboole_0(A) -> v1_relat_1(A))) # label(cc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 706 (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]. 56.07/55.10 707 (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]. 56.07/55.10 708 $T # label(t142_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 709 (all A all B (v1_relat_1(B) -> k9_relat_1(B,A) = k2_relat_1(k7_relat_1(B,A)))) # label(t148_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 710 (all A all B all C (v1_relat_1(C) -> k7_relat_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)))) # label(t107_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 711 (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]. 56.07/55.10 712 $T # label(t35_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 713 $T # label(t42_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 714 (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]. 56.07/55.10 715 (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]. 56.07/55.10 716 (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]. 56.07/55.10 717 (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]. 56.07/55.10 718 (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]. 56.07/55.10 719 (all A all B (v1_xboole_0(A) & v1_relat_1(B) -> v1_relat_1(k5_relat_1(B,A)) & v1_xboole_0(k5_relat_1(B,A)))) # label(fc10_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 720 (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]. 56.07/55.10 721 (all A (v1_relat_1(A) -> k10_relat_1(A,k2_relat_1(A)) = k1_relat_1(A))) # label(t169_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 722 (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]. 56.07/55.10 723 (all A all B (v1_relat_1(B) -> k3_xboole_0(k1_relat_1(B),A) = k1_relat_1(k7_relat_1(B,A)))) # label(t90_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 724 $T # label(t69_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 725 (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]. 56.07/55.10 726 (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]. 56.07/55.10 727 $T # label(dt_k3_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 728 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k5_relat_1(A,k2_xboole_0(B,C)) = k2_xboole_0(k5_relat_1(A,B),k5_relat_1(A,C)))))))) # label(t51_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 729 (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]. 56.07/55.10 730 (all A (v1_relat_1(A) -> (all B all C ((all D ((exists E (r2_hidden(k4_tarski(D,E),A) & r2_hidden(E,B))) <-> r2_hidden(D,C))) <-> C = k10_relat_1(A,B))))) # label(d14_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 731 (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]. 56.07/55.10 732 (all A all B (v1_xboole_0(A) & v1_relat_1(B) -> v1_relat_1(k5_relat_1(A,B)) & v1_xboole_0(k5_relat_1(A,B)))) # label(fc9_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 733 (all A all B all C (v1_relat_1(C) -> k9_relat_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)))) # label(t153_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 734 (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]. 56.07/55.10 735 (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]. 56.07/55.10 736 (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]. 56.07/55.10 737 (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]. 56.07/55.10 738 (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]. 56.07/55.10 739 (all A all B (v1_relat_1(B) -> (r1_tarski(A,k2_relat_1(B)) -> k2_relat_1(k8_relat_1(A,B)) = A))) # label(t120_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 740 (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]. 56.07/55.10 741 (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]. 56.07/55.10 742 (all A all B (v1_relat_1(A) & v1_relat_1(B) -> v1_relat_1(k4_xboole_0(A,B)))) # label(fc3_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 743 $T # label(t113_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 744 (all A all B (v1_relat_1(B) -> (r1_tarski(k1_relat_1(B),A) -> B = k5_relat_1(k6_relat_1(A),B)))) # label(t77_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 745 $T # label(t2_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 746 (exists A (v1_xboole_0(A) & v1_relat_1(A))) # label(rc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 747 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k5_relat_1(k5_relat_1(A,B),C) = k5_relat_1(A,k5_relat_1(B,C)))))))) # label(t55_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 748 (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]. 56.07/55.10 749 (all A all B all C (v1_relat_1(C) -> k8_relat_1(k4_xboole_0(A,B),C) = k4_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)))) # label(t136_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 750 (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]. 56.07/55.10 751 (all A k1_xboole_0 = k7_relat_1(k1_xboole_0,A)) # label(t111_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 752 $T # label(t8_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 753 (all A all B all C (v1_relat_1(C) -> k8_relat_1(A,k8_relat_1(B,C)) = k8_relat_1(k3_xboole_0(A,B),C))) # label(t127_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 754 (all A all B all C all D (v1_relat_1(D) -> (r2_hidden(B,C) & r2_hidden(k4_tarski(A,B),D) <-> r2_hidden(k4_tarski(A,B),k5_relat_1(D,k6_relat_1(C)))))) # label(t75_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 755 (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]. 56.07/55.10 756 (all A (v1_relat_1(A) <-> (all B -(r2_hidden(B,A) & (all C all D k4_tarski(C,D) != B))))) # label(d1_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 757 (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]. 56.07/55.10 758 (all A all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> B = k5_relat_1(B,k6_relat_1(A))))) # label(t79_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 759 (all A all B all C (v1_relat_1(C) -> k4_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)) = k7_relat_1(C,k4_xboole_0(A,B)))) # label(t109_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 760 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k9_relat_1(k5_relat_1(B,C),A) = k9_relat_1(C,k9_relat_1(B,A)))))) # label(t159_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 761 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C all D (k7_relat_1(B,D) = k7_relat_1(A,D) & r1_tarski(C,D) -> k7_relat_1(B,C) = k7_relat_1(A,C))))))) # label(t188_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 762 (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]. 56.07/55.10 763 (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]. 56.07/55.10 764 (all A k1_xboole_0 = k10_relat_1(k1_xboole_0,A)) # label(t172_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 765 (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]. 56.07/55.10 766 (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]. 56.07/55.10 767 $T # label(t58_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 768 (all A all B all C (v1_relat_1(C) -> (C = k1_tarski(k4_tarski(A,B)) -> k1_relat_1(C) = k1_tarski(A) & k2_relat_1(C) = k1_tarski(B)))) # label(t23_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 769 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k2_relat_1(k5_relat_1(A,B)) = k9_relat_1(B,k2_relat_1(A)))))) # label(t160_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 770 (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]. 56.07/55.10 771 $T # label(t36_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 772 (all A all B (v1_relat_1(B) -> k9_relat_1(B,A) = k9_relat_1(B,k3_xboole_0(k1_relat_1(B),A)))) # label(t145_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 773 (all A all B (v1_relat_1(A) & v1_relat_1(B) -> v1_relat_1(k2_xboole_0(A,B)))) # label(fc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 774 (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]. 56.07/55.10 775 (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]. 56.07/55.10 776 (all A all B all C (v1_relat_1(C) -> ((exists D (r2_hidden(k4_tarski(D,A),C) & r2_hidden(D,k1_relat_1(C)) & r2_hidden(D,B))) <-> r2_hidden(A,k9_relat_1(C,B))))) # label(t143_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 777 $T # label(t43_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 778 (all A all B (v1_relat_1(B) -> ((all C all D (r2_hidden(k4_tarski(C,D),B) <-> r2_hidden(C,A) & C = D)) <-> B = k6_relat_1(A)))) # label(d10_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 779 (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]. 56.07/55.10 780 (all A (v1_relat_1(A) -> A = k5_relat_1(k6_relat_1(k1_relat_1(A)),A))) # label(t78_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 781 $T # label(t114_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 782 (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]. 56.07/55.10 783 (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]. 56.07/55.10 784 (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]. 56.07/55.10 785 $T # label(t16_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.10 786 (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]. 56.07/55.10 787 (all A (v1_relat_1(A) -> k1_relat_1(A) = k2_relat_1(k4_relat_1(A)) & k2_relat_1(A) = k1_relat_1(k4_relat_1(A)))) # label(t37_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 788 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k8_relat_1(B,k8_relat_1(A,C)) = k8_relat_1(A,C)))) # label(t129_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 789 (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]. 56.07/55.11 790 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k10_relat_1(C,A),k10_relat_1(D,B))))))) # label(t180_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 791 (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]. 56.07/55.11 792 (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]. 56.07/55.11 793 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k7_relat_1(k7_relat_1(C,B),A) = k7_relat_1(C,A)))) # label(t103_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 794 (all A (v1_relat_1(A) -> v1_relat_1(k4_relat_1(A)))) # label(dt_k4_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 795 (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]. 56.07/55.11 796 (all A (v1_relat_1(A) -> (v3_relat_1(A) <-> (all B (r2_hidden(B,k2_relat_1(A)) -> k1_xboole_0 = B))))) # label(t184_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 797 (all A all B (v1_relat_1(B) -> k8_relat_1(A,k8_relat_1(A,B)) = k8_relat_1(A,B))) # label(t128_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 798 (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]. 56.07/55.11 799 (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]. 56.07/55.11 800 (all A k4_relat_1(k6_relat_1(A)) = k6_relat_1(A)) # label(t72_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 801 (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]. 56.07/55.11 802 (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]. 56.07/55.11 803 (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]. 56.07/55.11 804 $T # label(t84_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 805 (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]. 56.07/55.11 806 (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]. 56.07/55.11 807 (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]. 56.07/55.11 808 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k5_relat_1(A,C),k5_relat_1(B,D))))))))))) # label(t50_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 809 $T # label(t141_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 810 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> ((all D all E (r2_hidden(E,A) & r2_hidden(k4_tarski(D,E),B) <-> r2_hidden(k4_tarski(D,E),C))) <-> k8_relat_1(A,B) = C))))) # label(d12_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 811 (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]. 56.07/55.11 812 (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]. 56.07/55.11 813 (all A all B v1_relat_1(k1_tarski(k4_tarski(A,B)))) # label(t4_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 814 (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]. 56.07/55.11 815 (all A (v1_relat_1(A) -> k8_relat_1(k1_xboole_0,A) = k1_xboole_0)) # label(t137_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 816 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C all D (k7_relat_1(B,D) = k7_relat_1(A,D) & k7_relat_1(A,C) = k7_relat_1(B,C) -> k7_relat_1(B,k2_xboole_0(C,D)) = k7_relat_1(A,k2_xboole_0(C,D)))))))) # label(t185_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 817 (all A all B all C (v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),C) -> r2_hidden(B,k2_relat_1(C)) & r2_hidden(A,k1_relat_1(C))))) # label(t20_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 818 (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]. 56.07/55.11 819 (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]. 56.07/55.11 820 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k3_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k3_relat_1(A),k3_relat_1(B)))))) # label(t33_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 821 (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]. 56.07/55.11 822 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(A,B) -> r1_tarski(k2_relat_1(A),k2_relat_1(B)) & r1_tarski(k1_relat_1(A),k1_relat_1(B))))))) # label(t25_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 823 (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]. 56.07/55.11 824 (exists A (v3_relat_1(A) & v1_relat_1(A))) # label(rc3_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 825 $T # label(t11_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 826 (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]. 56.07/55.11 827 (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]. 56.07/55.11 828 (all A all B (v1_relat_1(B) -> (k9_relat_1(B,A) = k1_xboole_0 <-> r1_xboole_0(k1_relat_1(B),A)))) # label(t151_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 829 (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]. 56.07/55.11 830 (exists A (v1_relat_1(A) & (all B all C (r2_hidden(k4_tarski(B,C),A) <-> r2_hidden(B,f1_s1_relat_1) & p1_s1_relat_1(B,C) & r2_hidden(C,f2_s1_relat_1))))) # label(s1_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 831 (all A all B (v1_relat_1(B) -> (r1_tarski(A,k1_relat_1(B)) -> k1_relat_1(k7_relat_1(B,A)) = A))) # label(t91_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 832 (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]. 56.07/55.11 833 (all A (v1_relat_1(A) -> k3_relat_1(A) = k2_xboole_0(k1_relat_1(A),k2_relat_1(A)))) # label(d6_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 834 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 835 (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]. 56.07/55.11 836 (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]. 56.07/55.11 837 (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]. 56.07/55.11 838 (all A all B (v1_relat_1(B) -> -(k10_relat_1(B,A) = k1_xboole_0 & r1_tarski(A,k2_relat_1(B)) & A != k1_xboole_0))) # label(t174_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 839 $T # label(dt_k10_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 840 (all A (v1_relat_1(A) -> (r1_tarski(k2_relat_1(A),k1_tarski(k1_xboole_0)) <-> v3_relat_1(A)))) # label(d15_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 841 (all A (v1_relat_1(A) -> ((all B all C -r2_hidden(k4_tarski(B,C),A)) -> k1_xboole_0 = A))) # label(t56_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 842 $T # label(t1_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 843 (all A all B v1_relat_1(k2_zfmisc_1(A,B))) # label(t6_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 844 (all A all B all C (v1_relat_1(C) -> (C = k1_tarski(k4_tarski(A,B)) -> k3_relat_1(C) = k2_tarski(A,B)))) # label(t32_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 845 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (k1_relat_1(B) = A & k5_relat_1(B,D) = k6_relat_1(A) & k5_relat_1(C,B) = k6_relat_1(k1_relat_1(D)) & r1_tarski(k2_relat_1(C),A) -> D = C))))))) # label(t82_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 846 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k8_relat_1(A,k5_relat_1(B,C)) = k5_relat_1(B,k8_relat_1(A,C)))))) # label(t139_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 847 $T # label(dt_k9_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 848 (all A (v1_relat_1(A) -> k4_relat_1(k4_relat_1(A)) = A)) # label(involutiveness_k4_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 849 $T # label(t165_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 850 (all A v1_relat_1(k6_relat_1(A))) # label(dt_k6_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 851 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k1_relat_1(k5_relat_1(A,B)) = k10_relat_1(A,k1_relat_1(B)))))) # label(t182_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 852 (all A (v1_relat_1(A) -> k5_relat_1(A,k1_xboole_0) = k1_xboole_0 & k5_relat_1(k1_xboole_0,A) = k1_xboole_0)) # label(t62_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 853 (all A (v1_relat_1(A) -> (all B all C (v1_relat_1(C) -> (C = k7_relat_1(A,B) <-> (all D all E (r2_hidden(D,B) & r2_hidden(k4_tarski(D,E),A) <-> r2_hidden(k4_tarski(D,E),C)))))))) # label(d11_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 854 (all A all B (v1_relat_1(B) & v1_relat_1(A) -> v1_relat_1(k5_relat_1(A,B)))) # label(dt_k5_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 855 (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]. 56.07/55.11 856 (all A (A = k1_relat_1(k6_relat_1(A)) & A = k2_relat_1(k6_relat_1(A)))) # label(t71_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 857 (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]. 56.07/55.11 858 (all A all B (v1_relat_1(B) -> k10_relat_1(B,A) = k10_relat_1(B,k3_xboole_0(k2_relat_1(B),A)))) # label(t168_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 859 (all A (v1_relat_1(A) -> (all B ((all C ((exists D r2_hidden(k4_tarski(C,D),A)) <-> r2_hidden(C,B))) <-> k1_relat_1(A) = B)))) # label(d4_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 860 (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]. 56.07/55.11 861 $T # label(t12_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 862 $T # label(t61_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 863 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k2_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k2_relat_1(A),k2_relat_1(B)))))) # label(t26_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 864 (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]. 56.07/55.11 865 (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]. 56.07/55.11 866 (all A all B (v1_relat_1(B) -> -(-v3_relat_1(k7_relat_1(B,A)) & v3_relat_1(B)))) # label(t190_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 867 (all A all B (v1_relat_1(B) -> k7_relat_1(k7_relat_1(B,A),A) = k7_relat_1(B,A))) # label(t101_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 868 $T # label(t63_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 869 (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]. 56.07/55.11 870 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k9_relat_1(C,A),k9_relat_1(D,B))))))) # label(t158_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 871 (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]. 56.07/55.11 872 (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]. 56.07/55.11 873 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> ((all C all D (r2_hidden(k4_tarski(C,D),B) <-> r2_hidden(k4_tarski(D,C),A))) <-> B = k4_relat_1(A)))))) # label(d7_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 874 (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]. 56.07/55.11 875 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k10_relat_1(C,B)) <-> (exists D (r2_hidden(D,k2_relat_1(C)) & r2_hidden(D,B) & r2_hidden(k4_tarski(A,D),C)))))) # label(t166_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 876 (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]. 56.07/55.11 877 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k7_relat_1(C,A) = k7_relat_1(k7_relat_1(C,A),B)))) # label(t102_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 878 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k2_xboole_0(k1_relat_1(A),k1_relat_1(B)) = k1_relat_1(k2_xboole_0(A,B)))))) # label(t13_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 879 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 880 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k7_relat_1(k5_relat_1(B,C),A) = k5_relat_1(k7_relat_1(B,A),C))))) # label(t112_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 881 (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]. 56.07/55.11 882 (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]. 56.07/55.11 883 $T # label(t85_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 884 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k8_relat_1(A,k8_relat_1(B,C)) = k8_relat_1(A,C)))) # label(t130_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 885 (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]. 56.07/55.11 886 (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]. 56.07/55.11 887 (all A (v1_relat_1(A) -> (k1_xboole_0 = k2_relat_1(A) | k1_xboole_0 = k1_relat_1(A) -> A = k1_xboole_0))) # label(t64_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 888 $T # label(t162_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 889 (all A all B (v1_relat_1(B) -> (r1_xboole_0(k2_relat_1(B),A) <-> k1_xboole_0 = k10_relat_1(B,A)))) # label(t173_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 890 $T # label(t59_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 891 (all A (v1_xboole_0(A) -> v1_xboole_0(k2_relat_1(A)) & v1_relat_1(k2_relat_1(A)))) # label(fc8_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 892 (all A (v1_xboole_0(A) -> v1_xboole_0(k4_relat_1(A)) & v1_relat_1(k4_relat_1(A)))) # label(fc11_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 893 $T # label(t164_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 894 (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]. 56.07/55.11 895 (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]. 56.07/55.11 896 (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]. 56.07/55.11 897 (all A all B all C all D (v1_relat_1(D) -> (r2_hidden(k4_tarski(A,B),k5_relat_1(k6_relat_1(C),D)) <-> r2_hidden(A,C) & r2_hidden(k4_tarski(A,B),D)))) # label(t74_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 898 (all A (v1_relat_1(A) -> k1_xboole_0 = k9_relat_1(A,k1_xboole_0))) # label(t149_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 899 (all A k8_relat_1(A,k1_xboole_0) = k1_xboole_0) # label(t138_relat_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 900 (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]. 56.07/55.11 901 (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]. 56.07/55.11 902 (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]. 56.07/55.11 903 (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]. 56.07/55.11 904 (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]. 56.07/55.11 905 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k2_relat_1(k5_relat_1(C,B))) -> r2_hidden(A,k2_relat_1(B))))))) # label(t25_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 906 (all A all B k5_relat_1(k6_relat_1(B),k6_relat_1(A)) = k6_relat_1(k3_xboole_0(A,B))) # label(t43_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 907 $T # label(t41_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 908 (all A (v2_relat_1(A) & v1_relat_1(A) & v1_funct_1(A) -> v1_setfam_1(k2_relat_1(A)))) # label(fc6_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 909 $T # label(t128_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 910 (exists A ((all B (m1_subset_1(B,f1_s4_funct_1) -> k1_funct_1(A,B) = f2_s4_funct_1(B))) & v1_relat_1(A) & v1_funct_1(A) & k1_relat_1(A) = f1_s4_funct_1)) # label(s4_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 911 $T # label(t92_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 912 $T # label(t106_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 913 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) -> v2_funct_1(k8_relat_1(A,B))))) # label(t99_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 914 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(C,k1_funct_1(B,A)) = k1_funct_1(k5_relat_1(B,C),A)))))) # label(t23_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 915 (all A all B (v1_relat_1(B) -> (r2_hidden(A,k2_relat_1(B)) <-> k1_xboole_0 != k10_relat_1(B,k1_tarski(A))))) # label(t142_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 916 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) -> k3_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)) = k9_relat_1(C,k3_xboole_0(A,B))))) # label(t121_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 917 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) -> r1_tarski(k10_relat_1(B,k9_relat_1(B,A)),A)))) # label(t152_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 918 $T # label(t5_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 919 $T # label(t134_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 920 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> k10_relat_1(C,k4_xboole_0(A,B)) = k4_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)))) # label(t138_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 921 (all A (v1_funct_1(A) & v1_relat_1(A) -> A = k5_relat_1(k6_relat_1(k1_relat_1(A)),A) & k5_relat_1(A,k6_relat_1(k2_relat_1(A))) = A)) # label(t42_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 922 $T # label(t83_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 923 $T # label(t107_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 924 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) <-> (all B all C (r2_hidden(C,k1_relat_1(A)) & r2_hidden(B,k1_relat_1(A)) & k1_funct_1(A,C) = k1_funct_1(A,B) -> C = B))))) # label(d8_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 925 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,B) -> k8_relat_1(B,k8_relat_1(A,C)) = k8_relat_1(A,C) & k8_relat_1(A,k8_relat_1(B,C)) = k8_relat_1(A,C)))) # label(t97_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 926 $T # label(d10_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 927 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> k1_relat_1(k2_funct_1(A)) = k2_relat_1(A) & k1_relat_1(A) = k2_relat_1(k2_funct_1(A))))) # label(t55_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 928 $T # label(t10_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 929 $T # label(t90_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 930 (all A (v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)))) # label(fc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 931 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k2_relat_1(A) = k2_relat_1(k5_relat_1(B,A)) & v2_funct_1(A) -> r1_tarski(k1_relat_1(A),k2_relat_1(B))))))) # label(t51_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 932 $T # label(t100_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.11 933 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B all C k3_xboole_0(k9_relat_1(A,B),k9_relat_1(A,C)) = k9_relat_1(A,k3_xboole_0(B,C))) -> v2_funct_1(A)))) # label(t122_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 934 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k1_relat_1(C)) & r2_hidden(B,A) -> r2_hidden(k1_funct_1(C,B),k2_relat_1(k7_relat_1(C,A)))))) # label(t73_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 935 $T # label(t4_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 936 $T # label(t32_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 937 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,k2_relat_1(C)) & r1_tarski(B,k2_relat_1(C)) & k10_relat_1(C,B) = k10_relat_1(C,A) -> B = A))) # label(t161_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 938 $T # label(t29_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 939 $T # label(t112_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 940 (all A (v1_xboole_0(A) -> v1_funct_1(A))) # label(cc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 941 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) <-> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_relat_1(C),k1_relat_1(A)) & k5_relat_1(C,A) = k5_relat_1(B,A) & r1_tarski(k2_relat_1(B),k1_relat_1(A)) & k1_relat_1(B) = k1_relat_1(C) -> C = B)))))))) # label(t49_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 942 (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]. 56.07/55.12 943 $T # label(t129_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 944 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(A) = k2_relat_1(B) & k1_relat_1(B) = k2_relat_1(A) & v2_funct_1(A) & (all C all D (r2_hidden(D,k1_relat_1(B)) & r2_hidden(C,k1_relat_1(A)) -> (C = k1_funct_1(B,D) <-> k1_funct_1(A,C) = D))) -> B = k2_funct_1(A)))))) # label(t60_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 945 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k1_relat_1(A) = k1_relat_1(k5_relat_1(A,k2_funct_1(A))) & k2_relat_1(k5_relat_1(A,k2_funct_1(A))) = k1_relat_1(A)))) # label(t58_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 946 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k4_relat_1(A) = k2_funct_1(A)))) # label(d9_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 947 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k3_xboole_0(k1_relat_1(C),A)) -> k1_funct_1(C,B) = k1_funct_1(k5_relat_1(k6_relat_1(A),C),B)))) # label(t38_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 948 (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]. 56.07/55.12 949 $T # label(t94_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 950 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> A = k2_funct_1(k2_funct_1(A))))) # label(t65_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 951 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> ((all D (r2_hidden(k1_funct_1(A,D),k1_relat_1(B)) & r2_hidden(D,k1_relat_1(A)) <-> r2_hidden(D,k1_relat_1(C)))) & (all D (r2_hidden(D,k1_relat_1(C)) -> k1_funct_1(C,D) = k1_funct_1(B,k1_funct_1(A,D)))) -> C = k5_relat_1(A,B)))))))) # label(t20_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 952 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> k3_xboole_0(A,k9_relat_1(C,B)) = k9_relat_1(k8_relat_1(A,C),B))) # label(t126_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 953 $T # label(t69_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 954 (all A all B -((all C (v1_funct_1(C) & v1_relat_1(C) -> -(r1_tarski(k2_relat_1(C),A) & k1_relat_1(C) = B))) & -(B != k1_xboole_0 & A = k1_xboole_0))) # label(t18_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 955 $T # label(t77_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 956 (all A (v2_funct_1(A) & v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k4_relat_1(A)) & v1_funct_1(k4_relat_1(A)))) # label(fc3_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 957 (all A k6_relat_1(A) = k2_funct_1(k6_relat_1(A))) # label(t67_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 958 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) -> v2_funct_1(k7_relat_1(B,A))))) # label(t84_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 959 (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]. 56.07/55.12 960 (all A (v1_funct_1(A) <-> (all B all C all D (r2_hidden(k4_tarski(B,C),A) & r2_hidden(k4_tarski(B,D),A) -> D = C)))) # label(d1_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 961 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (B = k6_relat_1(A) <-> k1_relat_1(B) = A & (all C (r2_hidden(C,A) -> C = k1_funct_1(B,C)))))) # label(t34_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 962 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k1_relat_1(k7_relat_1(C,A))) -> k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B)))) # label(t70_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 963 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B all C k9_relat_1(A,k4_xboole_0(B,C)) = k4_xboole_0(k9_relat_1(A,B),k9_relat_1(A,C))) -> v2_funct_1(A)))) # label(t124_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 964 $T # label(t7_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 965 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(B) & k1_relat_1(B) = A & B = k5_relat_1(C,B) & r1_tarski(k2_relat_1(C),A) & A = k1_relat_1(C) -> C = k6_relat_1(A)))))) # label(t50_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 966 (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]. 56.07/55.12 967 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B -(r2_hidden(B,k1_relat_1(A)) & v1_xboole_0(k1_funct_1(A,B)))) <-> v2_relat_1(A)))) # label(d15_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 968 $T # label(t105_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 969 $T # label(t96_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 970 $T # label(t80_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 971 $T # label(t136_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 972 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,A) -> k1_funct_1(C,B) = k1_funct_1(k7_relat_1(C,A),B)))) # label(t72_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 973 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C ((r2_hidden(B,k1_relat_1(A)) -> (k1_funct_1(A,B) = C <-> r2_hidden(k4_tarski(B,C),A))) & (-r2_hidden(B,k1_relat_1(A)) -> (C = k1_xboole_0 <-> C = k1_funct_1(A,B))))))) # label(d4_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 974 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(k5_relat_1(C,B))) <-> r2_hidden(k1_funct_1(C,A),k1_relat_1(B)) & r2_hidden(A,k1_relat_1(C))))))) # label(t21_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 975 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> r2_hidden(k1_funct_1(B,A),k2_relat_1(B))))) # label(t12_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 976 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) & r1_xboole_0(A,B) -> r1_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B))))) # label(t125_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 977 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> k3_xboole_0(k1_relat_1(B),A) = k1_relat_1(k5_relat_1(k6_relat_1(A),B)))) # label(t37_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 978 $T # label(t141_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 979 $T # label(t78_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 980 $T # label(t11_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 981 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,B) -> k7_relat_1(k7_relat_1(C,B),A) = k7_relat_1(C,A) & k7_relat_1(k7_relat_1(C,A),B) = k7_relat_1(C,A)))) # label(t82_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 982 (all A all B (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k7_relat_1(A,B)) & v1_relat_1(k7_relat_1(A,B)))) # label(fc4_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 983 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> k9_relat_1(B,k10_relat_1(B,A)) = k3_xboole_0(A,k9_relat_1(B,k1_relat_1(B))))) # label(t148_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 984 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) & r2_hidden(A,k1_relat_1(B)) -> A = k1_funct_1(k5_relat_1(B,k2_funct_1(B)),A) & k1_funct_1(k2_funct_1(B),k1_funct_1(B,A)) = A))) # label(t56_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 985 (all A ((all B -(r2_hidden(B,A) & (all C all D B != k4_tarski(C,D)))) & (all B all C all D (r2_hidden(k4_tarski(B,D),A) & r2_hidden(k4_tarski(B,C),A) -> D = C)) -> v1_relat_1(A) & v1_funct_1(A))) # label(t2_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 986 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k1_relat_1(k5_relat_1(C,k6_relat_1(A)))) <-> r2_hidden(k1_funct_1(C,B),A) & r2_hidden(B,k1_relat_1(C))))) # label(t40_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 987 (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]. 56.07/55.12 988 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(A) = k2_relat_1(B) & v2_funct_1(k5_relat_1(B,A)) -> v2_funct_1(A) & v2_funct_1(B)))))) # label(t48_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 989 (exists A (v1_funct_1(A) & v2_funct_1(A) & v1_relat_1(A))) # label(rc3_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 990 $T # label(t135_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 991 $T # label(t81_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 992 $T # label(t109_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 993 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(B) -> v1_relat_1(k5_relat_1(A,B)) & v1_funct_1(k5_relat_1(A,B)))) # label(fc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 994 $T # label(t114_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 995 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (A = k1_relat_1(D) & k1_relat_1(C) = A & k5_relat_1(B,C) = k5_relat_1(B,D) -> C = D))))) & r1_tarski(k2_relat_1(B),A) -> k2_relat_1(B) = A))) # label(t33_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 996 $T # label(d7_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 997 (all A all B (r2_hidden(B,A) -> k1_funct_1(k6_relat_1(A),B) = B)) # label(t35_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 998 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> r1_tarski(k9_relat_1(C,k3_xboole_0(A,k10_relat_1(C,B))),k3_xboole_0(k9_relat_1(C,A),B)))) # label(t149_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 999 $T # label(t93_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1000 $T # label(dt_k1_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1001 (all A ((all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (A = k1_relat_1(B) & k1_relat_1(C) = A -> C = B))))) -> k1_xboole_0 = A)) # label(t16_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1002 $T # label(t6_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1003 (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]. 56.07/55.12 1004 (all A (k1_xboole_0 != A -> (all B exists C (v1_relat_1(C) & v1_funct_1(C) & k1_tarski(B) = k2_relat_1(C) & A = k1_relat_1(C))))) # label(t15_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1005 $T # label(t108_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1006 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k2_relat_1(B)) & v2_funct_1(B) -> A = k1_funct_1(k5_relat_1(k2_funct_1(B),B),A) & k1_funct_1(B,k1_funct_1(k2_funct_1(B),A)) = A))) # label(t57_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1007 (all A all B all C (p1_s1_funct_1(A,C) & p1_s1_funct_1(A,B) -> B = C)) -> (exists A (v1_relat_1(A) & v1_funct_1(A) & (all B all C (r2_hidden(k4_tarski(B,C),A) <-> r2_hidden(B,f1_s1_funct_1) & p1_s1_funct_1(B,C))))) # label(s1_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1008 $T # label(t98_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1009 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B (r2_hidden(B,k1_relat_1(A)) -> v1_xboole_0(k1_funct_1(A,B)))) <-> v3_relat_1(A)))) # label(d14_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1010 $T # label(t111_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1011 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> k1_tarski(k1_funct_1(B,A)) = k9_relat_1(B,k1_tarski(A))))) # label(t117_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1012 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) & v2_funct_1(A) -> k2_funct_1(k5_relat_1(A,B)) = k5_relat_1(k2_funct_1(B),k2_funct_1(A))))))) # label(t66_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1013 (all A -(r2_hidden(A,f1_s2_funct_1) & (all B -p1_s2_funct_1(A,B)))) & (all A all B all C (r2_hidden(A,f1_s2_funct_1) & p1_s2_funct_1(A,C) & p1_s2_funct_1(A,B) -> B = C)) -> (exists A (f1_s2_funct_1 = k1_relat_1(A) & v1_relat_1(A) & (all B (r2_hidden(B,f1_s2_funct_1) -> p1_s2_funct_1(B,k1_funct_1(A,B)))) & v1_funct_1(A))) # label(s2_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1014 $T # label(t39_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1015 (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]. 56.07/55.12 1016 $T # label(t113_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1017 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k2_relat_1(k5_relat_1(k2_funct_1(A),A)) = k2_relat_1(A) & k2_relat_1(A) = k1_relat_1(k5_relat_1(k2_funct_1(A),A))))) # label(t59_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1018 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B exists C r1_tarski(k10_relat_1(A,k1_tarski(B)),k1_tarski(C))) <-> v2_funct_1(A)))) # label(t159_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1019 $T # label(t127_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1020 (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]. 56.07/55.12 1021 $T # label(t74_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1022 (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]. 56.07/55.12 1023 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) -> k10_relat_1(k2_funct_1(B),A) = k9_relat_1(B,A)))) # label(t154_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1024 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (k10_relat_1(A,B) = C <-> (all D (r2_hidden(D,C) <-> r2_hidden(k1_funct_1(A,D),B) & r2_hidden(D,k1_relat_1(A)))))))) # label(d13_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1025 $T # label(t45_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1026 $T # label(t130_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1027 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_tarski(k9_relat_1(k8_relat_1(A,C),B),k9_relat_1(C,B)))) # label(t120_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1028 (all A v2_funct_1(k6_relat_1(A))) # label(t52_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1029 $T # label(t88_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1030 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k9_relat_1(B,k10_relat_1(B,A)),A))) # label(t145_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1031 $T # label(t1_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1032 (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]. 56.07/55.12 1033 (exists A (v1_funct_1(A) & v1_relat_1(A) & v2_relat_1(A))) # label(rc5_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1034 $T # label(t75_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1035 $T # label(t95_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1036 $T # label(d6_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1037 (exists A (f1_s3_funct_1 = k1_relat_1(A) & v1_funct_1(A) & v1_relat_1(A) & (all B (r2_hidden(B,f1_s3_funct_1) -> k1_funct_1(A,B) = f2_s3_funct_1(B))))) # label(s3_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1038 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(C) = k1_relat_1(B) & k2_relat_1(C) = k1_tarski(A) & k1_tarski(A) = k2_relat_1(B) -> B = C))))) # label(t17_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1039 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(k5_relat_1(B,A)) = k1_relat_1(B) -> r1_tarski(k2_relat_1(B),k1_relat_1(A))))))) # label(t27_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1040 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(A) & k6_relat_1(k1_relat_1(A)) = k5_relat_1(A,B) & k1_relat_1(B) = k2_relat_1(A) -> B = k2_funct_1(A)))))) # label(t63_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1041 (exists A (v3_relat_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc4_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1042 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k6_relat_1(k2_relat_1(A)) = k5_relat_1(B,A) & k1_relat_1(A) = k2_relat_1(B) & v2_funct_1(A) -> B = k2_funct_1(A)))))) # label(t64_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1043 $T # label(t133_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1044 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(k5_relat_1(C,B))) -> k1_funct_1(B,k1_funct_1(C,A)) = k1_funct_1(k5_relat_1(C,B),A)))))) # label(t22_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1045 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) & v2_funct_1(A) -> v2_funct_1(k5_relat_1(A,B))))))) # label(t46_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1046 $T # label(t3_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1047 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k1_relat_1(k8_relat_1(A,C))) <-> r2_hidden(k1_funct_1(C,B),A) & r2_hidden(B,k1_relat_1(C))))) # label(t86_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1048 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> v2_funct_1(k2_funct_1(A))))) # label(t62_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1049 (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]. 56.07/55.12 1050 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k10_relat_1(C,A),k10_relat_1(C,B)) & r1_tarski(A,k2_relat_1(C)) -> r1_tarski(A,B)))) # label(t158_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1051 $T # label(t103_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1052 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k2_funct_1(A)) & v1_funct_1(k2_funct_1(A)))) # label(dt_k2_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1053 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (B = k2_funct_1(A) <-> (all C all D ((r2_hidden(C,k2_relat_1(A)) & D = k1_funct_1(B,C) -> k1_funct_1(A,D) = C & r2_hidden(D,k1_relat_1(A))) & (r2_hidden(D,k1_relat_1(A)) & k1_funct_1(A,D) = C -> r2_hidden(C,k2_relat_1(A)) & D = k1_funct_1(B,C)))) & k1_relat_1(B) = k2_relat_1(A))))))) # label(t54_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1054 (exists A (v1_funct_1(A) & v1_xboole_0(A) & v1_relat_1(A))) # label(rc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1055 $T # label(t132_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1056 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) -> k10_relat_1(B,A) = k9_relat_1(k2_funct_1(B),A)))) # label(t155_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1057 $T # label(t36_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1058 $T # label(t110_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1059 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (C = k9_relat_1(A,B) <-> (all D ((exists E (D = k1_funct_1(A,E) & r2_hidden(E,B) & r2_hidden(E,k1_relat_1(A)))) <-> r2_hidden(D,C))))))) # label(d12_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1060 (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]. 56.07/55.12 1061 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((exists B (k5_relat_1(A,B) = k6_relat_1(k1_relat_1(A)) & v1_funct_1(B) & v1_relat_1(B))) -> v2_funct_1(A)))) # label(t53_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1062 $T # label(t91_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1063 $T # label(t131_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1064 $T # label(t115_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1065 $T # label(t26_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1066 (exists A (v1_funct_1(A) & v1_relat_1(A))) # label(rc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1067 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (B = k8_relat_1(A,C) <-> (all D (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(B,D) = k1_funct_1(C,D))) & (all D (r2_hidden(D,k1_relat_1(B)) <-> r2_hidden(k1_funct_1(C,D),A) & r2_hidden(D,k1_relat_1(C))))))))) # label(t85_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1068 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(C)) & B = k1_funct_1(C,A) <-> r2_hidden(k4_tarski(A,B),C)))) # label(t8_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1069 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B r1_tarski(k10_relat_1(A,k9_relat_1(A,B)),B)) -> v2_funct_1(A)))) # label(t153_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1070 $T # label(d11_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1071 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B -(r2_hidden(B,k2_relat_1(A)) & (all C k10_relat_1(A,k1_tarski(B)) != k1_tarski(C)))) <-> v2_funct_1(A)))) # label(t144_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.12 1072 (all A all B (v1_relat_1(B) -> ((all C -(k1_xboole_0 = k10_relat_1(B,k1_tarski(C)) & r2_hidden(C,A))) -> r1_tarski(A,k2_relat_1(B))))) # label(t143_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1073 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k5_relat_1(A,B) = A & k2_relat_1(A) = k1_relat_1(B) -> k6_relat_1(k1_relat_1(B)) = B))))) # label(t44_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1074 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k1_relat_1(C)) & r2_hidden(A,k1_relat_1(C)) -> k2_tarski(k1_funct_1(C,A),k1_funct_1(C,B)) = k9_relat_1(C,k2_tarski(A,B))))) # label(t118_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1075 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(k7_relat_1(B,A)),k2_relat_1(B)) & r1_tarski(k1_relat_1(k7_relat_1(B,A)),k1_relat_1(B)))) # label(t76_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1076 $T # label(d2_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1077 $T # label(t119_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1078 $T # label(t104_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1079 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(B,C) = k1_funct_1(A,C))) & k1_relat_1(A) = k1_relat_1(B) -> B = A))))) # label(t9_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1080 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),k1_relat_1(A)) & v2_funct_1(k5_relat_1(B,A)) -> v2_funct_1(B)))))) # label(t47_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1081 $T # label(t28_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1082 $T # label(t31_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1083 $T # label(t24_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1084 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k9_relat_1(k6_relat_1(A),B) = B)) # label(t162_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1085 $T # label(t30_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1086 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> v1_funct_1(k8_relat_1(A,B)) & v1_relat_1(k8_relat_1(A,B)))) # label(fc5_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1087 $T # label(t140_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1088 $T # label(t79_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1089 $T # label(t116_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1090 (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]. 56.07/55.13 1091 $T # label(t101_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1092 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B ((all C (r2_hidden(C,B) <-> (exists D (r2_hidden(D,k1_relat_1(A)) & k1_funct_1(A,D) = C)))) <-> B = k2_relat_1(A))))) # label(d5_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1093 $T # label(t102_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1094 $T # label(t13_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1095 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (A = k1_relat_1(C) & k2_relat_1(B) = A & k1_relat_1(D) = A & k5_relat_1(B,D) = k5_relat_1(B,C) -> D = C))))))) # label(t156_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1096 (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]. 56.07/55.13 1097 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k5_relat_1(k2_funct_1(A),A) = k6_relat_1(k2_relat_1(A)) & k6_relat_1(k1_relat_1(A)) = k5_relat_1(A,k2_funct_1(A))))) # label(t61_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1098 $T # label(d3_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1099 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k1_relat_1(k8_relat_1(A,C))) -> k1_funct_1(C,B) = k1_funct_1(k8_relat_1(A,C),B)))) # label(t87_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1100 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C -(r2_hidden(C,A) & (all D -(r2_hidden(D,k1_relat_1(B)) & C = k1_funct_1(B,D))))) -> r1_tarski(A,k2_relat_1(B))))) # label(t19_funct_1) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1101 (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]. 56.07/55.13 1102 (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]. 56.07/55.13 1103 (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]. 56.07/55.13 1104 (all A (v8_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)))) # label(t23_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1105 (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]. 56.07/55.13 1106 $T # label(t13_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1107 $T # label(t9_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1108 (all A (v1_relat_1(A) -> (all B ((all C all D (r2_hidden(k4_tarski(D,C),A) & r2_hidden(C,B) & r2_hidden(D,B) & r2_hidden(k4_tarski(C,D),A) -> D = C)) <-> r4_relat_2(A,B))))) # label(d4_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1109 (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]. 56.07/55.13 1110 (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]. 56.07/55.13 1111 (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]. 56.07/55.13 1112 (all A (v1_relat_1(A) -> (all B ((all C all D -(r2_hidden(C,B) & r2_hidden(D,B) & -r2_hidden(k4_tarski(C,D),A) & -r2_hidden(k4_tarski(D,C),A))) <-> r7_relat_2(A,B))))) # label(d7_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1113 (all A (v1_relat_1(A) -> (v2_relat_2(A) & v8_relat_2(A) -> v5_relat_2(A)))) # label(t25_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1114 (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]. 56.07/55.13 1115 (all A (v1_relat_1(A) -> (v5_relat_2(A) -> v2_relat_2(A) & v4_relat_2(A)))) # label(t26_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1116 (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]. 56.07/55.13 1117 $T # label(t1_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1118 (all A (v1_relat_1(A) -> (r1_tarski(k5_relat_1(A,A),A) <-> v8_relat_2(A)))) # label(t44_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1119 (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]. 56.07/55.13 1120 (all A (v1_relat_1(A) -> (all B (r2_relat_2(A,B) <-> (all C -(r2_hidden(C,B) & r2_hidden(k4_tarski(C,C),A))))))) # label(d2_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1121 (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]. 56.07/55.13 1122 $T # label(t7_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1123 $T # label(t5_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1124 (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]. 56.07/55.13 1125 (all A (v1_relat_1(A) -> (r6_relat_2(A,k3_relat_1(A)) <-> v6_relat_2(A)))) # label(d14_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1126 $T # label(t8_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1127 (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]. 56.07/55.13 1128 (all A (v1_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)))) # label(t24_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1129 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v4_relat_2(A) -> v4_relat_2(k3_xboole_0(A,B)) & v4_relat_2(k4_xboole_0(A,B))))))) # label(t41_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1130 $T # label(t4_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1131 (all A (v1_relat_1(A) -> (all B ((all C all D -(r2_hidden(C,B) & r2_hidden(k4_tarski(D,C),A) & r2_hidden(k4_tarski(C,D),A) & r2_hidden(D,B))) <-> r5_relat_2(A,B))))) # label(d5_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1132 (all A (v1_relat_1(A) -> (v7_relat_2(A) -> v1_relat_2(A) & v6_relat_2(A)))) # label(t46_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1133 (all A (v1_relat_1(A) -> (all B ((all C all D all E (r2_hidden(E,B) & r2_hidden(k4_tarski(C,D),A) & r2_hidden(C,B) & r2_hidden(D,B) & r2_hidden(k4_tarski(D,E),A) -> r2_hidden(k4_tarski(C,E),A))) <-> r8_relat_2(A,B))))) # label(d8_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1134 (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]. 56.07/55.13 1135 (all A (v1_relat_1(A) -> (v3_relat_2(A) <-> k4_relat_1(A) = A))) # label(t30_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1136 $T # label(t3_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1137 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v8_relat_2(A) & v8_relat_2(B) -> v8_relat_2(k3_xboole_0(A,B))))))) # label(t43_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1138 (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]. 56.07/55.13 1139 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v1_relat_2(A) & v1_relat_2(B) -> v1_relat_2(k2_xboole_0(A,B)) & v1_relat_2(k3_xboole_0(A,B))))))) # label(t31_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1140 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v3_relat_2(A) & v3_relat_2(B) -> v3_relat_2(k3_xboole_0(A,B)) & v3_relat_2(k4_xboole_0(A,B)) & v3_relat_2(k2_xboole_0(A,B))))))) # label(t35_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1141 (all A (v1_relat_1(A) -> (all B ((all C all D (r2_hidden(D,B) & r2_hidden(k4_tarski(C,D),A) & r2_hidden(C,B) -> r2_hidden(k4_tarski(D,C),A))) <-> r3_relat_2(A,B))))) # label(d3_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1142 $T # label(t2_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1143 $T # label(t14_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1144 (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]. 56.07/55.13 1145 (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]. 56.07/55.13 1146 (all A all B (v1_relat_1(B) -> (r4_relat_2(B,A) <-> r5_relat_2(k4_xboole_0(B,k6_relat_1(A)),A)))) # label(t19_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1147 $T # label(t10_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1148 (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]. 56.07/55.13 1149 $T # label(t15_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.07/55.13 1150 (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]. 56.16/55.13 1151 (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]. 56.16/55.13 1152 $T # label(t16_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1153 $T # label(t21_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1154 (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]. 56.16/55.13 1155 (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]. 56.16/55.13 1156 $T # label(t6_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1157 (all A (v1_relat_1(A) -> (all B ((all C (r2_hidden(C,B) -> r2_hidden(k4_tarski(C,C),A))) <-> r1_relat_2(A,B))))) # label(d1_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1158 (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]. 56.16/55.13 1159 (all A (v1_relat_1(A) -> (r3_relat_2(A,k3_relat_1(A)) <-> v3_relat_2(A)))) # label(d11_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1160 (all A (v1_relat_1(A) -> (v1_relat_2(A) -> k2_relat_1(k4_relat_1(A)) = k2_relat_1(A) & k1_relat_1(A) = k1_relat_1(k4_relat_1(A))))) # label(t29_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1161 (all A (v1_relat_1(A) -> (all B ((all C all D -(-r2_hidden(k4_tarski(C,D),A) & r2_hidden(C,B) & C != D & -r2_hidden(k4_tarski(D,C),A) & r2_hidden(D,B))) <-> r6_relat_2(A,B))))) # label(d6_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1162 $T # label(t11_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1163 $T # label(t12_relat_2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1164 (all A m1_ordinal1(k1_xboole_0,A)) # label(t45_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1165 (all A all B (v1_funct_1(A) & v3_ordinal1(B) & v1_relat_1(A) & v5_ordinal1(A) -> m1_ordinal1(k2_ordinal1(A,B),k2_relat_1(A)))) # label(dt_k2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1166 (all A all B all C all D all E all F -(r2_hidden(C,D) & r2_hidden(A,B) & r2_hidden(B,C) & r2_hidden(D,E) & r2_hidden(F,A) & r2_hidden(E,F))) # label(t6_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1167 (all A A != k1_ordinal1(A)) # label(t14_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1168 (all A (v3_ordinal1(A) -> (all B ((exists C ((all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k1_funct_1(C,D) = f3_s5_ordinal1(k2_ordinal1(C,D))))) & f3_s5_ordinal1(C) = B & v5_ordinal1(C) & v1_relat_1(C) & v1_funct_1(C) & k1_relat_1(C) = A)) <-> B = f2_s5_ordinal1(A))))) & (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s5_ordinal1)) -> k1_funct_1(f1_s5_ordinal1,A) = f2_s5_ordinal1(A)))) -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s5_ordinal1)) -> f3_s5_ordinal1(k2_ordinal1(f1_s5_ordinal1,A)) = k1_funct_1(f1_s5_ordinal1,A)))) # label(s5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1169 (exists A (v1_funct_1(A) & (all B (v3_ordinal1(B) -> (all C (v1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) -> (C = k2_ordinal1(A,B) & r2_hidden(B,f1_s4_ordinal1) -> k1_funct_1(A,B) = f2_s4_ordinal1(C)))))) & v1_relat_1(A) & v5_ordinal1(A) & k1_relat_1(A) = f1_s4_ordinal1)) # label(s4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1170 (all A all B -(r1_tarski(B,A) & r2_hidden(A,B))) # label(t7_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1171 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> r1_ordinal1(B,A) | r1_ordinal1(A,B))) # label(connectedness_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1172 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -(B != A & -r2_hidden(B,A) & -r2_hidden(A,B)))))) # label(t24_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1173 (all A all B (r2_hidden(A,B) | A = B <-> r2_hidden(A,k1_ordinal1(B)))) # label(t13_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1174 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> (r1_tarski(A,B) <-> r1_ordinal1(A,B)))) # label(redefinition_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1175 (exists A (v2_ordinal1(A) & v3_ordinal1(A) & v1_ordinal1(A))) # label(rc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1176 $T # label(t20_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1177 $T # label(t11_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1178 $T # label(dt_k1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1179 (exists A (v3_ordinal1(A) & p1_s1_ordinal1(A))) -> (exists A (p1_s1_ordinal1(A) & (all B (v3_ordinal1(B) -> (p1_s1_ordinal1(B) -> r1_ordinal1(A,B)))) & v3_ordinal1(A))) # label(s1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1180 (all A (v3_ordinal1(A) -> v3_ordinal1(k3_tarski(A)))) # label(t30_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1181 $T # label(t15_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1182 (all A -((all B (r2_hidden(B,A) -> v3_ordinal1(B))) & (all B (v3_ordinal1(B) -> -r1_tarski(A,B))))) # label(t36_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1183 (exists A (-v1_xboole_0(A) & v1_ordinal1(A) & v3_ordinal1(A) & v2_ordinal1(A))) # label(rc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1184 (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]. 56.16/55.13 1185 (exists A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A))) # label(rc4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1186 (all A (v1_ordinal1(A) & v2_ordinal1(A) -> v3_ordinal1(A))) # label(cc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1187 (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]. 56.16/55.13 1188 $T # label(t2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1189 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v5_ordinal1(A) <-> v3_ordinal1(k1_relat_1(A))))) # label(d7_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1190 f1_s3_ordinal1 = k1_relat_1(f3_s3_ordinal1) & k1_relat_1(f4_s3_ordinal1) = f1_s3_ordinal1 & (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) -> (r2_hidden(A,f1_s3_ordinal1) & k2_ordinal1(f3_s3_ordinal1,A) = B -> k1_funct_1(f3_s3_ordinal1,A) = f2_s3_ordinal1(B)))))) & (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) -> (B = k2_ordinal1(f4_s3_ordinal1,A) & r2_hidden(A,f1_s3_ordinal1) -> f2_s3_ordinal1(B) = k1_funct_1(f4_s3_ordinal1,A)))))) -> f4_s3_ordinal1 = f3_s3_ordinal1 # label(s3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1191 $T # label(t18_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1192 (exists A (v1_ordinal1(A) & v2_ordinal1(A) & v1_xboole_0(A) & v3_ordinal1(A) & v2_funct_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1193 (all A (v3_ordinal1(A) -> v2_ordinal1(k1_ordinal1(A)) & -v1_xboole_0(k1_ordinal1(A)) & v1_ordinal1(k1_ordinal1(A)) & v3_ordinal1(k1_ordinal1(A)))) # label(fc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1194 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> r1_ordinal1(A,A))) # label(reflexivity_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1195 (all A (v3_ordinal1(A) -> v1_ordinal1(A) & v2_ordinal1(A))) # label(cc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1196 (all A (v3_ordinal1(A) -> v3_ordinal1(k1_ordinal1(A)))) # label(t29_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1197 (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]. 56.16/55.13 1198 (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]. 56.16/55.13 1199 (all A all B (v3_ordinal1(B) -> (r2_hidden(A,B) -> v3_ordinal1(A)))) # label(t23_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1200 (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]. 56.16/55.13 1201 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> r3_xboole_0(A,B))))) # label(t25_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1202 (all A ((all B all C -(r2_hidden(C,A) & -r2_hidden(B,C) & C != B & -r2_hidden(C,B) & r2_hidden(B,A))) <-> v2_ordinal1(A))) # label(d3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1203 $T # label(t28_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1204 (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]. 56.16/55.13 1205 (all A all B (k1_ordinal1(A) = k1_ordinal1(B) -> A = B)) # label(t12_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1206 (all A -(all B (r2_hidden(B,A) <-> v3_ordinal1(B)))) # label(t37_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1207 (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]. 56.16/55.13 1208 (all A all B all C all D all E -(r2_hidden(A,B) & r2_hidden(E,A) & r2_hidden(B,C) & r2_hidden(D,E) & r2_hidden(C,D))) # label(t5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1209 $T # label(d5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1210 (all A exists B m1_ordinal1(B,A)) # label(existence_m1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1211 (all A -v1_xboole_0(k1_ordinal1(A))) # label(fc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1212 (all A all B (v1_relat_1(A) & v3_ordinal1(B) & v5_ordinal1(A) & v1_funct_1(A) -> k7_relat_1(A,B) = k2_ordinal1(A,B))) # label(redefinition_k2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1213 (all A (v4_ordinal1(A) <-> A = k3_tarski(A))) # label(d6_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1214 (all A (v1_xboole_0(A) -> v2_ordinal1(A) & v1_ordinal1(A) & v3_ordinal1(A))) # label(cc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1215 (all A all B (v3_ordinal1(B) -> -(r1_tarski(A,B) & (all C (v3_ordinal1(C) -> -((all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> r1_ordinal1(C,D)))) & r2_hidden(C,A)))) & k1_xboole_0 != A))) # label(t32_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1216 (all A -(all B (v3_ordinal1(B) -> r2_hidden(B,A)))) # label(t38_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1217 $T # label(t9_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1218 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> r2_hidden(B,A) | r1_ordinal1(A,B))))) # label(t26_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1219 (all A (v1_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(B,C) & r1_tarski(A,B) -> r2_hidden(A,C)))))))) # label(t22_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1220 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v3_ordinal1(k1_relat_1(A)) -> m1_ordinal1(A,k2_relat_1(A))))) # label(t46_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1221 $T # label(t17_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1222 $T # label(t44_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1223 $T # label(t16_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1224 (all A k2_xboole_0(A,k1_tarski(A)) = k1_ordinal1(A)) # label(d1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1225 $T # label(t1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.13 1226 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(A,k1_ordinal1(B)) <-> r1_ordinal1(A,B)))))) # label(t34_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1227 (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]. 56.16/55.14 1228 (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]. 56.16/55.14 1229 (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]. 56.16/55.14 1230 (all A all B (v5_ordinal1(B) & v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k2_relat_1(B),A) <-> m1_ordinal1(B,A)))) # label(d8_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1231 (all A r2_hidden(A,k1_ordinal1(A))) # label(t10_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1232 (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]. 56.16/55.14 1233 $T # label(t40_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1234 (all A (v2_ordinal1(A) & v1_ordinal1(A) <-> v3_ordinal1(A))) # label(d4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1235 (all A (v5_ordinal1(A) & v1_relat_1(A) & v1_funct_1(A) -> v1_ordinal1(k1_relat_1(A)) & v3_ordinal1(k1_relat_1(A)) & v2_ordinal1(k1_relat_1(A)))) # label(fc5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1236 $T # label(t8_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1237 (all A ((all B (r2_hidden(B,A) -> v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B))) & v6_ordinal1(A) -> v5_ordinal1(k3_tarski(A)) & v1_funct_1(k3_tarski(A)) & v1_relat_1(k3_tarski(A)))) # label(t49_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1238 (all A ((all B (r2_hidden(B,A) -> r1_tarski(B,A))) <-> v1_ordinal1(A))) # label(d2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1239 (all A (v3_ordinal1(A) -> (v4_ordinal1(A) <-> (all B (v3_ordinal1(B) -> (r2_hidden(B,A) -> r2_hidden(k1_ordinal1(B),A))))))) # label(t41_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1240 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v1_ordinal1(C) -> (r2_hidden(C,A) & r2_hidden(A,B) -> r2_hidden(C,B)))))))) # label(t19_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1241 (all A all B all C all D -(r2_hidden(B,C) & r2_hidden(D,A) & r2_hidden(A,B) & r2_hidden(C,D))) # label(t4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1242 $T # label(t43_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1243 (all A (v3_ordinal1(A) -> -(-v4_ordinal1(A) & (all B (v3_ordinal1(B) -> k1_ordinal1(B) != A))) & -((exists B (v3_ordinal1(B) & A = k1_ordinal1(B))) & v4_ordinal1(A)))) # label(t42_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1244 (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]. 56.16/55.14 1245 (all A ((all B (r2_hidden(B,A) -> v3_ordinal1(B) & r1_tarski(B,A))) -> v3_ordinal1(A))) # label(t31_ordinal1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1246 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> (all B -(r4_wellord1(A,k2_wellord1(A,k1_wellord1(A,B))) & r2_hidden(B,k3_relat_1(A))))))) # label(t57_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1247 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C all D (r2_hidden(k4_tarski(C,D),A) -> r2_hidden(k4_tarski(k1_funct_1(B,C),k1_funct_1(B,D)),A) & k1_funct_1(B,C) != k1_funct_1(B,D) | D = C)) & r1_tarski(k2_relat_1(B),k3_relat_1(A)) & k3_relat_1(A) = k1_relat_1(B) & v2_wellord1(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]. 56.16/55.14 1248 (all A all B (v1_relat_1(B) -> r1_tarski(k3_relat_1(k2_wellord1(B,A)),k3_relat_1(B)) & r1_tarski(k3_relat_1(k2_wellord1(B,A)),A))) # label(t20_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1249 (all A all B (v1_relat_1(B) -> (v2_wellord1(B) & r1_tarski(A,k3_relat_1(B)) -> ((all C (r2_hidden(C,A) -> (all D (r2_hidden(k4_tarski(D,C),B) -> r2_hidden(D,A))))) <-> -((all C -(r2_hidden(C,k3_relat_1(B)) & A = k1_wellord1(B,C))) & A != k3_relat_1(B)))))) # label(t36_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1250 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> -(-r4_wellord1(A,B) & v2_wellord1(A) & v2_wellord1(B) & (all C -(r2_hidden(C,k3_relat_1(B)) & r4_wellord1(A,k2_wellord1(B,k1_wellord1(B,C))))) & (all C -(r4_wellord1(k2_wellord1(A,k1_wellord1(A,C)),B) & r2_hidden(C,k3_relat_1(A))))))))) # label(t63_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1251 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (all E (v1_relat_1(E) & v1_funct_1(E) -> (r3_wellord1(A,B,D) & r3_wellord1(B,C,E) -> r3_wellord1(A,C,k5_relat_1(D,E))))))))))))) # label(t51_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1252 (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]. 56.16/55.14 1253 (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) -> (C = k3_wellord1(A,B) <-> r3_wellord1(A,B,C))))))))) # label(d9_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1254 (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]. 56.16/55.14 1255 (all A all B all C (v1_relat_1(C) -> k2_wellord1(C,k3_xboole_0(A,B)) = k2_wellord1(k2_wellord1(C,A),B))) # label(t26_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1256 (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) <-> (all D all E (r2_hidden(E,k3_relat_1(A)) & r2_hidden(D,k3_relat_1(A)) & r2_hidden(k4_tarski(k1_funct_1(C,D),k1_funct_1(C,E)),B) <-> r2_hidden(k4_tarski(D,E),A))) & v2_funct_1(C) & k2_relat_1(C) = k3_relat_1(B) & k3_relat_1(A) = k1_relat_1(C)))))))) # label(d7_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1257 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r4_wellord1(A,B) <-> (exists C (r3_wellord1(A,B,C) & v1_relat_1(C) & v1_funct_1(C)))))))) # label(d8_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1258 $T # label(t7_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1259 (all A all B (v1_relat_1(B) -> (r2_wellord1(B,A) -> (all C -((all D -((all E (r2_hidden(E,C) -> r2_hidden(k4_tarski(D,E),B))) & r2_hidden(D,C))) & r1_tarski(C,A) & C != k1_xboole_0))))) # label(t9_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1260 (all A (v1_relat_1(A) -> (all B (r4_relat_2(A,B) & r1_relat_2(A,B) & r1_wellord1(A,B) & r6_relat_2(A,B) & r8_relat_2(A,B) <-> r2_wellord1(A,B))))) # label(d5_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1261 (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) -> D = E | 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)))))))))) # label(t45_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1262 (all A all B all C (v1_relat_1(C) -> -(r2_hidden(B,k3_relat_1(C)) & A != B & r4_wellord1(k2_wellord1(C,k1_wellord1(C,A)),k2_wellord1(C,k1_wellord1(C,B))) & r2_hidden(A,k3_relat_1(C)) & v2_wellord1(C)))) # label(t58_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1263 (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]. 56.16/55.14 1264 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k2_wellord1(k2_wellord1(C,B),A) = k2_wellord1(C,A)))) # label(t29_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1265 $T # label(t1_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1266 (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,C) & r3_wellord1(A,B,D) -> C = D)))))))))) # label(t55_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1267 $T # label(t4_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1268 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r1_tarski(A,k3_relat_1(B)) & r3_wellord1(B,C,D) & v2_wellord1(B) -> r4_wellord1(k2_wellord1(B,A),k2_wellord1(C,k9_relat_1(D,A))) & r3_wellord1(k2_wellord1(B,A),k2_wellord1(C,k9_relat_1(D,A)),k7_relat_1(D,A))))))))) # label(t59_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1269 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> (all B -((all C -((all D (r2_hidden(D,B) -> r2_hidden(k4_tarski(C,D),A))) & r2_hidden(C,B))) & r1_tarski(B,k3_relat_1(A)) & B != k1_xboole_0))))) # label(t10_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1270 (all A all B all C all D (v1_relat_1(D) -> (all E (v1_relat_1(E) -> (v2_wellord1(D) & 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(A,k3_relat_1(D)) & r2_hidden(B,k3_relat_1(E)) & r2_hidden(C,k3_relat_1(E)) & v2_wellord1(E) -> 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]. 56.16/55.14 1271 (all A (v1_relat_1(A) -> (all B ((all C -(C != k1_xboole_0 & r1_tarski(C,B) & (all D -(r2_hidden(D,C) & r1_xboole_0(k1_wellord1(A,D),C))))) <-> r1_wellord1(A,B))))) # label(d3_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1272 (all A all B (v1_relat_1(B) -> r1_tarski(k2_wellord1(B,A),B) & r1_tarski(k2_wellord1(B,A),k2_zfmisc_1(A,A)))) # label(t15_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1273 $T # label(t56_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1274 (all A (v1_relat_1(A) -> (v4_relat_2(A) & v6_relat_2(A) & v1_wellord1(A) & v8_relat_2(A) & v1_relat_2(A) <-> v2_wellord1(A)))) # label(d4_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1275 (all A all B all C (v1_relat_1(C) -> (v2_wellord1(C) & r2_hidden(B,k3_relat_1(C)) & r2_hidden(A,k3_relat_1(C)) -> (B = A | r2_hidden(A,k1_wellord1(C,B)) <-> r1_tarski(k1_wellord1(C,A),k1_wellord1(C,B)))))) # label(t38_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1276 (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]. 56.16/55.14 1277 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k2_zfmisc_1(B,B)) & r2_hidden(A,C) <-> r2_hidden(A,k2_wellord1(C,B))))) # label(t16_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1278 $T # label(t44_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1279 (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)) <-> r2_hidden(k4_tarski(A,B),C))))) # label(t37_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1280 (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]. 56.16/55.14 1281 (all A (v1_relat_1(A) -> (all B all C (k1_wellord1(A,B) = C <-> (all D (r2_hidden(D,C) <-> B != D & r2_hidden(k4_tarski(D,B),A))))))) # label(d1_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1282 $T # label(t6_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1283 (all A (v1_relat_1(A) -> k2_wellord1(A,k3_relat_1(A)) = A)) # label(t30_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1284 (all A (v1_relat_1(A) -> (r1_wellord1(A,k3_relat_1(A)) <-> v1_wellord1(A)))) # label(t5_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1285 (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]. 56.16/55.14 1286 (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]. 56.16/55.14 1287 (all A all B (v1_relat_1(B) -> (v2_wellord1(B) & r1_tarski(A,k3_relat_1(B)) -> A = k3_relat_1(k2_wellord1(B,A))))) # label(t39_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1288 (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]. 56.16/55.14 1289 (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]. 56.16/55.14 1290 (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]. 56.16/55.14 1291 (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_wellord1(A) -> (all D -((all E -(r2_hidden(E,k3_relat_1(B)) & r4_wellord1(k2_wellord1(A,k1_wellord1(A,D)),k2_wellord1(B,k1_wellord1(B,E))))) & r2_hidden(D,k3_relat_1(A))))))))))) # label(t61_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1292 (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]. 56.16/55.14 1293 (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]. 56.16/55.14 1294 (all A (v1_relat_1(A) -> ((all B -(k1_xboole_0 != B & (all C -(r2_hidden(C,B) & r1_xboole_0(k1_wellord1(A,C),B))) & r1_tarski(B,k3_relat_1(A)))) <-> v1_wellord1(A)))) # label(d2_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1295 (all A (v1_relat_1(A) -> (v2_wellord1(A) <-> r2_wellord1(A,k3_relat_1(A))))) # label(t8_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1296 (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]. 56.16/55.14 1297 (all A all B (v1_relat_1(B) -> k8_relat_1(A,k7_relat_1(B,A)) = k2_wellord1(B,A))) # label(t18_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1298 $T # label(t14_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1299 (all A (v1_relat_1(A) -> r4_wellord1(A,A))) # label(t48_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1300 (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) -> (v1_wellord1(A) -> v1_wellord1(B)) & (v4_relat_2(A) -> v4_relat_2(B)) & (v6_relat_2(A) -> v6_relat_2(B)) & (v1_relat_2(A) -> v1_relat_2(B)) & (v8_relat_2(A) -> v8_relat_2(B))))))))) # label(t53_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1301 (all A all B all C (v1_relat_1(C) -> (r2_hidden(B,k3_relat_1(C)) & v2_wellord1(C) & r2_hidden(A,k3_relat_1(C)) & (all D (r2_hidden(D,k1_wellord1(C,A)) -> r2_hidden(k4_tarski(D,B),C) & B != D)) -> r2_hidden(k4_tarski(A,B),C)))) # label(t42_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1302 (all A all B (v1_relat_1(B) -> -(r1_tarski(A,k3_relat_1(B)) & (all C -(r2_hidden(C,k3_relat_1(B)) & r4_wellord1(k2_wellord1(B,k1_wellord1(B,C)),k2_wellord1(B,A)))) & v2_wellord1(B) & -r4_wellord1(B,k2_wellord1(B,A))))) # label(t64_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1303 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> (all B -((all C -(r2_hidden(k4_tarski(B,C),A) & (all D -(r2_hidden(D,k3_relat_1(A)) & r2_hidden(k4_tarski(B,D),A) & -r2_hidden(k4_tarski(C,D),A) & D != B)) & r2_hidden(C,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)))) | k1_xboole_0 = k3_relat_1(A)))) # label(t12_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1304 $T # label(t46_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1305 (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]. 56.16/55.14 1306 (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) -> r3_wellord1(B,A,k2_funct_1(C))))))))) # label(t49_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1307 (all A (v1_relat_1(A) -> -(v2_wellord1(A) & k3_relat_1(A) != k1_xboole_0 & (all B -(r2_hidden(B,k3_relat_1(A)) & (all C (r2_hidden(C,k3_relat_1(A)) -> r2_hidden(k4_tarski(B,C),A)))))))) # label(t11_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1308 (all A all B (v1_relat_1(A) & v1_relat_1(B) -> v1_relat_1(k3_wellord1(A,B)) & v1_funct_1(k3_wellord1(A,B)))) # label(dt_k3_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1309 (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]. 56.16/55.14 1310 (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]. 56.16/55.14 1311 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r4_wellord1(A,B) & r4_wellord1(B,C) -> r4_wellord1(A,C)))))))) # label(t52_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1312 $T # label(dt_k1_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1313 (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 -((all E -(k9_relat_1(C,k1_wellord1(A,D)) = k1_wellord1(B,E) & r2_hidden(E,k3_relat_1(B)))) & r2_hidden(D,k3_relat_1(A))))))))))) # label(t60_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1314 (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]. 56.16/55.14 1315 (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]. 56.16/55.14 1316 $T # label(t34_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1317 (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]. 56.16/55.14 1318 $T # label(t3_wellord1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1319 (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]. 56.16/55.14 1320 (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]. 56.16/55.14 1321 (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]. 56.16/55.14 1322 (all A all B all C all D (r2_hidden(C,A) & r2_hidden(D,B) -> m2_relset_1(k1_tarski(k4_tarski(C,D)),A,B))) # label(t8_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1323 (all A all B m2_relset_1(k1_xboole_0,A,B)) # label(t25_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1324 (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]. 56.16/55.14 1325 (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]. 56.16/55.14 1326 (all A all B all C (m2_relset_1(C,B,A) -> ((all D -((all E -r2_hidden(k4_tarski(D,E),C)) & r2_hidden(D,B))) <-> k4_relset_1(B,A,C) = B))) # label(t22_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1327 (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]. 56.16/55.14 1328 $T # label(t44_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1329 (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]. 56.16/55.14 1330 (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]. 56.16/55.14 1331 (all A all B all C (v1_relat_1(C) -> (r1_tarski(k2_relat_1(C),B) & r1_tarski(k1_relat_1(C),A) -> m2_relset_1(C,A,B)))) # label(t11_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1332 $T # label(t40_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1333 (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]. 56.16/55.14 1334 $T # label(t41_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1335 (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]. 56.16/55.14 1336 (all A all B all C (m1_relset_1(C,A,B) -> k5_relset_1(A,B,C) = k2_relat_1(C))) # label(redefinition_k5_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1337 (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]. 56.16/55.14 1338 (all A all B all C (m2_relset_1(C,B,A) -> (m2_relset_1(C,B,k1_xboole_0) -> C = k1_xboole_0))) # label(t27_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1339 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) -> (all D (m1_subset_1(D,A) -> ((exists E (r2_hidden(k4_tarski(D,E),C) & m1_subset_1(E,B))) <-> r2_hidden(D,k4_relset_1(A,B,C))))))))))) # label(t47_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1340 (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]. 56.16/55.14 1341 $T # label(t20_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1342 (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]. 56.16/55.14 1343 (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]. 56.16/55.14 1344 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> C = k2_relset_1(A,B,C,C))) # label(idempotence_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1345 (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]. 56.16/55.14 1346 (all A all B all C all D (m2_relset_1(D,A,B) -> (r1_tarski(B,C) -> k9_relset_1(A,B,C,D) = D))) # label(t36_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1347 (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]. 56.16/55.14 1348 (all A all B all C all D (m2_relset_1(D,A,B) -> (r1_tarski(k6_relat_1(C),D) -> r1_tarski(C,k4_relset_1(A,B,D)) & r1_tarski(C,k5_relset_1(A,B,D))))) # label(t30_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.14 1349 (all A all B all C all D all E (m2_relset_1(E,A,C) -> (r1_tarski(C,D) & r1_tarski(A,B) -> m2_relset_1(E,B,D)))) # label(t17_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1350 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) -> (all D (m1_subset_1(D,A) -> -((all E (m1_subset_1(E,B) -> -r2_hidden(E,k5_relset_1(A,B,C)))) & r2_hidden(D,k4_relset_1(A,B,C))))))))))) # label(t49_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1351 $T # label(t7_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1352 (all A all B (m2_relset_1(B,A,A) -> k5_relat_1(B,k6_relat_1(A)) = B & B = k5_relat_1(k6_relat_1(A),B))) # label(t45_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1353 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> k2_relset_1(A,B,C,D) = k3_xboole_0(C,D))) # label(redefinition_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1354 (all A all B all C (m2_relset_1(C,A,B) -> k5_relset_1(A,B,C) = k10_relset_1(A,B,C,A) & k11_relset_1(A,B,C,B) = k4_relset_1(A,B,C))) # label(t38_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1355 (all A all B all C (m2_relset_1(C,A,B) <-> m1_relset_1(C,A,B))) # label(redefinition_m2_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1356 $T # label(t2_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1357 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,B) -> (all E (m2_relset_1(E,B,C) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,C) -> ((exists H (r2_hidden(k4_tarski(F,H),D) & r2_hidden(k4_tarski(H,G),E) & m1_subset_1(H,B))) <-> r2_hidden(k4_tarski(F,G),k7_relset_1(A,B,B,C,D,E))))))))))))))))) # label(t51_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1358 (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]. 56.16/55.15 1359 $T # label(t5_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1360 (all A all B all C (m2_relset_1(C,A,B) -> k5_relset_1(A,B,C) = k4_relset_1(B,A,k6_relset_1(A,B,C)) & k5_relset_1(B,A,k6_relset_1(A,B,C)) = k4_relset_1(A,B,C))) # label(t24_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1361 $T # label(t1_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1362 (all A all B all C all D (m2_relset_1(D,A,B) -> -(r2_hidden(C,D) & (all E all F -(r2_hidden(E,A) & C = k4_tarski(E,F) & r2_hidden(F,B)))))) # label(t6_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1363 (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]. 56.16/55.15 1364 (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]. 56.16/55.15 1365 (all A all B all C (r1_tarski(C,k2_zfmisc_1(A,B)) <-> m1_relset_1(C,A,B))) # label(d1_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1366 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1367 $T # label(t37_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1368 (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]. 56.16/55.15 1369 $T # label(t43_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1370 (all A all B all C (m2_relset_1(C,A,B) -> ((all D -(r2_hidden(D,B) & (all E -r2_hidden(k4_tarski(E,D),C)))) <-> B = k5_relset_1(A,B,C)))) # label(t23_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1371 (all A all B all C (m2_relset_1(C,A,B) -> (r1_tarski(k6_relat_1(B),C) -> k5_relset_1(A,B,C) = B & r1_tarski(B,k4_relset_1(A,B,C))))) # label(t32_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1372 (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]. 56.16/55.15 1373 (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]. 56.16/55.15 1374 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> k2_xboole_0(C,D) = k1_relset_1(A,B,C,D))) # label(redefinition_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1375 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> k2_relset_1(A,B,C,D) = k2_relset_1(A,B,D,C))) # label(commutativity_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1376 $T # label(t18_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1377 (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]. 56.16/55.15 1378 (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]. 56.16/55.15 1379 (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]. 56.16/55.15 1380 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,C) -> (all E (m1_subset_1(E,A) -> (r2_hidden(E,k11_relset_1(A,C,D,B)) <-> (exists F (r2_hidden(k4_tarski(E,F),D) & m1_subset_1(F,C) & r2_hidden(F,B)))))))))))))) # label(t53_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1381 $T # label(t3_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1382 (all A all B exists C m1_relset_1(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1383 (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]. 56.16/55.15 1384 (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]. 56.16/55.15 1385 $T # label(t21_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1386 (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]. 56.16/55.15 1387 (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]. 56.16/55.15 1388 (exists A (m2_relset_1(A,f1_s1_relset_1,f2_s1_relset_1) & (all B all C (p1_s1_relset_1(B,C) & r2_hidden(B,f1_s1_relset_1) & r2_hidden(C,f2_s1_relset_1) <-> r2_hidden(k4_tarski(B,C),A))))) # label(s1_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1389 (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]. 56.16/55.15 1390 $T # label(t42_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1391 (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]. 56.16/55.15 1392 (all A all B all C (m2_relset_1(C,A,B) -> (m2_relset_1(C,k1_xboole_0,B) -> C = k1_xboole_0))) # label(t26_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1393 (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]. 56.16/55.15 1394 (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]. 56.16/55.15 1395 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> k1_relset_1(A,B,C,C) = C)) # label(idempotence_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1396 (all A all B all C all D (m1_relset_1(C,A,B) -> k11_relset_1(A,B,C,D) = k10_relat_1(C,D))) # label(redefinition_k11_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1397 (all A r1_tarski(k6_relat_1(A),k2_zfmisc_1(A,A))) # label(t28_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1398 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> m2_relset_1(k3_relset_1(A,B,C,D),A,B))) # label(dt_k3_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1399 (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]. 56.16/55.15 1400 (all A all B all C all D (m1_relset_1(C,A,B) -> k9_relat_1(C,D) = k10_relset_1(A,B,C,D))) # label(redefinition_k10_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1401 (all A all B all C (m1_relset_1(C,A,B) -> k6_relset_1(A,B,C) = k4_relat_1(C))) # label(redefinition_k6_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1402 (all A all B all C all D all E all F (m1_relset_1(E,A,B) & m1_relset_1(F,C,D) -> m2_relset_1(k7_relset_1(A,B,C,D,E,F),A,D))) # label(dt_k7_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1403 (all A all B exists C m2_relset_1(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1404 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> k1_relset_1(A,B,D,C) = k1_relset_1(A,B,C,D))) # label(commutativity_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1405 (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]. 56.16/55.15 1406 (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]. 56.16/55.15 1407 (all A m2_relset_1(k6_relat_1(A),A,A)) # label(t29_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1408 (all A all B all C all D all E all F (m1_relset_1(F,C,D) & m1_relset_1(E,A,B) -> k5_relat_1(E,F) = k7_relset_1(A,B,C,D,E,F))) # label(redefinition_k7_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1409 (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]. 56.16/55.15 1410 (all A (-v1_xboole_0(A) -> k6_relat_1(A) != k1_xboole_0)) # label(t46_relset_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1411 (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]. 56.16/55.15 1412 $T # label(t155_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1413 (all A all B all C (k4_partfun1(A,B) = C <-> (all D ((exists E (r1_tarski(k2_relat_1(E),B) & v1_funct_1(E) & D = E & r1_tarski(k1_relat_1(E),A) & v1_relat_1(E))) <-> r2_hidden(D,C))))) # label(d5_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1414 (all A all B -v1_xboole_0(k4_partfun1(A,B))) # label(fc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1415 $T # label(t42_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1416 (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]. 56.16/55.15 1417 $T # label(d2_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1418 (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]. 56.16/55.15 1419 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> r1_partfun1(k3_partfun1(C,A,B),C))) # label(t147_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1420 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (D = k5_partfun1(A,B,C) <-> (all E ((exists F (m2_relset_1(F,A,B) & r1_partfun1(C,F) & v1_partfun1(F,A,B) & E = F & v1_funct_1(F))) <-> r2_hidden(E,D))))))) # label(d7_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1421 (all A k4_partfun1(k1_xboole_0,A) = k1_tarski(k1_xboole_0)) # label(t122_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1422 $T # label(t129_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1423 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (-r1_xboole_0(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) -> r1_partfun1(C,D)))))) # label(t185_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1424 $T # label(t20_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1425 $T # label(t156_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1426 $T # label(d1_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1427 $T # label(t164_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1428 $T # label(t98_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1429 $T # label(t5_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1430 $T # label(t4_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1431 (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]. 56.16/55.15 1432 (exists A (v1_relat_1(A) & v1_funct_1(A) & (all B (r2_hidden(B,f1_s1_partfun1) -> (-p1_s1_partfun1(B) -> f3_s1_partfun1(B) = k1_funct_1(A,B)) & (p1_s1_partfun1(B) -> k1_funct_1(A,B) = f2_s1_partfun1(B)))) & f1_s1_partfun1 = k1_relat_1(A))) # label(s1_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1433 $T # label(t40_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1434 (all A all B all C (m2_relset_1(C,A,B) -> (k4_relset_1(A,B,C) = A <-> v1_partfun1(C,A,B)))) # label(d4_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1435 $T # label(t108_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1436 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> k3_partfun1(C,A,B) = C)) # label(t87_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1437 $T # label(t161_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1438 $T # label(t134_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1439 $T # label(t6_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1440 $T # label(t184_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1441 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (v2_funct_1(C) -> m2_relset_1(k2_funct_1(C),B,A) & v1_funct_1(k2_funct_1(C))))) # label(t39_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1442 (all A all B all C all D all E (v1_relat_1(E) & v1_funct_1(E) -> (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k3_partfun1(E,A,C),k3_partfun1(E,B,D))))) # label(t84_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1443 $T # label(t109_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1444 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> -((all E (m2_relset_1(E,A,B) & v1_funct_1(E) -> -(r1_partfun1(C,E) & r1_partfun1(D,E) & v1_partfun1(E,A,B)))) & r1_partfun1(C,D) & (B = k1_xboole_0 -> A = k1_xboole_0)))))) # label(t162_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1445 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k2_xboole_0(A,B) = C -> (all D (r2_hidden(D,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(B,D) = k1_funct_1(A,D)))))))))) # label(t3_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1446 (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]. 56.16/55.15 1447 $T # label(t152_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1448 $T # label(t159_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1449 (all A all B all C all D (m1_relset_1(C,A,B) & v1_funct_1(C) -> k2_partfun1(A,B,C,D) = k7_relat_1(C,D))) # label(redefinition_k2_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1450 (all A all B (v1_funct_1(B) & m2_relset_1(B,k1_xboole_0,A) -> k1_tarski(B) = k5_partfun1(k1_xboole_0,A,B))) # label(t175_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1451 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_partfun1(k8_relat_1(A,B),B))) # label(t145_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1452 $T # label(t133_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1453 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> k3_partfun1(D,B,k3_xboole_0(A,C)) = k9_relset_1(B,C,A,k3_partfun1(D,B,C)))) # label(t97_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1454 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(k1_funct_1(D,A),C) & r2_hidden(A,B) & k1_tarski(A) = k1_relat_1(D) -> v1_funct_1(D) & m2_relset_1(D,B,C)))) # label(t72_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1455 (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]. 56.16/55.15 1456 (all A all B all C all D (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k4_partfun1(A,C),k4_partfun1(B,D)))) # label(t128_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1457 $T # label(dt_k5_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1458 $T # label(t50_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1459 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> m2_relset_1(k8_relset_1(A,B,D,C),C,B) & v1_funct_1(k8_relset_1(A,B,D,C)))) # label(t43_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1460 (all A all B (p1_s5_partfun1(A,B) -> r2_hidden(f4_s5_partfun1(A,B),f3_s5_partfun1))) -> (exists A (v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1) & (all B all C (r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1,A)) -> f4_s5_partfun1(B,C) = k1_funct_1(A,k4_tarski(B,C)))) & (all B all C (p1_s5_partfun1(B,C) & r2_hidden(C,f2_s5_partfun1) & r2_hidden(B,f1_s5_partfun1) <-> r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1,A)))))) # label(s5_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1461 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_partfun1(A,B) <-> (all C (r2_hidden(C,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(A,C) = k1_funct_1(B,C)))))))) # label(d6_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1462 (all A exists B (v4_relat_2(B) & v1_relat_1(B) & m1_relset_1(B,A,A) & v3_relat_2(B) & v1_partfun1(B,A,A) & v8_relat_2(B) & v1_relat_2(B))) # label(rc3_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1463 $T # label(t167_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1464 (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]. 56.16/55.15 1465 (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]. 56.16/55.15 1466 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((exists C (r1_tarski(B,C) & r1_tarski(A,C) & v1_relat_1(C) & v1_funct_1(C))) <-> r1_partfun1(A,B)))))) # label(t131_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1467 $T # label(t8_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1468 $T # label(t103_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1469 (all A all B all C (m1_subset_1(C,k4_partfun1(A,B)) -> m2_relset_1(C,A,B) & v1_funct_1(C))) # label(t121_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1470 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,B) -> r1_partfun1(A,B)))))) # label(t135_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1471 $T # label(t75_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1472 (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]. 56.16/55.15 1473 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_xboole_0) -> k9_relat_1(C,B) = k1_xboole_0)) # label(t67_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1474 $T # label(t177_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1475 $T # label(t151_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1476 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k9_relat_1(C,A),B) & r1_tarski(A,k1_relat_1(C)) -> v1_partfun1(k3_partfun1(C,A,B),A,B)))) # label(t117_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1477 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r2_hidden(C,k4_relset_1(A,B,D)) -> r2_hidden(k1_funct_1(D,C),B)))) # label(t27_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1478 (all A all B (v1_funct_1(B) & m2_relset_1(B,k1_xboole_0,A) -> k4_relset_1(k1_xboole_0,A,B) = k1_xboole_0 & k2_relat_1(B) = k1_xboole_0)) # label(t54_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1479 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> m2_relset_1(B,k1_relat_1(B),A) & v1_funct_1(B)))) # label(t25_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1480 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_xboole_0) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,k1_xboole_0) -> D = C)))) # label(t65_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1481 $T # label(t150_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1482 $T # label(t16_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1483 $T # label(t165_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1484 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (v1_partfun1(C,A,B) & v1_partfun1(D,A,B) & r1_partfun1(C,D) -> D = C))))) # label(t148_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1485 (all A all B (m2_relset_1(B,A,k1_xboole_0) & v1_funct_1(B) -> k1_xboole_0 = B)) # label(t64_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1486 (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]. 56.16/55.15 1487 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(C) = k1_xboole_0 -> v1_funct_1(C) & m2_relset_1(C,A,B)))) # label(t55_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1488 (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]. 56.16/55.15 1489 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (v2_funct_1(C) -> v2_funct_1(k3_partfun1(C,A,B))))) # label(t94_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1490 (all A all B (m2_relset_1(B,A,k1_xboole_0) & v1_funct_1(B) -> (A != k1_xboole_0 -> k1_xboole_0 = k5_partfun1(A,k1_xboole_0,B)))) # label(t172_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1491 $T # label(t21_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1492 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> k10_relat_1(C,B) = k4_relset_1(A,B,C))) # label(t53_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.15 1493 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (r2_hidden(D,k4_relset_1(A,B,C)) & r2_hidden(E,k4_relset_1(A,B,C)) & k1_funct_1(C,E) = k1_funct_1(C,D) -> E = D))))) -> v2_funct_1(C)))) # label(t38_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1494 (all A all B (m2_relset_1(k1_xboole_0,A,B) & v1_funct_1(k1_xboole_0))) # label(t56_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1495 (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]. 56.16/55.16 1496 $T # label(t52_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1497 $T # label(t118_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1498 $T # label(t88_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1499 $T # label(t149_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1500 (all A all B (r2_hidden(A,f1_s2_partfun1) & p1_s2_partfun1(A,B) -> r2_hidden(B,f2_s2_partfun1))) & (all A all B all C (p1_s2_partfun1(A,B) & p1_s2_partfun1(A,C) & r2_hidden(A,f1_s2_partfun1) -> B = C)) -> (exists A (v1_funct_1(A) & (all B (r2_hidden(B,k4_relset_1(f1_s2_partfun1,f2_s2_partfun1,A)) -> p1_s2_partfun1(B,k1_funct_1(A,B)))) & (all B (r2_hidden(B,f1_s2_partfun1) & (exists C p1_s2_partfun1(B,C)) <-> r2_hidden(B,k4_relset_1(f1_s2_partfun1,f2_s2_partfun1,A)))) & m2_relset_1(A,f1_s2_partfun1,f2_s2_partfun1))) # label(s2_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1501 $T # label(t104_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1502 $T # label(t154_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1503 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (k5_partfun1(A,B,C) = k1_tarski(C) <-> v1_partfun1(C,A,B)))) # label(t174_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1504 (all A all B all C all D (m1_relset_1(C,A,B) & v1_funct_1(C) -> m2_relset_1(k2_partfun1(A,B,C,D),A,B) & v1_funct_1(k2_partfun1(A,B,C,D)))) # label(dt_k2_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1505 $T # label(t181_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1506 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> -(r1_partfun1(C,D) & r1_xboole_0(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) & (B = k1_xboole_0 -> k1_xboole_0 = A)))))) # label(t186_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1507 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> v1_funct_1(k8_relset_1(A,B,D,C)) & m2_relset_1(k8_relset_1(A,B,D,C),A,B))) # label(t44_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1508 (all A all B all C all D (m2_relset_1(D,A,k1_tarski(B)) & v1_funct_1(D) -> (r2_hidden(C,k4_relset_1(A,k1_tarski(B),D)) -> B = k1_funct_1(D,C)))) # label(t73_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1509 (all A (v1_relat_1(A) & v3_relat_2(A) & v8_relat_2(A) -> v1_relat_2(A) & v1_relat_1(A))) # label(cc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1510 (all A all B (v1_funct_1(B) & m2_relset_1(B,k1_xboole_0,A) -> B = k1_xboole_0)) # label(t57_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1511 $T # label(t153_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1512 $T # label(t15_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1513 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r2_hidden(D,k5_partfun1(A,B,C)) -> v1_partfun1(D,A,B)))))) # label(t169_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1514 $T # label(t166_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1515 (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]. 56.16/55.16 1516 (all A all B (v1_funct_1(B) & v1_relat_1(A) & v1_relat_1(B) & v1_funct_1(A) -> r1_partfun1(A,A))) # label(reflexivity_r1_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1517 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> r2_hidden(C,k4_partfun1(A,B)))) # label(t119_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1518 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> -((all C (r2_hidden(C,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(B,C) = k1_funct_1(A,C))) & (all C (v1_funct_1(C) & v1_relat_1(C) -> k2_xboole_0(A,B) != C))))))) # label(t2_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1519 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_partfun1(k3_partfun1(k1_xboole_0,A,B),C))) # label(t142_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1520 (all A all B all C (m2_relset_1(C,A,B) -> C = k5_relat_1(k6_relat_1(A),C))) # label(t36_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1521 $T # label(t13_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1522 (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]. 56.16/55.16 1523 (all A all B exists C (v1_funct_1(C) & m1_relset_1(C,A,B) & v1_relat_1(C))) # label(rc2_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1524 $T # label(t178_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1525 $T # label(t111_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1526 $T # label(t163_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1527 (all A (v1_relat_1(A) & v1_funct_1(A) -> k3_partfun1(A,k1_relat_1(A),k2_relat_1(A)) = A)) # label(t86_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1528 (exists A (v1_xboole_0(A) & v1_relat_1(A) & v2_funct_1(A) & v1_funct_1(A))) # label(rc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1529 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (k4_relset_1(A,B,D) = k4_relset_1(A,B,C) & (all E (m1_subset_1(E,A) -> (r2_hidden(E,k4_relset_1(A,B,C)) -> k1_funct_1(D,E) = k1_funct_1(C,E)))) -> C = D))))) # label(t34_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1530 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_xboole_0) -> k10_relat_1(C,B) = k1_xboole_0)) # label(t68_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1531 (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]. 56.16/55.16 1532 $T # label(t100_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1533 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,k1_xboole_0,A) -> k9_relat_1(C,B) = k1_xboole_0)) # label(t60_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1534 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v1_partfun1(k3_partfun1(C,A,B),A,B) -> r1_tarski(k9_relat_1(C,A),B)))) # label(t116_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1535 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_relat_1(E) -> r1_tarski(k1_partfun1(C,A,A,B,k3_partfun1(D,C,A),k3_partfun1(E,A,B)),k3_partfun1(k5_relat_1(D,E),C,B)))))) # label(t92_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1536 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m2_relset_1(E,A,B) & v1_funct_1(E) -> (v1_partfun1(E,A,B) & r1_partfun1(D,E) & r1_partfun1(C,E) -> r1_partfun1(C,D)))))))) # label(t158_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1537 $T # label(t105_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1538 (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]. 56.16/55.16 1539 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (all E (v1_relat_1(E) & v1_funct_1(E) -> (r1_tarski(k3_xboole_0(k2_relat_1(D),k1_relat_1(E)),A) -> k3_partfun1(k5_relat_1(D,E),C,B) = k1_partfun1(C,A,A,B,k3_partfun1(D,C,A),k3_partfun1(E,A,B))))))) # label(t93_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1540 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> -((all E (m1_subset_1(E,A) -> -(r2_hidden(E,k4_relset_1(A,B,D)) & k1_funct_1(D,E) = C))) & r2_hidden(C,k2_relat_1(D))))) # label(t26_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1541 $T # label(t160_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1542 $T # label(t17_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1543 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (k1_xboole_0 = B & v1_partfun1(C,A,B) -> A = k1_xboole_0))) # label(t99_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1544 $T # label(t19_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1545 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(A) & m2_relset_1(A,k1_relat_1(A),k2_relat_1(A)))) # label(t24_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1546 $T # label(t7_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1547 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,k1_xboole_0,A) -> (all D (v1_funct_1(D) & m2_relset_1(D,k1_xboole_0,B) -> C = D)))) # label(t58_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1548 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> r1_partfun1(A,B)))))) # label(t138_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1549 $T # label(t9_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1550 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((exists C (k2_xboole_0(A,B) = C & v1_relat_1(C) & v1_funct_1(C))) <-> r1_partfun1(A,B)))))) # label(t130_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1551 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,C) & r1_tarski(B,C) -> r1_partfun1(A,B)))))))) # label(t139_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1552 (all A all B (v1_partfun1(k3_partfun1(k1_xboole_0,A,B),A,B) -> A = k1_xboole_0)) # label(t114_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1553 (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]. 56.16/55.16 1554 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r1_tarski(k2_relat_1(D),C) -> m2_relset_1(D,A,C) & v1_funct_1(D)))) # label(t29_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1555 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_xboole_0 = k2_relat_1(C) -> m2_relset_1(C,A,B) & v1_funct_1(C)))) # label(t63_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1556 (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]. 56.16/55.16 1557 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C k7_relat_1(k8_relat_1(C,A),B) = k3_partfun1(A,B,C)))) # label(d3_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1558 (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]. 56.16/55.16 1559 $T # label(t179_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1560 (all A all B all C (p1_s4_partfun1(A,B,C) & r2_hidden(B,f2_s4_partfun1) & r2_hidden(A,f1_s4_partfun1) -> r2_hidden(C,f3_s4_partfun1))) & (all A all B all C all D (p1_s4_partfun1(A,B,D) & p1_s4_partfun1(A,B,C) & r2_hidden(B,f2_s4_partfun1) & r2_hidden(A,f1_s4_partfun1) -> D = C)) -> (exists A (m2_relset_1(A,k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1) & v1_funct_1(A) & (all B all C (r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1,A)) -> p1_s4_partfun1(B,C,k1_funct_1(A,k4_tarski(B,C))))) & (all B all C (r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1,A)) <-> r2_hidden(C,f2_s4_partfun1) & (exists D p1_s4_partfun1(B,C,D)) & r2_hidden(B,f1_s4_partfun1))))) # label(s4_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1561 (all A (v3_relat_2(k6_relat_1(A)) & v8_relat_2(k6_relat_1(A)) & v1_relat_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)))) # label(fc2_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1562 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,k1_tarski(A),B) -> r1_tarski(k9_relat_1(D,C),k1_tarski(k1_funct_1(D,A))))) # label(t71_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1563 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k1_relat_1(A),k1_relat_1(B)) -> (r1_partfun1(A,B) <-> (all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(B,C) = k1_funct_1(A,C))))))))) # label(t132_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1564 (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]. 56.16/55.16 1565 (all A k1_tarski(k1_xboole_0) = k4_partfun1(A,k1_xboole_0)) # label(t123_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1566 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(A,B) & r2_hidden(A,k1_relat_1(D)) & r2_hidden(k1_funct_1(D,A),C) <-> r2_hidden(A,k4_relset_1(B,C,k3_partfun1(D,B,C)))))) # label(t78_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1567 $T # label(t173_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1568 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> m2_relset_1(k7_relat_1(k8_relat_1(A,C),B),B,A) & v1_funct_1(k7_relat_1(k8_relat_1(A,C),B)))) # label(t47_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1569 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> k9_relat_1(C,A) = k2_relat_1(C))) # label(t51_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1570 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> v1_partfun1(B,k1_xboole_0,A))) # label(t112_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1571 $T # label(t14_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1572 $T # label(t89_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1573 $T # label(t23_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1574 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r1_tarski(B,C) -> v1_funct_1(D) & m2_relset_1(D,A,C)))) # label(t31_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1575 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(k4_relset_1(A,B,D),C) -> v1_funct_1(D) & m2_relset_1(D,C,B)))) # label(t28_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1576 (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]. 56.16/55.16 1577 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_partfun1(A,B) & k1_relat_1(A) = k1_relat_1(B) -> A = B))))) # label(t136_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1578 $T # label(t157_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1579 $T # label(t183_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1580 (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]. 56.16/55.16 1581 (all A all B all C all D all E all F (m1_relset_1(F,C,D) & v1_funct_1(E) & m1_relset_1(E,A,B) & v1_funct_1(F) -> k5_relat_1(E,F) = k1_partfun1(A,B,C,D,E,F))) # label(redefinition_k1_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1582 (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]. 56.16/55.16 1583 $T # label(t41_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1584 $T # label(t48_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1585 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(A,B) & r2_hidden(A,k1_relat_1(D)) & r2_hidden(k1_funct_1(D,A),C) -> k1_funct_1(D,A) = k1_funct_1(k3_partfun1(D,B,C),A)))) # label(t79_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1586 $T # label(t18_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1587 $T # label(t124_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1588 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(D,k5_partfun1(A,B,C)) -> r1_partfun1(C,D)))))) # label(t171_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1589 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,k1_xboole_0) -> v2_funct_1(B))) # label(t66_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1590 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> m2_relset_1(k9_relset_1(A,B,C,D),A,C) & v1_funct_1(k9_relset_1(A,B,C,D)))) # label(t45_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1591 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,k1_xboole_0) -> k4_relset_1(A,k1_xboole_0,B) = k1_xboole_0 & k1_xboole_0 = k2_relat_1(B))) # label(t62_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1592 (all A all B all C (m2_relset_1(C,A,k1_tarski(B)) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,k1_tarski(B)) & v1_funct_1(D) -> (k4_relset_1(A,k1_tarski(B),D) = k4_relset_1(A,k1_tarski(B),C) -> D = C))))) # label(t74_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1593 (all A all B all C all D all E all F (v1_funct_1(E) & m1_relset_1(E,A,B) & v1_funct_1(F) & m1_relset_1(F,C,D) -> v1_funct_1(k1_partfun1(A,B,C,D,E,F)) & m2_relset_1(k1_partfun1(A,B,C,D,E,F),A,D))) # label(dt_k1_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1594 (all A all B k3_partfun1(k1_xboole_0,A,B) = k1_xboole_0) # label(t91_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1595 (all A all B (v1_funct_1(B) & v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) -> (r1_partfun1(A,B) -> r1_partfun1(B,A)))) # label(symmetry_r1_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1596 $T # label(dt_k4_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1597 $T # label(t137_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1598 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) -> k2_funct_1(k3_partfun1(C,A,B)) = k3_partfun1(k2_funct_1(C),B,A)))) # label(t95_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1599 $T # label(t102_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1600 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,B),C) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(A,B),C) -> (k4_relset_1(k2_zfmisc_1(A,B),C,D) = k4_relset_1(k2_zfmisc_1(A,B),C,E) & (all F all G (r2_hidden(k4_tarski(F,G),k4_relset_1(k2_zfmisc_1(A,B),C,D)) -> k1_funct_1(E,k4_tarski(F,G)) = k1_funct_1(D,k4_tarski(F,G)))) -> E = D))))) # label(t35_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1601 $T # label(t22_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1602 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r1_tarski(A,C) -> m2_relset_1(D,C,B) & v1_funct_1(D)))) # label(t30_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1603 $T # label(t11_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1604 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (r2_hidden(D,k5_partfun1(A,B,C)) -> m2_relset_1(D,A,B) & v1_funct_1(D))))) # label(t168_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1605 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_relat_1(C),B) & r1_tarski(A,k1_relat_1(C)) -> v1_partfun1(k3_partfun1(C,A,B),A,B)))) # label(t115_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1606 $T # label(t101_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.16 1607 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> m2_relset_1(k9_relset_1(A,B,C,D),A,B) & v1_funct_1(k9_relset_1(A,B,C,D)))) # label(t46_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1608 $T # label(t90_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1609 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> k1_tarski(k1_xboole_0) = k5_partfun1(k1_xboole_0,A,B))) # label(t176_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1610 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_relat_1(E) & v1_funct_1(E) -> (r1_partfun1(C,E) & r1_tarski(D,C) -> r1_partfun1(D,E)))))))) # label(t140_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1611 (all A k6_relat_1(A) = k6_partfun1(A)) # label(redefinition_k6_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1612 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r1_tarski(C,D) -> m2_relset_1(C,A,B) & v1_funct_1(C)))))) # label(t33_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1613 $T # label(t180_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1614 $T # label(t110_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1615 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> r1_tarski(k2_relat_1(k3_partfun1(C,A,B)),k2_relat_1(C)) & r1_tarski(k4_relset_1(A,B,k3_partfun1(C,A,B)),k1_relat_1(C)))) # label(t77_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1616 $T # label(t170_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1617 $T # label(t106_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1618 $T # label(t182_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1619 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v1_partfun1(k3_partfun1(C,A,B),A,B) -> r1_tarski(A,k1_relat_1(C))))) # label(t113_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1620 (all A (p1_s3_partfun1(A) -> r2_hidden(f3_s3_partfun1(A),f2_s3_partfun1))) -> (exists A (v1_funct_1(A) & m2_relset_1(A,f1_s3_partfun1,f2_s3_partfun1) & (all B (r2_hidden(B,k4_relset_1(f1_s3_partfun1,f2_s3_partfun1,A)) <-> p1_s3_partfun1(B) & r2_hidden(B,f1_s3_partfun1))) & (all B (r2_hidden(B,k4_relset_1(f1_s3_partfun1,f2_s3_partfun1,A)) -> k1_funct_1(A,B) = f3_s3_partfun1(B))))) # label(s3_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1621 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_partfun1(k7_relat_1(k8_relat_1(A,C),B),C))) # label(t146_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1622 (all A all B all C all D all E (m2_relset_1(E,A,B) & v1_funct_1(E) -> (r1_tarski(B,D) & r1_tarski(A,C) -> m2_relset_1(E,C,D) & v1_funct_1(E)))) # label(t32_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1623 $T # label(t107_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1624 $T # label(t12_partfun1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1625 (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]. 56.16/55.17 1626 (all A all B all C all D all E all F (k3_zfmisc_1(D,E,F) = k3_zfmisc_1(A,B,C) -> C = F & B = E & A = D | k1_xboole_0 = B | C = k1_xboole_0 | k1_xboole_0 = A)) # label(t36_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1627 (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]. 56.16/55.17 1628 $T # label(dt_k19_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1629 (all A all B all C all D (-(-r1_tarski(A,k4_zfmisc_1(C,D,A,B)) & -r1_tarski(A,k4_zfmisc_1(A,B,C,D)) & -r1_tarski(A,k4_zfmisc_1(B,C,D,A)) & -r1_tarski(A,k4_zfmisc_1(D,A,B,C))) -> k1_xboole_0 = A)) # label(t63_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1630 (all A all B all C all D -(-(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> E != k10_mcart_1(A,B,C,D,E) & k9_mcart_1(A,B,C,D,E) != E & E != k8_mcart_1(A,B,C,D,E) & E != k11_mcart_1(A,B,C,D,E))) & A != k1_xboole_0 & k1_xboole_0 != D & k1_xboole_0 != C & k1_xboole_0 != B)) # label(t62_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1631 (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]. 56.16/55.17 1632 (all A all B all C all D all E all F -(E != k1_xboole_0 & k1_xboole_0 != F & B != k1_xboole_0 & C != k1_xboole_0 & k1_xboole_0 != D & (exists G (m1_subset_1(G,k3_zfmisc_1(A,B,C)) & (exists H (m1_subset_1(H,k3_zfmisc_1(D,E,F)) & -(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(A,B,C,G) = k5_mcart_1(D,E,F,H)) & H = G)))) & A != k1_xboole_0)) # label(t75_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1633 $T # label(t21_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1634 (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(J,E) & F = k4_mcart_1(G,H,I,J) & r2_hidden(I,D) & r2_hidden(G,B) & r2_hidden(H,C))))) -> k4_zfmisc_1(B,C,D,E) = A)) # label(t85_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1635 (all A all B all C all D k4_zfmisc_1(k1_tarski(A),k1_tarski(B),k1_tarski(C),k1_tarski(D)) = k1_tarski(k4_mcart_1(A,B,C,D))) # label(t65_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1636 (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) -> A = E & F = B & C = G & H = D)) # label(t33_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1637 (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) -> A = k1_xboole_0 | B = k1_xboole_0 | C = k1_xboole_0 | D = k1_xboole_0 | A = E & F = B & H = D & G = C)) # label(t56_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1638 (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]. 56.16/55.17 1639 (all A all B all C all D all E all F (m1_subset_1(D,k1_zfmisc_1(A)) & m1_subset_1(F,k1_zfmisc_1(C)) & m1_subset_1(E,k1_zfmisc_1(B)) -> 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]. 56.16/55.17 1640 (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]. 56.16/55.17 1641 (all A all B all C k3_zfmisc_1(k1_tarski(A),k1_tarski(B),k1_tarski(C)) = k1_tarski(k3_mcart_1(A,B,C))) # label(t39_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1642 (all A all B all C all D all E all F all G all H -(k1_xboole_0 != B & D != k1_xboole_0 & A != k1_xboole_0 & C != k1_xboole_0 & k1_xboole_0 != F & G != k1_xboole_0 & (exists I (m1_subset_1(I,k4_zfmisc_1(A,B,C,D)) & (exists J (m1_subset_1(J,k4_zfmisc_1(E,F,G,H)) & -(k11_mcart_1(A,B,C,D,I) = k11_mcart_1(E,F,G,H,J) & k9_mcart_1(A,B,C,D,I) = k9_mcart_1(E,F,G,H,J) & k10_mcart_1(A,B,C,D,I) = k10_mcart_1(E,F,G,H,J) & k8_mcart_1(A,B,C,D,I) = k8_mcart_1(E,F,G,H,J)) & J = I)))) & H != k1_xboole_0 & E != k1_xboole_0)) # label(t86_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1643 (all A all B all C all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> -(A != k1_xboole_0 & k1_xboole_0 != B & C != k1_xboole_0 & (exists E exists F exists G (-(E = k5_mcart_1(A,B,C,D) & k7_mcart_1(A,B,C,D) = G & k6_mcart_1(A,B,C,D) = F) & D = k3_mcart_1(E,F,G)))))) # label(t68_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1644 (all A all B all C all D ((all E ((exists F exists G exists H (r2_hidden(F,B) & r2_hidden(G,C) & r2_hidden(H,D) & E = k3_mcart_1(F,G,H))) <-> r2_hidden(E,A))) -> A = k3_zfmisc_1(B,C,D))) # label(t74_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1645 (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(k9_mcart_1(A,B,C,D,I),F) & r2_hidden(k10_mcart_1(A,B,C,D,I),G) & r2_hidden(k8_mcart_1(A,B,C,D,I),E) & r2_hidden(k11_mcart_1(A,B,C,D,I),H)))))))))))) # label(t87_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1646 (all A k2_mcart_1(k2_mcart_1(A)) = k20_mcart_1(A)) # label(d17_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1647 (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]. 56.16/55.17 1648 (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]. 56.16/55.17 1649 (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]. 56.16/55.17 1650 (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(F,k1_zfmisc_1(B)) & m1_subset_1(G,k1_zfmisc_1(C)) -> 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]. 56.16/55.17 1651 (all A all B all C all D -(D != k1_xboole_0 & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,B) -> (F = k9_mcart_1(A,B,C,D,E) <-> (all G all H all I all J (E = k4_mcart_1(G,H,I,J) -> F = H))))))) & B != k1_xboole_0 & C != k1_xboole_0 & k1_xboole_0 != A)) # label(d9_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1652 (all A all B all C all D k4_zfmisc_1(A,B,C,D) = k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,B),C),D)) # label(t53_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1653 (all A k17_mcart_1(A) = k1_mcart_1(k1_mcart_1(A))) # label(d14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1654 (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 -> F = D))))))) -> B = k1_xboole_0 | k1_xboole_0 = A | k5_mcart_1(A,B,C,E) = D | k1_xboole_0 = C))) # label(t69_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1655 (all A all B all C all D k3_mcart_1(k4_tarski(A,B),C,D) = k4_mcart_1(A,B,C,D)) # label(t32_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1656 (all A all B all C (r2_hidden(A,k2_zfmisc_1(k1_tarski(B),C)) -> k1_mcart_1(A) = B & r2_hidden(k2_mcart_1(A),C))) # label(t12_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1657 (all A all B all C all D all E all F all G all H (m1_subset_1(H,k1_zfmisc_1(D)) & m1_subset_1(E,k1_zfmisc_1(A)) & m1_subset_1(G,k1_zfmisc_1(C)) & m1_subset_1(F,k1_zfmisc_1(B)) -> 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]. 56.16/55.17 1658 (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]. 56.16/55.17 1659 $T # label(dt_k18_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1660 (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 & (C = k2_mcart_1(A) | k2_mcart_1(A) = D))) # label(t18_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1661 (all A all B all C -(-(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> (all E (m1_subset_1(E,C) -> (k7_mcart_1(A,B,C,D) = E <-> (all F all G all H (k3_mcart_1(F,G,H) = D -> H = E))))))) & k1_xboole_0 != A & k1_xboole_0 != B & k1_xboole_0 != C)) # label(d7_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1662 (all A all B all C all D -(D != k1_xboole_0 & k1_xboole_0 != B & A != k1_xboole_0 & C != 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 (E = k4_mcart_1(G,H,I,J) -> F = G))))))))) # label(d8_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1663 (all A all B all C all D all E all F k6_enumset1(k3_mcart_1(A,C,E),k3_mcart_1(A,D,E),k3_mcart_1(A,C,F),k3_mcart_1(A,D,F),k3_mcart_1(B,C,E),k3_mcart_1(B,D,E),k3_mcart_1(B,C,F),k3_mcart_1(B,D,F)) = k3_zfmisc_1(k2_tarski(A,B),k2_tarski(C,D),k2_tarski(E,F))) # label(t46_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1664 (all A -(A != k1_xboole_0 & (all B -(r2_hidden(B,A) & (all C all D -(k4_tarski(C,D) = B & (r2_hidden(C,A) | r2_hidden(D,A)))))))) # label(t9_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1665 (all A all B all C -(k1_xboole_0 != B & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> k7_mcart_1(A,B,C,D) != D & D != k6_mcart_1(A,B,C,D) & k5_mcart_1(A,B,C,D) != D)) & C != k1_xboole_0 & k1_xboole_0 != A)) # label(t51_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1666 (all A all B all C all D (A != k1_xboole_0 & C != k1_xboole_0 & k1_xboole_0 != B & k1_xboole_0 != D <-> k1_xboole_0 != k4_zfmisc_1(A,B,C,D))) # label(t55_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1667 (all A all B all C all D all E all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,D) -> (F = k4_mcart_1(G,H,I,J) -> E = H))))))))) -> k1_xboole_0 = D | k9_mcart_1(A,B,C,D,F) = E | k1_xboole_0 = B | C = k1_xboole_0 | k1_xboole_0 = A))) # label(t80_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1668 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> k1_mcart_1(k1_funct_1(A,C)) = k1_funct_1(B,C))) & k1_relat_1(B) = k1_relat_1(A) <-> B = k15_mcart_1(A)))))) # label(d12_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1669 (all A all B all C (r2_hidden(A,k2_zfmisc_1(k1_tarski(B),k1_tarski(C))) -> B = k1_mcart_1(A) & C = k2_mcart_1(A))) # label(t14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1670 (all A all B all C -(k1_xboole_0 != A & -(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 != C & k1_xboole_0 != B)) # label(d6_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1671 (all A all B all C all D all E all F (k3_zfmisc_1(D,E,F) = k3_zfmisc_1(A,B,C) -> F = C & B = E & A = D | k1_xboole_0 = k3_zfmisc_1(A,B,C))) # label(t37_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1672 (all A -((all B -((all C all D all E -(B = k3_mcart_1(C,D,E) & (r2_hidden(C,A) | r2_hidden(D,A)))) & r2_hidden(B,A))) & A != k1_xboole_0)) # label(t29_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1673 (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]. 56.16/55.17 1674 (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(k7_mcart_1(A,B,C,G),F) & r2_hidden(k6_mcart_1(A,B,C,G),E) & r2_hidden(k5_mcart_1(A,B,C,G),D)))))))))) # label(t76_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1675 (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]. 56.16/55.17 1676 (all A all B all C all D all E all F (k17_mcart_1(k4_tarski(k4_tarski(A,B),C)) = A & E = k20_mcart_1(k4_tarski(F,k4_tarski(D,E))) & D = k19_mcart_1(k4_tarski(F,k4_tarski(D,E))) & k18_mcart_1(k4_tarski(k4_tarski(A,B),C)) = B)) # label(t89_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1677 (all A k18_mcart_1(A) = k2_mcart_1(k1_mcart_1(A))) # label(d15_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1678 (all A all B all C all D -(k1_xboole_0 != B & -(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)))) & k1_xboole_0 != A & k1_xboole_0 != C & D != k1_xboole_0)) # label(t60_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1679 (all A all B all C -(C != k1_xboole_0 & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> D = k3_mcart_1(k5_mcart_1(A,B,C,D),k6_mcart_1(A,B,C,D),k7_mcart_1(A,B,C,D)))) & k1_xboole_0 != B & k1_xboole_0 != A)) # label(t48_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1680 (all A all B all C all D all E all F all G all H (-r1_xboole_0(k4_zfmisc_1(A,B,C,D),k4_zfmisc_1(E,F,G,H)) -> -r1_xboole_0(B,F) & -r1_xboole_0(A,E) & -r1_xboole_0(C,G) & -r1_xboole_0(D,H))) # label(t64_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1681 (all A ((exists B exists C A = k4_tarski(B,C)) -> (all B ((all C all D (k4_tarski(C,D) = A -> D = B)) <-> k2_mcart_1(A) = B)))) # label(d2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1682 (all A all B all C all D all E all F (r2_hidden(k3_mcart_1(A,B,C),k3_zfmisc_1(D,E,F)) <-> r2_hidden(C,F) & r2_hidden(B,E) & r2_hidden(A,D))) # label(t73_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1683 (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) -> J = E))))))))) -> A = k1_xboole_0 | k1_xboole_0 = C | D = k1_xboole_0 | E = k11_mcart_1(A,B,C,D,F) | B = k1_xboole_0))) # label(t82_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1684 (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]. 56.16/55.17 1685 (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]. 56.16/55.17 1686 (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]. 56.16/55.17 1687 (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))))))))) -> B = k1_xboole_0 | k8_mcart_1(A,B,C,D,F) = E | k1_xboole_0 = D | k1_xboole_0 = A | C = k1_xboole_0))) # label(t79_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1688 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k16_mcart_1(A) = 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)))))) # label(d13_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1689 (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]. 56.16/55.17 1690 (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) -> G = D))))))) -> A = k1_xboole_0 | C = k1_xboole_0 | k6_mcart_1(A,B,C,E) = D | B = k1_xboole_0))) # label(t70_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1691 (all A all B (B = k2_mcart_1(k4_tarski(A,B)) & k1_mcart_1(k4_tarski(A,B)) = A)) # label(t7_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1692 (all A -(k1_xboole_0 != A & (all B -((all C all D all E all F all G (r2_hidden(E,F) & r2_hidden(G,B) & r2_hidden(F,G) & r2_hidden(D,E) & r2_hidden(C,D) -> r1_xboole_0(C,A))) & r2_hidden(B,A))))) # label(t6_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1693 (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]. 56.16/55.17 1694 (all A -(A != k1_xboole_0 & (all B -(r2_hidden(B,A) & (all C all D (r2_hidden(D,B) & r2_hidden(C,D) -> r1_xboole_0(C,A))))))) # label(t3_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1695 (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 = H))))))) -> k1_xboole_0 = C | A = k1_xboole_0 | k7_mcart_1(A,B,C,E) = D | B = k1_xboole_0))) # label(t71_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1696 (all A all B -(k1_xboole_0 != A & B != k1_xboole_0 & -(all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> C != k2_mcart_1(C) & k1_mcart_1(C) != C)))) # label(t26_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1697 (all A all B (k2_zfmisc_1(A,B) != k1_xboole_0 -> (all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> C != k1_mcart_1(C) & k2_mcart_1(C) != C)))) # label(t66_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1698 (all A all B all C all D all E all F (m1_subset_1(F,k1_zfmisc_1(C)) & m1_subset_1(E,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(A)) -> 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]. 56.16/55.17 1699 (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 & (k1_mcart_1(A) = B | k1_mcart_1(A) = C))) # label(t17_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1700 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k16_mcart_1(A)) & v1_funct_1(k16_mcart_1(A)))) # label(dt_k16_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1701 (all A all B all C all D -((exists E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) & (exists F exists G exists H exists I (-(k8_mcart_1(A,B,C,D,E) = F & k10_mcart_1(A,B,C,D,E) = H & k11_mcart_1(A,B,C,D,E) = I & k9_mcart_1(A,B,C,D,E) = G) & E = k4_mcart_1(F,G,H,I))))) & D != k1_xboole_0 & k1_xboole_0 != C & k1_xboole_0 != A & B != k1_xboole_0)) # label(t59_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1702 $T # label(t22_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1703 (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]. 56.16/55.17 1704 (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]. 56.16/55.17 1705 (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 (k4_mcart_1(G,H,I,J) = E -> I = F))))))) & k1_xboole_0 != D & k1_xboole_0 != A & B != k1_xboole_0 & k1_xboole_0 != C)) # label(d10_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1706 (all A all B all C (k3_zfmisc_1(A,B,C) != k1_xboole_0 <-> A != k1_xboole_0 & k1_xboole_0 != C & k1_xboole_0 != B)) # label(t35_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1707 (all A -((all B -((all C all D all E all F -((r2_hidden(D,A) | r2_hidden(C,A)) & k4_mcart_1(C,D,E,F) = B)) & r2_hidden(B,A))) & k1_xboole_0 != A)) # label(t34_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1708 (all A all B all C -(k1_xboole_0 != C & k1_xboole_0 != A & k1_xboole_0 != B & (exists D ((exists E exists F exists G (-(k6_mcart_1(A,B,C,D) = F & k5_mcart_1(A,B,C,D) = E & G = k7_mcart_1(A,B,C,D)) & k3_mcart_1(E,F,G) = D)) & m1_subset_1(D,k3_zfmisc_1(A,B,C)))))) # label(t47_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.17 1709 (all A ((exists B exists C A = k4_tarski(B,C)) -> k4_tarski(k1_mcart_1(A),k2_mcart_1(A)) = A)) # label(t8_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1710 (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(A,B) & r1_tarski(C,D) -> 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]. 56.16/55.18 1711 (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) -> k1_xboole_0 = k4_zfmisc_1(A,B,C,D) | G = C & F = B & E = A & D = H)) # label(t57_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1712 (all A all B all C all D all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> -((exists F exists G exists H exists I (k4_mcart_1(F,G,H,I) = E & -(k10_mcart_1(A,B,C,D,E) = H & k9_mcart_1(A,B,C,D,E) = G & k8_mcart_1(A,B,C,D,E) = F & k11_mcart_1(A,B,C,D,E) = I))) & B != k1_xboole_0 & A != k1_xboole_0 & C != k1_xboole_0 & D != k1_xboole_0))) # label(t78_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1713 (all A k19_mcart_1(A) = k1_mcart_1(k2_mcart_1(A))) # label(d16_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1714 (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]. 56.16/55.18 1715 $T # label(dt_k17_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1716 (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]. 56.16/55.18 1717 (all A all B all C all D k2_tarski(k3_mcart_1(A,B,C),k3_mcart_1(A,B,D)) = k3_zfmisc_1(k1_tarski(A),k1_tarski(B),k2_tarski(C,D))) # label(t42_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1718 (all A all B all C (r2_hidden(A,k2_zfmisc_1(B,C)) -> k2_mcart_1(A) != A & k1_mcart_1(A) != A)) # label(t67_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1719 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(C,k1_zfmisc_1(A)) -> 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]. 56.16/55.18 1720 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k2_zfmisc_1(C,D) = k12_mcart_1(A,B,C,D))) # label(redefinition_k12_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1721 $T # label(dt_k1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1722 (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]. 56.16/55.18 1723 (all A all B all C -(A != k1_xboole_0 & B != k1_xboole_0 & -(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))))) & k1_xboole_0 != C)) # label(d5_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1724 (all A -((all B -(r2_hidden(B,A) & r1_xboole_0(B,A))) & A != k1_xboole_0)) # label(t1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1725 (all A all B (k4_zfmisc_1(B,B,B,B) = k4_zfmisc_1(A,A,A,A) -> B = A)) # label(t58_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1726 (all A -(A != k1_xboole_0 & (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))))))) # label(t4_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1727 (all A all B all C all D all E all F (k3_mcart_1(A,B,C) = k3_mcart_1(D,E,F) -> B = E & C = F & D = A)) # label(t28_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1728 (all A (v1_funct_1(A) & v1_relat_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]. 56.16/55.18 1729 (all A all B all C all D -(k1_xboole_0 != A & k1_xboole_0 != B & k1_xboole_0 != C & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> k2_mcart_1(E) = k11_mcart_1(A,B,C,D,E) & k2_mcart_1(k1_mcart_1(E)) = k10_mcart_1(A,B,C,D,E) & k1_mcart_1(k1_mcart_1(k1_mcart_1(E))) = k8_mcart_1(A,B,C,D,E) & k2_mcart_1(k1_mcart_1(k1_mcart_1(E))) = k9_mcart_1(A,B,C,D,E))) & D != k1_xboole_0)) # label(t61_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1730 (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,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 -> F = J))))))) & k1_xboole_0 != B & A != k1_xboole_0 & k1_xboole_0 != D & C != k1_xboole_0)) # label(d11_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1731 (all A all B -(k1_xboole_0 != A & k1_xboole_0 != B & -(all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> k4_tarski(k1_mcart_1(C),k2_mcart_1(C)) = C)))) # label(t24_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1732 (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]. 56.16/55.18 1733 (all A all B all C all D all E all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,D) -> (k4_mcart_1(G,H,I,J) = F -> E = I))))))))) -> k1_xboole_0 = A | k1_xboole_0 = C | E = k10_mcart_1(A,B,C,D,F) | k1_xboole_0 = D | B = k1_xboole_0))) # label(t81_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1734 (all A all B all C (r2_hidden(A,k2_zfmisc_1(B,C)) -> A = k4_tarski(k1_mcart_1(A),k2_mcart_1(A)))) # label(t23_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1735 (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]. 56.16/55.18 1736 (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(B,E) & -r1_xboole_0(C,F) & -r1_xboole_0(A,D))) # label(t52_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1737 $T # label(dt_k4_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1738 (all A all B all C all D all E -((all F all G all H all I -(r2_hidden(F,B) & r2_hidden(H,D) & r2_hidden(I,E) & k4_mcart_1(F,G,H,I) = A & r2_hidden(G,C))) & r2_hidden(A,k4_zfmisc_1(B,C,D,E)))) # label(t83_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1739 (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]. 56.16/55.18 1740 $T # label(dt_k2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1741 (all A all B all C -(C != k1_xboole_0 & k1_xboole_0 != A & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> k1_mcart_1(k1_mcart_1(D)) = k5_mcart_1(A,B,C,D) & k2_mcart_1(k1_mcart_1(D)) = k6_mcart_1(A,B,C,D) & k7_mcart_1(A,B,C,D) = k2_mcart_1(D))) & k1_xboole_0 != B)) # label(t50_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1742 $T # label(t30_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1743 (all A -(k1_xboole_0 != A & (all B -((all C all D all E all F (r2_hidden(E,F) & r2_hidden(F,B) & r2_hidden(D,E) & r2_hidden(C,D) -> r1_xboole_0(C,A))) & r2_hidden(B,A))))) # label(t5_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1744 (all A -((all B -(r2_hidden(B,A) & (all C (r2_hidden(C,B) -> r1_xboole_0(C,A))))) & A != k1_xboole_0)) # label(t2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1745 $T # label(dt_k20_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1746 $T # label(t27_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1747 (all A all B all C all D all E (r2_hidden(A,k2_zfmisc_1(k2_tarski(B,C),k2_tarski(D,E))) -> (D = k2_mcart_1(A) | k2_mcart_1(A) = E) & (C = k1_mcart_1(A) | B = k1_mcart_1(A)))) # label(t19_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1748 (all A ((exists B exists C A = k4_tarski(B,C)) -> (all B ((all C all D (A = k4_tarski(C,D) -> C = B)) <-> k1_mcart_1(A) = B)))) # label(d1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1749 (all A all B (k3_zfmisc_1(B,B,B) = k3_zfmisc_1(A,A,A) -> B = A)) # label(t38_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1750 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(k2_tarski(B,C),D)) -> (k1_mcart_1(A) = B | k1_mcart_1(A) = C) & r2_hidden(k2_mcart_1(A),D))) # label(t15_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1751 $T # label(dt_k3_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1752 (all A all B all C all D k2_tarski(k3_mcart_1(A,C,D),k3_mcart_1(B,C,D)) = k3_zfmisc_1(k2_tarski(A,B),k1_tarski(C),k1_tarski(D))) # label(t40_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1753 (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) & r2_hidden(F,C) & k3_mcart_1(E,F,G) = A & r2_hidden(G,D))))) # label(t72_mcart_1) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1754 (all A (-v1_xboole_0(A) -> -((all B (v1_funct_1(B) & v1_relat_1(B) -> -(A = k1_relat_1(B) & (all C (r2_hidden(C,A) -> r2_hidden(k1_funct_1(B,C),C)))))) & (all B -(k1_xboole_0 = B & r2_hidden(B,A)))))) # label(t28_wellord2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1755 $T # label(t18_wellord2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1756 (all A all B (r2_wellord2(A,B) -> r2_wellord2(B,A))) # label(symmetry_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1757 $T # label(t19_wellord2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1758 (all A -((all B all C -(r2_hidden(B,f2_s2_wellord2) & p1_s2_wellord2(A,B,C) & r2_hidden(C,f3_s2_wellord2))) & r2_hidden(A,f1_s2_wellord2))) -> (exists A (v1_relat_1(A) & v1_funct_1(A) & (exists B (k1_relat_1(A) = f1_s2_wellord2 & 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) & v1_funct_1(B))))) # label(s2_wellord2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1759 (all A (v3_ordinal1(A) -> v1_wellord1(k1_wellord2(A)))) # label(t6_wellord2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1760 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r4_wellord1(k1_wellord2(A),k1_wellord2(B)) -> B = A))))) # label(t11_wellord2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1761 (all A v4_relat_2(k1_wellord2(A))) # label(t5_wellord2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1762 (all A all B (r2_wellord2(A,B) <-> r2_tarski(A,B))) # label(redefinition_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1763 (all A v8_relat_2(k1_wellord2(A))) # label(t3_wellord2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1764 (all A (v1_relat_1(A) -> v3_ordinal1(k2_wellord2(A)))) # label(dt_k2_wellord2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1765 (all A v1_relat_2(k1_wellord2(A))) # label(t2_wellord2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1766 (all A -(r2_hidden(A,f1_s1_wellord2) & (all B -(r2_hidden(B,f2_s1_wellord2) & p1_s1_wellord2(A,B))))) -> (exists A (r1_tarski(k2_relat_1(A),f2_s1_wellord2) & v1_relat_1(A) & v1_funct_1(A) & (all B (r2_hidden(B,f1_s1_wellord2) -> p1_s1_wellord2(B,k1_funct_1(A,B)))) & k1_relat_1(A) = f1_s1_wellord2)) # label(s1_wellord2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1767 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> (all B (v3_ordinal1(B) -> (r4_wellord1(A,k1_wellord2(B)) <-> B = k2_wellord2(A))))))) # label(d2_wellord2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1768 (all A (v1_relat_1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r4_wellord1(A,k1_wellord2(B)) & r4_wellord1(A,k1_wellord2(C)) -> C = B))))))) # label(t12_wellord2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1769 (all A all B r2_wellord2(A,A)) # label(reflexivity_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1770 (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]. 56.16/55.18 1771 (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]. 56.16/55.18 1772 (all A all B (r1_tarski(A,B) -> k2_wellord1(k1_wellord2(B),A) = k1_wellord2(A))) # label(t8_wellord2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1773 (all A (v1_relat_1(A) -> -((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)))) & (all B (v3_ordinal1(B) -> -r4_wellord1(A,k1_wellord2(B)))) & v2_wellord1(A)))) # label(t13_wellord2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1774 (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]. 56.16/55.18 1775 $T # label(t16_wellord2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1776 (all A exists B (r2_wellord1(B,A) & v1_relat_1(B))) # label(t26_wellord2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1777 (all A (v3_ordinal1(A) -> v6_relat_2(k1_wellord2(A)))) # label(t4_wellord2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1778 $T # label(t24_wellord2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1779 (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]. 56.16/55.18 1780 $T # label(t23_wellord2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1781 (all A all B (r2_wellord2(A,B) <-> (exists C (A = k1_relat_1(C) & k2_relat_1(C) = B & v1_funct_1(C) & v2_funct_1(C) & v1_relat_1(C))))) # label(d4_wellord2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1782 (all A all B (v1_relat_1(B) -> (r2_wellord1(B,A) -> v2_wellord1(k2_wellord1(B,A)) & k3_relat_1(k2_wellord1(B,A)) = A))) # label(t25_wellord2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1783 $T # label(t1_wellord2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1784 $T # label(t21_wellord2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1785 (all A v1_relat_1(k1_wellord2(A))) # label(dt_k1_wellord2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1786 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(A,B) -> k1_wellord1(k1_wellord2(B),A) = A))))) # label(t10_wellord2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1787 (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]. 56.16/55.18 1788 (all A all B (v1_relat_1(B) -> (A = k3_relat_1(B) & (all C all D (r2_hidden(C,A) & r2_hidden(D,A) -> (r2_hidden(k4_tarski(C,D),B) <-> r1_tarski(C,D)))) <-> k1_wellord2(A) = B))) # label(d1_wellord2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1789 (all A (v3_ordinal1(A) -> v2_wellord1(k1_wellord2(A)))) # label(t7_wellord2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1790 $T # label(t20_wellord2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1791 (all A (-v1_xboole_0(A) -> -((all B all C (r2_hidden(B,A) & r2_hidden(C,A) -> r1_xboole_0(B,C) | B = C)) & (all B exists C (r2_hidden(C,A) & (all D k3_xboole_0(B,C) != k1_tarski(D)))) & (all B -(r2_hidden(B,A) & B = k1_xboole_0))))) # label(t27_wellord2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1792 $T # label(t15_wellord2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1793 (all A exists B (v1_relat_1(B) & v2_funct_1(B) & v1_funct_2(B,A,A) & v2_funct_2(B,A,A) & v3_funct_2(B,A,A) & v1_funct_1(B) & m1_relset_1(B,A,A))) # label(rc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1794 $T # label(t81_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1795 $T # label(t125_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1796 (all A all B all C (v1_funct_1(k9_funct_2(A,B,C)) & m2_relset_1(k9_funct_2(A,B,C),k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & v1_funct_2(k9_funct_2(A,B,C),k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)))) # label(dt_k9_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1797 (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]. 56.16/55.18 1798 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r1_tarski(D,C) -> r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D))))))) # label(t165_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1799 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E -(r2_hidden(E,k2_funct_2(A,B,D,C)) & (all F -(r2_hidden(F,A) & r2_hidden(F,C) & k1_funct_1(D,F) = E)))))) # label(t115_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1800 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (k5_partfun1(A,B,D) = k5_partfun1(A,B,C) & (all E B != k1_tarski(E)) -> C = D))))) # label(t168_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1801 $T # label(t157_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1802 $T # label(t111_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1803 $T # label(t137_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1804 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> (all C (m1_relset_1(C,A,B) -> (v1_funct_2(C,A,B) & v1_funct_1(C) -> v1_partfun1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) & -v1_xboole_0(C)))))) # label(cc6_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1805 $T # label(t69_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1806 $T # label(t84_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1807 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> r1_tarski(k5_partfun1(A,B,C),k1_funct_2(A,B)))) # label(t159_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1808 (all A (m1_subset_1(A,f1_s13_funct_2) -> m1_subset_1(f3_s13_funct_2(A),f2_s13_funct_2))) -> (exists A (v1_funct_2(A,f1_s13_funct_2,f2_s13_funct_2) & (all B (m1_subset_1(B,f1_s13_funct_2) -> k8_funct_2(f1_s13_funct_2,f2_s13_funct_2,A,B) = f3_s13_funct_2(B))) & m2_relset_1(A,f1_s13_funct_2,f2_s13_funct_2) & v1_funct_1(A))) # label(s13_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1809 $T # label(t78_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1810 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (k6_partfun1(A) = k1_partfun1(A,B,B,A,C,D) -> A = k2_relat_1(D) & v2_funct_1(C) | B = k1_xboole_0))))) # label(t29_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1811 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> (r1_partfun1(C,E) & r1_partfun1(D,E) -> r1_partfun1(C,D) | k1_xboole_0 = B & k1_xboole_0 != A))))))) # label(t151_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1812 (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]. 56.16/55.18 1813 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(k2_relat_1(D),C) -> k1_xboole_0 = B & A != k1_xboole_0 | m2_relset_1(D,A,C) & v1_funct_1(D) & v1_funct_2(D,A,C)))) # label(t8_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1814 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> -(r2_hidden(C,B) & (all E -(k1_funct_1(D,E) = C & r2_hidden(E,A))) & k2_relat_1(D) = B))) # label(t17_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1815 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> -((all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> -r1_partfun1(C,D))) & (B = k1_xboole_0 -> k1_xboole_0 = A)))) # label(t148_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.16/55.18 1816 (all A all B (v3_funct_2(B,A,A) & v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> (all C (v1_funct_2(C,A,A) & v1_funct_1(C) & m2_relset_1(C,A,A) & v3_funct_2(C,A,A) -> (k5_funct_2(A,B,C) = k6_partfun1(A) -> k6_funct_2(A,B) = C))))) # label(t87_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1817 (all A all B all C all D all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (all F (v1_funct_1(F) & m2_relset_1(F,B,C) & v1_funct_2(F,B,C) -> -((k1_xboole_0 = C -> k1_xboole_0 = B) & (k1_xboole_0 = B -> k1_xboole_0 = A) & -r1_tarski(k3_funct_2(A,B,E,D),k3_funct_2(A,C,k1_partfun1(A,B,B,C,E,F),k2_funct_2(B,C,F,D)))))))) # label(t53_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1818 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) & v1_funct_2(C,A,B) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> ((all E (m1_subset_1(E,A) -> k1_funct_1(D,E) = k1_funct_1(C,E))) -> D = C))))) # label(t113_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1819 (all A all B (m2_relset_1(B,A,A) & v1_funct_1(B) & v1_funct_2(B,A,A) -> r2_hidden(B,k1_funct_2(A,A)))) # label(t12_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1820 $T # label(t163_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1821 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m2_relset_1(E,B,C) & v1_funct_1(E) & v1_funct_2(E,B,C) -> (k2_relat_1(E) = C & B = k2_relat_1(D) -> k2_relat_1(k1_partfun1(A,B,B,C,D,E)) = C | B = k1_xboole_0 | C = k1_xboole_0))))) # label(t20_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1822 (all A -(r2_hidden(A,f1_s1_funct_2) & (all B -(r2_hidden(B,f2_s1_funct_2) & p1_s1_funct_2(A,B))))) -> (exists A ((all B (r2_hidden(B,f1_s1_funct_2) -> p1_s1_funct_2(B,k1_funct_1(A,B)))) & v1_funct_1(A) & v1_funct_2(A,f1_s1_funct_2,f2_s1_funct_2) & m2_relset_1(A,f1_s1_funct_2,f2_s1_funct_2))) # label(s1_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1823 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> v1_partfun1(k3_partfun1(B,A,A),A,A))) # label(t134_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1824 (all A all B all C (m1_relset_1(B,A,A) & v1_funct_2(C,A,A) & v1_funct_2(B,A,A) & m1_relset_1(C,A,A) & v1_funct_1(C) & v1_funct_1(B) -> k4_funct_2(A,B,C) = k5_relat_1(B,C))) # label(redefinition_k4_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1825 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (m2_relset_1(E,B,C) & v1_funct_2(E,B,C) & v1_funct_1(E) -> (v2_funct_1(E) & k2_relat_1(k1_partfun1(A,B,B,C,D,E)) = C -> k2_relat_1(D) = B | k1_xboole_0 = C))))) # label(t28_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1826 (all A all B all C (C = k1_funct_2(A,B) <-> (all D ((exists E (r1_tarski(k2_relat_1(E),B) & D = E & v1_funct_1(E) & k1_relat_1(E) = A & v1_relat_1(E))) <-> r2_hidden(D,C))))) # label(d2_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1827 (all A all B all C all D all E (v1_funct_1(D) & v1_funct_1(E) & m1_relset_1(E,B,C) & v1_funct_2(E,B,C) & m1_relset_1(D,A,B) & v1_funct_2(D,A,B) & -v1_xboole_0(B) -> v1_funct_2(k7_funct_2(A,B,C,D,E),A,C) & m2_relset_1(k7_funct_2(A,B,C,D,E),A,C) & v1_funct_1(k7_funct_2(A,B,C,D,E)))) # label(dt_k7_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1828 $T # label(t91_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1829 $T # label(t98_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1830 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) & v1_funct_2(C,A,B) -> (all D (v1_funct_1(D) & v1_funct_2(D,B,A) & m2_relset_1(D,B,A) -> (k1_partfun1(B,A,A,B,D,C) = k6_partfun1(B) -> B = k2_relat_1(C)))))) # label(t24_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1831 $T # label(t97_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1832 (all A all B all C (v1_funct_2(C,A,B) & v1_funct_1(C) & m2_relset_1(C,A,B) -> ((k1_xboole_0 = B -> A = k1_xboole_0) -> (v2_funct_1(C) <-> (all D all E (k1_funct_1(C,D) = k1_funct_1(C,E) & r2_hidden(E,A) & r2_hidden(D,A) -> D = E)))))) # label(t25_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1833 (all A all B all C all D all E all F (v1_funct_2(F,k2_zfmisc_1(A,B),C) & m2_relset_1(F,k2_zfmisc_1(A,B),C) & v1_funct_1(F) -> (r2_hidden(E,B) & r2_hidden(D,A) -> r2_hidden(k1_funct_1(F,k4_tarski(D,E)),C) | k1_xboole_0 = C))) # label(t119_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1834 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (r1_tarski(C,A) -> r1_tarski(C,k3_funct_2(A,B,D,k2_funct_2(A,B,D,C))) | A != k1_xboole_0 & B = k1_xboole_0))) # label(t50_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1835 (all A all B all C (v1_funct_2(C,A,A) & v3_funct_2(C,A,A) & m2_relset_1(C,A,A) & v1_funct_1(C) -> (r1_tarski(B,A) -> B = k3_funct_2(A,A,C,k2_funct_2(A,A,C,B)) & k2_funct_2(A,A,C,k3_funct_2(A,A,C,B)) = B))) # label(t92_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1836 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (B != k1_xboole_0 -> (all E (r2_hidden(k1_funct_1(D,E),C) & r2_hidden(E,A) <-> r2_hidden(E,k10_relat_1(D,C))))))) # label(t46_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1837 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(C,k1_funct_2(A,B)) -> A = k1_relat_1(C) & r1_tarski(k2_relat_1(C),B)))) # label(t169_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1838 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_relat_1(E) & v1_funct_1(E) -> (r2_hidden(C,A) -> k1_xboole_0 = B | k1_funct_1(E,k1_funct_1(D,C)) = k1_funct_1(k5_relat_1(D,E),C)))))) # label(t21_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1839 f3_s11_funct_2 != f4_s11_funct_2 -> (exists A (v1_funct_1(A) & f5_s11_funct_2 = k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,f3_s11_funct_2) & f6_s11_funct_2 = k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,f4_s11_funct_2) & v1_funct_2(A,f1_s11_funct_2,f2_s11_funct_2) & m2_relset_1(A,f1_s11_funct_2,f2_s11_funct_2) & (all B (m1_subset_1(B,f1_s11_funct_2) -> -(B != f4_s11_funct_2 & k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,B) != f7_s11_funct_2(B) & f3_s11_funct_2 != B))))) # label(s11_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1840 (all A all B all C (m1_relset_1(C,A,B) -> (v1_funct_1(C) & v1_partfun1(C,A,B) -> v1_funct_2(C,A,B) & v1_funct_1(C)))) # label(cc1_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1841 (all A all B exists C (v1_funct_1(C) & m1_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_relat_1(C))) # label(rc1_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1842 $T # label(t72_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1843 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> ((B = k1_xboole_0 -> A = k1_xboole_0) -> (r1_partfun1(C,D) <-> (all E (r2_hidden(E,k4_relset_1(A,B,C)) -> k1_funct_1(C,E) = k1_funct_1(D,E))))))))) # label(t145_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1844 (all A (m1_subset_1(A,f1_s7_funct_2) -> (all B (m1_subset_1(B,f2_s7_funct_2) -> (exists C (p1_s7_funct_2(A,B,C) & m1_subset_1(C,f3_s7_funct_2))))))) -> (exists A (v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(f1_s7_funct_2,f2_s7_funct_2),f3_s7_funct_2) & v1_funct_2(A,k2_zfmisc_1(f1_s7_funct_2,f2_s7_funct_2),f3_s7_funct_2) & (all B (m1_subset_1(B,f1_s7_funct_2) -> (all C (m1_subset_1(C,f2_s7_funct_2) -> p1_s7_funct_2(B,C,k1_funct_1(A,k4_tarski(B,C))))))))) # label(s7_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1845 (all A all B all C (v3_funct_2(B,A,A) & v1_funct_2(C,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) & m1_relset_1(B,A,A) & m1_relset_1(C,A,A) & v3_funct_2(C,A,A) & v1_funct_1(C) -> k5_funct_2(A,B,C) = k5_relat_1(B,C))) # label(redefinition_k5_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1846 $T # label(t57_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1847 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) -> (k4_funct_2(A,B,C) = B & k2_relat_1(B) = A -> k6_partfun1(A) = C))))) # label(t75_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1848 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> k2_funct_2(A,A,B,A) = k2_relat_1(B))) # label(t79_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1849 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_xboole_0 = k1_relat_1(B) -> m2_relset_1(B,k1_xboole_0,A) & v1_funct_2(B,k1_xboole_0,A) & v1_funct_1(B)))) # label(t55_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1850 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (B = k2_relat_1(C) & v2_funct_1(C) -> k6_partfun1(A) = k5_relat_1(C,k2_funct_1(C)) & k6_partfun1(B) = k5_relat_1(k2_funct_1(C),C) | B = k1_xboole_0))) # label(t35_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1851 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> -((all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (exists E (r2_hidden(E,k4_relset_1(A,B,C)) & k1_funct_1(D,E) != k1_funct_1(C,E))))) & (B = k1_xboole_0 -> k1_xboole_0 = A)))) # label(t136_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1852 (all A all B all C all D (v1_funct_2(D,A,B) & v1_funct_1(D) & m2_relset_1(D,A,B) -> (all E (v1_funct_2(E,B,C) & m2_relset_1(E,B,C) & v1_funct_1(E) -> (v2_funct_1(k1_partfun1(A,B,B,C,D,E)) -> A != k1_xboole_0 & B = k1_xboole_0 | v2_funct_1(D) | k1_xboole_0 != B & C = k1_xboole_0))))) # label(t26_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1853 (all A all B (-v1_xboole_0(B) -> (all C (m1_relset_1(C,A,B) -> (v1_funct_1(C) & v1_funct_2(C,A,B) -> v1_funct_1(C) & v1_funct_2(C,A,B) & v1_partfun1(C,A,B)))))) # label(cc5_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1854 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> ((all D -(r2_hidden(D,B) & (all E -(r2_hidden(E,A) & k1_funct_1(C,E) = D)))) -> k2_relat_1(C) = B | k1_xboole_0 = B))) # label(t16_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1855 $T # label(t93_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1856 $T # label(t147_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1857 $T # label(t56_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1858 $T # label(t52_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1859 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> -(-((all D all E (m2_relset_1(E,D,A) & v1_funct_1(E) & v1_funct_2(E,D,A) -> (all F (v1_funct_1(F) & v1_funct_2(F,D,A) & m2_relset_1(F,D,A) -> (k1_partfun1(D,A,A,B,F,C) = k1_partfun1(D,A,A,B,E,C) -> F = E))))) <-> v2_funct_1(C)) & B != k1_xboole_0 & A != k1_xboole_0))) # label(t27_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1860 $T # label(t128_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 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) -> (all E (m2_relset_1(E,B,C) & v1_funct_2(E,B,C) & v1_funct_1(E) -> (-(B = k1_xboole_0 & C != k1_xboole_0 & A != k1_xboole_0) -> v1_funct_2(k1_partfun1(A,B,B,C,D,E),A,C) & m2_relset_1(k1_partfun1(A,B,B,C,D,E),A,C) & v1_funct_1(k1_partfun1(A,B,B,C,D,E))))))) # label(t19_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1862 $T # label(t117_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1863 $T # label(t138_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1864 $T # label(t15_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1865 $T # label(t129_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1866 $T # label(t68_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1867 $T # label(t102_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1868 (all A all B all C (m1_relset_1(C,A,B) -> (v2_funct_2(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) & v2_funct_1(C) -> v3_funct_2(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C)))) # label(cc3_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1869 (all A all B (r2_hidden(B,f2_s6_funct_2) & r2_hidden(A,f1_s6_funct_2) -> r2_hidden(f4_s6_funct_2(A,B),f3_s6_funct_2))) -> (exists A (m2_relset_1(A,k2_zfmisc_1(f1_s6_funct_2,f2_s6_funct_2),f3_s6_funct_2) & (all B all C (r2_hidden(B,f1_s6_funct_2) & r2_hidden(C,f2_s6_funct_2) -> k1_funct_1(A,k4_tarski(B,C)) = f4_s6_funct_2(B,C))) & v1_funct_2(A,k2_zfmisc_1(f1_s6_funct_2,f2_s6_funct_2),f3_s6_funct_2) & v1_funct_1(A))) # label(s6_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1870 $T # label(t108_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1871 (all A all B all C all D (v1_funct_2(D,k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) -> k9_funct_2(A,B,C) = D)) # label(d5_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1872 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (m2_relset_1(E,B,C) & v1_funct_2(E,B,C) & v1_funct_1(E) -> (k2_relat_1(D) = B & v2_funct_1(k1_partfun1(A,B,B,C,D,E)) -> C = k1_xboole_0 & B != k1_xboole_0 | v2_funct_1(E) & v2_funct_1(D)))))) # label(t30_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1873 $T # label(t140_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1874 (all A all B (m1_relset_1(B,A,A) -> (v1_funct_1(B) & v1_partfun1(B,A,A) & v1_relat_2(B) & v1_funct_2(B,A,A) -> v1_funct_1(B) & v2_funct_1(B) & v2_funct_2(B,A,A) & v3_funct_2(B,A,A) & v1_funct_2(B,A,A)))) # label(cc4_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1875 $T # label(t58_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1876 (all A (r2_hidden(A,f1_s9_funct_2) -> (-p1_s9_funct_2(A) -> r2_hidden(f4_s9_funct_2(A),f2_s9_funct_2)) & (p1_s9_funct_2(A) -> r2_hidden(f3_s9_funct_2(A),f2_s9_funct_2)))) -> (exists A (v1_funct_1(A) & v1_funct_2(A,f1_s9_funct_2,f2_s9_funct_2) & m2_relset_1(A,f1_s9_funct_2,f2_s9_funct_2) & (all B (r2_hidden(B,f1_s9_funct_2) -> (-p1_s9_funct_2(B) -> k1_funct_1(A,B) = f4_s9_funct_2(B)) & (p1_s9_funct_2(B) -> k1_funct_1(A,B) = f3_s9_funct_2(B)))))) # label(s9_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1877 $T # label(t110_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1878 $T # label(t13_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1879 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,k1_tarski(B)) & m2_relset_1(D,A,k1_tarski(B)) -> (r2_hidden(C,A) -> k1_funct_1(D,C) = B))) # label(t65_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1880 $T # label(t139_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1881 (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]. 56.22/55.19 1882 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (A = k1_relat_1(C) & (all D (r2_hidden(D,A) -> r2_hidden(k1_funct_1(C,D),B))) -> v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C)))) # label(t5_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1883 $T # label(t124_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1884 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (B != k1_xboole_0 -> (all E ((exists F (r2_hidden(F,C) & E = k1_funct_1(D,F) & r2_hidden(F,A))) -> r2_hidden(E,k9_relat_1(D,C))))))) # label(t43_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1885 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (r1_partfun1(C,D) -> r2_hidden(D,k5_partfun1(A,B,C)) | k1_xboole_0 = B & A != k1_xboole_0))))) # label(t155_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1886 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (r2_hidden(C,A) -> r2_hidden(k1_funct_1(D,C),k2_relat_1(D)) | k1_xboole_0 = B))) # label(t6_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1887 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(k4_relset_1(A,B,D),k4_relset_1(A,B,C)) & r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) -> r1_tarski(D,C)))))) # label(t166_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1888 (all A all B (m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (m2_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) -> ((all D (r2_hidden(D,k4_relset_1(A,A,B)) -> k1_funct_1(B,D) = k1_funct_1(C,D))) <-> r1_partfun1(B,C)))))) # label(t146_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1889 (all A all B all C all D all E (v1_funct_2(D,A,B) & m1_relset_1(D,A,B) & v1_funct_1(E) & v1_funct_2(E,B,C) & m1_relset_1(E,B,C) & v1_funct_1(D) & -v1_xboole_0(B) -> k7_funct_2(A,B,C,D,E) = k5_relat_1(D,E))) # label(redefinition_k7_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1890 (all A all B all C all D (m2_relset_1(D,k1_tarski(A),B) & v1_funct_1(D) & v1_funct_2(D,k1_tarski(A),B) -> (k1_xboole_0 != B -> r1_tarski(k2_funct_2(k1_tarski(A),B,D,C),k1_tarski(k1_funct_1(D,A)))))) # label(t64_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1891 $T # label(t39_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1892 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (v2_funct_1(C) & (all E all F ((k1_funct_1(C,F) = E & r2_hidden(F,A) -> r2_hidden(E,B) & F = k1_funct_1(D,E)) & (F = k1_funct_1(D,E) & r2_hidden(E,B) -> E = k1_funct_1(C,F) & r2_hidden(F,A)))) & k2_relat_1(C) = B -> k2_funct_1(C) = D | k1_xboole_0 = B | k1_xboole_0 = A))))) # label(t34_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1893 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> ((all E (r2_hidden(E,A) -> k1_funct_1(D,E) = k1_funct_1(C,E))) -> D = C))))) # label(t18_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1894 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (r1_tarski(A,C) -> D = k2_partfun1(A,B,D,C)))) # label(t40_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1895 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> B = k1_xboole_0 & A != k1_xboole_0 | v1_partfun1(C,A,B)))) # label(t132_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1896 (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]. 56.22/55.19 1897 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,k1_tarski(A),B) & m2_relset_1(C,k1_tarski(A),B) -> (B != k1_xboole_0 -> k2_relat_1(C) = k1_tarski(k1_funct_1(C,A))))) # label(t62_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1898 $T # label(t105_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1899 $T # label(t144_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1900 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (v2_funct_2(C,A,B) & v2_funct_1(C) <-> v3_funct_2(C,A,B)))) # label(d4_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1901 $T # label(t127_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1902 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) -> (all C (m2_relset_1(C,A,A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,A) & m2_relset_1(D,A,A) -> (r1_partfun1(C,D) & r1_partfun1(B,D) -> r1_partfun1(B,C)))))))) # label(t152_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1903 (all A all B all C (m1_relset_1(C,A,B) -> (v1_funct_1(C) & v3_funct_2(C,A,B) & v1_funct_2(C,A,B) -> v2_funct_2(C,A,B) & v1_funct_1(C) & v1_funct_2(C,A,B) & v2_funct_1(C)))) # label(cc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1904 (exists A (f4_s10_funct_2 = k8_funct_2(f1_s10_funct_2,f2_s10_funct_2,A,f3_s10_funct_2) & v1_funct_2(A,f1_s10_funct_2,f2_s10_funct_2) & m2_relset_1(A,f1_s10_funct_2,f2_s10_funct_2) & (all B (m1_subset_1(B,f1_s10_funct_2) -> (B != f3_s10_funct_2 -> k8_funct_2(f1_s10_funct_2,f2_s10_funct_2,A,B) = f5_s10_funct_2(B)))) & v1_funct_1(A))) # label(s10_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1905 $T # label(t54_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1906 (all A all B (v3_funct_2(B,A,A) & m1_relset_1(B,A,A) & v1_funct_1(B) & v1_funct_2(B,A,A) -> k6_funct_2(A,B) = k2_funct_1(B))) # label(redefinition_k6_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1907 (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]. 56.22/55.19 1908 $T # label(t80_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1909 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> (k2_relat_1(B) = A & v2_funct_1(B) -> m2_relset_1(B,A,A) & v3_funct_2(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B)))) # label(t83_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1910 $T # label(t107_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1911 (all A -v1_xboole_0(k1_funct_2(A,A))) # label(fc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1912 (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]. 56.22/55.19 1913 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (r2_hidden(D,k5_partfun1(A,B,C)) -> v1_funct_2(D,A,B) & v1_funct_1(D) & m2_relset_1(D,A,B))))) # label(t158_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1914 (all A all B -(r2_hidden(A,f1_s5_funct_2) & r2_hidden(B,f2_s5_funct_2) & (all C -(p1_s5_funct_2(A,B,C) & r2_hidden(C,f3_s5_funct_2))))) -> (exists A (v1_funct_1(A) & (all B all C (r2_hidden(B,f1_s5_funct_2) & r2_hidden(C,f2_s5_funct_2) -> p1_s5_funct_2(B,C,k1_funct_1(A,k4_tarski(B,C))))) & v1_funct_2(A,k2_zfmisc_1(f1_s5_funct_2,f2_s5_funct_2),f3_s5_funct_2) & m2_relset_1(A,k2_zfmisc_1(f1_s5_funct_2,f2_s5_funct_2),f3_s5_funct_2))) # label(s5_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1915 $T # label(t89_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1916 (all A all B all C (m2_relset_1(C,A,B) -> (k1_xboole_0 = B -> (k1_xboole_0 = C <-> v1_funct_2(C,A,B)) | A = k1_xboole_0) & ((k1_xboole_0 = B -> k1_xboole_0 = A) -> (A = k4_relset_1(A,B,C) <-> v1_funct_2(C,A,B))))) # label(d1_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1917 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (r2_hidden(C,A) -> B = k1_xboole_0 | r2_hidden(k1_funct_1(D,C),B)))) # label(t7_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1918 (all A all B all C all D (m1_subset_1(D,A) & v1_funct_1(C) & -v1_xboole_0(A) & m1_relset_1(C,A,B) & v1_funct_2(C,A,B) -> k1_funct_1(C,D) = k8_funct_2(A,B,C,D))) # label(redefinition_k8_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1919 $T # label(t1_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1920 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (v1_funct_2(C,A,A) & m2_relset_1(C,A,A) & v1_funct_1(C) -> (v2_funct_1(B) & k4_funct_2(A,C,B) = B -> k6_partfun1(A) = C))))) # label(t76_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1921 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (v1_partfun1(C,A,B) -> v1_funct_2(C,A,B) & v1_funct_1(C) & m2_relset_1(C,A,B)))) # label(t131_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1922 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> ((k1_xboole_0 = B -> k1_xboole_0 = A) -> k5_partfun1(A,B,k3_partfun1(C,A,B)) = k1_tarski(C)))) # label(t161_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1923 (all A all B (m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (v1_funct_2(C,A,A) & m2_relset_1(C,A,A) & v1_funct_1(C) -> (r1_partfun1(B,C) -> r2_hidden(C,k5_partfun1(A,A,B))))))) # label(t156_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1924 $T # label(t33_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.19 1925 (all A all B all C all D (v1_funct_2(D,k2_zfmisc_1(A,B),C) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (all E (m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_2(E,k2_zfmisc_1(A,B),C) & v1_funct_1(E) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> k1_funct_1(E,k4_tarski(F,G)) = k1_funct_1(D,k4_tarski(F,G)))))) -> D = E))))) # label(t120_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1926 (exists A (m2_relset_1(A,k2_zfmisc_1(f1_s8_funct_2,f2_s8_funct_2),f3_s8_funct_2) & v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(f1_s8_funct_2,f2_s8_funct_2),f3_s8_funct_2) & (all B (m1_subset_1(B,f1_s8_funct_2) -> (all C (m1_subset_1(C,f2_s8_funct_2) -> f4_s8_funct_2(B,C) = k1_funct_1(A,k4_tarski(B,C)))))))) # label(s8_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1927 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (m2_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) -> (r1_partfun1(B,C) -> C = B))))) # label(t143_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1928 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (B = k2_relat_1(C) & v2_funct_1(C) -> m2_relset_1(k2_funct_1(C),B,A) & v1_funct_2(k2_funct_1(C),B,A) & v1_funct_1(k2_funct_1(C))))) # label(t31_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1929 $T # label(t96_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1930 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m1_relset_1(B,A,A) & v3_funct_2(B,A,A) -> v1_funct_1(k6_funct_2(A,B)) & v1_funct_2(k6_funct_2(A,B),A,A) & v3_funct_2(k6_funct_2(A,B),A,A) & m2_relset_1(k6_funct_2(A,B),A,A))) # label(dt_k6_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1931 $T # label(t42_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1932 $T # label(t106_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1933 (all A all B all C all D (v1_funct_2(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,B),C) -> (all E (v1_funct_2(E,k2_zfmisc_1(A,B),C) & m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_1(E) -> ((all F all G (r2_hidden(G,B) & r2_hidden(F,A) -> k1_funct_1(E,k4_tarski(F,G)) = k1_funct_1(D,k4_tarski(F,G)))) -> E = D))))) # label(t118_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1934 $T # label(t2_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1935 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (v2_funct_2(C,A,B) <-> B = k2_relat_1(C)))) # label(d3_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1936 $T # label(t153_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1937 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> ((k1_xboole_0 = B -> A = k1_xboole_0) -> A = k3_funct_2(A,B,C,B)))) # label(t48_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1938 (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]. 56.22/55.20 1939 (all A all B (v3_funct_2(B,A,A) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> k5_funct_2(A,B,k6_funct_2(A,B)) = k6_partfun1(A) & k6_partfun1(A) = k5_funct_2(A,k6_funct_2(A,B),B))) # label(t88_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1940 (all A all B (m2_relset_1(B,A,A) & v1_funct_1(B) & v1_funct_2(B,A,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) -> (k2_relat_1(B) = A & A = k2_relat_1(C) -> A = k2_relat_1(k4_funct_2(A,B,C))))))) # label(t73_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1941 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> ((B = k1_xboole_0 -> A = k1_xboole_0) -> A = k3_funct_2(A,B,C,k2_funct_2(A,B,C,A))))) # label(t51_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1942 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> ((all E k1_tarski(E) != B) & r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) -> r1_tarski(D,C)))))) # label(t167_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1943 $T # label(t150_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1944 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> -((k1_xboole_0 = B -> A = k1_xboole_0) & (all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> -(r1_partfun1(C,E) & r1_partfun1(D,E)))) & r1_partfun1(C,D)))))) # label(t154_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1945 (all A all B all C (m2_relset_1(C,A,B) -> k7_relset_1(A,A,A,B,k6_partfun1(A),C) = C & k7_relset_1(A,B,B,B,C,k6_partfun1(B)) = C)) # label(t23_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1946 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) & v1_funct_2(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (r1_partfun1(C,D) -> D = C | k1_xboole_0 = B & k1_xboole_0 != A))))) # label(t142_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1947 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> (v2_funct_1(B) -> (all C all D (r2_hidden(D,A) & r2_hidden(C,A) & k1_funct_1(B,D) = k1_funct_1(B,C) -> C = D))))) # label(t85_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1948 $T # label(t114_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1949 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,k1_xboole_0,A) & v1_funct_2(C,k1_xboole_0,A) -> k1_xboole_0 = k3_funct_2(k1_xboole_0,A,C,B))) # label(t60_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1950 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (r1_tarski(B,C) -> m2_relset_1(D,A,C) & v1_funct_1(D) & v1_funct_2(D,A,C) | k1_xboole_0 != A & B = k1_xboole_0))) # label(t9_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1951 (exists A (v1_funct_1(A) & (all B (m1_subset_1(B,f1_s4_funct_2) -> f3_s4_funct_2(B) = k8_funct_2(f1_s4_funct_2,f2_s4_funct_2,A,B))) & m2_relset_1(A,f1_s4_funct_2,f2_s4_funct_2) & v1_funct_2(A,f1_s4_funct_2,f2_s4_funct_2))) # label(s4_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1952 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) & v1_funct_2(D,A,B) -> r1_tarski(k9_relat_1(D,C),B))) # label(t44_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1953 (all A (m1_subset_1(A,f1_s12_funct_2) -> r2_hidden(f3_s12_funct_2(A),f2_s12_funct_2))) -> (exists A ((all B (m1_subset_1(B,f1_s12_funct_2) -> f3_s12_funct_2(B) = k8_funct_2(f1_s12_funct_2,f2_s12_funct_2,A,B))) & m2_relset_1(A,f1_s12_funct_2,f2_s12_funct_2) & v1_funct_2(A,f1_s12_funct_2,f2_s12_funct_2) & v1_funct_1(A))) # label(s12_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1954 (all A all B all C (m1_relset_1(B,A,A) & v1_funct_1(B) & v1_funct_2(C,A,A) & m1_relset_1(C,A,A) & v1_funct_1(C) & v1_funct_2(B,A,A) -> v1_funct_2(k4_funct_2(A,B,C),A,A) & m2_relset_1(k4_funct_2(A,B,C),A,A) & v1_funct_1(k4_funct_2(A,B,C)))) # label(dt_k4_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1955 $T # label(t95_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1956 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> A = k4_relset_1(A,A,B) & r1_tarski(k2_relat_1(B),A))) # label(t67_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1957 (all A (m1_subset_1(A,f1_s14_funct_2) -> (exists B (p1_s14_funct_2(A,B) & m1_subset_1(B,f2_s14_funct_2))))) -> (exists A (m2_relset_1(A,f1_s14_funct_2,f2_s14_funct_2) & v1_funct_2(A,f1_s14_funct_2,f2_s14_funct_2) & (all B (m1_subset_1(B,f1_s14_funct_2) -> p1_s14_funct_2(B,k8_funct_2(f1_s14_funct_2,f2_s14_funct_2,A,B)))) & v1_funct_1(A))) # label(s14_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1958 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> ((all D -(r2_hidden(D,B) & k1_xboole_0 = k3_funct_2(A,B,C,k1_tarski(D)))) <-> k2_relat_1(C) = B))) # label(t49_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1959 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (k1_xboole_0 != B -> ((all D (k1_xboole_0 != D -> (all E (m2_relset_1(E,B,D) & v1_funct_2(E,B,D) & v1_funct_1(E) -> (all F (m2_relset_1(F,B,D) & v1_funct_2(F,B,D) & v1_funct_1(F) -> (k1_partfun1(A,B,B,D,C,F) = k1_partfun1(A,B,B,D,C,E) -> F = E))))))) <-> k2_relat_1(C) = B)))) # label(t22_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1960 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) & v1_funct_2(C,A,B) -> ((B = k1_xboole_0 -> A = k1_xboole_0) -> v1_partfun1(k3_partfun1(C,A,B),A,B)))) # label(t133_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1961 $T # label(t94_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1962 $T # label(t126_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1963 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> r1_tarski(k10_relat_1(D,C),A))) # label(t47_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1964 (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]. 56.22/55.20 1965 $T # label(t104_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1966 $T # label(t90_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1967 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> k5_partfun1(A,A,k3_partfun1(B,A,A)) = k1_tarski(B))) # label(t162_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1968 (all A all B all C (v1_funct_1(B) & v3_funct_2(C,A,A) & v1_funct_2(C,A,A) & v3_funct_2(B,A,A) & m1_relset_1(C,A,A) & v1_funct_1(C) & m1_relset_1(B,A,A) & v1_funct_2(B,A,A) -> m2_relset_1(k5_funct_2(A,B,C),A,A) & v1_funct_1(k5_funct_2(A,B,C)) & v1_funct_2(k5_funct_2(A,B,C),A,A) & v3_funct_2(k5_funct_2(A,B,C),A,A))) # label(dt_k5_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1969 $T # label(t71_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1970 (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]. 56.22/55.20 1971 $T # label(t103_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1972 (all A all B all C (m2_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(B,A) -> k1_funct_1(D,k1_funct_1(C,B)) = k1_funct_1(k5_relat_1(C,D),B)))))) # label(t70_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1973 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> ((B = k1_xboole_0 -> A = k1_xboole_0) -> k2_funct_2(A,B,C,A) = k2_relat_1(C)))) # label(t45_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1974 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k2_relat_1(B),A) -> v1_funct_2(B,k1_relat_1(B),A) & v1_funct_1(B) & m2_relset_1(B,k1_relat_1(B),A)))) # label(t4_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1975 $T # label(t112_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1976 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (A = k4_relset_1(A,B,C) -> v1_funct_2(C,A,B) & v1_funct_1(C) & m2_relset_1(C,A,B)))) # label(t130_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1977 (all A all B k1_funct_2(A,B) = k5_partfun1(A,B,k3_partfun1(k1_xboole_0,A,B))) # label(t160_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1978 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> k3_funct_2(A,A,B,k2_funct_2(A,A,B,A)) = A)) # label(t82_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1979 (all A (k1_xboole_0 != A -> k1_xboole_0 = k1_funct_2(A,k1_xboole_0))) # label(t14_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1980 (all A all B all C all D (m1_relset_1(C,A,B) & v1_funct_1(C) -> k3_funct_2(A,B,C,D) = k10_relat_1(C,D))) # label(redefinition_k3_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1981 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_1(D) -> (v2_funct_1(C) & k2_relat_1(C) = B & k6_partfun1(A) = k1_partfun1(A,B,B,A,C,D) -> A = k1_xboole_0 | k2_funct_1(C) = D | B = k1_xboole_0))))) # label(t36_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1982 $T # label(t122_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1983 $T # label(t101_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1984 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) -> (exists C (v1_funct_1(C) & m2_relset_1(C,A,A) & r1_partfun1(B,C) & v1_funct_2(C,A,A))))) # label(t149_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1985 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,k1_xboole_0,A) & m2_relset_1(C,k1_xboole_0,A) -> k2_funct_2(k1_xboole_0,A,C,B) = k1_xboole_0)) # label(t59_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1986 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E -(r2_hidden(E,k2_funct_2(A,B,D,C)) & (all F (m1_subset_1(F,A) -> -(E = k1_funct_1(D,F) & r2_hidden(F,C)))))))) # label(t116_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1987 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> ((B = k1_xboole_0 -> A = k1_xboole_0) -> r2_hidden(C,k1_funct_2(A,B))))) # label(t11_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1988 $T # label(t135_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1989 $T # label(t100_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1990 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_2(A,k1_relat_1(A),k2_relat_1(A)) & m2_relset_1(A,k1_relat_1(A),k2_relat_1(A)) & v1_funct_1(A))) # label(t3_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1991 $T # label(t123_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1992 $T # label(t109_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1993 (all A all B (m2_relset_1(B,A,A) -> B = k7_relset_1(A,A,A,A,k6_partfun1(A),B) & k7_relset_1(A,A,A,A,B,k6_partfun1(A)) = B)) # label(t74_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1994 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> -(B != k1_xboole_0 & (exists D (m2_relset_1(D,B,A) & k6_partfun1(A) = k1_partfun1(A,B,B,A,C,D) & v1_funct_2(D,B,A) & v1_funct_1(D))) & -v2_funct_1(C)))) # label(t37_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1995 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (r1_tarski(C,A) -> k1_xboole_0 != A & k1_xboole_0 = B | m2_relset_1(k2_partfun1(A,B,D,C),C,B) & v1_funct_1(k2_partfun1(A,B,D,C)) & v1_funct_2(k2_partfun1(A,B,D,C),C,B)))) # label(t38_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1996 (all A all B (v1_funct_2(B,A,A) & v3_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v3_funct_2(C,A,A) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) -> (C = k5_funct_2(A,B,C) -> B = k6_partfun1(A)))))) # label(t86_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1997 $T # label(t99_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1998 (all A all B all C all D all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> (r2_hidden(C,A) & r2_hidden(k1_funct_1(E,C),D) -> k1_funct_1(k9_relset_1(A,B,D,E),C) = k1_funct_1(E,C) | B = k1_xboole_0))) # label(t41_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 1999 $T # label(t10_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 2000 (all A all B all C (v1_funct_2(C,k1_tarski(A),B) & v1_funct_1(C) & m2_relset_1(C,k1_tarski(A),B) -> (k1_xboole_0 != B -> r2_hidden(k1_funct_1(C,A),B)))) # label(t61_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 2001 $T # label(t63_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 2002 $T # label(dt_k1_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 2003 (all A (m1_subset_1(A,f1_s3_funct_2) -> (exists B (p1_s3_funct_2(A,B) & m1_subset_1(B,f2_s3_funct_2))))) -> (exists A (m2_relset_1(A,f1_s3_funct_2,f2_s3_funct_2) & v1_funct_2(A,f1_s3_funct_2,f2_s3_funct_2) & v1_funct_1(A) & (all B (m1_subset_1(B,f1_s3_funct_2) -> p1_s3_funct_2(B,k8_funct_2(f1_s3_funct_2,f2_s3_funct_2,A,B)))))) # label(s3_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 2004 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_tarski(B)) -> (all D (m2_relset_1(D,A,k1_tarski(B)) & v1_funct_2(D,A,k1_tarski(B)) & v1_funct_1(D) -> k1_tarski(D) = k5_partfun1(A,k1_tarski(B),C))))) # label(t164_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 2005 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (v2_funct_1(D) & r2_hidden(C,A) -> B = k1_xboole_0 | C = k1_funct_1(k2_funct_1(D),k1_funct_1(D,C))))) # label(t32_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 2006 (all A all B all C all D (v1_funct_2(C,A,B) & m1_subset_1(D,A) & -v1_xboole_0(A) & v1_funct_1(C) & m1_relset_1(C,A,B) -> m1_subset_1(k8_funct_2(A,B,C,D),B))) # label(dt_k8_funct_2) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 2007 (all A all B all C (np__1 = k1_funct_1(k4_funct_3(B,C),A) -> r2_hidden(A,B))) # label(t42_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 2008 (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) & k2_zfmisc_1(A,B) = k1_relat_1(C) & (all E all F (r2_hidden(E,A) & r2_hidden(F,B) -> k1_funct_1(C,k4_tarski(E,F)) = k1_funct_1(D,k4_tarski(E,F)))) -> D = C))))) # label(t6_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 2009 (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]. 56.22/55.20 2010 (all A all B all C all D all E (-v1_xboole_0(B) & m1_relset_1(E,A,C) & v1_funct_1(D) & m1_relset_1(D,A,B) & v1_funct_1(E) & v1_funct_2(E,A,C) & v1_funct_2(D,A,B) & -v1_xboole_0(C) -> v1_funct_1(k14_funct_3(A,B,C,D,E)) & m2_relset_1(k14_funct_3(A,B,C,D,E),A,k2_zfmisc_1(B,C)) & v1_funct_2(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]. 56.22/55.20 2011 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k7_relat_1(k6_relat_1(A),B) = k6_funct_3(A,B))) # label(t53_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 2012 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B)) = k2_relat_1(k15_funct_3(A,B)))))) # label(t88_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 2013 (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 (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]. 56.22/55.20 2014 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_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]. 56.22/55.20 2015 (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(E,B) & r2_hidden(D,A) -> D = k1_funct_1(C,k4_tarski(D,E))))))) # label(d5_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 2016 (all A all 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)) & v1_funct_1(k5_funct_3(A,B)))) # label(dt_k5_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 2017 (all A all B all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m2_relset_1(E,A,C) & v1_funct_1(E) & v1_funct_2(E,A,C) -> (all F (v1_funct_2(F,B,D) & v1_funct_1(F) & m2_relset_1(F,B,D) -> k13_funct_3(k5_relat_1(k9_funct_3(A,B),E),k5_relat_1(k10_funct_3(A,B),F)) = k16_funct_3(A,B,C,D,E,F))))))))) # label(t98_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 2018 $T # label(t65_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 2019 (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) -> -((B = k1_xboole_0 -> A = k1_xboole_0) & -(v1_funct_1(k13_funct_3(D,E)) & 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))) & (C = k1_xboole_0 -> k1_xboole_0 = A)))))) # label(t78_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 2020 (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]. 56.22/55.20 2021 (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]. 56.22/55.20 2022 (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(B) = k1_relat_1(A) & k1_relat_1(D) = k1_relat_1(C) & k13_funct_3(A,B) = k13_funct_3(D,C) -> A = D & B = C))))))))) # label(t74_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 2023 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k4_funct_3(A,B) = C <-> k1_relat_1(C) = B & (all D (r2_hidden(D,B) -> (r2_hidden(D,A) -> k1_funct_1(C,D) = np__1) & (-r2_hidden(D,A) -> np__0 = k1_funct_1(C,D))))))) # label(d3_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 2024 (all A (v1_funct_1(A) & v1_relat_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]. 56.22/55.20 2025 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_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]. 56.22/55.20 2026 (all A (v1_funct_1(k12_funct_3(A)) & v1_funct_2(k12_funct_3(A),A,k2_zfmisc_1(A,A)) & m2_relset_1(k12_funct_3(A),A,k2_zfmisc_1(A,A)))) # label(dt_k12_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 2027 (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]. 56.22/55.20 2028 (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))) -> k3_tarski(k10_relat_1(k3_funct_3(B),A)) = k9_relat_1(B,k3_tarski(A))))) # label(t32_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 2029 (all A all B (m2_relset_1(k10_funct_3(A,B),k2_zfmisc_1(A,B),B) & v1_funct_1(k10_funct_3(A,B)) & v1_funct_2(k10_funct_3(A,B),k2_zfmisc_1(A,B),B))) # label(dt_k10_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 2030 (all A (v1_relat_1(A) & v1_funct_1(A) -> k1_xboole_0 = k1_funct_1(k1_funct_3(A),k1_xboole_0))) # label(t9_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 2031 (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_2(F,C,D) & v1_funct_1(F) & m2_relset_1(F,C,D) -> v1_funct_2(k15_funct_3(E,F),k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) & 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)))))) # label(t95_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 2032 $T # label(t45_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.20 2033 (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]. 56.22/55.20 2034 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_zfmisc_1(k2_relat_1(A)) = k1_relat_1(B) & (all C (r1_tarski(C,k2_relat_1(A)) -> k10_relat_1(A,C) = k1_funct_1(B,C))) <-> k3_funct_3(A) = B))))) # label(d2_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2035 $T # label(t63_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2036 $T # label(t85_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2037 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> ((k1_xboole_0 = B -> k1_xboole_0 = A) -> v1_funct_1(k1_funct_3(C)) & 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))))) # label(t22_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2038 (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]. 56.22/55.21 2039 (all A all B k4_funct_3(A,B) = k5_funct_3(A,B)) # label(redefinition_k5_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2040 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(B) = A & (all C (r2_hidden(C,A) -> k1_funct_1(B,C) = k4_tarski(C,C))) <-> B = k11_funct_3(A)))) # label(d7_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2041 (all A all B (v1_funct_1(B) & v1_relat_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]. 56.22/55.21 2042 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_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]. 56.22/55.21 2043 (all A all B all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,C) & v1_funct_1(D) & v1_funct_2(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]. 56.22/55.21 2044 (all A (v1_relat_1(A) & v1_funct_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]. 56.22/55.21 2045 (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]. 56.22/55.21 2046 (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 & k1_relat_1(B) = A -> k1_relat_1(k13_funct_3(B,C)) = A))))) # label(t70_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2047 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (r1_tarski(B,k1_zfmisc_1(k1_relat_1(A))) & v2_funct_1(A) -> k10_relat_1(k3_funct_3(A),B) = k9_relat_1(k1_funct_3(A),B))))) # label(t37_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2048 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k8_funct_3(A,B) = C <-> (all D all E (r2_hidden(D,A) & r2_hidden(E,B) -> k1_funct_1(C,k4_tarski(D,E)) = E)) & k1_relat_1(C) = k2_zfmisc_1(A,B)))) # label(d6_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2049 $T # label(t51_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2050 (all A all B (v1_relat_1(B) & v1_funct_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]. 56.22/55.21 2051 (all A all B (v1_funct_1(B) & v1_relat_1(B) & v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k15_funct_3(A,B)) & v1_relat_1(k15_funct_3(A,B)))) # label(dt_k15_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2052 (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_2(E,A,C) & m2_relset_1(E,A,C) & v1_funct_1(E) -> 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]. 56.22/55.21 2053 (all A all B (-v1_xboole_0(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> k10_relat_1(k13_funct_3(C,D),k2_zfmisc_1(A,B)) = k3_xboole_0(k10_relat_1(C,A),k10_relat_1(D,B)))))))) # label(t77_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2054 (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) -> (k1_relat_1(C) = k3_xboole_0(k1_relat_1(A),k1_relat_1(B)) & (all D (r2_hidden(D,k1_relat_1(C)) -> k1_funct_1(C,D) = k4_tarski(k1_funct_1(A,D),k1_funct_1(B,D)))) <-> k13_funct_3(A,B) = C))))))) # label(d8_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2055 (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]. 56.22/55.21 2056 $T # label(d4_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2057 $T # label(t46_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2058 $T # label(t11_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2059 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C all D (r2_hidden(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]. 56.22/55.21 2060 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k1_funct_3(A)) & v1_funct_2(k1_funct_3(A),k1_zfmisc_1(k1_relat_1(A)),k1_zfmisc_1(k2_relat_1(A))) & m2_relset_1(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]. 56.22/55.21 2061 $T # label(t67_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2062 (all A all B (v1_funct_1(B) & v1_relat_1(B) & v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k13_funct_3(A,B)) & v1_funct_1(k13_funct_3(A,B)))) # label(dt_k13_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2063 (all A all B all C (r2_hidden(A,k4_xboole_0(B,C)) -> np__0 = k1_funct_1(k4_funct_3(C,B),A))) # label(t43_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2064 (all A all B all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,C) & v1_funct_2(D,A,C) & v1_funct_1(D) -> (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]. 56.22/55.21 2065 (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,B) & k1_relat_1(D) = B & 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]. 56.22/55.21 2066 (all A all B (v1_funct_1(k4_funct_3(A,B)) & v1_relat_1(k4_funct_3(A,B)))) # label(dt_k4_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2067 (all A (v1_relat_1(k11_funct_3(A)) & v1_funct_1(k11_funct_3(A)))) # label(dt_k11_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2068 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_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]. 56.22/55.21 2069 $T # label(t50_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2070 (all A all 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) & v1_funct_1(k9_funct_3(A,B)))) # label(dt_k9_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2071 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) & v1_funct_2(D,A,B) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,C) & v1_funct_2(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]. 56.22/55.21 2072 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v1_funct_1(k6_funct_3(A,B)) & m2_relset_1(k6_funct_3(A,B),B,A) & v1_funct_2(k6_funct_3(A,B),B,A))) # label(dt_k6_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2073 $T # label(t57_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2074 (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(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]. 56.22/55.21 2075 (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]. 56.22/55.21 2076 (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]. 56.22/55.21 2077 (all A all B -(r2_hidden(A,f1_s1_funct_3) & (all C -p1_s1_funct_3(A,B,C)) & r2_hidden(B,f2_s1_funct_3))) & (all A all B all C all D (p1_s1_funct_3(A,B,C) & r2_hidden(B,f2_s1_funct_3) & r2_hidden(A,f1_s1_funct_3) & p1_s1_funct_3(A,B,D) -> C = D)) -> (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]. 56.22/55.21 2078 (all A (v1_funct_1(A) & v1_relat_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]. 56.22/55.21 2079 $T # label(t44_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2080 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> k10_relat_1(k15_funct_3(C,D),k2_zfmisc_1(A,B)) = k2_zfmisc_1(k10_relat_1(C,A),k10_relat_1(D,B)))))) # label(t94_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2081 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> (all F (v1_funct_2(F,A,C) & m2_relset_1(F,A,C) & v1_funct_1(F) -> (all G (v1_funct_1(G) & m2_relset_1(G,A,C) & v1_funct_2(G,A,C) -> (k13_funct_3(D,F) = k13_funct_3(E,G) -> k1_xboole_0 != A & C = k1_xboole_0 | F = G & D = E | B = k1_xboole_0 & A != k1_xboole_0))))))))) # label(t83_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2082 (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(k10_relat_1(k1_funct_3(B),A))))) # label(t19_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2083 (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]. 56.22/55.21 2084 $T # label(t7_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2085 (all A all B (v1_relat_1(B) & v1_funct_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]. 56.22/55.21 2086 $T # label(t64_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2087 (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]. 56.22/55.21 2088 (all A all B all C all D all E all F (m1_relset_1(E,A,C) & m1_relset_1(F,B,D) & v1_funct_2(E,A,C) & v1_funct_1(F) & v1_funct_2(F,B,D) & v1_funct_1(E) -> 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)) & v1_funct_1(k16_funct_3(A,B,C,D,E,F)))) # label(dt_k16_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2089 $T # label(t41_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2090 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,k2_tarski(np__0,np__1)) & v1_funct_2(B,A,k2_tarski(np__0,np__1)) -> 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]. 56.22/55.21 2091 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) -> k9_relat_1(k3_funct_3(B),A) = k10_relat_1(k1_funct_3(B),A)))) # label(t34_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2092 (all A all B all C (-v1_xboole_0(B) & v1_funct_2(C,A,B) & v1_funct_1(C) & m1_relset_1(C,A,B) -> k2_funct_3(A,B,C) = k1_funct_3(C))) # label(redefinition_k2_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2093 (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]. 56.22/55.21 2094 (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) -> 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]. 56.22/55.21 2095 $T # label(t23_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2096 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(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)) = k15_funct_3(A,B))))) # label(t87_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2097 (all A (v1_relat_1(A) & v1_funct_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]. 56.22/55.21 2098 $T # label(t52_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2099 (all A all B (k1_xboole_0 != A -> k2_relat_1(k7_funct_3(B,A)) = B)) # label(t60_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2100 (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,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]. 56.22/55.21 2101 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (B = k1_funct_3(A) <-> (all C (r1_tarski(C,k1_relat_1(A)) -> k9_relat_1(A,C) = k1_funct_1(B,C))) & k1_zfmisc_1(k1_relat_1(A)) = k1_relat_1(B)))))) # label(d1_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2102 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> k5_relat_1(k1_funct_3(A),k1_funct_3(B)) = k1_funct_3(k5_relat_1(A,B)))))) # label(t20_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2103 (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]. 56.22/55.21 2104 (all A all B (v1_relat_1(B) & v1_funct_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]. 56.22/55.21 2105 (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]. 56.22/55.21 2106 (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]. 56.22/55.21 2107 $T # label(t26_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2108 $T # label(t55_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2109 (all A (v1_funct_1(A) & v1_relat_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]. 56.22/55.21 2110 (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) = k1_relat_1(C) & r1_tarski(k2_relat_1(C),A) & r1_tarski(k2_relat_1(D),B) -> D = k5_relat_1(k13_funct_3(C,D),k10_funct_3(A,B)) & k5_relat_1(k13_funct_3(C,D),k9_funct_3(A,B)) = C))))) # label(t72_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2111 (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]. 56.22/55.21 2112 (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]. 56.22/55.21 2113 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> k13_funct_3(k5_relat_1(B,A),k5_relat_1(D,C)) = k5_relat_1(k13_funct_3(B,D),k15_funct_3(A,C)))))))))) # label(t91_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2114 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_2(E,A,C) & m2_relset_1(E,A,C) & v1_funct_1(E) -> D = k7_funct_2(A,k2_zfmisc_1(B,C),B,k14_funct_3(A,B,C,D,E),k9_funct_3(B,C)) & E = k7_funct_2(A,k2_zfmisc_1(B,C),C,k14_funct_3(A,B,C,D,E),k10_funct_3(B,C)))))))))) # label(t82_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2115 $T # label(t58_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2116 (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(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]. 56.22/55.21 2117 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,k1_zfmisc_1(k1_relat_1(B))) -> k3_tarski(k9_relat_1(k1_funct_3(B),A)) = k9_relat_1(B,k3_tarski(A))))) # label(t16_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2118 (all A k11_funct_3(A) = k12_funct_3(A)) # label(redefinition_k12_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2119 (all A all B all C all D (v1_funct_2(D,A,B) & v1_funct_1(D) & m2_relset_1(D,A,B) -> (all E (m2_relset_1(E,A,C) & v1_funct_2(E,A,C) & v1_funct_1(E) -> -(-(E = k5_relat_1(k13_funct_3(D,E),k10_funct_3(B,C)) & k5_relat_1(k13_funct_3(D,E),k9_funct_3(B,C)) = D) & (k1_xboole_0 = C -> A = k1_xboole_0) & (B = k1_xboole_0 -> A = k1_xboole_0)))))) # label(t81_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2120 (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,A,B) & m2_relset_1(E,A,B) -> (all F (v1_funct_2(F,C,D) & v1_funct_1(F) & m2_relset_1(F,C,D) -> (all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,C) -> k1_funct_1(k16_funct_3(A,C,B,D,E,F),k4_tarski(G,H)) = k4_tarski(k8_funct_2(A,B,E,G),k8_funct_2(C,D,F,H)))))))))))))))))) # label(t96_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2121 (all 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 (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (all F (v1_funct_1(F) & m2_relset_1(F,A,C) & v1_funct_2(F,A,C) -> (all G (m2_relset_1(G,A,C) & v1_funct_1(G) & v1_funct_2(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]. 56.22/55.21 2122 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k3_funct_3(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))))) # label(t39_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2123 (exists A ((all B all C (r2_hidden(B,f1_s2_funct_3) & r2_hidden(C,f2_s2_funct_3) -> k1_funct_1(A,k4_tarski(B,C)) = f3_s2_funct_3(B,C))) & k2_zfmisc_1(f1_s2_funct_3,f2_s2_funct_3) = k1_relat_1(A) & v1_relat_1(A) & v1_funct_1(A))) # label(s2_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2124 (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]. 56.22/55.21 2125 (all A all B (v1_relat_1(B) & v1_funct_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]. 56.22/55.21 2126 (all A all B all C all D all E (v1_funct_1(D) & v1_funct_2(E,A,C) & m1_relset_1(E,A,C) & m1_relset_1(D,A,B) & -v1_xboole_0(C) & v1_funct_1(E) & v1_funct_2(D,A,B) & -v1_xboole_0(B) -> k13_funct_3(D,E) = k14_funct_3(A,B,C,D,E))) # label(redefinition_k14_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2127 (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]. 56.22/55.21 2128 (all A all B (k1_xboole_0 != A -> k2_relat_1(k8_funct_3(A,B)) = B)) # label(t62_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2129 (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]. 56.22/55.21 2130 (all A all B (v1_funct_1(B) & v1_relat_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]. 56.22/55.21 2131 (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(C) = A & k1_relat_1(B) = 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]. 56.22/55.21 2132 (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(B,A),k1_relat_1(C)) & r1_tarski(A,k1_relat_1(B)) -> r1_tarski(A,k1_relat_1(k5_relat_1(B,C)))))))) # label(t3_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2133 (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]. 56.22/55.21 2134 (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) & v1_funct_2(F,C,D) & m2_relset_1(F,C,D) -> -((D = k1_xboole_0 -> C = k1_xboole_0) & (k1_xboole_0 = B -> k1_xboole_0 = A) & 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))))))) # label(t97_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2135 $T # label(t54_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2136 $T # label(t40_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2137 (all A all B all C all D all E all F (v1_funct_2(E,A,C) & v1_funct_1(F) & v1_funct_2(F,B,D) & m1_relset_1(E,A,C) & m1_relset_1(F,B,D) & v1_funct_1(E) -> 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]. 56.22/55.21 2138 (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]. 56.22/55.21 2139 (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) -> (k15_funct_3(A,B) = C <-> (all D all E (r2_hidden(D,k1_relat_1(A)) & r2_hidden(E,k1_relat_1(B)) -> k4_tarski(k1_funct_1(A,D),k1_funct_1(B,E)) = k1_funct_1(C,k4_tarski(D,E)))) & k1_relat_1(C) = k2_zfmisc_1(k1_relat_1(A),k1_relat_1(B))))))))) # label(d9_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2140 (all A all B all C (-v1_xboole_0(B) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & v1_funct_1(C) -> v1_funct_1(k2_funct_3(A,B,C)) & m2_relset_1(k2_funct_3(A,B,C),k1_zfmisc_1(A),k1_zfmisc_1(B)) & v1_funct_2(k2_funct_3(A,B,C),k1_zfmisc_1(A),k1_zfmisc_1(B)))) # label(dt_k2_funct_3) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2141 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_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]. 56.22/55.21 2142 (all A ((exists B (A = B & p1_s10_domain_1(B) & p2_s10_domain_1(B) & m1_subset_1(B,f1_s10_domain_1))) <-> r2_hidden(A,a_0_3_domain_1))) # label(fraenkel_a_0_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.21 2143 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(C,k1_zfmisc_1(B)) -> (r2_hidden(A,a_3_1_domain_1(B,C,D)) <-> (exists E (m1_subset_1(E,B) & r2_hidden(E,D) & r2_hidden(E,C) & E = A))))) # label(fraenkel_a_3_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2144 (all A all B all C (-v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(B)) -> (r2_hidden(A,a_2_2_domain_1(B,C)) <-> (exists D (m1_subset_1(D,B) & A = D & -r2_hidden(D,C)))))) # label(fraenkel_a_2_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2145 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k7_subset_1(A,B,C) = a_3_5_domain_1(A,B,C))))))) # label(t62_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2146 (all A all B (-v1_xboole_0(B) -> ((exists C (m1_subset_1(C,B) & A = C & p2_s5_domain_1(C))) <-> r2_hidden(A,a_1_4_domain_1(B))))) # label(fraenkel_a_1_4_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2147 (all A all B all C all D (m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) & -v1_xboole_0(A) & -v1_xboole_0(C) & -v1_xboole_0(B) -> k15_domain_1(A,B,C,D) = k18_mcart_1(D))) # label(redefinition_k15_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2148 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(C,k1_zfmisc_1(B)) -> (r2_hidden(A,a_3_5_domain_1(B,C,D)) <-> (exists E (m1_subset_1(E,B) & E = A & (-r2_hidden(E,C) <-> r2_hidden(E,D))))))) # label(fraenkel_a_3_5_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2149 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> ((all F ((exists G (m1_subset_1(G,B) & (exists H ((exists I ((exists J (m1_subset_1(J,E) & F = k4_mcart_1(G,H,I,J))) & m1_subset_1(I,D))) & m1_subset_1(H,C))))) <-> r2_hidden(F,A))) -> k4_zfmisc_1(B,C,D,E) = A))))))))))) # label(t32_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2150 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(D) & -v1_xboole_0(C) -> ((exists E exists F exists G (A = k4_domain_1(B,C,D,E,F,G) & m1_subset_1(G,D) & m1_subset_1(E,B) & p1_s3_domain_1(E,F,G) & m1_subset_1(F,C))) <-> r2_hidden(A,a_3_8_domain_1(B,C,D))))) # label(fraenkel_a_3_8_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2151 (all A all B all C all D (m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(B)) & -v1_xboole_0(B) -> ((exists E ((r2_hidden(E,C) | r2_hidden(E,D)) & m1_subset_1(E,B) & A = E)) <-> r2_hidden(A,a_3_2_domain_1(B,C,D))))) # label(fraenkel_a_3_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2152 (all A ((exists B (p1_s10_domain_1(B) & A = B & m1_subset_1(B,f1_s10_domain_1))) <-> r2_hidden(A,a_0_4_domain_1))) # label(fraenkel_a_0_4_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2153 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> a_3_4_domain_1(A,B,C) = k7_subset_1(A,B,C))))))) # label(t61_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2154 (all A all B all C all D (-v1_xboole_0(C) & m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) & -v1_xboole_0(A) & -v1_xboole_0(B) -> m1_subset_1(k14_domain_1(A,B,C,D),A))) # label(dt_k14_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2155 (all A (-v1_xboole_0(A) -> m1_subset_1(a_1_2_domain_1(A),k1_zfmisc_1(A)))) # label(s1_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2156 $T # label(t29_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2157 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,k1_zfmisc_1(A)) -> (all F (m1_subset_1(F,k1_zfmisc_1(B)) -> (all G (m1_subset_1(G,k1_zfmisc_1(C)) -> (all H (m1_subset_1(H,k1_zfmisc_1(D)) -> k14_mcart_1(A,B,C,D,E,F,G,H) = a_8_0_domain_1(A,B,C,D,E,F,G,H))))))))))))))))) # label(t55_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2158 $T # label(t37_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2159 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(C,k1_zfmisc_1(B)) & -v1_xboole_0(B) -> (r2_hidden(A,a_3_6_domain_1(B,C,D)) <-> (exists E (m1_subset_1(E,B) & (-r2_hidden(E,D) <-> r2_hidden(E,C)) & E = A))))) # label(fraenkel_a_3_6_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2160 (all A (r2_hidden(A,a_0_1_domain_1) <-> (exists B (A = f3_s8_domain_1(B) & p1_s8_domain_1(B) & m1_subset_1(B,f1_s8_domain_1))))) # label(fraenkel_a_0_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2161 $T # label(t47_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2162 (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(k15_domain_1(A,B,C,D),B))) # label(dt_k15_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2163 (all A all B all C all D (m1_subset_1(C,k1_zfmisc_1(B)) & -v1_xboole_0(B) & m1_subset_1(D,k1_zfmisc_1(B)) -> ((exists E (r2_hidden(E,C) & -r2_hidden(E,D) & m1_subset_1(E,B) & E = A)) <-> r2_hidden(A,a_3_3_domain_1(B,C,D))))) # label(fraenkel_a_3_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2164 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,k3_zfmisc_1(B,C,D)) -> (k6_mcart_1(B,C,D,E) = A <-> (all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,C) -> (all H (m1_subset_1(H,D) -> (E = k4_domain_1(B,C,D,F,G,H) -> A = G)))))))))))))))) # label(t25_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2165 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> m1_subset_1(a_3_8_domain_1(A,B,C),k1_zfmisc_1(k3_zfmisc_1(A,B,C))))))))) # label(s3_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2166 (all A all B (-v1_xboole_0(B) -> ((exists C (A = C & m1_subset_1(C,B) & p1_s5_domain_1(C))) <-> r2_hidden(A,a_1_3_domain_1(B))))) # label(fraenkel_a_1_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2167 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (r2_hidden(A,k3_zfmisc_1(B,C,D)) <-> (exists E ((exists F (m1_subset_1(F,C) & (exists G (m1_subset_1(G,D) & k3_mcart_1(E,F,G) = A)))) & m1_subset_1(E,B)))))))))) # label(t15_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2168 $T # label(t30_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2169 (all A all B all C all D all E all F all G (m1_subset_1(E,k1_zfmisc_1(B)) & -v1_xboole_0(D) & -v1_xboole_0(B) & m1_subset_1(F,k1_zfmisc_1(C)) & m1_subset_1(G,k1_zfmisc_1(D)) & -v1_xboole_0(C) -> ((exists H exists I exists J (m1_subset_1(H,B) & r2_hidden(J,G) & r2_hidden(I,F) & A = k4_domain_1(B,C,D,H,I,J) & m1_subset_1(I,C) & m1_subset_1(J,D) & r2_hidden(H,E))) <-> r2_hidden(A,a_6_0_domain_1(B,C,D,E,F,G))))) # label(fraenkel_a_6_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2170 (all A (-v1_xboole_0(A) -> a_1_0_domain_1(A) = A)) # label(t48_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2171 $T # label(t18_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2172 (all A all B all C all D all E all F all G all H (m1_subset_1(E,A) & m1_subset_1(G,A) & m1_subset_1(C,A) & -v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(F,A) & m1_subset_1(H,A) & m1_subset_1(D,A) -> k5_enumset1(B,C,D,E,F,G,H) = k12_domain_1(A,B,C,D,E,F,G,H))) # label(redefinition_k12_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2173 $T # label(t5_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2174 (all A all B all C all D (m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) & -v1_xboole_0(B) & -v1_xboole_0(C) & -v1_xboole_0(A) -> k14_domain_1(A,B,C,D) = k17_mcart_1(D))) # label(redefinition_k14_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2175 (all A (r2_hidden(A,a_0_0_domain_1) <-> (exists B (m1_subset_1(B,f1_s7_domain_1) & p1_s7_domain_1(B) & A = B)))) # label(fraenkel_a_0_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2176 (all A all B all C all D all E all F all G all H all I (m1_subset_1(G,A) & m1_subset_1(I,A) & m1_subset_1(E,A) & m1_subset_1(B,A) & m1_subset_1(C,A) & m1_subset_1(H,A) & m1_subset_1(F,A) & m1_subset_1(D,A) & -v1_xboole_0(A) -> m1_subset_1(k13_domain_1(A,B,C,D,E,F,G,H,I),k1_zfmisc_1(A)))) # label(dt_k13_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2177 (all A all B all C all D all E all F (m1_subset_1(C,A) & -v1_xboole_0(A) & m1_subset_1(D,A) & m1_subset_1(F,A) & m1_subset_1(E,A) & m1_subset_1(B,A) -> m1_subset_1(k10_domain_1(A,B,C,D,E,F),k1_zfmisc_1(A)))) # label(dt_k10_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2178 (all A all B all C all D all E (-v1_xboole_0(C) & -v1_xboole_0(D) & -v1_xboole_0(B) & -v1_xboole_0(E) -> (r2_hidden(A,a_4_2_domain_1(B,C,D,E)) <-> (exists F exists G exists H exists I (m1_subset_1(G,C) & p1_s4_domain_1(F,G,H,I) & m1_subset_1(I,E) & m1_subset_1(F,B) & A = k5_domain_1(B,C,D,E,F,G,H,I) & m1_subset_1(H,D)))))) # label(fraenkel_a_4_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2179 (all A all B all C (-v1_xboole_0(B) & -v1_xboole_0(C) -> ((exists D exists E (m1_subset_1(E,C) & A = k1_domain_1(B,C,D,E) & m1_subset_1(D,B))) <-> r2_hidden(A,a_2_0_domain_1(B,C))))) # label(fraenkel_a_2_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2180 (all A all B (-v1_xboole_0(B) -> ((exists C (A = C & p1_s6_domain_1(C) & m1_subset_1(C,B))) <-> r2_hidden(A,a_1_5_domain_1(B))))) # label(fraenkel_a_1_5_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2181 (all A all B all C (m1_subset_1(C,A) & -v1_xboole_0(A) & m1_subset_1(B,A) -> k2_tarski(B,C) = k7_domain_1(A,B,C))) # label(redefinition_k7_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2182 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,k2_zfmisc_1(A,B)) & -v1_xboole_0(B) -> k1_mcart_1(C) = k2_domain_1(A,B,C))) # label(redefinition_k2_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2183 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> ((all E (r2_hidden(E,A) <-> (exists F ((exists G (m1_subset_1(G,C) & (exists H (m1_subset_1(H,D) & E = k3_mcart_1(F,G,H))))) & m1_subset_1(F,B))))) -> A = k3_zfmisc_1(B,C,D)))))))))) # label(t16_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2184 (all A all B all C (m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> m1_subset_1(k7_domain_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k7_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2185 (all A all B all C all D all E all F all G (m1_subset_1(C,A) & m1_subset_1(E,A) & m1_subset_1(D,A) & m1_subset_1(B,A) & -v1_xboole_0(A) & m1_subset_1(G,A) & m1_subset_1(F,A) -> k4_enumset1(B,C,D,E,F,G) = k11_domain_1(A,B,C,D,E,F,G))) # label(redefinition_k11_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2186 $T # label(t46_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2187 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> m1_subset_1(a_2_3_domain_1(A,B),k1_zfmisc_1(k2_zfmisc_1(A,B))))))) # label(s2_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2188 (all A all B all C (m1_subset_1(C,k2_zfmisc_1(A,B)) & -v1_xboole_0(B) & -v1_xboole_0(A) -> m1_subset_1(k2_domain_1(A,B,C),A))) # label(dt_k2_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2189 $T # label(t38_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2190 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> k3_zfmisc_1(A,B,C) = a_3_0_domain_1(A,B,C))))))) # label(t50_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2191 (all A all B all C all D all E all F all G all H (m1_subset_1(G,A) & m1_subset_1(H,A) & -v1_xboole_0(A) & m1_subset_1(D,A) & m1_subset_1(F,A) & m1_subset_1(E,A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> m1_subset_1(k12_domain_1(A,B,C,D,E,F,G,H),k1_zfmisc_1(A)))) # label(dt_k12_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2192 $T # label(t39_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2193 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_1_domain_1(B)) <-> (exists C (m1_subset_1(C,B) & -$T & A = C))))) # label(fraenkel_a_1_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2194 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> a_3_2_domain_1(A,B,C) = k4_subset_1(A,B,C))))))) # label(t59_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2195 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> ((exists F (m1_subset_1(F,B) & (exists G (m1_subset_1(G,C) & (exists H ((exists I (k4_mcart_1(F,G,H,I) = A & m1_subset_1(I,E))) & m1_subset_1(H,D))))))) <-> r2_hidden(A,k4_zfmisc_1(B,C,D,E))))))))))) # label(t31_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2196 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) -> k6_domain_1(A,B) = k1_tarski(B))) # label(redefinition_k6_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2197 $T # label(t13_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2198 (all A all B all C all D all E all F (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(F,C) & m1_subset_1(E,B) & m1_subset_1(D,A) & -v1_xboole_0(C) -> k4_domain_1(A,B,C,D,E,F) = k3_mcart_1(D,E,F))) # label(redefinition_k4_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2199 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k7_subset_1(A,B,C) = a_3_6_domain_1(A,B,C))))))) # label(t63_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2200 $T # label(t2_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2201 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(B)) -> a_4_1_domain_1(A,B,C,D) = k12_mcart_1(A,B,C,D))))))))) # label(t53_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2202 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> (all E (m1_subset_1(E,k3_zfmisc_1(A,B,C)) -> (k5_mcart_1(A,B,C,E) = k5_mcart_1(A,B,C,D) & k6_mcart_1(A,B,C,D) = k6_mcart_1(A,B,C,E) & k7_mcart_1(A,B,C,E) = k7_mcart_1(A,B,C,D) -> E = D))))))))))) # label(t28_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2203 $T # label(t8_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2204 (all A all B all C all D all E all F all G all H all I (m1_subset_1(E,A) & m1_subset_1(F,A) & m1_subset_1(C,A) & -v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(D,A) & m1_subset_1(G,A) & m1_subset_1(I,A) & m1_subset_1(H,A) -> k13_domain_1(A,B,C,D,E,F,G,H,I) = k6_enumset1(B,C,D,E,F,G,H,I))) # label(redefinition_k13_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2205 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k7_domain_1(A,C,B) = k7_domain_1(A,B,C))) # label(commutativity_k7_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2206 (all A all B all C all D (-v1_xboole_0(C) & m1_subset_1(D,k2_zfmisc_1(A,k2_zfmisc_1(B,C))) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k19_mcart_1(D) = k16_domain_1(A,B,C,D))) # label(redefinition_k16_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2207 (all A all B all C all D (m1_subset_1(D,A) & m1_subset_1(C,A) & -v1_xboole_0(A) & m1_subset_1(B,A) -> k1_enumset1(B,C,D) = k8_domain_1(A,B,C,D))) # label(redefinition_k8_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2208 $T # label(t14_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2209 (all A all B all C all D all E all F all G (m1_subset_1(B,A) & m1_subset_1(C,A) & m1_subset_1(G,A) & m1_subset_1(F,A) & -v1_xboole_0(A) & m1_subset_1(D,A) & m1_subset_1(E,A) -> m1_subset_1(k11_domain_1(A,B,C,D,E,F,G),k1_zfmisc_1(A)))) # label(dt_k11_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2210 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (m1_subset_1(F,k4_zfmisc_1(B,C,D,E)) -> ((all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (all I (m1_subset_1(I,D) -> (all J (m1_subset_1(J,E) -> (k5_domain_1(B,C,D,E,G,H,I,J) = F -> H = A))))))))) <-> A = k9_mcart_1(B,C,D,E,F)))))))))))) # label(t41_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2211 $T # label(t6_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2212 (all A all B all C all D all E (m1_subset_1(D,A) & m1_subset_1(E,A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k2_enumset1(B,C,D,E) = k9_domain_1(A,B,C,D,E))) # label(redefinition_k9_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2213 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> a_3_7_domain_1(A,B,C) = k7_subset_1(A,B,C))))))) # label(t64_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2214 $T # label(t36_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2215 (all A ((exists B exists C (m1_subset_1(C,f2_s9_domain_1) & m1_subset_1(B,f1_s9_domain_1) & p1_s9_domain_1(B,C) & f4_s9_domain_1(B,C) = A)) <-> r2_hidden(A,a_0_2_domain_1))) # label(fraenkel_a_0_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2216 $T # label(t4_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2217 (all A all B all C (-v1_xboole_0(B) & -v1_xboole_0(C) -> (r2_hidden(A,a_2_3_domain_1(B,C)) <-> (exists D exists E (m1_subset_1(E,C) & p1_s2_domain_1(D,E) & k1_domain_1(B,C,D,E) = A & m1_subset_1(D,B)))))) # label(fraenkel_a_2_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2218 $T # label(t21_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2219 $T # label(t10_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2220 (all A all B all C all D all E all F (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(D,A) & m1_subset_1(F,A) & m1_subset_1(E,A) & m1_subset_1(B,A) -> k3_enumset1(B,C,D,E,F) = k10_domain_1(A,B,C,D,E,F))) # label(redefinition_k10_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2221 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (all E (m1_subset_1(E,k1_zfmisc_1(B)) -> (all F (m1_subset_1(F,k1_zfmisc_1(C)) -> a_6_0_domain_1(A,B,C,D,E,F) = k13_mcart_1(A,B,C,D,E,F))))))))))))) # label(t54_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2222 (all A all B all C (-v1_xboole_0(B) & m1_subset_1(C,k2_zfmisc_1(A,B)) & -v1_xboole_0(A) -> k3_domain_1(A,B,C) = k2_mcart_1(C))) # label(redefinition_k3_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2223 $T # label(t11_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2224 $T # label(t19_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2225 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> -(r2_hidden(A,k2_zfmisc_1(B,C)) & (all D (m1_subset_1(D,B) -> (all E (m1_subset_1(E,C) -> A != k4_tarski(D,E)))))))))) # label(t9_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2226 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_2_domain_1(B)) <-> (exists C (m1_subset_1(C,B) & p1_s1_domain_1(C) & A = C))))) # label(fraenkel_a_1_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2227 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(B)) -> (r2_hidden(A,a_3_4_domain_1(B,C,D)) <-> (exists E ((-r2_hidden(E,C) & r2_hidden(E,D) | r2_hidden(E,C) & -r2_hidden(E,D)) & m1_subset_1(E,B) & E = A))))) # label(fraenkel_a_3_4_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2228 $T # label(t7_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2229 (all A all B all C all D all E all F (m1_subset_1(E,B) & m1_subset_1(F,C) & m1_subset_1(D,A) & -v1_xboole_0(C) & -v1_xboole_0(A) & -v1_xboole_0(B) -> m1_subset_1(k4_domain_1(A,B,C,D,E,F),k3_zfmisc_1(A,B,C)))) # label(dt_k4_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2230 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> a_2_2_domain_1(A,B) = k3_subset_1(A,B))))) # label(t57_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2231 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(D,k2_zfmisc_1(A,k2_zfmisc_1(B,C))) & -v1_xboole_0(C) -> m1_subset_1(k17_domain_1(A,B,C,D),C))) # label(dt_k17_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.22 2232 $T # label(t1_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2233 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> a_3_1_domain_1(A,B,C) = k5_subset_1(A,B,C))))))) # label(t58_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2234 $T # label(t34_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2235 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> a_3_3_domain_1(A,B,C) = k6_subset_1(A,B,C))))))) # label(t60_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2236 $T # label(t27_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2237 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (m1_subset_1(F,k4_zfmisc_1(B,C,D,E)) -> (A = k10_mcart_1(B,C,D,E,F) <-> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (all I (m1_subset_1(I,D) -> (all J (m1_subset_1(J,E) -> (k5_domain_1(B,C,D,E,G,H,I,J) = F -> I = A)))))))))))))))))))) # label(t42_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2238 (all A all B (-v1_xboole_0(B) -> ((exists C (m1_subset_1(C,B) & p2_s6_domain_1(C) & C = A)) <-> r2_hidden(A,a_1_6_domain_1(B))))) # label(fraenkel_a_1_6_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2239 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> a_4_0_domain_1(A,B,C,D) = k4_zfmisc_1(A,B,C,D))))))))) # label(t51_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2240 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (m1_subset_1(F,k4_zfmisc_1(B,C,D,E)) -> (k11_mcart_1(B,C,D,E,F) = A <-> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (all I (m1_subset_1(I,D) -> (all J (m1_subset_1(J,E) -> (k5_domain_1(B,C,D,E,G,H,I,J) = F -> A = J)))))))))))))))))))) # label(t43_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2241 (all A all B all C (m1_subset_1(C,k2_zfmisc_1(A,B)) & -v1_xboole_0(B) & -v1_xboole_0(A) -> m1_subset_1(k3_domain_1(A,B,C),B))) # label(dt_k3_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2242 (all A (r2_hidden(A,a_0_5_domain_1) <-> (exists B (B = A & m1_subset_1(B,f1_s10_domain_1) & p2_s10_domain_1(B))))) # label(fraenkel_a_0_5_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2243 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (m1_subset_1(F,k4_zfmisc_1(B,C,D,E)) -> ((all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (all I (m1_subset_1(I,D) -> (all J (m1_subset_1(J,E) -> (k5_domain_1(B,C,D,E,G,H,I,J) = F -> G = A))))))))) <-> A = k8_mcart_1(B,C,D,E,F)))))))))))) # label(t40_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2244 (all A all B all C all D all E (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & m1_subset_1(E,A) & m1_subset_1(D,A) -> m1_subset_1(k9_domain_1(A,B,C,D,E),k1_zfmisc_1(A)))) # label(dt_k9_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2245 $T # label(t20_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2246 $T # label(t22_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2247 (all A all B all C all D (m1_subset_1(D,A) & m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> m1_subset_1(k8_domain_1(A,B,C,D),k1_zfmisc_1(A)))) # label(dt_k8_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2248 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> k2_zfmisc_1(A,B) = a_2_0_domain_1(A,B))))) # label(t49_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2249 $T # label(t44_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2250 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(D) & -v1_xboole_0(C) -> (r2_hidden(A,a_3_0_domain_1(B,C,D)) <-> (exists E exists F exists G (A = k4_domain_1(B,C,D,E,F,G) & m1_subset_1(E,B) & m1_subset_1(F,C) & m1_subset_1(G,D)))))) # label(fraenkel_a_3_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2251 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(D,k2_zfmisc_1(A,k2_zfmisc_1(B,C))) & -v1_xboole_0(A) -> m1_subset_1(k16_domain_1(A,B,C,D),B))) # label(dt_k16_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2252 (all A all B all C (-v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(B)) -> (r2_hidden(A,a_2_1_domain_1(B,C)) <-> (exists D (m1_subset_1(D,B) & D = A & r2_hidden(D,C)))))) # label(fraenkel_a_2_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2253 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> m1_subset_1(a_4_2_domain_1(A,B,C,D),k1_zfmisc_1(k4_zfmisc_1(A,B,C,D))))))))))) # label(s4_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2254 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (p1_s5_domain_1(B) -> p2_s5_domain_1(B)))) -> r1_tarski(a_1_3_domain_1(A),a_1_4_domain_1(A))))) # label(s5_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2255 (all A all B all C all D all E all F all G all H (-v1_xboole_0(D) & m1_subset_1(F,B) & m1_subset_1(H,D) & m1_subset_1(E,A) & -v1_xboole_0(B) & -v1_xboole_0(A) & -v1_xboole_0(C) & m1_subset_1(G,C) -> k5_domain_1(A,B,C,D,E,F,G,H) = k4_mcart_1(E,F,G,H))) # label(redefinition_k5_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2256 $T # label(t23_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2257 (all A all B all C all D all E (-v1_xboole_0(B) & -v1_xboole_0(D) & -v1_xboole_0(E) & -v1_xboole_0(C) -> ((exists F exists G exists H exists I (m1_subset_1(F,B) & m1_subset_1(H,D) & k5_domain_1(B,C,D,E,F,G,H,I) = A & m1_subset_1(I,E) & m1_subset_1(G,C))) <-> r2_hidden(A,a_4_0_domain_1(B,C,D,E))))) # label(fraenkel_a_4_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2258 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> ((all F (r2_hidden(F,A) <-> (exists G (m1_subset_1(G,B) & (exists H (m1_subset_1(H,C) & (exists I ((exists J (m1_subset_1(J,E) & F = k4_mcart_1(G,H,I,J))) & m1_subset_1(I,D))))))))) <-> A = k4_zfmisc_1(B,C,D,E)))))))))))) # label(t33_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2259 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> ((all E ((exists F (m1_subset_1(F,B) & (exists G (m1_subset_1(G,C) & (exists H (E = k3_mcart_1(F,G,H) & m1_subset_1(H,D))))))) <-> r2_hidden(E,A))) <-> k3_zfmisc_1(B,C,D) = A))))))))) # label(t17_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2260 (all A all B (m1_subset_1(B,A) & -v1_xboole_0(A) -> m1_subset_1(k6_domain_1(A,B),k1_zfmisc_1(A)))) # label(dt_k6_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2261 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(C) & -v1_xboole_0(B) & m1_subset_1(D,k2_zfmisc_1(A,k2_zfmisc_1(B,C))) -> k17_domain_1(A,B,C,D) = k20_mcart_1(D))) # label(redefinition_k17_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2262 $T # label(t3_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2263 (all A all B all C all D all E all F all G all H all I (-v1_xboole_0(E) & m1_subset_1(H,k1_zfmisc_1(D)) & -v1_xboole_0(D) & -v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(G,k1_zfmisc_1(C)) & m1_subset_1(I,k1_zfmisc_1(E)) & m1_subset_1(F,k1_zfmisc_1(B)) -> ((exists J exists K exists L exists M (r2_hidden(K,G) & m1_subset_1(L,D) & m1_subset_1(M,E) & r2_hidden(L,H) & r2_hidden(M,I) & r2_hidden(J,F) & A = k5_domain_1(B,C,D,E,J,K,L,M) & m1_subset_1(K,C) & m1_subset_1(J,B))) <-> r2_hidden(A,a_8_0_domain_1(B,C,D,E,F,G,H,I))))) # label(fraenkel_a_8_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2264 (all A (-v1_xboole_0(A) -> k1_subset_1(A) = a_1_1_domain_1(A))) # label(t56_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2265 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(D,B) & -v1_xboole_0(A) & m1_subset_1(C,A) -> k4_tarski(C,D) = k1_domain_1(A,B,C,D))) # label(redefinition_k1_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2266 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_0_domain_1(B)) <-> (exists C (m1_subset_1(C,B) & A = C))))) # label(fraenkel_a_1_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2267 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> a_2_1_domain_1(A,B) = B)))) # label(t52_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2268 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,k3_zfmisc_1(B,C,D)) -> (A = k7_mcart_1(B,C,D,E) <-> (all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,C) -> (all H (m1_subset_1(H,D) -> (k4_domain_1(B,C,D,F,G,H) = E -> H = A)))))))))))))))) # label(t26_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2269 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (p2_s6_domain_1(B) <-> p1_s6_domain_1(B)))) -> a_1_5_domain_1(A) = a_1_6_domain_1(A)))) # label(s6_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2270 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(C,k1_zfmisc_1(B)) & -v1_xboole_0(B) -> ((exists E (-(r2_hidden(E,D) <-> r2_hidden(E,C)) & m1_subset_1(E,B) & A = E)) <-> r2_hidden(A,a_3_7_domain_1(B,C,D))))) # label(fraenkel_a_3_7_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2271 (all A all B all C all D (m1_subset_1(C,A) & m1_subset_1(D,B) & -v1_xboole_0(A) & -v1_xboole_0(B) -> m1_subset_1(k1_domain_1(A,B,C,D),k2_zfmisc_1(A,B)))) # label(dt_k1_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2272 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> (k11_mcart_1(A,B,C,D,E) = k11_mcart_1(A,B,C,D,F) & k10_mcart_1(A,B,C,D,E) = k10_mcart_1(A,B,C,D,F) & k9_mcart_1(A,B,C,D,F) = k9_mcart_1(A,B,C,D,E) & k8_mcart_1(A,B,C,D,F) = k8_mcart_1(A,B,C,D,E) -> F = E))))))))))))) # label(t45_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2273 (all A all B all C all D all E (m1_subset_1(D,k1_zfmisc_1(B)) & -v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(E,k1_zfmisc_1(C)) -> ((exists F exists G (m1_subset_1(F,B) & k1_domain_1(B,C,F,G) = A & r2_hidden(F,D) & r2_hidden(G,E) & m1_subset_1(G,C))) <-> r2_hidden(A,a_4_1_domain_1(B,C,D,E))))) # label(fraenkel_a_4_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2274 (all A all B all C all D all E all F all G all H (m1_subset_1(F,B) & m1_subset_1(G,C) & m1_subset_1(H,D) & -v1_xboole_0(D) & -v1_xboole_0(C) & -v1_xboole_0(B) & m1_subset_1(E,A) & -v1_xboole_0(A) -> m1_subset_1(k5_domain_1(A,B,C,D,E,F,G,H),k4_zfmisc_1(A,B,C,D)))) # label(dt_k5_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2275 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,k3_zfmisc_1(B,C,D)) -> ((all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,C) -> (all H (m1_subset_1(H,D) -> (k4_domain_1(B,C,D,F,G,H) = E -> F = A))))))) <-> A = k5_mcart_1(B,C,D,E)))))))))) # label(t24_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2276 $T # label(t35_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2277 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> (all D (m1_subset_1(D,k2_zfmisc_1(A,B)) -> (k2_mcart_1(D) = k2_mcart_1(C) & k1_mcart_1(D) = k1_mcart_1(C) -> C = D))))))))) # label(t12_domain_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2278 $T # label(t10_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2279 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> (v1_binop_1(B,A) -> (r1_binop_1(A,C,B) <-> r2_binop_1(A,C,B))))))) # label(t16_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2280 $T # label(t3_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2281 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> ((all D (m1_subset_1(D,A) -> D = k2_binop_1(A,A,A,C,D,B))) <-> r2_binop_1(A,B,C)))))))) # label(d17_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2282 (all A all B (v1_funct_1(B) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> m1_subset_1(k3_binop_1(A,B),A))) # label(dt_k3_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2283 $T # label(dt_k1_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2284 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (r6_binop_1(A,B,C) <-> r5_binop_1(A,B,C) & r4_binop_1(A,B,C)))))) # label(d11_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2285 (all A all B all C all D all E all F (-v1_xboole_0(B) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & m1_subset_1(F,B) & v1_funct_1(D) & -v1_xboole_0(A) & m1_subset_1(E,A) & v1_funct_2(D,k2_zfmisc_1(A,B),C) -> m1_subset_1(k2_binop_1(A,B,C,D,E,F),C))) # label(dt_k2_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2286 $T # label(t7_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2287 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> (v1_binop_1(B,A) -> (r3_binop_1(A,C,B) <-> r2_binop_1(A,C,B))))))) # label(t15_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2288 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (r3_binop_1(A,C,B) & r3_binop_1(A,D,B) -> C = D))))))) # label(t18_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2289 (all A all B all C all D all E all F (-v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m1_subset_1(F,B) & m1_subset_1(E,A) & -v1_xboole_0(A) & m1_relset_1(D,k2_zfmisc_1(A,B),C) -> k1_binop_1(D,E,F) = k2_binop_1(A,B,C,D,E,F))) # label(redefinition_k2_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2290 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (v1_binop_1(C,A) -> (r6_binop_1(A,C,B) <-> r5_binop_1(A,C,B))))))))) # label(t27_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2291 (all A (m1_relset_1(A,k2_zfmisc_1(k1_xboole_0,k1_xboole_0),k1_xboole_0) -> (v1_funct_2(A,k2_zfmisc_1(k1_xboole_0,k1_xboole_0),k1_xboole_0) & v1_funct_1(A) -> v1_xboole_0(A) & v1_funct_2(A,k2_zfmisc_1(k1_xboole_0,k1_xboole_0),k1_xboole_0) & v1_binop_1(A,k1_xboole_0) & v2_binop_1(A,k1_xboole_0) & v1_funct_1(A)))) # label(cc1_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2292 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) -> (all E (v1_funct_2(E,k2_zfmisc_1(A,B),C) & m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_1(E) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> k2_binop_1(A,B,C,E,F,G) = k2_binop_1(A,B,C,D,F,G))))) -> E = D))))))))))) # label(t2_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2293 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (r7_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> k1_funct_1(B,k1_binop_1(C,D,E)) = k1_binop_1(C,k1_funct_1(B,D),k1_funct_1(B,E))))))))))) # label(d12_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2294 (all A all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (r2_binop_1(A,D,B) & r1_binop_1(A,C,B) -> D = C))))))) # label(t17_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2295 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (r7_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> k8_funct_2(A,A,B,k2_binop_1(A,A,A,C,D,E)) = k2_binop_1(A,A,A,C,k8_funct_2(A,A,B,D),k8_funct_2(A,A,B,E))))))))))))) # label(d20_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2296 (all A (-v1_xboole_0(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (v1_binop_1(C,A) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k2_binop_1(A,A,A,C,k2_binop_1(A,A,A,B,D,E),F) = k2_binop_1(A,A,A,B,k2_binop_1(A,A,A,C,D,F),k2_binop_1(A,A,A,C,E,F)))))))) <-> r6_binop_1(A,C,B))))))))) # label(t25_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2297 (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]. 56.22/55.23 2298 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (r4_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k2_binop_1(A,A,A,C,k2_binop_1(A,A,A,B,D,E),k2_binop_1(A,A,A,B,D,F)) = k2_binop_1(A,A,A,B,D,k2_binop_1(A,A,A,C,E,F))))))))))))))) # label(d18_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2299 $T # label(t19_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2300 (all A all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> ((exists C (r3_binop_1(A,C,B) & m1_subset_1(C,A))) -> (all C (m1_subset_1(C,A) -> (r3_binop_1(A,C,B) <-> k3_binop_1(A,B) = C)))))) # label(d8_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2301 (all A (-v1_xboole_0(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (v2_binop_1(B,A) <-> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> k2_binop_1(A,A,A,B,k2_binop_1(A,A,A,B,C,D),E) = k2_binop_1(A,A,A,B,C,k2_binop_1(A,A,A,B,D,E))))))))))))) # label(d14_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2302 (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]. 56.22/55.23 2303 (all A all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (v1_binop_1(B,A) <-> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> k1_binop_1(B,C,D) = k1_binop_1(B,D,C)))))))) # label(d2_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2304 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (v1_binop_1(C,A) -> (r6_binop_1(A,C,B) <-> r4_binop_1(A,C,B))))))))) # label(t26_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.23 2305 (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]. 56.22/55.23 2306 (exists A (m2_relset_1(A,k2_zfmisc_1(f1_s2_binop_1,f1_s2_binop_1),f1_s2_binop_1) & (all B (m1_subset_1(B,f1_s2_binop_1) -> (all C (m1_subset_1(C,f1_s2_binop_1) -> k2_binop_1(f1_s2_binop_1,f1_s2_binop_1,f1_s2_binop_1,A,B,C) = f2_s2_binop_1(B,C))))) & v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(f1_s2_binop_1,f1_s2_binop_1),f1_s2_binop_1))) # label(s2_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2307 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (v1_binop_1(B,A) <-> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> k2_binop_1(A,A,A,B,C,D) = k2_binop_1(A,A,A,B,D,C)))))))))) # label(d13_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2308 (all A all B (m1_subset_1(B,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (r3_binop_1(A,B,C) <-> r1_binop_1(A,B,C) & r2_binop_1(A,B,C)))))) # label(d7_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2309 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (r4_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k1_binop_1(C,k1_binop_1(B,D,E),k1_binop_1(B,D,F)) = k1_binop_1(B,D,k1_binop_1(C,E,F))))))))))))) # label(d9_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2310 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (v2_binop_1(B,A) <-> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> k1_binop_1(B,C,k1_binop_1(B,D,E)) = k1_binop_1(B,k1_binop_1(B,C,D),E)))))))))) # label(d3_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2311 $T # label(t20_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2312 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> ((all D (m1_subset_1(D,A) -> k2_binop_1(A,A,A,C,B,D) = D)) <-> r1_binop_1(A,B,C)))))))) # label(d16_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2313 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (v3_binop_1(B,A) <-> (all C (m1_subset_1(C,A) -> C = k1_binop_1(B,C,C)))))) # label(d4_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2314 (all A all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> (r3_binop_1(A,C,B) <-> (all D (m1_subset_1(D,A) -> D = k1_binop_1(B,C,D) & k1_binop_1(B,D,C) = D))))))) # label(t11_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2315 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> (v1_binop_1(B,A) -> ((all D (m1_subset_1(D,A) -> D = k1_binop_1(B,C,D))) <-> r3_binop_1(A,C,B))))))) # label(t12_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2316 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (v1_binop_1(C,A) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k2_binop_1(A,A,A,C,D,k2_binop_1(A,A,A,B,E,F)) = k2_binop_1(A,A,A,B,k2_binop_1(A,A,A,C,D,E),k2_binop_1(A,A,A,C,D,F)))))))) <-> r6_binop_1(A,C,B))))))))) # label(t24_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2317 $T # label(t21_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2318 $T # label(t6_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2319 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> (v1_binop_1(B,A) -> (r3_binop_1(A,C,B) <-> (all D (m1_subset_1(D,A) -> k1_binop_1(B,D,C) = D)))))))) # label(t13_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2320 (all A all B (m1_subset_1(B,A) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (r2_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> D = k1_binop_1(C,D,B)))))))) # label(d6_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2321 (all A all B (m1_subset_1(B,A) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (r1_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> k1_binop_1(C,B,D) = D))))))) # label(d5_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2322 $T # label(t5_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2323 $T # label(t9_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2324 (all A (m1_subset_1(A,f1_s1_binop_1) -> (all B (m1_subset_1(B,f1_s1_binop_1) -> (exists C (m1_subset_1(C,f1_s1_binop_1) & p1_s1_binop_1(A,B,C))))))) -> (exists A ((all B (m1_subset_1(B,f1_s1_binop_1) -> (all C (m1_subset_1(C,f1_s1_binop_1) -> p1_s1_binop_1(B,C,k2_binop_1(f1_s1_binop_1,f1_s1_binop_1,f1_s1_binop_1,A,B,C)))))) & v1_funct_2(A,k2_zfmisc_1(f1_s1_binop_1,f1_s1_binop_1),f1_s1_binop_1) & v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(f1_s1_binop_1,f1_s1_binop_1),f1_s1_binop_1))) # label(s1_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2325 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (v1_binop_1(C,A) -> (r4_binop_1(A,C,B) <-> r5_binop_1(A,C,B))))))))) # label(t28_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2326 $T # label(t1_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2327 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k2_binop_1(A,A,A,B,k2_binop_1(A,A,A,C,D,E),F) = k2_binop_1(A,A,A,C,k2_binop_1(A,A,A,B,D,F),k2_binop_1(A,A,A,B,E,F)))))))) <-> r5_binop_1(A,B,C)))))))) # label(d19_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2328 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> (v1_binop_1(B,A) -> (r3_binop_1(A,C,B) <-> r1_binop_1(A,C,B))))))) # label(t14_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2329 $T # label(t4_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2330 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k1_binop_1(C,k1_binop_1(B,D,F),k1_binop_1(B,E,F)) = k1_binop_1(B,k1_binop_1(C,D,E),F) & k1_binop_1(C,k1_binop_1(B,D,E),k1_binop_1(B,D,F)) = k1_binop_1(B,D,k1_binop_1(C,E,F)))))))) <-> r6_binop_1(A,B,C)))))) # label(t23_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2331 $T # label(t22_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2332 $T # label(t8_binop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2333 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C k7_relat_1(k13_funct_3(A,B),C) = k13_funct_3(A,k7_relat_1(B,C))))))) # label(t11_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2334 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_zfmisc_1(k2_relat_1(B),k2_relat_1(C)),k1_relat_1(A)) -> k1_relat_1(k3_funcop_1(A,B,C)) = k3_xboole_0(k1_relat_1(B),k1_relat_1(C))))))))) # label(t84_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2335 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (v2_binop_1(C,B) -> k8_funcop_1(B,A,C,E,k7_funcop_1(B,A,C,D,F)) = k7_funcop_1(B,A,C,k8_funcop_1(B,A,C,E,D),F)))))))))))))) # label(t74_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2336 (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]. 56.22/55.24 2337 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (v1_relat_1(C) & v1_funct_1(C) -> k5_relat_1(k13_funct_3(k2_funcop_1(k1_relat_1(C),B),C),A) = k5_funcop_1(A,B,C))))) # label(d5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2338 (exists A (v1_funct_1(A) & v1_funcop_1(A) & v1_relat_1(A))) # label(rc1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2339 $T # label(dt_k2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2340 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> k13_funct_3(A,B) = k1_funcop_1(k13_funct_3(B,A)))))) # label(t6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2341 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D k4_funcop_1(k5_relat_1(C,A),B,D) = k5_relat_1(k4_funcop_1(C,B,D),A)))))))) # label(t38_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2342 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (v2_binop_1(C,B) -> k8_funcop_1(B,A,C,k2_binop_1(B,B,B,C,E,F),D) = k8_funcop_1(B,A,C,E,k8_funcop_1(B,A,C,F,D))))))))))))))) # label(t77_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2343 (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]. 56.22/55.24 2344 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C k13_funct_3(k7_relat_1(A,C),B) = k7_relat_1(k13_funct_3(A,B),C)))))) # label(t10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2345 (all A all B all C all D all E (v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & v1_funct_2(D,B,A) & m1_relset_1(E,B,A) & v1_funct_1(E) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & -v1_xboole_0(B) & v1_funct_2(E,B,A) & m1_relset_1(D,B,A) & v1_funct_1(C) & -v1_xboole_0(A) -> v1_funct_2(k6_funcop_1(A,B,C,D,E),B,A) & m2_relset_1(k6_funcop_1(A,B,C,D,E),B,A) & v1_funct_1(k6_funcop_1(A,B,C,D,E)))) # label(dt_k6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2346 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B k7_relat_1(k1_funcop_1(A),B) = k1_funcop_1(k7_relat_1(A,B))))) # label(t7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2347 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D k5_relat_1(k6_partfun1(B),k5_funcop_1(C,D,A)) = k5_funcop_1(C,D,k7_relat_1(A,B))))))) # label(t46_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2348 (all A k12_funct_3(A) = k13_funct_3(k6_partfun1(A),k6_partfun1(A))) # label(t2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2349 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) & v1_funct_2(D,A,B) -> (all E (m1_subset_1(E,B) -> v1_funct_1(k4_funcop_1(C,D,E)) & v1_funct_2(k4_funcop_1(C,D,E),A,B) & m2_relset_1(k4_funcop_1(C,D,E),A,B))))))))))) # label(t59_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2350 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C all D (v1_relat_1(D) & v1_funct_1(D) -> (all E (k7_relat_1(B,C) = k7_relat_1(A,C) -> k7_relat_1(k4_funcop_1(D,A,E),C) = k7_relat_1(k4_funcop_1(D,B,E),C))))))))) # label(t36_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2351 (all A (v1_relat_1(k2_funcop_1(k1_xboole_0,A)) & v1_xboole_0(k2_funcop_1(k1_xboole_0,A)) & v1_funct_1(k2_funcop_1(k1_xboole_0,A)) & v2_funct_1(k2_funcop_1(k1_xboole_0,A)))) # label(fc2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2352 (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]. 56.22/55.24 2353 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (all F (m1_subset_1(F,B) -> (v2_binop_1(C,B) -> k6_funcop_1(B,A,C,k7_funcop_1(B,A,C,D,F),E) = k6_funcop_1(B,A,C,D,k8_funcop_1(B,A,C,F,E))))))))))))))) # label(t75_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2354 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> m2_relset_1(k5_funcop_1(C,E,D),A,B) & v1_funct_2(k5_funcop_1(C,E,D),A,B) & v1_funct_1(k5_funcop_1(C,E,D)))))))))))) # label(t65_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2355 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> m2_relset_1(k3_funcop_1(C,D,E),A,B) & v1_funct_2(k3_funcop_1(C,D,E),A,B) & v1_funct_1(k3_funcop_1(C,D,E)))))))))))) # label(t47_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2356 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (k1_tarski(B) = k2_relat_1(A) -> k2_funcop_1(k1_relat_1(A),B) = A)))) # label(t15_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2357 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D k4_funcop_1(C,k5_relat_1(B,A),D) = k5_relat_1(B,k4_funcop_1(C,A,D))))))))) # label(t37_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2358 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B ((all C (r2_hidden(C,k1_relat_1(A)) -> B = k1_funct_1(A,C))) -> A = k2_funcop_1(k1_relat_1(A),B))))) # label(t17_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2359 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> k5_relat_1(k3_funcop_1(D,B,C),A) = k3_funcop_1(k5_relat_1(D,A),B,C))))))))) # label(t32_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2360 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m2_relset_1(E,B,B) & v1_funct_2(E,B,B) & v1_funct_1(E) -> k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,k6_partfun1(B),E)) = k6_funcop_1(B,A,C,D,k7_funct_2(A,B,B,D,E)))))))))))) # label(t51_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2361 (all A all B all C (r2_hidden(B,C) -> A = k10_relat_1(k2_funcop_1(A,B),C))) # label(t20_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2362 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (all E (m2_relset_1(E,B,A) & v1_funct_2(E,B,A) & v1_funct_1(E) -> (all F (m1_subset_1(F,A) -> ((all G (m1_subset_1(G,B) -> k8_funct_2(B,A,D,G) = k2_binop_1(A,A,A,C,F,k8_funct_2(B,A,E,G)))) -> D = k8_funcop_1(A,B,C,F,E)))))))))))))) # label(t67_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2363 (all A all B k2_zfmisc_1(A,k1_tarski(B)) = k2_funcop_1(A,B)) # label(d2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2364 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> (all D (v1_funct_2(D,A,A) & m2_relset_1(D,A,A) & v1_funct_1(D) -> k2_binop_1(A,A,A,B,k8_funct_2(A,A,D,C),C) = k8_funct_2(A,A,k6_funcop_1(A,A,B,D,k6_partfun1(A)),C))))))))) # label(t55_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2365 (all A all B all C (v1_relat_1(A) & v1_relat_1(B) & v1_funct_1(A) & v1_funct_1(B) -> v1_relat_1(k4_funcop_1(A,B,C)) & v1_funct_1(k4_funcop_1(A,B,C)))) # label(fc5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2366 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (v2_binop_1(C,B) -> k7_funcop_1(B,A,C,k7_funcop_1(B,A,C,D,E),F) = k7_funcop_1(B,A,C,D,k2_binop_1(B,B,B,C,E,F))))))))))))))) # label(t78_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2367 (all A (k1_relat_1(k2_funcop_1(k1_xboole_0,A)) = k1_xboole_0 & k1_xboole_0 = k2_relat_1(k2_funcop_1(k1_xboole_0,A)))) # label(t16_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2368 $T # label(t12_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2369 $T # label(t40_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2370 $T # label(dt_k3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2371 (all A all B all C all D all E (m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(E) & m1_relset_1(E,B,A) & v1_funct_1(C) & -v1_xboole_0(A) & -v1_xboole_0(B) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_subset_1(D,A) & v1_funct_2(E,B,A) -> k5_funcop_1(C,D,E) = k8_funcop_1(A,B,C,D,E))) # label(redefinition_k8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2372 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) & v1_funct_2(D,A,B) -> k6_funcop_1(B,A,C,D,D) = k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,k6_partfun1(B),k6_partfun1(B))))))))))) # label(t53_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2373 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> k3_funcop_1(A,B,C) = k5_relat_1(k13_funct_3(B,C),A))))))) # label(d3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2374 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k1_funcop_1(A)) & v1_funct_1(k1_funcop_1(A)))) # label(dt_k1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2375 (all A (-v1_xboole_0(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> k2_binop_1(A,A,A,B,C,C) = k8_funct_2(A,A,k7_funcop_1(A,A,B,k6_partfun1(A),C),C))))))) # label(t64_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2376 $T # label(t5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2377 (all A all B A = k10_relat_1(k2_funcop_1(A,B),k1_tarski(B))) # label(t21_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2378 $T # label(t8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2379 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C all D (v1_relat_1(D) & v1_funct_1(D) -> (all E (k7_relat_1(B,C) = k7_relat_1(A,C) -> k7_relat_1(k5_funcop_1(D,E,B),C) = k7_relat_1(k5_funcop_1(D,E,A),C))))))))) # label(t43_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2380 (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]. 56.22/55.24 2381 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_1(D) & -v1_xboole_0(C) -> D = k10_funcop_1(A,B,C,k10_funcop_1(A,B,C,D)))) # label(involutiveness_k10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2382 (all A all B all C all D all E (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(E,B,A) & v1_funct_2(E,B,A) & v1_funct_1(E) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & -v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(D,A) -> v1_funct_2(k8_funcop_1(A,B,C,D,E),B,A) & v1_funct_1(k8_funcop_1(A,B,C,D,E)) & m2_relset_1(k8_funcop_1(A,B,C,D,E),B,A))) # label(dt_k8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2383 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_2(D,B,A) & v1_funct_1(D) & m2_relset_1(D,B,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> k2_binop_1(A,A,A,C,E,k8_funct_2(B,A,D,F)) = k8_funct_2(B,A,k8_funcop_1(A,B,C,E,D),F))))))))))))) # label(t66_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2384 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C all D (r2_hidden(C,k1_relat_1(k5_funcop_1(B,D,A))) -> k1_funct_1(k5_funcop_1(B,D,A),C) = k1_binop_1(B,D,k1_funct_1(A,C)))))))) # label(t42_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2385 (all A all B all C all D (v1_funct_2(D,A,k2_zfmisc_1(B,C)) & v1_funct_1(D) & -v1_xboole_0(A) & -v1_xboole_0(C) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & -v1_xboole_0(B) -> k2_relat_1(D) = k9_funcop_1(A,B,C,D))) # label(redefinition_k9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2386 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D all E (v1_funct_1(E) & v1_relat_1(E) -> (k7_relat_1(A,D) = k7_relat_1(B,D) -> k7_relat_1(k3_funcop_1(E,C,B),D) = k7_relat_1(k3_funcop_1(E,C,A),D)))))))))) # label(t30_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2387 (all A all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,B) -> v1_funct_2(k2_funcop_1(A,C),A,B) & m2_relset_1(k2_funcop_1(A,C),A,B) & v1_funct_1(k2_funcop_1(A,C)))))) # label(t58_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2388 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D all E (v1_funct_1(E) & v1_relat_1(E) -> (k7_relat_1(A,D) = k7_relat_1(B,D) -> k7_relat_1(k3_funcop_1(E,A,C),D) = k7_relat_1(k3_funcop_1(E,B,C),D)))))))))) # label(t29_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2389 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k1_relat_1(k3_funcop_1(C,A,B)) = k1_relat_1(D) & (all E (r2_hidden(E,k1_relat_1(k3_funcop_1(C,A,B))) -> k1_funct_1(D,E) = k1_binop_1(C,k1_funct_1(A,E),k1_funct_1(B,E)))) -> D = k3_funcop_1(C,A,B)))))))))) # label(t27_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2390 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_2(D,A,B) & v1_funct_1(D) & m2_relset_1(D,A,B) -> (all E (m1_subset_1(E,B) -> k7_funct_2(A,B,B,D,k7_funcop_1(B,B,C,k6_partfun1(B),E)) = k7_funcop_1(B,A,C,D,E))))))))))) # label(t63_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2391 (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]. 56.22/55.24 2392 $T # label(t33_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2393 $T # label(dt_k4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2394 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) & v1_funct_2(D,A,B) -> (all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (all F (v1_funct_1(F) & m2_relset_1(F,A,B) & v1_funct_2(F,A,B) -> (v2_binop_1(C,B) -> k6_funcop_1(B,A,C,k6_funcop_1(B,A,C,D,E),F) = k6_funcop_1(B,A,C,D,k6_funcop_1(B,A,C,E,F))))))))))))))) # label(t76_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2395 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C k3_funcop_1(B,A,k2_funcop_1(k1_relat_1(A),C)) = k4_funcop_1(B,A,C)))))) # label(t34_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2396 (all A all B all C all D all E (m1_relset_1(C,k2_zfmisc_1(A,A),A) & m1_relset_1(D,B,A) & m1_subset_1(E,A) & v1_funct_1(D) & -v1_xboole_0(B) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_2(D,B,A) & v1_funct_1(C) & -v1_xboole_0(A) -> v1_funct_2(k7_funcop_1(A,B,C,D,E),B,A) & m2_relset_1(k7_funcop_1(A,B,C,D,E),B,A) & v1_funct_1(k7_funcop_1(A,B,C,D,E)))) # label(dt_k7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2397 (all A (-v1_xboole_0(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> k2_binop_1(A,A,A,B,C,C) = k8_funct_2(A,A,k6_funcop_1(A,A,B,k6_partfun1(A),k6_partfun1(A)),C))))))) # label(t56_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2398 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D k5_funcop_1(C,D,k5_relat_1(B,A)) = k5_relat_1(B,k5_funcop_1(C,D,A))))))))) # label(t44_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2399 (all A all B all C all D (v1_funct_2(D,A,k2_zfmisc_1(B,C)) & -v1_xboole_0(B) & -v1_xboole_0(C) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_1(D) & -v1_xboole_0(A) -> v1_funct_1(k10_funcop_1(A,B,C,D)) & v1_funct_2(k10_funcop_1(A,B,C,D),A,k2_zfmisc_1(C,B)) & m2_relset_1(k10_funcop_1(A,B,C,D),A,k2_zfmisc_1(C,B)))) # label(dt_k10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2400 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B (r2_hidden(B,k1_relat_1(A)) -> v1_relat_1(k1_funct_1(A,B)) & v1_funct_1(k1_funct_1(A,B)))) <-> v1_funcop_1(A)))) # label(d6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2401 (all A all B all C k7_relat_1(k2_funcop_1(A,B),C) = k2_funcop_1(k3_xboole_0(A,C),B)) # label(t18_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2402 (all A all B all C all D all E (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & m1_relset_1(D,B,A) & v1_funct_1(E) & m1_relset_1(E,B,A) & -v1_xboole_0(B) & -v1_xboole_0(A) & v1_funct_2(D,B,A) & v1_funct_2(E,B,A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) -> k6_funcop_1(A,B,C,D,E) = k3_funcop_1(C,D,E))) # label(redefinition_k6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2403 (all A all B (r1_tarski(k2_relat_1(k2_funcop_1(A,B)),k1_tarski(B)) & A = k1_relat_1(k2_funcop_1(A,B)))) # label(t19_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2404 (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]. 56.22/55.24 2405 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> (v3_binop_1(C,A) -> k8_funct_2(B,A,D,E) = k8_funct_2(B,A,k8_funcop_1(A,B,C,k8_funct_2(B,A,D,E),D),E)))))))))))) # label(t82_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2406 (all A all B (v1_funcop_1(A) & v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k1_funct_1(A,B)) & v1_relat_1(k1_funct_1(A,B)))) # label(fc7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.24 2407 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) -> k9_funcop_1(A,C,B,k10_funcop_1(A,B,C,D)) = k4_relat_1(k9_funcop_1(A,B,C,D)))))))))) # label(t73_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.25 2408 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (v3_binop_1(C,B) -> D = k6_funcop_1(B,A,C,D,D)))))))))) # label(t81_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.25 2409 (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]. 56.22/55.25 2410 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C k5_funcop_1(B,C,A) = k3_funcop_1(B,k2_funcop_1(k1_relat_1(A),C),A)))))) # label(t41_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.25 2411 (all A k1_funcop_1(k12_funct_3(A)) = k12_funct_3(A)) # label(t9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.25 2412 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_1(D) & v1_funct_2(D,B,A) & m2_relset_1(D,B,A) -> (all E (m1_subset_1(E,B) -> (v3_binop_1(C,A) -> k8_funct_2(B,A,D,E) = k8_funct_2(B,A,k7_funcop_1(A,B,C,D,k8_funct_2(B,A,D,E)),E)))))))))))) # label(t83_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.25 2413 (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]. 56.22/55.25 2414 $T # label(t62_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.25 2415 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) & v1_funct_2(D,A,B) -> (all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (all F (m2_relset_1(F,A,B) & v1_funct_1(F) & v1_funct_2(F,A,B) -> ((all G (m1_subset_1(G,A) -> k2_binop_1(B,B,B,C,k8_funct_2(A,B,D,G),k8_funct_2(A,B,E,G)) = k8_funct_2(A,B,F,G))) -> k6_funcop_1(B,A,C,D,E) = F))))))))))))) # label(t49_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.25 2416 (all A all B (v1_relat_1(A) & v1_funcop_1(A) & v1_funct_1(B) & v1_relat_1(B) & v1_funct_1(A) -> v1_funct_1(k5_relat_1(B,A)) & v1_funcop_1(k5_relat_1(B,A)) & v1_relat_1(k5_relat_1(B,A)))) # label(fc8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.25 2417 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) -> m2_relset_1(k2_relat_1(D),B,C))))))))) # label(t72_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.25 2418 $T # label(t68_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.25 2419 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) & v1_funct_2(D,A,B) -> (all E (m1_subset_1(E,B) -> k7_funct_2(A,B,B,D,k8_funcop_1(B,B,C,E,k6_partfun1(B))) = k8_funcop_1(B,A,C,E,D))))))))))) # label(t69_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.25 2420 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> k3_funcop_1(D,k5_relat_1(C,A),k5_relat_1(C,B)) = k5_relat_1(C,k3_funcop_1(D,A,B)))))))))) # label(t31_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.25 2421 (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]. 56.22/55.25 2422 $T # label(dt_k5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.25 2423 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_xboole_0 = k1_relat_1(A) & k1_relat_1(B) = k1_xboole_0 -> A = B))))) # label(t4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.25 2424 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D k5_relat_1(k5_funcop_1(C,D,B),A) = k5_funcop_1(k5_relat_1(C,A),D,B)))))))) # label(t45_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.25 2425 (all A all B all C (r2_hidden(C,B) -> m2_relset_1(k2_funcop_1(A,C),A,B) & v1_funct_2(k2_funcop_1(A,C),A,B) & v1_funct_1(k2_funcop_1(A,C)))) # label(t57_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.25 2426 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_1(E) & m2_relset_1(E,B,B) & v1_funct_2(E,B,B) -> k6_funcop_1(B,A,C,k7_funct_2(A,B,B,D,E),D) = k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,E,k6_partfun1(B))))))))))))) # label(t52_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.25 2427 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (r2_hidden(D,k1_relat_1(k3_funcop_1(C,A,B))) -> k1_binop_1(C,k1_funct_1(A,D),k1_funct_1(B,D)) = k1_funct_1(k3_funcop_1(C,A,B),D))))))))) # label(t28_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.25 2428 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C -(r2_hidden(C,k1_relat_1(A)) & k1_xboole_0 != B & k1_xboole_0 = k1_relat_1(k5_relat_1(k2_funcop_1(B,C),A)))))) # label(t24_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.25 2429 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & -v1_xboole_0(B) & -v1_xboole_0(A) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & -v1_xboole_0(C) -> m2_relset_1(k9_funcop_1(A,B,C,D),B,C))) # label(dt_k9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.25 2430 $T # label(t50_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.25 2431 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) & v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k5_funcop_1(A,B,C)) & v1_relat_1(k5_funcop_1(A,B,C)))) # label(fc6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.25 2432 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> (all D all E (k4_tarski(D,E) = k1_funct_1(A,C) -> k1_funct_1(B,C) = k4_tarski(E,D))) & -(k1_funct_1(B,C) != k1_funct_1(A,C) & (all D all E k4_tarski(D,E) != k1_funct_1(A,C))))) & k1_relat_1(B) = k1_relat_1(A) <-> B = k1_funcop_1(A)))))) # label(d1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.25 2433 (all A all B all C (v1_relat_1(A) & v1_relat_1(B) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_1(B) & v1_funct_1(A) -> v1_relat_1(k3_funcop_1(A,B,C)) & v1_funct_1(k3_funcop_1(A,B,C)))) # label(fc4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.25 2434 (all A all B all C all D (m1_relset_1(D,A,k2_zfmisc_1(B,C)) & -v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & -v1_xboole_0(C) & -v1_xboole_0(A) -> k1_funcop_1(D) = k10_funcop_1(A,B,C,D))) # label(redefinition_k10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.25 2435 (all A (v1_relat_1(A) -> (all B all C (k2_zfmisc_1(B,C) = A -> k1_relat_1(A) = B & k2_relat_1(A) = C | C = k1_xboole_0 | B = k1_xboole_0)))) # label(t1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.25 2436 (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]. 56.22/55.25 2437 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(B) = k1_relat_1(A) -> k1_relat_1(k5_relat_1(C,A)) = k1_relat_1(k5_relat_1(C,B))))))))) # label(t3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.25 2438 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> k8_funct_2(B,A,k7_funcop_1(A,B,C,D,E),F) = k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,F),E))))))))))))) # label(t60_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.25 2439 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_1(D) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) -> (all E (m1_subset_1(E,A) -> k4_tarski(k2_mcart_1(k8_funct_2(A,k2_zfmisc_1(B,C),D,E)),k1_mcart_1(k8_funct_2(A,k2_zfmisc_1(B,C),D,E))) = k1_funct_1(k1_funcop_1(D),E))))))))))) # label(t71_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.25 2440 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_2(E,A,B) & v1_funct_1(E) & m2_relset_1(E,A,B) -> (v1_binop_1(C,B) -> k6_funcop_1(B,A,C,E,D) = k6_funcop_1(B,A,C,D,E)))))))))))) # label(t80_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.25 2441 (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]. 56.22/55.25 2442 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (all E (m2_relset_1(E,B,A) & v1_funct_1(E) & v1_funct_2(E,B,A) -> (all F (m1_subset_1(F,B) -> k8_funct_2(B,A,k6_funcop_1(A,B,C,D,E),F) = k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,F),k8_funct_2(B,A,E,F)))))))))))))) # label(t48_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.25 2443 (all A all B (v1_xboole_0(B) -> v1_xboole_0(k2_funcop_1(B,A)) & v1_funct_1(k2_funcop_1(B,A)) & v2_funct_1(k2_funcop_1(B,A)) & v1_relat_1(k2_funcop_1(B,A)))) # label(fc3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.25 2444 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (m1_subset_1(E,B) -> (v1_binop_1(C,B) -> k7_funcop_1(B,A,C,D,E) = k8_funcop_1(B,A,C,E,D)))))))))))) # label(t79_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.25 2445 (all A (-v1_xboole_0(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (all D (m2_relset_1(D,A,A) & v1_funct_1(D) & v1_funct_2(D,A,A) -> k2_binop_1(A,A,A,B,C,k8_funct_2(A,A,D,C)) = k8_funct_2(A,A,k6_funcop_1(A,A,B,k6_partfun1(A),D),C))))))))) # label(t54_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.25 2446 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D k4_funcop_1(C,k7_relat_1(A,B),D) = k5_relat_1(k6_partfun1(B),k4_funcop_1(C,A,D))))))) # label(t39_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.25 2447 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,A) & m2_relset_1(E,B,A) -> (all F (m1_subset_1(F,A) -> ((all G (m1_subset_1(G,B) -> k2_binop_1(A,A,A,C,k8_funct_2(B,A,E,G),F) = k8_funct_2(B,A,D,G))) -> D = k7_funcop_1(A,B,C,E,F)))))))))))))) # label(t61_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.25 2448 (all A all B (A != k1_xboole_0 -> k1_tarski(B) = k2_relat_1(k2_funcop_1(A,B)))) # label(t14_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.22/55.25 2449 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_subset_1(E,A) & v1_funct_2(D,B,A) & v1_funct_1(D) & -v1_xboole_0(A) & v1_funct_1(C) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & m1_relset_1(D,B,A) -> k7_funcop_1(A,B,C,D,E) = k4_funcop_1(C,D,E))) # label(redefinition_k7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 56.28/55.25 2450 (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) -> B = A | C = E & F = D)) # label(t72_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.25 2451 (all A all B (v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(A) & v1_relat_1(B) -> v1_funct_1(k3_funct_4(A,B)) & v1_relat_1(k3_funct_4(A,B)))) # label(dt_k3_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.25 2452 (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 (v1_relat_1(D) & v1_funct_1(D) -> (r1_partfun1(A,B) & r1_tarski(k2_relat_1(D),k1_relat_1(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]. 56.28/55.25 2453 (all A all B all C all D all E all F all G (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) -> 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]. 56.28/55.25 2454 (all A (v1_relat_1(A) & v1_funct_1(A) -> A = k1_funct_4(k1_xboole_0,A))) # label(t21_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.25 2455 (all A all B all C k2_funcop_1(k2_tarski(A,B),C) = k4_funct_4(A,B,C,C)) # label(t68_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.25 2456 (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(A),k2_relat_1(k1_funct_4(B,A))))))) # label(t19_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.25 2457 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k1_relat_1(B),k1_relat_1(k1_funct_4(A,B))) & r1_tarski(k1_relat_1(A),k1_relat_1(k1_funct_4(A,B))))))) # label(t11_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.25 2458 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> ((all D all E 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))))) & (all D ((exists E exists F exists G exists H (r2_hidden(k4_tarski(E,F),k1_relat_1(A)) & r2_hidden(k4_tarski(G,H),k1_relat_1(B)) & k4_tarski(k4_tarski(E,G),k4_tarski(F,H)) = D)) <-> r2_hidden(D,k1_relat_1(C)))) <-> C = k3_funct_4(A,B)))))))) # label(d3_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.25 2459 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(C) = k2_zfmisc_1(A,B) -> k2_zfmisc_1(B,A) = k1_relat_1(k2_funct_4(C))))) # label(t47_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.25 2460 (all A (v1_relat_1(A) & v1_funct_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]. 56.28/55.25 2461 (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) -> (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]. 56.28/55.25 2462 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (r1_xboole_0(k1_relat_1(B),C) & r1_tarski(k1_relat_1(A),C) -> k7_relat_1(k1_funct_4(A,B),C) = A)))))) # label(t82_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.25 2463 (all A all B all C all D all E (v1_funct_1(E) & v1_relat_1(E) -> (D = k1_funct_1(E,B) & k1_relat_1(E) = k2_tarski(A,B) & k1_funct_1(E,A) = C -> k4_funct_4(A,B,C,D) = E))) # label(t69_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.25 2464 (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) -> (k1_relat_1(E) = k2_zfmisc_1(A,B) & k2_zfmisc_1(C,D) = k1_relat_1(F) -> k1_relat_1(k3_funct_4(E,F)) = k2_zfmisc_1(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D))))))) # label(t61_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.25 2465 (all A all B all C all D (m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) -> (k1_xboole_0 != C -> D = k2_funct_4(k2_funct_4(D))))) # label(t55_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.25 2466 (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]. 56.28/55.25 2467 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> k5_relat_1(B,A) = k5_relat_1(B,k7_relat_1(A,k2_relat_1(B))))))) # label(t2_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.25 2468 (all A (v1_relat_1(A) & v1_funct_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]. 56.28/55.25 2469 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k2_funct_4(A)) & v1_relat_1(k2_funct_4(A)))) # label(dt_k2_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.25 2470 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_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]. 56.28/55.25 2471 (all A all B (v1_funct_1(B) & v1_funct_1(A) & v1_relat_1(B) & v1_relat_1(A) -> A = k1_funct_4(A,A))) # label(idempotence_k1_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.25 2472 $T # label(t3_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.25 2473 (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_1(k1_funct_4(C,D)) & m2_relset_1(k1_funct_4(C,D),A,B))))) # label(t41_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.25 2474 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_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]. 56.28/55.25 2475 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C k7_relat_1(A,k2_xboole_0(B,C)) = k1_funct_4(k7_relat_1(A,B),k7_relat_1(A,C))))) # label(t83_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.25 2476 (all A all B all C all D all E all F all G (m2_relset_1(G,k2_zfmisc_1(A,B),C) & v1_funct_1(G) & v1_funct_2(G,k2_zfmisc_1(A,B),C) -> (all H (m2_relset_1(H,k2_zfmisc_1(D,E),F) & v1_funct_2(H,k2_zfmisc_1(D,E),F) & v1_funct_1(H) -> -(-(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))) & F != k1_xboole_0 & k1_xboole_0 != C))))) # label(t63_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.25 2477 (all A -((all B -((all C all D k4_tarski(C,D) != B) & r2_hidden(B,A))) & (all B all C -r1_tarski(A,k2_zfmisc_1(B,C))))) # label(t1_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.25 2478 (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]. 56.28/55.25 2479 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(B) = k1_relat_1(C) -> k1_funct_4(A,C) = k1_funct_4(k1_funct_4(A,B),C)))))))) # label(t78_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.25 2480 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_funct_4(A,B) = k2_xboole_0(A,B) <-> r1_partfun1(A,B)))))) # label(t31_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.26 2481 (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)) -> k2_funct_4(k2_funct_4(C)) = C))) # label(t53_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.26 2482 (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(C,A)))))) # label(t12_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.26 2483 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k1_funct_4(A,B)) & v1_funct_1(k1_funct_4(A,B)))) # label(dt_k1_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.26 2484 (all A all B all C (v1_relat_1(C) & v1_funct_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]. 56.28/55.26 2485 (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]. 56.28/55.26 2486 (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) -> (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]. 56.28/55.26 2487 (all A all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) & v1_funct_1(C) & v1_funct_2(C,A,B) -> (all D (v1_funct_2(D,A,B) & v1_funct_1(D) & m2_relset_1(D,A,B) -> D = k1_funct_4(C,D))))))) # label(t40_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.26 2488 (all A all B all C all D (B != A -> k2_tarski(C,D) = k2_relat_1(k4_funct_4(A,B,C,D)))) # label(t67_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.26 2489 (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)) -> k2_relat_1(k2_funct_4(C)) = k2_relat_1(C)))) # label(t48_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.26 2490 (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]. 56.28/55.26 2491 (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]. 56.28/55.26 2492 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B A = k1_funct_4(A,k7_relat_1(A,B))))) # label(t80_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.26 2493 (all A (v1_relat_1(A) & v1_funct_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]. 56.28/55.26 2494 (all A all B all C (-v1_xboole_0(C) -> (all D (v1_funct_2(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,B),C) -> D = k2_funct_4(k2_funct_4(D)))))) # label(t56_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.26 2495 (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_partfun1(A,k1_funct_4(B,C)) -> r1_partfun1(A,C)))))))) # label(t28_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.26 2496 (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]. 56.28/55.26 2497 (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) & v1_funct_2(G,k2_zfmisc_1(A,B),E) & m2_relset_1(G,k2_zfmisc_1(A,B),E) -> (all H (m2_relset_1(H,k2_zfmisc_1(C,D),F) & v1_funct_2(H,k2_zfmisc_1(C,D),F) & v1_funct_1(H) -> 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]. 56.28/55.26 2498 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(B)) & 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]. 56.28/55.26 2499 (all A all B all C all D (A != B -> C = k1_funct_1(k4_funct_4(A,B,C,D),A) & D = k1_funct_1(k4_funct_4(A,B,C,D),B))) # label(t66_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.26 2500 (all A all B all C all D (m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> m2_relset_1(k2_funct_4(D),k2_zfmisc_1(B,A),C) & v1_funct_1(k2_funct_4(D)))) # label(t49_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.26 2501 (all A (v1_relat_1(A) & v1_funct_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]. 56.28/55.26 2502 $T # label(dt_k4_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.26 2503 (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]. 56.28/55.26 2504 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C all D (r1_xboole_0(C,D) & r1_tarski(k1_relat_1(A),C) & r1_tarski(k1_relat_1(B),D) -> B = k7_relat_1(k1_funct_4(A,B),D) & k7_relat_1(k1_funct_4(A,B),C) = A)))))) # label(t81_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.26 2505 (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)) -> k1_funct_4(A,B) = k1_funct_4(B,A)))))) # label(t36_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.26 2506 (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]. 56.28/55.26 2507 (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]. 56.28/55.26 2508 (all A all B all C all D (A != C -> k4_funct_4(A,C,B,D) = k2_tarski(k4_tarski(A,B),k4_tarski(C,D)))) # label(t71_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.26 2509 (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)) -> k7_relat_1(k1_funct_4(A,B),k1_relat_1(A)) = A))))) # label(t34_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.26 2510 (all A all B (v1_funct_2(B,A,A) & v1_funct_1(B) & m2_relset_1(B,A,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(C,A,A) -> C = k1_funct_4(B,C))))) # label(t39_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.26 2511 (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]. 56.28/55.26 2512 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_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]. 56.28/55.26 2513 (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) -> (v1_partfun1(D,A,B) -> k1_funct_4(C,D) = D))))) # label(t37_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.26 2514 (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]. 56.28/55.26 2515 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> r1_tarski(k7_relat_1(k8_relat_1(A,C),B),C))) # label(t9_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.26 2516 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k1_funct_4(A,B),k2_xboole_0(A,B)))))) # label(t30_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.26 2517 (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)) & r1_partfun1(B,C) -> k1_funct_1(k1_funct_4(B,C),A) = k1_funct_1(B,A)))))) # label(t16_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.26 2518 (all A all B all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) -> 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(t51_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.26 2519 (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]. 56.28/55.26 2520 (all A all B all C all D all E (v1_relat_1(E) & v1_funct_1(E) -> (all F (v1_relat_1(F) & v1_funct_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]. 56.28/55.26 2521 (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(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]. 56.28/55.26 2522 (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]. 56.28/55.26 2523 (all A all B all C all D all E (m1_subset_1(E,A) & m1_subset_1(D,A) & -v1_xboole_0(A) -> v1_funct_2(k5_funct_4(A,B,C,D,E),k2_tarski(B,C),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))) # label(dt_k5_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.26 2524 (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) -> k1_funct_4(k1_funct_4(A,B),C) = k1_funct_4(A,k1_funct_4(B,C)))))))) # label(t15_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.26 2525 (all A all B all C all D all E (v1_relat_1(E) & v1_funct_1(E) -> (all F (v1_relat_1(F) & v1_funct_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]. 56.28/55.26 2526 (all A all B k2_funcop_1(k1_tarski(A),B) = k1_tarski(k4_tarski(A,B))) # label(t70_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.26 2527 (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]. 56.28/55.26 2528 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,B),C) -> k2_funct_4(k2_funct_4(D)) = D)) # label(t54_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.26 2529 (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)) -> k1_funct_4(A,B) = B))))) # label(t20_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.26 2530 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(B,A) = k1_funct_1(k1_funct_4(C,B),A)))))) # label(t14_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.28/55.26 2531 (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]. 56.29/55.26 2532 (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_tarski(A,k1_funct_4(A,B))))))) # label(t33_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.29/55.26 2533 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_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]. 56.29/55.26 2534 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C k7_relat_1(k1_funct_4(A,B),C) = k1_funct_4(k7_relat_1(A,C),k7_relat_1(B,C))))))) # label(t75_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.29/55.26 2535 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> ((k1_xboole_0 = B -> k1_xboole_0 = A) -> D = k1_funct_4(C,D)))))) # label(t38_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.29/55.26 2536 (all A all B all C all D all E (m1_subset_1(E,A) & m1_subset_1(D,A) & -v1_xboole_0(A) -> k4_funct_4(B,C,D,E) = k5_funct_4(A,B,C,D,E))) # label(redefinition_k5_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.29/55.26 2537 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (B = k2_funct_4(A) <-> (all C all D (r2_hidden(k4_tarski(C,D),k1_relat_1(A)) -> k1_funct_1(A,k4_tarski(C,D)) = k1_funct_1(B,k4_tarski(D,C)))) & (all C (r2_hidden(C,k1_relat_1(B)) <-> (exists D exists E (k4_tarski(E,D) = C & r2_hidden(k4_tarski(D,E),k1_relat_1(A))))))))))) # label(d2_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.29/55.26 2538 (all A all B k1_funct_4(k6_partfun1(A),k6_partfun1(B)) = k6_partfun1(k2_xboole_0(A,B))) # label(t23_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.29/55.26 2539 (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]. 56.29/55.26 2540 (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]. 56.29/55.26 2541 (all A all B all C all D (r1_tarski(k2_funcop_1(A,B),k2_funcop_1(C,D)) -> k1_xboole_0 = A | D = B)) # label(t7_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.29/55.26 2542 (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) -> (k1_funct_4(A,B) = C <-> k1_relat_1(C) = k2_xboole_0(k1_relat_1(A),k1_relat_1(B)) & (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(A,D) = k1_funct_1(C,D)) & (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(B,D) = k1_funct_1(C,D))))))))))) # label(d1_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.29/55.26 2543 (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]. 56.29/55.26 2544 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_funct_4(A,B) = k1_funct_4(B,A) <-> r1_partfun1(A,B)))))) # label(t35_funct_4) # label(axiom) # label(non_clause). [assumption]. 56.29/55.26 2545 (all A all B (v3_ordinal1(A) & v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) -> v3_ordinal1(k13_ordinal2(A,B)))) # label(dt_k13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.29/55.26 2546 (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]. 56.29/55.26 2547 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v1_relat_1(C) & v1_funct_1(C) & f4_s16_ordinal2 = k1_funct_1(C,k1_xboole_0) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f5_s16_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> k1_funct_1(C,D) = f6_s16_ordinal2(D,k2_ordinal1(C,D)) | D = k1_xboole_0))) & k1_ordinal2(C) = B & v1_ordinal2(C) & k1_ordinal1(A) = k1_relat_1(C) & v5_ordinal1(C))) <-> B = f3_s16_ordinal2(A)))))) & v4_ordinal1(f2_s16_ordinal2) & f2_s16_ordinal2 = k1_relat_1(f1_s16_ordinal2) & (all A (v3_ordinal1(A) -> (r2_hidden(A,f2_s16_ordinal2) -> f3_s16_ordinal2(A) = k1_funct_1(f1_s16_ordinal2,A)))) & f2_s16_ordinal2 != k1_xboole_0 -> f6_s16_ordinal2(f2_s16_ordinal2,f1_s16_ordinal2) = f3_s16_ordinal2(f2_s16_ordinal2) # label(s16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.34/55.31 2548 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -((exists C (v1_relat_1(C) & v1_funct_1(C) & k1_funct_1(C,k1_xboole_0) = f2_s13_ordinal2 & k1_ordinal2(C) = A & v5_ordinal1(C) & k1_relat_1(C) = k1_ordinal1(f1_s13_ordinal2) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s13_ordinal2)) -> k1_funct_1(C,k1_ordinal1(D)) = f3_s13_ordinal2(D,k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(f1_s13_ordinal2)) & v4_ordinal1(D) -> f4_s13_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D) | k1_xboole_0 = D))) & v1_ordinal2(C))) & B != A & (exists C (f2_s13_ordinal2 = k1_funct_1(C,k1_xboole_0) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(f1_s13_ordinal2)) & v4_ordinal1(D) -> k1_xboole_0 = D | k1_funct_1(C,D) = f4_s13_ordinal2(D,k2_ordinal1(C,D))))) & B = k1_ordinal2(C) & v1_funct_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & k1_ordinal1(f1_s13_ordinal2) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s13_ordinal2)) -> f3_s13_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & v1_relat_1(C)))))))) # label(s13_ordinal2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 56.34/55.31 2549 (exists A (v3_ordinal1(A) & (exists B (v1_relat_1(B) & v1_funct_1(B) & f2_s13_ordinal2 = k1_funct_1(B,k1_xboole_0) & (all C (v3_ordinal1(C) -> (r2_hidden(k1_ordinal1(C),k1_ordinal1(f1_s13_ordinal2)) -> k1_funct_1(B,k1_ordinal1(C)) = f3_s13_ordinal2(C,k1_funct_1(B,C))))) & A = k1_ordinal2(B) & v1_ordinal2(B) & (all C (v3_ordinal1(C) -> (r2_hidden(C,k1_ordinal1(f1_s13_ordinal2)) & v4_ordinal1(C) -> C = k1_xboole_0 | f4_s13_ordinal2(C,k2_ordinal1(B,C)) = k1_funct_1(B,C)))) & k1_relat_1(B) = k1_ordinal1(f1_s13_ordinal2) & v5_ordinal1(B))))) # label(s13_ordinal2_AndRHS) # label(axiom) # label(non_clause). [assumption]. 56.34/55.31 2550 $T # label(t38_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.34/55.31 2551 (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]. 56.34/55.31 2552 (all A (v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> (v3_ordinal2(A) <-> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (C = k1_funct_1(A,B) & v4_ordinal1(B) & r2_hidden(B,k1_relat_1(A)) -> k1_xboole_0 = B | r1_ordinal2(C,k2_ordinal1(A,B)))))))))) # label(d17_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.34/55.31 2553 (all A (v3_ordinal1(A) -> (all B (B = f1_s8_ordinal2(A) <-> (exists C (v1_funct_1(C) & B = k1_ordinal2(C) & v1_relat_1(C) & v5_ordinal1(C) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> D = k1_xboole_0 | f4_s8_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f3_s8_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & k1_funct_1(C,k1_xboole_0) = f2_s8_ordinal2 & k1_relat_1(C) = k1_ordinal1(A))))))) -> f2_s8_ordinal2 = f1_s8_ordinal2(k1_xboole_0) # label(s8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.34/55.31 2554 $T # label(t40_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.34/55.31 2555 (all A (v3_ordinal1(A) -> A = k2_ordinal2(A))) # label(t10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.34/55.31 2556 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) -> (k1_ordinal1(A) = k1_relat_1(B) -> k1_funct_1(B,A) = k1_ordinal2(B)))))) # label(t7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.38 2557 $T # label(t39_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.38 2558 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k16_ordinal2(A,k1_ordinal1(B)) = k15_ordinal2(A,k16_ordinal2(A,B)))))) # label(t61_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.38 2559 (all A (v3_ordinal1(A) -> k15_ordinal2(A,k1_xboole_0) = k1_xboole_0)) # label(t55_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.38 2560 $T # label(t64_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.38 2561 k1_relat_1(f5_s4_ordinal2) = f1_s4_ordinal2 & (r2_hidden(k1_xboole_0,f1_s4_ordinal2) -> f2_s4_ordinal2 = k1_funct_1(f6_s4_ordinal2,k1_xboole_0)) & (all A (v3_ordinal1(A) -> (r2_hidden(A,f1_s4_ordinal2) & v4_ordinal1(A) -> A = k1_xboole_0 | k1_funct_1(f6_s4_ordinal2,A) = f4_s4_ordinal2(A,k2_ordinal1(f6_s4_ordinal2,A))))) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f1_s4_ordinal2) -> k1_funct_1(f5_s4_ordinal2,k1_ordinal1(A)) = f3_s4_ordinal2(A,k1_funct_1(f5_s4_ordinal2,A))))) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f1_s4_ordinal2) -> f3_s4_ordinal2(A,k1_funct_1(f6_s4_ordinal2,A)) = k1_funct_1(f6_s4_ordinal2,k1_ordinal1(A))))) & k1_relat_1(f6_s4_ordinal2) = f1_s4_ordinal2 & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & r2_hidden(A,f1_s4_ordinal2) -> k1_funct_1(f5_s4_ordinal2,A) = f4_s4_ordinal2(A,k2_ordinal1(f5_s4_ordinal2,A)) | k1_xboole_0 = A))) & (r2_hidden(k1_xboole_0,f1_s4_ordinal2) -> k1_funct_1(f5_s4_ordinal2,k1_xboole_0) = f2_s4_ordinal2) -> f5_s4_ordinal2 = f6_s4_ordinal2 # label(s4_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.38 2562 (all A all B -((exists C (v5_ordinal1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s7_ordinal2)) -> k1_funct_1(C,k1_ordinal1(D)) = f3_s7_ordinal2(D,k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(f1_s7_ordinal2)) & v4_ordinal1(D) -> k1_funct_1(C,D) = f4_s7_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & v1_funct_1(C) & v1_relat_1(C) & B = k1_ordinal2(C) & k1_ordinal1(f1_s7_ordinal2) = k1_relat_1(C) & k1_funct_1(C,k1_xboole_0) = f2_s7_ordinal2)) & A != B & (exists C (k1_ordinal2(C) = A & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(f1_s7_ordinal2)) -> k1_xboole_0 = D | f4_s7_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s7_ordinal2)) -> k1_funct_1(C,k1_ordinal1(D)) = f3_s7_ordinal2(D,k1_funct_1(C,D))))) & f2_s7_ordinal2 = k1_funct_1(C,k1_xboole_0) & k1_ordinal1(f1_s7_ordinal2) = k1_relat_1(C) & v5_ordinal1(C) & v1_relat_1(C) & v1_funct_1(C))))) # label(s7_ordinal2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 56.38/55.38 2563 (exists A exists B (v1_funct_1(B) & (all C (v3_ordinal1(C) -> (v4_ordinal1(C) & r2_hidden(C,k1_ordinal1(f1_s7_ordinal2)) -> C = k1_xboole_0 | f4_s7_ordinal2(C,k2_ordinal1(B,C)) = k1_funct_1(B,C)))) & v5_ordinal1(B) & k1_ordinal2(B) = A & k1_relat_1(B) = k1_ordinal1(f1_s7_ordinal2) & f2_s7_ordinal2 = k1_funct_1(B,k1_xboole_0) & (all C (v3_ordinal1(C) -> (r2_hidden(k1_ordinal1(C),k1_ordinal1(f1_s7_ordinal2)) -> f3_s7_ordinal2(C,k1_funct_1(B,C)) = k1_funct_1(B,k1_ordinal1(C))))) & v1_relat_1(B))) # label(s7_ordinal2_AndRHS) # label(axiom) # label(non_clause). [assumption]. 56.38/55.38 2564 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(B,C) -> A = k1_xboole_0 | r2_hidden(k15_ordinal2(B,A),k15_ordinal2(C,A))))))))) # label(t57_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.38 2565 (all A (v4_ordinal2(A) <-> r2_hidden(A,k5_ordinal2))) # label(d21_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.38 2566 (all A v3_ordinal1(k7_ordinal2(A))) # label(dt_k7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.38 2567 (all A (v3_ordinal1(A) -> (all B (m1_ordinal1(B,A) -> v1_ordinal2(B))))) # label(cc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.38 2568 (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]. 56.38/55.39 2569 $T # label(t6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.39 2570 (all A r1_tarski(k3_ordinal2(A),k2_ordinal2(A))) # label(t15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.39 2571 (all A (v3_ordinal1(A) -> (all B all C (r2_hidden(A,B) & r1_tarski(B,C) -> r1_ordinal1(k6_ordinal2(C),k6_ordinal2(B)))))) # label(t24_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.39 2572 (all A (v3_ordinal1(A) -> (all B (v1_ordinal2(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B) -> k12_ordinal2(k2_ordinal1(B,A)) = k13_ordinal2(A,B))))) # label(d15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.39 2573 $T # label(t20_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.39 2574 (exists A (v5_ordinal1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s2_ordinal2) -> f2_s2_ordinal2(B) = k1_funct_1(A,B)))) & k1_relat_1(A) = f1_s2_ordinal2 & v1_funct_1(A) & v1_relat_1(A))) # label(s2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.39 2575 $T # label(t8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.39 2576 (all A (v3_ordinal1(A) -> r1_ordinal1(k3_tarski(A),A))) # label(t5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.39 2577 $T # label(t42_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.39 2578 (all A (v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> k9_ordinal2(A) = k6_ordinal2(k2_relat_1(A)))) # label(d10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.39 2579 (all A all B (k2_ordinal2(A) = B <-> (all C (v3_ordinal1(C) & r2_hidden(C,A) <-> r2_hidden(C,B))))) # label(d2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.39 2580 (all A (v3_ordinal1(A) -> (all B (f4_s9_ordinal2(A) = B <-> (exists C (v1_funct_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f2_s9_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & f1_s9_ordinal2 = k1_funct_1(C,k1_xboole_0) & B = k1_ordinal2(C) & k1_relat_1(C) = k1_ordinal1(A) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> D = k1_xboole_0 | f3_s9_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & v5_ordinal1(C) & v1_relat_1(C))))))) -> (all A (v3_ordinal1(A) -> f4_s9_ordinal2(k1_ordinal1(A)) = f2_s9_ordinal2(A,f4_s9_ordinal2(A)))) # label(s9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.39 2581 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> v3_ordinal1(k10_ordinal2(A)))) # label(dt_k10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.39 2582 (all A all B (v5_ordinal1(A) & v1_relat_1(A) & v1_funct_1(A) & v3_ordinal1(B) & v1_ordinal2(A) -> v1_ordinal1(k1_funct_1(A,B)) & v3_ordinal1(k1_funct_1(A,B)) & v2_ordinal1(k1_funct_1(A,B)))) # label(fc3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.39 2583 (all A (v3_ordinal1(A) -> k16_ordinal2(A,k4_ordinal2) = A & k4_ordinal2 = k16_ordinal2(k4_ordinal2,A))) # label(t63_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.39 2584 k1_relat_1(f1_s10_ordinal2) = f2_s10_ordinal2 & v4_ordinal1(f2_s10_ordinal2) & k1_xboole_0 != f2_s10_ordinal2 & (all A (v3_ordinal1(A) -> (r2_hidden(A,f2_s10_ordinal2) -> f3_s10_ordinal2(A) = k1_funct_1(f1_s10_ordinal2,A)))) & (all A (v3_ordinal1(A) -> (all B (B = f3_s10_ordinal2(A) <-> (exists C (v1_funct_1(C) & k1_ordinal2(C) = B & k1_relat_1(C) = k1_ordinal1(A) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> k1_xboole_0 = D | f6_s10_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & f4_s10_ordinal2 = k1_funct_1(C,k1_xboole_0) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f5_s10_ordinal2(D,k1_funct_1(C,D))))) & v5_ordinal1(C) & v1_relat_1(C))))))) -> f3_s10_ordinal2(f2_s10_ordinal2) = f6_s10_ordinal2(f2_s10_ordinal2,f1_s10_ordinal2) # label(s10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.39 2585 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> k1_funct_1(A,k3_tarski(k1_relat_1(A))) = k1_ordinal2(A))) # label(d1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.39 2586 (all A r1_tarski(k2_ordinal2(A),A)) # label(t9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.39 2587 (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]. 56.38/55.39 2588 (all A all B (B = k3_ordinal2(A) <-> (all C (r2_hidden(C,B) <-> r2_hidden(C,A) & (exists D (v3_ordinal1(D) & C = D & v4_ordinal1(D))))))) # label(d3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.39 2589 (all A (v3_ordinal1(A) -> k14_ordinal2(A,k1_xboole_0) = A)) # label(t44_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.39 2590 (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]. 56.38/55.39 2591 (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]. 56.38/55.39 2592 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v1_funct_1(C) & v5_ordinal1(C) & f2_s14_ordinal2 = k1_funct_1(C,k1_xboole_0) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> D = k1_xboole_0 | f4_s14_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f3_s14_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & k1_ordinal1(A) = k1_relat_1(C) & k1_ordinal2(C) = B & v1_relat_1(C) & v1_ordinal2(C))) <-> f1_s14_ordinal2(A) = B))))) -> f1_s14_ordinal2(k1_xboole_0) = f2_s14_ordinal2 # label(s14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.39 2593 (all A (v3_ordinal1(A) -> (exists B ((exists C (v4_ordinal1(B) & A = k14_ordinal2(B,C) & v3_ordinal1(C) & v4_ordinal2(C))) & v3_ordinal1(B))))) # label(t65_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.39 2594 (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]. 56.38/55.39 2595 (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]. 56.38/55.39 2596 (all A (v3_ordinal1(A) -> k3_tarski(k1_ordinal1(A)) = A)) # label(t2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.39 2597 (all A (v3_ordinal1(A) -> k1_ordinal1(A) = k7_ordinal2(k1_tarski(A)))) # label(t31_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.39 2598 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k14_ordinal2(k15_ordinal2(A,B),B) = k15_ordinal2(k1_ordinal1(A),B))))) # label(t53_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.39 2599 (exists A ((r2_hidden(k1_xboole_0,f1_s11_ordinal2) -> k1_funct_1(A,k1_xboole_0) = f2_s11_ordinal2) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s11_ordinal2) & v4_ordinal1(B) -> k1_funct_1(A,B) = f4_s11_ordinal2(B,k2_ordinal1(A,B)) | k1_xboole_0 = B))) & k1_relat_1(A) = f1_s11_ordinal2 & v5_ordinal1(A) & v1_ordinal2(A) & (all B (v3_ordinal1(B) -> (r2_hidden(k1_ordinal1(B),f1_s11_ordinal2) -> k1_funct_1(A,k1_ordinal1(B)) = f3_s11_ordinal2(B,k1_funct_1(A,B))))) & v1_funct_1(A) & v1_relat_1(A))) # label(s11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.39 2600 $T # label(t41_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.39 2601 (all A (v1_funct_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & v1_relat_1(A) -> ((exists B (v3_ordinal1(B) & r1_ordinal2(B,A))) -> (all B (v3_ordinal1(B) -> (r1_ordinal2(B,A) <-> B = k12_ordinal2(A))))))) # label(d14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.39 2602 $T # label(dt_k3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.39 2603 (all A k1_setfam_1(k2_ordinal2(A)) = k6_ordinal2(A)) # label(d6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.39 2604 (all A all B (v3_ordinal1(B) -> (B = k7_ordinal2(A) <-> (all C (v3_ordinal1(C) -> (r1_tarski(k2_ordinal2(A),C) -> r1_ordinal1(B,C)))) & r1_tarski(k2_ordinal2(A),B)))) # label(d7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.39 2605 $T # label(dt_k1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.39 2606 (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]. 56.38/55.39 2607 (all A (v5_ordinal1(A) & v1_relat_1(A) & v1_funct_1(A) & v1_ordinal2(A) -> ((all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(C,k1_relat_1(A)) & r2_hidden(B,C) -> r2_hidden(k1_funct_1(A,B),k1_funct_1(A,C))))))) <-> v2_ordinal2(A)))) # label(d16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.39 2608 (exists A (v1_relat_1(A) & v5_ordinal1(A) & k1_relat_1(A) = f1_s5_ordinal2 & (all B (v3_ordinal1(B) -> (v4_ordinal1(B) & r2_hidden(B,f1_s5_ordinal2) -> k1_funct_1(A,B) = f4_s5_ordinal2(B,k2_ordinal1(A,B)) | k1_xboole_0 = B))) & (r2_hidden(k1_xboole_0,f1_s5_ordinal2) -> k1_funct_1(A,k1_xboole_0) = f2_s5_ordinal2) & (all B (v3_ordinal1(B) -> (r2_hidden(k1_ordinal1(B),f1_s5_ordinal2) -> k1_funct_1(A,k1_ordinal1(B)) = f3_s5_ordinal2(B,k1_funct_1(A,B))))) & v1_funct_1(A))) # label(s5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.39 2609 (all A (v3_ordinal1(A) -> (all B ((all C (v3_ordinal1(C) -> (r2_hidden(C,B) -> r1_ordinal1(A,C)))) -> k2_ordinal2(B) = k1_xboole_0 | r1_ordinal1(A,k6_ordinal2(B)))))) # label(t23_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.39 2610 (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]. 56.38/55.39 2611 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> ((exists D (v1_funct_1(D) & (all E (v3_ordinal1(E) -> (v4_ordinal1(E) & r2_hidden(E,k1_ordinal1(A)) -> k3_tarski(k8_ordinal2(k2_ordinal1(D,E))) = k1_funct_1(D,E) | k1_xboole_0 = E))) & k1_relat_1(D) = k1_ordinal1(A) & v5_ordinal1(D) & v1_relat_1(D) & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(A)) -> k1_funct_1(D,k1_ordinal1(E)) = k14_ordinal2(k1_funct_1(D,E),B)))) & k1_xboole_0 = k1_funct_1(D,k1_xboole_0) & k1_ordinal2(D) = C & v1_ordinal2(D))) <-> k15_ordinal2(A,B) = C))))))) # label(d19_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.39 2612 (all A (v5_ordinal1(A) & v1_relat_1(A) & v1_funct_1(A) -> (all B (v3_ordinal1(B) -> (k10_ordinal2(A) = B <-> (exists C (v1_funct_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(A)) -> k1_funct_1(C,D) = k7_ordinal2(k2_relat_1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),D))))))) & B = k9_ordinal2(C) & v1_relat_1(C) & v1_ordinal2(C) & k1_relat_1(A) = k1_relat_1(C) & v5_ordinal1(C)))))))) # label(d11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.39 2613 (all A r1_tarski(k3_ordinal2(A),A)) # label(t13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.39 2614 (all A (v3_ordinal1(A) -> (all B (v1_ordinal2(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B) -> (k1_xboole_0 != A -> (r1_ordinal2(A,B) <-> (all C (v3_ordinal1(C) -> (all D (v3_ordinal1(D) -> -(r2_hidden(A,D) & r2_hidden(C,A) & (all E (v3_ordinal1(E) -> -(r2_hidden(E,k1_relat_1(B)) & (all F (v3_ordinal1(F) -> (r1_ordinal1(E,F) & r2_hidden(F,k1_relat_1(B)) -> r2_hidden(C,k1_funct_1(B,F)) & r2_hidden(k1_funct_1(B,F),D)))))))))))))) & (k1_xboole_0 = A -> (r1_ordinal2(A,B) <-> (exists C ((all D (v3_ordinal1(D) -> (r1_ordinal1(C,D) & r2_hidden(D,k1_relat_1(B)) -> k1_xboole_0 = k1_funct_1(B,D)))) & r2_hidden(C,k1_relat_1(B)) & v3_ordinal1(C))))))))) # label(d13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.38/55.39 2615 (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]. 56.38/55.39 2616 (all A (v3_ordinal1(A) -> A = k14_ordinal2(k1_xboole_0,A))) # label(t47_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.47/55.48 2617 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> v3_ordinal1(k14_ordinal2(A,B)))) # label(dt_k14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.47/55.48 2618 $T # label(t43_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.47/55.48 2619 (exists A (v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) & v1_relat_1(A))) # label(rc2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.47/55.48 2620 $T # label(t12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.47/55.48 2621 p1_s1_ordinal2(k1_xboole_0) & (all A (v3_ordinal1(A) -> (p1_s1_ordinal2(A) -> p1_s1_ordinal2(k1_ordinal1(A))))) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(B,A) -> p1_s1_ordinal2(B)))) -> p1_s1_ordinal2(A) | A = k1_xboole_0))) -> (all A (v3_ordinal1(A) -> p1_s1_ordinal2(A))) # label(s1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.47/55.48 2622 (all A (v3_ordinal1(A) -> k1_xboole_0 = k15_ordinal2(k1_xboole_0,A))) # label(t52_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.47/55.48 2623 (all A (v3_ordinal1(A) -> k7_ordinal2(A) = A)) # label(t26_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.47/55.48 2624 (all A (v3_ordinal1(A) -> k4_ordinal2 = k16_ordinal2(A,k1_xboole_0))) # label(t60_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.47/55.48 2625 (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]. 56.47/55.48 2626 $T # label(t18_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.47/55.48 2627 $T # label(t21_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.47/55.48 2628 (exists A (v4_ordinal1(A) & v2_ordinal1(A) & v1_ordinal1(A) & v3_ordinal1(A))) # label(rc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.47/55.48 2629 (all A (v3_ordinal1(A) -> (exists B (r2_hidden(A,B) & v3_ordinal1(B) & v4_ordinal1(B))))) # label(t16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.47/55.48 2630 $T # label(dt_k2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.47/55.48 2631 (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]. 56.47/55.48 2632 (all A (v3_ordinal1(A) -> (r2_hidden(A,f3_s6_ordinal2) & v4_ordinal1(A) -> A = k1_xboole_0 | f6_s6_ordinal2(A,k2_ordinal1(f1_s6_ordinal2,A)) = k1_funct_1(f1_s6_ordinal2,A)))) & (r2_hidden(k1_xboole_0,f3_s6_ordinal2) -> f4_s6_ordinal2 = k1_funct_1(f1_s6_ordinal2,k1_xboole_0)) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f3_s6_ordinal2) -> k1_funct_1(f1_s6_ordinal2,k1_ordinal1(A)) = f5_s6_ordinal2(A,k1_funct_1(f1_s6_ordinal2,A))))) & k1_relat_1(f1_s6_ordinal2) = f3_s6_ordinal2 & (all A (v3_ordinal1(A) -> (all B (f2_s6_ordinal2(A) = B <-> (exists C ((all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_funct_1(C,D) = f6_s6_ordinal2(D,k2_ordinal1(C,D)) | D = k1_xboole_0))) & k1_relat_1(C) = k1_ordinal1(A) & f4_s6_ordinal2 = k1_funct_1(C,k1_xboole_0) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f5_s6_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & B = k1_ordinal2(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C))))))) -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s6_ordinal2)) -> k1_funct_1(f1_s6_ordinal2,A) = f2_s6_ordinal2(A)))) # label(s6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.47/55.48 2633 (all A all B (v3_ordinal1(B) -> v1_funct_1(k2_funcop_1(A,B)) & v1_relat_1(k2_funcop_1(A,B)) & v1_ordinal2(k2_funcop_1(A,B)))) # label(fc4_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.47/55.48 2634 (all A (v1_ordinal2(A) & v5_ordinal1(A) & v1_relat_1(A) & v1_funct_1(A) -> v3_ordinal1(k12_ordinal2(A)))) # label(dt_k12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.47/55.48 2635 $T # label(t37_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.47/55.48 2636 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v1_ordinal2(C) & v5_ordinal1(C) & v1_funct_1(C) & k8_ordinal2(C) = B & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(A)) -> k6_ordinal2(k2_relat_1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),D)))) = k1_funct_1(C,D)))) & k1_relat_1(A) = k1_relat_1(C) & v1_relat_1(C))) <-> k11_ordinal2(A) = B))))) # label(d12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.47/55.48 2637 (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]. 56.47/55.48 2638 $T # label(t33_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.47/55.48 2639 (all A (v3_ordinal1(A) -> k1_ordinal1(A) = k14_ordinal2(A,k4_ordinal2))) # label(t48_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.47/55.48 2640 (all A all B (v1_ordinal2(A) & v3_ordinal1(B) & v1_funct_1(A) & v1_relat_1(A) & v5_ordinal1(A) -> v1_funct_1(k7_relat_1(A,B)) & v1_relat_1(k7_relat_1(A,B)) & v1_ordinal2(k7_relat_1(A,B)))) # label(fc2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.47/55.48 2641 (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]. 56.47/55.48 2642 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> v3_ordinal1(k16_ordinal2(A,B)))) # label(dt_k16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.47/55.48 2643 $T # label(dt_k5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.47/55.48 2644 (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]. 56.47/55.48 2645 (exists A (v1_relat_1(A) & v1_funct_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s3_ordinal2) -> f2_s3_ordinal2(B) = k1_funct_1(A,B)))) & f1_s3_ordinal2 = k1_relat_1(A))) # label(s3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.47/55.48 2646 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v1_funct_1(C) & v1_ordinal2(C) & k1_ordinal1(A) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> k1_funct_1(C,D) = f3_s15_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & v1_relat_1(C) & f1_s15_ordinal2 = k1_funct_1(C,k1_xboole_0) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f2_s15_ordinal2(D,k1_funct_1(C,D))))) & B = k1_ordinal2(C) & v5_ordinal1(C))) <-> B = f4_s15_ordinal2(A)))))) -> (all A (v3_ordinal1(A) -> f4_s15_ordinal2(k1_ordinal1(A)) = f2_s15_ordinal2(A,f4_s15_ordinal2(A)))) # label(s15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.47/55.48 2647 (all A (k5_ordinal2 = A <-> (all B (v3_ordinal1(B) -> (v4_ordinal1(B) & r2_hidden(k1_xboole_0,B) -> r1_tarski(A,B)))) & v3_ordinal1(A) & v4_ordinal1(A) & r2_hidden(k1_xboole_0,A))) # label(d5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.47/55.48 2648 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> (all C (v5_ordinal1(C) & v1_relat_1(C) & v1_funct_1(C) & v1_ordinal2(C) -> ((all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k14_ordinal2(B,D) = k1_funct_1(C,D)))) & A = k1_relat_1(C) -> k14_ordinal2(B,A) = k8_ordinal2(C)))) | A = k1_xboole_0))))) # label(t46_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.47/55.48 2649 (all A (v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> v3_ordinal1(k8_ordinal2(A)))) # label(dt_k8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.47/55.48 2650 (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]. 56.47/55.48 2651 (all A (v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> k9_ordinal2(A) = k6_ordinal2(k2_relat_1(A)) & k7_ordinal2(k2_relat_1(A)) = k8_ordinal2(A))) # label(t35_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.47/55.48 2652 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((exists B (r1_tarski(k2_relat_1(A),B) & v3_ordinal1(B))) <-> v1_ordinal2(A)))) # label(d8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.47/55.48 2653 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_ordinal2(B) -> (r2_hidden(A,k1_relat_1(B)) -> v3_ordinal1(k1_funct_1(B,A))))))) # label(t34_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2654 (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]. 56.58/55.62 2655 (all A (v3_ordinal1(A) -> r1_tarski(k1_ordinal1(A),k1_zfmisc_1(A)))) # label(t3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2656 k1_relat_1(f1_s12_ordinal2) = f3_s12_ordinal2 & (all A (v3_ordinal1(A) -> (r2_hidden(A,f3_s12_ordinal2) & v4_ordinal1(A) -> k1_xboole_0 = A | f6_s12_ordinal2(A,k2_ordinal1(f1_s12_ordinal2,A)) = k1_funct_1(f1_s12_ordinal2,A)))) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f3_s12_ordinal2) -> k1_funct_1(f1_s12_ordinal2,k1_ordinal1(A)) = f5_s12_ordinal2(A,k1_funct_1(f1_s12_ordinal2,A))))) & (r2_hidden(k1_xboole_0,f3_s12_ordinal2) -> k1_funct_1(f1_s12_ordinal2,k1_xboole_0) = f4_s12_ordinal2) & (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (f2_s12_ordinal2(A) = B <-> (exists C (v1_ordinal2(C) & k1_relat_1(C) = k1_ordinal1(A) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_funct_1(C,D) = f6_s12_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & k1_ordinal2(C) = B & v5_ordinal1(C) & v1_funct_1(C) & k1_funct_1(C,k1_xboole_0) = f4_s12_ordinal2 & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f5_s12_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & v1_relat_1(C)))))))) -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s12_ordinal2)) -> k1_funct_1(f1_s12_ordinal2,A) = f2_s12_ordinal2(A)))) # label(s12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2657 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (C = k14_ordinal2(A,B) <-> (exists D (A = k1_funct_1(D,k1_xboole_0) & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(B)) -> k1_funct_1(D,k1_ordinal1(E)) = k1_ordinal1(k1_funct_1(D,E))))) & (all E (v3_ordinal1(E) -> (v4_ordinal1(E) & r2_hidden(E,k1_ordinal1(B)) -> k1_xboole_0 = E | k8_ordinal2(k2_ordinal1(D,E)) = k1_funct_1(D,E)))) & v1_ordinal2(D) & v1_relat_1(D) & v1_funct_1(D) & k1_relat_1(D) = k1_ordinal1(B) & C = k1_ordinal2(D) & v5_ordinal1(D)))))))))) # label(d18_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2658 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> (all C (v1_funct_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & v1_relat_1(C) -> ((all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k15_ordinal2(D,B) = k1_funct_1(C,D)))) & k1_relat_1(C) = A -> k3_tarski(k8_ordinal2(C)) = k15_ordinal2(A,B)))) | k1_xboole_0 = A))))) # label(t54_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2659 $T # label(t36_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2660 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (k16_ordinal2(A,B) = C <-> (exists D (C = k1_ordinal2(D) & k1_ordinal1(B) = k1_relat_1(D) & k4_ordinal2 = k1_funct_1(D,k1_xboole_0) & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(B)) -> k15_ordinal2(A,k1_funct_1(D,E)) = k1_funct_1(D,k1_ordinal1(E))))) & v1_funct_1(D) & v1_relat_1(D) & v5_ordinal1(D) & (all E (v3_ordinal1(E) -> (v4_ordinal1(E) & r2_hidden(E,k1_ordinal1(B)) -> k1_xboole_0 = E | k12_ordinal2(k2_ordinal1(D,E)) = k1_funct_1(D,E)))) & v1_ordinal2(D)))))))))) # label(d20_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2661 (all A (v3_ordinal1(A) -> k15_ordinal2(A,k4_ordinal2) = A & k15_ordinal2(k4_ordinal2,A) = A)) # label(t56_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2662 (all A v3_ordinal1(k6_ordinal2(A))) # label(dt_k6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2663 (all A (v3_ordinal1(A) -> (r2_hidden(k1_xboole_0,A) & v4_ordinal1(A) -> r1_ordinal1(k5_ordinal2,A)))) # label(t19_ordinal2_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2664 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) -> k8_ordinal2(A) = k7_ordinal2(k2_relat_1(A)))) # label(d9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2665 (all A (v3_ordinal1(A) -> (all B -((all C (v3_ordinal1(C) -> -(r1_ordinal1(A,C) & r2_hidden(C,B)))) & r2_hidden(A,k7_ordinal2(B)))))) # label(t29_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2666 (all A r1_ordinal1(k6_ordinal2(A),k7_ordinal2(A))) # label(t32_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2667 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> (all C (v5_ordinal1(C) & v1_funct_1(C) & v1_ordinal2(C) & v1_relat_1(C) -> (A = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k1_funct_1(C,D) = k16_ordinal2(B,D)))) -> k16_ordinal2(B,A) = k12_ordinal2(C)))) | A = k1_xboole_0))))) # label(t62_ordinal2) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2668 $T # label(t11_finset_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2669 (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]. 56.58/55.62 2670 (all A all B (v1_funct_1(A) & v1_finset_1(B) & v1_relat_1(A) -> v1_finset_1(k9_relat_1(A,B)))) # label(fc13_finset_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2671 (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]. 56.58/55.62 2672 (all A ((all B (r2_hidden(B,A) -> v1_finset_1(B))) & v1_finset_1(A) <-> v1_finset_1(k3_tarski(A)))) # label(t25_finset_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2673 $T # label(t9_finset_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2674 (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]. 56.58/55.62 2675 (exists A (v1_relat_1(A) & v1_funct_1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s1_finset_1) -> (p1_s1_finset_1(B) -> f2_s1_finset_1(B) = k1_funct_1(A,B)) & (-p1_s1_finset_1(B) -> k1_funct_1(A,B) = f3_s1_finset_1(B))))) & k1_relat_1(A) = f1_s1_finset_1)) # label(s1_finset_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2676 (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]. 56.58/55.62 2677 (all A (v1_finset_1(A) <-> v1_finset_1(k1_zfmisc_1(A)))) # label(t24_finset_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2678 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v1_finset_1(k1_relat_1(A)) <-> v1_finset_1(A)))) # label(t29_finset_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2679 (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]. 56.58/55.62 2680 (all A all B (v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k2_zfmisc_1(A,B)))) # label(fc14_finset_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2681 (all A (v1_finset_1(k1_tarski(A)) & -v1_xboole_0(k1_tarski(A)))) # label(fc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2682 (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]. 56.58/55.62 2683 (all A all B all C v1_finset_1(k1_enumset1(A,B,C))) # label(fc3_finset_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2684 (all A -((all B -(r2_hidden(B,A) & (all C (r2_hidden(C,A) -> r1_tarski(B,C))))) & v6_ordinal1(A) & k1_xboole_0 != A & v1_finset_1(A))) # label(t30_finset_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2685 (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]. 56.58/55.62 2686 (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]. 56.58/55.62 2687 (all A -(v1_finset_1(A) & (all B -((all C (r2_hidden(C,A) -> r1_tarski(C,B))) & r2_hidden(B,A))) & v6_ordinal1(A) & A != k1_xboole_0)) # label(t31_finset_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2688 $T # label(t1_finset_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2689 (all A all B (r1_tarski(B,f1_s2_finset_1) & p1_s2_finset_1(B) & r2_hidden(A,f1_s2_finset_1) -> p1_s2_finset_1(k2_xboole_0(B,k1_tarski(A))))) & p1_s2_finset_1(k1_xboole_0) & v1_finset_1(f1_s2_finset_1) -> p1_s2_finset_1(f1_s2_finset_1) # label(s2_finset_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2690 $T # label(t3_finset_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2691 (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]. 56.58/55.62 2692 (all A all B all C all D (v1_finset_1(B) & v1_finset_1(C) & v1_finset_1(D) & v1_finset_1(A) -> v1_finset_1(k4_zfmisc_1(A,B,C,D)))) # label(t21_finset_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2693 $T # label(t10_finset_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2694 (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(rc3_finset_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2695 (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]. 56.58/55.62 2696 (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]. 56.58/55.62 2697 (all A (v1_xboole_0(A) -> v1_finset_1(A))) # label(cc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2698 (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]. 56.58/55.62 2699 (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]. 56.58/55.62 2700 (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]. 56.58/55.62 2701 (all A exists B (v1_xboole_0(B) & v2_ordinal1(B) & v3_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B) & v2_funct_1(B) & v1_ordinal1(B) & v4_ordinal2(B) & v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)))) # label(rc2_finset_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2702 (all A all B (v1_finset_1(A) & v1_finset_1(B) -> v1_finset_1(k2_xboole_0(A,B)))) # label(fc9_finset_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2703 (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]. 56.58/55.62 2704 (all A all B all C all D (v1_finset_1(A) & v1_finset_1(D) & v1_finset_1(C) & v1_finset_1(B) -> v1_finset_1(k4_zfmisc_1(A,B,C,D)))) # label(fc16_finset_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2705 $T # label(t2_finset_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2706 (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]. 56.58/55.62 2707 $T # label(t6_finset_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2708 (all A all B all C (v1_finset_1(A) & v1_finset_1(B) & v1_finset_1(C) -> v1_finset_1(k3_zfmisc_1(A,B,C)))) # label(fc15_finset_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2709 (all A all B all C (v1_finset_1(C) & v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k3_zfmisc_1(A,B,C)))) # label(t20_finset_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2710 (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]. 56.58/55.62 2711 $T # label(t5_finset_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2712 $T # label(t12_finset_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2713 $T # label(t7_finset_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2714 (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]. 56.58/55.62 2715 $T # label(t4_finset_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2716 (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 (r1_tarski(C,D) & r2_hidden(D,B) -> C = D)) & r2_hidden(C,B)))))))) # label(t18_finset_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2717 (exists A (v1_finset_1(A) & -v1_xboole_0(A))) # label(rc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2718 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v1_finset_1(k10_relat_1(B,A)) & r1_tarski(A,k2_relat_1(B)) -> v1_finset_1(A)))) # label(t27_finset_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2719 (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]. 56.58/55.62 2720 (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]. 56.58/55.62 2721 (all A ((exists B (v1_relat_1(B) & v1_funct_1(B) & k2_relat_1(B) = A & r2_hidden(k1_relat_1(B),k5_ordinal2))) <-> v1_finset_1(A))) # label(d1_finset_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2722 (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]. 56.58/55.62 2723 (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]. 56.58/55.62 2724 $T # label(t8_finset_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2725 (exists A (v1_finsub_1(A) & v3_finsub_1(A) & -v1_xboole_0(A) & v4_finsub_1(A) & v2_finsub_1(A))) # label(rc1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2726 (all A all B (m1_subset_1(B,k5_finsub_1(A)) -> v1_finset_1(B))) # label(cc3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2727 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,A) & v4_finsub_1(A) & m1_subset_1(C,A) -> m1_subset_1(k2_finsub_1(A,B,C),A))) # label(dt_k2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2728 (all A (v1_finsub_1(A) & v3_finsub_1(A) <-> v4_finsub_1(A))) # label(d4_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2729 (all A (v3_finsub_1(A) <-> (all B all C (r2_hidden(C,A) & r2_hidden(B,A) -> r2_hidden(k4_xboole_0(B,C),A))))) # label(d3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2730 (all A all B all C (-v1_xboole_0(A) & v4_finsub_1(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> k4_finsub_1(A,B,C) = k4_finsub_1(A,C,B))) # label(commutativity_k4_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2731 (all A (v1_finsub_1(k5_finsub_1(A)) & -v1_xboole_0(k5_finsub_1(A)) & v3_finsub_1(k5_finsub_1(A)) & v4_finsub_1(k5_finsub_1(A)))) # label(fc2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2732 $T # label(t29_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2733 (all A all B all C (m1_subset_1(C,A) & -v1_xboole_0(A) & m1_subset_1(B,A) & v4_finsub_1(A) -> B = k3_finsub_1(A,B,B))) # label(idempotence_k3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2734 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> r2_hidden(k5_xboole_0(B,C),A) & r2_hidden(k2_xboole_0(B,C),A))))) -> v4_finsub_1(A)))) # label(t17_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2735 (all A all B all C (v4_finsub_1(A) & m1_subset_1(C,A) & -v1_xboole_0(A) & m1_subset_1(B,A) -> m1_subset_1(k3_finsub_1(A,B,C),A))) # label(dt_k3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2736 $T # label(t4_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2737 (all A all B all C (v4_finsub_1(A) & m1_subset_1(B,A) & -v1_xboole_0(A) & m1_subset_1(C,A) -> k3_xboole_0(B,C) = k3_finsub_1(A,B,C))) # label(redefinition_k3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2738 $T # label(t12_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2739 (all A all B all C (v4_finsub_1(A) & -v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> m1_subset_1(k1_finsub_1(A,B,C),A))) # label(dt_k1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2740 (all A all B all C (v4_finsub_1(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k4_xboole_0(B,C) = k2_finsub_1(A,B,C))) # label(redefinition_k2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2741 (all A all B (r1_tarski(A,B) -> r1_tarski(k5_finsub_1(A),k5_finsub_1(B)))) # label(t23_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2742 (all A (v1_finset_1(A) -> k5_finsub_1(A) = k1_zfmisc_1(A))) # label(t27_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2743 (all A (v4_finsub_1(A) & -v1_xboole_0(A) -> r2_hidden(k1_xboole_0,A))) # label(t18_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2744 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> r2_hidden(k3_xboole_0(B,C),A) & r2_hidden(k5_xboole_0(B,C),A))))) -> v4_finsub_1(A)))) # label(t16_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2745 (all A (v4_finsub_1(k1_zfmisc_1(A)) & v1_finsub_1(k1_zfmisc_1(A)) & -v1_xboole_0(k1_zfmisc_1(A)) & v3_finsub_1(k1_zfmisc_1(A)))) # label(fc1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2746 $T # label(t7_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2747 $T # label(t5_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2748 (all A all B all C (m1_subset_1(C,A) & v4_finsub_1(A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k3_finsub_1(A,B,C) = k3_finsub_1(A,C,B))) # label(commutativity_k3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2749 $T # label(t2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2750 (all A v4_finsub_1(k5_finsub_1(A))) # label(dt_k5_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2751 (all A (v4_finsub_1(A) -> v1_finsub_1(A) & v3_finsub_1(A))) # label(cc1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2752 $T # label(t31_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2753 (all A all B all C (-v1_xboole_0(A) & v4_finsub_1(A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> k1_finsub_1(A,B,C) = k2_xboole_0(B,C))) # label(redefinition_k1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2754 (all A all B (m1_subset_1(B,k5_finsub_1(A)) -> m1_subset_1(B,k1_zfmisc_1(A)))) # label(t32_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2755 $T # label(t9_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2756 (all A (v4_finsub_1(A) & -v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & v4_finsub_1(B) -> -v1_xboole_0(k3_xboole_0(A,B)) & v4_finsub_1(k3_xboole_0(A,B)))))) # label(t21_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2757 (all A all B all C (m1_subset_1(C,A) & -v1_xboole_0(A) & v4_finsub_1(A) & m1_subset_1(B,A) -> m1_subset_1(k4_finsub_1(A,B,C),A))) # label(dt_k4_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2758 (all A r1_tarski(k5_finsub_1(A),k1_zfmisc_1(A))) # label(t26_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2759 $T # label(t6_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2760 $T # label(t1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2761 (all A all B (m1_subset_1(B,k5_finsub_1(A)) -> v1_finset_1(B))) # label(t30_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2762 (all A (v4_finsub_1(A) <-> (all B all C (r2_hidden(B,A) & r2_hidden(C,A) -> r2_hidden(k4_xboole_0(B,C),A) & r2_hidden(k2_xboole_0(B,C),A))))) # label(t10_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2763 (all A all B r1_tarski(k2_xboole_0(k5_finsub_1(A),k5_finsub_1(B)),k5_finsub_1(k2_xboole_0(A,B)))) # label(t25_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2764 (all A (v1_finsub_1(A) & v3_finsub_1(A) -> v4_finsub_1(A))) # label(cc2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2765 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (v1_finset_1(A) -> m1_subset_1(B,k5_finsub_1(A))))) # label(t34_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2766 (all A (v2_finsub_1(A) <-> (all B all C (r2_hidden(C,A) & r2_hidden(B,A) -> r2_hidden(k3_xboole_0(B,C),A))))) # label(d2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2767 $T # label(t22_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2768 (all A all B all C (v4_finsub_1(C) & -v1_xboole_0(C) -> (m1_subset_1(B,C) & m1_subset_1(A,C) -> m1_subset_1(k5_xboole_0(A,B),C)))) # label(t14_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2769 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> r2_hidden(k5_xboole_0(B,C),A) & r2_hidden(k4_xboole_0(B,C),A))))) -> v4_finsub_1(A)))) # label(t15_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2770 (all A all B (v4_finsub_1(B) -> ((all C (r1_tarski(C,A) & v1_finset_1(C) <-> r2_hidden(C,B))) <-> k5_finsub_1(A) = B))) # label(d5_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2771 (all A all B all C (v4_finsub_1(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k5_xboole_0(B,C) = k4_finsub_1(A,B,C))) # label(redefinition_k4_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2772 $T # label(t11_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2773 $T # label(t3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2774 (all A all B all C (v4_finsub_1(A) & m1_subset_1(C,A) & -v1_xboole_0(A) & m1_subset_1(B,A) -> k1_finsub_1(A,C,B) = k1_finsub_1(A,B,C))) # label(commutativity_k1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2775 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & v4_finsub_1(A) -> B = k1_finsub_1(A,B,B))) # label(idempotence_k1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2776 (all A all B all C (-v1_xboole_0(C) & v4_finsub_1(C) -> (m1_subset_1(B,C) & m1_subset_1(A,C) -> m1_subset_1(k3_xboole_0(A,B),C)))) # label(t13_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2777 (all A all B k3_xboole_0(k5_finsub_1(A),k5_finsub_1(B)) = k5_finsub_1(k3_xboole_0(A,B))) # label(t24_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2778 (all A ((all B all C (r2_hidden(B,A) & r2_hidden(C,A) -> r2_hidden(k2_xboole_0(B,C),A))) <-> v1_finsub_1(A))) # label(d1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2779 $T # label(t33_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2780 $T # label(t19_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2781 (all A v4_finsub_1(k1_zfmisc_1(A))) # label(t20_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2782 $T # label(t8_finsub_1) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2783 (all A k1_xboole_0 = k3_binop_1(k5_finsub_1(A),k9_setwiseo(A))) # label(t55_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2784 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (m1_subset_1(D,k5_finsub_1(B)) -> (all E (v1_funct_2(E,B,A) & v1_funct_1(E) & m2_relset_1(E,B,A) -> (v3_binop_1(C,A) & v2_binop_1(C,A) & v1_binop_1(C,A) -> D = k1_xboole_0 | (all F (m1_subset_1(F,A) -> ((all G (m1_subset_1(G,B) -> (r2_hidden(G,D) -> F = k8_funct_2(B,A,E,G)))) -> F = k7_setwiseo(B,A,C,D,E))))))))))))))) # label(t33_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2785 (all A all B all C -(r1_tarski(A,k2_xboole_0(B,k1_tarski(C))) & -r2_hidden(C,A) & -r1_tarski(A,B))) # label(t5_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2786 (all A r3_binop_1(k5_finsub_1(A),k1_setwiseo(A),k9_setwiseo(A))) # label(t52_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2787 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(A)) -> -(k1_xboole_0 != B & (all C (m1_subset_1(C,A) -> -r2_hidden(C,B)))))))) # label(t18_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.62 2788 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (m1_subset_1(D,k5_finsub_1(B)) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,A) & m2_relset_1(E,B,A) -> (v1_binop_1(C,A) & v3_binop_1(C,A) & v2_binop_1(C,A) -> (all F (m1_subset_1(F,B) -> (r2_hidden(F,D) -> k2_binop_1(A,A,A,C,k8_funct_2(B,A,E,F),k7_setwiseo(B,A,C,D,E)) = k7_setwiseo(B,A,C,D,E))))))))))))))) # label(t31_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.63 2789 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> k4_xboole_0(k9_relat_1(C,B),A) = k9_relat_1(C,k4_xboole_0(B,k10_relat_1(C,A))))) # label(t11_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.63 2790 (all A all B all C (m1_subset_1(B,k5_finsub_1(A)) & m1_subset_1(C,k5_finsub_1(A)) -> m1_subset_1(k6_setwiseo(A,B,C),k5_finsub_1(A)))) # label(dt_k6_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.63 2791 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,B,A) & v1_funct_2(C,B,A) -> (all D (m1_subset_1(D,B) -> k2_funct_2(B,A,C,k1_tarski(D)) = k1_tarski(k8_funct_2(B,A,C,D)))))))))) # label(t13_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.63 2792 $T # label(t66_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.63 2793 $T # label(t20_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.63 2794 (all A all B (m1_subset_1(B,A) & -v1_xboole_0(A) -> m1_subset_1(k2_setwiseo(A,B),k5_finsub_1(A)))) # label(dt_k2_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.63 2795 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k5_finsub_1(A)) -> (all D all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> ((all F (m1_subset_1(F,A) -> (r2_hidden(F,C) -> r2_hidden(k8_funct_2(A,B,E,F),D)))) -> r1_tarski(k2_funct_2(A,B,E,C),D)))))))))) # label(t15_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.63 2796 $T # label(t48_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.63 2797 (all A all B all C (m1_subset_1(C,k5_finsub_1(A)) & m1_subset_1(B,k5_finsub_1(A)) -> m1_subset_1(k5_setwiseo(A,B,C),k5_finsub_1(A)))) # label(dt_k5_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.63 2798 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (m1_subset_1(D,k5_finsub_1(A)) -> (all E (m2_relset_1(E,A,B) & v1_funct_1(E) & v1_funct_2(E,A,B) -> (v3_binop_1(C,B) & v1_binop_1(C,B) & v2_binop_1(C,B) -> (all F (m1_subset_1(F,B) -> (k2_funct_2(A,B,E,D) = k2_setwiseo(B,F) -> F = k7_setwiseo(A,B,C,D,E))))))))))))))) # label(t34_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.63 2799 (all A all B all C all D (m1_relset_1(C,A,B) & v1_funct_1(C) & -v1_xboole_0(B) & m1_subset_1(D,k5_finsub_1(A)) & v1_funct_2(C,A,B) & -v1_xboole_0(A) -> m1_subset_1(k8_setwiseo(A,B,C,D),k5_finsub_1(B)))) # label(dt_k8_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.63 2800 (all A (-v1_xboole_0(A) -> (all B all C (m2_relset_1(C,A,k5_finsub_1(B)) & v1_funct_2(C,A,k5_finsub_1(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,A) -> k8_funct_2(A,k5_finsub_1(B),C,D) = k10_setwiseo(A,B,k2_setwiseo(A,D),C))))))) # label(t56_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.63 2801 (all A v3_binop_1(k9_setwiseo(A),k5_finsub_1(A))) # label(t49_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.63 2802 (all A all B all C (m1_subset_1(C,k5_finsub_1(A)) & m1_subset_1(B,k5_finsub_1(A)) -> k4_xboole_0(B,C) = k6_setwiseo(A,B,C))) # label(redefinition_k6_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.63 2803 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k2_tarski(B,C) = k3_setwiseo(A,B,C))) # label(redefinition_k3_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.63 2804 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (all D (m1_subset_1(D,k5_finsub_1(B)) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,A) & m2_relset_1(E,B,A) -> (v1_binop_1(C,A) & v2_binop_1(C,A) & v3_binop_1(C,A) -> k1_xboole_0 = D | (all F (m1_subset_1(F,B) -> k7_setwiseo(B,A,C,k5_setwiseo(B,D,k2_setwiseo(B,F)),E) = k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,D,E),k8_funct_2(B,A,E,F))))))))))))))) # label(t29_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.63 2805 (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 (m1_subset_1(D,k5_finsub_1(B)) -> (all E (m2_relset_1(E,B,A) & v1_funct_2(E,B,A) & v1_funct_1(E) -> (v3_binop_1(C,A) & v1_binop_1(C,A) & v1_setwiseo(C,A) & v2_binop_1(C,A) -> (all F (m1_subset_1(F,B) -> k7_setwiseo(B,A,C,k5_setwiseo(B,D,k2_setwiseo(B,F)),E) = k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,D,E),k8_funct_2(B,A,E,F))))))))))))))) # label(t41_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.63 2806 (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) -> (r2_hidden(B,k8_funct_2(A,k5_finsub_1(A),k11_setwiseo(A),D)) & r2_hidden(C,k8_funct_2(A,k5_finsub_1(A),k11_setwiseo(A),D)) -> B = C))))))))) # label(t69_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.63 2807 (all A all B all C all D (m1_subset_1(C,k5_finsub_1(A)) & m1_relset_1(D,A,k5_finsub_1(B)) & -v1_xboole_0(A) & v1_funct_1(D) & v1_funct_2(D,A,k5_finsub_1(B)) -> m1_subset_1(k10_setwiseo(A,B,C,D),k5_finsub_1(B)))) # label(dt_k10_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.63 2808 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all 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) -> (v1_setwiseo(D,B) & v3_binop_1(D,B) & v2_binop_1(D,B) & v1_binop_1(D,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,k5_finsub_1(C)) & m2_relset_1(E,A,k5_finsub_1(C)) -> (all F (v1_funct_2(F,k5_finsub_1(C),B) & m2_relset_1(F,k5_finsub_1(C),B) & v1_funct_1(F) -> ((all G (m1_subset_1(G,k5_finsub_1(C)) -> (all H (m1_subset_1(H,k5_finsub_1(C)) -> k8_funct_2(k5_finsub_1(C),B,F,k5_setwiseo(C,G,H)) = k2_binop_1(B,B,B,D,k8_funct_2(k5_finsub_1(C),B,F,G),k8_funct_2(k5_finsub_1(C),B,F,H)))))) & k8_funct_2(k5_finsub_1(C),B,F,k1_setwiseo(C)) = k3_binop_1(B,D) -> (all G (m1_subset_1(G,k5_finsub_1(A)) -> k8_funct_2(k5_finsub_1(C),B,F,k10_setwiseo(A,C,G,E)) = k7_setwiseo(A,B,D,G,k7_funct_2(A,k5_finsub_1(C),B,E,F)))))))))))))))) # label(t65_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.63 2809 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C all D (m1_subset_1(D,k5_finsub_1(A)) -> (all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (all F (v1_funct_2(F,B,k5_finsub_1(C)) & m2_relset_1(F,B,k5_finsub_1(C)) & v1_funct_1(F) -> k10_setwiseo(B,C,k8_setwiseo(A,B,E,D),F) = k10_setwiseo(A,C,D,k7_funct_2(A,B,k5_finsub_1(C),E,F)))))))))))) # label(t63_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.63 2810 (all A (-v1_xboole_0(A) -> (all B all C (m2_relset_1(C,A,k5_finsub_1(B)) & v1_funct_2(C,A,k5_finsub_1(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,k5_finsub_1(A)) -> k3_tarski(k8_setwiseo(A,k5_finsub_1(B),C,D)) = k10_setwiseo(A,B,D,C))))))) # label(t61_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.63 2811 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(A)) -> k10_setwiseo(A,A,B,k11_setwiseo(A)) = B)))) # label(t71_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.63 2812 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (v2_binop_1(C,B) & v1_setwiseo(C,B) & v3_binop_1(C,B) & v1_binop_1(C,B) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_2(E,k2_zfmisc_1(D,D),D) & v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(D,D),D) -> (v1_setwiseo(E,D) & v2_binop_1(E,D) & v1_binop_1(E,D) & v3_binop_1(E,D) -> (all F (v1_funct_1(F) & m2_relset_1(F,A,B) & v1_funct_2(F,A,B) -> (all G (v1_funct_1(G) & m2_relset_1(G,B,D) & v1_funct_2(G,B,D) -> ((all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,B) -> k2_binop_1(D,D,D,E,k8_funct_2(B,D,G,H),k8_funct_2(B,D,G,I)) = k8_funct_2(B,D,G,k2_binop_1(B,B,B,C,H,I)))))) & k8_funct_2(B,D,G,k3_binop_1(B,C)) = k3_binop_1(D,E) -> (all H (m1_subset_1(H,k5_finsub_1(A)) -> k7_setwiseo(A,D,E,H,k7_funct_2(A,B,D,F,G)) = k8_funct_2(B,D,G,k7_setwiseo(A,B,C,H,F))))))))))))))))))))) # label(t45_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.63 2813 (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) -> (v3_binop_1(C,A) & v1_binop_1(C,A) & v1_setwiseo(C,A) & v2_binop_1(C,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (all F (m1_subset_1(F,k5_finsub_1(B)) -> k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,E,D),k7_setwiseo(B,A,C,F,D)) = k7_setwiseo(B,A,C,k5_setwiseo(B,E,F),D)))))))))))))) # label(t42_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.63 2814 (all A (-v1_xboole_0(A) -> (all B all C (v1_funct_1(C) & v1_funct_2(C,A,k5_finsub_1(B)) & m2_relset_1(C,A,k5_finsub_1(B)) -> (all D (m1_subset_1(D,k5_finsub_1(A)) -> (all E (r2_hidden(E,k10_setwiseo(A,B,D,C)) <-> (exists F (r2_hidden(E,k8_funct_2(A,k5_finsub_1(B),C,F)) & m1_subset_1(F,A) & r2_hidden(F,D))))))))))) # label(t70_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.63 2815 (all A exists B (v1_xboole_0(B) & v1_finset_1(B) & m1_subset_1(B,k5_finsub_1(A)))) # label(rc1_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.63 2816 (all A v1_setwiseo(k9_setwiseo(A),k5_finsub_1(A))) # label(t53_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.63 2817 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C all D (v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & m2_relset_1(D,k2_zfmisc_1(A,A),A) -> (v3_binop_1(D,A) & v2_binop_1(D,A) & v1_binop_1(D,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (k1_xboole_0 != E -> (all F (v1_funct_2(F,B,k5_finsub_1(C)) & m2_relset_1(F,B,k5_finsub_1(C)) & v1_funct_1(F) -> (all G (v1_funct_1(G) & m2_relset_1(G,k5_finsub_1(C),A) & v1_funct_2(G,k5_finsub_1(C),A) -> ((all H (m1_subset_1(H,k5_finsub_1(C)) -> (all I (m1_subset_1(I,k5_finsub_1(C)) -> k8_funct_2(k5_finsub_1(C),A,G,k5_setwiseo(C,H,I)) = k2_binop_1(A,A,A,D,k8_funct_2(k5_finsub_1(C),A,G,H),k8_funct_2(k5_finsub_1(C),A,G,I)))))) -> k7_setwiseo(B,A,D,E,k7_funct_2(B,k5_finsub_1(C),A,F,G)) = k8_funct_2(k5_finsub_1(C),A,G,k10_setwiseo(B,C,E,F))))))))))))))))) # label(t64_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.63 2818 (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) -> (v2_binop_1(C,A) & v1_binop_1(C,A) & v1_setwiseo(C,A) -> (all D (v1_funct_1(D) & v1_funct_2(D,B,A) & m2_relset_1(D,B,A) -> k7_setwiseo(B,A,C,k1_setwiseo(B),D) = k3_binop_1(A,C)))))))))) # label(t40_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.63 2819 (all A (-v1_xboole_0(A) -> (exists B (v1_finset_1(B) & -v1_xboole_0(B) & m1_subset_1(B,k5_finsub_1(A)))))) # label(rc2_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.63 2820 (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_setwiseo(B,A) -> (all C (m1_subset_1(C,A) -> C = k2_binop_1(A,A,A,B,k3_binop_1(A,B),C) & k2_binop_1(A,A,A,B,C,k3_binop_1(A,B)) = C))))))) # label(t23_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.63 2821 (all A all B (v1_funct_2(B,A,k5_finsub_1(A)) & m2_relset_1(B,A,k5_finsub_1(A)) & v1_funct_1(B) -> (k11_setwiseo(A) = B <-> (all C (r2_hidden(C,A) -> k1_funct_1(B,C) = k1_tarski(C)))))) # label(d6_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.63 2822 (all A v2_binop_1(k9_setwiseo(A),k5_finsub_1(A))) # label(t51_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.58/55.63 2823 (all A (m1_subset_1(A,f1_s3_setwiseo) -> p1_s3_setwiseo(k2_setwiseo(f1_s3_setwiseo,A)))) & (all A (m1_subset_1(A,k5_finsub_1(f1_s3_setwiseo)) -> (all B (m1_subset_1(B,k5_finsub_1(f1_s3_setwiseo)) -> (p1_s3_setwiseo(A) & p1_s3_setwiseo(B) -> A = k1_xboole_0 | p1_s3_setwiseo(k5_setwiseo(f1_s3_setwiseo,A,B)) | B = k1_xboole_0))))) -> (all A (m1_subset_1(A,k5_finsub_1(f1_s3_setwiseo)) -> (k1_xboole_0 != A -> p1_s3_setwiseo(A)))) # label(s3_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.65 2824 (all A all B all C (r2_hidden(A,B) | A = C <-> r2_hidden(A,k2_xboole_0(B,k1_tarski(C))))) # label(t6_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.65 2825 $T # label(t47_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.65 2826 (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,A),A) & m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) -> (v1_setwiseo(D,A) & v2_binop_1(D,A) & v1_binop_1(D,A) & v3_binop_1(D,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (all F (m2_relset_1(F,B,C) & v1_funct_2(F,B,C) & v1_funct_1(F) -> (all G (v1_funct_1(G) & m2_relset_1(G,C,A) & v1_funct_2(G,C,A) -> k7_setwiseo(B,A,D,E,k7_funct_2(B,C,A,F,G)) = k7_setwiseo(C,A,D,k8_setwiseo(B,C,F,E),G)))))))))))))))) # label(t44_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.65 2827 (all A (-v1_xboole_0(A) -> (all B all C (m2_relset_1(C,A,k5_finsub_1(B)) & v1_funct_1(C) & v1_funct_2(C,A,k5_finsub_1(B)) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> k5_setwiseo(B,k8_funct_2(A,k5_finsub_1(B),C,D),k8_funct_2(A,k5_finsub_1(B),C,E)) = k10_setwiseo(A,B,k3_setwiseo(A,D,E),C))))))))) # label(t57_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.65 2828 $T # label(t46_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.65 2829 (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 (m1_subset_1(D,k5_finsub_1(A)) -> (all E (v1_funct_2(E,A,B) & v1_funct_1(E) & m2_relset_1(E,A,B) -> (v1_binop_1(C,B) & v2_binop_1(C,B) -> D = k1_xboole_0 & -v1_setwiseo(C,B) | (all F (m1_subset_1(F,B) -> ((exists G (m2_relset_1(G,k5_finsub_1(A),B) & v1_funct_1(G) & v1_funct_2(G,k5_finsub_1(A),B) & k8_funct_2(k5_finsub_1(A),B,G,D) = F & (all H (m1_subset_1(H,B) -> (r3_binop_1(B,H,C) -> k1_funct_1(G,k1_xboole_0) = H))) & (all H (m1_subset_1(H,k5_finsub_1(A)) -> (r1_tarski(H,D) -> (all I (m1_subset_1(I,A) -> (r2_hidden(I,k6_setwiseo(A,D,H)) -> k2_binop_1(B,B,B,C,k8_funct_2(k5_finsub_1(A),B,G,H),k8_funct_2(A,B,E,I)) = k8_funct_2(k5_finsub_1(A),B,G,k5_setwiseo(A,H,k2_setwiseo(A,I)))))) | k1_xboole_0 = H))) & (all H (m1_subset_1(H,A) -> k8_funct_2(k5_finsub_1(A),B,G,k2_setwiseo(A,H)) = k8_funct_2(A,B,E,H))))) <-> F = k7_setwiseo(A,B,C,D,E))))))))))))))) # label(d3_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.65 2830 (all A (-v1_xboole_0(A) -> (all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,k5_finsub_1(B)) & m2_relset_1(D,A,k5_finsub_1(B)) -> (all E (m2_relset_1(E,k5_finsub_1(B),k5_finsub_1(C)) & v1_funct_1(E) & v1_funct_2(E,k5_finsub_1(B),k5_finsub_1(C)) -> ((all F (m1_subset_1(F,k5_finsub_1(B)) -> (all G (m1_subset_1(G,k5_finsub_1(B)) -> k5_setwiseo(C,k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,F),k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,G)) = k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,k5_setwiseo(B,F,G)))))) & k1_setwiseo(C) = k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,k1_setwiseo(B)) -> (all F (m1_subset_1(F,k5_finsub_1(A)) -> k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,k10_setwiseo(A,B,F,D)) = k10_setwiseo(A,C,F,k7_funct_2(A,k5_finsub_1(B),k5_finsub_1(C),D,E))))))))))) # label(t72_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.65 2831 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,B,A) & m2_relset_1(C,B,A) -> (all D (m1_subset_1(D,B) -> r2_hidden(D,k3_funct_2(B,A,C,k1_tarski(k8_funct_2(B,A,C,D)))))))))))) # label(t12_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.65 2832 (all A all B all C (m1_subset_1(C,A) & -v1_xboole_0(A) & m1_subset_1(B,A) -> m1_subset_1(k3_setwiseo(A,B,C),k5_finsub_1(A)))) # label(dt_k3_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.65 2833 (all A all B all C r1_tarski(k1_tarski(A),k1_enumset1(A,B,C))) # label(t3_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.65 2834 (all A all B all C all D all E (m1_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(E,A,B) & m1_relset_1(E,A,B) & -v1_xboole_0(B) & -v1_xboole_0(A) & v1_funct_1(E) & m1_subset_1(D,k5_finsub_1(A)) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> m1_subset_1(k7_setwiseo(A,B,C,D,E),B))) # label(dt_k7_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.65 2835 (all A all B (m1_subset_1(B,k5_finsub_1(A)) -> (all C (r1_tarski(C,B) -> m1_subset_1(C,k5_finsub_1(A)))))) # label(t16_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.65 2836 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (all D (m2_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_1(D) -> (v2_binop_1(C,A) & v3_binop_1(C,A) & v1_binop_1(C,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (all F (m1_subset_1(F,k5_finsub_1(B)) -> -(k1_xboole_0 != F & k1_xboole_0 != E & k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,E,D),k7_setwiseo(B,A,C,F,D)) != k7_setwiseo(B,A,C,k5_setwiseo(B,E,F),D))))))))))))))) # label(t30_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.65 2837 $T # label(t1_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.65 2838 (all A (-v1_xboole_0(A) -> (all B all C (m1_subset_1(C,A) -> (C = B <-> r2_hidden(B,k8_funct_2(A,k5_finsub_1(A),k11_setwiseo(A),C))))))) # label(t68_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.65 2839 (all A (-v1_xboole_0(A) -> (all B all C (m2_relset_1(C,A,k5_finsub_1(B)) & v1_funct_1(C) & v1_funct_2(C,A,k5_finsub_1(B)) -> k10_setwiseo(A,B,k1_setwiseo(A),C) = k1_xboole_0)))) # label(t59_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.65 2840 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (v3_binop_1(C,A) & v1_binop_1(C,A) & v2_binop_1(C,A) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> k7_setwiseo(B,A,C,k3_setwiseo(B,E,F),D) = k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,E),k8_funct_2(B,A,D,F))))))))))))))) # label(t27_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.65 2841 (all A v1_binop_1(k9_setwiseo(A),k5_finsub_1(A))) # label(t50_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.65 2842 (all A all B (m2_relset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k5_finsub_1(A)) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k5_finsub_1(A)) -> (B = k9_setwiseo(A) <-> (all C (m1_subset_1(C,k5_finsub_1(A)) -> (all D (m1_subset_1(D,k5_finsub_1(A)) -> k2_binop_1(k5_finsub_1(A),k5_finsub_1(A),k5_finsub_1(A),B,C,D) = k5_setwiseo(A,C,D)))))))) # label(d4_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.65 2843 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,B,A) & m2_relset_1(C,B,A) -> (all D (m1_subset_1(D,k5_finsub_1(B)) -> (k1_xboole_0 = k2_funct_2(B,A,C,D) -> D = k1_xboole_0))))))))) # label(t19_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.65 2844 (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) -> (v1_setwiseo(B,A) <-> (exists C (r3_binop_1(A,C,B) & m1_subset_1(C,A)))))))) # label(d2_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.65 2845 (all A (v1_funct_1(k11_setwiseo(A)) & v1_funct_2(k11_setwiseo(A),A,k5_finsub_1(A)) & m2_relset_1(k11_setwiseo(A),A,k5_finsub_1(A)))) # label(dt_k11_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.65 2846 (all A (v1_funct_1(k9_setwiseo(A)) & v1_funct_2(k9_setwiseo(A),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k5_finsub_1(A)) & m2_relset_1(k9_setwiseo(A),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k5_finsub_1(A)))) # label(dt_k9_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.65 2847 (all A all B all C (m1_subset_1(B,k5_finsub_1(A)) & m1_subset_1(C,k5_finsub_1(A)) -> k5_setwiseo(A,C,B) = k5_setwiseo(A,B,C))) # label(commutativity_k5_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.65 2848 $T # label(t10_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.65 2849 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) -> (r6_binop_1(A,D,C) & v1_binop_1(C,A) & v3_binop_1(C,A) & v2_binop_1(C,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (E != k1_xboole_0 -> (all F (v1_funct_1(F) & v1_funct_2(F,B,A) & m2_relset_1(F,B,A) -> (all G (m1_subset_1(G,A) -> k7_setwiseo(B,A,C,E,k7_funcop_1(A,B,D,F,G)) = k2_binop_1(A,A,A,D,k7_setwiseo(B,A,C,E,F),G))))))))))))))))) # label(t37_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2850 $T # label(t17_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2851 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (v1_binop_1(C,B) & v2_binop_1(C,B) & v1_setwiseo(C,B) & v3_binop_1(C,B) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> (all F (m1_subset_1(F,k5_finsub_1(A)) -> (all G (m1_subset_1(G,k5_finsub_1(A)) -> (k8_setwiseo(A,B,D,F) = k8_setwiseo(A,B,E,G) -> k7_setwiseo(A,B,C,F,D) = k7_setwiseo(A,B,C,G,E))))))))))))))))) # label(t43_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2852 (all A all B all C (m1_subset_1(C,k5_finsub_1(A)) & m1_subset_1(B,k5_finsub_1(A)) -> k5_setwiseo(A,B,B) = B)) # label(idempotence_k5_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2853 (all A all B all C (m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k3_setwiseo(A,B,C) = k3_setwiseo(A,C,B))) # label(commutativity_k3_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2854 (all A (-v1_xboole_0(A) -> (all B all C (m1_subset_1(C,k5_finsub_1(A)) -> (all D (m2_relset_1(D,A,k5_finsub_1(B)) & v1_funct_1(D) & v1_funct_2(D,A,k5_finsub_1(B)) -> k7_setwiseo(A,k5_finsub_1(B),k9_setwiseo(B),C,D) = k10_setwiseo(A,B,C,D))))))) # label(d5_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2855 (all A r3_binop_1(k5_finsub_1(A),k3_binop_1(k5_finsub_1(A),k9_setwiseo(A)),k9_setwiseo(A))) # label(t54_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2856 (all A all B all C r1_tarski(k2_tarski(A,B),k1_enumset1(A,B,C))) # label(t4_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2857 (all A all B (m1_subset_1(B,A) & -v1_xboole_0(A) -> k1_tarski(B) = k2_setwiseo(A,B))) # label(redefinition_k2_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2858 (all A (m1_subset_1(A,k5_finsub_1(f1_s4_setwiseo)) -> (all B (m1_subset_1(B,f1_s4_setwiseo) -> (p1_s4_setwiseo(A) -> p1_s4_setwiseo(k5_setwiseo(f1_s4_setwiseo,A,k2_setwiseo(f1_s4_setwiseo,B)))))))) & p1_s4_setwiseo(k1_setwiseo(f1_s4_setwiseo)) -> (all A (m1_subset_1(A,k5_finsub_1(f1_s4_setwiseo)) -> p1_s4_setwiseo(A))) # label(s4_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2859 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (m1_subset_1(D,k5_finsub_1(A)) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (v3_binop_1(C,B) & v2_binop_1(C,B) & v1_binop_1(C,B) -> -v1_setwiseo(C,B) & k1_xboole_0 = D | (all F (m1_subset_1(F,B) -> ((exists G (v1_funct_2(G,k5_finsub_1(A),B) & k8_funct_2(k5_finsub_1(A),B,G,D) = F & (all H (m1_subset_1(H,k5_finsub_1(A)) -> (r1_tarski(H,D) -> H = k1_xboole_0 | (all I (m1_subset_1(I,A) -> (r2_hidden(I,D) -> k2_binop_1(B,B,B,C,k8_funct_2(k5_finsub_1(A),B,G,H),k8_funct_2(A,B,E,I)) = k8_funct_2(k5_finsub_1(A),B,G,k5_setwiseo(A,H,k2_setwiseo(A,I))))))))) & v1_funct_1(G) & m2_relset_1(G,k5_finsub_1(A),B) & (all H (m1_subset_1(H,A) -> k8_funct_2(A,B,E,H) = k8_funct_2(k5_finsub_1(A),B,G,k2_setwiseo(A,H)))) & (all H (m1_subset_1(H,B) -> (r3_binop_1(B,H,C) -> k1_funct_1(G,k1_xboole_0) = H))))) <-> F = k7_setwiseo(A,B,C,D,E))))))))))))))) # label(t25_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2860 (all A (v1_xboole_0(k1_setwiseo(A)) & m1_subset_1(k1_setwiseo(A),k5_finsub_1(A)))) # label(dt_k1_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2861 (all A all B all C (m1_subset_1(B,k5_finsub_1(A)) & m1_subset_1(C,k5_finsub_1(A)) -> k5_setwiseo(A,B,C) = k2_xboole_0(B,C))) # label(redefinition_k5_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2862 (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) -> (v1_setwiseo(B,A) <-> r3_binop_1(A,k3_binop_1(A,B),B)))))) # label(t22_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2863 (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_1(C) & v1_funct_2(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) -> (v1_binop_1(C,A) & v3_binop_1(C,A) & v2_binop_1(C,A) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,B) -> k7_setwiseo(B,A,C,k4_setwiseo(B,E,F,G),D) = k2_binop_1(A,A,A,C,k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,E),k8_funct_2(B,A,D,F)),k8_funct_2(B,A,D,G))))))))))))))))) # label(t28_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2864 $T # label(t7_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2865 (all A (m1_subset_1(A,k5_finsub_1(f1_s2_setwiseo)) -> (all B (m1_subset_1(B,f1_s2_setwiseo) -> (p1_s2_setwiseo(A) -> r2_hidden(B,A) | p1_s2_setwiseo(k5_setwiseo(f1_s2_setwiseo,A,k2_setwiseo(f1_s2_setwiseo,B)))))))) & p1_s2_setwiseo(k1_setwiseo(f1_s2_setwiseo)) -> (all A (m1_subset_1(A,k5_finsub_1(f1_s2_setwiseo)) -> p1_s2_setwiseo(A))) # label(s2_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2866 (all A all B all C all D (-v1_xboole_0(A) & m1_subset_1(D,A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> k4_setwiseo(A,B,C,D) = k1_enumset1(B,C,D))) # label(redefinition_k4_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2867 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(A)) -> (all C (r2_hidden(C,B) -> m1_subset_1(C,A))))))) # label(t14_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2868 (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) -> (v1_binop_1(C,B) & v3_binop_1(C,B) & v2_binop_1(C,B) -> (all D (-v1_xboole_0(D) -> (all E (m2_relset_1(E,k2_zfmisc_1(D,D),D) & v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(D,D),D) -> (v3_binop_1(E,D) & v2_binop_1(E,D) & v1_binop_1(E,D) -> (all F (v1_funct_1(F) & m2_relset_1(F,A,B) & v1_funct_2(F,A,B) -> (all G (v1_funct_2(G,B,D) & m2_relset_1(G,B,D) & v1_funct_1(G) -> ((all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,B) -> k2_binop_1(D,D,D,E,k8_funct_2(B,D,G,H),k8_funct_2(B,D,G,I)) = k8_funct_2(B,D,G,k2_binop_1(B,B,B,C,H,I)))))) -> (all H (m1_subset_1(H,k5_finsub_1(A)) -> (H != k1_xboole_0 -> k8_funct_2(B,D,G,k7_setwiseo(A,B,C,H,F)) = k7_setwiseo(A,D,E,H,k7_funct_2(A,B,D,F,G)))))))))))))))))))))) # label(t39_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2869 (all A all B all C (r1_tarski(k2_xboole_0(A,k1_tarski(B)),C) <-> r1_tarski(A,C) & r2_hidden(B,C))) # label(t8_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2870 (all A (-v1_xboole_0(A) -> (all B all C (v1_funct_1(C) & m2_relset_1(C,A,k5_finsub_1(B)) & v1_funct_2(C,A,k5_finsub_1(B)) -> (all D (m1_subset_1(D,k5_finsub_1(A)) -> (all E (m1_subset_1(E,k5_finsub_1(A)) -> k10_setwiseo(A,B,k5_setwiseo(A,D,E),C) = k5_setwiseo(B,k10_setwiseo(A,B,D,C),k10_setwiseo(A,B,E,C)))))))))) # label(t62_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2871 (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) -> (v3_binop_1(C,B) & v2_binop_1(C,B) & v1_binop_1(C,B) -> (all D (v1_funct_2(D,A,B) & v1_funct_1(D) & m2_relset_1(D,A,B) -> (all E (m2_relset_1(E,A,B) & v1_funct_1(E) & v1_funct_2(E,A,B) -> (all F (m1_subset_1(F,k5_finsub_1(A)) -> (all G (m1_subset_1(G,k5_finsub_1(A)) -> (k2_funct_2(A,B,E,G) = k2_funct_2(A,B,D,F) -> k7_setwiseo(A,B,C,F,D) = k7_setwiseo(A,B,C,G,E) | k1_xboole_0 = F)))))))))))))))) # label(t35_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2872 (all A all B all C all D (m1_subset_1(D,A) & -v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> m1_subset_1(k4_setwiseo(A,B,C,D),k5_finsub_1(A)))) # label(dt_k4_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2873 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,A,k5_finsub_1(A)) & m2_relset_1(B,A,k5_finsub_1(A)) -> (B = k11_setwiseo(A) <-> (all C (m1_subset_1(C,A) -> k2_setwiseo(A,C) = k8_funct_2(A,k5_finsub_1(A),B,C)))))))) # label(t67_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2874 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & m2_relset_1(D,k2_zfmisc_1(A,A),A) -> (v3_binop_1(C,A) & v2_binop_1(C,A) & r6_binop_1(A,D,C) & v1_binop_1(C,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (k1_xboole_0 != E -> (all F (v1_funct_1(F) & v1_funct_2(F,B,A) & m2_relset_1(F,B,A) -> (all G (m1_subset_1(G,A) -> k2_binop_1(A,A,A,D,G,k7_setwiseo(B,A,C,E,F)) = k7_setwiseo(B,A,C,E,k8_funcop_1(A,B,D,G,F)))))))))))))))))) # label(t36_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2875 (all A all B all C all D (v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,k5_finsub_1(A)) & -v1_xboole_0(A) & -v1_xboole_0(B) & v1_funct_1(C) -> k9_relat_1(C,D) = k8_setwiseo(A,B,C,D))) # label(redefinition_k8_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2876 $T # label(t24_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2877 $T # label(t2_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2878 $T # label(t9_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2879 (all A (-v1_xboole_0(A) -> (all B all C (m2_relset_1(C,A,k5_finsub_1(B)) & v1_funct_1(C) & v1_funct_2(C,A,k5_finsub_1(B)) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,k5_finsub_1(A)) -> k10_setwiseo(A,B,k5_setwiseo(A,E,k2_setwiseo(A,D)),C) = k5_setwiseo(B,k10_setwiseo(A,B,E,C),k8_funct_2(A,k5_finsub_1(B),C,D)))))))))) # label(t60_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2880 (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,A),A) & m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) -> (v1_binop_1(D,A) & v3_binop_1(D,A) & v2_binop_1(D,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (E != k1_xboole_0 -> (all F (v1_funct_1(F) & m2_relset_1(F,B,C) & v1_funct_2(F,B,C) -> (all G (v1_funct_2(G,C,A) & m2_relset_1(G,C,A) & v1_funct_1(G) -> k7_setwiseo(C,A,D,k8_setwiseo(B,C,F,E),G) = k7_setwiseo(B,A,D,E,k7_funct_2(B,C,A,F,G)))))))))))))))))) # label(t38_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2881 (all A (-v1_xboole_0(A) -> (all B all C (m2_relset_1(C,A,k5_finsub_1(B)) & v1_funct_2(C,A,k5_finsub_1(B)) & 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) -> k5_setwiseo(B,k5_setwiseo(B,k8_funct_2(A,k5_finsub_1(B),C,D),k8_funct_2(A,k5_finsub_1(B),C,E)),k8_funct_2(A,k5_finsub_1(B),C,F)) = k10_setwiseo(A,B,k4_setwiseo(A,D,E,F),C))))))))))) # label(t58_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2882 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (m2_relset_1(D,B,A) & v1_funct_1(D) & v1_funct_2(D,B,A) -> (v3_binop_1(C,A) & v2_binop_1(C,A) & v1_binop_1(C,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (all F (m1_subset_1(F,k5_finsub_1(B)) -> (r1_tarski(E,F) -> k7_setwiseo(B,A,C,F,D) = k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,E,D),k7_setwiseo(B,A,C,F,D)) | k1_xboole_0 = E)))))))))))))) # label(t32_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2883 (exists A (m2_relset_1(A,f1_s1_setwiseo,k5_finsub_1(f1_s1_setwiseo)) & v1_funct_2(A,f1_s1_setwiseo,k5_finsub_1(f1_s1_setwiseo)) & v1_funct_1(A) & (all B (m1_subset_1(B,f1_s1_setwiseo) -> (all C (m1_subset_1(C,f1_s1_setwiseo) -> (r2_hidden(C,k8_funct_2(f1_s1_setwiseo,k5_finsub_1(f1_s1_setwiseo),A,B)) <-> p1_s1_setwiseo(C,B) & r2_hidden(C,f2_s1_setwiseo)))))))) # label(s1_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2884 (all A k1_setwiseo(A) = k1_xboole_0) # label(d1_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2885 $T # label(t21_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2886 (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) -> (v2_binop_1(C,A) & v1_binop_1(C,A) -> (all E (m1_subset_1(E,B) -> k8_funct_2(B,A,D,E) = k7_setwiseo(B,A,C,k2_setwiseo(B,E),D)))))))))))) # label(t26_setwiseo) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2887 (all A (r2_hidden(A,a_0_16_fraenkel) <-> (exists B (k8_funct_2(f1_s9_fraenkel,f2_s9_fraenkel,f4_s9_fraenkel,B) = A & r2_hidden(B,f3_s9_fraenkel) & p1_s9_fraenkel(B) & m1_subset_1(B,f1_s9_fraenkel))))) # label(fraenkel_a_0_16_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2888 (all A (m1_subset_1(A,f1_s8_fraenkel) -> (all B (m1_subset_1(B,f2_s8_fraenkel) -> (p1_s8_fraenkel(A,B) <-> p2_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_15_fraenkel = a_0_14_fraenkel # label(s8_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2889 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> m1_fraenkel(k2_setwiseo(k1_zfmisc_1(k2_zfmisc_1(A,B)),C),A,B))) # label(t10_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2890 (all A (r2_hidden(A,a_0_3_fraenkel) <-> (exists B exists C (m1_subset_1(C,f2_s2_fraenkel) & m1_subset_1(B,f1_s2_fraenkel) & p2_s2_fraenkel(B,C) & A = f3_s2_fraenkel(B,C))))) # label(fraenkel_a_0_3_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2891 (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) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B))))) # label(dt_m2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2892 (all A (m1_subset_1(A,f1_s9_fraenkel) -> (r2_hidden(A,f3_s9_fraenkel) -> (p1_s9_fraenkel(A) <-> p2_s9_fraenkel(A))))) & k7_relat_1(f4_s9_fraenkel,f3_s9_fraenkel) = k7_relat_1(f5_s9_fraenkel,f3_s9_fraenkel) -> a_0_16_fraenkel = a_0_17_fraenkel # label(s9_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2893 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(A) = f5_s25_fraenkel(B)))))) & v1_finset_1(f3_s25_fraenkel) -> v1_finset_1(a_0_40_fraenkel) # label(s25_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2894 (exists A (m1_subset_1(A,k5_finsub_1(f1_s24_fraenkel)) & (all B (m1_subset_1(B,f1_s24_fraenkel) -> (r2_hidden(B,A) <-> (exists C (p1_s24_fraenkel(B,C) & B = f4_s24_fraenkel(C) & m1_subset_1(C,f2_s24_fraenkel) & r2_hidden(C,f3_s24_fraenkel)))))))) # label(s24_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2895 (all A ((all B (r2_hidden(B,A) -> v1_funct_1(B) & v1_relat_1(B))) <-> v1_fraenkel(A))) # label(d1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2896 (all A (m1_subset_1(A,f1_s7_fraenkel) -> (all B (m1_subset_1(B,f2_s7_fraenkel) -> f4_s7_fraenkel(A,B) = f3_s7_fraenkel(A,B))))) -> a_0_12_fraenkel = a_0_13_fraenkel # label(s7_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2897 (all A (r2_hidden(A,a_0_0_fraenkel) <-> (exists B (A = f2_s1_fraenkel(B) & m1_subset_1(B,f1_s1_fraenkel) & p1_s1_fraenkel(B))))) # label(fraenkel_a_0_0_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.67 2898 (all A (m1_subset_1(A,f1_s6_fraenkel) -> (p1_s6_fraenkel(A) -> f3_s6_fraenkel(A) = f2_s6_fraenkel(A)))) -> a_0_11_fraenkel = a_0_10_fraenkel # label(s6_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2899 $T # label(t12_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2900 (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]. 56.68/55.68 2901 (all A (r2_hidden(A,a_0_2_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s2_fraenkel) & p1_s2_fraenkel(B,C) & m1_subset_1(C,f2_s2_fraenkel) & f3_s2_fraenkel(B,C) = A)))) # label(fraenkel_a_0_2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2902 (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]. 56.68/55.68 2903 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]. 56.68/55.68 2904 (all A ((exists B (p1_s14_fraenkel(B) & p2_s14_fraenkel(B) & A = f2_s14_fraenkel(B) & m1_subset_1(B,f1_s14_fraenkel))) <-> r2_hidden(A,a_0_26_fraenkel))) # label(fraenkel_a_0_26_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2905 (all A (-v1_xboole_0(A) -> (all B all C all D (r1_tarski(D,A) & r1_tarski(C,B) -> k1_funct_2(C,D) = k1_xboole_0 | (all E (m1_subset_1(E,k1_funct_2(C,D)) -> (exists F (m2_fraenkel(F,B,A,k1_fraenkel(B,A)) & k7_relat_1(F,C) = E)))))))) # label(t14_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2906 (all A (r2_hidden(A,a_0_10_fraenkel) <-> (exists B (p1_s6_fraenkel(B) & A = f2_s6_fraenkel(B) & m1_subset_1(B,f1_s6_fraenkel))))) # label(fraenkel_a_0_10_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2907 (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]. 56.68/55.68 2908 (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]. 56.68/55.68 2909 (all A ((exists B (f2_s14_fraenkel(B) = A & r2_hidden(B,a_0_25_fraenkel) & p1_s14_fraenkel(B) & m1_subset_1(B,f1_s14_fraenkel))) <-> r2_hidden(A,a_0_24_fraenkel))) # label(fraenkel_a_0_24_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2910 (all A (m1_subset_1(A,f1_s16_fraenkel) -> (all B (m1_subset_1(B,f2_s16_fraenkel) -> -((all C (m1_subset_1(C,f1_s16_fraenkel) -> -(f3_s16_fraenkel(C,B) = f3_s16_fraenkel(A,B) & p2_s16_fraenkel(C,B)))) & p1_s16_fraenkel(A,B)))))) -> r1_tarski(a_0_30_fraenkel,a_0_31_fraenkel) # label(s16_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2911 $T # label(t13_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2912 (all A (r2_hidden(A,a_0_29_fraenkel) <-> (exists B exists C (f3_s15_fraenkel(B,C) = A & p1_s15_fraenkel(B,C) & m1_subset_1(B,f1_s15_fraenkel) & p2_s15_fraenkel(B) & m1_subset_1(C,f2_s15_fraenkel))))) # label(fraenkel_a_0_29_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2913 (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]. 56.68/55.68 2914 (all A (-v1_xboole_0(A) -> (all B all C all D (r1_tarski(D,A) & r1_tarski(C,B) -> 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]. 56.68/55.68 2915 (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) -> -(r2_hidden(A,f2_s23_fraenkel) & (all B (m1_subset_1(B,f1_s23_fraenkel) -> -(r2_hidden(B,f2_s23_fraenkel) & (all C (m1_subset_1(C,f1_s23_fraenkel) -> (p1_s23_fraenkel(C,B) & r2_hidden(C,f2_s23_fraenkel) -> p1_s23_fraenkel(B,C)))) & p1_s23_fraenkel(B,A))))))) # label(s23_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2916 (all A ((exists B exists C (p1_s11_fraenkel(B,C) & m1_subset_1(B,f1_s11_fraenkel) & m1_subset_1(C,f2_s11_fraenkel) & 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]. 56.68/55.68 2917 (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]. 56.68/55.68 2918 (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) & f4_s19_fraenkel = B))))) -> a_0_35_fraenkel = a_0_34_fraenkel # label(s19_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2919 (all A (r2_hidden(A,a_0_40_fraenkel) <-> (exists B (m2_fraenkel(B,f1_s25_fraenkel,f2_s25_fraenkel,k1_fraenkel(f1_s25_fraenkel,f2_s25_fraenkel)) & A = f5_s25_fraenkel(B) & r1_tarski(k2_funct_2(f1_s25_fraenkel,f2_s25_fraenkel,B,f3_s25_fraenkel),f4_s25_fraenkel))))) # label(fraenkel_a_0_40_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2920 (all A ((exists B (p2_s1_fraenkel(B) & m1_subset_1(B,f1_s1_fraenkel) & A = f2_s1_fraenkel(B))) <-> r2_hidden(A,a_0_1_fraenkel))) # label(fraenkel_a_0_1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2921 (all A (r2_hidden(A,a_0_25_fraenkel) <-> (exists B (m1_subset_1(B,f1_s14_fraenkel) & B = A & p2_s14_fraenkel(B))))) # label(fraenkel_a_0_25_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2922 (all A (r2_hidden(A,a_0_28_fraenkel) <-> (exists B (m1_subset_1(B,f1_s15_fraenkel) & p2_s15_fraenkel(B) & A = B)))) # label(fraenkel_a_0_28_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2923 (all A (m1_subset_1(A,f1_s5_fraenkel) -> f3_s5_fraenkel(A) = f2_s5_fraenkel(A))) -> a_0_8_fraenkel = a_0_9_fraenkel # label(s5_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2924 $T # label(t7_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2925 (all A (r2_hidden(A,a_0_14_fraenkel) <-> (exists B exists C (f3_s8_fraenkel(B,C) = A & m1_subset_1(C,f2_s8_fraenkel) & p1_s8_fraenkel(B,C) & m1_subset_1(B,f1_s8_fraenkel))))) # label(fraenkel_a_0_14_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2926 (all A (r2_hidden(A,a_0_17_fraenkel) <-> (exists B (p2_s9_fraenkel(B) & r2_hidden(B,f3_s9_fraenkel) & A = k8_funct_2(f1_s9_fraenkel,f2_s9_fraenkel,f5_s9_fraenkel,B) & m1_subset_1(B,f1_s9_fraenkel))))) # label(fraenkel_a_0_17_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2927 (all A all B v1_fraenkel(k1_funct_2(A,B))) # label(fc1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2928 (all A (r2_hidden(A,a_0_18_fraenkel) <-> (exists B (p1_s10_fraenkel(B) & B = A & m1_subset_1(B,f1_s10_fraenkel))))) # label(fraenkel_a_0_18_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2929 (all A ((exists B (A = f3_s20_fraenkel(B,f4_s20_fraenkel) & p1_s20_fraenkel(B,f4_s20_fraenkel) & m1_subset_1(B,f1_s20_fraenkel))) <-> r2_hidden(A,a_0_37_fraenkel))) # label(fraenkel_a_0_37_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2930 $T # label(t4_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2931 (all A (r2_hidden(A,a_0_33_fraenkel) <-> (exists B (-r2_hidden(f3_s18_fraenkel(B),f2_s18_fraenkel) & f3_s18_fraenkel(B) = A & p1_s18_fraenkel(B) & m1_subset_1(B,f1_s18_fraenkel))))) # label(fraenkel_a_0_33_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2932 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_fraenkel(k1_tarski(A)))) # label(t8_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2933 (all A ((exists B exists C (m1_subset_1(B,f1_s8_fraenkel) & A = f3_s8_fraenkel(C,B) & m1_subset_1(C,f2_s8_fraenkel) & p2_s8_fraenkel(B,C))) <-> r2_hidden(A,a_0_15_fraenkel))) # label(fraenkel_a_0_15_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2934 (all A ((exists B (p2_s3_fraenkel(B) & f2_s3_fraenkel(B) = A & m1_subset_1(B,f1_s3_fraenkel))) <-> r2_hidden(A,a_0_5_fraenkel))) # label(fraenkel_a_0_5_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2935 (all A all B all C (-v1_xboole_0(C) & v1_fraenkel(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]. 56.68/55.68 2936 $T # label(t9_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2937 (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]. 56.68/55.68 2938 (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) & A = f3_s4_fraenkel(B,C))))) # label(fraenkel_a_0_7_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2939 $T # label(t1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2940 (all A ((exists B exists C (f5_s22_fraenkel(B,C) = A & m1_subset_1(C,f2_s22_fraenkel) & m1_subset_1(B,f1_s22_fraenkel) & r2_hidden(C,f4_s22_fraenkel) & r2_hidden(B,f3_s22_fraenkel))) <-> r2_hidden(A,a_0_39_fraenkel))) # label(fraenkel_a_0_39_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2941 (all A ((exists B exists C (m1_subset_1(C,f2_s4_fraenkel) & f3_s4_fraenkel(B,C) = A & p1_s4_fraenkel(B,C) & m1_subset_1(B,f1_s4_fraenkel))) <-> r2_hidden(A,a_0_6_fraenkel))) # label(fraenkel_a_0_6_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2942 (all A ((exists B (m1_subset_1(B,f1_s5_fraenkel) & p1_s5_fraenkel(B) & f3_s5_fraenkel(B) = A)) <-> r2_hidden(A,a_0_9_fraenkel))) # label(fraenkel_a_0_9_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2943 (all A ((exists B exists C (m1_subset_1(C,f2_s16_fraenkel) & p2_s16_fraenkel(B,C) & f3_s16_fraenkel(B,C) = A & 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]. 56.68/55.68 2944 (all A ((exists B exists C (m1_subset_1(B,f1_s13_fraenkel) & p1_s13_fraenkel(B,C) & p2_s13_fraenkel(f4_s13_fraenkel(B,C)) & m1_subset_1(C,f2_s13_fraenkel) & f4_s13_fraenkel(B,C) = A)) <-> r2_hidden(A,a_0_23_fraenkel))) # label(fraenkel_a_0_23_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2945 (all A ((exists B (p1_s5_fraenkel(B) & A = f2_s5_fraenkel(B) & m1_subset_1(B,f1_s5_fraenkel))) <-> r2_hidden(A,a_0_8_fraenkel))) # label(fraenkel_a_0_8_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2946 (all A ((exists B exists C (p1_s16_fraenkel(B,C) & f3_s16_fraenkel(B,C) = A & m1_subset_1(C,f2_s16_fraenkel) & 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]. 56.68/55.68 2947 (all A ((exists B exists C (p1_s15_fraenkel(B,C) & m1_subset_1(C,f2_s15_fraenkel) & r2_hidden(B,a_0_28_fraenkel) & f3_s15_fraenkel(B,C) = A & m1_subset_1(B,f1_s15_fraenkel))) <-> r2_hidden(A,a_0_27_fraenkel))) # label(fraenkel_a_0_27_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2948 (exists A (v1_fraenkel(A) & -v1_xboole_0(A))) # label(rc1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2949 (all A all B all C (-v1_xboole_0(B) & m1_fraenkel(C,A,B) -> (all D (m1_subset_1(D,C) <-> m2_fraenkel(D,A,B,C))))) # label(redefinition_m2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2950 (all A (r2_hidden(A,a_0_22_fraenkel) <-> (exists B exists C (m1_subset_1(C,f2_s13_fraenkel) & p1_s13_fraenkel(B,C) & A = f4_s13_fraenkel(B,C) & m1_subset_1(B,f1_s13_fraenkel))))) # label(fraenkel_a_0_22_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2951 (all A (r2_hidden(A,a_0_4_fraenkel) <-> (exists B (f2_s3_fraenkel(B) = A & m1_subset_1(B,f1_s3_fraenkel) & p1_s3_fraenkel(B))))) # label(fraenkel_a_0_4_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2952 (all A ((exists B exists C (m1_subset_1(B,f1_s20_fraenkel) & C = f4_s20_fraenkel & m1_subset_1(C,f2_s20_fraenkel) & f3_s20_fraenkel(B,C) = A & p1_s20_fraenkel(B,C))) <-> r2_hidden(A,a_0_36_fraenkel))) # label(fraenkel_a_0_36_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2953 (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]. 56.68/55.68 2954 (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]. 56.68/55.68 2955 (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]. 56.68/55.68 2956 (all A (v1_fraenkel(A) -> (all B (r1_tarski(B,A) -> v1_fraenkel(B))))) # label(t17_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2957 (all A ((exists B exists C (m1_subset_1(B,f1_s12_fraenkel) & m1_subset_1(C,f2_s12_fraenkel) & p1_s12_fraenkel(B,C) & A = f3_s12_fraenkel(B,C))) <-> r2_hidden(A,a_0_20_fraenkel))) # label(fraenkel_a_0_20_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2958 (all A (r2_hidden(A,a_0_35_fraenkel) <-> (exists B (m1_subset_1(B,f1_s19_fraenkel) & p1_s19_fraenkel(B,f4_s19_fraenkel) & A = f3_s19_fraenkel(B,f4_s19_fraenkel))))) # label(fraenkel_a_0_35_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2959 (all A (m1_subset_1(A,f1_s3_fraenkel) -> (p1_s3_fraenkel(A) <-> p2_s3_fraenkel(A)))) -> a_0_4_fraenkel = a_0_5_fraenkel # label(s3_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2960 (all A all B exists C m1_fraenkel(C,A,B)) # label(existence_m1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2961 (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]. 56.68/55.68 2962 (all A all B all C (-v1_xboole_0(B) & m1_fraenkel(C,A,B) -> (exists D m2_fraenkel(D,A,B,C)))) # label(existence_m2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2963 (all A (-v1_xboole_0(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 (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (k7_relat_1(D,E) = k7_relat_1(C,E) -> (all F (m1_subset_1(F,A) -> (r2_hidden(F,E) -> k8_funct_2(A,B,C,F) = k8_funct_2(A,B,D,F)))))))))))))) # label(t3_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2964 v1_finset_1(f2_s21_fraenkel) -> v1_finset_1(a_0_38_fraenkel) # label(s21_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2965 (all A ((exists B exists C (m1_subset_1(C,f2_s7_fraenkel) & p1_s7_fraenkel(B,C) & m1_subset_1(B,f1_s7_fraenkel) & f3_s7_fraenkel(B,C) = A)) <-> r2_hidden(A,a_0_12_fraenkel))) # label(fraenkel_a_0_12_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2966 $T # label(t2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2967 (all A ((exists B exists C (A = f4_s7_fraenkel(B,C) & m1_subset_1(B,f1_s7_fraenkel) & m1_subset_1(C,f2_s7_fraenkel) & p1_s7_fraenkel(B,C))) <-> r2_hidden(A,a_0_13_fraenkel))) # label(fraenkel_a_0_13_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2968 (all A all B (v1_finset_1(A) & v1_finset_1(B) -> v1_finset_1(k1_funct_2(A,B)))) # label(t16_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2969 (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]. 56.68/55.68 2970 (all A ((exists B (p1_s17_fraenkel(B) & m1_subset_1(B,f1_s17_fraenkel) & A = f3_s17_fraenkel(B) & r2_hidden(f3_s17_fraenkel(B),f2_s17_fraenkel))) <-> r2_hidden(A,a_0_32_fraenkel))) # label(fraenkel_a_0_32_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2971 (all A (r2_hidden(A,a_0_34_fraenkel) <-> (exists B exists C (p2_s19_fraenkel(B,C) & m1_subset_1(B,f1_s19_fraenkel) & m1_subset_1(C,f2_s19_fraenkel) & A = f3_s19_fraenkel(B,C))))) # label(fraenkel_a_0_34_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2972 (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 (v1_funct_2(A,f1_s26_fraenkel,f2_s26_fraenkel) & (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_1(A))) # label(s26_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2973 (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]. 56.68/55.68 2974 (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]. 56.68/55.68 2975 (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]. 56.68/55.68 2976 (all A (r2_hidden(A,a_0_21_fraenkel) <-> (exists B (m1_subset_1(B,f3_s13_fraenkel) & p2_s13_fraenkel(B) & r2_hidden(B,a_0_22_fraenkel) & A = B)))) # label(fraenkel_a_0_21_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2977 (all A ((exists B (A = f3_s6_fraenkel(B) & m1_subset_1(B,f1_s6_fraenkel) & p1_s6_fraenkel(B))) <-> r2_hidden(A,a_0_11_fraenkel))) # label(fraenkel_a_0_11_fraenkel) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2978 $T # label(dt_k3_numbers) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2979 (all A (r2_hidden(A,a_0_0_numbers) <-> (exists B (B = A & m1_subset_1(B,k1_funct_2(k2_tarski(np__0,k13_arytm_3),k1_numbers)) & k1_funct_1(B,k13_arytm_3) = np__0)))) # label(fraenkel_a_0_0_numbers) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2980 $T # label(dt_k1_numbers) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2981 $T # label(dt_k4_numbers) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2982 $T # label(dt_k2_numbers) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2983 (exists A (-v1_xboole_0(A) & v3_xreal_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A) & -v2_xreal_0(A))) # label(rc3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2984 (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]. 56.68/55.68 2985 (all A all B (v1_xreal_0(B) & -v2_xreal_0(B) & -v3_xreal_0(A) & v1_xreal_0(A) -> v1_xreal_0(k7_xcmplx_0(B,A)) & -v2_xreal_0(k7_xcmplx_0(B,A)) & v1_xcmplx_0(k7_xcmplx_0(B,A)))) # label(fc28_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2986 (all A all B (-v2_xreal_0(B) & v3_xreal_0(A) & v1_xreal_0(B) & v1_xreal_0(A) -> v3_xreal_0(k2_xcmplx_0(A,B)) & -v1_xboole_0(k2_xcmplx_0(A,B)) & -v2_xreal_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)))) # label(fc11_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2987 (all A (-v1_xboole_0(A) & v1_xreal_0(A) & -v3_xreal_0(A) -> v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A))) # label(cc4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2988 (all A (-v3_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(k4_xcmplx_0(A)) & -v2_xreal_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)))) # label(fc14_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2989 (all A all B (-v2_xreal_0(A) & v1_xreal_0(B) & v1_xreal_0(A) & -v2_xreal_0(B) -> v1_xcmplx_0(k2_xcmplx_0(A,B)) & -v2_xreal_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)))) # label(fc8_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2990 (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]. 56.68/55.68 2991 (all A all B (v1_xreal_0(A) & -v3_xreal_0(A) & -v3_xreal_0(B) & v1_xreal_0(B) -> v1_xcmplx_0(k7_xcmplx_0(A,B)) & -v3_xreal_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)))) # label(fc29_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2992 (all A (r2_hidden(A,k1_numbers) <-> v1_xreal_0(A))) # label(d1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2993 (exists A (v1_xcmplx_0(A) & -v2_xreal_0(A) & v1_xboole_0(A) & -v3_xreal_0(A) & v1_xreal_0(A))) # label(rc4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2994 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)))) # label(fc6_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2995 (all A all B (-v2_xreal_0(A) & v1_xreal_0(A) & v1_xreal_0(B) & -v3_xreal_0(B) -> v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & -v2_xreal_0(k3_xcmplx_0(A,B)))) # label(fc21_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2996 (all A all B (-v3_xreal_0(A) & v1_xreal_0(A) & v1_xreal_0(B) & -v3_xreal_0(B) -> v1_xreal_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)) & -v3_xreal_0(k3_xcmplx_0(A,B)))) # label(fc24_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2997 (all A all B (-v2_xreal_0(B) & -v2_xreal_0(A) & v1_xreal_0(B) & v1_xreal_0(A) -> v1_xreal_0(k3_xcmplx_0(A,B)) & -v3_xreal_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc23_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2998 (all A all B (v1_xreal_0(B) & -v2_xreal_0(B) & v2_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(k6_xcmplx_0(B,A)) & v3_xreal_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & -v2_xreal_0(k6_xcmplx_0(B,A)) & -v1_xboole_0(k6_xcmplx_0(B,A)))) # label(fc18_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 2999 (all A (v1_xreal_0(A) -> v1_xcmplx_0(A))) # label(cc2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 3000 (all A (v1_xreal_0(A) -> v1_xreal_0(k5_xcmplx_0(A)) & v1_xcmplx_0(k5_xcmplx_0(A)))) # label(fc2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 3001 (all A (-v1_xboole_0(A) & -v2_xreal_0(A) & v1_xreal_0(A) -> v1_xreal_0(A) & v3_xreal_0(A) & v1_xcmplx_0(A))) # label(cc6_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 3002 (all A (v4_ordinal2(A) -> v1_xreal_0(A))) # label(cc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 3003 (exists A (-v3_xreal_0(A) & v2_xreal_0(A) & -v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A))) # label(rc2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 3004 (all A (v2_xreal_0(A) & v1_xreal_0(A) -> -v3_xreal_0(A) & -v1_xboole_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A))) # label(cc3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 3005 (all A (-v2_xreal_0(A) & v1_xreal_0(A) -> -v2_xreal_0(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(A)) & v1_xcmplx_0(k5_xcmplx_0(A)))) # label(fc25_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 3006 (all A all B (v1_xreal_0(B) & v2_xreal_0(A) & v1_xreal_0(A) & -v2_xreal_0(B) -> v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & -v1_xboole_0(k6_xcmplx_0(A,B)) & -v3_xreal_0(k6_xcmplx_0(A,B)) & v2_xreal_0(k6_xcmplx_0(A,B)))) # label(fc17_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 3007 (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]. 56.68/55.68 3008 (all A (-v3_xreal_0(A) & v1_xreal_0(A) -> -v3_xreal_0(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(A)) & v1_xcmplx_0(k5_xcmplx_0(A)))) # label(fc26_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.68 3009 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> v1_xreal_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3010 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r2_hidden(A,k2_arytm_2) & r2_hidden(B,k2_arytm_2) -> (r1_xreal_0(A,B) <-> (exists C (m1_subset_1(C,k2_arytm_2) & (exists D (A = C & m1_subset_1(D,k2_arytm_2) & r1_arytm_2(C,D) & B = D)))))) & (r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) -> (r1_xreal_0(A,B) <-> (exists C (m1_subset_1(C,k2_arytm_2) & (exists D (k4_tarski(np__0,C) = A & r1_arytm_2(D,C) & B = k4_tarski(np__0,D) & m1_subset_1(D,k2_arytm_2))))))) & -(-(r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2))) & -(r1_xreal_0(A,B) <-> r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(B,k2_arytm_2)) & -(r2_hidden(A,k2_arytm_2) & r2_hidden(B,k2_arytm_2))))))) # label(d2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3011 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) & -v2_xreal_0(B) & -v3_xreal_0(A) -> v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & -v3_xreal_0(k6_xcmplx_0(A,B)))) # label(fc15_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3012 (all A all B (-v2_xreal_0(B) & -v3_xreal_0(A) & v1_xreal_0(A) & v1_xreal_0(B) -> v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) & -v2_xreal_0(k7_xcmplx_0(A,B)))) # label(fc27_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3013 (all A all B (v1_xreal_0(A) & -v3_xreal_0(B) & v1_xreal_0(B) & v2_xreal_0(A) -> v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v2_xreal_0(k2_xcmplx_0(A,B)) & -v3_xreal_0(k2_xcmplx_0(A,B)) & -v1_xboole_0(k2_xcmplx_0(A,B)))) # label(fc9_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3014 (all A all B (v1_xreal_0(A) & -v2_xreal_0(B) & -v3_xreal_0(A) & v1_xreal_0(B) -> -v2_xreal_0(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)))) # label(fc16_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3015 (all A (v1_xreal_0(A) -> (v3_xreal_0(A) <-> -r1_xreal_0(np__0,A)))) # label(d4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3016 (all A all B (v3_xreal_0(A) & -v3_xreal_0(B) & v1_xreal_0(A) & v1_xreal_0(B) -> v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & -v2_xreal_0(k6_xcmplx_0(A,B)) & -v1_xboole_0(k6_xcmplx_0(A,B)) & v3_xreal_0(k6_xcmplx_0(A,B)))) # label(fc19_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3017 (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]. 56.68/55.69 3018 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & v3_xreal_0(A) & -v2_xreal_0(B) -> v1_xreal_0(k2_xcmplx_0(B,A)) & -v1_xboole_0(k2_xcmplx_0(B,A)) & v3_xreal_0(k2_xcmplx_0(B,A)) & -v2_xreal_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)))) # label(fc12_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3019 (exists A (v1_xcmplx_0(A) & v1_xreal_0(A))) # label(rc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3020 (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]. 56.68/55.69 3021 (all A all B (-v3_xreal_0(A) & v1_xreal_0(A) & -v3_xreal_0(B) & v1_xreal_0(B) -> v1_xcmplx_0(k2_xcmplx_0(A,B)) & -v3_xreal_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)))) # label(fc7_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3022 (all A (-v2_xreal_0(A) & v1_xreal_0(A) -> -v3_xreal_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)))) # label(fc13_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3023 (all A (v3_xreal_0(A) & v1_xreal_0(A) -> -v1_xboole_0(A) & v1_xreal_0(A) & -v2_xreal_0(A) & v1_xcmplx_0(A))) # label(cc5_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3024 (all A all B (v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & -v3_xreal_0(B) -> v1_xcmplx_0(k6_xcmplx_0(B,A)) & -v3_xreal_0(k6_xcmplx_0(B,A)) & v2_xreal_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & -v1_xboole_0(k6_xcmplx_0(B,A)))) # label(fc20_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3025 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> r1_xreal_0(B,A) | r1_xreal_0(A,B))) # label(connectedness_r1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3026 (all A all B (-v3_xreal_0(B) & -v2_xreal_0(A) & v1_xreal_0(B) & v1_xreal_0(A) -> v1_xreal_0(k3_xcmplx_0(B,A)) & v1_xcmplx_0(k3_xcmplx_0(B,A)) & -v2_xreal_0(k3_xcmplx_0(B,A)))) # label(fc22_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3027 (all A all B (-v3_xreal_0(B) & v1_xreal_0(B) & v2_xreal_0(A) & v1_xreal_0(A) -> -v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v2_xreal_0(k2_xcmplx_0(B,A)) & -v3_xreal_0(k2_xcmplx_0(B,A)))) # label(fc10_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3028 (all A all B (-v2_xreal_0(B) & v1_xreal_0(A) & -v2_xreal_0(A) & v1_xreal_0(B) -> v1_xcmplx_0(k7_xcmplx_0(A,B)) & -v3_xreal_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)))) # label(fc30_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3029 (all A (v1_xboole_0(A) & v1_xreal_0(A) -> v1_xreal_0(A) & -v2_xreal_0(A) & -v3_xreal_0(A) & v1_xcmplx_0(A))) # label(cc7_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3030 (all A (-v2_xreal_0(A) & -v3_xreal_0(A) & v1_xreal_0(A) -> v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A))) # label(cc8_xreal_0) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3031 (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]. 56.68/55.69 3032 (all A (v1_xreal_0(A) -> -r1_xreal_0(k2_xcmplx_0(A,np__1),k1_int_1(A)) & -r1_xreal_0(A,k6_xcmplx_0(k1_int_1(A),np__1)))) # label(t50_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3033 (all A all B (v1_int_1(A) & v1_int_1(B) -> r2_int_1(A,A))) # label(reflexivity_r2_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3034 (all A (m1_subset_1(A,k4_numbers) -> v1_int_1(A))) # label(cc1_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3035 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> v1_xreal_0(k6_xcmplx_0(A,B)) & v1_int_1(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)))) # label(fc9_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3036 (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]. 56.68/55.69 3037 (all A (v1_xreal_0(A) -> v1_int_1(k1_int_1(A)))) # label(dt_k1_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3038 $T # label(t49_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3039 $T # label(t31_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3040 $T # label(t1_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3041 (all A (v1_xreal_0(A) -> A = k2_xcmplx_0(k1_int_1(A),k4_int_1(A)))) # label(t68_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3042 (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]. 56.68/55.69 3043 $T # label(t24_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3044 (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]. 56.68/55.69 3045 (all A all B (v1_int_1(B) & m1_subset_1(A,k5_numbers) -> v1_xcmplx_0(k3_xcmplx_0(B,A)) & v1_xreal_0(k3_xcmplx_0(B,A)) & v1_int_1(k3_xcmplx_0(B,A)))) # label(fc7_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3046 (all A (v1_int_1(A) -> k6_int_1(A,A) = np__0)) # label(t77_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3047 (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]. 56.68/55.69 3048 $T # label(t12_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3049 (exists A v1_int_1(A)) # label(rc2_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3050 (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]. 56.68/55.69 3051 (all A ((all B (-(all C (m2_subset_1(C,k1_numbers,k5_numbers) -> B != k1_real_1(C) & C != B)) <-> r2_hidden(B,A))) <-> k4_numbers = A)) # label(d1_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3052 $T # label(t9_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3053 $T # label(t29_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3054 (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]. 56.68/55.69 3055 (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(k3_xcmplx_0(A,D),k3_xcmplx_0(B,E),C)))))))))))) # label(t39_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3056 (all A (v1_int_1(A) -> (p1_s4_int_1(A) -> p1_s4_int_1(k6_xcmplx_0(A,np__1)) & p1_s4_int_1(k2_xcmplx_0(A,np__1))))) & p1_s4_int_1(f1_s4_int_1) -> (all A (v1_int_1(A) -> p1_s4_int_1(A))) # label(s4_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3057 $T # label(t28_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3058 (all A all B (m1_subset_1(A,k5_numbers) & v1_int_1(B) -> v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_int_1(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)))) # label(fc6_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3059 (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]. 56.68/55.69 3060 (all A (v1_int_1(A) -> v1_int_1(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)))) # label(fc3_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3061 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (k2_xcmplx_0(B,A) = C -> r1_xreal_0(B,C)))))))) # label(t19_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3062 (exists A (m1_subset_1(A,k1_numbers) & v1_xreal_0(A) & v1_int_1(A) & v1_xcmplx_0(A))) # label(rc1_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3063 (all A (v1_int_1(A) -> v1_xcmplx_0(A) & v1_xreal_0(A))) # label(cc4_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3064 $T # label(t27_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3065 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(A,k1_int_1(A)) & v1_int_1(A)) & -(-v1_int_1(A) & r1_xreal_0(A,k1_int_1(A))))) # label(t48_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3066 (all A all B (v1_int_1(A) & v1_int_1(B) -> v1_int_1(k6_int_1(A,B)))) # label(dt_k6_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3067 (all A (v1_xreal_0(A) -> (k4_int_1(A) = np__0 <-> v1_int_1(A)))) # label(t71_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3068 (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]. 56.68/55.69 3069 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> k2_xcmplx_0(k1_int_1(A),B) = k1_int_1(k2_xcmplx_0(A,B)))))) # label(t51_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3070 (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]. 56.68/55.69 3071 (all A (v1_xreal_0(A) -> k1_int_1(k4_int_1(A)) = np__0)) # label(t70_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3072 (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]. 56.68/55.69 3073 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (A = np__1 & k1_real_1(np__1) = B | k1_real_1(np__1) = A & np__1 = B <-> k3_xcmplx_0(A,B) = k1_real_1(np__1)))))) # label(t23_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3074 (all A (v1_int_1(A) -> (p1_s5_int_1(A) -> r1_xreal_0(f1_s5_int_1,A)))) & (exists A (p1_s5_int_1(A) & v1_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]. 56.68/55.69 3075 (all A all B (v1_int_1(A) & v1_int_1(B) -> v1_int_1(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)))) # label(fc1_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3076 (all A (v1_int_1(A) -> (p1_s6_int_1(A) -> r1_xreal_0(A,f1_s6_int_1)))) & (exists A (v1_int_1(A) & p1_s6_int_1(A))) -> (exists A (v1_int_1(A) & p1_s6_int_1(A) & (all B (v1_int_1(B) -> (p1_s6_int_1(B) -> r1_xreal_0(B,A)))))) # label(s6_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3077 $T # label(t67_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3078 (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]. 56.68/55.69 3079 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (np__0 != B -> k6_xcmplx_0(A,k3_xcmplx_0(k5_int_1(A,B),B)) = k6_int_1(A,B)) & (np__0 = B -> np__0 = k6_int_1(A,B)))))) # label(d8_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3080 $T # label(t56_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3081 $T # label(t25_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3082 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> (-r1_xreal_0(k2_xcmplx_0(A,np__1),B) & r1_xreal_0(A,B) <-> k2_int_1(A) = B))))) # label(d5_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3083 (all A (v1_xreal_0(A) -> -((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> A != k1_real_1(B) & B != A)) & v1_int_1(A)))) # label(t8_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3084 (all A all B (v1_int_1(A) & v1_int_1(B) -> v1_int_1(k5_int_1(A,B)))) # label(dt_k5_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3085 (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]. 56.68/55.69 3086 (all A (v1_xreal_0(A) -> (np__0 != A -> np__1 = k1_int_1(k7_xcmplx_0(A,A))))) # label(t74_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3087 (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]. 56.68/55.69 3088 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(k2_int_1(A),k1_int_1(A)) & v1_int_1(A)) & -(r1_xreal_0(k2_int_1(A),k1_int_1(A)) & -v1_int_1(A)))) # label(t60_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3089 (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]. 56.68/55.69 3090 $T # label(t46_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3091 (all A (m1_subset_1(A,k5_numbers) -> v1_int_1(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)) & -v2_xreal_0(k4_xcmplx_0(A)))) # label(fc5_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3092 (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]. 56.68/55.69 3093 (all A (v1_xreal_0(A) -> (r1_xreal_0(np__0,A) -> r1_xreal_0(np__0,k2_int_1(A)) & r1_xreal_0(np__0,k1_int_1(A)) & m2_subset_1(k2_int_1(A),k1_numbers,k5_numbers) & m2_subset_1(k1_int_1(A),k1_numbers,k5_numbers)))) # label(t80_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3094 (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]. 56.68/55.69 3095 (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]. 56.68/55.69 3096 $T # label(t3_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3097 $T # label(t15_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3098 $T # label(t6_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3099 (all A (r2_hidden(A,k4_numbers) <-> v1_int_1(A))) # label(d2_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3100 (all A (m1_subset_1(A,k5_numbers) -> -v3_xreal_0(A) & v1_ordinal1(A) & v3_ordinal1(A) & v1_int_1(A) & v1_xreal_0(A) & v1_xcmplx_0(A) & v4_ordinal2(A) & v2_ordinal1(A))) # label(cc2_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3101 $T # label(t13_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3102 (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]. 56.68/55.69 3103 (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]. 56.68/55.69 3104 (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]. 56.68/55.69 3105 (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]. 56.68/55.69 3106 $T # label(t10_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3107 (all A (v1_xreal_0(A) -> (all B (v4_ordinal2(B) -> (A = B | A = k4_xcmplx_0(B) -> v1_int_1(A)))))) # label(t7_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3108 $T # label(dt_k3_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3109 (all A all B (v1_int_1(B) & m1_subset_1(A,k5_numbers) -> v1_xreal_0(k6_xcmplx_0(B,A)) & v1_int_1(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)))) # label(fc8_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3110 (all A (v1_xreal_0(A) -> -r1_xreal_0(np__1,k4_int_1(A)) & r1_xreal_0(np__0,k4_int_1(A)))) # label(t69_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3111 (all A (v1_int_1(A) -> k5_int_1(A,np__0) = np__0)) # label(t75_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3112 $T # label(t73_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3113 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (r1_int_1(k2_xcmplx_0(A,C),B,C) <-> r1_int_1(A,B,C)))))))) # label(t42_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3114 (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]. 56.68/55.69 3115 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(k2_int_1(A),A) & v1_int_1(A)) & -(r1_xreal_0(k2_int_1(A),A) & -v1_int_1(A)))) # label(t55_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3116 (all A (v1_xreal_0(A) -> (v1_int_1(A) -> v1_int_1(k6_xcmplx_0(A,np__1)) & v1_int_1(k2_xcmplx_0(A,np__1))))) # label(t17_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3117 (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]. 56.68/55.69 3118 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (r1_xreal_0(A,C) & r1_xreal_0(A,B) -> C = B | r1_xreal_0(k2_xcmplx_0(A,np__1),B) | r1_xreal_0(k2_xcmplx_0(A,np__1),C)))))))) # label(t45_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3119 $T # label(t5_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3120 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (r2_int_1(A,B) <-> (exists C (k3_xcmplx_0(A,C) = B & v1_int_1(C)))))))) # label(d9_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3121 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (r1_int_1(k6_xcmplx_0(A,C),B,C) <-> r1_int_1(A,B,C)))))))) # label(t43_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3122 (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]. 56.68/55.69 3123 $T # label(t2_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3124 $T # label(t11_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3125 (all A (v1_int_1(A) -> (p1_s2_int_1(A) & r1_xreal_0(f1_s2_int_1,A) -> p1_s2_int_1(k2_xcmplx_0(A,np__1))))) & 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)))) # label(s2_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3126 (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) -> (k3_xcmplx_0(A,B) = C & r1_int_1(D,E,C) -> r1_int_1(D,E,A)))))))))))) # label(t41_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3127 $T # label(t4_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3128 (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]. 56.68/55.69 3129 (all A (v1_xreal_0(A) -> v1_int_1(k2_int_1(A)))) # label(dt_k2_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3130 (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(k6_xcmplx_0(A,D),k6_xcmplx_0(B,E),C)))))))))))) # label(t38_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3131 $T # label(t30_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3132 (all A (v1_xreal_0(A) -> (v1_int_1(A) <-> k2_int_1(A) = k1_int_1(A)))) # label(t59_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3133 $T # label(t14_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3134 (all A (v4_ordinal2(A) -> v1_int_1(A))) # label(cc3_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3135 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> (-r1_xreal_0(B,k6_xcmplx_0(A,np__1)) & r1_xreal_0(B,A) <-> B = k1_int_1(A)))))) # label(d4_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3136 (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]. 56.68/55.69 3137 (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]. 56.68/55.69 3138 (all A (v1_xreal_0(A) -> k1_int_1(k2_int_1(A)) = k2_int_1(A))) # label(t62_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3139 (all A (v1_int_1(A) -> (np__0 != A -> k5_int_1(A,A) = np__1))) # label(t76_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3140 (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]. 56.68/55.69 3141 (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(B,D,C) & r1_int_1(A,B,C) -> r1_int_1(A,D,C)))))))))) # label(t36_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3142 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (k1_real_1(np__1) = A & k1_real_1(np__1) = B | A = np__1 & B = np__1 <-> k3_xcmplx_0(A,B) = np__1))))) # label(t22_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3143 (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]. 56.68/55.69 3144 (all A all B (v1_int_1(A) & v1_int_1(B) -> v1_int_1(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)))) # label(fc4_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3145 $T # label(t26_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3146 $T # label(t53_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3147 (all A (v1_xreal_0(A) -> (v1_int_1(A) <-> A = k1_int_1(A)))) # label(t47_int_1) # label(axiom) # label(non_clause). [assumption]. 56.68/55.69 3148 (all A (v1_xreal_0(A) -> (A = k2_int_1(A) <-> v1_int_1(A)))) # label(t54_int_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.69 3149 (all A (v1_xreal_0(A) -> (k2_int_1(A) = k1_int_1(A) <-> k2_int_1(A) != k2_xcmplx_0(k1_int_1(A),np__1)))) # label(t66_int_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.69 3150 (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]. 56.72/55.69 3151 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (r1_xreal_0(C,A) & r1_xreal_0(B,A) -> r1_xreal_0(B,k6_xcmplx_0(A,np__1)) | r1_xreal_0(C,k6_xcmplx_0(A,np__1)) | C = B))))))) # label(t44_int_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.69 3152 (all A all B (m1_subset_1(B,k3_numbers) & m1_subset_1(A,k3_numbers) -> k16_binop_2(A,B) = k6_xcmplx_0(A,B))) # label(redefinition_k16_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.69 3153 (all A (v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & v1_funct_1(A) -> ((all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> k11_binop_2(B,C) = k2_binop_1(k1_numbers,k1_numbers,k1_numbers,A,B,C))))) <-> A = k35_binop_2))) # label(d11_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.69 3154 (all A (m1_subset_1(A,k2_numbers) -> A = k1_binop_2(k1_binop_2(A)))) # label(involutiveness_k1_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.69 3155 (all A (m1_subset_1(A,k4_numbers) -> m1_subset_1(k19_binop_2(A),k4_numbers))) # label(dt_k19_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.69 3156 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> k2_xcmplx_0(A,B) = k9_binop_2(A,B))) # label(redefinition_k9_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.69 3157 (all A all B (m1_subset_1(B,k4_numbers) & m1_subset_1(A,k4_numbers) -> k6_xcmplx_0(A,B) = k21_binop_2(A,B))) # label(redefinition_k21_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.69 3158 (all A (m2_relset_1(A,k2_numbers,k2_numbers) & v1_funct_1(A) & v1_funct_2(A,k2_numbers,k2_numbers) -> (k25_binop_2 = A <-> (all B (m1_subset_1(B,k2_numbers) -> k8_funct_2(k2_numbers,k2_numbers,A,B) = k1_binop_2(B)))))) # label(d1_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.69 3159 (all A (v1_funct_2(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) & v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) -> (A = k48_binop_2 <-> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k24_binop_2(B,C) = k2_binop_1(k5_numbers,k5_numbers,k5_numbers,A,B,C)))))))) # label(d24_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.69 3160 (all A all B (m1_subset_1(A,k3_numbers) & m1_subset_1(B,k3_numbers) -> m1_subset_1(k18_binop_2(A,B),k3_numbers))) # label(dt_k18_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.69 3161 (all A (m1_subset_1(A,k2_numbers) -> m1_subset_1(k1_binop_2(A),k2_numbers))) # label(dt_k1_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.69 3162 (all A (v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) & m2_relset_1(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) -> ((all B (m1_subset_1(B,k2_numbers) -> (all C (m1_subset_1(C,k2_numbers) -> k2_binop_1(k2_numbers,k2_numbers,k2_numbers,A,B,C) = k5_binop_2(B,C))))) <-> k29_binop_2 = A))) # label(d5_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.69 3163 (all A (v1_funct_2(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) & m2_relset_1(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) & v1_funct_1(A) -> ((all B (m1_subset_1(B,k4_numbers) -> (all C (m1_subset_1(C,k4_numbers) -> k2_binop_1(k4_numbers,k4_numbers,k4_numbers,A,B,C) = k21_binop_2(B,C))))) <-> k45_binop_2 = A))) # label(d21_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.69 3164 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> k5_binop_2(A,B) = k5_binop_2(B,A))) # label(commutativity_k5_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.69 3165 (all A (m2_relset_1(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) & v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) -> (k27_binop_2 = A <-> (all B (m1_subset_1(B,k2_numbers) -> (all C (m1_subset_1(C,k2_numbers) -> k2_binop_1(k2_numbers,k2_numbers,k2_numbers,A,B,C) = k3_binop_2(B,C)))))))) # label(d3_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3166 (all A (m1_subset_1(A,k1_numbers) -> k4_xcmplx_0(A) = k7_binop_2(A))) # label(redefinition_k7_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3167 (all A all B (m1_subset_1(A,k3_numbers) & m1_subset_1(B,k3_numbers) -> m1_subset_1(k17_binop_2(A,B),k3_numbers))) # label(dt_k17_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3168 (all A (m1_subset_1(A,k3_numbers) -> m1_subset_1(k14_binop_2(A),k3_numbers))) # label(dt_k14_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3169 (all A (v1_funct_2(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) & v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) -> (A = k28_binop_2 <-> (all B (m1_subset_1(B,k2_numbers) -> (all C (m1_subset_1(C,k2_numbers) -> k2_binop_1(k2_numbers,k2_numbers,k2_numbers,A,B,C) = k4_binop_2(B,C)))))))) # label(d4_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3170 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k9_binop_2(B,A) = k9_binop_2(A,B))) # label(commutativity_k9_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3171 (all A (v1_funct_1(A) & m2_relset_1(A,f1_s1_binop_2,f2_s1_binop_2) & v1_funct_2(A,f1_s1_binop_2,f2_s1_binop_2) -> (all B (v1_funct_2(B,f1_s1_binop_2,f2_s1_binop_2) & m2_relset_1(B,f1_s1_binop_2,f2_s1_binop_2) & v1_funct_1(B) -> ((all C (m1_subset_1(C,f1_s1_binop_2) -> k8_funct_2(f1_s1_binop_2,f2_s1_binop_2,B,C) = f3_s1_binop_2(C))) & (all C (m1_subset_1(C,f1_s1_binop_2) -> f3_s1_binop_2(C) = k8_funct_2(f1_s1_binop_2,f2_s1_binop_2,A,C))) -> B = A))))) # label(s1_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3172 (all A (m1_subset_1(A,k3_numbers) -> k13_binop_2(k13_binop_2(A)) = A)) # label(involutiveness_k13_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3173 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> m1_subset_1(k12_binop_2(A,B),k1_numbers))) # label(dt_k12_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3174 (all A (v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) & m2_relset_1(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) -> ((all B (m1_subset_1(B,k3_numbers) -> (all C (m1_subset_1(C,k3_numbers) -> k2_binop_1(k3_numbers,k3_numbers,k3_numbers,A,B,C) = k15_binop_2(B,C))))) <-> A = k39_binop_2))) # label(d15_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3175 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> m2_subset_1(k23_binop_2(A,B),k1_numbers,k5_numbers))) # label(dt_k23_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3176 (all A (m1_subset_1(A,k4_numbers) -> k19_binop_2(A) = k4_xcmplx_0(A))) # label(redefinition_k19_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3177 (all A all B (m1_subset_1(B,k3_numbers) & m1_subset_1(A,k3_numbers) -> m1_subset_1(k16_binop_2(A,B),k3_numbers))) # label(dt_k16_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3178 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k10_binop_2(A,B) = k6_xcmplx_0(A,B))) # label(redefinition_k10_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3179 (all A all B (m1_subset_1(B,k4_numbers) & m1_subset_1(A,k4_numbers) -> k3_xcmplx_0(A,B) = k22_binop_2(A,B))) # label(redefinition_k22_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3180 (all A all B (m1_subset_1(A,k4_numbers) & m1_subset_1(B,k4_numbers) -> k20_binop_2(A,B) = k2_xcmplx_0(A,B))) # label(redefinition_k20_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3181 (all A (v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(f1_s2_binop_2,f1_s2_binop_2),f1_s2_binop_2) & v1_funct_2(A,k2_zfmisc_1(f1_s2_binop_2,f1_s2_binop_2),f1_s2_binop_2) -> (all B (v1_funct_2(B,k2_zfmisc_1(f1_s2_binop_2,f1_s2_binop_2),f1_s2_binop_2) & v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(f1_s2_binop_2,f1_s2_binop_2),f1_s2_binop_2) -> ((all C (m1_subset_1(C,f1_s2_binop_2) -> (all D (m1_subset_1(D,f1_s2_binop_2) -> k2_binop_1(f1_s2_binop_2,f1_s2_binop_2,f1_s2_binop_2,B,C,D) = f2_s2_binop_2(C,D))))) & (all C (m1_subset_1(C,f1_s2_binop_2) -> (all D (m1_subset_1(D,f1_s2_binop_2) -> k2_binop_1(f1_s2_binop_2,f1_s2_binop_2,f1_s2_binop_2,A,C,D) = f2_s2_binop_2(C,D))))) -> B = A))))) # label(s2_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3182 (all A all B (m1_subset_1(B,k3_numbers) & m1_subset_1(A,k3_numbers) -> k15_binop_2(A,B) = k15_binop_2(B,A))) # label(commutativity_k15_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3183 (all A all B (m1_subset_1(B,k3_numbers) & m1_subset_1(A,k3_numbers) -> k15_binop_2(A,B) = k2_xcmplx_0(A,B))) # label(redefinition_k15_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3184 (all A all B (m1_subset_1(B,k5_numbers) & m1_subset_1(A,k5_numbers) -> k23_binop_2(A,B) = k2_xcmplx_0(A,B))) # label(redefinition_k23_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3185 (all A (m1_subset_1(A,k3_numbers) -> v1_xreal_0(A) & v1_rat_1(A) & v1_xcmplx_0(A))) # label(cc1_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3186 (all A (m1_subset_1(A,k1_numbers) -> m1_subset_1(k7_binop_2(A),k1_numbers))) # label(dt_k7_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3187 (all A (m1_subset_1(A,k2_numbers) -> A = k2_binop_2(k2_binop_2(A)))) # label(involutiveness_k2_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3188 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> m1_subset_1(k3_binop_2(A,B),k2_numbers))) # label(dt_k3_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3189 (all A (v1_funct_2(A,k3_numbers,k3_numbers) & v1_funct_1(A) & m2_relset_1(A,k3_numbers,k3_numbers) -> ((all B (m1_subset_1(B,k3_numbers) -> k13_binop_2(B) = k8_funct_2(k3_numbers,k3_numbers,A,B))) <-> k37_binop_2 = A))) # label(d13_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3190 (all A (m1_subset_1(A,k2_numbers) -> m1_subset_1(k2_binop_2(A),k2_numbers))) # label(dt_k2_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3191 (all A all B (m1_subset_1(B,k4_numbers) & m1_subset_1(A,k4_numbers) -> k22_binop_2(B,A) = k22_binop_2(A,B))) # label(commutativity_k22_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3192 (all A (m1_subset_1(A,k1_numbers) -> k8_binop_2(A) = k5_xcmplx_0(A))) # label(redefinition_k8_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3193 (all A (v1_funct_2(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) & m2_relset_1(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) & v1_funct_1(A) -> ((all B (m1_subset_1(B,k2_numbers) -> (all C (m1_subset_1(C,k2_numbers) -> k2_binop_1(k2_numbers,k2_numbers,k2_numbers,A,B,C) = k6_binop_2(B,C))))) <-> A = k30_binop_2))) # label(d6_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3194 (all A (v1_funct_2(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) & m2_relset_1(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) & v1_funct_1(A) -> (A = k44_binop_2 <-> (all B (m1_subset_1(B,k4_numbers) -> (all C (m1_subset_1(C,k4_numbers) -> k20_binop_2(B,C) = k2_binop_1(k4_numbers,k4_numbers,k4_numbers,A,B,C)))))))) # label(d20_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3195 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> k11_binop_2(A,B) = k3_xcmplx_0(A,B))) # label(redefinition_k11_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3196 (all A (m2_relset_1(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) & v1_funct_2(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) & v1_funct_1(A) -> ((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k23_binop_2(B,C) = k2_binop_1(k5_numbers,k5_numbers,k5_numbers,A,B,C))))) <-> A = k47_binop_2))) # label(d23_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3197 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> m1_subset_1(k4_binop_2(A,B),k2_numbers))) # label(dt_k4_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3198 (all A (m2_relset_1(A,k1_numbers,k1_numbers) & v1_funct_1(A) & v1_funct_2(A,k1_numbers,k1_numbers) -> ((all B (m1_subset_1(B,k1_numbers) -> k7_binop_2(B) = k8_funct_2(k1_numbers,k1_numbers,A,B))) <-> k31_binop_2 = A))) # label(d7_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3199 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> k24_binop_2(B,A) = k24_binop_2(A,B))) # label(commutativity_k24_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3200 (all A (m2_relset_1(A,k3_numbers,k3_numbers) & v1_funct_2(A,k3_numbers,k3_numbers) & v1_funct_1(A) -> (k38_binop_2 = A <-> (all B (m1_subset_1(B,k3_numbers) -> k14_binop_2(B) = k8_funct_2(k3_numbers,k3_numbers,A,B)))))) # label(d14_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3201 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> m1_subset_1(k9_binop_2(A,B),k1_numbers))) # label(dt_k9_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3202 (all A (v1_funct_1(A) & v1_funct_2(A,k4_numbers,k4_numbers) & m2_relset_1(A,k4_numbers,k4_numbers) -> ((all B (m1_subset_1(B,k4_numbers) -> k8_funct_2(k4_numbers,k4_numbers,A,B) = k19_binop_2(B))) <-> k43_binop_2 = A))) # label(d19_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3203 (all A all B (m1_subset_1(A,k3_numbers) & m1_subset_1(B,k3_numbers) -> k18_binop_2(A,B) = k7_xcmplx_0(A,B))) # label(redefinition_k18_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3204 (all A (m1_subset_1(A,k1_numbers) -> m1_subset_1(k8_binop_2(A),k1_numbers))) # label(dt_k8_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3205 (all A (v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) & m2_relset_1(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) -> (k41_binop_2 = A <-> (all B (m1_subset_1(B,k3_numbers) -> (all C (m1_subset_1(C,k3_numbers) -> k2_binop_1(k3_numbers,k3_numbers,k3_numbers,A,B,C) = k17_binop_2(B,C)))))))) # label(d17_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3206 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> m1_subset_1(k11_binop_2(A,B),k1_numbers))) # label(dt_k11_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3207 (all A (v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & v1_funct_1(A) -> (A = k33_binop_2 <-> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> k2_binop_1(k1_numbers,k1_numbers,k1_numbers,A,B,C) = k9_binop_2(B,C)))))))) # label(d9_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3208 (all A (v1_funct_1(A) & v1_funct_2(A,k2_numbers,k2_numbers) & m2_relset_1(A,k2_numbers,k2_numbers) -> ((all B (m1_subset_1(B,k2_numbers) -> k2_binop_2(B) = k8_funct_2(k2_numbers,k2_numbers,A,B))) <-> k26_binop_2 = A))) # label(d2_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3209 (all A all B (m1_subset_1(B,k4_numbers) & m1_subset_1(A,k4_numbers) -> m1_subset_1(k20_binop_2(A,B),k4_numbers))) # label(dt_k20_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3210 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> k3_binop_2(A,B) = k3_binop_2(B,A))) # label(commutativity_k3_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3211 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> k6_xcmplx_0(A,B) = k4_binop_2(A,B))) # label(redefinition_k4_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3212 (all A (m1_subset_1(A,k1_numbers) -> k7_binop_2(k7_binop_2(A)) = A)) # label(involutiveness_k7_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3213 (all A (v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & v1_funct_1(A) -> (A = k34_binop_2 <-> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> k10_binop_2(B,C) = k2_binop_1(k1_numbers,k1_numbers,k1_numbers,A,B,C)))))))) # label(d10_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3214 (all A (m1_subset_1(A,k2_numbers) -> k1_binop_2(A) = k4_xcmplx_0(A))) # label(redefinition_k1_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3215 (all A (m1_subset_1(A,k3_numbers) -> A = k14_binop_2(k14_binop_2(A)))) # label(involutiveness_k14_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3216 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> k5_binop_2(A,B) = k3_xcmplx_0(A,B))) # label(redefinition_k5_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3217 (all A all B (m1_subset_1(B,k5_numbers) & m1_subset_1(A,k5_numbers) -> m2_subset_1(k24_binop_2(A,B),k1_numbers,k5_numbers))) # label(dt_k24_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3218 (all A (m1_subset_1(A,k2_numbers) -> k2_binop_2(A) = k5_xcmplx_0(A))) # label(redefinition_k2_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3219 (all A (v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) & v1_funct_2(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) -> (k40_binop_2 = A <-> (all B (m1_subset_1(B,k3_numbers) -> (all C (m1_subset_1(C,k3_numbers) -> k2_binop_1(k3_numbers,k3_numbers,k3_numbers,A,B,C) = k16_binop_2(B,C)))))))) # label(d16_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3220 (all A (m1_subset_1(A,k3_numbers) -> m1_subset_1(k13_binop_2(A),k3_numbers))) # label(dt_k13_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3221 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> k2_xcmplx_0(A,B) = k3_binop_2(A,B))) # label(redefinition_k3_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3222 (all A all B (m1_subset_1(B,k3_numbers) & m1_subset_1(A,k3_numbers) -> k17_binop_2(A,B) = k3_xcmplx_0(A,B))) # label(redefinition_k17_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3223 (all A all B (m1_subset_1(A,k4_numbers) & m1_subset_1(B,k4_numbers) -> m1_subset_1(k22_binop_2(A,B),k4_numbers))) # label(dt_k22_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3224 (all A all B (m1_subset_1(B,k4_numbers) & m1_subset_1(A,k4_numbers) -> k20_binop_2(A,B) = k20_binop_2(B,A))) # label(commutativity_k20_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3225 (all A (v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) & m2_relset_1(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) -> ((all B (m1_subset_1(B,k3_numbers) -> (all C (m1_subset_1(C,k3_numbers) -> k2_binop_1(k3_numbers,k3_numbers,k3_numbers,A,B,C) = k18_binop_2(B,C))))) <-> A = k42_binop_2))) # label(d18_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3226 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> m1_subset_1(k10_binop_2(A,B),k1_numbers))) # label(dt_k10_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3227 (all A (m1_subset_1(A,k3_numbers) -> k13_binop_2(A) = k4_xcmplx_0(A))) # label(redefinition_k13_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3228 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> k7_xcmplx_0(A,B) = k12_binop_2(A,B))) # label(redefinition_k12_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3229 (all A (m2_relset_1(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) & v1_funct_2(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) & v1_funct_1(A) -> (A = k46_binop_2 <-> (all B (m1_subset_1(B,k4_numbers) -> (all C (m1_subset_1(C,k4_numbers) -> k22_binop_2(B,C) = k2_binop_1(k4_numbers,k4_numbers,k4_numbers,A,B,C)))))))) # label(d22_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3230 (all A all B (m1_subset_1(B,k5_numbers) & m1_subset_1(A,k5_numbers) -> k24_binop_2(A,B) = k3_xcmplx_0(A,B))) # label(redefinition_k24_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3231 (all A (m1_subset_1(A,k4_numbers) -> k19_binop_2(k19_binop_2(A)) = A)) # label(involutiveness_k19_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3232 (all 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) & v1_funct_1(A) -> ((all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> k2_binop_1(k1_numbers,k1_numbers,k1_numbers,A,B,C) = k12_binop_2(B,C))))) <-> A = k36_binop_2))) # label(d12_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3233 (all A all B (m1_subset_1(B,k4_numbers) & m1_subset_1(A,k4_numbers) -> m1_subset_1(k21_binop_2(A,B),k4_numbers))) # label(dt_k21_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3234 (all A (m2_relset_1(A,k1_numbers,k1_numbers) & v1_funct_2(A,k1_numbers,k1_numbers) & v1_funct_1(A) -> (k32_binop_2 = A <-> (all B (m1_subset_1(B,k1_numbers) -> k8_binop_2(B) = k8_funct_2(k1_numbers,k1_numbers,A,B)))))) # label(d8_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3235 (all A all B (m1_subset_1(B,k3_numbers) & m1_subset_1(A,k3_numbers) -> k17_binop_2(A,B) = k17_binop_2(B,A))) # label(commutativity_k17_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3236 (all A (m1_subset_1(A,k1_numbers) -> k8_binop_2(k8_binop_2(A)) = A)) # label(involutiveness_k8_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3237 (all A all B (m1_subset_1(A,k3_numbers) & m1_subset_1(B,k3_numbers) -> m1_subset_1(k15_binop_2(A,B),k3_numbers))) # label(dt_k15_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3238 (all A (m1_subset_1(A,k3_numbers) -> k14_binop_2(A) = k5_xcmplx_0(A))) # label(redefinition_k14_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3239 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k11_binop_2(B,A) = k11_binop_2(A,B))) # label(commutativity_k11_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3240 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> m1_subset_1(k6_binop_2(A,B),k2_numbers))) # label(dt_k6_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3241 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> m1_subset_1(k5_binop_2(A,B),k2_numbers))) # label(dt_k5_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3242 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> k6_binop_2(A,B) = k7_xcmplx_0(A,B))) # label(redefinition_k6_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3243 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> k23_binop_2(A,B) = k23_binop_2(B,A))) # label(commutativity_k23_binop_2) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3244 (all A all B (v1_int_1(A) & v1_int_1(B) -> v4_membered(k2_tarski(A,B)) & v1_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)))) # label(fc15_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3245 (all A all B (v5_membered(A) -> v2_membered(k3_xboole_0(A,B)) & v5_membered(k3_xboole_0(A,B)) & v1_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)))) # label(fc35_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3246 (all A (v2_membered(A) -> (all B (v2_membered(B) -> (r1_xboole_0(A,B) <-> (all C (v1_xreal_0(C) -> -(r2_hidden(C,B) & r2_hidden(C,A))))))))) # label(d17_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3247 (all A (v4_membered(A) -> v3_membered(A))) # label(cc2_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3248 (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]. 56.72/55.70 3249 (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]. 56.72/55.70 3250 (all A all B (v5_membered(A) & v5_membered(B) -> v3_membered(k5_xboole_0(A,B)) & v4_membered(k5_xboole_0(A,B)) & v5_membered(k5_xboole_0(A,B)) & v2_membered(k5_xboole_0(A,B)) & v1_membered(k5_xboole_0(A,B)))) # label(fc46_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3251 (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]. 56.72/55.70 3252 (all A (v2_membered(A) -> r1_tarski(A,k1_numbers))) # label(t2_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3253 (all A all B all C (v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) -> v1_membered(k1_enumset1(A,B,C)))) # label(fc17_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3254 (all A (v4_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v2_membered(B) & v3_membered(B) & v1_membered(B) & v4_membered(B))))) # label(cc19_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3255 (all A (v1_membered(A) -> ((all B (v1_xcmplx_0(B) -> r2_hidden(B,A))) -> A = k2_numbers))) # label(t11_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3256 (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]. 56.72/55.70 3257 (all A all B (v4_membered(A) -> v2_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) & v1_membered(k3_xboole_0(A,B)))) # label(fc33_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3258 (exists A (v5_membered(A) & -v1_xboole_0(A) & v2_membered(A) & v4_membered(A) & v3_membered(A) & v1_membered(A))) # label(rc1_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3259 (all A (v3_membered(A) -> r1_tarski(A,k3_numbers))) # label(t3_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3260 (all A (v4_membered(A) -> (all B (v4_membered(B) -> ((all C (v1_int_1(C) -> (r2_hidden(C,A) -> r2_hidden(C,B)))) <-> r1_tarski(A,B)))))) # label(d9_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3261 (exists A ((all B (v1_xcmplx_0(B) -> (r2_hidden(B,A) <-> p1_s1_membered(B)))) & v1_membered(A))) # label(s1_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3262 (exists A (v5_membered(A) & (all B (v4_ordinal2(B) -> (p1_s5_membered(B) <-> r2_hidden(B,A)))))) # label(s5_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3263 (all A (v1_xreal_0(A) -> v2_membered(k1_tarski(A)) & v1_membered(k1_tarski(A)))) # label(fc8_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3264 (all A (v2_membered(A) -> v1_membered(A))) # label(cc4_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3265 (all A (v5_membered(A) -> (all B (v5_membered(B) -> ((all C (v4_ordinal2(C) -> (r2_hidden(C,A) <-> r2_hidden(C,B)))) <-> A = B))))) # label(d15_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3266 (all A (v3_membered(A) -> (all B (v3_membered(B) -> ((all C (v1_rat_1(C) -> (r2_hidden(C,B) <-> r2_hidden(C,A)))) <-> A = B))))) # label(d13_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3267 (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]. 56.72/55.70 3268 (all A (-v1_xboole_0(A) & v1_membered(A) -> (exists B (v1_xcmplx_0(B) & r2_hidden(B,A))))) # label(t6_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3269 (all A (v5_membered(A) -> v4_membered(A))) # label(cc1_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3270 (all A all B (v4_membered(A) -> v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)))) # label(fc34_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3271 (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]. 56.72/55.70 3272 (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]. 56.72/55.70 3273 (all A (v5_membered(A) <-> (all B (r2_hidden(B,A) -> v4_ordinal2(B))))) # label(d5_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3274 (all A (v3_membered(A) -> ((all B (v1_rat_1(B) -> r2_hidden(B,A))) -> A = k3_numbers))) # label(t13_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3275 (all A all B (v4_membered(B) & v4_membered(A) -> v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) & v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)))) # label(fc25_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3276 (all A all B (v5_membered(A) -> v2_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)) & v5_membered(k4_xboole_0(A,B)) & v1_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)))) # label(fc41_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3277 (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]. 56.72/55.70 3278 (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]. 56.72/55.70 3279 (all A (v4_membered(A) -> ((all B (v1_int_1(B) -> r2_hidden(B,A))) -> A = k4_numbers))) # label(t14_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3280 (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]. 56.72/55.70 3281 (all A (v2_membered(A) & -v1_xboole_0(A) -> (exists B (v1_xreal_0(B) & r2_hidden(B,A))))) # label(t7_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3282 (all A (v1_membered(A) -> r1_tarski(A,k2_numbers))) # label(t1_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3283 (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]. 56.72/55.70 3284 (all A (v4_membered(A) -> (all B (v4_membered(B) -> ((all C (v1_int_1(C) -> -(r2_hidden(C,A) & r2_hidden(C,B)))) <-> r1_xboole_0(A,B)))))) # label(d19_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3285 (all A all B (r2_hidden(B,A) & v2_membered(B) -> v2_membered(k1_setfam_1(A)))) # label(t27_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3286 (all A all B (v4_membered(B) -> (r1_tarski(A,B) -> v4_membered(A)))) # label(t19_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3287 (all A (m1_subset_1(A,k1_zfmisc_1(k5_numbers)) -> v4_membered(A) & v5_membered(A) & v3_membered(A) & v1_membered(A) & v2_membered(A))) # label(cc9_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3288 (exists A (v2_membered(A) & (all B (v1_xreal_0(B) -> (r2_hidden(B,A) <-> p1_s2_membered(B)))))) # label(s2_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3289 (all A (v5_membered(A) -> (all B (v5_membered(B) -> ((all C (v4_ordinal2(C) -> -(r2_hidden(C,B) & r2_hidden(C,A)))) <-> r1_xboole_0(A,B)))))) # label(d20_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3290 (all A all B (v3_membered(A) -> v3_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v1_membered(k4_xboole_0(A,B)))) # label(fc39_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3291 (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]. 56.72/55.70 3292 (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]. 56.72/55.70 3293 (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]. 56.72/55.70 3294 (all A (v3_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v3_membered(B) & v2_membered(B) & v1_membered(B))))) # label(cc18_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3295 (all A all B (v2_membered(B) -> (r1_tarski(A,B) -> v2_membered(A)))) # label(t17_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.70 3296 (all A (m1_subset_1(A,k1_zfmisc_1(k2_numbers)) -> v1_membered(A))) # label(cc5_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3297 (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]. 56.72/55.71 3298 (all A all B (v4_membered(B) & r2_hidden(B,A) -> v4_membered(k1_setfam_1(A)))) # label(t29_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3299 (all A all B (v4_membered(A) -> v3_membered(k4_xboole_0(A,B)) & v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)))) # label(fc40_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3300 (all A (v1_xboole_0(A) -> v5_membered(A) & v4_membered(A) & v2_membered(A) & v1_membered(A) & v3_membered(A))) # label(cc15_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3301 (all A all B (v2_membered(B) & v2_membered(A) -> v2_membered(k5_xboole_0(A,B)) & v1_membered(k5_xboole_0(A,B)))) # label(fc43_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3302 (all A all B (v3_membered(A) & v3_membered(B) -> v2_membered(k2_xboole_0(A,B)) & v1_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)))) # label(fc24_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3303 (all A all B (v5_membered(B) -> (r1_tarski(A,B) -> v5_membered(A)))) # label(t20_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3304 (all A all B (v3_membered(B) -> (r1_tarski(A,B) -> v3_membered(A)))) # label(t18_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3305 (all A (v5_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v1_membered(B) & v3_membered(B) & v5_membered(B) & v4_membered(B) & v2_membered(B))))) # label(cc20_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3306 (all A (v1_int_1(A) -> v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)))) # label(fc10_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3307 (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]. 56.72/55.71 3308 (all A all B (v1_membered(A) -> v1_membered(k4_xboole_0(A,B)))) # label(fc37_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3309 (all A (v2_membered(A) <-> (all B (r2_hidden(B,A) -> v1_xreal_0(B))))) # label(d2_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3310 (all A (v5_membered(A) -> (all B (m1_subset_1(B,A) -> v4_ordinal2(B) & v1_rat_1(B) & v1_xcmplx_0(B) & v1_int_1(B) & v1_xreal_0(B))))) # label(cc14_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3311 (all A all B all C (v4_ordinal2(A) & v4_ordinal2(B) & v4_ordinal2(C) -> v4_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)) & v5_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)) & v1_membered(k1_enumset1(A,B,C)))) # label(fc21_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3312 (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]. 56.72/55.71 3313 (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]. 56.72/55.71 3314 (all A ((all B (r2_hidden(B,A) -> v1_xcmplx_0(B))) <-> v1_membered(A))) # label(d1_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3315 (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]. 56.72/55.71 3316 (all A all B (v5_membered(A) -> v5_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v1_membered(k3_xboole_0(B,A)))) # label(fc36_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3317 (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]. 56.72/55.71 3318 (all A (m1_subset_1(A,k1_zfmisc_1(k4_numbers)) -> v2_membered(A) & v4_membered(A) & v1_membered(A) & v3_membered(A))) # label(cc8_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3319 (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]. 56.72/55.71 3320 (all A (m1_subset_1(A,k1_zfmisc_1(k3_numbers)) -> v2_membered(A) & v3_membered(A) & v1_membered(A))) # label(cc7_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3321 (all A all B (v3_membered(A) -> v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)))) # label(fc31_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3322 (all A (v4_membered(A) -> (all B (m1_subset_1(B,A) -> v1_int_1(B) & v1_rat_1(B) & v1_xcmplx_0(B) & v1_xreal_0(B))))) # label(cc13_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3323 (all A (v5_membered(A) -> r1_tarski(A,k5_numbers))) # label(t5_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3324 (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]. 56.72/55.71 3325 (all A (v3_membered(A) -> v2_membered(A))) # label(cc3_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3326 (all A (v1_rat_1(A) -> v3_membered(k1_tarski(A)) & v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)))) # label(fc9_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3327 (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]. 56.72/55.71 3328 (all A (-v1_xboole_0(A) & v3_membered(A) -> (exists B (r2_hidden(B,A) & v1_rat_1(B))))) # label(t8_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3329 (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]. 56.72/55.71 3330 (all A all B (v2_membered(A) -> v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)))) # label(fc38_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3331 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> v2_membered(k2_tarski(A,B)) & v1_membered(k2_tarski(A,B)))) # label(fc13_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3332 (all A (v2_membered(A) -> (all B (v2_membered(B) -> ((all C (v1_xreal_0(C) -> (r2_hidden(C,A) <-> r2_hidden(C,B)))) <-> B = A))))) # label(d12_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3333 (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]. 56.72/55.71 3334 (all A all B (v1_membered(B) -> (r1_tarski(A,B) -> v1_membered(A)))) # label(t16_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3335 (all A (v1_xcmplx_0(A) -> v1_membered(k1_tarski(A)))) # label(fc7_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3336 (all A all B (v2_membered(B) & v2_membered(A) -> v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)))) # label(fc23_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3337 (all A (v4_membered(A) -> r1_tarski(A,k4_numbers))) # label(t4_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3338 (exists A ((all B (v1_int_1(B) -> (r2_hidden(B,A) <-> p1_s4_membered(B)))) & v4_membered(A))) # label(s4_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3339 (all A all B (v4_ordinal2(A) & v4_ordinal2(B) -> v4_membered(k2_tarski(A,B)) & v5_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v1_membered(k2_tarski(A,B)))) # label(fc16_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3340 (all A all B (v4_membered(B) & v4_membered(A) -> v3_membered(k5_xboole_0(A,B)) & v2_membered(k5_xboole_0(A,B)) & v1_membered(k5_xboole_0(A,B)) & v4_membered(k5_xboole_0(A,B)))) # label(fc45_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3341 (all A (v4_membered(A) -> (all B (v4_membered(B) -> (A = B <-> (all C (v1_int_1(C) -> (r2_hidden(C,B) <-> r2_hidden(C,A))))))))) # label(d14_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3342 (all A all B all C (v1_int_1(A) & v1_int_1(B) & v1_int_1(C) -> v1_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)) & v4_membered(k1_enumset1(A,B,C)))) # label(fc20_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3343 (all A (-v1_xboole_0(A) & v4_membered(A) -> (exists B (r2_hidden(B,A) & v1_int_1(B))))) # label(t9_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3344 (all A (v4_membered(A) <-> (all B (r2_hidden(B,A) -> v1_int_1(B))))) # label(d4_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3345 (all A (v5_membered(A) -> (all B (v5_membered(B) -> (r1_tarski(A,B) <-> (all C (v4_ordinal2(C) -> (r2_hidden(C,A) -> r2_hidden(C,B))))))))) # label(d10_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3346 (all A all B (v1_membered(A) -> v1_membered(k3_xboole_0(B,A)))) # label(fc28_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3347 (all A (v1_membered(A) -> (all B (v1_membered(B) -> (B = A <-> (all C (v1_xcmplx_0(C) -> (r2_hidden(C,B) <-> r2_hidden(C,A))))))))) # label(d11_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3348 (all A all B (v1_rat_1(B) & v1_rat_1(A) -> v3_membered(k2_tarski(A,B)) & v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)))) # label(fc14_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3349 (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]. 56.72/55.71 3350 (all A all B (v1_membered(A) -> v1_membered(k3_xboole_0(A,B)))) # label(fc27_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3351 (all A all B (v3_membered(B) & v3_membered(A) -> v3_membered(k5_xboole_0(A,B)) & v1_membered(k5_xboole_0(A,B)) & v2_membered(k5_xboole_0(A,B)))) # label(fc44_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3352 (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]. 56.72/55.71 3353 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> v1_membered(A) & v2_membered(A))) # label(cc6_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3354 (all A all B (v5_membered(A) & v5_membered(B) -> v2_membered(k2_xboole_0(A,B)) & v5_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) & v1_membered(k2_xboole_0(A,B)))) # label(fc26_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3355 (all A (v4_ordinal2(A) -> v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v5_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)))) # label(fc11_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3356 (all A (v2_membered(A) -> (all B (v2_membered(B) -> (r1_tarski(A,B) <-> (all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r2_hidden(C,B))))))))) # label(d7_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3357 (all A all B (v2_membered(A) -> v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)))) # label(fc29_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3358 (all A (v3_membered(A) <-> (all B (r2_hidden(B,A) -> v1_rat_1(B))))) # label(d3_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3359 (all A all B all C (v1_rat_1(B) & v1_rat_1(C) & v1_rat_1(A) -> v3_membered(k1_enumset1(A,B,C)) & v1_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)))) # label(fc19_membered) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3360 $T # label(t3_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3361 $T # label(t17_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3362 $T # label(t16_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3363 $T # label(t12_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3364 $T # label(t9_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3365 (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]. 56.72/55.71 3366 (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]. 56.72/55.71 3367 (all A (v1_finset_1(A) -> v2_ordinal1(k1_card_1(A)) & v3_ordinal1(k1_card_1(A)) & v1_ordinal1(k1_card_1(A)) & v1_finset_1(k1_card_1(A)) & v1_card_1(k1_card_1(A)))) # label(fc2_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3368 (all A (v3_ordinal1(A) -> r1_ordinal1(k1_card_1(A),A))) # label(t24_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3369 $T # label(t11_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3370 (all A -(v1_finset_1(A) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> -r2_wellord2(A,B))))) # label(t74_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3371 (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]. 56.72/55.71 3372 (all A all B all C (r1_tarski(A,B) & r1_tarski(B,C) & r2_wellord2(A,C) -> r2_wellord2(A,B) & r2_wellord2(B,C))) # label(t44_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3373 (all A (v1_finset_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k4_card_1(A) = B <-> k1_card_1(B) = k1_card_1(A)))))) # label(d11_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3374 $T # label(t31_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3375 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k1_card_1(A) = k1_card_1(B) -> B = A))))) # label(t71_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3376 (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]. 56.72/55.71 3377 $T # label(t19_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3378 (all A exists B (r2_wellord2(A,B) & v3_ordinal1(B))) # label(t4_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3379 $T # label(d9_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3380 $T # label(d2_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3381 $T # label(t5_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3382 (all A (v1_finset_1(A) -> (all B (v1_finset_1(B) -> (r2_wellord2(A,B) -> k4_card_1(B) = k4_card_1(A)))))) # label(t81_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3383 (all A all B ((exists C (v1_funct_1(C) & B = k1_relat_1(C) & v1_relat_1(C) & r1_tarski(A,k2_relat_1(C)))) <-> r1_tarski(k1_card_1(A),k1_card_1(B)))) # label(t28_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3384 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (r2_hidden(A,B) <-> r1_tarski(A,B) & B != A))))) # label(t13_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3385 (all A (m1_subset_1(A,k5_numbers) -> v2_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_finset_1(A) & v1_card_1(A) & -v3_xreal_0(A) & v1_xreal_0(A) & v3_ordinal1(A) & v1_ordinal1(A))) # label(cc3_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3386 (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]. 56.72/55.71 3387 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r1_xreal_0(A,B) <-> r1_tarski(k1_card_1(A),k1_card_1(B))))))) # label(t72_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3388 $T # label(t55_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3389 $T # label(t75_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3390 (all A (v1_card_1(A) -> r2_hidden(A,k2_card_1(A)))) # label(t32_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3391 (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]. 56.72/55.71 3392 (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]. 56.72/55.71 3393 (all A (r2_wellord2(A,k1_xboole_0) <-> A = k1_xboole_0)) # label(t46_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3394 (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]. 56.72/55.71 3395 (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]. 56.72/55.71 3396 $T # label(t6_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3397 $T # label(t37_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3398 (exists A (v2_ordinal1(A) & v1_finset_1(A) & v1_ordinal1(A) & v3_ordinal1(A) & v1_card_1(A))) # label(rc2_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3399 (all A np__1 = k4_card_1(k1_tarski(A))) # label(t79_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3400 $T # label(t67_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3401 (all A all B (r1_tarski(k1_zfmisc_1(A),B) -> r2_hidden(k1_card_1(A),k1_card_1(B)) & -r2_wellord2(A,B))) # label(t45_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3402 (all A (v3_ordinal1(A) -> (v4_ordinal1(A) -> k1_xboole_0 = A | (all B (v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) -> (A = k1_relat_1(B) & (all C (v3_ordinal1(C) -> (r2_hidden(C,A) -> k3_card_1(C) = k1_funct_1(B,C)))) -> k3_card_1(A) = k1_card_1(k8_ordinal2(B)))))))) # label(t40_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3403 (all A v1_card_1(k1_card_1(A))) # label(dt_k1_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3404 $T # label(t63_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3405 $T # label(t2_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3406 (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]. 56.72/55.71 3407 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k1_nat_1(A,np__1) = k1_ordinal1(A))) # label(t52_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3408 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k2_card_1(k1_card_1(A)) = k1_card_1(k1_nat_1(A,np__1)))) # label(t76_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3409 (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]. 56.72/55.71 3410 (all A all B (r1_tarski(k1_card_1(A),k1_card_1(B)) <-> (exists C (v1_relat_1(C) & v1_funct_1(C) & v2_funct_1(C) & r1_tarski(k2_relat_1(C),B) & k1_relat_1(C) = A)))) # label(t26_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3411 $T # label(t62_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3412 (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]. 56.72/55.71 3413 (all A v1_card_1(k2_card_1(A))) # label(dt_k2_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3414 (all A (v1_finset_1(A) -> v1_finset_1(k2_card_1(A)))) # label(t82_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3415 (all A -r2_wellord2(A,k1_zfmisc_1(A))) # label(t29_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3416 (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]. 56.72/55.71 3417 (all A (v1_card_1(A) -> ((all B (v1_card_1(B) -> (r2_hidden(B,A) -> p1_s1_card_1(B)))) & v2_card_1(A) -> A = k1_xboole_0 | p1_s1_card_1(A)))) & (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]. 56.72/55.71 3418 (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]. 56.72/55.71 3419 $T # label(t70_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3420 (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]. 56.72/55.71 3421 $T # label(t54_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3422 (all A r2_hidden(k1_card_1(k1_xboole_0),k2_card_1(A))) # label(t33_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3423 (exists A v1_card_1(A)) # label(rc1_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3424 $T # label(d10_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3425 $T # label(t15_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3426 (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]. 56.72/55.71 3427 $T # label(t10_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3428 $T # label(t1_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3429 (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]. 56.72/55.71 3430 (all A (r2_hidden(A,k5_ordinal2) -> v1_card_1(A))) # label(t65_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3431 (all A all B all C all D (r2_hidden(C,A) & r2_hidden(D,B) & 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]. 56.72/55.71 3432 (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]. 56.72/55.71 3433 (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]. 56.72/55.71 3434 (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]. 56.72/55.71 3435 $T # label(t77_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3436 $T # label(t20_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3437 (all A (v3_ordinal1(A) -> (all B ((exists C (v5_ordinal1(C) & k1_ordinal2(C) = B & k1_relat_1(C) = k1_ordinal1(A) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_funct_1(C,D) = k1_card_1(k8_ordinal2(k2_ordinal1(C,D))) | k1_xboole_0 = D))) & v1_relat_1(C) & k1_card_1(k5_numbers) = k1_funct_1(C,k1_xboole_0) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = k2_card_1(k3_tarski(k1_tarski(k1_funct_1(C,D))))))) & v1_funct_1(C))) <-> k3_card_1(A) = B)))) # label(d8_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3438 $T # label(dt_k3_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3439 (all A (m1_subset_1(A,k5_numbers) -> v1_xcmplx_0(A) & v1_card_1(A) & v1_xreal_0(A) & v3_ordinal1(A) & v2_ordinal1(A) & v4_ordinal2(A) & -v3_xreal_0(A) & v1_ordinal1(A))) # label(cc2_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3440 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,k1_relat_1(B)) & v2_funct_1(B) -> r2_wellord2(A,k9_relat_1(B,A))))) # label(t60_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3441 (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]. 56.72/55.71 3442 (all A all B (k1_card_1(k1_tarski(B)) = k1_card_1(A) <-> (exists C k1_tarski(C) = A))) # label(t49_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.71 3443 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (k3_card_1(B) = k3_card_1(A) -> B = A))))) # label(t42_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3444 (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]. 56.72/55.72 3445 (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]. 56.72/55.72 3446 (all A all B all C all D (r1_xboole_0(A,B) & r1_xboole_0(C,D) & r2_wellord2(A,C) & r2_wellord2(B,D) -> r2_wellord2(k2_xboole_0(A,B),k2_xboole_0(C,D)))) # label(t58_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3447 $T # label(d4_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3448 (all A all B (r2_wellord2(A,k1_tarski(B)) <-> (exists C A = k1_tarski(C)))) # label(t48_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3449 (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]. 56.72/55.72 3450 $T # label(t53_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3451 (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]. 56.72/55.72 3452 (all A all B (r2_wellord2(A,B) & v1_finset_1(A) -> v1_finset_1(B))) # label(t68_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3453 (all A (v3_ordinal1(A) -> r2_hidden(A,k2_card_1(A)))) # label(t36_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3454 $T # label(d3_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3455 (all A (v1_card_1(A) <-> (exists B (v3_ordinal1(B) & B = A & (all C (v3_ordinal1(C) -> (r2_wellord2(C,B) -> r1_ordinal1(B,C)))))))) # label(d1_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3456 $T # label(t57_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3457 $T # label(t18_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3458 (all A all B (v1_card_1(B) -> (r2_wellord2(A,B) <-> k1_card_1(A) = B))) # label(d5_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3459 (all A (v1_card_1(A) -> v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A))) # label(cc1_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3460 (all A (v1_finset_1(A) & v1_card_1(A) -> (exists B (m2_subset_1(B,k1_numbers,k5_numbers) & A = k1_card_1(B))))) # label(t86_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3461 (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]. 56.72/55.72 3462 $T # label(t7_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3463 (all A k4_ordinal2 = k1_card_1(k1_tarski(A))) # label(t50_card_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3464 (all A exists B (m1_relset_1(B,k5_numbers,A) & v1_funct_1(B) & v1_finseq_1(B) & v1_finset_1(B) & v1_relat_1(B))) # label(rc2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3465 (all A all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_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]. 56.72/55.72 3466 (all A all B all 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)) & v1_funct_1(k11_finseq_1(A,B,C)))) # label(fc8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3467 (exists A (v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_xboole_0(A) & v1_finseq_1(A) & v2_funct_1(A))) # label(rc3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3468 (all A (v1_relat_1(k9_finseq_1(A)) & v1_funct_1(k9_finseq_1(A)))) # label(dt_k9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3469 (exists A all B (r2_hidden(B,A) <-> (exists C (v1_finseq_1(C) & B = C & p1_s4_finseq_1(C) & v1_relat_1(C) & v1_funct_1(C) & r2_hidden(C,k13_finseq_1(f1_s4_finseq_1)))))) # label(s4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3470 (all A (v1_finseq_1(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(k4_finseq_1(A),k4_finseq_1(k7_finseq_1(A,B))))))) # label(t39_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3471 (all A all B all C k7_finseq_1(k7_finseq_1(k9_finseq_1(A),k9_finseq_1(B)),k9_finseq_1(C)) = k11_finseq_1(A,B,C)) # label(d10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3472 $T # label(dt_k5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3473 (all A (v4_ordinal2(A) -> (all B (-v1_xboole_0(B) -> (exists C (A = k3_finseq_1(C) & m2_finseq_1(C,B))))))) # label(t24_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3474 (all A -v1_xboole_0(k13_finseq_1(A))) # label(fc9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3475 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & -v1_xboole_0(B) & v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> v1_funct_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) & -v1_xboole_0(k7_finseq_1(A,B)) & v1_relat_1(k7_finseq_1(A,B)))) # label(fc13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3476 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (B = k9_finseq_1(A) <-> k3_finseq_1(B) = np__1 & A = k1_funct_1(B,np__1)))) # label(t57_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3477 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (k10_finseq_1(A,B) = C <-> k1_funct_1(C,np__1) = A & k3_finseq_1(C) = np__2 & B = k1_funct_1(C,np__2)))) # label(t61_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3478 (all A (v1_funct_1(A) & v1_relat_1(A) -> -((exists B (m2_subset_1(B,k1_numbers,k5_numbers) & r1_tarski(k1_relat_1(A),k2_finseq_1(B)))) & (all B (v1_finseq_1(B) & v1_relat_1(B) & v1_funct_1(B) -> -r1_tarski(A,B)))))) # label(t15_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3479 (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))) -> r1_xreal_0(B,np__0) | r2_hidden(B,k2_finseq_1(A)) & r2_hidden(B,k2_finseq_1(k2_xcmplx_0(A,C)))))))))) # label(t82_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3480 (exists A (v1_funct_1(A) & v1_relat_1(A) & v2_finseq_1(A))) # label(rc5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3481 (all A (v4_ordinal2(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) & v1_finseq_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) & v1_finseq_1(C) -> (C = k7_relat_1(B,k2_finseq_1(A)) & r1_xreal_0(A,k3_finseq_1(B)) -> k3_finseq_1(C) = A & k2_finseq_1(A) = k4_finseq_1(C)))))))) # label(t21_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3482 (all A k9_finseq_1(A) = k5_finseq_1(A)) # label(redefinition_k9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3483 (all A (m2_finseq_1(k6_finseq_1(A),A) & v1_xboole_0(k6_finseq_1(A)))) # label(dt_k6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3484 (all A (v1_funct_1(A) & v1_relat_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_relat_1(k5_relat_1(B,A)) & v1_finseq_1(k5_relat_1(B,A)) & v1_funct_1(k5_relat_1(B,A))))))) # label(t20_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3485 $T # label(t13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3486 (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) -> (k1_xboole_0 = k7_finseq_1(A,B) -> k1_xboole_0 = A & B = k1_xboole_0))))) # label(t48_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3487 $T # label(dt_k13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3488 $T # label(dt_k10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3489 (all A (v1_relat_1(A) -> v1_relat_1(k17_finseq_1(A)))) # label(dt_k17_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3490 (exists A (v1_funct_1(A) & v1_finseq_1(A) & k3_finseq_1(A) = f1_s2_finseq_1 & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(B,k2_finseq_1(f1_s2_finseq_1)) -> f2_s2_finseq_1(B) = k1_funct_1(A,B)))) & v1_relat_1(A))) # label(s2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3491 (all A all B (m2_finseq_1(B,A) -> (all C (v4_ordinal2(C) -> (r1_xreal_0(k3_finseq_1(B),C) -> B = k16_finseq_1(A,B,C)))))) # label(t79_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3492 (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 ((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) & k4_finseq_1(A) = k2_finseq_1(f2_s5_finseq_1))) # label(s5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3493 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> ((all C all D (r2_hidden(k4_tarski(C,D),B) <-> (exists E (D = k1_funct_1(E,k3_finseq_1(E)) & k1_funct_1(E,np__1) = C & r1_xreal_0(np__1,k3_finseq_1(E)) & v1_relat_1(E) & v1_finseq_1(E) & (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_funct_1(E))) & r2_hidden(D,k3_relat_1(A)) & r2_hidden(C,k3_relat_1(A)))) <-> k17_finseq_1(A) = B))))) # label(d16_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3494 $T # label(t31_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3495 (all A all B all C all D (v1_finseq_1(D) & v1_relat_1(D) & v1_funct_1(D) -> (k11_finseq_1(A,B,C) = D <-> np__3 = k3_finseq_1(D) & C = k1_funct_1(D,np__3) & A = k1_funct_1(D,np__1) & B = k1_funct_1(D,np__2)))) # label(t62_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3496 (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]. 56.72/55.72 3497 (all A k1_xboole_0 = k6_finseq_1(A)) # label(d6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3498 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_tarski(k2_finseq_1(A),k2_finseq_1(B)) <-> r1_xreal_0(A,B)))))) # label(t7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3499 (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]. 56.72/55.72 3500 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> ((all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(B)) -> k1_funct_1(B,D) = k1_funct_1(C,k1_nat_1(k3_finseq_1(A),D))))) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(A)) -> k1_funct_1(C,D) = k1_funct_1(A,D)))) & k4_finseq_1(C) = k2_finseq_1(k1_nat_1(k3_finseq_1(A),k3_finseq_1(B))) <-> k7_finseq_1(A,B) = C))))))) # label(d7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3501 (all A (v1_finseq_1(A) & v1_relat_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_relat_1(A) & v1_finseq_1(A) -> p1_s3_finseq_1(A))) # label(s3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3502 (all A (v4_ordinal2(A) -> np__0 = A | r2_hidden(A,k2_finseq_1(A)))) # label(t5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3503 (all A ((exists B (v4_ordinal2(B) & r1_tarski(A,k2_finseq_1(B)))) -> (all B (m2_finseq_1(B,k5_numbers) -> (k2_relat_1(B) = A & (all C (v4_ordinal2(C) -> (all D (v4_ordinal2(D) -> (all E (v4_ordinal2(E) -> (all F (v4_ordinal2(F) -> -(r1_xreal_0(np__1,C) & -r1_xreal_0(D,C) & r1_xreal_0(D,k3_finseq_1(B)) & r1_xreal_0(F,E) & E = k1_funct_1(B,C) & F = k1_funct_1(B,D)))))))))) <-> k14_finseq_1(A) = B))))) # label(d13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3504 $T # label(t54_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3505 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> v1_relat_1(k8_relat_1(A,B)) & v2_finseq_1(k8_relat_1(A,B)) & v1_funct_1(k7_relat_1(B,A)) & v1_relat_1(k7_relat_1(B,A)) & v1_funct_1(k8_relat_1(A,B)) & v2_finseq_1(k7_relat_1(B,A)))) # label(t69_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3506 (exists A (-v1_xboole_0(A) & v1_finset_1(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A))) # label(rc8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3507 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> k4_finseq_1(A) = k1_relat_1(A))) # label(redefinition_k4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3508 (all A all B (v4_ordinal2(B) -> (r2_hidden(A,a_1_0_finseq_1(B)) <-> (exists C (m2_subset_1(C,k1_numbers,k5_numbers) & A = C & r1_xreal_0(C,B) & r1_xreal_0(np__1,C)))))) # label(fraenkel_a_1_0_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3509 (all A (v4_ordinal2(A) -> (all B (v1_funct_1(B) & v1_finseq_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]. 56.72/55.72 3510 (all A (v1_relat_1(A) & v1_funct_1(A) & v2_finseq_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]. 56.72/55.72 3511 (all A all B all C (k11_finseq_1(A,B,C) = k7_finseq_1(k9_finseq_1(A),k10_finseq_1(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]. 56.72/55.72 3512 (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]. 56.72/55.72 3513 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> v1_finset_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(cc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3514 (exists A (v2_funct_1(A) & v1_finset_1(A) & v1_relat_1(A) & v1_funct_1(A) & v1_xboole_0(A))) # label(rc6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3515 (all A all B (m1_finseq_1(B,A) -> v1_funct_1(k16_finseq_1(A,B,np__0)) & v1_relat_1(k16_finseq_1(A,B,np__0)) & v1_xboole_0(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)) & v2_funct_1(k16_finseq_1(A,B,np__0)))) # label(fc15_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3516 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> A = k7_relat_1(k7_finseq_1(A,B),k4_finseq_1(A)))))) # label(t33_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3517 $T # label(t34_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3518 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_xreal_0(A,B) -> k5_subset_1(k5_numbers,k2_finseq_1(B),k2_finseq_1(A)) = k2_finseq_1(A)))))) # label(t9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3519 (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]. 56.72/55.72 3520 (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]. 56.72/55.72 3521 (all A (v1_funct_1(A) & v1_relat_1(A) & v1_finseq_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_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]. 56.72/55.72 3522 (all A (v4_ordinal2(A) -> k2_finseq_1(A) = k4_xboole_0(k2_finseq_1(k2_xcmplx_0(A,np__1)),k1_tarski(k2_xcmplx_0(A,np__1))))) # label(t12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3523 (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_funct_1(C) & v1_relat_1(C) & v1_finseq_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)) & k7_finseq_1(C,D) = k7_finseq_1(A,B) & (all E (v1_funct_1(E) & v1_finseq_1(E) & v1_relat_1(E) -> C != k7_finseq_1(A,E)))))))))))) # label(t64_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3524 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) -> m2_finseq_1(k12_finseq_1(A,B),A))) # label(dt_k12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3525 (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(k2_relat_1(A),k2_relat_1(k7_finseq_1(B,A))))))) # label(t43_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3526 (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]. 56.72/55.72 3527 (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]. 56.72/55.72 3528 $T # label(t28_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3529 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (np__0 = k3_finseq_1(A) <-> k6_finseq_1(B) = A)))) # label(t32_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3530 (all A all B (v1_funct_1(A) & v1_finseq_1(A) & v1_finseq_1(B) & v1_relat_1(A) & v1_funct_1(B) & v1_relat_1(B) -> v1_finseq_1(k7_finseq_1(A,B)) & v1_funct_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]. 56.72/55.72 3531 (all A all B (v1_funct_1(B) & v1_relat_1(B) & v1_finseq_1(B) -> (m1_finseq_1(B,A) <-> r1_tarski(k2_relat_1(B),A)))) # label(d4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3532 (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]. 56.72/55.72 3533 (all A all B (v1_finseq_1(k10_finseq_1(A,B)) & v1_funct_1(k10_finseq_1(A,B)) & v1_relat_1(k10_finseq_1(A,B)) & v1_finset_1(k10_finseq_1(A,B)))) # label(fc7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3534 (all A k9_finseq_1(A) = k1_tarski(k4_tarski(np__1,A))) # label(t52_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3535 (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 (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)) & C = k1_nat_1(k3_finseq_1(A),D)))) & r2_hidden(C,k4_finseq_1(k7_finseq_1(A,B)))))))))) # label(t38_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3536 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> v2_finseq_1(A) & v1_relat_1(A) & v1_funct_1(A))) # label(t68_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3537 (all A all B all C (m1_finseq_1(C,A) & m1_finseq_1(B,A) -> k8_finseq_1(A,B,C) = k7_finseq_1(B,C))) # label(redefinition_k8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3538 (all A (v1_funct_1(k5_finseq_1(A)) & v1_relat_1(k5_finseq_1(A)))) # label(fc3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3539 (all A (v2_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k15_finseq_1(A)) & v1_finset_1(k15_finseq_1(A)) & v1_finseq_1(k15_finseq_1(A)) & v1_relat_1(k15_finseq_1(A)))) # label(fc10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.72 3540 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) & v1_finseq_1(B) -> k2_relat_1(k7_finseq_1(A,B)) = k2_xboole_0(k2_relat_1(A),k2_relat_1(B)))))) # label(t44_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3541 (all A (v1_fraenkel(k13_finseq_1(A)) & -v1_xboole_0(k13_finseq_1(A)))) # label(fc16_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3542 (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]. 56.72/55.73 3543 (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]. 56.72/55.73 3544 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B all C (p1_s1_finseq_1(A,B) & r2_hidden(A,k2_finseq_1(f1_s1_finseq_1)) & p1_s1_finseq_1(A,C) -> B = C)))) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> -((all B -p1_s1_finseq_1(A,B)) & r2_hidden(A,k2_finseq_1(f1_s1_finseq_1))))) -> (exists A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) & k2_finseq_1(f1_s1_finseq_1) = k4_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))))))) # label(s1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3545 (all A (v1_relat_1(A) -> (v1_finseq_1(A) <-> (exists B (m2_subset_1(B,k1_numbers,k5_numbers) & k1_relat_1(A) = k2_finseq_1(B)))))) # label(d2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3546 $T # label(t49_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3547 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_finseq_1(B) & v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_finseq_1(C) & v1_relat_1(C) & v1_funct_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]. 56.72/55.73 3548 (exists A (v1_funct_1(A) & v1_finset_1(A) & v1_relat_1(A) & -v1_xboole_0(A))) # label(rc7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3549 (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) -> r1_tarski(k2_relat_1(A),k2_relat_1(k7_finseq_1(A,B))))))) # label(t42_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3550 (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]. 56.72/55.73 3551 (all A (v1_funct_1(A) & v1_relat_1(A) & v1_finseq_1(A) -> -(k1_xboole_0 != A & (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C k7_finseq_1(B,k9_finseq_1(C)) != A)))))) # label(t63_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3552 (all A (v1_funct_1(A) & v1_relat_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]. 56.72/55.73 3553 $T # label(dt_k11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3554 (all A (v4_ordinal2(A) -> v1_finset_1(k1_finseq_1(A)))) # label(fc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3555 (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]. 56.72/55.73 3556 $T # label(t67_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3557 (all A all B ((all C (m2_finseq_1(C,A) <-> r2_hidden(C,B))) <-> B = k13_finseq_1(A))) # label(d11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3558 (all A all B (m2_finseq_1(B,A) -> (all C (v4_ordinal2(C) -> (r1_xreal_0(C,k3_finseq_1(B)) -> k3_finseq_1(k16_finseq_1(A,B,C)) = C))))) # label(t80_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3559 $T # label(t30_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3560 (all A r2_hidden(k1_xboole_0,k13_finseq_1(A))) # label(t66_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3561 (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]. 56.72/55.73 3562 (all A (v1_finset_1(A) & v1_funct_1(A) & v1_relat_1(A) -> v1_finset_1(k1_relat_1(A)))) # label(fc17_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3563 (all A all B k10_finseq_1(A,B) = k7_finseq_1(k9_finseq_1(A),k9_finseq_1(B))) # label(d9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3564 (all A (v4_ordinal2(A) -> A = k4_card_1(k2_finseq_1(A)))) # label(t78_finseq_1_AndLHS) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3565 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> A = k4_card_1(A) & k4_card_1(k1_card_1(A)) = A)) # label(t78_finseq_1_AndRHS) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3566 (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]. 56.72/55.73 3567 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> -((all D (m2_subset_1(D,k1_numbers,k5_numbers) -> -(r2_hidden(k1_nat_1(k3_finseq_1(C),D),k4_finseq_1(k7_finseq_1(C,B))) & D = A))) & r2_hidden(A,k4_finseq_1(B))))))) # label(t40_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3568 (exists A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A))) # label(rc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3569 (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]. 56.72/55.73 3570 (all A all B (m1_subset_1(B,A) & -v1_xboole_0(A) -> k5_finseq_1(B) = k12_finseq_1(A,B))) # label(redefinition_k12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3571 $T # label(t70_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3572 (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]. 56.72/55.73 3573 (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) -> (v2_funct_1(A) & v2_funct_1(B) & k2_relat_1(B) = k2_relat_1(A) -> k3_finseq_1(A) = k3_finseq_1(B)))))) # label(t65_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3574 (all A exists B m1_finseq_1(B,A)) # label(existence_m1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3575 (all A (v1_finset_1(A) <-> (exists B (v1_finseq_1(B) & v1_relat_1(B) & A = k2_relat_1(B) & v1_funct_1(B))))) # label(t73_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3576 (all A exists B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_xboole_0(B) & m1_finseq_1(B,A) & v1_finset_1(B) & v2_funct_1(B))) # label(rc4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3577 (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]. 56.72/55.73 3578 (all A k5_finseq_1(A) = k1_tarski(k4_tarski(np__1,A))) # label(d5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3579 (all A all B (m1_finseq_1(B,A) <-> m2_finseq_1(B,A))) # label(redefinition_m2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3580 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (k9_finseq_1(A) = B <-> A = k1_funct_1(B,np__1) & k2_finseq_1(np__1) = k1_relat_1(B)))) # label(d8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3581 (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]. 56.72/55.73 3582 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> k7_finseq_1(k1_xboole_0,A) = A & k7_finseq_1(A,k1_xboole_0) = A)) # label(t47_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3583 (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]. 56.72/55.73 3584 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,C) & r1_xreal_0(C,k3_finseq_1(B)) -> k1_funct_1(B,C) = k1_funct_1(k7_finseq_1(A,B),k1_nat_1(k3_finseq_1(A),C))))))))) # label(t86_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3585 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (k1_xboole_0 = A <-> k4_finseq_1(A) = k1_xboole_0))) # label(t26_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3586 (all A (v2_finseq_1(A) & v1_funct_1(A) & v1_relat_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]. 56.72/55.73 3587 (all A (v1_relat_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & -v1_xboole_0(k5_finseq_1(A)))) # label(fc12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3588 $T # label(t51_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3589 (all A (v4_ordinal2(A) -> k1_finseq_1(A) = k2_finseq_1(A))) # label(redefinition_k2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3590 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) & v1_finseq_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]. 56.72/55.73 3591 (all A (v1_finseq_1(A) & v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,C) & r1_xreal_0(C,k3_finseq_1(A)) -> k1_funct_1(A,C) = k1_funct_1(k7_finseq_1(A,B),C)))))))) # label(t85_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3592 (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) -> k3_finseq_1(k7_finseq_1(A,B)) = k1_nat_1(k3_finseq_1(A),k3_finseq_1(B)))))) # label(t35_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3593 (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]. 56.72/55.73 3594 $T # label(dt_k1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3595 (all A (v1_funct_1(A) & v1_relat_1(A) & v1_finseq_1(A) -> (k1_xboole_0 = A <-> k1_xboole_0 = k2_relat_1(A)))) # label(t27_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3596 (all A all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_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]. 56.72/55.73 3597 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_finseq_1(B) & v1_relat_1(B) & v1_funct_1(B) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,C) & r1_xreal_0(C,k3_finseq_1(A)) -> k1_funct_1(A,C) = k1_funct_1(B,C)))) & k3_finseq_1(B) = k3_finseq_1(A) -> A = B))))) # label(t18_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3598 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_finseq_1(B) & v1_relat_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]. 56.72/55.73 3599 (all A all B (v1_funct_1(B) & v1_relat_1(B) & v1_finseq_1(B) -> -((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(r2_hidden(C,k4_finseq_1(B)) & A = k4_tarski(C,k1_funct_1(B,C))))) & r2_hidden(A,B)))) # label(t16_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3600 $T # label(t53_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3601 (all A (v1_finseq_1(A) & v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (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]. 56.72/55.73 3602 (all A (v1_relat_1(A) & v1_finset_1(A) -> v1_finset_1(k2_relat_1(A)))) # label(fc11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3603 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (B = k9_finseq_1(A) <-> k1_tarski(A) = k2_relat_1(B) & k3_finseq_1(B) = np__1))) # label(t56_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3604 $T # label(t22_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3605 (all A all B (v1_funct_1(A) & v1_funct_1(B) & -v1_xboole_0(B) & v1_relat_1(B) & v1_finseq_1(B) & v1_finseq_1(A) & v1_relat_1(A) -> v1_funct_1(k7_finseq_1(B,A)) & -v1_xboole_0(k7_finseq_1(B,A)) & v1_relat_1(k7_finseq_1(B,A)) & v1_finseq_1(k7_finseq_1(B,A)) & v1_finset_1(k7_finseq_1(B,A)))) # label(fc14_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3606 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (k2_finseq_1(A) = k5_subset_1(k5_numbers,k2_finseq_1(A),k2_finseq_1(B)) -> r1_xreal_0(A,B)))))) # label(t10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3607 (all A all B (m2_finseq_1(B,A) -> m2_relset_1(B,k5_numbers,A) & v1_funct_1(B) & v1_finseq_1(B))) # label(dt_m2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3608 (all A m2_finseq_1(k1_xboole_0,A)) # label(t29_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3609 (all A m2_finseq_1(k14_finseq_1(A),k5_numbers)) # label(dt_k14_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3610 $T # label(t1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3611 (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 (v4_ordinal2(C) -> (r1_xreal_0(C,k3_finseq_1(k7_finseq_1(A,B))) -> k1_funct_1(k7_finseq_1(A,B),C) = k1_funct_1(B,k6_xcmplx_0(C,k3_finseq_1(A))) | r1_xreal_0(C,k3_finseq_1(A))))))))) # label(t37_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3612 (all A (v1_funct_1(A) & v1_relat_1(A) & v1_finseq_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(A,k7_finseq_1(B,C)) = k7_finseq_1(k7_finseq_1(A,B),C))))))) # label(t45_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3613 (all A exists B m2_finseq_1(B,A)) # label(existence_m2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3614 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r2_hidden(A,k2_finseq_1(B)) <-> r1_xreal_0(np__1,A) & r1_xreal_0(A,B)))))) # label(t3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3615 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (A = k1_xboole_0 <-> k3_finseq_1(A) = np__0))) # label(t25_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3616 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k2_finseq_1(B) = k1_relat_1(A) <-> B = k3_finseq_1(A)))))) # label(d3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3617 (all A all B all C (v1_funct_1(k11_finseq_1(A,B,C)) & v1_relat_1(k11_finseq_1(A,B,C)))) # label(fc6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3618 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) & v1_finseq_1(B) -> (k4_finseq_1(A) = k4_finseq_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)))) -> B = A))))) # label(t17_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3619 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers))) # label(dt_k3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3620 (all A (v4_ordinal2(A) -> k1_finseq_1(A) = a_1_0_finseq_1(A))) # label(d1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3621 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (k2_finseq_1(A) = k2_finseq_1(B) -> A = B))))) # label(t8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3622 (all A -((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> -r2_wellord2(A,k2_finseq_1(B)))) & v1_finset_1(A))) # label(t77_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3623 $T # label(t2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3624 (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) <-> k1_xboole_0 = A))) # label(t72_finseq_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3625 (all A (v1_relat_1(A) -> (all B (v1_relat_2(A) & r1_tarski(B,k3_relat_1(A)) -> k3_relat_1(k2_wellord1(A,B)) = B)))) # label(t181_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3626 $T # label(t154_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3627 (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]. 56.72/55.73 3628 (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]. 56.72/55.73 3629 $T # label(t22_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3630 $T # label(t60_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3631 (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]. 56.72/55.73 3632 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (r2_hidden(A,k1_orders_1(B)) <-> r1_tarski(A,B)))))) # label(t5_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3633 (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]. 56.72/55.73 3634 $T # label(t69_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3635 $T # label(t39_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3636 (all A (v1_relat_1(A) -> (all B all C (r1_tarski(C,B) & r2_orders_1(A,B) -> r2_orders_1(A,C))))) # label(t131_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3637 (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]. 56.72/55.73 3638 (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]. 56.72/55.73 3639 (all A (v1_relat_1(A) -> (all B (v6_relat_2(A) & r7_orders_1(A,B) -> r9_orders_1(A,B))))) # label(t159_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3640 $T # label(t48_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3641 $T # label(t116_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3642 (all A (v1_relat_1(A) -> (all B (r3_orders_1(A,B) -> v4_relat_2(k2_wellord1(A,B)) & v1_relat_2(k2_wellord1(A,B)) & v8_relat_2(k2_wellord1(A,B)) & m2_relset_1(k2_wellord1(A,B),B,B) & v1_partfun1(k2_wellord1(A,B),B,B))))) # label(t142_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3643 $T # label(t82_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3644 $T # label(t76_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3645 $T # label(t83_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3646 $T # label(t101_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3647 (all A (v1_relat_1(A) -> (all B all C (r3_orders_1(A,B) & r1_tarski(C,B) -> r3_orders_1(A,C))))) # label(t134_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3648 $T # label(t17_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3649 (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]. 56.72/55.73 3650 $T # label(t27_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3651 $T # label(t78_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.73 3652 $T # label(t144_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3653 $T # label(t40_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3654 (all A (-v1_xboole_0(A) -> -v1_xboole_0(k1_orders_1(A)))) # label(fc1_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3655 $T # label(t56_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3656 (all A (v1_relat_1(A) -> (all B -(r2_orders_1(A,B) & (all C -r6_orders_1(A,C)) & r4_orders_1(A,B) & k3_relat_1(A) = B)))) # label(t173_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3657 (all A (v1_relat_1(A) -> (v2_orders_1(A) <-> v4_relat_2(A) & v1_relat_2(A) & v8_relat_2(A)))) # label(d4_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3658 $T # label(t30_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3659 (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]. 56.72/55.74 3660 (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) -> v2_orders_1(B))) # label(t110_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3661 (all A (v1_relat_1(A) -> (all B (r9_orders_1(A,B) & v4_relat_2(A) -> r7_orders_1(A,B))))) # label(t157_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3662 $T # label(t103_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3663 $T # label(t42_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3664 $T # label(dt_k1_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3665 $T # label(t41_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3666 (all A (v1_relat_1(A) -> (all B (r6_orders_1(A,B) <-> r2_hidden(B,k3_relat_1(A)) & (all C -(r2_hidden(k4_tarski(B,C),A) & r2_hidden(C,k3_relat_1(A)) & C != B)))))) # label(d11_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3667 (all A (v1_relat_1(A) -> (all B ((all C -(r1_tarski(C,B) & (all D -((all E (r2_hidden(E,C) -> r2_hidden(k4_tarski(E,D),A))) & r2_hidden(D,B))) & v3_orders_1(k2_wellord1(A,C)))) <-> r4_orders_1(A,B))))) # label(d9_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3668 $T # label(t45_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3669 (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) & r2_hidden(C,k3_relat_1(A)) & C != B)))))) # label(d12_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3670 (all A (v1_relat_1(A) -> (v8_relat_2(A) & v6_relat_2(A) & v4_relat_2(A) & v1_relat_2(A) <-> v3_orders_1(A)))) # label(d5_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3671 (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]. 56.72/55.74 3672 $T # label(t28_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3673 (all A (v1_relat_1(A) -> (v2_orders_1(A) -> v1_orders_1(A)))) # label(t109_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3674 (all A -((all B -((all C -(r2_hidden(C,A) & C != B & r1_tarski(B,C))) & r2_hidden(B,A))) & (all B (r1_tarski(B,A) & v6_ordinal1(B) -> B = k1_xboole_0 | r2_hidden(k3_tarski(B),A))) & k1_xboole_0 != A)) # label(t177_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3675 (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 -(r1_tarski(B,A) & v6_ordinal1(B) & (all C -(r2_hidden(C,A) & (all D (r2_hidden(D,B) -> r1_tarski(D,C))))))))) # label(t175_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3676 (all A (v1_relat_1(A) -> (v1_orders_1(A) <-> v1_relat_2(A) & v8_relat_2(A)))) # label(d3_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3677 $T # label(t123_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3678 (all A all B (v8_relat_2(B) & v1_partfun1(B,A,A) & v1_relat_2(B) & m2_relset_1(B,A,A) & v4_relat_2(B) -> A = k3_relat_1(B))) # label(t100_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3679 (all A all B (m2_relset_1(B,A,A) -> (r1_relat_2(B,A) -> A = k3_relat_1(B) & k4_relset_1(A,A,B) = A))) # label(t98_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3680 (all A (v1_relat_1(A) -> (all B -(k1_xboole_0 = B & r4_orders_1(A,B))))) # label(t149_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3681 $T # label(t64_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3682 $T # label(t34_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3683 (all A (v1_relat_1(A) -> (all B (r2_wellord1(A,B) -> v1_partfun1(k2_wellord1(A,B),B,B) & m2_relset_1(k2_wellord1(A,B),B,B) & v1_relat_2(k2_wellord1(A,B)) & v4_relat_2(k2_wellord1(A,B)) & v8_relat_2(k2_wellord1(A,B)))))) # label(t143_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3684 $T # label(t59_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3685 (all A (v1_relat_1(A) -> (all B all C (r6_relat_2(A,B) & r1_tarski(C,B) -> r6_relat_2(A,C))))) # label(t186_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3686 $T # label(t155_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3687 (all A all B (v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v4_relat_2(B) & v1_relat_2(B) & v8_relat_2(B) -> r2_orders_1(B,A))) # label(t140_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3688 (all A all B (v1_relat_1(B) -> (r1_relat_2(B,A) & r6_relat_2(B,A) <-> r7_relat_2(B,A)))) # label(t92_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3689 (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]. 56.72/55.74 3690 (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]. 56.72/55.74 3691 $T # label(t1_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3692 (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) | C = B)))))) # label(d13_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3693 (all A -((all B (v6_ordinal1(B) & r1_tarski(B,A) -> r2_hidden(k1_setfam_1(B),A) | k1_xboole_0 = B)) & (all B -(r2_hidden(B,A) & (all C -(r2_hidden(C,A) & C != B & r1_tarski(C,B))))) & k1_xboole_0 != A)) # label(t178_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3694 (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]. 56.72/55.74 3695 (all A (v1_relat_1(A) -> (all B (r3_orders_1(A,B) <-> r1_relat_2(A,B) & r6_relat_2(A,B) & r8_relat_2(A,B) & r4_relat_2(A,B))))) # label(d8_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3696 (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]. 56.72/55.74 3697 (all A (v1_relat_1(A) -> (all B (r5_orders_1(k4_relat_1(A),B) <-> r4_orders_1(A,B))))) # label(t151_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3698 $T # label(t147_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3699 (all A (v1_relat_1(A) -> (all B (r5_orders_1(A,B) <-> r4_orders_1(k4_relat_1(A),B))))) # label(t152_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3700 (all A all B all C all D all E (v8_relat_2(E) & v4_relat_2(E) & m2_relset_1(E,A,A) & v1_partfun1(E,A,A) & v1_relat_2(E) -> (r2_hidden(C,A) & r2_hidden(D,A) & r2_hidden(B,A) & r2_hidden(k4_tarski(B,C),E) & r2_hidden(k4_tarski(C,D),E) -> r2_hidden(k4_tarski(B,D),E)))) # label(t14_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3701 (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]. 56.72/55.74 3702 (all A all B all C (v1_relat_1(C) -> (r4_relat_2(C,A) & r1_tarski(B,A) -> r4_relat_2(C,B)))) # label(t94_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.72/55.74 3703 $T # label(t58_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3704 $T # label(t3_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3705 $T # label(t20_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3706 $T # label(t10_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3707 $T # label(t38_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3708 $T # label(t46_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3709 (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]. 56.78/55.79 3710 $T # label(t2_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3711 $T # label(t44_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3712 (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]. 56.78/55.79 3713 (all A all B (v4_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v1_relat_2(B) -> r1_orders_1(B,A))) # label(t139_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3714 $T # label(t88_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3715 (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]. 56.78/55.79 3716 (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]. 56.78/55.79 3717 $T # label(t11_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3718 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> v1_orders_1(A) & v3_orders_1(A) & v2_orders_1(A)))) # label(t107_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3719 (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) -> (v6_relat_2(B) -> v3_orders_1(B)))) # label(t112_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3720 (all A (-v1_xboole_0(A) -> (-r2_hidden(k1_xboole_0,A) -> (all B (v1_funct_2(B,A,k3_tarski(A)) & m2_relset_1(B,A,k3_tarski(A)) & v1_funct_1(B) -> (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]. 56.78/55.79 3721 $T # label(t29_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3722 $T # label(t31_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3723 $T # label(t62_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3724 $T # label(t53_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3725 $T # label(t72_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3726 $T # label(t43_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3727 (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]. 56.78/55.79 3728 $T # label(t54_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3729 $T # label(t49_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3730 (all A -((all B (m1_subset_1(B,f1_s1_orders_1) -> (exists C (r2_hidden(C,A) & m1_subset_1(C,f1_s1_orders_1) & -p1_s1_orders_1(C,B))))) & r1_tarski(A,f1_s1_orders_1) & (all B (m1_subset_1(B,f1_s1_orders_1) -> (all C (m1_subset_1(C,f1_s1_orders_1) -> -(r2_hidden(C,A) & -p1_s1_orders_1(B,C) & -p1_s1_orders_1(C,B) & r2_hidden(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(B,C) & p1_s1_orders_1(A,B) -> p1_s1_orders_1(A,C)))))))) & (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(A,B) & p1_s1_orders_1(B,A) -> B = A))))) -> (exists A ((all B (m1_subset_1(B,f1_s1_orders_1) -> -(p1_s1_orders_1(A,B) & A != B))) & m1_subset_1(A,f1_s1_orders_1))) # label(s1_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3731 $T # label(t168_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3732 $T # label(t32_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3733 $T # label(t18_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3734 (all A (v1_relat_1(A) -> (all B -(B = k3_relat_1(A) & (all C (v1_relat_1(C) -> -(B = k3_relat_1(C) & r3_orders_1(C,B) & r1_tarski(A,C)))) & r2_orders_1(A,B))))) # label(t179_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3735 (all A all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v4_relat_2(B) & v8_relat_2(B) & v1_relat_2(B) -> v1_orders_1(B))) # label(t111_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3736 (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]. 56.78/55.79 3737 $T # label(t153_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3738 $T # label(t84_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3739 $T # label(t80_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3740 $T # label(t81_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3741 (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]. 56.78/55.79 3742 $T # label(t167_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3743 $T # label(t89_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3744 (all A (v1_relat_1(A) -> (all B (r2_orders_1(A,B) -> v4_relat_2(k2_wellord1(A,B)) & m2_relset_1(k2_wellord1(A,B),B,B) & v8_relat_2(k2_wellord1(A,B)) & v1_partfun1(k2_wellord1(A,B),B,B) & v1_relat_2(k2_wellord1(A,B)))))) # label(t141_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3745 $T # label(t63_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3746 $T # label(t77_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3747 $T # label(t21_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3748 $T # label(t71_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3749 $T # label(t50_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3750 $T # label(t86_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3751 (all A (v1_relat_1(A) -> (v3_orders_1(A) -> v2_orders_1(A) & v1_orders_1(A)))) # label(t108_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3752 $T # label(t24_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3753 (all A (v1_relat_1(A) -> (all B (r2_hidden(B,k3_relat_1(A)) & (all C (r2_hidden(C,k3_relat_1(A)) -> C = B | r2_hidden(k4_tarski(B,C),A))) <-> r9_orders_1(A,B))))) # label(d14_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3754 $T # label(t61_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3755 $T # label(t68_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3756 (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]. 56.78/55.79 3757 $T # label(t75_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3758 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B -(v1_finset_1(B) & r1_tarski(B,k2_relat_1(A)) & (all C -(v1_finset_1(C) & r1_tarski(C,k1_relat_1(A)) & k9_relat_1(A,C) = B)))))) # label(t195_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3759 $T # label(t170_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3760 (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]. 56.78/55.79 3761 $T # label(t25_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3762 $T # label(t23_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3763 (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]. 56.78/55.79 3764 $T # label(t74_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3765 $T # label(t36_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3766 $T # label(t16_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3767 $T # label(t26_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3768 (all A (-(k3_tarski(A) != k1_xboole_0 & (all B -(r2_hidden(B,A) & k1_xboole_0 != B))) & -(k1_xboole_0 = k3_tarski(A) & (exists B (k1_xboole_0 != B & r2_hidden(B,A)))))) # label(t91_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3769 (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]. 56.78/55.79 3770 (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]. 56.78/55.79 3771 $T # label(t15_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3772 (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]. 56.78/55.79 3773 $T # label(t19_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3774 $T # label(t57_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3775 (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]. 56.78/55.79 3776 (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]. 56.78/55.79 3777 (all A (v1_relat_1(A) -> (all B all C (r1_tarski(C,k3_relat_1(A)) & r8_orders_1(A,B) & v1_relat_2(A) & r2_hidden(B,C) -> r4_orders_1(A,C))))) # label(t161_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3778 (all A all B all C (v1_relat_1(C) -> (r8_relat_2(C,A) & r1_tarski(B,A) -> r8_relat_2(C,B)))) # label(t95_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3779 (all A (v1_relat_1(A) -> (all B all C (r2_wellord1(A,B) & r1_tarski(C,B) -> r2_wellord1(A,C))))) # label(t187_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3780 (all A (r1_orders_1(k6_partfun1(A),A) & r2_orders_1(k6_partfun1(A),A))) # label(t146_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3781 (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]. 56.78/55.79 3782 (all A (-v1_xboole_0(A) -> (exists B m1_orders_1(B,A)))) # label(existence_m1_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3783 (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]. 56.78/55.79 3784 $T # label(t52_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3785 (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]. 56.78/55.79 3786 $T # label(t8_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3787 $T # label(t9_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.79 3788 $T # label(t117_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.80 3789 (all A all B all C all D (v1_relat_2(D) & v1_partfun1(D,A,A) & m2_relset_1(D,A,A) & v8_relat_2(D) & v4_relat_2(D) -> (r2_hidden(C,A) & r2_hidden(B,A) & r2_hidden(k4_tarski(B,C),D) & r2_hidden(k4_tarski(C,B),D) -> B = C))) # label(t13_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.80 3790 $T # label(t122_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.80 3791 $T # label(t47_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.80 3792 (all A (v1_relat_1(A) -> (all B (r1_orders_1(A,B) <-> r1_relat_2(A,B) & r8_relat_2(A,B))))) # label(d6_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.80 3793 (all A (v1_relat_1(A) -> (all B all C (r1_tarski(C,k3_relat_1(A)) & r9_orders_1(A,B) & r2_hidden(B,C) & v1_relat_2(A) -> r5_orders_1(A,C))))) # label(t162_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.78/55.80 3794 (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]. 56.83/55.85 3795 (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]. 56.83/55.85 3796 $T # label(t55_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3797 $T # label(t65_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3798 $T # label(t70_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3799 $T # label(t67_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3800 (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]. 56.83/55.85 3801 $T # label(t79_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3802 $T # label(t145_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3803 $T # label(t156_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3804 $T # label(t85_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3805 $T # label(t33_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3806 $T # label(t148_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3807 $T # label(t37_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3808 (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]. 56.83/55.85 3809 $T # label(t73_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3810 (all A (-v1_xboole_0(A) -> r2_hidden(A,k1_orders_1(A)))) # label(t7_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3811 $T # label(t102_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3812 (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) -> A = k4_relset_1(A,A,B) & k5_relset_1(A,A,B) = A)) # label(t99_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3813 (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]. 56.83/55.85 3814 (all A -((all B -(r2_hidden(B,A) & (all C -(r2_hidden(C,A) & r1_tarski(C,B) & B != C)))) & A != k1_xboole_0 & (all B -(r1_tarski(B,A) & (all C -((all D (r2_hidden(D,B) -> r1_tarski(C,D))) & r2_hidden(C,A))) & v6_ordinal1(B))))) # label(t176_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3815 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (m1_subset_1(A,k1_zfmisc_1(B)) <-> r2_hidden(A,k1_orders_1(B))))))) # label(t6_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3816 $T # label(t118_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3817 (all A (v1_relat_1(A) -> (all B (r2_wellord1(A,B) -> r1_orders_1(A,B) & r2_orders_1(A,B) & r3_orders_1(A,B))))) # label(t124_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3818 (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]. 56.83/55.85 3819 (all A (v2_orders_1(k6_partfun1(A)) & v1_orders_1(k6_partfun1(A)))) # label(t120_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3820 $T # label(t171_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3821 (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) -> B = A))))) & (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(B,C) & p1_s2_orders_1(A,B) -> 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 (-p1_s2_orders_1(B,C) & m1_subset_1(C,f1_s2_orders_1) & r2_hidden(C,A))))) & (all B (m1_subset_1(B,f1_s2_orders_1) -> (all C (m1_subset_1(C,f1_s2_orders_1) -> -(-p1_s2_orders_1(B,C) & r2_hidden(C,A) & -p1_s2_orders_1(C,B) & r2_hidden(B,A)))))))) -> (exists A ((all B (m1_subset_1(B,f1_s2_orders_1) -> -(p1_s2_orders_1(B,A) & B != A))) & m1_subset_1(A,f1_s2_orders_1))) # label(s2_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3822 (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]. 56.83/55.85 3823 $T # label(t51_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3824 $T # label(t87_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3825 (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]. 56.83/55.85 3826 (all A all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) -> k3_relat_1(B) = A)) # label(t97_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3827 (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]. 56.83/55.85 3828 $T # label(t66_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3829 (all A (v1_relat_1(A) -> (all B (r5_orders_1(A,B) <-> (all C -((all D -(r2_hidden(D,B) & (all E (r2_hidden(E,C) -> r2_hidden(k4_tarski(D,E),A))))) & v3_orders_1(k2_wellord1(A,C)) & r1_tarski(C,B))))))) # label(d10_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3830 $T # label(t121_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3831 (all A (v1_relat_1(A) -> (all B -(r2_orders_1(A,B) & r5_orders_1(A,B) & (all C -r7_orders_1(A,C)) & B = k3_relat_1(A))))) # label(t174_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3832 (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]. 56.83/55.85 3833 $T # label(t35_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3834 (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]. 56.83/55.85 3835 $T # label(t172_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3836 $T # label(t90_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3837 (all A (v1_relat_1(A) -> (all B (r6_orders_1(k4_relat_1(A),B) <-> r7_orders_1(A,B))))) # label(t163_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3838 $T # label(t169_orders_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3839 (all A all B (m1_relset_1(B,A,A) & v3_relat_2(B) & v1_partfun1(B,A,A) & v8_relat_2(B) -> k8_eqrel_1(A,B) = k7_eqrel_1(A,B))) # label(redefinition_k8_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3840 (all A all B (m2_relset_1(B,A,A) -> (exists C (v3_relat_2(C) & v1_partfun1(C,A,A) & (all D (v3_relat_2(D) & v1_partfun1(D,A,A) & v8_relat_2(D) & m2_relset_1(D,A,A) -> (r1_tarski(B,D) -> r1_tarski(C,D)))) & m2_relset_1(C,A,A) & r1_tarski(B,C) & v8_relat_2(C))))) # label(t20_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3841 (all A all B all C (m1_relset_1(B,A,A) & m1_relset_1(C,A,A) -> k3_xboole_0(B,C) = k2_eqrel_1(A,B,C))) # label(redefinition_k2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3842 (all A all B (v1_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> -((exists C r2_hidden(C,A)) & k1_xboole_0 = B))) # label(t14_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3843 $T # label(t15_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3844 (all A k2_zfmisc_1(A,A) = k1_eqrel_1(A)) # label(d1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3845 (all A all B (v3_relat_2(B) & m2_relset_1(B,A,A) & v8_relat_2(B) & v1_partfun1(B,A,A) -> (all C (v8_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v3_relat_2(C) -> (all D (v8_relat_2(D) & v1_partfun1(D,A,A) & m2_relset_1(D,A,A) & v3_relat_2(D) -> (D = k3_eqrel_1(A,B,C) -> (all E -(k6_eqrel_1(A,D,E) != k6_eqrel_1(A,B,E) & k6_eqrel_1(A,D,E) != k6_eqrel_1(A,C,E) & r2_hidden(E,A)))))))))) # label(t37_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3846 (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]. 56.83/55.85 3847 (all A all B (m1_eqrel_1(B,A) -> v1_setfam_1(B))) # label(cc2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3848 (all A all B (m2_relset_1(B,A,A) & v3_relat_2(B) & v1_partfun1(B,A,A) & v1_relat_2(B) -> (all C (r2_hidden(C,A) -> r2_hidden(C,k6_eqrel_1(A,B,C)))))) # label(t28_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3849 $T # label(t41_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3850 (all A all B all C (m1_relset_1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(C,A,A) & v1_partfun1(C,A,A) & v8_relat_2(C) & v3_relat_2(C) -> k4_eqrel_1(A,B,C) = k4_eqrel_1(A,C,B))) # label(commutativity_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3851 (all A all B (v8_relat_2(B) & v3_relat_2(B) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) -> m1_subset_1(k7_eqrel_1(A,B),k1_zfmisc_1(k1_zfmisc_1(A))))) # label(dt_k7_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3852 (all A all B all C (v3_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v8_relat_2(C) -> (all D (r2_hidden(D,A) -> (r2_hidden(B,k6_eqrel_1(A,C,D)) <-> k6_eqrel_1(A,C,B) = k6_eqrel_1(A,C,D)))))) # label(t31_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3853 (all A (v1_relat_2(k1_eqrel_1(A)) & v1_partfun1(k1_eqrel_1(A),A,A) & v3_relat_2(k1_eqrel_1(A)) & v1_relat_1(k1_eqrel_1(A)) & v8_relat_2(k1_eqrel_1(A)))) # label(fc2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3854 (all A (m2_relset_1(k6_partfun1(A),A,A) & v3_relat_2(k6_partfun1(A)) & v1_partfun1(k6_partfun1(A),A,A) & v8_relat_2(k6_partfun1(A)))) # label(t6_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3855 (all A all B all C all D (v1_partfun1(D,A,A) & m2_relset_1(D,A,A) & v3_relat_2(D) -> (r2_hidden(k4_tarski(B,C),D) -> r2_hidden(k4_tarski(C,B),D)))) # label(t12_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3856 (all A (v1_relat_2(k1_eqrel_1(A)) & v1_partfun1(k1_eqrel_1(A),A,A) & v1_relat_1(k1_eqrel_1(A)))) # label(fc1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3857 (all A all B (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> (all C all D -(-r1_xboole_0(k6_eqrel_1(A,B,C),k6_eqrel_1(A,B,D)) & r2_hidden(D,A) & k6_eqrel_1(A,B,D) != k6_eqrel_1(A,B,C) & r2_hidden(C,A))))) # label(t32_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3858 (all A all B all C all D (v3_relat_2(D) & v8_relat_2(D) & m2_relset_1(D,B,B) & v1_partfun1(D,B,B) -> (all E (v8_relat_2(E) & v1_partfun1(E,B,B) & m2_relset_1(E,B,B) & v3_relat_2(E) -> (r2_hidden(A,B) -> ((exists F (k1_funct_1(F,np__1) = A & r1_xreal_0(np__1,k3_finseq_1(F)) & v1_funct_1(F) & v1_relat_1(F) & v1_finseq_1(F) & k1_funct_1(F,k3_finseq_1(F)) = C & (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,G) -> r2_hidden(k4_tarski(k1_funct_1(F,G),k1_funct_1(F,k1_nat_1(G,np__1))),k3_eqrel_1(B,D,E)) | r1_xreal_0(k3_finseq_1(F),G)))))) <-> r2_hidden(k4_tarski(A,C),k5_eqrel_1(B,D,E)))))))) # label(t36_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3859 (all A all B (v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) -> (k1_xboole_0 = A -> k7_eqrel_1(A,B) = k1_xboole_0))) # label(t40_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3860 (all A (r1_relat_2(k6_partfun1(A),A) & r8_relat_2(k6_partfun1(A),A) & r3_relat_2(k6_partfun1(A),A))) # label(t4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3861 $T # label(t10_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3862 (all A all B all C (v3_relat_2(C) & v3_relat_2(B) & m1_relset_1(B,A,A) & v1_partfun1(C,A,A) & m1_relset_1(C,A,A) & v8_relat_2(C) & v1_partfun1(B,A,A) & v8_relat_2(B) -> v1_partfun1(k4_eqrel_1(A,B,C),A,A) & m2_relset_1(k4_eqrel_1(A,B,C),A,A) & v3_relat_2(k4_eqrel_1(A,B,C)) & v8_relat_2(k4_eqrel_1(A,B,C)))) # label(dt_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3863 (all A all B all C (m1_relset_1(B,A,A) & m1_relset_1(C,A,A) -> m2_relset_1(k2_eqrel_1(A,B,C),A,A))) # label(dt_k2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3864 (all A all B (v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v3_relat_2(B) & v1_relat_2(B) -> (all C k6_eqrel_1(A,B,C) = k10_relset_1(A,A,B,k1_tarski(C))))) # label(d4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3865 (all A all B all C (v3_relat_2(B) & v3_relat_2(C) & v8_relat_2(C) & v8_relat_2(B) & v1_partfun1(C,A,A) & m1_relset_1(C,A,A) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) -> k3_xboole_0(B,C) = k4_eqrel_1(A,B,C))) # label(redefinition_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3866 (all A all B (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> ((all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(D,C) <-> (exists E (D = k6_eqrel_1(A,B,E) & r2_hidden(E,A)))))) <-> C = k7_eqrel_1(A,B)))))) # label(d5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3867 (all A all B (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> (all C (v8_relat_2(C) & v3_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) -> (all D (m2_relset_1(D,A,A) & v1_partfun1(D,A,A) & v8_relat_2(D) & v3_relat_2(D) -> (r1_tarski(k3_eqrel_1(A,B,C),D) & (all E (v8_relat_2(E) & v1_partfun1(E,A,A) & v3_relat_2(E) & m2_relset_1(E,A,A) -> (r1_tarski(k3_eqrel_1(A,B,C),E) -> r1_tarski(D,E)))) <-> k5_eqrel_1(A,B,C) = D))))))) # label(d3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3868 $T # label(t8_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3869 (all A all B (v3_relat_2(B) & v1_partfun1(B,A,A) & v1_relat_2(B) & m2_relset_1(B,A,A) -> (all C -((all D -r2_hidden(C,k6_eqrel_1(A,B,D))) & r2_hidden(C,A))))) # label(t29_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3870 $T # label(t2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3871 (all A all B (m1_eqrel_1(B,A) -> (exists C (m2_relset_1(C,A,A) & v8_relat_2(C) & v1_partfun1(C,A,A) & k7_eqrel_1(A,C) = B & v3_relat_2(C))))) # label(t43_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3872 (all A all B (v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) & m2_relset_1(B,A,A) -> k4_eqrel_1(A,k6_partfun1(A),B) = k6_partfun1(A))) # label(t17_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3873 (all A all B all C (v3_relat_2(C) & v1_partfun1(C,B,B) & m2_relset_1(C,B,B) & v8_relat_2(C) -> -(r2_hidden(A,k7_eqrel_1(B,C)) & (all D (m1_subset_1(D,B) -> k6_eqrel_1(B,C,D) != A))))) # label(t45_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3874 (all A all B all C (v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v1_partfun1(C,A,A) & m1_relset_1(C,A,A) & v8_relat_2(C) & v3_relat_2(C) & v3_relat_2(B) -> k5_eqrel_1(A,B,C) = k5_eqrel_1(A,C,B))) # label(commutativity_k5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3875 $T # label(t9_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3876 (all A all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> (all C (v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v8_relat_2(C) & v3_relat_2(C) -> B = k4_eqrel_1(A,B,k5_eqrel_1(A,B,C)))))) # label(t24_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3877 (all A (v1_partfun1(k1_eqrel_1(A),A,A) & v8_relat_2(k1_eqrel_1(A)) & m2_relset_1(k1_eqrel_1(A),A,A) & v3_relat_2(k1_eqrel_1(A)))) # label(t7_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3878 (all A all B all C (v1_partfun1(C,A,A) & v3_relat_2(C) & v8_relat_2(C) & m2_relset_1(C,A,A) -> (all D (r2_hidden(D,A) -> (r2_hidden(k4_tarski(D,B),C) <-> k6_eqrel_1(A,C,B) = k6_eqrel_1(A,C,D)))))) # label(t44_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.83/55.85 3879 (all A all B all C all D (v1_partfun1(D,A,A) & m2_relset_1(D,A,A) & v1_relat_2(D) & v3_relat_2(D) -> (r2_hidden(k4_tarski(B,C),D) <-> r2_hidden(B,k6_eqrel_1(A,D,C))))) # label(t27_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.85 3880 (all A all B (m2_relset_1(B,A,A) -> (v3_relat_2(B) & k3_relat_1(B) = A & v1_relat_2(B) & v8_relat_2(B) <-> v1_partfun1(B,A,A) & v8_relat_2(B) & m2_relset_1(B,A,A) & v3_relat_2(B)))) # label(t16_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.85 3881 $T # label(d2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.85 3882 (all A all B (m2_relset_1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) & v1_partfun1(B,A,A) -> m1_eqrel_1(k7_eqrel_1(A,B),A))) # label(t42_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.85 3883 (all A all B (m1_relset_1(B,A,A) & v8_relat_2(B) & v1_partfun1(B,A,A) & v3_relat_2(B) & -v1_xboole_0(A) -> -v1_xboole_0(k7_eqrel_1(A,B)))) # label(fc3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.85 3884 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k1_xboole_0 != A -> (m1_eqrel_1(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r2_hidden(C,B) -> C != k1_xboole_0 & (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> -(r2_hidden(D,B) & C != D & -r1_xboole_0(C,D))))))) & k5_setfam_1(A,B) = A)) & (k1_xboole_0 = A -> (B = k1_xboole_0 <-> m1_eqrel_1(B,A))))) # label(d6_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.85 3885 $T # label(t26_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.85 3886 (all A all B all C (v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v1_relat_2(B) & v3_relat_2(B) -> m1_subset_1(k6_eqrel_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k6_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.85 3887 (all A all B (v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) & m2_relset_1(B,A,A) -> (all C (m2_relset_1(C,A,A) & v8_relat_2(C) & v3_relat_2(C) & v1_partfun1(C,A,A) -> B = k5_eqrel_1(A,B,k4_eqrel_1(A,B,C)))))) # label(t25_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.85 3888 (all A all B all C all D all E (m2_relset_1(E,A,A) & v1_partfun1(E,A,A) & v8_relat_2(E) -> (r2_hidden(k4_tarski(C,D),E) & r2_hidden(k4_tarski(B,C),E) -> r2_hidden(k4_tarski(B,D),E)))) # label(t13_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.85 3889 $T # label(t5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.85 3890 $T # label(t3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.85 3891 (all A all B all C (v3_relat_2(B) & v8_relat_2(B) & v8_relat_2(C) & m1_relset_1(C,A,A) & v1_partfun1(C,A,A) & v3_relat_2(C) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) -> k5_eqrel_1(A,B,B) = B)) # label(idempotence_k5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.85 3892 (all A all B (v1_partfun1(B,A,A) & v8_relat_2(B) & -v1_xboole_0(A) & m1_relset_1(B,A,A) & v3_relat_2(B) -> v1_setfam_1(k7_eqrel_1(A,B)) & -v1_xboole_0(k7_eqrel_1(A,B)))) # label(fc4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.85 3893 (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]. 56.88/55.85 3894 (all A all B (r2_hidden(B,A) -> k6_eqrel_1(A,k1_eqrel_1(A),B) = A)) # label(t34_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.85 3895 (all A all B (m2_relset_1(B,A,A) -> B = k2_eqrel_1(A,k1_eqrel_1(A),B))) # label(t18_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.85 3896 (all A all B all C (m1_relset_1(B,A,A) & v3_relat_2(B) & v3_relat_2(C) & v1_partfun1(C,A,A) & m1_relset_1(C,A,A) & v8_relat_2(C) & v1_partfun1(B,A,A) & v8_relat_2(B) -> m2_relset_1(k5_eqrel_1(A,B,C),A,A) & v8_relat_2(k5_eqrel_1(A,B,C)) & v1_partfun1(k5_eqrel_1(A,B,C),A,A) & v3_relat_2(k5_eqrel_1(A,B,C)))) # label(dt_k5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.85 3897 (all A all B all C (m2_relset_1(C,A,A) & v1_relat_2(C) & v1_partfun1(C,A,A) -> (r2_hidden(B,A) -> r2_hidden(k4_tarski(B,B),C)))) # label(t11_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.85 3898 (all A all B all C all D all E (m2_relset_1(E,A,A) & v1_partfun1(E,A,A) & v8_relat_2(E) & v3_relat_2(E) & v1_relat_2(E) -> (r2_hidden(D,k6_eqrel_1(A,E,C)) & r2_hidden(B,k6_eqrel_1(A,E,C)) -> r2_hidden(k4_tarski(B,D),E)))) # label(t30_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.85 3899 (all A all B all C (m1_relset_1(B,A,A) & m1_relset_1(C,A,A) -> B = k2_eqrel_1(A,B,B))) # label(idempotence_k2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.85 3900 (all A m2_relset_1(k1_eqrel_1(A),A,A)) # label(dt_k1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.85 3901 $T # label(t21_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.85 3902 $T # label(t39_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.85 3903 (all A all B (v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) & m2_relset_1(B,A,A) -> B = k5_eqrel_1(A,B,B))) # label(t22_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.85 3904 $T # label(t1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.85 3905 (all A all B (v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) -> (all C (v8_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v3_relat_2(C) -> -(k1_eqrel_1(A) = k3_eqrel_1(A,B,C) & k1_eqrel_1(A) != B & C != k1_eqrel_1(A)))))) # label(t38_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.85 3906 (all A all B (m1_relset_1(B,A,A) & v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) -> m1_eqrel_1(k8_eqrel_1(A,B),A))) # label(dt_k8_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.85 3907 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(A,A)))) -> ((all C (r2_hidden(C,B) -> v1_partfun1(C,A,A) & v3_relat_2(C) & v8_relat_2(C) & m2_relset_1(C,A,A))) -> k1_xboole_0 = B | v8_relat_2(k6_setfam_1(k2_zfmisc_1(A,A),B)) & m2_relset_1(k6_setfam_1(k2_zfmisc_1(A,A),B),A,A) & v1_partfun1(k6_setfam_1(k2_zfmisc_1(A,A),B),A,A) & v3_relat_2(k6_setfam_1(k2_zfmisc_1(A,A),B))))) # label(t19_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.85 3908 (all A all B all C (m1_relset_1(C,A,A) & m1_relset_1(B,A,A) -> k2_eqrel_1(A,C,B) = k2_eqrel_1(A,B,C))) # label(commutativity_k2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.85 3909 (all A all B all C (v8_relat_2(B) & v1_partfun1(C,A,A) & m1_relset_1(C,A,A) & v8_relat_2(C) & v1_partfun1(B,A,A) & v3_relat_2(B) & m1_relset_1(B,A,A) & v3_relat_2(C) -> k4_eqrel_1(A,B,B) = B)) # label(idempotence_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.85 3910 (all A all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> (all C (v8_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v3_relat_2(C) -> k5_eqrel_1(A,C,B) = k5_eqrel_1(A,B,C))))) # label(t23_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.85 3911 (all A all B (p1_s1_eqrel_1(A,B) -> p1_s1_eqrel_1(B,A))) & (all A (r2_hidden(A,f1_s1_eqrel_1) -> p1_s1_eqrel_1(A,A))) & (all A all B all C (p1_s1_eqrel_1(A,B) & p1_s1_eqrel_1(B,C) -> p1_s1_eqrel_1(A,C))) -> (exists A (m2_relset_1(A,f1_s1_eqrel_1,f1_s1_eqrel_1) & v8_relat_2(A) & (all B all C (r2_hidden(B,f1_s1_eqrel_1) & r2_hidden(C,f1_s1_eqrel_1) & p1_s1_eqrel_1(B,C) <-> r2_hidden(k4_tarski(B,C),A))) & v1_partfun1(A,f1_s1_eqrel_1,f1_s1_eqrel_1) & v3_relat_2(A))) # label(s1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.85 3912 (all A all B (v1_partfun1(B,A,A) & v3_relat_2(B) & v8_relat_2(B) & m2_relset_1(B,A,A) -> ((exists C k6_eqrel_1(A,B,C) = A) -> B = k1_eqrel_1(A)))) # label(t35_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.85 3913 (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]. 56.88/55.85 3914 (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]. 56.88/55.85 3915 (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]. 56.88/55.85 3916 (all A exists B m1_eqrel_1(B,A)) # label(existence_m1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.85 3917 (all A all B all C (m1_relset_1(C,A,A) & m1_relset_1(B,A,A) -> k3_eqrel_1(A,C,B) = k3_eqrel_1(A,B,C))) # label(commutativity_k3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3918 (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]. 56.88/55.86 3919 (all A all B (r1_tarski(k4_xboole_0(k2_funct_5(A),k2_funct_5(B)),k2_funct_5(k4_xboole_0(A,B))) & r1_tarski(k4_xboole_0(k1_funct_5(A),k1_funct_5(B)),k1_funct_5(k4_xboole_0(A,B))))) # label(t8_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3920 (all A (k1_xboole_0 = k2_funct_5(A) <-> k1_xboole_0 = k1_funct_5(A))) # label(t19_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3921 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_relat_1(C),k1_funct_2(A,B)) -> A = k1_xboole_0 | C = k3_funct_5(k4_funct_5(C)) & C = k5_funct_5(k6_funct_5(C))))) # label(t55_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3922 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k6_funct_5(C) = k6_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(t54_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3923 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k3_funct_5(A)) & v1_funct_1(k3_funct_5(A)))) # label(dt_k3_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3924 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> -(k1_xboole_0 != k2_zfmisc_1(A,B) & r2_hidden(C,B) & (all E (v1_funct_1(E) & v1_relat_1(E) -> -(A = k1_relat_1(E) & r1_tarski(k2_relat_1(E),k2_relat_1(D)) & (all F (r2_hidden(F,A) -> k1_funct_1(D,k4_tarski(F,C)) = k1_funct_1(E,F))) & k1_funct_1(k5_funct_5(D),C) = E))) & k1_relat_1(D) = k2_zfmisc_1(A,B)))) # label(t39_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3925 (all A all B all C all D (k2_tarski(B,D) = k2_funct_5(k2_tarski(k4_tarski(A,B),k4_tarski(C,D))) & k2_tarski(A,C) = k1_funct_5(k2_tarski(k4_tarski(A,B),k4_tarski(C,D))))) # label(t16_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3926 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k2_zfmisc_1(A,B) = k1_relat_1(D) & k2_zfmisc_1(A,B) = k1_relat_1(C) & k5_funct_5(C) = k5_funct_5(D) -> C = D))))) # label(t52_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3927 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_relat_1(C),k4_partfun1(A,B)) -> r1_tarski(k1_relat_1(k6_funct_5(C)),k2_zfmisc_1(A,k1_relat_1(C))) & r1_tarski(k1_relat_1(k4_funct_5(C)),k2_zfmisc_1(k1_relat_1(C),A))))) # label(t44_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3928 (all A (k1_funct_5(A) = k1_xboole_0 | k2_funct_5(A) = k1_xboole_0 -> (all B all C -r2_hidden(k4_tarski(B,C),A)))) # label(t18_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3929 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(C) = k2_zfmisc_1(A,B) -> k4_funct_5(k3_funct_5(C)) = C & C = k6_funct_5(k5_funct_5(C))))) # label(t56_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3930 $T # label(t14_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3931 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_funct_1(k5_funct_5(B),A) = C & r2_hidden(A,k1_relat_1(k5_funct_5(B))) -> 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) & r1_tarski(k1_relat_1(C),k1_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(C,D) = k1_funct_1(B,k4_tarski(D,A)) & r2_hidden(k4_tarski(D,A),k1_relat_1(B))))))))) # label(t41_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3932 (all A k1_tarski(k1_xboole_0) = k1_funct_2(k1_xboole_0,A)) # label(t64_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3933 (all A (v1_relat_1(A) -> k1_relat_1(A) = k1_funct_5(A) & k2_relat_1(A) = k2_funct_5(A))) # label(t21_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3934 (all A ((all B all C -r2_hidden(k4_tarski(B,C),A)) -> k2_funct_5(A) = k1_xboole_0 & k1_funct_5(A) = k1_xboole_0)) # label(t17_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3935 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_relat_1(C),k1_funct_2(A,B)) -> r1_tarski(k2_relat_1(k6_funct_5(C)),B) & r1_tarski(k2_relat_1(k4_funct_5(C)),B)))) # label(t48_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3936 (all A all B all C all D (r2_wellord2(A,B) & r2_wellord2(C,D) -> k1_card_1(k1_funct_2(B,D)) = k1_card_1(k1_funct_2(A,C)) & r2_wellord2(k1_funct_2(A,C),k1_funct_2(B,D)))) # label(t67_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3937 (all A all B all C (r2_hidden(k4_tarski(A,B),C) -> r2_hidden(B,k2_funct_5(C)) & r2_hidden(A,k1_funct_5(C)))) # label(t4_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3938 (all A (v1_funct_1(A) & v1_relat_1(A) -> k6_funct_5(A) = k2_funct_4(k4_funct_5(A)))) # label(d6_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3939 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> -((all E (v1_funct_1(E) & v1_relat_1(E) -> -(r1_tarski(k2_relat_1(E),k2_relat_1(D)) & E = k1_funct_1(k3_funct_5(D),C) & (all F (r2_hidden(F,B) -> k1_funct_1(D,k4_tarski(C,F)) = k1_funct_1(E,F))) & B = k1_relat_1(E)))) & r2_hidden(C,A) & k2_zfmisc_1(A,B) = k1_relat_1(D) & k2_zfmisc_1(A,B) != k1_xboole_0))) # label(t36_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3940 (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(k2_relat_1(k4_funct_5(C)),B) & r1_tarski(k2_relat_1(k6_funct_5(C)),B)))) # label(t47_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3941 (all A all B all C (A != B -> k1_card_1(k1_funct_2(k2_tarski(A,B),C)) = k1_card_1(k2_zfmisc_1(C,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]. 56.88/55.86 3942 (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]. 56.88/55.86 3943 $T # label(t24_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3944 (all A all B (k2_xboole_0(k2_funct_5(A),k2_funct_5(B)) = k2_funct_5(k2_xboole_0(A,B)) & k2_xboole_0(k1_funct_5(A),k1_funct_5(B)) = k1_funct_5(k2_xboole_0(A,B)))) # label(t6_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3945 $T # label(t3_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3946 (all A all B all C (r1_xboole_0(A,B) -> r2_wellord2(k1_funct_2(k2_xboole_0(A,B),C),k2_zfmisc_1(k1_funct_2(A,C),k1_funct_2(B,C))) & k1_card_1(k2_zfmisc_1(k1_funct_2(A,C),k1_funct_2(B,C))) = k1_card_1(k1_funct_2(k2_xboole_0(A,B),C)))) # label(t69_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3947 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B all C -r2_hidden(k4_tarski(B,C),k1_relat_1(A))) -> k1_xboole_0 = k3_funct_5(A) & k5_funct_5(A) = k1_xboole_0))) # label(t34_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3948 (all A all B all C all D (k1_card_1(C) = k1_card_1(D) & k1_card_1(B) = k1_card_1(A) -> k1_card_1(k1_funct_2(B,D)) = k1_card_1(k1_funct_2(A,C)))) # label(t68_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3949 (exists A (v1_funct_1(A) & (all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(B,f1_s1_funct_5) -> f2_s1_funct_5(B) = k1_funct_1(A,B)))) & k1_relat_1(A) = f1_s1_funct_5 & v1_relat_1(A))) # label(s1_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3950 (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]. 56.88/55.86 3951 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k4_funct_5(A) = B <-> (all C all D (v1_funct_1(D) & v1_relat_1(D) -> (D = k1_funct_1(A,k1_mcart_1(C)) & r2_hidden(C,k1_relat_1(B)) -> k1_funct_1(D,k2_mcart_1(C)) = k1_funct_1(B,C)))) & (all C ((exists D exists E (v1_funct_1(E) & v1_relat_1(E) & (exists F (k1_funct_1(A,D) = E & r2_hidden(F,k1_relat_1(E)) & r2_hidden(D,k1_relat_1(A)) & C = k4_tarski(D,F))))) <-> r2_hidden(C,k1_relat_1(B))))))))) # label(d4_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3952 (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)) & k1_funct_1(k3_funct_5(C),A) = D -> r2_hidden(B,k1_relat_1(D)) & k1_funct_1(D,B) = k1_funct_1(C,k4_tarski(A,B))))))) # label(t27_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3953 (all A all B (r2_wellord2(A,k1_funct_2(k1_tarski(B),A)) & k1_card_1(A) = k1_card_1(k1_funct_2(k1_tarski(B),A)))) # label(t65_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3954 (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(D) = k4_funct_5(C) & r1_tarski(k2_relat_1(C),k1_funct_2(A,B)) & r1_tarski(k2_relat_1(D),k1_funct_2(A,B)) -> k1_xboole_0 = A | D = C))))) # label(t53_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3955 (all A (v1_relat_1(A) & v1_funct_1(A) -> k1_funct_5(k1_relat_1(A)) = k2_funct_5(k1_relat_1(k2_funct_4(A))) & k2_funct_5(k1_relat_1(A)) = k1_funct_5(k1_relat_1(k2_funct_4(A))))) # label(t20_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3956 $T # label(dt_k2_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3957 (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]. 56.88/55.86 3958 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k2_zfmisc_1(A,B) = k1_relat_1(C) -> r1_tarski(k2_relat_1(k3_funct_5(C)),k1_funct_2(B,k2_relat_1(C))) & r1_tarski(k2_relat_1(k5_funct_5(C)),k1_funct_2(A,k2_relat_1(C)))))) # label(t42_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3959 $T # label(t25_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3960 $T # label(t2_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3961 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(k5_funct_5(B))) -> v1_relat_1(k1_funct_1(k5_funct_5(B),A)) & v1_funct_1(k1_funct_1(k5_funct_5(B),A))))) # label(t40_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3962 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k3_funct_5(C) = k3_funct_5(D) & k2_zfmisc_1(A,B) = k1_relat_1(C) & k2_zfmisc_1(A,B) = k1_relat_1(D) -> C = D))))) # label(t51_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3963 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_relat_1(C),k4_partfun1(A,B)) -> C = k3_funct_5(k4_funct_5(C)) & C = k5_funct_5(k6_funct_5(C)) | r2_hidden(k1_xboole_0,k2_relat_1(C))))) # label(t58_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3964 (all A all B k1_funct_2(A,k1_tarski(B)) = k1_tarski(k2_funcop_1(A,B))) # label(t66_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3965 (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_funct_5(k1_relat_1(A))) & (all D (v1_relat_1(D) & v1_funct_1(D) -> -(D = k1_funct_1(B,C) & 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_relat_1(B) = k1_funct_5(k1_relat_1(A)) <-> k3_funct_5(A) = B))))) # label(d3_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3966 (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]. 56.88/55.86 3967 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),k1_relat_1(C)) -> r2_hidden(B,k1_relat_1(k5_funct_5(C))) & v1_funct_1(k1_funct_1(k5_funct_5(C),B)) & v1_relat_1(k1_funct_1(k5_funct_5(C),B))))) # label(t28_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3968 (all A (v1_funct_1(A) & v1_relat_1(A) -> k3_funct_5(k2_funct_4(A)) = k5_funct_5(A))) # label(d5_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3969 (all A all B (k1_tarski(B) = k2_funct_5(k1_tarski(k4_tarski(A,B))) & k1_tarski(A) = k1_funct_5(k1_tarski(k4_tarski(A,B))))) # label(t15_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3970 (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_funct_1(k5_funct_5(C),B) = D & r2_hidden(k4_tarski(A,B),k1_relat_1(C)) -> 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]. 56.88/55.86 3971 (all A all B ((all C (r2_hidden(C,B) <-> (exists D r2_hidden(k4_tarski(D,C),A)))) <-> k2_funct_5(A) = B)) # label(d2_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3972 (all A all B (-(k1_xboole_0 = k2_zfmisc_1(B,A) & k1_xboole_0 = k2_zfmisc_1(A,B) & A = k1_xboole_0) -> k1_funct_5(k2_zfmisc_1(B,A)) = B & k2_funct_5(k2_zfmisc_1(A,B)) = B)) # label(t11_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3973 (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(C),k4_partfun1(A,B)) & r1_tarski(k2_relat_1(D),k4_partfun1(A,B)) -> r2_hidden(k1_xboole_0,k2_relat_1(D)) | r2_hidden(k1_xboole_0,k2_relat_1(C)) | D = C))))) # label(t61_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3974 (all A all B (r1_tarski(k1_funct_5(k2_zfmisc_1(A,B)),A) & r1_tarski(k2_funct_5(k2_zfmisc_1(A,B)),B))) # label(t12_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3975 (all A all B all C (B != A -> k1_card_1(k1_funct_2(C,k2_tarski(A,B))) = k1_card_1(k1_zfmisc_1(C)) & r2_wellord2(k1_funct_2(C,k2_tarski(A,B)),k1_zfmisc_1(C)))) # label(t72_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3976 (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 = k4_funct_5(k3_funct_5(C)) & k6_funct_5(k5_funct_5(C)) = C))) # label(t57_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3977 (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]. 56.88/55.86 3978 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k5_funct_5(D) = k5_funct_5(C) & r1_tarski(k1_relat_1(D),k2_zfmisc_1(A,B)) & r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> D = C))))) # label(t60_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3979 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k2_zfmisc_1(A,B) = k1_relat_1(C) -> k1_relat_1(k5_funct_5(C)) = B & A = k1_relat_1(k3_funct_5(C)) | k2_zfmisc_1(A,B) = k1_xboole_0))) # label(t31_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3980 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k4_funct_5(A)) & v1_relat_1(k4_funct_5(A)))) # label(dt_k4_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3981 $T # label(t22_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3982 $T # label(t23_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3983 (all A all B ((all C ((exists D r2_hidden(k4_tarski(C,D),A)) <-> r2_hidden(C,B))) <-> B = k1_funct_5(A))) # label(d1_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3984 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r1_tarski(k2_relat_1(D),k4_partfun1(A,B)) & r1_tarski(k2_relat_1(C),k4_partfun1(A,B)) & k6_funct_5(C) = k6_funct_5(D) -> r2_hidden(k1_xboole_0,k2_relat_1(C)) | r2_hidden(k1_xboole_0,k2_relat_1(D)) | C = D))))) # label(t62_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3985 (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]. 56.88/55.86 3986 (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)) & k1_funct_1(C,A) = D & r2_hidden(B,k1_relat_1(D)) -> r2_hidden(k1_funct_1(D,B),k2_relat_1(k6_funct_5(C))) & k1_funct_1(k6_funct_5(C),k4_tarski(B,A)) = k1_funct_1(D,B) & r2_hidden(k4_tarski(B,A),k1_relat_1(k6_funct_5(C)))))))) # label(t46_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3987 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (D = k1_funct_1(C,A) & r2_hidden(A,k1_relat_1(C)) & r2_hidden(B,k1_relat_1(D)) -> 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]. 56.88/55.86 3988 (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]. 56.88/55.86 3989 (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) & k2_zfmisc_1(A,k1_relat_1(C)) = k1_relat_1(k6_funct_5(C))))) # label(t33_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3990 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_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)) & r1_tarski(k1_relat_1(C),k2_funct_5(k1_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))))))))) # label(t38_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3991 (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]. 56.88/55.86 3992 (all A all B (r1_tarski(k5_xboole_0(k1_funct_5(A),k1_funct_5(B)),k1_funct_5(k5_xboole_0(A,B))) & r1_tarski(k5_xboole_0(k2_funct_5(A),k2_funct_5(B)),k2_funct_5(k5_xboole_0(A,B))))) # label(t9_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3993 (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)) -> r1_tarski(k1_relat_1(k3_funct_5(C)),A) & r1_tarski(k1_relat_1(k5_funct_5(C)),B)))) # label(t32_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3994 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(A,k1_relat_1(k3_funct_5(B))) -> v1_funct_1(k1_funct_1(k3_funct_5(B),A)) & v1_relat_1(k1_funct_1(k3_funct_5(B),A))))) # label(t37_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 3995 (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]. 56.88/55.86 3996 (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]. 56.88/55.86 3997 (all A (v1_relat_1(A) & v1_funct_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]. 56.88/55.86 3998 (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]. 56.88/55.86 3999 $T # label(dt_k1_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.86 4000 (all A (v1_funct_1(A) & v1_relat_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)))) -> k6_funct_5(A) = k1_xboole_0 & k4_funct_5(A) = k1_xboole_0))) # label(t35_funct_5) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4001 $T # label(dt_m1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4002 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(A,B)) -> k3_finseq_1(C) = A)))))) # label(t109_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4003 (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_finseq_1(C) & v1_funct_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(B) = A & k3_finseq_1(C) = A -> B = C))))))) # label(t10_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4004 (all 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(B),k1_tarski(A)),k1_relat_1(C)) -> v1_finseq_1(k4_funcop_1(C,B,A)) & v1_funct_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]. 56.88/55.87 4005 (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]. 56.88/55.87 4006 (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]. 56.88/55.87 4007 (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]. 56.88/55.87 4008 (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]. 56.88/55.87 4009 (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]. 56.88/55.87 4010 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,B) -> (all E (v1_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) -> (all F (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]. 56.88/55.87 4011 (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]. 56.88/55.87 4012 (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_relat_1(C) & v1_funct_1(C) & v1_finseq_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]. 56.88/55.87 4013 (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]. 56.88/55.87 4014 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_2(B,A,k4_finseq_2(np__3,A)) -> (exists C ((exists D ((exists E (m1_subset_1(E,A) & k11_finseq_1(C,D,E) = B)) & m1_subset_1(D,A))) & m1_subset_1(C,A))))))) # label(t123_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4015 $T # label(t106_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4016 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(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(k5_relat_1(B,A)) & v1_relat_1(k5_relat_1(B,A)) & v1_finseq_1(k5_relat_1(B,A)))))) # label(t44_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4017 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B k7_finseq_1(k2_finseq_2(A,B),k9_finseq_1(B)) = k2_finseq_2(k1_nat_1(A,np__1),B)))) # label(t74_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4018 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,B) -> (all F (v1_funct_1(F) & m2_relset_1(F,k2_zfmisc_1(A,B),C) & v1_funct_2(F,k2_zfmisc_1(A,B),C) -> (all G (m2_finseq_1(G,B) -> (k12_finseq_1(B,E) = G -> 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]. 56.88/55.87 4019 (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]. 56.88/55.87 4020 (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]. 56.88/55.87 4021 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_funct_1(B) & v1_finseq_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 B != k7_finseq_1(C,k9_finseq_1(D)))))))))) # label(t21_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4022 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (all D (v1_funct_2(D,k5_numbers,B) & v1_funct_1(D) & m2_relset_1(D,k5_numbers,B) -> (k2_partfun1(k5_numbers,B,D,k2_finseq_1(A)) = C -> A = k3_finseq_1(C)))))))))) # label(t32_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4023 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (B = k2_finseq_1(A) -> (all C (v1_funct_1(C) & v1_relat_1(C) & v1_finseq_1(C) -> (all D (m2_finseq_1(D,B) -> (r1_xreal_0(A,k3_finseq_1(C)) -> v1_relat_1(k5_relat_1(D,C)) & v1_finseq_1(k5_relat_1(D,C)) & v1_funct_1(k5_relat_1(D,C)))))))))))) # label(t34_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4024 (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]. 56.88/55.87 4025 (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]. 56.88/55.87 4026 (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) -> k1_partfun1(k5_numbers,A,A,B,k6_finseq_1(A),C) = k6_finseq_1(B))))) # label(t38_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4027 (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) & 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) -> m2_finseq_1(k4_funcop_1(E,F,D),C))))))))))))) # label(t97_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4028 (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]. 56.88/55.87 4029 (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_relat_1(D) & v1_funct_1(D) -> (all E (m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_1(E) & 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]. 56.88/55.87 4030 $T # label(t29_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4031 (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]. 56.88/55.87 4032 (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 -> k1_partfun1(k5_numbers,D,D,E,F,G) = k11_finseq_1(k1_funct_1(G,A),k1_funct_1(G,B),k1_funct_1(G,C))))))))))) # label(t41_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4033 (all A all B (-v1_xboole_0(B) & m1_finseq_2(B,A) -> (exists C m2_finseq_2(C,A,B)))) # label(existence_m2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4034 (all A (v1_funct_1(A) & v1_relat_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)) -> k5_relat_1(k11_finseq_1(B,C,D),A) = k11_finseq_1(k1_funct_1(A,B),k1_funct_1(A,C),k1_funct_1(A,D)))))) # label(t146_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4035 (all A (v4_ordinal2(A) -> (all B (v1_funct_1(B) & v1_relat_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]. 56.88/55.87 4036 (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(F,D,k4_finseq_2(C,D)) & m2_finseq_2(E,D,k4_finseq_2(B,D)) & A = k8_finseq_1(D,E,F)))))) # label(fraenkel_a_3_0_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4037 (all A (v4_ordinal2(A) -> A = k3_finseq_1(k1_finseq_2(A)))) # label(t55_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4038 (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_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]. 56.88/55.87 4039 (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]. 56.88/55.87 4040 (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]. 56.88/55.87 4041 (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,D,C) & D = k8_finseq_1(B,C,D))))))))) # label(t115_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4042 (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) -> (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]. 56.88/55.87 4043 $T # label(t7_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4044 (all A k2_finseq_2(np__1,A) = k9_finseq_1(A)) # label(t73_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4045 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_2_finseq_2(B)) <-> (exists C exists D exists E (A = k11_finseq_1(C,D,E) & m1_subset_1(C,B) & m1_subset_1(D,B) & m1_subset_1(E,B)))))) # label(fraenkel_a_1_2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4046 (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]. 56.88/55.87 4047 (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_finseq_1(C) & v1_relat_1(C) & v1_funct_1(C) -> (k7_relat_1(C,k2_finseq_1(A)) = B -> k3_finseq_1(B) = k3_square_1(A,k3_finseq_1(C))))))))) # label(t24_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4048 (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]. 56.88/55.87 4049 (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) -> -(k1_nat_1(A,B) = k3_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 & A = k3_finseq_1(D) & C = k7_finseq_1(D,E))))))))))))) # label(t25_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4050 (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]. 56.88/55.87 4051 (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]. 56.88/55.87 4052 (all A all B (-v1_xboole_0(B) -> ((exists C exists D (m1_subset_1(D,B) & A = k10_finseq_1(C,D) & m1_subset_1(C,B))) <-> r2_hidden(A,a_1_1_finseq_2(B))))) # label(fraenkel_a_1_1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4053 (all A (v4_ordinal2(A) -> (all B (v1_finseq_1(k2_funcop_1(k2_finseq_1(A),B)) & v1_funct_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]. 56.88/55.87 4054 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_0_finseq_2(B)) <-> (exists C (m1_subset_1(C,B) & A = k12_finseq_1(B,C)))))) # label(fraenkel_a_1_0_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4055 (all A (v4_ordinal2(A) -> m2_relset_1(k1_finseq_2(A),k2_finseq_1(A),k2_finseq_1(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)) & v1_funct_1(k1_finseq_2(A)))) # label(t65_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4056 (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_finseq_1(D) & v1_relat_1(D) -> (all E (m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_2(E,k2_zfmisc_1(A,B),C) & v1_funct_1(E) -> (all F (m2_finseq_1(F,A) -> (all G (m2_finseq_1(G,B) -> (D = k3_funcop_1(E,F,G) & k3_finseq_1(F) = k3_finseq_1(G) -> k3_finseq_1(D) = k3_finseq_1(F) & k3_finseq_1(G) = k3_finseq_1(D)))))))))))))))) # label(t86_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4057 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_finseq_1(B) & v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_finseq_1(C) & v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v3_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) -> (r1_xreal_0(A,k3_finseq_1(B)) & k5_relat_1(D,B) = C -> A = k3_finseq_1(C)))))))))) # label(t47_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4058 (all A all B all C (m2_finseq_1(C,A) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) & v1_funct_2(D,A,B) -> m2_finseq_1(k1_partfun1(k5_numbers,A,A,B,C,D),B))))) # label(t36_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4059 (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]. 56.88/55.87 4060 (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]. 56.88/55.87 4061 (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_1(F) & m2_relset_1(F,C,D) & v1_funct_2(F,C,D) -> (k10_finseq_1(A,B) = E -> k10_finseq_1(k1_funct_1(F,A),k1_funct_1(F,B)) = k1_partfun1(k5_numbers,C,C,D,E,F)))))))))) # label(t40_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4062 (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]. 56.88/55.87 4063 (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]. 56.88/55.87 4064 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k4_square_1(A,np__0) = A & np__0 = k3_square_1(np__0,A) & k3_square_1(A,np__0) = np__0 & A = k4_square_1(np__0,A))) # label(t6_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4065 (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]. 56.88/55.87 4066 (all A (v4_ordinal2(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,B) -> (np__0 != A -> (all D (m1_subset_1(D,k2_finseq_1(A)) -> k1_funct_1(k2_finseq_2(A,C),D) = C))))))))) # label(t71_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4067 (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]. 56.88/55.87 4068 (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]. 56.88/55.87 4069 (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_2(D,k2_finseq_1(A),k2_finseq_1(A)) & v3_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_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(t135_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4070 $T # label(t53_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4071 (all A all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_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]. 56.88/55.87 4072 (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]. 56.88/55.87 4073 (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) & v1_funct_2(H,k2_zfmisc_1(A,B),C) & m2_relset_1(H,k2_zfmisc_1(A,B),C) -> (all I (m2_finseq_1(I,A) -> (I = k11_finseq_1(D,E,F) -> k4_funcop_1(H,I,G) = k11_finseq_1(k2_binop_1(A,B,C,H,D,G),k2_binop_1(A,B,C,H,E,G),k2_binop_1(A,B,C,H,F,G))))))))))))))))))))) # label(t102_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4074 $T # label(t17_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4075 (all A (v4_ordinal2(A) -> v1_relat_1(k1_finseq_2(A)) & v1_funct_1(k1_finseq_2(A)) & v1_finseq_1(k1_finseq_2(A)))) # label(dt_k1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4076 $T # label(t67_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4077 (all A all B (m1_finseq_2(B,A) & -v1_xboole_0(B) -> (all C (m2_finseq_2(C,A,B) -> m2_finseq_1(C,A))))) # label(dt_m2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4078 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) & v1_finseq_1(C) -> (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) -> (k5_relat_1(D,B) = C & r1_xreal_0(A,k3_finseq_1(B)) & k2_relat_1(D) = k2_finseq_1(A) -> A = k3_finseq_1(C)))))))))) # label(t45_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4079 (all A all B all C (v4_ordinal2(B) -> ((exists D (D = A & B = k3_finseq_1(D) & m2_finseq_2(D,C,k3_finseq_2(C)))) <-> r2_hidden(A,a_2_0_finseq_2(B,C))))) # label(fraenkel_a_2_0_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4080 (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]. 56.88/55.87 4081 (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_2(C,k4_finseq_1(A),k4_finseq_1(A)) & v1_funct_1(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)) -> (B = k5_relat_1(C,A) -> k3_finseq_1(A) = k3_finseq_1(B)))))))) # label(t48_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.87 4082 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,B) -> (all J (v1_funct_1(J) & m2_relset_1(J,k2_zfmisc_1(A,B),C) & v1_funct_2(J,k2_zfmisc_1(A,B),C) -> (all K (m2_finseq_1(K,A) -> (all L (m2_finseq_1(L,B) -> (k11_finseq_1(D,E,F) = K & L = k11_finseq_1(G,H,I) -> 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]. 56.88/55.87 4083 (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]. 56.88/55.87 4084 (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]. 56.88/55.87 4085 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m2_relset_1(E,k2_zfmisc_1(B,C),D) & v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(B,C),D) -> (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]. 56.88/55.88 4086 $T # label(t108_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4087 (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 (m2_finseq_2(F,C,k4_finseq_2(B,C)) & D = k8_finseq_1(C,E,F))) & m2_finseq_2(E,C,k4_finseq_2(A,C)))))))))))) # label(t126_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4088 (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) -> (all H (m2_finseq_1(H,B) -> (H = k12_finseq_1(B,E) & k12_finseq_1(A,D) = G -> k12_finseq_1(C,k2_binop_1(A,B,C,F,D,E)) = k3_funcop_1(F,G,H)))))))))))))))))) # label(t88_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4089 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]. 56.88/55.88 4090 (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 (v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) & m2_relset_1(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]. 56.88/55.88 4091 (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]. 56.88/55.88 4092 (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]. 56.88/55.88 4093 (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]. 56.88/55.88 4094 (all A all B k2_relat_1(k10_finseq_1(A,B)) = k2_tarski(A,B)) # label(t147_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4095 (all A k1_xboole_0 = k2_finseq_2(np__0,A)) # label(t72_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4096 (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,k2_zfmisc_1(A,B),C) & v1_funct_1(E) & 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]. 56.88/55.88 4097 (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]. 56.88/55.88 4098 (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]. 56.88/55.88 4099 (all A all B (v4_ordinal2(A) -> v1_finseq_1(k2_finseq_2(A,B)) & v1_relat_1(k2_finseq_2(A,B)) & v1_funct_1(k2_finseq_2(A,B)))) # label(dt_k2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4100 (all A exists B m1_finseq_2(B,A)) # label(existence_m1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4101 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_finseq_1(A),B) & m2_relset_1(C,k2_finseq_1(A),B) & v1_funct_1(C) -> m2_finseq_1(C,B))))))) # label(t28_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4102 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (-v1_xboole_0(C) -> (all D (m2_finseq_1(D,C) -> -((all E (m2_finseq_1(E,C) -> (all F (m2_finseq_1(F,C) -> -(D = k8_finseq_1(C,E,F) & B = k3_finseq_1(F) & k3_finseq_1(E) = A))))) & k3_finseq_1(D) = k1_nat_1(A,B)))))))))) # label(t26_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4103 (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]. 56.88/55.88 4104 (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]. 56.88/55.88 4105 (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]. 56.88/55.88 4106 (all A (-v1_xboole_0(A) -> a_1_0_finseq_2(A) = k4_finseq_2(np__1,A))) # label(t116_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4107 (all A k3_finseq_2(A) = k13_finseq_1(A)) # label(redefinition_k3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4108 (all A all B (v1_funct_1(B) & v1_relat_1(B) & v1_finseq_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) & v1_finseq_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (C = k5_funcop_1(D,A,B) & r1_tarski(k2_zfmisc_1(k1_tarski(A),k2_relat_1(B)),k1_relat_1(D)) -> k3_finseq_1(B) = k3_finseq_1(C)))))))) # label(t81_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4109 (all A all B all C k1_enumset1(A,B,C) = k2_relat_1(k11_finseq_1(A,B,C))) # label(t148_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4110 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> -(r2_hidden(A,k2_relat_1(B)) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(r2_hidden(C,k4_finseq_1(B)) & k1_funct_1(B,C) = A)))))) # label(t11_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4111 (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 (v1_funct_1(F) & m2_relset_1(F,k2_zfmisc_1(B,C),D) & v1_funct_2(F,k2_zfmisc_1(B,C),D) -> (all G (m2_finseq_2(G,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]. 56.88/55.88 4112 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(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)) -> (r1_xreal_0(B,k3_finseq_1(C)) -> B = np__0 & np__0 != A | v1_relat_1(k5_relat_1(D,C)) & v1_finseq_1(k5_relat_1(D,C)) & v1_funct_1(k5_relat_1(D,C))))))))))) # label(t42_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4113 (all A all 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) & v1_finseq_1(D) -> (k7_finseq_1(C,k9_finseq_1(A)) = k7_finseq_1(D,k9_finseq_1(B)) -> D = C & A = B))))) # label(t20_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4114 (all A exists B (-v1_xboole_0(B) & m1_finseq_2(B,A))) # label(rc1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4115 (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) -> k6_finseq_1(C) = k3_funcop_1(D,E,k6_finseq_1(B)) & k6_finseq_1(C) = k3_funcop_1(D,k6_finseq_1(A),F))))))))))))) # label(t87_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4116 (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]. 56.88/55.88 4117 $T # label(t103_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4118 (all A k10_finseq_1(A,A) = k2_finseq_2(np__2,A)) # label(t75_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4119 (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]. 56.88/55.88 4120 (all A k11_finseq_1(A,A,A) = k2_finseq_2(np__3,A)) # label(t76_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4121 (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) -> (r1_tarski(k2_zfmisc_1(k2_relat_1(B),k1_tarski(A)),k1_relat_1(D)) & C = k4_funcop_1(D,B,A) -> k3_finseq_1(B) = k3_finseq_1(C)))))))) # label(t83_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4122 (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]. 56.88/55.88 4123 (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]. 56.88/55.88 4124 (all A (v4_ordinal2(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> k5_relat_1(k1_finseq_2(A),B) = k7_relat_1(B,k2_finseq_1(A)))))) # label(t63_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4125 (all A (-v1_xboole_0(A) -> k4_finseq_2(np__2,A) = a_1_1_finseq_2(A))) # label(t119_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4126 (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_2(D,k2_finseq_1(A),k2_finseq_1(A)) & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_1(D) -> (k2_relat_1(D) = 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(t134_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4127 (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_1(H) & v1_funct_2(H,k2_zfmisc_1(A,B),C) -> (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 -> k10_finseq_1(k2_binop_1(A,B,C,H,D,F),k2_binop_1(A,B,C,H,E,G)) = k3_funcop_1(H,I,J)))))))))))))))))))))) # label(t89_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4128 (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]. 56.88/55.88 4129 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (B = k7_relat_1(C,k2_finseq_1(A)) & r1_xreal_0(k3_finseq_1(C),A) -> B = C))))))) # label(t23_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4130 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (-v1_xboole_0(C) & m1_finseq_2(C,B) -> -v1_xboole_0(C) & m1_finseq_2(C,A))))))) # label(t107_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4131 (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) & k8_finseq_1(B,D,k12_finseq_1(B,E)) = C)) & m2_finseq_2(D,B,k4_finseq_2(A,B)))))))))) # label(t137_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4132 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_2(B,A,k4_finseq_2(np__1,A)) -> (exists C (B = k12_finseq_1(A,C) & m1_subset_1(C,A))))))) # label(t117_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4133 (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) -> (r1_tarski(k2_relat_1(A),k1_relat_1(C)) & k5_relat_1(A,C) = B -> k3_finseq_1(A) = k3_finseq_1(B)))))))) # label(t33_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4134 (all A (-v1_xboole_0(k13_finseq_1(A)) & m1_finseq_2(k13_finseq_1(A),A))) # label(t104_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4135 (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) & v1_relat_1(E) & v1_finseq_1(E) -> (all F (v1_funct_2(F,k2_zfmisc_1(A,B),C) & m2_relset_1(F,k2_zfmisc_1(A,B),C) & v1_funct_1(F) -> (all G (m2_finseq_1(G,B) -> (E = k5_funcop_1(F,D,G) -> k3_finseq_1(G) = k3_finseq_1(E)))))))))))))))) # label(t92_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4136 (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]. 56.88/55.88 4137 (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_2(E,k2_zfmisc_1(A,B),C) & m2_relset_1(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]. 56.88/55.88 4138 (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) -> (A = k3_square_1(B,C) -> 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]. 56.88/55.88 4139 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r1_xreal_0(A,B) -> k2_square_1(np__0,k6_xcmplx_0(A,B)) = np__0))))) # label(t3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4140 (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]. 56.88/55.88 4141 (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]. 56.88/55.88 4142 (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_relat_1(k5_funcop_1(C,A,B)) & v1_finseq_1(k5_funcop_1(C,A,B)) & v1_funct_1(k5_funcop_1(C,A,B))))))) # label(t80_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4143 (all A all B (m1_subset_1(B,k4_finseq_2(np__0,A)) -> B = k6_finseq_1(A))) # label(t113_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4144 (all A all B (-v1_xboole_0(B) -> (all C (v1_finseq_1(C) & v1_relat_1(C) & v1_funct_1(C) -> (all D (m2_finseq_1(D,A) -> (all E (v1_funct_2(E,A,B) & v1_funct_1(E) & m2_relset_1(E,A,B) -> (k1_partfun1(k5_numbers,A,A,B,D,E) = C -> k3_finseq_1(D) = k3_finseq_1(C)))))))))) # label(t37_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4145 (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_1(G) & v1_funct_2(G,k2_zfmisc_1(A,B),C) -> (all H (m2_finseq_1(H,A) -> (k10_finseq_1(D,E) = H -> 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]. 56.88/55.88 4146 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m2_finseq_1(C,B) -> m2_finseq_1(C,A))))))) # label(t27_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4147 (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]. 56.88/55.88 4148 (all A (v4_ordinal2(A) -> (all B a_2_0_finseq_2(A,B) = k4_finseq_2(A,B)))) # label(d4_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4149 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_funct_1(B) & v1_relat_1(B) & v1_finseq_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(A,k4_finseq_1(k7_finseq_1(B,C)))))))))) # label(t18_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4150 (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]. 56.88/55.88 4151 (exists A ((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(B,k2_finseq_1(f1_s1_finseq_2)) -> f3_s1_finseq_2(B) = k1_funct_1(A,B)))) & k3_finseq_1(A) = f1_s1_finseq_2 & m2_finseq_1(A,f2_s1_finseq_2))) # label(s1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4152 (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]. 56.88/55.88 4153 (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]. 56.88/55.88 4154 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> k1_funct_2(k2_finseq_1(A),B) = k4_finseq_2(A,B))))) # label(t111_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4155 (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_2(E,B,C) & v1_funct_1(E) & m2_relset_1(E,B,C) -> (D = k9_finseq_1(A) -> k1_partfun1(k5_numbers,B,B,C,D,E) = k9_finseq_1(k1_funct_1(E,A))))))))))) # label(t39_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4156 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_finseq_1(A),k2_finseq_1(A)) & m2_relset_1(C,k2_finseq_1(A),k2_finseq_1(A)) -> (r1_xreal_0(A,k3_finseq_1(B)) -> v1_finseq_1(k5_relat_1(C,B)) & v1_relat_1(k5_relat_1(C,B)) & v1_funct_1(k5_relat_1(C,B))))))))) # label(t43_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4157 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k5_numbers,B) & m2_relset_1(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]. 56.88/55.88 4158 (all A (v1_funct_1(A) & v1_relat_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]. 56.88/55.88 4159 (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]. 56.88/55.88 4160 (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]. 56.88/55.88 4161 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_finseq_1(B) & v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,C) & k3_finseq_1(A) = k3_finseq_1(B) & r1_tarski(B,C) -> A = B))))))) # label(t149_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4162 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> (all C (m2_relset_1(C,k4_finseq_1(B),k4_finseq_1(B)) & v1_funct_2(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]. 56.88/55.88 4163 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (A != np__0 -> (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]. 56.88/55.88 4164 $T # label(t12_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4165 (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]. 56.88/55.88 4166 (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_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 & k2_relat_1(C) = k4_finseq_1(A) -> k3_finseq_1(B) = k3_finseq_1(A)))))))) # label(t46_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4167 (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]. 56.88/55.88 4168 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (-v1_xboole_0(C) -> (all D (m2_finseq_1(D,C) -> (all E (v1_funct_2(E,k2_finseq_1(A),k2_finseq_1(B)) & m2_relset_1(E,k2_finseq_1(A),k2_finseq_1(B)) & v1_funct_1(E) -> (r1_xreal_0(B,k3_finseq_1(D)) -> m2_finseq_1(k1_partfun1(k2_finseq_1(A),k2_finseq_1(B),k5_numbers,C,E,D),C) | B = np__0 & np__0 != A))))))))))) # label(t49_finseq_2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4169 (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]. 56.88/55.88 4170 (all A all B (r2_hidden(A,k1_classes1(B)) -> r2_hidden(k1_zfmisc_1(A),k1_classes1(B)))) # label(t7_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4171 (all A all B all C (v3_ordinal1(C) -> (r2_hidden(B,k4_classes1(C)) & r2_hidden(A,k4_classes1(C)) <-> r2_hidden(k4_tarski(A,B),k4_classes1(k1_ordinal1(k1_ordinal1(C))))))) # label(t51_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4172 (all A (v1_classes1(A) <-> (all B all C (r2_hidden(B,A) & r1_tarski(C,B) -> r2_hidden(C,A))))) # label(d1_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4173 (all A all B all C (v3_ordinal1(C) -> (r2_hidden(A,a_2_0_classes1(B,C)) <-> (exists D ((exists E (r2_hidden(E,k3_classes1(B,C)) & m1_subset_1(E,k1_classes1(B)) & r1_tarski(D,E))) & D = A & m1_subset_1(D,k1_classes1(B))))))) # label(fraenkel_a_2_0_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4174 (all A -v1_xboole_0(k1_classes1(A))) # label(fc1_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4175 (all A all B all C all D (v1_funct_1(C) & v3_ordinal1(D) & v5_ordinal1(C) & v1_relat_1(C) -> ((exists E (m1_subset_1(E,k1_classes1(B)) & (exists F (r1_tarski(E,F) & r2_hidden(F,k1_funct_1(C,D)) & m1_subset_1(F,k1_classes1(B)))) & E = A)) <-> r2_hidden(A,a_3_0_classes1(B,C,D))))) # label(fraenkel_a_3_0_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.88 4176 (all A all B k5_classes1(k2_xboole_0(A,B)) = k2_xboole_0(k5_classes1(A),k5_classes1(B))) # label(t67_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4177 (all A (v1_ordinal1(A) -> (all B (v3_ordinal1(B) -> (B != k1_xboole_0 -> v1_ordinal1(k3_classes1(A,B))))))) # label(t25_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4178 (all A r2_hidden(A,k1_classes1(A))) # label(t5_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4179 (all A k1_tarski(A) = k3_classes1(A,k1_xboole_0)) # label(t10_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4180 (all A (v3_ordinal1(A) -> r1_tarski(k3_tarski(k4_classes1(A)),k4_classes1(A)))) # label(t40_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4181 (all A all B all C (v3_ordinal1(C) -> (r2_hidden(k2_tarski(A,B),k4_classes1(k1_ordinal1(C))) <-> r2_hidden(A,k4_classes1(C)) & r2_hidden(B,k4_classes1(C))))) # label(t50_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4182 (all A all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal1(B,C) -> r1_tarski(k3_classes1(A,B),k3_classes1(A,C))))))) # label(t19_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4183 (all A all B (v3_ordinal1(B) -> (r2_hidden(A,k4_classes1(B)) -> r2_hidden(k3_tarski(A),k4_classes1(B))))) # label(t41_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4184 $T # label(t3_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4185 (all A exists B (v3_ordinal1(B) & (all C (v3_ordinal1(C) -> -(k3_classes1(A,C) = k1_classes1(A) & r2_hidden(C,B)))) & k3_classes1(A,B) = k1_classes1(A))) # label(t23_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4186 (all A (v3_ordinal1(A) -> (v4_ordinal1(A) -> k1_xboole_0 = A | (all B (r2_hidden(B,k4_classes1(A)) <-> (exists C (v3_ordinal1(C) & r2_hidden(B,k4_classes1(C)) & r2_hidden(C,A)))))))) # label(t35_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4187 (all A all B all C (v3_ordinal1(C) -> (r2_hidden(A,k3_classes1(B,C)) -> r2_hidden(k1_zfmisc_1(A),k3_classes1(B,k1_ordinal1(C)))))) # label(t15_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4188 (all A all B (v3_ordinal1(B) -> m1_subset_1(k3_classes1(A,B),k1_zfmisc_1(k1_classes1(A))))) # label(dt_k3_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4189 (all A all B (r2_hidden(A,B) -> r2_hidden(k6_classes1(A),k6_classes1(B)))) # label(t76_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4190 (all A all B (v3_ordinal1(B) -> r1_tarski(k3_classes1(A,B),k3_classes1(A,k1_ordinal1(B))))) # label(t18_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4191 (all A (v3_ordinal1(A) -> r1_tarski(k4_classes1(A),k4_classes1(k1_ordinal1(A))))) # label(t39_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4192 (all A (v1_ordinal1(A) -> v1_ordinal1(k1_classes1(A)))) # label(t27_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4193 (all A all B (r1_tarski(A,B) -> r1_ordinal1(k6_classes1(A),k6_classes1(B)))) # label(t75_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4194 (all A all B (v1_ordinal1(A) & v1_ordinal1(B) -> v1_ordinal1(k3_xboole_0(A,B)))) # label(t56_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4195 (all A all B (r2_hidden(A,k1_classes1(B)) -> r2_hidden(k1_card_1(A),k1_card_1(k1_classes1(B))))) # label(t28_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4196 (all A all B (v3_ordinal1(B) -> k2_xboole_0(k2_xboole_0(a_2_0_classes1(A,B),a_2_1_classes1(A,B)),k3_xboole_0(k1_zfmisc_1(k3_classes1(A,B)),k1_classes1(A))) = k3_classes1(A,k1_ordinal1(B)))) # label(t11_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4197 (all A all B (r1_tarski(A,B) & v1_ordinal1(B) -> r1_tarski(k5_classes1(A),B))) # label(t60_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4198 (all A (v3_ordinal1(A) -> k5_classes1(A) = A)) # label(t64_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4199 (all A all B (v3_ordinal1(B) -> (k3_classes1(A,k1_ordinal1(B)) = k3_classes1(A,B) -> k3_classes1(A,B) = k1_classes1(A)))) # label(t21_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4200 $T # label(dt_k4_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4201 (all A exists B (k1_classes1(A) = k3_classes1(A,B) & v3_ordinal1(B))) # label(t22_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4202 (all A -(v1_ordinal1(A) & (all B (v3_ordinal1(B) -> -r1_tarski(k1_classes1(A),k4_classes1(B)))))) # label(t53_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4203 (all A all B all C (v3_ordinal1(C) -> ((exists D (k1_zfmisc_1(D) = A & r2_hidden(D,k3_classes1(B,C)) & m1_subset_1(D,k1_classes1(B)))) <-> r2_hidden(A,a_2_1_classes1(B,C))))) # label(fraenkel_a_2_1_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4204 $T # label(dt_k1_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4205 (all A all B all C all D (v1_relat_1(C) & v1_funct_1(C) & v3_ordinal1(D) & v5_ordinal1(C) -> ((exists E (r2_hidden(E,k1_funct_1(C,D)) & A = k1_zfmisc_1(E) & m1_subset_1(E,k1_classes1(B)))) <-> r2_hidden(A,a_3_1_classes1(B,C,D))))) # label(fraenkel_a_3_1_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4206 $T # label(dt_k5_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4207 (all A k5_classes1(k5_classes1(A)) = k5_classes1(A)) # label(t66_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4208 (all A all B -((all C (v3_ordinal1(C) -> -(-r2_hidden(A,k3_classes1(B,C)) & r2_hidden(A,k3_classes1(B,k1_ordinal1(C)))))) & r2_hidden(A,k1_classes1(B)) & B != A)) # label(t24_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4209 $T # label(dt_k2_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4210 $T # label(t70_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4211 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r1_tarski(k4_classes1(A),k4_classes1(B)) <-> r1_ordinal1(A,B)))))) # label(t43_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4212 (all A (v3_ordinal1(A) -> k6_classes1(k4_classes1(A)) = A)) # label(t72_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4213 (all A k1_ordinal1(k6_classes1(A)) = k6_classes1(k1_zfmisc_1(A))) # label(t71_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4214 (all A (v3_ordinal1(A) -> (all B (B = k4_classes1(A) <-> (exists C (v1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = k1_zfmisc_1(k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> D = k1_xboole_0 | k3_tarski(k2_relat_1(k2_ordinal1(C,D))) = k1_funct_1(C,D)))) & k1_xboole_0 = k1_funct_1(C,k1_xboole_0) & v1_funct_1(C) & k1_ordinal2(C) = B & k1_relat_1(C) = k1_ordinal1(A) & v5_ordinal1(C))))))) # label(d6_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4215 (all A all B all C (v3_ordinal1(C) -> (r2_hidden(B,k4_classes1(C)) & r1_tarski(A,B) -> r2_hidden(A,k4_classes1(C))))) # label(t47_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4216 (all A all B (v3_ordinal1(B) -> (r1_tarski(A,k4_classes1(B)) <-> r2_hidden(A,k4_classes1(k1_ordinal1(B)))))) # label(t36_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4217 (all A all B (k1_classes1(A) = B <-> (all C (r1_classes1(A,C) -> r1_tarski(B,C))) & r1_classes1(A,B))) # label(d4_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4218 (all A all B -(r2_hidden(A,k1_classes1(B)) & r2_tarski(A,k1_classes1(B)))) # label(t29_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4219 (all A exists B (r1_tarski(A,k4_classes1(B)) & v3_ordinal1(B))) # label(t69_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4220 (all A all B (r1_tarski(A,B) -> r1_tarski(k5_classes1(A),k5_classes1(B)))) # label(t65_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4221 (all A (v1_ordinal1(A) -> A = k5_classes1(A))) # label(t62_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4222 (all A (v3_ordinal1(A) -> v1_ordinal1(k4_classes1(A)))) # label(t37_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4223 (all A all B all C (r1_tarski(C,k1_classes1(B)) & r1_tarski(A,k1_classes1(B)) -> r1_tarski(k2_zfmisc_1(A,C),k1_classes1(B)))) # label(t32_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4224 (all A all B (v3_ordinal1(B) -> (v4_ordinal1(B) -> k3_classes1(A,B) = a_2_2_classes1(A,B) | k1_xboole_0 = B))) # label(t12_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4225 (all A (v3_ordinal1(A) -> A = k6_classes1(A))) # label(t81_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4226 (all A (v3_ordinal1(A) -> k4_classes1(k1_ordinal1(A)) = k1_zfmisc_1(k4_classes1(A)))) # label(t34_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4227 (all A all B (v3_ordinal1(B) -> (r2_hidden(A,k4_classes1(B)) -> r1_tarski(A,k4_classes1(B))))) # label(t38_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4228 (all A exists B (k3_classes1(A,k1_ordinal1(B)) = k3_classes1(A,B) & v3_ordinal1(B))) # label(t20_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4229 (all A (v2_classes1(A) <-> (all B -(r1_tarski(B,A) & -r2_hidden(B,A) & -r2_tarski(B,A))) & (all B (r2_hidden(B,A) -> r2_hidden(k1_zfmisc_1(B),A))) & v1_classes1(A))) # label(d2_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4230 (all A all B ((all C ((exists D (v1_funct_1(D) & (exists E (r2_hidden(C,k1_funct_1(D,E)) & (all F (m2_subset_1(F,k1_numbers,k5_numbers) -> k3_tarski(k1_funct_1(D,F)) = k1_funct_1(D,k1_nat_1(F,np__1)))) & k5_numbers = k1_relat_1(D) & A = k1_funct_1(D,np__0) & m2_subset_1(E,k1_numbers,k5_numbers))) & v1_relat_1(D))) <-> r2_hidden(C,B))) <-> B = k5_classes1(A))) # label(d7_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4231 (all A all B (v3_ordinal1(B) -> (r1_tarski(A,k4_classes1(B)) <-> r1_ordinal1(k6_classes1(A),B)))) # label(t73_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4232 (all A all B all C all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(A,k3_classes1(B,D)) -> r2_hidden(C,k3_classes1(B,D)) | k1_xboole_0 = D | k1_zfmisc_1(A) != C & -r1_tarski(C,A)))) # label(t17_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4233 (all A all B (v3_ordinal1(B) -> (all C (k2_classes1(A,B) = C <-> (exists D ((all E (v3_ordinal1(E) -> (v4_ordinal1(E) & r2_hidden(E,k1_ordinal1(B)) -> k1_xboole_0 = E | k3_xboole_0(k3_tarski(k2_relat_1(k2_ordinal1(D,E))),k1_classes1(A)) = k1_funct_1(D,E)))) & k1_tarski(A) = k1_funct_1(D,k1_xboole_0) & k1_ordinal2(D) = C & v5_ordinal1(D) & v1_relat_1(D) & v1_funct_1(D) & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(B)) -> k1_funct_1(D,k1_ordinal1(E)) = k2_xboole_0(k2_xboole_0(a_3_0_classes1(A,D,E),a_3_1_classes1(A,D,E)),k3_xboole_0(k1_zfmisc_1(k1_funct_1(D,E)),k1_classes1(A)))))) & k1_ordinal1(B) = k1_relat_1(D))))))) # label(d5_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4234 (all A all B (v3_ordinal1(B) -> (k3_xboole_0(k4_classes1(B),k1_classes1(A)) = k3_xboole_0(k4_classes1(k1_ordinal1(B)),k1_classes1(A)) & v1_ordinal1(A) -> r1_tarski(k1_classes1(A),k4_classes1(B))))) # label(t52_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4235 (all A all B all C (v3_ordinal1(C) -> (v4_ordinal1(C) -> (r2_hidden(B,k3_classes1(A,C)) <-> (exists D (v3_ordinal1(D) & r2_hidden(B,k3_classes1(A,D)) & r2_hidden(D,C)))) | k1_xboole_0 = C))) # label(t16_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4236 (all A all B -(r1_tarski(A,k1_classes1(B)) & -r2_tarski(A,k1_classes1(B)) & -r2_hidden(A,k1_classes1(B)))) # label(t8_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4237 (all A all B (v3_ordinal1(B) -> (B = k6_classes1(A) <-> (all C (v3_ordinal1(C) -> (r1_tarski(A,k4_classes1(C)) -> r1_ordinal1(B,C)))) & r1_tarski(A,k4_classes1(B))))) # label(d8_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4238 (all A v3_ordinal1(k6_classes1(A))) # label(dt_k6_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4239 (all A (k1_xboole_0 = A <-> k6_classes1(A) = k1_xboole_0)) # label(t79_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4240 (all A all B all C all D (v3_ordinal1(D) -> (r2_hidden(B,k3_classes1(C,D)) & r1_tarski(A,B) -> r2_hidden(A,k3_classes1(C,k1_ordinal1(D)))))) # label(t14_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4241 (all A all B (v3_ordinal1(B) -> -(k6_classes1(A) = k1_ordinal1(B) & (all C -(k6_classes1(C) = B & r2_hidden(C,A)))))) # label(t80_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4242 $T # label(t4_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4243 (all A all B (v3_ordinal1(B) -> ((all C (r2_hidden(C,A) -> r2_hidden(k6_classes1(C),B))) <-> r1_ordinal1(k6_classes1(A),B)))) # label(t77_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4244 (all A all B r1_tarski(k5_classes1(k3_xboole_0(A,B)),k3_xboole_0(k5_classes1(A),k5_classes1(B)))) # label(t68_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4245 (all A all B (v3_ordinal1(B) -> (r2_hidden(k1_tarski(A),k4_classes1(k1_ordinal1(B))) <-> r2_hidden(A,k4_classes1(B))))) # label(t49_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4246 $T # label(t1_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4247 (all A all B all C (r2_hidden(B,k1_classes1(A)) & r2_hidden(C,k1_classes1(A)) -> r2_hidden(k2_tarski(B,C),k1_classes1(A)) & r2_hidden(k1_tarski(B),k1_classes1(A)))) # label(t30_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4248 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(k4_classes1(A),k4_classes1(B)) <-> r2_hidden(A,B)))))) # label(t42_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4249 (all A v1_ordinal1(k5_classes1(A))) # label(t58_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4250 $T # label(t57_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4251 (all A all B (v3_ordinal1(B) -> (r1_ordinal1(B,k6_classes1(A)) <-> (all C (v3_ordinal1(C) -> -(r2_hidden(C,B) & (all D -(r2_hidden(D,A) & r1_ordinal1(C,k6_classes1(D)))))))))) # label(t78_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4252 (all A all B (v3_ordinal1(B) -> (r2_hidden(k1_zfmisc_1(A),k4_classes1(k1_ordinal1(B))) <-> r2_hidden(A,k4_classes1(B))))) # label(t48_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4253 (all A (v3_ordinal1(A) -> r1_tarski(A,k4_classes1(A)))) # label(t44_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4254 (all A (v1_ordinal1(A) -> r1_tarski(k3_tarski(A),A))) # label(t54_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4255 (all A r1_tarski(A,k5_classes1(A))) # label(t59_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4256 (all A all B all C (v3_ordinal1(C) -> (r2_hidden(A,a_2_2_classes1(B,C)) <-> (exists D ((exists E (v3_ordinal1(E) & r2_hidden(E,C) & r2_hidden(D,k3_classes1(B,E)))) & A = D & m1_subset_1(D,k1_classes1(B))))))) # label(fraenkel_a_2_2_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4257 (all A all B (v3_ordinal1(B) -> k3_classes1(A,B) = k2_classes1(A,B))) # label(redefinition_k3_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4258 (all A (v2_classes1(A) <-> (all B (r1_tarski(B,A) & r2_hidden(k1_card_1(B),k1_card_1(A)) -> r2_hidden(B,A))) & v1_classes1(A) & (all B (r2_hidden(B,A) -> r2_hidden(k1_zfmisc_1(B),A))))) # label(t2_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4259 (all A all B (r1_classes1(A,B) <-> v2_classes1(B) & r2_hidden(A,B))) # label(d3_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4260 (all A all B all C (r1_tarski(C,A) & r2_hidden(A,k1_classes1(B)) -> r2_hidden(C,k1_classes1(B)))) # label(t6_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4261 (all A (k3_classes1(A,k4_ordinal2) != k3_classes1(A,k1_xboole_0) & r2_hidden(k3_classes1(A,k1_xboole_0),k3_classes1(A,k4_ordinal2)))) # label(t26_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4262 (all A all B all C (r2_hidden(C,k1_classes1(A)) & r2_hidden(B,k1_classes1(A)) -> r2_hidden(k4_tarski(B,C),k1_classes1(A)))) # label(t31_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4263 (all A all B all C (v3_ordinal1(C) -> (-((all D -(r2_hidden(D,k3_classes1(B,C)) & (r1_tarski(A,D) | k1_zfmisc_1(D) = A))) & -(r2_hidden(A,k1_classes1(B)) & r1_tarski(A,k3_classes1(B,C)))) <-> r2_hidden(A,k3_classes1(B,k1_ordinal1(C)))))) # label(t13_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4264 (all A all B (v3_ordinal1(B) -> (r2_hidden(k6_classes1(A),B) <-> r2_hidden(A,k4_classes1(B))))) # label(t74_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4265 (all A (v3_ordinal1(A) -> (all B (r2_hidden(B,k4_classes1(A)) -> -r2_tarski(B,k4_classes1(A)) & r2_hidden(k1_card_1(B),k1_card_1(k4_classes1(A))))))) # label(t45_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4266 (all A all B (r2_hidden(k1_card_1(A),k1_card_1(k1_classes1(B))) & r1_tarski(A,k1_classes1(B)) -> r2_hidden(A,k1_classes1(B)))) # label(t9_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4267 (all A all B (v1_ordinal1(A) & v1_ordinal1(B) -> v1_ordinal1(k2_xboole_0(A,B)))) # label(t55_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4268 (all A all B ((all C (v1_ordinal1(C) & r1_tarski(A,C) -> r1_tarski(B,C))) & r1_tarski(A,B) & v1_ordinal1(B) -> k5_classes1(A) = B)) # label(t61_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4269 (all A (v4_ordinal1(k6_classes1(k1_classes1(A))) & k6_classes1(k1_classes1(A)) != k1_xboole_0)) # label(t82_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4270 (all A all B (v3_ordinal1(B) -> (r1_tarski(A,k4_classes1(B)) <-> r1_tarski(k1_zfmisc_1(A),k4_classes1(k1_ordinal1(B)))))) # label(t46_classes1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4271 (all A (v1_relat_1(A) & v1_card_3(A) & v1_funct_1(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]. 56.88/55.89 4272 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,B) -> r1_tarski(k3_card_3(A),k3_card_3(B))))))) # label(t35_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4273 (all A all B all C ((all D (r2_hidden(D,C) <-> (exists E (r2_hidden(E,B) & v1_funct_1(E) & v1_relat_1(E) & D = k1_funct_1(E,A))))) <-> C = k5_card_3(A,B))) # label(d6_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4274 (all A (v1_funct_1(A) & v1_relat_1(A) -> k3_tarski(k2_relat_1(A)) = k3_card_3(A))) # label(d4_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4275 (all A all B (v1_relat_1(B) & v1_funct_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]. 56.88/55.89 4276 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k1_card_3(A)) & v1_relat_1(k1_card_3(A)) & v1_card_3(k1_card_3(A)))) # label(dt_k1_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4277 $T # label(t1_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4278 (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]. 56.88/55.89 4279 (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]. 56.88/55.89 4280 $T # label(t5_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4281 (all A k1_xboole_0 = k5_card_3(A,k1_xboole_0)) # label(t24_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4282 $T # label(dt_k5_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4283 (all A all B k2_funcop_1(A,k1_card_1(B)) = k1_card_3(k2_funcop_1(A,B))) # label(t10_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4284 (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]. 56.88/55.89 4285 $T # label(t7_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.89 4286 (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]. 56.88/55.89 4287 (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]. 56.88/55.90 4288 (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) -> (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(k6_card_3(A),k6_card_3(B))))))) # label(t43_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4289 (all A all B k3_card_3(k2_card_3(k2_funcop_1(A,B))) = k2_zfmisc_1(B,A)) # label(t36_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4290 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) -> (all B (v1_card_3(B) & v1_funct_1(B) & v1_relat_1(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]. 56.88/55.90 4291 k1_xboole_0 != f1_s3_card_3 & (all A all B all C (p1_s3_card_3(B,C) & p1_s3_card_3(A,B) -> p1_s3_card_3(A,C))) & (all A all B (p1_s3_card_3(B,A) | p1_s3_card_3(A,B))) -> (exists A ((all B (r2_hidden(B,f1_s3_card_3) -> p1_s3_card_3(A,B))) & r2_hidden(A,f1_s3_card_3))) # label(s3_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4292 (exists A (v1_card_3(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc1_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4293 (all A all B k3_card_3(k2_funcop_1(k1_tarski(A),B)) = B) # label(t17_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4294 (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]. 56.88/55.90 4295 (all A (v1_funct_1(A) & v1_card_3(A) & v1_relat_1(A) -> (k7_card_3(A) = np__0 <-> r2_hidden(k1_xboole_0,k2_relat_1(A))))) # label(t44_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4296 (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]. 56.88/55.90 4297 (all A (v1_card_1(A) -> np__0 = k6_card_3(k2_funcop_1(k1_xboole_0,A)))) # label(t48_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4298 (all A all B all C (p1_s2_card_3(B,C) & p1_s2_card_3(A,B) -> p1_s2_card_3(A,C))) & (all A all B (p1_s2_card_3(A,B) & p1_s2_card_3(B,A) -> A = B)) & f1_s2_card_3 != k1_xboole_0 -> (exists A ((all B -(A != B & p1_s2_card_3(B,A) & r2_hidden(B,f1_s2_card_3))) & r2_hidden(A,f1_s2_card_3))) # label(s2_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4299 (all A all B (v1_card_1(B) -> v1_relat_1(k2_funcop_1(A,B)) & v1_ordinal2(k2_funcop_1(A,B)) & v1_card_3(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)))) # label(fc2_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4300 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) -> (all B (v1_card_3(B) & v1_funct_1(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]. 56.88/55.90 4301 $T # label(t21_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4302 (all A (v1_funct_1(A) & v1_relat_1(A) & v2_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]. 56.88/55.90 4303 (all A (v1_card_1(A) -> (all B k6_card_3(k2_funcop_1(k1_tarski(B),A)) = A))) # label(t50_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4304 (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]. 56.88/55.90 4305 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (B = k4_card_3(A) <-> (all C (r2_hidden(C,B) <-> (exists D ((all E (r2_hidden(E,k1_relat_1(A)) -> r2_hidden(k1_funct_1(D,E),k1_funct_1(A,E)))) & v1_funct_1(D) & k1_relat_1(D) = k1_relat_1(A) & D = C & v1_relat_1(D))))))))) # label(d5_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4306 (all A (v1_card_3(A) & v1_funct_1(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]. 56.88/55.90 4307 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> r1_tarski(k1_funct_1(A,C),k1_funct_1(B,C)))) & k1_relat_1(B) = k1_relat_1(A) -> r1_tarski(k4_card_3(A),k4_card_3(B))))))) # label(t38_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4308 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) -> (all B (v1_card_3(B) & v1_funct_1(B) & v1_relat_1(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]. 56.88/55.90 4309 (all A (v1_funct_1(A) & v1_relat_1(A) & v1_card_3(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_card_3(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(k7_card_3(A),k7_card_3(B))))))) # label(t45_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4310 (all A (v1_funct_1(A) & v1_card_3(A) & v1_relat_1(A) -> r1_tarski(k1_card_1(k3_card_3(A)),k6_card_3(A)))) # label(t55_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4311 (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]. 56.88/55.90 4312 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_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]. 56.88/55.90 4313 (all A (v1_card_3(A) & v1_relat_1(A) & v1_funct_1(A) -> A = k1_card_3(A))) # label(t8_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4314 (all A (v1_funct_1(A) & v1_relat_1(A) -> (r2_hidden(k1_xboole_0,k2_relat_1(A)) <-> k1_xboole_0 = k4_card_3(A)))) # label(t37_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4315 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_card_3(B) & v1_funct_1(B) & v1_relat_1(B) -> (k1_card_3(A) = B <-> k1_relat_1(B) = k1_relat_1(A) & (all C (r2_hidden(C,k1_relat_1(A)) -> k1_card_1(k1_funct_1(A,C)) = k1_funct_1(B,C)))))))) # label(d2_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4316 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(C)) & r2_hidden(B,k1_relat_1(C)) -> B = A | r1_xboole_0(k1_funct_1(k2_card_3(C),A),k1_funct_1(k2_card_3(C),B))))) # label(t13_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4317 $T # label(t2_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4318 $T # label(dt_k4_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4319 $T # label(t41_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4320 (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]. 56.88/55.90 4321 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (B = k2_card_3(A) <-> (all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(B,C) = k2_zfmisc_1(k1_funct_1(A,C),k1_tarski(C)))) & k1_relat_1(B) = k1_relat_1(A)))))) # label(d3_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4322 $T # label(t6_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4323 (all A all B (v1_funct_1(A) & v1_card_3(A) & v1_relat_1(A) -> v1_relat_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)) & v1_card_3(k7_relat_1(A,B)))) # label(fc1_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4324 (all A all B (k1_xboole_0 != A -> B = k3_card_3(k2_funcop_1(A,B)))) # label(t16_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4325 (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]. 56.88/55.90 4326 (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]. 56.88/55.90 4327 (all A (v1_card_3(A) & v1_funct_1(A) & v1_relat_1(A) -> v1_card_1(k6_card_3(A)))) # label(dt_k6_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4328 (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]. 56.88/55.90 4329 $T # label(t42_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4330 (all A (v1_relat_1(A) & v1_card_3(A) & v1_funct_1(A) -> v1_card_1(k7_card_3(A)))) # label(dt_k7_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4331 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(A,k3_card_3(k2_card_3(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(k2_mcart_1(A),k1_relat_1(B))))) # label(t33_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4332 $T # label(dt_k3_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4333 (exists A ((all B (r2_hidden(B,f1_s4_card_3) -> (all C (r2_hidden(C,k1_funct_1(A,B)) <-> r2_hidden(C,f2_s4_card_3(B)) & p1_s4_card_3(B,C))))) & v1_funct_1(A) & f1_s4_card_3 = k1_relat_1(A) & v1_relat_1(A))) # label(s4_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4334 (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]. 56.88/55.90 4335 (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]. 56.88/55.90 4336 (all A all B k2_card_3(k2_funcop_1(k1_tarski(A),B)) = k2_funcop_1(k1_tarski(A),k2_zfmisc_1(B,k1_tarski(A)))) # label(t12_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4337 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(A,k4_card_3(B)) <-> k1_relat_1(B) = k1_relat_1(A) & (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]. 56.88/55.90 4338 (all A (v1_card_3(A) & v1_funct_1(A) & v1_relat_1(A) -> k1_card_1(k4_card_3(A)) = k7_card_3(A))) # label(d8_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4339 (all A (v1_card_1(A) -> (all B ((all C (r2_hidden(C,B) -> r2_hidden(k1_card_1(C),A))) & v6_ordinal1(B) -> r1_tarski(k1_card_1(k3_tarski(B)),A))))) # label(t62_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4340 (all A all B all C k5_card_3(C,k2_xboole_0(A,B)) = k2_xboole_0(k5_card_3(C,A),k5_card_3(C,B))) # label(t27_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4341 (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]. 56.88/55.90 4342 $T # label(t23_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4343 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> -((all C all D A != k4_tarski(C,D)) & r2_hidden(A,k3_card_3(k2_card_3(B)))))) # label(t32_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4344 (exists A (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) & (all B (r2_hidden(B,f1_s1_card_3) -> k1_funct_1(A,B) = f2_s1_card_3(B))) & k1_relat_1(A) = f1_s1_card_3)) # label(s1_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4345 (all A -(v6_ordinal1(A) & (all B -(k3_tarski(B) = k3_tarski(A) & (all C -(r1_tarski(C,B) & C != k1_xboole_0 & (all D -((all E (r2_hidden(E,C) -> r1_tarski(D,E))) & r2_hidden(D,C))))) & r1_tarski(B,A))))) # label(t61_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4346 (all A (v1_funct_1(A) & v1_relat_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]. 56.88/55.90 4347 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B (r2_hidden(B,k1_relat_1(A)) -> v1_card_1(k1_funct_1(A,B)))) <-> v1_card_3(A)))) # label(d1_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4348 (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]. 56.88/55.90 4349 (all A all B all C (v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & v1_funct_1(C) & v1_setfam_1(B) -> -v1_xboole_0(k4_card_3(C)) & v1_fraenkel(k4_card_3(C)))) # label(fc4_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4350 $T # label(t4_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4351 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) -> k6_card_3(A) = k1_card_1(k3_card_3(k2_card_3(A))))) # label(d7_card_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4352 (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]. 56.88/55.90 4353 (all A r1_tarski(k4_classes1(k1_card_1(k1_classes1(A))),k1_classes1(A))) # label(t29_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4354 (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]. 56.88/55.90 4355 (all A (v1_classes2(A) & -v1_xboole_0(A) -> A = k4_classes1(k2_ordinal2(A)))) # label(t54_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4356 (all A (v2_classes1(A) -> v1_classes1(A))) # label(cc1_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4357 (all A (v2_classes1(A) & v1_ordinal1(A) -> v1_classes2(A))) # label(cc3_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4358 (all A (v1_card_1(A) -> (all B (v2_classes1(B) & r2_hidden(A,B) -> r1_tarski(A,B))))) # label(t18_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4359 (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]. 56.88/55.90 4360 (all A all B all C (m1_subset_1(C,A) & -v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(B,A) -> k8_classes2(A,C,B) = k8_classes2(A,B,C))) # label(commutativity_k8_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4361 (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]. 56.88/55.90 4362 (all A (v2_classes1(A) -> v4_ordinal1(k1_card_1(A)))) # label(t20_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4363 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> k1_funct_2(B,C) = k12_classes2(A,B,C))) # label(redefinition_k12_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4364 (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]. 56.88/55.90 4365 (all A all B (-(-(r2_hidden(k1_card_1(A),k1_card_1(k1_classes1(B))) & r1_tarski(A,k1_classes1(B))) & -(r2_hidden(A,k1_classes1(B)) & r1_tarski(A,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]. 56.88/55.90 4366 (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]. 56.88/55.90 4367 (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]. 56.88/55.90 4368 (all A v1_ordinal1(k5_classes1(A))) # label(fc5_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4369 (all A (v3_ordinal1(A) -> v1_classes2(k1_classes1(A)))) # label(t53_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4370 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & v1_classes2(A) & m1_subset_1(B,A) -> m1_subset_1(k8_classes2(A,B,C),A))) # label(dt_k8_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4371 (all A (v1_ordinal1(A) -> -v1_xboole_0(k1_classes1(A)) & v1_ordinal1(k1_classes1(A)) & v1_classes1(k1_classes1(A)) & v2_classes1(k1_classes1(A)) & v1_classes2(k1_classes1(A)))) # label(fc6_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4372 (all A all B (-v1_xboole_0(B) & v1_classes2(B) -> (r2_hidden(A,B) -> r2_hidden(k1_setfam_1(A),B) & r2_hidden(k1_zfmisc_1(A),B) & r2_hidden(k3_tarski(A),B)))) # label(t65_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4373 (all A (v3_ordinal1(A) -> (all B (r2_hidden(A,k2_ordinal2(k1_classes1(B))) -> r2_hidden(k1_card_1(k4_classes1(A)),k1_card_1(k1_classes1(B))) & r2_hidden(k4_classes1(A),k1_classes1(B)))))) # label(t27_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4374 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> k10_classes2(A,B,C) = k5_xboole_0(B,C))) # label(redefinition_k10_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4375 (all A (v2_classes1(A) -> r1_tarski(k4_classes1(k1_card_1(A)),A))) # label(t28_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4376 (all A all B all C (v1_classes2(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> m1_subset_1(k11_classes2(A,B,C),A))) # label(dt_k11_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4377 (all A all B (v2_classes1(A) & r2_hidden(B,k1_card_1(A)) -> r2_hidden(B,A))) # label(t14_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4378 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & v1_classes2(B) -> (all C (-v1_xboole_0(C) & v1_classes2(C) -> (r2_hidden(A,B) & r2_hidden(B,C) -> r2_hidden(A,C)))))))) # label(t59_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4379 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & v1_classes2(A) -> k11_classes2(A,B,C) = k2_zfmisc_1(B,C))) # label(redefinition_k11_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4380 $T # label(t60_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4381 $T # label(dt_k16_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4382 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & v1_classes2(A) -> k10_classes2(A,B,C) = k10_classes2(A,C,B))) # label(commutativity_k10_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4383 (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]. 56.88/55.90 4384 (all A (v2_classes1(A) -> A = k1_xboole_0 | k1_card_1(A) != np__0 & v4_ordinal1(k1_card_1(A)) & k1_xboole_0 != k1_card_1(A))) # label(t21_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4385 (all A all B (v1_ordinal1(A) & v2_classes1(A) & r2_hidden(B,A) -> r2_hidden(k6_classes1(B),A))) # label(t30_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4386 (all A v2_classes1(k4_classes1(k1_card_1(k1_classes1(A))))) # label(t40_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4387 (all A (-v1_xboole_0(k1_classes1(A)) & v2_classes1(k1_classes1(A)) & v1_classes1(k1_classes1(A)))) # label(fc1_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4388 (all A (v3_ordinal1(A) -> (all B (B = k16_classes2(A) <-> (exists C (v1_funct_1(C) & v5_ordinal1(C) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> D = k1_xboole_0 | k15_classes2(k3_card_3(k2_ordinal1(C,D))) = k1_funct_1(C,D)))) & k1_ordinal1(A) = k1_relat_1(C) & B = k1_ordinal2(C) & v1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_classes1(k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & k13_classes2 = k1_funct_1(C,k1_xboole_0))))))) # label(d5_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4389 (all A (v3_ordinal1(A) -> (all B (v2_classes1(B) & r2_hidden(A,B) -> r1_tarski(A,B) & r2_hidden(k1_ordinal1(A),B))))) # label(t6_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4390 (all A (v3_ordinal1(A) -> k1_classes1(k16_classes2(A)) = k16_classes2(k1_ordinal1(A)))) # label(t76_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4391 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & v1_classes2(B) -> r3_xboole_0(A,B))))) # label(t58_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4392 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & v1_classes2(A) -> k5_classes2(A,B,C) = k5_classes2(A,C,B))) # label(commutativity_k5_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4393 (all A (v1_classes2(A) & -v1_xboole_0(A) -> v1_classes2(k1_classes1(A)) & -v1_xboole_0(k1_classes1(A)))) # label(t52_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4394 (all A all B (v1_ordinal1(B) & v2_classes1(A) & r2_hidden(B,A) -> r2_hidden(B,k4_classes1(k1_card_1(A))))) # label(t43_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4395 (all A (v1_ordinal1(A) -> v1_classes2(k1_classes1(A)))) # label(t51_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4396 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & v1_classes2(A) -> k8_classes2(A,B,B) = B)) # label(idempotence_k8_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4397 $T # label(t47_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4398 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) & v1_classes2(A) -> k1_setfam_1(B) = k4_classes2(A,B))) # label(redefinition_k4_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4399 (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]. 56.88/55.90 4400 $T # label(t72_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4401 (all A (v1_ordinal1(A) & v2_classes1(A) -> k4_classes1(k1_card_1(A)) = A)) # label(t32_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4402 (all A all B all C (v2_classes1(A) & r2_hidden(B,A) & r2_hidden(C,A) -> r2_hidden(k4_tarski(B,C),A))) # label(t4_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4403 $T # label(t48_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4404 (all A k1_card_1(k1_classes1(A)) = k1_card_1(k4_classes1(k1_card_1(k1_classes1(A))))) # label(t36_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4405 (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(k5_classes2(A,B,C),A))) # label(dt_k5_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4406 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) & v1_classes2(A) -> m1_subset_1(k4_classes2(A,B),A))) # label(dt_k4_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4407 (all A all B (v2_classes1(A) -> -(r1_tarski(B,A) & r2_hidden(k1_card_1(B),k1_card_1(A))) & -(r1_tarski(B,A) & r2_hidden(B,A)) & -(r2_hidden(B,A) & v1_ordinal1(A)) | r1_tarski(k1_funct_2(B,A),A))) # label(t23_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4408 (all A all B (m1_subset_1(B,A) & -v1_xboole_0(A) & v1_classes2(A) -> k1_classes2(A,B) = k1_tarski(B))) # label(redefinition_k1_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4409 (all A all B all C (v1_classes2(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k2_xboole_0(B,C) = k7_classes2(A,B,C))) # label(redefinition_k7_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4410 (all A (-v1_xboole_0(A) & v1_classes2(A) -> r1_tarski(k1_classes1(k1_xboole_0),A) & r1_tarski(k13_classes2,A) & r1_tarski(k16_classes2(k1_xboole_0),A))) # label(t79_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4411 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (-v1_xboole_0(B) & v1_classes2(B) -> v1_classes2(k2_xboole_0(A,B)) & -v1_xboole_0(k2_xboole_0(A,B)) & -v1_xboole_0(k3_xboole_0(A,B)) & v1_classes2(k3_xboole_0(A,B)))))) # label(t61_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4412 (all A (v1_classes2(A) & -v1_xboole_0(A) -> v1_ordinal1(k2_ordinal2(A)) & v2_ordinal1(k2_ordinal2(A)) & v3_ordinal1(k2_ordinal2(A)))) # label(fc2_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.90 4413 (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]. 56.88/55.90 4414 (all A (v3_ordinal1(A) -> (all B -(v1_ordinal1(B) & (all C -(A = k6_classes1(C) & r2_hidden(C,B))) & r2_hidden(A,k6_classes1(B)))))) # label(t41_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4415 (all A (-v1_xboole_0(A) & v1_classes2(A) -> v3_ordinal1(k2_ordinal2(A)))) # label(t50_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4416 (all A (-v1_xboole_0(A) & v1_classes2(A) -> v1_ordinal1(k1_classes1(A)) & v1_classes2(k1_classes1(A)) & -v1_xboole_0(k1_classes1(A)) & v1_classes1(k1_classes1(A)) & v2_classes1(k1_classes1(A)))) # label(fc3_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4417 (all A (v1_ordinal1(A) & v2_classes1(A) <-> v1_classes2(A))) # label(d1_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4418 (all A all B all C (m1_subset_1(B,A) & v1_classes2(A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> m1_subset_1(k10_classes2(A,B,C),A))) # label(dt_k10_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4419 (all A (v2_classes1(A) -> v2_classes1(k4_classes1(k1_card_1(A))))) # label(t39_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4420 $T # label(t49_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4421 (all A all B all C (-v1_xboole_0(C) & v1_classes2(C) -> (r2_hidden(A,C) & r2_hidden(B,C) -> r2_hidden(k2_tarski(A,B),C) & r2_hidden(k4_tarski(A,B),C)))) # label(t64_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4422 (all A (v1_classes2(A) -> v1_ordinal1(A) & v2_classes1(A) & v1_classes1(A))) # label(cc2_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4423 (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]. 56.88/55.91 4424 (all A all B all C (v1_classes2(A) & m1_subset_1(B,A) & -v1_xboole_0(A) & m1_subset_1(C,A) -> m1_subset_1(k9_classes2(A,B,C),A))) # label(dt_k9_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4425 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & v1_classes2(B) -> -(-r2_hidden(A,B) & -r2_hidden(B,A) & A != B))))) # label(t56_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4426 (all A (v3_ordinal1(A) -> v1_ordinal1(k4_classes1(A)))) # label(fc7_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4427 (all A all B all C (-v1_xboole_0(C) & v1_classes2(C) -> (r2_hidden(B,C) & r2_hidden(A,C) -> r2_hidden(k1_funct_2(A,B),C) & r2_hidden(k2_zfmisc_1(A,B),C)))) # label(t67_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4428 $T # label(t74_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4429 (all A all B (v1_classes2(B) & -v1_xboole_0(B) -> (r2_hidden(A,B) -> r2_hidden(k1_tarski(A),B)))) # label(t63_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4430 (exists A (v1_ordinal1(A) & v2_classes1(A) & v1_classes2(A) & v1_classes1(A) & -v1_xboole_0(A))) # label(rc1_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4431 $T # label(t2_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4432 (all A all B (v1_classes2(A) & -v1_xboole_0(A) & m1_subset_1(B,A) -> k3_classes2(A,B) = k3_tarski(B))) # label(redefinition_k3_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4433 (all A all B all C (m1_subset_1(B,A) & -v1_xboole_0(A) & m1_subset_1(C,A) & v1_classes2(A) -> k2_tarski(B,C) = k5_classes2(A,B,C))) # label(redefinition_k5_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4434 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(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)))) -> k15_classes2(k3_card_3(B)) = k16_classes2(A) | k1_xboole_0 = A))))) # label(t78_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4435 (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]. 56.88/55.91 4436 (all A all B (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(B,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]. 56.88/55.91 4437 (all A all B (r2_hidden(A,k1_classes1(B)) & v1_ordinal1(A) -> r1_tarski(A,k1_classes1(B)))) # label(t9_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4438 (all A all B all C (m1_subset_1(B,A) & v1_classes2(A) & -v1_xboole_0(A) & m1_subset_1(C,A) -> B = k7_classes2(A,B,B))) # label(idempotence_k7_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4439 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) & v1_classes2(A) -> k6_classes2(A,B,C) = k4_tarski(B,C))) # label(redefinition_k6_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4440 $T # label(t68_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4441 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) & v1_classes2(A) -> m1_subset_1(k3_classes2(A,B),A))) # label(dt_k3_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4442 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> m1_subset_1(k12_classes2(A,B,C),A))) # label(dt_k12_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4443 (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]. 56.88/55.91 4444 (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]. 56.88/55.91 4445 (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]. 56.88/55.91 4446 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & v1_classes2(A) -> k7_classes2(A,C,B) = k7_classes2(A,B,C))) # label(commutativity_k7_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4447 (all A (v2_classes1(A) -> k2_ordinal2(A) = k1_card_1(A))) # label(t10_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4448 (all A all B -(-r2_hidden(A,k4_classes1(k1_card_1(k1_classes1(B)))) & r1_tarski(A,k4_classes1(k1_card_1(k1_classes1(B)))) & -r2_wellord2(A,k4_classes1(k1_card_1(k1_classes1(B)))))) # label(t38_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4449 (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]. 56.88/55.91 4450 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (exists B (m1_subset_1(B,A) & -v1_xboole_0(B))))) # label(rc2_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4451 (all A all B all C (v1_classes2(A) & -v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> m1_subset_1(k6_classes2(A,B,C),A))) # label(dt_k6_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4452 (all A (v3_ordinal1(A) -> (all B (r2_hidden(A,k1_classes1(B)) -> r2_hidden(k1_ordinal1(A),k1_classes1(B)) & r1_tarski(A,k1_classes1(B)))))) # label(t7_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4453 (all A all B (v1_classes2(B) & -v1_xboole_0(B) -> (k15_classes2(A) = B <-> (all C (v1_classes2(C) & -v1_xboole_0(C) -> (r1_tarski(A,C) -> r1_tarski(B,C)))) & r1_tarski(A,B)))) # label(d4_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4454 (all A (v1_classes2(A) & -v1_xboole_0(A) -> r2_hidden(k1_xboole_0,A))) # label(t62_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4455 (all A (v1_ordinal1(A) -> k1_classes1(A) = k4_classes1(k1_card_1(k1_classes1(A))))) # label(t46_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4456 (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]. 56.88/55.91 4457 (all A all B (r2_hidden(B,A) & v2_classes1(A) -> r1_tarski(k1_classes1(B),A))) # label(t5_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4458 (all A (v1_card_1(A) -> (all B (v2_classes1(B) & r2_hidden(A,k1_card_1(B)) -> r2_hidden(A,B))))) # label(t16_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4459 (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]. 56.88/55.91 4460 (all A all B (m1_subset_1(B,A) & -v1_xboole_0(A) & v1_classes2(A) -> k2_classes2(A,B) = k1_zfmisc_1(B))) # label(redefinition_k2_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4461 (all A (-v1_xboole_0(k15_classes2(A)) & v1_classes2(k15_classes2(A)))) # label(dt_k15_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4462 (all A (k1_card_1(k1_classes1(A)) != k1_xboole_0 & v4_ordinal1(k1_card_1(k1_classes1(A))) & k1_card_1(k1_classes1(A)) != np__0)) # label(t22_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4463 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & v1_classes2(A) & -v1_xboole_0(A) -> k9_classes2(A,B,C) = k4_xboole_0(B,C))) # label(redefinition_k9_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4464 (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]. 56.88/55.91 4465 (all A (v1_classes2(A) & -v1_xboole_0(A) -> v4_ordinal1(k2_ordinal2(A)) & k2_ordinal2(A) != k1_xboole_0)) # label(t55_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4466 (all A (v3_ordinal1(A) -> v1_ordinal1(k1_classes1(A)) & v1_classes1(k1_classes1(A)) & v1_classes2(k1_classes1(A)) & v2_classes1(k1_classes1(A)) & -v1_xboole_0(k1_classes1(A)))) # label(fc4_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4467 (all A (v5_ordinal1(A) & v1_relat_1(A) & v1_funct_1(A) -> ((all B (v3_ordinal1(B) -> (r2_hidden(B,k1_relat_1(A)) -> k4_classes1(B) = k1_funct_1(A,B)))) & v4_ordinal1(k1_relat_1(A)) -> k3_card_3(A) = k4_classes1(k1_relat_1(A))))) # label(t25_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4468 (all A k2_ordinal2(k1_classes1(A)) = k1_card_1(k1_classes1(A))) # label(t11_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4469 (all A all B all C (v1_classes2(A) & m1_subset_1(C,A) & -v1_xboole_0(A) & m1_subset_1(B,A) -> m1_subset_1(k7_classes2(A,B,C),A))) # label(dt_k7_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4470 (all A all B (v1_classes1(A) & r2_hidden(B,A) -> r2_hidden(k1_card_1(B),k1_card_1(A)) & -r2_wellord2(B,A))) # label(t1_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4471 (all A all B all C (-v1_xboole_0(C) & v1_classes2(C) -> (r2_hidden(B,C) & r2_hidden(A,C) -> r2_hidden(k2_xboole_0(A,B),C) & r2_hidden(k4_xboole_0(A,B),C) & r2_hidden(k5_xboole_0(A,B),C) & r2_hidden(k3_xboole_0(A,B),C)))) # label(t66_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4472 (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]. 56.88/55.91 4473 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (v1_classes2(B) & -v1_xboole_0(B) -> r2_hidden(B,A) | r1_tarski(A,B))))) # label(t57_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4474 (all A all B -(-r2_wellord2(B,k4_classes1(k1_card_1(A))) & -r2_hidden(B,k4_classes1(k1_card_1(A))) & r1_tarski(B,k4_classes1(k1_card_1(A))) & v2_classes1(A))) # label(t37_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4475 $T # label(t73_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4476 (all A (v3_ordinal1(A) -> (all B (r2_hidden(A,k2_ordinal2(B)) & v2_classes1(B) -> r1_tarski(k1_card_1(k4_classes1(A)),k1_card_1(B)))))) # label(t33_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4477 (all A (v3_ordinal1(A) -> v2_classes1(k16_classes2(A)) & -v1_xboole_0(k16_classes2(A)) & v1_classes1(k16_classes2(A)) & v1_classes2(k16_classes2(A)) & v1_ordinal1(k16_classes2(A)))) # label(fc8_classes2) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4478 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (k2_finseq_1(k2_xcmplx_0(A,B)) = k2_finseq_1(A) -> B = np__0))))) # label(t18_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4479 (all A all B (v4_ordinal2(B) -> (r1_tarski(A,k2_finseq_1(B)) -> v2_funct_1(k14_finseq_1(A))))) # label(t99_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4480 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> k7_relat_1(k1_finseq_2(k2_xcmplx_0(A,B)),k2_finseq_1(A)) = k1_finseq_2(A))))) # label(t56_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4481 (all A (v4_ordinal2(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (-r2_hidden(A,k4_finseq_1(B)) -> B = k2_finseq_3(A,B)) & -(r2_hidden(A,k4_finseq_1(B)) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(k3_finseq_1(B) = k1_nat_1(C,np__1) & C = k3_finseq_1(k2_finseq_3(A,B)))))))))) # label(t113_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4482 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (r1_tarski(k2_relat_1(A),B) <-> k1_xboole_0 = k1_finseq_3(A,B))))) # label(t75_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4483 (all A all B all C (v4_ordinal2(C) -> (k2_finseq_1(C) = k2_tarski(A,B) -> B = A | k2_tarski(A,B) = k2_tarski(np__1,np__2) & C = np__2))) # label(t23_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4484 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (k1_xboole_0 != k2_relat_1(A) -> r2_hidden(np__1,k4_finseq_1(A))))) # label(t34_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4485 (all A all B all C k9_finseq_1(A) != k10_finseq_1(B,C)) # label(t40_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4486 (all A all B k1_xboole_0 != k10_finseq_1(A,B)) # label(t38_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4487 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> k14_finseq_1(k2_finseq_1(A)) = k7_relat_1(k14_finseq_1(k2_finseq_1(k2_xcmplx_0(A,B))),k2_finseq_1(A)))))) # label(t53_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4488 (all A all B all C all D k11_finseq_1(B,C,D) != k9_finseq_1(A)) # label(t41_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4489 (all A all B (A != B <-> v2_funct_1(k10_finseq_1(A,B)))) # label(t103_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4490 (all A (v4_ordinal2(A) -> A = k3_finseq_1(k14_finseq_1(k2_finseq_1(A))))) # label(t52_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4491 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C k7_finseq_1(k1_finseq_3(A,C),k1_finseq_3(B,C)) = k1_finseq_3(k7_finseq_1(A,B),C)))))) # label(t80_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4492 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v4_ordinal2(B) -> (r2_hidden(B,k4_finseq_1(A)) <-> r1_xreal_0(B,k3_finseq_1(A)) & r1_xreal_0(np__1,B)))))) # label(t27_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4493 (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(B)) <-> r1_xreal_0(k3_finseq_1(A),k3_finseq_1(B))))))) # label(t32_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4494 (all A all B all C k4_finseq_1(k11_finseq_1(A,B,C)) = k2_finseq_1(np__3)) # label(t30_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4495 (all A (v4_ordinal2(A) -> (np__0 != A -> k14_finseq_1(k1_tarski(A)) = k9_finseq_1(A)))) # label(t50_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4496 (all A (v1_funct_1(A) & v1_relat_1(A) & v1_finseq_1(A) -> (all B (k1_tarski(B) = k2_relat_1(A) & v2_funct_1(A) -> A = k9_finseq_1(B))))) # label(t106_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4497 (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 (r2_hidden(C,k4_finseq_1(A)) -> r2_hidden(C,k4_finseq_1(k7_finseq_1(A,B))))))))) # label(t24_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4498 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (k2_relat_1(k1_finseq_3(A,B)) = k2_relat_1(A) -> r1_xboole_0(B,k2_relat_1(A)))))) # label(t74_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4499 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (r1_xboole_0(k2_relat_1(A),k2_relat_1(B)) & v2_funct_1(A) & v2_funct_1(B) <-> v2_funct_1(k7_finseq_1(A,B))))))) # label(t98_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4500 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_finseq_1(B) & v1_relat_1(B) & v1_funct_1(B) -> (all C (v4_ordinal2(C) -> (all D (v4_ordinal2(D) -> (k7_relat_1(A,k2_finseq_1(C)) = B & k2_xcmplx_0(C,D) = k3_finseq_1(A) -> k2_finseq_1(C) = k4_finseq_1(B)))))))))) # label(t60_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4501 (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 (v4_ordinal2(C) -> (k2_xcmplx_0(C,np__1) = k3_finseq_1(A) & B = k7_relat_1(A,k2_finseq_1(C)) -> k7_finseq_1(B,k9_finseq_1(k1_funct_1(A,k2_xcmplx_0(C,np__1)))) = A))))))) # label(t61_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4502 (all A (v4_ordinal2(A) -> k1_tarski(k2_xcmplx_0(A,np__1)) = k6_subset_1(k5_numbers,k2_finseq_1(k2_xcmplx_0(A,np__1)),k2_finseq_1(A)))) # label(t16_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4503 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B all C (k2_tarski(B,C) = k2_relat_1(A) & v2_funct_1(A) -> np__2 = k3_finseq_1(A) | C = B)))) # label(t107_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4504 (all A (v1_funct_1(A) & v1_relat_1(A) & v1_finseq_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) & v1_finseq_1(B) -> (all C all D (v4_ordinal2(D) -> (k7_relat_1(A,k2_finseq_1(D)) = B & k2_xcmplx_0(D,np__1) = k3_finseq_1(A) -> (k7_finseq_1(k1_finseq_3(B,C),k9_finseq_1(k1_funct_1(A,k2_xcmplx_0(D,np__1)))) = k1_finseq_3(A,C) <-> -r2_hidden(k1_funct_1(A,k2_xcmplx_0(D,np__1)),C))))))))) # label(t91_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4505 $T # label(t47_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4506 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B k1_finseq_3(A,B) = k5_relat_1(k14_finseq_1(k4_xboole_0(k4_finseq_1(A),k10_relat_1(A,B))),A)))) # label(d1_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4507 (all A (v4_ordinal2(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_1(C,B) -> m2_finseq_1(k2_finseq_3(A,C),B))))))) # label(t114_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4508 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (r1_xboole_0(B,k2_relat_1(A)) <-> A = k1_finseq_3(A,B))))) # label(t76_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4509 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (k3_finseq_1(k1_finseq_3(A,B)) = k3_finseq_1(A) -> r1_xboole_0(B,k2_relat_1(A)))))) # label(t68_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4510 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B all C (v4_ordinal2(C) -> (r2_hidden(C,k4_finseq_1(A)) -> (all D (v1_finset_1(D) -> -(-r2_hidden(k1_funct_1(A,C),B) & k1_funct_1(A,C) != k1_funct_1(k1_finseq_3(A,B),k6_xcmplx_0(C,k4_card_1(D))) & D = a_3_0_finseq_3(A,B,C))))))))) # label(t92_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4511 (all A all B all C all D (v1_finseq_1(B) & v1_relat_1(B) & v4_ordinal2(D) & v1_funct_1(B) -> (r2_hidden(A,a_3_0_finseq_3(B,C,D)) <-> (exists E (r2_hidden(E,k4_finseq_1(B)) & r1_xreal_0(E,D) & r2_hidden(k1_funct_1(B,E),C) & E = A & m2_subset_1(E,k1_numbers,k5_numbers)))))) # label(fraenkel_a_3_0_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4512 $T # label(t65_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4513 (all A (v4_ordinal2(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> r1_tarski(k2_relat_1(k2_finseq_3(A,B)),k2_relat_1(B)))))) # label(t115_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4514 $T # label(t21_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4515 (all A (v1_finseq_1(A) & v1_relat_1(A) & v1_funct_1(A) -> (all B k3_finseq_1(k1_finseq_3(A,B)) = k6_xcmplx_0(k3_finseq_1(A),k4_card_1(k10_relat_1(A,B)))))) # label(t66_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4516 (all A all B all C (k1_finseq_3(k10_finseq_1(A,B),C) = k1_xboole_0 <-> r2_hidden(B,C) & r2_hidden(A,C))) # label(t84_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4517 $T # label(t8_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4518 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (-r2_hidden(B,k2_relat_1(A)) <-> A = k1_finseq_3(A,k1_tarski(B)))))) # label(t77_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4519 $T # label(t101_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4520 (all A (v4_ordinal2(A) -> -r2_hidden(k2_xcmplx_0(A,np__1),k2_finseq_1(A)))) # label(t9_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4521 (all A (v1_funct_1(A) & v1_relat_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_funct_1(C) & v1_finseq_1(C) -> (k3_finseq_1(A) = k1_nat_1(k3_finseq_1(B),k3_finseq_1(C)) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(B)) -> k1_funct_1(B,D) = k1_funct_1(A,D)))) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(C)) -> k1_funct_1(A,k1_nat_1(k3_finseq_1(B),D)) = k1_funct_1(C,D)))) -> k7_finseq_1(B,C) = A))))))) # label(t43_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4522 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (A != np__0 -> r2_hidden(A,k2_finseq_1(k2_xcmplx_0(A,B)))))))) # label(t10_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4523 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B r1_tarski(k4_finseq_1(k1_finseq_3(A,B)),k4_finseq_1(A))))) # label(t70_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4524 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_finset_1(B) -> (r1_tarski(B,k2_relat_1(A)) & v2_funct_1(A) -> k3_finseq_1(k1_finseq_3(A,B)) = k6_xcmplx_0(k3_finseq_1(A),k4_card_1(B))))))) # label(t96_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4525 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B r1_xreal_0(k3_finseq_1(k1_finseq_3(A,B)),k3_finseq_1(A))))) # label(t67_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4526 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r2_hidden(k2_xcmplx_0(A,B),k2_finseq_1(A)) -> B = np__0))))) # label(t11_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4527 (all A all B all C all D all E k10_finseq_1(A,B) != k11_finseq_1(C,D,E)) # label(t42_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4528 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> r3_xboole_0(k2_finseq_1(A),k2_finseq_1(B)))))) # label(t20_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4529 (all A k1_xboole_0 = k1_finseq_3(k1_xboole_0,A)) # label(t81_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4530 $T # label(t36_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4531 (all A all B all C (r2_hidden(A,B) -> r2_hidden(C,B) | k9_finseq_1(C) = k1_finseq_3(k10_finseq_1(A,C),B))) # label(t85_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4532 (all A (v4_ordinal2(A) -> (all B all C (m2_finseq_1(C,B) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r1_xreal_0(D,A) -> k1_funct_1(C,D) = k1_funct_1(k16_finseq_1(B,C,A),D)))))))) # label(t121_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4533 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B r1_tarski(k2_relat_1(k1_finseq_3(A,B)),k2_relat_1(A))))) # label(t73_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4534 (all A all B (-r2_hidden(A,B) <-> k9_finseq_1(A) = k1_finseq_3(k9_finseq_1(A),B))) # label(t82_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4535 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B k2_relat_1(k1_finseq_3(A,B)) = k4_xboole_0(k2_relat_1(A),B)))) # label(t72_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4536 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B -(B = np__0 & r2_hidden(B,k4_finseq_1(A)))))) # label(t26_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4537 (all A all B all C (k1_finseq_3(k10_finseq_1(A,B),C) = k10_finseq_1(A,B) <-> -r2_hidden(B,C) & -r2_hidden(A,C))) # label(t89_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4538 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r2_hidden(A,k2_finseq_1(B)) -> r1_xreal_0(A,C) | r2_hidden(k6_xcmplx_0(A,C),k2_finseq_1(B))))))))) # label(t13_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4539 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B all C all D (k2_relat_1(A) = k1_enumset1(B,C,D) & v2_funct_1(A) -> C = B | D = B | k3_finseq_1(A) = np__3 | C = D)))) # label(t110_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4540 (all A (v4_ordinal2(A) -> (all B (v1_finset_1(B) -> (r1_tarski(B,k2_finseq_1(A)) -> k4_finseq_1(k14_finseq_1(B)) = k2_finseq_1(k4_card_1(B))))))) # label(t45_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4541 (all A all B k4_finseq_1(k10_finseq_1(A,B)) = k2_finseq_1(np__2)) # label(t29_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4542 (all A (v4_ordinal2(A) -> (all B (v1_finseq_1(B) & v1_relat_1(B) & v1_funct_1(B) -> (all C (r2_hidden(A,k4_finseq_1(B)) -> k1_funct_1(B,A) = k1_funct_1(k7_finseq_1(k9_finseq_1(C),B),k2_xcmplx_0(A,np__1)))))))) # label(t112_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4543 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (r2_hidden(B,k2_relat_1(A)) -> r2_hidden(np__1,k4_finseq_1(A)))))) # label(t33_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4544 (all A (v4_ordinal2(A) -> (all B (v1_finset_1(B) -> (r1_tarski(B,k2_finseq_1(A)) -> k3_finseq_1(k14_finseq_1(B)) = k4_card_1(B)))))) # label(t44_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4545 (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 k4_card_1(k10_relat_1(k7_finseq_1(A,B),C)) = k1_nat_1(k4_card_1(k10_relat_1(A,C)),k4_card_1(k10_relat_1(B,C)))))))) # label(t63_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4546 (all A all B all C (k1_finseq_3(k10_finseq_1(A,B),C) = k9_finseq_1(B) -> -r2_hidden(B,C) & r2_hidden(A,C) | B = A)) # label(t86_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4547 (all A (v4_ordinal2(A) -> k14_finseq_1(k2_finseq_1(A)) = k1_finseq_2(A))) # label(t54_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4548 (all A all B all C (B != A & A != C & C != B <-> v2_funct_1(k11_finseq_1(A,B,C)))) # label(t104_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4549 (all A all B all C (k9_finseq_1(A) = k1_finseq_3(k10_finseq_1(A,B),C) -> A = B | -r2_hidden(A,C) & r2_hidden(B,C))) # label(t88_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4550 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B all C (v4_ordinal2(C) -> (k6_xcmplx_0(k3_finseq_1(A),k4_card_1(k10_relat_1(A,B))) = C -> k4_finseq_1(k1_finseq_3(A,B)) = k2_finseq_1(C)))))) # label(t69_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4551 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r2_hidden(C,k2_finseq_1(A)) & A = k2_xcmplx_0(B,np__1) -> B = k3_finseq_1(k14_finseq_1(k4_xboole_0(k2_finseq_1(A),k1_tarski(C))))))))))) # label(t116_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.91 4552 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B all C -(B != C & k10_finseq_1(B,C) != A & k10_finseq_1(C,B) != A & k2_tarski(B,C) = k2_relat_1(A) & v2_funct_1(A))))) # label(t108_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4553 $T # label(t37_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4554 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r2_hidden(k6_xcmplx_0(A,B),k2_finseq_1(A)) <-> -r1_xreal_0(A,B)))))) # label(t14_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4555 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (k3_finseq_1(A) = k2_xcmplx_0(C,np__1) & r2_hidden(B,k4_finseq_1(A)) -> k3_finseq_1(k2_finseq_3(B,A)) = C))))))) # label(t118_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4556 (all A all B all C k11_finseq_1(A,B,C) != k1_xboole_0) # label(t39_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4557 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (r2_hidden(B,k2_relat_1(A)) & v2_funct_1(A) -> k6_xcmplx_0(k3_finseq_1(A),np__1) = k3_finseq_1(k1_finseq_3(A,k1_tarski(B))))))) # label(t97_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4558 (all A all B all C (r2_hidden(C,B) -> r2_hidden(A,B) | k9_finseq_1(A) = k1_finseq_3(k10_finseq_1(A,C),B))) # label(t87_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4559 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r1_xreal_0(D,C) & k3_finseq_1(A) = k1_nat_1(C,np__1) & r1_xreal_0(B,D) & r2_hidden(B,k4_finseq_1(A)) -> k1_funct_1(k2_finseq_3(B,A),D) = k1_funct_1(A,k1_nat_1(D,np__1))))))))))) # label(t120_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4560 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v2_funct_1(A) -> k6_xcmplx_0(k3_finseq_1(A),k4_card_1(k3_xboole_0(B,k2_relat_1(A)))) = k3_finseq_1(k1_finseq_3(A,B)))))) # label(t95_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4561 (all A (v1_funct_1(A) & v1_relat_1(A) & v1_finseq_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (k1_nat_1(C,np__1) = k3_finseq_1(A) -> k1_funct_1(k2_finseq_3(B,A),D) = k1_funct_1(A,D) | r1_xreal_0(B,D)))))))))) # label(t119_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4562 (all A all B (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> v1_finseq_1(k1_finseq_3(A,B)) & v1_funct_1(k1_finseq_3(A,B)) & v1_relat_1(k1_finseq_3(A,B)))) # label(dt_k1_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4563 (all A v2_funct_1(k9_finseq_1(A))) # label(t102_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4564 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_xreal_0(A,B) <-> k7_relat_1(k1_finseq_2(A),k2_finseq_1(B)) = k1_finseq_2(A)))))) # label(t58_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4565 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (-r1_xreal_0(B,A) -> r2_hidden(k2_xcmplx_0(A,np__1),k2_finseq_1(B))))))) # label(t12_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4566 (all A (v4_ordinal2(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> k5_relat_1(k14_finseq_1(k4_xboole_0(k4_finseq_1(B),k1_tarski(A))),B) = k2_finseq_3(A,B))))) # label(d2_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4567 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) & v1_finseq_1(B) -> (k3_finseq_1(A) = k3_finseq_1(B) <-> k4_finseq_1(A) = k4_finseq_1(B)))))) # label(t31_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4568 (all A all B (r2_hidden(A,B) <-> k1_finseq_3(k9_finseq_1(A),B) = k1_xboole_0)) # label(t83_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4569 (all A (v1_funct_1(A) & v1_relat_1(A) & v1_finseq_1(A) -> (all B (r2_hidden(B,k4_finseq_1(A)) -> m2_subset_1(B,k1_numbers,k5_numbers))))) # label(t25_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4570 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B all C (m2_finseq_1(A,B) -> m2_finseq_1(k1_finseq_3(A,C),B))))) # label(t93_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4571 (all A (v1_funct_1(A) & v1_relat_1(A) & v1_finseq_1(A) -> (all B (v4_ordinal2(B) -> (A = k7_relat_1(A,k2_finseq_1(B)) <-> r1_xreal_0(k3_finseq_1(A),B)))))) # label(t55_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4572 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> A = k1_finseq_3(A,k1_xboole_0))) # label(t78_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4573 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v4_ordinal2(B) -> (r2_hidden(B,k4_finseq_1(A)) <-> m2_subset_1(k6_xcmplx_0(k3_finseq_1(A),B),k1_numbers,k5_numbers) & m2_subset_1(k6_xcmplx_0(B,np__1),k1_numbers,k5_numbers)))))) # label(t28_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4574 (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 r1_tarski(k10_relat_1(A,C),k10_relat_1(k7_finseq_1(A,B),C))))))) # label(t64_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4575 (all A (v4_ordinal2(A) -> v2_funct_1(k1_finseq_2(A)))) # label(t100_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4576 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) & v1_finseq_1(B) -> (all C all D (v4_ordinal2(D) -> (B = k7_relat_1(A,k2_finseq_1(D)) & k3_finseq_1(A) = k2_xcmplx_0(D,np__1) -> (r2_hidden(k1_funct_1(A,k2_xcmplx_0(D,np__1)),C) <-> k1_finseq_3(B,C) = k1_finseq_3(A,C))))))))) # label(t90_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4577 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (k1_tarski(B) = k2_relat_1(A) & v2_funct_1(A) -> k3_finseq_1(A) = np__1)))) # label(t105_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4578 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> -(-r1_xreal_0(A,np__0) & -r1_xreal_0(B,A) & k14_finseq_1(k2_tarski(A,B)) != k10_finseq_1(A,B)))))) # label(t51_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4579 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v2_funct_1(A) -> v2_funct_1(k1_finseq_3(A,B)))))) # label(t94_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4580 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> r1_tarski(k2_finseq_1(A),k2_finseq_1(k2_xcmplx_0(A,B))))))) # label(t19_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4581 (all A (v4_ordinal2(A) -> k2_finseq_1(k2_xcmplx_0(A,np__1)) != k2_finseq_1(A))) # label(t17_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4582 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(k7_relat_1(A,B)) & v1_finseq_1(k7_relat_1(A,B)) & v1_relat_1(k7_relat_1(A,B)) <-> (exists C (m2_subset_1(C,k1_numbers,k5_numbers) & k3_xboole_0(B,k4_finseq_1(A)) = k2_finseq_1(C))))))) # label(t62_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4583 (all A all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (all D (v4_ordinal2(D) -> (all E (v4_ordinal2(E) -> (all F (v4_ordinal2(F) -> -(r1_tarski(A,k2_finseq_1(B)) & r1_xreal_0(E,F) & -r1_xreal_0(D,C) & r1_xreal_0(F,k3_finseq_1(k14_finseq_1(A))) & C = k1_funct_1(k14_finseq_1(A),F) & k1_funct_1(k14_finseq_1(A),E) = D & r1_xreal_0(np__1,E)))))))))))) # label(t46_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4584 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) & v4_ordinal2(A) -> v1_relat_1(k2_finseq_3(A,B)) & v1_finseq_1(k2_finseq_3(A,B)) & v1_funct_1(k2_finseq_3(A,B)))) # label(dt_k2_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4585 (all A (v1_funct_1(A) & v1_relat_1(A) & v1_finseq_1(A) -> (all B (k4_finseq_1(k1_finseq_3(A,B)) = k4_finseq_1(A) -> r1_xboole_0(B,k2_relat_1(A)))))) # label(t71_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4586 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v4_ordinal2(C) -> (all D (v4_ordinal2(D) -> (k3_finseq_1(A) = k2_xcmplx_0(C,D) & B = k7_relat_1(A,k2_finseq_1(C)) -> C = k3_finseq_1(B)))))))))) # label(t59_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4587 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> k1_xboole_0 = k1_finseq_3(A,k2_relat_1(A)))) # label(t79_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4588 (all A all B all C (v4_ordinal2(C) -> (all D (v4_ordinal2(D) -> (r1_tarski(B,k2_finseq_1(D)) & r1_tarski(A,k2_finseq_1(C)) -> ((all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (all F (m2_subset_1(F,k1_numbers,k5_numbers) -> -(r2_hidden(F,B) & r1_xreal_0(F,E) & r2_hidden(E,A)))))) <-> k14_finseq_1(k2_xboole_0(A,B)) = k8_finseq_1(k5_numbers,k14_finseq_1(A),k14_finseq_1(B)))))))) # label(t48_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4589 (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) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (D = k1_nat_1(C,np__1) & r2_hidden(A,k2_finseq_1(C)) & r2_hidden(B,k2_finseq_1(D)) -> (r1_xreal_0(B,A) & r1_xreal_0(A,C) -> k1_nat_1(A,np__1) = k1_funct_1(k14_finseq_1(k4_xboole_0(k2_finseq_1(D),k1_tarski(B))),A)) & (r1_xreal_0(np__1,A) -> r1_xreal_0(B,A) | A = k1_funct_1(k14_finseq_1(k4_xboole_0(k2_finseq_1(D),k1_tarski(B))),A))))))))))) # label(t117_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4590 (all A all B (v4_ordinal2(B) -> (k2_finseq_1(B) = k1_tarski(A) -> A = np__1 & B = np__1))) # label(t22_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4591 (all A (v4_ordinal2(A) -> (-r2_hidden(A,k2_finseq_1(A)) <-> k1_xboole_0 = k2_finseq_1(A)))) # label(t7_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4592 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (k1_finseq_2(B) = k7_relat_1(k1_finseq_2(A),k2_finseq_1(B)) <-> r1_xreal_0(B,A)))))) # label(t57_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4593 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B all C all D (v2_funct_1(k11_finseq_1(B,C,D)) & k2_relat_1(A) = k1_enumset1(B,C,D) & v2_funct_1(A) -> k3_finseq_1(A) = np__3)))) # label(t109_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4594 $T # label(t35_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4595 (all A (v4_ordinal2(A) -> r1_xboole_0(k2_finseq_1(A),k1_tarski(k2_xcmplx_0(A,np__1))))) # label(t15_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4596 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> -(-v1_xboole_0(B) & (all C (m1_subset_1(C,A) -> (all D (m2_finseq_1(D,A) -> -(k8_finseq_1(A,k12_finseq_1(A,C),D) = B & k1_funct_1(B,np__1) = C)))))))))) # label(t111_finseq_3) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4597 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (v1_ordinal1(B) & v1_zf_model(A) & r2_zfrefle1(A,B) -> v1_zf_model(B)))))) # label(t10_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4598 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) -> (v2_ordinal2(B) -> v2_ordinal2(k1_ordinal3(A,B))))))) # label(t15_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4599 (all A (-v1_xboole_0(A) -> r1_zfrefle1(A,k1_subset_1(k9_zf_lang)))) # label(t1_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4600 (all A (-v1_xboole_0(A) -> (r1_zfrefle1(A,k2_zfrefle1) & v1_ordinal1(A) -> v1_zf_model(A)))) # label(t5_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4601 (all A (v3_ordinal1(A) -> r4_zfrefle1(k1_ordinal1(A),k4_ordinal2))) # label(t25_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4602 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (r2_zfrefle1(A,B) <-> (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> (r2_zf_model(B,C) <-> r2_zf_model(A,C))))))))) # label(t7_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4603 (all A (v1_classes2(A) & -v1_xboole_0(A) -> -(r2_hidden(k5_ordinal2,A) & (all B (m1_ordinal4(B,A) -> (all C (-v1_xboole_0(C) -> -(r2_zfrefle1(C,A) & k4_classes1(B) = C & r4_zfrefle1(B,k5_ordinal2))))))))) # label(t41_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4604 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> (r2_zfrefle1(A,B) -> r2_zfrefle1(B,A)))) # label(symmetry_r2_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4605 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r4_zfrefle1(A,B) & r4_zfrefle1(B,A) -> B = A))))) # label(t23_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4606 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (m1_ordinal4(B,A) -> (B != k1_xboole_0 -> -v1_xboole_0(k4_classes1(B)) & m1_subset_1(k4_classes1(B),A)))))) # label(t34_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4607 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k9_zf_lang)) -> (r1_zfrefle1(A,B) <-> (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> (r2_hidden(C,B) -> r2_zf_model(A,C))))))))) # label(d1_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4608 $T # label(t11_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4609 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (m1_ordinal4(B,A) -> -r4_zfrefle1(k2_ordinal2(A),B))))) # label(t29_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4610 $T # label(dt_k1_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4611 (all A (v3_ordinal1(A) -> (r4_zfrefle1(A,k1_xboole_0) -> A = k1_xboole_0))) # label(t28_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4612 (all A (-v1_xboole_0(A) & v1_classes2(A) -> -(r2_hidden(k5_ordinal2,A) & (all B (m2_ordinal4(B,A) -> -(v2_ordinal2(B) & (all C (m1_ordinal4(C,A) -> (all D (-v1_xboole_0(D) -> (C = k4_ordinal4(A,B,C) & k4_classes1(C) = D -> k1_xboole_0 = C | r3_zfrefle1(D,A)))))) & v3_ordinal2(B))))))) # label(t35_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4613 (all A (-v1_xboole_0(A) -> (v1_zf_model(A) -> r1_zfrefle1(A,k2_zfrefle1)))) # label(t4_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4614 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (m1_ordinal4(B,A) -> (all C (m2_ordinal4(C,A) -> -(v3_ordinal2(C) & (all D (m1_ordinal4(D,A) -> -(D = k4_ordinal4(A,C,D) & r4_zfrefle1(D,k5_ordinal2) & r2_hidden(B,D)))) & v2_ordinal2(C) & r2_hidden(k5_ordinal2,A)))))))) # label(t31_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4615 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (m1_ordinal4(B,A) -> -(r2_hidden(k5_ordinal2,A) & (all C (m1_ordinal4(C,A) -> (all D (-v1_xboole_0(D) -> -(k4_classes1(C) = D & r2_hidden(B,C) & r3_zfrefle1(D,A))))))))))) # label(t36_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4616 (all A -(r2_hidden(A,f1_s1_zfrefle1) & (all B -p1_s1_zfrefle1(A,B)))) -> (exists A (v1_relat_1(A) & k1_relat_1(A) = f1_s1_zfrefle1 & (all B (r2_hidden(B,f1_s1_zfrefle1) -> p1_s1_zfrefle1(B,k1_funct_1(A,B)))) & v1_funct_1(A))) # label(s1_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4617 (all A all B (k1_card_1(A) = k1_card_1(B) | r2_wellord2(A,B) -> k1_card_1(k1_zfmisc_1(A)) = k1_card_1(k1_zfmisc_1(B)) & r2_wellord2(k1_zfmisc_1(A),k1_zfmisc_1(B)))) # label(t13_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4618 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (m1_ordinal4(B,A) -> -(r2_hidden(k5_ordinal2,A) & (all C (m1_ordinal4(C,A) -> (all D (-v1_xboole_0(D) -> -(D = k4_classes1(C) & r2_zfrefle1(D,A) & r2_hidden(B,C))))))))))) # label(t40_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4619 $T # label(t18_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4620 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (r2_zfrefle1(A,B) <-> (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> (k1_xboole_0 = k2_zf_model(C) -> (r2_zf_model(A,C) <-> r2_zf_model(B,C)))))))))) # label(d2_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.92 4621 (all A (v1_classes2(A) & -v1_xboole_0(A) -> -((all B (m1_ordinal4(B,A) -> (all C (-v1_xboole_0(C) -> -(r4_zfrefle1(B,k5_ordinal2) & r3_zfrefle1(C,A) & C = k4_classes1(B)))))) & r2_hidden(k5_ordinal2,A)))) # label(t37_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.93 4622 (all A (A = k1_zfrefle1 <-> (all B (r2_hidden(B,A) <-> -(B != k9_zf_model & B != k7_zf_model & k6_zf_model != B & B != k8_zf_model & k10_zf_model != B & (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> -(k11_zf_model(C) = B & r1_xboole_0(k1_enumset1(k2_zf_lang(np__0),k2_zf_lang(np__1),k2_zf_lang(np__2)),k2_zf_model(C)))))) & r2_hidden(B,k9_zf_lang))))) # label(d4_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.93 4623 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v1_relat_1(C) & k8_ordinal2(C) = A & v2_ordinal2(C) & v1_ordinal2(C) & v5_ordinal1(C) & v1_funct_1(C) & k1_relat_1(C) = B & r1_tarski(k2_relat_1(C),A))) <-> r4_zfrefle1(A,B)))))) # label(d5_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.93 4624 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,B,k1_funct_2(k2_ordinal2(A),k2_ordinal2(A))) & v1_funct_1(C) & m2_relset_1(C,B,k1_funct_2(k2_ordinal2(A),k2_ordinal2(A))) -> -((all D (m2_ordinal4(D,A) -> -(v2_ordinal2(D) & k2_ordinal4(A) = k4_ordinal4(A,D,k2_ordinal4(A)) & (all E (m1_ordinal4(E,A) -> k7_ordinal2(k2_xboole_0(k1_tarski(k4_ordinal4(A,D,E)),k9_relat_1(k4_funct_5(C),k2_zfmisc_1(B,k1_tarski(k6_ordinal4(A,E)))))) = k4_ordinal4(A,D,k6_ordinal4(A,E)))) & (all E (m1_ordinal4(E,A) -> (v4_ordinal1(E) -> k4_ordinal4(A,D,E) = k8_ordinal2(k2_ordinal1(D,E)) | k2_ordinal4(A) = E))) & v3_ordinal2(D)))) & r2_hidden(k1_card_1(B),k1_card_1(A))))))))) # label(t14_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.93 4625 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (m1_ordinal1(B,A) & v2_relat_1(B) & v1_zf_refle(B,A) -> -((all C (m2_ordinal4(C,A) -> -(v2_ordinal2(C) & (all D (m1_ordinal4(D,A) -> (D = k4_ordinal4(A,C,D) -> r3_zfrefle1(k5_zf_refle(A,B,D),k4_zf_refle(A,B)) | D = k1_xboole_0))) & v3_ordinal2(C)))) & (all C (m1_ordinal4(C,A) -> (v4_ordinal1(C) -> C = k1_xboole_0 | k3_card_3(k2_ordinal1(B,C)) = k5_zf_refle(A,B,C)))) & (all C (m1_ordinal4(C,A) -> (all D (m1_ordinal4(D,A) -> (r2_hidden(C,D) -> r1_tarski(k5_zf_refle(A,B,C),k5_zf_refle(A,B,D))))))) & r2_hidden(k5_ordinal2,A)))))) # label(t32_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.93 4626 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> ((all C (m1_subset_1(C,k1_zfmisc_1(k9_zf_lang)) -> (r1_zfrefle1(A,C) <-> r1_zfrefle1(B,C)))) <-> r2_zfrefle1(A,B)))))) # label(t8_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.93 4627 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v1_ordinal2(B) & v5_ordinal1(B) & v1_funct_1(B) -> (v4_ordinal1(k1_relat_1(B)) & v2_ordinal2(B) & r1_ordinal2(A,B) -> k1_relat_1(B) = k1_xboole_0 | r4_zfrefle1(A,k1_relat_1(B))))))) # label(t24_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.93 4628 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (m1_ordinal1(B,A) & v2_relat_1(B) & v1_zf_refle(B,A) -> -(r2_hidden(k5_ordinal2,A) & (all C (m1_ordinal4(C,A) -> (all D (m1_ordinal4(D,A) -> (r2_hidden(C,D) -> r1_tarski(k5_zf_refle(A,B,C),k5_zf_refle(A,B,D))))))) & (all C (m2_ordinal4(C,A) -> -(v2_ordinal2(C) & v3_ordinal2(C) & (all D (m1_ordinal4(D,A) -> (k4_ordinal4(A,C,D) = D -> r2_zfrefle1(k5_zf_refle(A,B,D),k4_zf_refle(A,B)) | D = k1_xboole_0)))))) & (all C (m1_ordinal4(C,A) -> (v4_ordinal1(C) -> C = k1_xboole_0 | k5_zf_refle(A,B,C) = k3_card_3(k2_ordinal1(B,C)))))))))) # label(t38_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.93 4629 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k9_zf_lang)) -> (all C (m1_subset_1(C,k1_zfmisc_1(k9_zf_lang)) -> (r1_zfrefle1(A,C) & r1_zfrefle1(A,B) -> r1_zfrefle1(A,k4_subset_1(k9_zf_lang,B,C))))))))) # label(t3_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.93 4630 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r4_zfrefle1(B,C) & r4_zfrefle1(A,B) -> r4_zfrefle1(A,C)))))))) # label(t21_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.93 4631 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r4_zfrefle1(A,B) -> (v4_ordinal1(B) <-> v4_ordinal1(A))))))) # label(t27_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.93 4632 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (r3_zfrefle1(A,B) <-> r1_tarski(A,B) & (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> (all D (v1_funct_2(D,k1_zf_lang,A) & m2_relset_1(D,k1_zf_lang,A) & v1_funct_1(D) -> (r1_zf_model(B,k2_zf_lang1(k1_zf_lang,A,B,D),C) <-> r1_zf_model(A,D,C))))))))))) # label(d3_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.93 4633 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (-v1_xboole_0(B) & v1_classes2(B) -> (r1_tarski(k2_relat_1(A),B) & r2_hidden(k1_relat_1(A),B) -> r2_hidden(k2_relat_1(A),B)))))) # label(t12_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.93 4634 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v1_ordinal2(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C) -> k1_ordinal3(A,k2_ordinal1(C,B)) = k2_ordinal1(k1_ordinal3(A,C),B))))))) # label(t16_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.93 4635 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> r4_zfrefle1(A,A))) # label(reflexivity_r4_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.93 4636 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (exists B (k2_zf_model(B) = k1_xboole_0 & (all C (-v1_xboole_0(C) -> (r2_zf_model(C,B) <-> r2_zf_model(C,A)))) & m2_finseq_1(B,k5_numbers) & v1_zf_lang(B))))) # label(t6_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.93 4637 (all A all B (v1_ordinal2(B) & v1_funct_1(B) & v1_relat_1(B) & v5_ordinal1(B) -> (r2_hidden(A,k2_relat_1(B)) -> v3_ordinal1(A)))) # label(t19_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.93 4638 (all A (-v1_xboole_0(A) & v1_classes2(A) -> -(r2_hidden(k5_ordinal2,A) & (all B (m2_ordinal4(B,A) -> -(v2_ordinal2(B) & v3_ordinal2(B) & (all C (m1_ordinal4(C,A) -> (all D (-v1_xboole_0(D) -> (C = k4_ordinal4(A,B,C) & k4_classes1(C) = D -> C = k1_xboole_0 | r2_zfrefle1(D,A)))))))))))) # label(t39_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.93 4639 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v5_ordinal1(B) & v1_ordinal2(B) & v1_funct_1(B) -> (v2_ordinal2(B) & v3_ordinal2(B) -> v3_ordinal2(k1_ordinal3(A,B))))))) # label(t17_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.93 4640 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -((all C (v3_ordinal1(C) -> k1_ordinal1(C) != A)) & r4_zfrefle1(A,k1_ordinal1(B))))))) # label(t26_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.93 4641 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (m1_ordinal4(B,A) -> r2_hidden(k4_classes1(B),A))))) # label(t33_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.93 4642 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(A) -> r1_tarski(k2_relat_1(A),k8_ordinal2(A)))) # label(t20_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.93 4643 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> r3_zfrefle1(A,A))) # label(reflexivity_r3_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.93 4644 (all A (-v1_xboole_0(A) & v1_classes2(A) -> -(r2_hidden(k5_ordinal2,A) & (all B (m1_ordinal4(B,A) -> (all C (-v1_xboole_0(C) -> -(r4_zfrefle1(B,k5_ordinal2) & v1_zf_model(C) & C = k4_classes1(B))))))))) # label(t42_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.93 4645 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> r2_zfrefle1(A,A))) # label(reflexivity_r2_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.93 4646 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r4_zfrefle1(A,B) -> r1_tarski(B,A)))))) # label(t22_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.93 4647 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (m1_ordinal4(B,A) -> (all C (m2_ordinal4(C,A) -> -(v2_ordinal2(C) & v3_ordinal2(C) & r2_hidden(k5_ordinal2,A) & (all D (m1_ordinal4(D,A) -> -(r2_hidden(B,D) & D = k4_ordinal4(A,C,D))))))))))) # label(t30_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.93 4648 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (r3_zfrefle1(A,B) -> r2_zfrefle1(A,B)))))) # label(t9_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.94 4649 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k9_zf_lang)) -> (all C (m1_subset_1(C,k1_zfmisc_1(k9_zf_lang)) -> (r1_zfrefle1(A,C) & r1_tarski(B,C) -> r1_zfrefle1(A,B)))))))) # label(t2_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.94 4650 (all A all B (-v1_xboole_0(B) & v1_classes2(B) -> -(r2_hidden(A,B) & r2_hidden(k5_ordinal2,B) & (all C (-v1_xboole_0(C) -> -(v1_zf_model(C) & r2_hidden(C,B) & r2_hidden(A,C))))))) # label(t43_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.94 4651 (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) -> (k20_qc_lang1(A) = B <-> (exists C (m1_subset_1(C,k8_qc_lang1) & k14_qc_lang1(B,C) = A)))))))) # label(d26_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.94 4652 (all A (m1_subset_1(A,k8_qc_lang1) -> -(v3_qc_lang1(A) & v2_qc_lang1(A)) & -(v2_qc_lang1(A) & v4_qc_lang1(A)) & -(v5_qc_lang1(A) & v4_qc_lang1(A)) & -(v4_qc_lang1(A) & v3_qc_lang1(A)) & -(v2_qc_lang1(A) & v5_qc_lang1(A)) & -(v3_qc_lang1(A) & v5_qc_lang1(A)))) # label(t51_qc_lang1_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 56.88/55.94 4653 (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]. 56.88/55.94 4654 (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]. 56.88/55.94 4655 $T # label(dt_k1_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.94 4656 $T # label(t28_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.94 4657 (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) -> k7_finseq_1(k12_finseq_1(k5_qc_lang1,A),B) = k9_qc_lang1(A,B)))))) # label(d11_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.94 4658 $T # label(t13_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.94 4659 (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]. 56.88/55.94 4660 (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 & (v4_qc_lang1(A) -> k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) = np__2) & (v3_qc_lang1(A) -> k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) = np__1) & (v5_qc_lang1(A) -> np__3 = k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1))) & -((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)))) # label(t49_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.94 4661 $T # label(t42_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.94 4662 $T # label(t6_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.94 4663 (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]. 56.88/55.94 4664 (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 (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))))))) & p1_s1_qc_lang1(k11_qc_lang1) & (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) -> p1_s1_qc_lang1(k12_qc_lang1(A))))) -> (all A (m1_subset_1(A,k8_qc_lang1) -> p1_s1_qc_lang1(A))) # label(s1_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.88/55.94 4665 (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]. 56.98/55.96 4666 $T # label(t43_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4667 (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]. 56.98/55.96 4668 (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) = 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)))))) # label(d16_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4669 $T # label(t31_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4670 (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]. 56.98/55.96 4671 (all A (r2_hidden(k9_finseq_1(k4_tarski(np__0,np__0)),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_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))))))) & m1_subset_1(A,k1_zfmisc_1(k13_finseq_1(k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)))) & (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)))) <-> v1_qc_lang1(A))) # label(d9_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4672 $T # label(t39_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4673 (all A (m1_subset_1(A,k8_qc_lang1) -> A = k10_qc_lang1(A))) # label(d12_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4674 (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]. 56.98/55.96 4675 (all A (m1_subset_1(A,k8_qc_lang1) -> ((exists B (m2_subset_1(B,k1_numbers,k5_numbers) & (exists C ((exists D (m1_qc_lang1(D,B) & A = k9_qc_lang1(C,D))) & m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(B)))))) <-> v2_qc_lang1(A)))) # label(d17_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4676 $T # label(t38_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4677 $T # label(t8_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4678 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang1(A) -> np__3 != k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) & k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) != np__2 & np__1 != k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) & np__0 != k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1))))) # label(t50_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4679 $T # label(t27_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4680 $T # label(t14_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4681 $T # label(t7_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4682 $T # label(t5_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4683 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k1_zfmisc_1(k2_qc_lang1)) -> ((exists C (m2_relset_1(C,k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1)) & B = k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,A) & v1_funct_2(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 & (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))) & (v4_qc_lang1(D) -> k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,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)))) & (v2_qc_lang1(D) -> k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,D) = a_1_2_qc_lang1(D)) & (v5_qc_lang1(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))) = k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,D)))) & v1_funct_1(C))) <-> B = k24_qc_lang1(A)))))) # label(d29_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4684 (all A (m1_subset_1(A,k8_qc_lang1) -> -(k11_qc_lang1 != A & -v4_qc_lang1(A) & -v5_qc_lang1(A) & -v2_qc_lang1(A) & -v3_qc_lang1(A)))) # label(t33_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4685 $T # label(t20_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4686 (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]. 56.98/55.96 4687 (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]. 56.98/55.96 4688 (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(B,C))) <-> k18_qc_lang1(A) = B)))))) # label(d24_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4689 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A)) -> np__2 != k1_mcart_1(B) & np__3 != k1_mcart_1(B) & np__1 != k1_mcart_1(B) & np__0 != k1_mcart_1(B))))) # label(t48_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4690 $T # label(t12_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4691 (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]. 56.98/55.96 4692 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_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(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(k11_qc_lang1) & (p1_s2_qc_lang1(k21_qc_lang1(A)) & v5_qc_lang1(A) -> p1_s2_qc_lang1(A)))) -> (all A (m1_subset_1(A,k8_qc_lang1) -> p1_s2_qc_lang1(A))) # label(s2_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4693 (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]. 56.98/55.96 4694 (all A (m1_subset_1(A,k8_qc_lang1) -> (v3_qc_lang1(A) <-> (exists B (m1_subset_1(B,k8_qc_lang1) & k12_qc_lang1(B) = A))))) # label(d18_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4695 (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]. 56.98/55.96 4696 (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]. 56.98/55.96 4697 $T # label(t41_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4698 (all A all B (m1_subset_1(A,k8_qc_lang1) & m1_subset_1(B,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]. 56.98/55.96 4699 $T # label(t44_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4700 (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]. 56.98/55.96 4701 $T # label(dt_k5_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4702 (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 & m1_subset_1(C,k5_qc_lang1) & k6_qc_lang1(C) = B))))) # label(fraenkel_a_1_0_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4703 (all A (m1_subset_1(A,k8_qc_lang1) -> (v5_qc_lang1(A) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (B = k21_qc_lang1(A) <-> (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]. 56.98/55.96 4704 $T # label(t17_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4705 (all A all B (m2_finseq_1(B,k1_qc_lang1) -> (r2_hidden(A,a_1_1_qc_lang1(B)) <-> (exists C (m2_subset_1(C,k1_numbers,k5_numbers) & r2_hidden(k1_funct_1(B,C),k2_qc_lang1) & r1_xreal_0(C,k3_finseq_1(B)) & r1_xreal_0(np__1,C) & A = k1_funct_1(B,C)))))) # label(fraenkel_a_1_1_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4706 $T # label(t24_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4707 $T # label(t30_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4708 (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]. 56.98/55.96 4709 $T # label(t32_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4710 (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]. 56.98/55.96 4711 (all A all B (m1_subset_1(A,k5_qc_lang1) & m1_finseq_1(B,k1_qc_lang1) -> m1_subset_1(k9_qc_lang1(A,B),k8_qc_lang1))) # label(dt_k9_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4712 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) <-> (exists B ((exists C (m1_subset_1(C,k8_qc_lang1) & A = k13_qc_lang1(B,C))) & m1_subset_1(B,k8_qc_lang1)))))) # label(d19_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4713 (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]. 56.98/55.96 4714 (all A (m1_subset_1(A,k2_qc_lang1) -> k23_qc_lang1(A) = k1_tarski(A))) # label(redefinition_k23_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4715 $T # label(t26_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4716 (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]. 56.98/55.96 4717 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (v1_finseq_1(C) & v1_relat_1(C) & v1_funct_1(C) -> (k7_finseq_1(k10_qc_lang1(B),C) = k10_qc_lang1(A) -> k10_qc_lang1(A) = k10_qc_lang1(B)))))))) # label(t37_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4718 $T # label(t3_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4719 $T # label(t16_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4720 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang1(A) -> (all B (m2_finseq_1(B,k1_qc_lang1) -> ((exists C ((exists D ((exists E (E = B & k9_qc_lang1(D,E) = A & m1_qc_lang1(E,C))) & m2_subset_1(D,k5_qc_lang1,k7_qc_lang1(C)))) & m2_subset_1(C,k1_numbers,k5_numbers))) <-> B = k16_qc_lang1(A))))))) # label(d22_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4721 (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]. 56.98/55.96 4722 $T # label(t25_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4723 (all A (m1_subset_1(A,k8_qc_lang1) -> (k1_xboole_0 = k24_qc_lang1(A) <-> v6_qc_lang1(A)))) # label(d30_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4724 (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]. 56.98/55.96 4725 (all A (m1_subset_1(A,k8_qc_lang1) -> (v3_qc_lang1(A) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (A = k12_qc_lang1(B) <-> k17_qc_lang1(A) = B)))))) # label(d23_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4726 $T # label(t29_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4727 (all A all B (m1_subset_1(B,k8_qc_lang1) -> ((exists C (A = k1_funct_1(k16_qc_lang1(B),C) & r1_xreal_0(np__1,C) & r2_hidden(k1_funct_1(k16_qc_lang1(B),C),k2_qc_lang1) & r1_xreal_0(C,k3_finseq_1(k16_qc_lang1(B))) & m2_subset_1(C,k1_numbers,k5_numbers))) <-> r2_hidden(A,a_1_2_qc_lang1(B))))) # label(fraenkel_a_1_2_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4728 $T # label(t9_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4729 (all A (m1_subset_1(A,k8_qc_lang1) -> ((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))))) <-> v5_qc_lang1(A)))) # label(d20_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4730 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A)) -> A = k6_qc_lang1(B))))) # label(t35_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4731 (all A (m1_subset_1(A,k8_qc_lang1) -> (k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) = np__0 -> A = k11_qc_lang1) & (np__2 = k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) -> v4_qc_lang1(A)) & (np__3 = k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) -> 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__1 -> v3_qc_lang1(A)))) # label(t36_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4732 $T # label(t11_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4733 (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]. 56.98/55.96 4734 (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) & k13_qc_lang1(C,B) = A)) <-> B = k19_qc_lang1(A))))))) # label(d25_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4735 (all A ((exists B exists C (m2_subset_1(C,k1_numbers,k5_numbers) & m2_subset_1(B,k1_numbers,k5_numbers) & r1_xreal_0(np__7,B) & k4_tarski(B,C) = A)) <-> r2_hidden(A,a_0_0_qc_lang1))) # label(fraenkel_a_0_0_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4736 (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]. 56.98/55.96 4737 (exists A (v1_funct_1(A) & v1_funct_2(A,k8_qc_lang1,f1_s3_qc_lang1) & m2_relset_1(A,k8_qc_lang1,f1_s3_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)) & (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)) & (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)) & (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)))))) & k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,k11_qc_lang1) = f2_s3_qc_lang1)) # label(s3_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.96 4738 (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]. 56.98/55.97 4739 $T # label(t18_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4740 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_finseq_1(B,k1_qc_lang1) -> (A = k3_finseq_1(B) <-> m1_qc_lang1(B,A)))))) # label(d8_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4741 $T # label(t19_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4742 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang1(A) -> (all B (m1_subset_1(B,k5_qc_lang1) -> (B = k15_qc_lang1(A) <-> (exists C ((exists D (m1_qc_lang1(D,C) & (exists E (B = E & A = k9_qc_lang1(E,D) & m2_subset_1(E,k5_qc_lang1,k7_qc_lang1(C)))))) & m2_subset_1(C,k1_numbers,k5_numbers))))))))) # label(d21_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4743 $T # label(t40_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4744 (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]. 56.98/55.97 4745 (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]. 56.98/55.97 4746 (all A (m2_finseq_1(A,k1_qc_lang1) -> k22_qc_lang1(A) = a_1_1_qc_lang1(A))) # label(d28_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4747 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> a_1_0_qc_lang1(A) = k7_qc_lang1(A))) # label(d7_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4748 (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]. 56.98/55.97 4749 (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]. 56.98/55.97 4750 $T # label(t22_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4751 $T # label(t15_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4752 (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]. 56.98/55.97 4753 (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]. 56.98/55.97 4754 (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]. 56.98/55.97 4755 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) -> k13_qc_lang1(k18_qc_lang1(A),k19_qc_lang1(A)) = A))) # label(t4_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4756 $T # label(t44_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4757 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang2(A) -> v3_qc_lang1(A) & v3_qc_lang1(k19_qc_lang1(k17_qc_lang1(A))) & v4_qc_lang1(k17_qc_lang1(A))))) # label(t50_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4758 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k14_qc_lang2(k4_qc_lang2(A,B)) = 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) & k13_qc_lang2(k4_qc_lang2(A,B)) = A)))) # label(t47_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4759 (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) -> (k6_qc_lang2(F,G,E) = k8_qc_lang2(A,B,C,D) -> k14_qc_lang1(C,D) = E & G = B & F = A))))))))))))))) # label(t29_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4760 (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]. 56.98/55.97 4761 (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(C,E,A) = k7_qc_lang2(D,F,B) -> C = D & B = A & F = E))))))))))))) # label(t23_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4762 (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]. 56.98/55.97 4763 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r2_qc_lang2(A,B) & r2_qc_lang2(B,A) -> A = B))))) # label(t78_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4764 (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(C,E,G,A) = k9_qc_lang2(D,F,H,B) -> A = B & C = D & G = H & F = E))))))))))))))))) # label(t30_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4765 (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]. 56.98/55.97 4766 (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)) <-> k9_qc_lang1(C,D) = A))))))))) # label(t100_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4767 $T # label(t10_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4768 (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]. 56.98/55.97 4769 (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]. 56.98/55.97 4770 (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]. 56.98/55.97 4771 (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]. 56.98/55.97 4772 (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]. 56.98/55.97 4773 (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]. 56.98/55.97 4774 (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(A,B) & r3_qc_lang2(B,C) -> r3_qc_lang2(A,C)))))))) # label(t76_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4775 (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(B,C) & r3_qc_lang2(A,C)))))))) # label(t90_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4776 (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]. 56.98/55.97 4777 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r1_qc_lang2(B,A) & r2_qc_lang2(A,B)))))) # label(t81_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4778 $T # label(t40_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4779 $T # label(t57_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4780 (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]. 56.98/55.97 4781 $T # label(t34_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4782 (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]. 56.98/55.97 4783 $T # label(t35_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4784 (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]. 56.98/55.97 4785 (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]. 56.98/55.97 4786 (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]. 56.98/55.97 4787 (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) -> (k8_qc_lang2(A,B,C,D) = k14_qc_lang1(F,E) -> k6_qc_lang2(B,C,D) = E & A = F))))))))))))) # label(t28_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4788 (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) -> (k14_qc_lang1(C,E) = k6_qc_lang2(A,B,D) -> A = C & k14_qc_lang1(B,D) = E))))))))))) # label(t22_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4789 (all A all B all C (m1_subset_1(A,k2_qc_lang1) & m1_subset_1(B,k2_qc_lang1) & m1_subset_1(C,k8_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]. 56.98/55.97 4790 (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) -> k5_qc_lang2(A,k5_qc_lang2(B,C)) = k7_qc_lang2(A,B,C))))))) # label(d7_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4791 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (k15_qc_lang2(A) = B <-> (all C (r2_hidden(C,B) <-> (exists D (C = D & r2_qc_lang2(D,A) & m1_subset_1(D,k8_qc_lang1))))))))) # label(d23_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4792 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v3_qc_lang1(A) -> (r1_qc_lang2(B,A) <-> B = k17_qc_lang1(A))))))) # label(t65_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4793 (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]. 56.98/55.97 4794 (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]. 56.98/55.97 4795 (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) & r3_qc_lang2(A,B)) & -(r2_qc_lang2(A,B) & r3_qc_lang2(B,C)) & -(r1_qc_lang2(B,C) & r2_qc_lang2(A,B)) & -(r1_qc_lang2(B,C) & r3_qc_lang2(A,B)) & -(r1_qc_lang2(A,B) & r3_qc_lang2(B,C)) & -(r1_qc_lang2(A,B) & r2_qc_lang2(B,C))) -> r3_qc_lang2(A,C)))))))) # label(t83_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4796 $T # label(t69_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4797 (all A (m1_subset_1(A,k8_qc_lang1) -> (v3_qc_lang1(A) -> k15_qc_lang2(A) = k2_xboole_0(k15_qc_lang2(k17_qc_lang1(A)),k1_tarski(A))))) # label(t117_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4798 (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]. 56.98/55.97 4799 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> r3_qc_lang2(k13_qc_lang1(A,k12_qc_lang1(B)),k2_qc_lang2(A,B)) & r3_qc_lang2(A,k2_qc_lang2(A,B)) & r3_qc_lang2(B,k2_qc_lang2(A,B)) & r3_qc_lang2(k12_qc_lang1(B),k2_qc_lang2(A,B)))))) # label(t93_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4800 (all A (m1_subset_1(A,k8_qc_lang1) -> (r2_qc_lang2(A,k11_qc_lang1) <-> r3_qc_lang2(A,k1_qc_lang2)))) # label(t88_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4801 (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]. 56.98/55.97 4802 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang2(A) <-> (exists B ((exists C (m1_subset_1(C,k8_qc_lang1) & A = k5_qc_lang2(B,C))) & m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)))))) # label(d13_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4803 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> ((exists C (m2_subset_1(C,k1_numbers,k5_numbers) & (exists D (v1_finseq_1(D) & r1_xreal_0(np__1,C) & C = k3_finseq_1(D) & B = k1_funct_1(D,C) & k1_funct_1(D,np__1) = A & v1_relat_1(D) & (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> -((all F (m1_subset_1(F,k8_qc_lang1) -> (all G (m1_subset_1(G,k8_qc_lang1) -> -(k1_funct_1(D,E) = F & r1_qc_lang2(F,G) & G = k1_funct_1(D,k1_nat_1(E,np__1))))))) & -r1_xreal_0(C,E) & r1_xreal_0(np__1,E)))) & v1_funct_1(D))))) <-> r2_qc_lang2(A,B)))))) # label(d21_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4804 (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]. 56.98/55.97 4805 $T # label(t37_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4806 $T # label(t70_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4807 (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]. 56.98/55.97 4808 (all A (m1_subset_1(A,k8_qc_lang1) -> (v3_qc_lang2(A) -> v2_qc_lang2(k19_qc_lang1(A)) & v4_qc_lang1(A) & v2_qc_lang2(k18_qc_lang1(A))))) # label(t51_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4809 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> A = k10_qc_lang2(k3_qc_lang2(A,B)) & k17_qc_lang1(k3_qc_lang2(A,B)) = k13_qc_lang1(k12_qc_lang1(A),k12_qc_lang1(B)) & k11_qc_lang2(k3_qc_lang2(A,B)) = B)))) # label(t45_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4810 (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]. 56.98/55.97 4811 $T # label(t15_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4812 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r3_qc_lang2(A,B) & (all C (m1_subset_1(C,k8_qc_lang1) -> -r1_qc_lang2(C,B)))))))) # label(t75_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4813 (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)) -> -r1_qc_lang2(A,B) & -r2_qc_lang2(A,B) & -r3_qc_lang2(A,B) | r2_hidden(A,k15_qc_lang2(C))))))))) # label(t120_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4814 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k3_qc_lang2(A,B) = k12_qc_lang1(k13_qc_lang1(k12_qc_lang1(A),k12_qc_lang1(B))))))) # label(d3_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4815 (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]. 56.98/55.97 4816 (all A all B all C all D (m1_subset_1(B,k2_qc_lang1) & m1_subset_1(A,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]. 56.98/55.97 4817 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k2_qc_lang2(A,B) = k12_qc_lang1(k13_qc_lang1(A,k12_qc_lang1(B))))))) # label(d2_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4818 (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(D,F,H,B) = k8_qc_lang2(C,E,G,A) -> D = C & H = G & A = B & E = F))))))))))))))))) # label(t27_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4819 (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) -> A = C & B = D))))))))) # label(t16_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4820 (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(C,D) = k13_qc_lang1(A,B) -> D = B & A = C))))))))) # label(t3_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4821 $T # label(t39_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4822 (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]. 56.98/55.97 4823 (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(A,k13_qc_lang1(B,C)) <-> A = C | B = A))))))) # label(t62_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4824 $T # label(t12_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4825 (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]. 56.98/55.97 4826 (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]. 56.98/55.97 4827 (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) -> A = k20_qc_lang1(k6_qc_lang2(A,B,C)) & v5_qc_lang1(k6_qc_lang2(A,B,C)) & k14_qc_lang1(B,C) = k21_qc_lang1(k6_qc_lang2(A,B,C)))))))) # label(t25_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4828 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v4_qc_lang1(A) -> (k18_qc_lang1(A) = B | k19_qc_lang1(A) = B <-> r1_qc_lang2(B,A))))))) # label(t66_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4829 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k17_qc_lang1(k2_qc_lang2(A,B)) = k13_qc_lang1(A,k12_qc_lang1(B)) & B = k11_qc_lang2(k2_qc_lang2(A,B)) & A = k12_qc_lang2(k2_qc_lang2(A,B)))))) # label(t46_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4830 (all A all B (m1_subset_1(A,k2_qc_lang1) & m1_subset_1(B,k8_qc_lang1) -> m1_subset_1(k5_qc_lang2(A,B),k8_qc_lang1))) # label(dt_k5_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4831 (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]. 56.98/55.97 4832 $T # label(t41_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4833 (all A (m1_subset_1(A,k8_qc_lang1) -> (v1_qc_lang2(A) -> v2_qc_lang2(A) & v3_qc_lang1(A) & v3_qc_lang1(k19_qc_lang1(k17_qc_lang1(A))) & v3_qc_lang1(k18_qc_lang1(k17_qc_lang1(A))) & v4_qc_lang1(k17_qc_lang1(A))))) # label(t49_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4834 (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) -> k6_qc_lang2(B,C,D) = k21_qc_lang1(k8_qc_lang2(A,B,C,D)) & k20_qc_lang1(k8_qc_lang2(A,B,C,D)) = A & v5_qc_lang1(k8_qc_lang2(A,B,C,D)))))))))) # label(t33_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4835 (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]. 56.98/55.97 4836 (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]. 56.98/55.97 4837 $T # label(t102_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4838 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang2(A) -> v5_qc_lang1(k17_qc_lang1(A)) & v3_qc_lang1(A) & v3_qc_lang1(k21_qc_lang1(k17_qc_lang1(A)))))) # label(t52_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4839 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (B = A <-> r1_qc_lang2(A,k12_qc_lang1(B))))))) # label(t60_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4840 $T # label(dt_k15_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4841 (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]. 56.98/55.97 4842 (all A (m1_subset_1(A,k8_qc_lang1) -> (v3_qc_lang2(A) -> k4_qc_lang2(k13_qc_lang2(A),k14_qc_lang2(A)) = A))) # label(t55_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4843 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r1_xreal_0(k3_finseq_1(k10_qc_lang1(B)),k3_finseq_1(k10_qc_lang1(A))) & r1_qc_lang2(A,B)))))) # label(t71_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4844 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k21_qc_lang1(k14_qc_lang1(A,B)) = B & A = k20_qc_lang1(k14_qc_lang1(A,B)))))) # label(t8_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4845 (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]. 56.98/55.97 4846 (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]. 56.98/55.97 4847 (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) -> k6_qc_lang2(A,B,C) = k14_qc_lang1(A,k14_qc_lang1(B,C)))))))) # label(d6_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4848 (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]. 56.98/55.97 4849 (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]. 56.98/55.97 4850 (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]. 56.98/55.97 4851 (all A (m1_subset_1(A,k8_qc_lang1) -> k11_qc_lang2(k18_qc_lang1(A)) = k14_qc_lang2(A))) # label(d19_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4852 (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) -> k5_qc_lang2(A,k7_qc_lang2(B,C,D)) = k9_qc_lang2(A,B,C,D))))))))) # label(d9_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4853 (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]. 56.98/55.97 4854 (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(A,B) = k4_qc_lang2(C,D) -> A = C & B = D))))))))) # label(t18_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4855 (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) -> E = k5_qc_lang2(B,D) & A = C))))))))))) # label(t24_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4856 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> k15_qc_lang2(k14_qc_lang1(B,A)) = k2_xboole_0(k15_qc_lang2(A),k1_tarski(k14_qc_lang1(B,A))))))) # label(t112_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4857 (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]. 56.98/55.97 4858 (all A (m1_subset_1(A,k8_qc_lang1) -> ((exists B ((exists C (m1_subset_1(C,k8_qc_lang1) & k3_qc_lang2(B,C) = A)) & m1_subset_1(B,k8_qc_lang1))) <-> v1_qc_lang2(A)))) # label(d10_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4859 (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]. 56.98/55.97 4860 (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(A,k13_qc_lang1(B,C)) <-> r2_qc_lang2(A,B) | r2_qc_lang2(A,C)))))))) # label(t89_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4861 (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)) & k6_qc_lang2(A,B,C) = k14_qc_lang1(A,k14_qc_lang1(B,C)))))))) # label(t20_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4862 (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]. 56.98/55.97 4863 (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) -> B = A & C = D))))))))) # label(t19_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4864 $T # label(t11_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4865 (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)) <-> B = A))))))) # label(t63_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4866 (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]. 56.98/55.97 4867 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v5_qc_lang1(A) -> (B = k21_qc_lang1(A) <-> r1_qc_lang2(B,A))))))) # label(t67_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4868 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r1_qc_lang2(B,A) & v2_qc_lang1(A)))))) # label(t64_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4869 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (-(B != k12_qc_lang1(A) & (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> k14_qc_lang1(C,A) != B)) & (all C (m1_subset_1(C,k8_qc_lang1) -> k13_qc_lang1(C,A) != B & B != k13_qc_lang1(A,C)))) <-> r1_qc_lang2(A,B)))))) # label(d20_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4870 $T # label(t9_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.97 4871 (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]. 56.98/55.97 4872 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> r3_qc_lang2(A,k3_qc_lang2(A,B)) & r3_qc_lang2(k12_qc_lang1(B),k3_qc_lang2(A,B)) & r3_qc_lang2(k13_qc_lang1(k12_qc_lang1(A),k12_qc_lang1(B)),k3_qc_lang2(A,B)) & r3_qc_lang2(B,k3_qc_lang2(A,B)) & r3_qc_lang2(k12_qc_lang1(A),k3_qc_lang2(A,B)))))) # label(t94_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4873 (all A (m1_subset_1(A,k8_qc_lang1) -> ((exists B (m1_subset_1(B,k8_qc_lang1) & (exists C (m1_subset_1(C,k8_qc_lang1) & k4_qc_lang2(B,C) = A)))) <-> v3_qc_lang2(A)))) # label(d12_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4874 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r1_xreal_0(k3_finseq_1(k10_qc_lang1(B)),k3_finseq_1(k10_qc_lang1(A))) & r3_qc_lang2(A,B)))))) # label(t74_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4875 $T # label(t43_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4876 $T # label(t68_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4877 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> A = k18_qc_lang1(k13_qc_lang1(A,B)) & B = k19_qc_lang1(k13_qc_lang1(A,B)))))) # label(t5_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4878 (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]. 56.98/55.98 4879 $T # label(t42_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4880 (all A all B all C (m1_subset_1(B,k2_qc_lang1) & m1_subset_1(C,k8_qc_lang1) & m1_subset_1(A,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]. 56.98/55.98 4881 (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 & G = B & E = k5_qc_lang2(C,D)))))))))))))))) # label(t32_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4882 (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]. 56.98/55.98 4883 (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]. 56.98/55.98 4884 (all A (m1_subset_1(A,k8_qc_lang1) -> (k15_qc_lang2(A) = k1_tarski(A) <-> A = k11_qc_lang1 | v2_qc_lang1(A)))) # label(t116_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4885 (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(A,C) = k14_qc_lang1(B,D) -> A = B & D = C))))))))) # label(t6_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4886 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r3_qc_lang2(A,B) & r3_qc_lang2(B,A)))))) # label(t80_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4887 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r3_qc_lang2(A,B) & r2_qc_lang2(B,A)))))) # label(t79_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4888 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k4_qc_lang2(A,B) = k13_qc_lang1(k2_qc_lang2(A,B),k2_qc_lang2(B,A)))))) # label(d4_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4889 $T # label(t106_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4890 (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) -> (r3_qc_lang2(A,k14_qc_lang1(C,B)) <-> r2_qc_lang2(A,B)))))))) # label(t91_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4891 (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,B) & r2_qc_lang2(B,C) -> r2_qc_lang2(A,C)))))))) # label(t77_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4892 $T # label(t36_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4893 (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) -> B = A & E = F & D = C))))))))))))) # label(t21_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4894 (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]. 56.98/55.98 4895 (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]. 56.98/55.98 4896 (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]. 56.98/55.98 4897 (all A (m1_subset_1(A,k8_qc_lang1) -> (k11_qc_lang1 = A <-> r2_qc_lang2(A,k11_qc_lang1)))) # label(t99_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4898 (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]. 56.98/55.98 4899 (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,k12_qc_lang1(B)) = k17_qc_lang1(k5_qc_lang2(A,B)))))) # label(t48_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4900 (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)),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))) = k15_qc_lang2(k4_qc_lang2(A,B)))))) # label(t115_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4901 (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]. 56.98/55.98 4902 (all A all B (m1_subset_1(A,k8_qc_lang1) & m1_subset_1(B,k8_qc_lang1) -> -r3_qc_lang2(A,A))) # label(irreflexivity_r3_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4903 (all A (m1_subset_1(A,k8_qc_lang1) -> (v5_qc_lang1(A) -> A = k14_qc_lang1(k20_qc_lang1(A),k21_qc_lang1(A))))) # label(t7_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4904 (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) -> k8_qc_lang2(A,B,C,D) = k14_qc_lang1(A,k6_qc_lang2(B,C,D)))))))))) # label(d8_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4905 $T # label(d17_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4906 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r3_qc_lang2(A,B) & r1_qc_lang2(B,A)))))) # label(t82_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4907 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) -> k15_qc_lang2(A) = k2_xboole_0(k2_xboole_0(k15_qc_lang2(k18_qc_lang1(A)),k15_qc_lang2(k19_qc_lang1(A))),k1_tarski(A))))) # label(t118_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4908 (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) & r2_hidden(k1_funct_1(C,D),k4_qc_lang1) & r1_xreal_0(D,k3_finseq_1(C)) & m2_subset_1(D,k1_numbers,k5_numbers))) <-> r2_hidden(A,a_2_0_cqc_lang(B,C))))) # label(fraenkel_a_2_0_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4909 (all A all B (m1_subset_1(A,k7_cqc_lang) & m1_subset_1(B,k7_cqc_lang) -> k13_cqc_lang(A,B) = k3_qc_lang2(A,B))) # label(redefinition_k13_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4910 (all A all B (m1_subset_1(B,k7_cqc_lang) & m1_subset_1(A,k7_cqc_lang) -> k11_cqc_lang(A,B) = k13_qc_lang1(A,B))) # label(redefinition_k11_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4911 (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) -> k12_qc_lang1(k17_cqc_lang(k17_qc_lang1(B),A)) = k17_cqc_lang(B,A)))))) # label(t31_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4912 (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]. 56.98/55.98 4913 (all A all B all C (m2_subset_1(B,k1_numbers,k5_numbers) & m1_qc_lang1(C,B) -> ((exists D (r2_hidden(k1_funct_1(C,D),k3_qc_lang1) & r1_xreal_0(np__1,D) & m2_subset_1(D,k1_numbers,k5_numbers) & k1_funct_1(C,D) = A & r1_xreal_0(D,k3_finseq_1(C)))) <-> r2_hidden(A,a_2_1_cqc_lang(B,C))))) # label(fraenkel_a_2_1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4914 (all A all B (m1_subset_1(B,k7_cqc_lang) & m1_subset_1(A,k2_qc_lang1) -> 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]. 56.98/55.98 4915 (all A (m1_subset_1(A,k8_qc_lang1) -> (k1_xboole_0 = k6_qc_lang3(A) & k5_qc_lang3(A) = k1_xboole_0 <-> m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)))) # label(t13_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4916 (all A all B all C all D all E (m1_subset_1(D,A) & -v1_xboole_0(A) & m1_subset_1(E,A) -> k1_cqc_lang(B,C,D,E) = k2_cqc_lang(A,B,C,D,E))) # label(redefinition_k2_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4917 (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]. 56.98/55.98 4918 (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]. 56.98/55.98 4919 $T # label(t25_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4920 (all A all B B = k1_funct_1(k3_cqc_lang(A,B),A)) # label(t6_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4921 (all A (m1_subset_1(A,k7_cqc_lang) -> k12_qc_lang1(A) = k10_cqc_lang(A))) # label(redefinition_k10_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4922 (all A all B (m1_subset_1(A,k7_cqc_lang) & m1_subset_1(B,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]. 56.98/55.98 4923 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> k9_cqc_lang = k17_cqc_lang(k9_cqc_lang,A))) # label(t28_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4924 (all A (-(-r2_hidden(A,k4_qc_lang1) & -r2_hidden(A,k2_qc_lang1) & -r2_hidden(A,k3_qc_lang1)) <-> r2_hidden(A,k1_qc_lang1))) # label(t7_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4925 (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 (m2_relset_1(C,k7_cqc_lang,f1_s9_cqc_lang) & f3_s9_cqc_lang = k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k9_cqc_lang) & k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,A) = B & v1_funct_2(C,k7_cqc_lang,f1_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)) -> f4_s9_cqc_lang(G,I,H) = k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k8_cqc_lang(G,I,H)) & 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)) & k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k11_cqc_lang(D,E)) = 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)) & 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)))))))))))))) & v1_funct_1(C)))))))) -> f7_s9_cqc_lang(f8_s9_cqc_lang,f2_s9_cqc_lang(f9_s9_cqc_lang)) = f2_s9_cqc_lang(k15_cqc_lang(f8_s9_cqc_lang,f9_s9_cqc_lang)) # label(s9_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4926 (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)) -> (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) & (p1_s1_cqc_lang(B) & p1_s1_cqc_lang(A) -> p1_s1_cqc_lang(k11_cqc_lang(A,B))) & p1_s1_cqc_lang(k8_cqc_lang(D,F,E)))))))))))))) -> (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]. 56.98/55.98 4927 (all A ((exists B (B = A & k1_xboole_0 = k5_qc_lang3(B) & k6_qc_lang3(B) = k1_xboole_0 & 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]. 56.98/55.98 4928 (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) -> k17_cqc_lang(k9_qc_lang1(C,D),B) = k9_qc_lang1(C,k5_cqc_lang(A,D,k6_cqc_lang(k3_qc_lang3(np__0),B))))))))))) # label(t30_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4929 (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]. 56.98/55.98 4930 (all A all B all C (m1_subset_1(B,k7_qc_lang1(A)) & m1_subset_1(A,k5_numbers) & m1_qc_lang1(C,A) & v1_cqc_lang(C,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]. 56.98/55.98 4931 $T # label(t1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4932 (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]. 56.98/55.98 4933 (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) -> (A != B -> 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]. 56.98/55.98 4934 $T # label(t3_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4935 (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]. 56.98/55.98 4936 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m1_subset_1(B,f1_s6_cqc_lang) -> (f3_s6_cqc_lang(A) = B <-> (exists C (m2_relset_1(C,k7_cqc_lang,f1_s6_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_s6_cqc_lang,C,k11_cqc_lang(D,E)) = 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,k10_cqc_lang(D)) = f8_s6_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,D)) & 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,k15_cqc_lang(F,D)) = f10_s6_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,D)))))))))))))) & k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k9_cqc_lang) = f2_s6_cqc_lang & B = k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,A) & v1_funct_2(C,k7_cqc_lang,f1_s6_cqc_lang) & v1_funct_1(C)))))))) -> f3_s6_cqc_lang(k8_cqc_lang(f5_s6_cqc_lang,f6_s6_cqc_lang,f7_s6_cqc_lang)) = f4_s6_cqc_lang(f5_s6_cqc_lang,f6_s6_cqc_lang,f7_s6_cqc_lang) # label(s6_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4937 (all A all B (m1_finseq_1(A,k1_qc_lang1) & v1_funct_1(B) & m1_relset_1(B,k4_qc_lang1,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]. 56.98/55.98 4938 (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) -> (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)) & k9_cqc_lang = k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,k9_cqc_lang) & (v2_qc_lang1(E) -> k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,E) = k9_qc_lang1(k15_qc_lang1(E),k4_cqc_lang(k16_qc_lang1(E),k6_cqc_lang(k3_qc_lang3(np__0),B)))) & (v4_qc_lang1(E) -> k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,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)))) & (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)))) & m2_relset_1(D,k8_qc_lang1,k8_qc_lang1) & v1_funct_1(D) & v1_funct_2(D,k8_qc_lang1,k8_qc_lang1) & C = k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,A))) <-> k17_cqc_lang(A,B) = C))))))) # label(d6_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4939 (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]. 56.98/55.98 4940 (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,f2_s3_cqc_lang,k9_cqc_lang) = f4_s3_cqc_lang & k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,k9_cqc_lang) = f4_s3_cqc_lang & (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,f2_s3_cqc_lang,k11_cqc_lang(A,B)) = 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)) & 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)) & f8_s3_cqc_lang(C,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,k15_cqc_lang(C,A)) & 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))))))))))))) -> f3_s3_cqc_lang = f2_s3_cqc_lang # label(s3_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4941 (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]. 56.98/55.98 4942 (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]. 56.98/55.98 4943 (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]. 56.98/55.98 4944 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m1_subset_1(B,f1_s5_cqc_lang) -> (f2_s5_cqc_lang(A) = B <-> (exists C (v1_funct_2(C,k7_cqc_lang,f1_s5_cqc_lang) & 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 (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_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,k15_cqc_lang(F,D)) = f7_s5_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,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)) & 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)) = k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k11_cqc_lang(D,E)))))))))))))) & k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k9_cqc_lang) = f3_s5_cqc_lang & v1_funct_1(C) & B = k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,A)))))))) -> f3_s5_cqc_lang = f2_s5_cqc_lang(k9_cqc_lang) # label(s5_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.98 4945 (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_1_cqc_lang(A,C) & a_2_0_cqc_lang(A,C) = k1_xboole_0 <-> m2_subset_1(k9_qc_lang1(B,C),k8_qc_lang1,k7_cqc_lang)))))))) # label(t17_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 4946 (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]. 56.98/55.99 4947 (all A all B all C (m1_subset_1(A,k5_numbers) & v1_cqc_lang(C,A) & m1_subset_1(B,k7_qc_lang1(A)) & m1_qc_lang1(C,A) -> k8_cqc_lang(A,B,C) = k9_qc_lang1(B,C))) # label(redefinition_k8_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 4948 (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]. 56.98/55.99 4949 (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) -> k17_cqc_lang(B,A) = k9_qc_lang1(k15_qc_lang1(B),k4_cqc_lang(k16_qc_lang1(B),k6_cqc_lang(k3_qc_lang3(np__0),A)))))))) # label(t29_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 4950 $T # label(t4_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 4951 (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 (m1_qc_lang1(F,E) & v1_cqc_lang(F,E) -> (all G (m2_subset_1(G,k5_qc_lang1,k7_qc_lang1(E)) -> f3_s2_cqc_lang(E,G,F) = k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k8_cqc_lang(E,G,F)) & 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,k10_cqc_lang(B)) & k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k15_cqc_lang(D,B)) = f6_s2_cqc_lang(D,k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,B)) & 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)) = k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k11_cqc_lang(B,C)))))))))))))) & 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]. 56.98/55.99 4952 (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]. 56.98/55.99 4953 (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) -> k17_cqc_lang(k13_qc_lang1(B,C),A) = k13_qc_lang1(k17_cqc_lang(B,A),k17_cqc_lang(C,A)))))))) # label(t34_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 4954 $T # label(t9_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 4955 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m1_qc_lang1(B,A) -> (k1_xboole_0 = a_2_1_cqc_lang(A,B) & a_2_0_cqc_lang(A,B) = k1_xboole_0 <-> m1_qc_lang1(B,A) & v1_cqc_lang(B,A)))))) # label(t15_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 4956 (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_2(C,k7_cqc_lang,f1_s7_cqc_lang) & B = k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,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)) -> 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)) & f4_s7_cqc_lang(G,I,H) = k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k8_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)) & f8_s7_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,D)) = k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k15_cqc_lang(F,D)))))))))))))) & m2_relset_1(C,k7_cqc_lang,f1_s7_cqc_lang) & v1_funct_1(C) & f3_s7_cqc_lang = k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k9_cqc_lang)))))))) -> f2_s7_cqc_lang(k10_cqc_lang(f6_s7_cqc_lang)) = f5_s7_cqc_lang(f2_s7_cqc_lang(f6_s7_cqc_lang)) # label(s7_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 4957 (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) -> k17_cqc_lang(B,A) = B))))) # label(t35_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 4958 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k6_qc_lang3(k17_cqc_lang(B,A)) = k6_qc_lang3(B))))) # label(t41_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 4959 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m1_subset_1(B,f1_s8_cqc_lang) -> ((exists C (v1_funct_1(C) & v1_funct_2(C,k7_cqc_lang,f1_s8_cqc_lang) & f3_s8_cqc_lang = k8_funct_2(k7_cqc_lang,f1_s8_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_s8_cqc_lang(G,I,H) = k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k8_cqc_lang(G,I,H)) & f5_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,k10_cqc_lang(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)) & f9_s8_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,D)) = k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k15_cqc_lang(F,D)))))))))))))) & B = k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,A) & m2_relset_1(C,k7_cqc_lang,f1_s8_cqc_lang))) <-> f2_s8_cqc_lang(A) = B))))) -> 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]. 56.98/55.99 4960 (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]. 56.98/55.99 4961 $T # label(dt_k3_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 4962 (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]. 56.98/55.99 4963 (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]. 56.98/55.99 4964 (all A all B (m1_subset_1(B,k7_cqc_lang) & m1_subset_1(A,k2_qc_lang1) -> 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]. 56.98/55.99 4965 (all A all B all C (v1_funct_1(C) & m1_relset_1(C,k4_qc_lang1,k1_qc_lang1) & m1_qc_lang1(B,A) & m1_subset_1(A,k5_numbers) -> m1_qc_lang1(k5_cqc_lang(A,B,C),A))) # label(dt_k5_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 4966 (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]. 56.98/55.99 4967 (all A all B all C all D all E (m1_subset_1(E,A) & m1_subset_1(D,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]. 56.98/55.99 4968 (all A all B (m1_subset_1(A,k2_qc_lang1) & m1_subset_1(B,k7_cqc_lang) -> k5_qc_lang2(A,B) = k16_cqc_lang(A,B))) # label(redefinition_k16_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 4969 (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) -> (k4_cqc_lang(A,B) = C <-> (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(B,k1_funct_1(A,D)) = k1_funct_1(C,D))))) & k3_finseq_1(C) = k3_finseq_1(A)))))))) # label(d3_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 4970 (all A all B (m1_subset_1(B,k7_cqc_lang) & m1_subset_1(A,k2_qc_lang1) -> k15_cqc_lang(A,B) = k14_qc_lang1(A,B))) # label(redefinition_k15_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 4971 (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]. 56.98/55.99 4972 (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]. 56.98/55.99 4973 (all A all B all C all D ((B = A -> k1_cqc_lang(A,B,C,D) = C) & (B != A -> D = k1_cqc_lang(A,B,C,D)))) # label(d1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 4974 $T # label(t26_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 4975 $T # label(t8_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 4976 (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]. 56.98/55.99 4977 (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]. 56.98/55.99 4978 $T # label(dt_k1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 4979 (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]. 56.98/55.99 4980 $T # label(t14_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 4981 $T # label(t12_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 4982 (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]. 56.98/55.99 4983 (exists A ((exists B (v1_funct_1(B) & v1_funct_2(B,k7_cqc_lang,f1_s4_cqc_lang) & A = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,f2_s4_cqc_lang) & f3_s4_cqc_lang = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,k9_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 (m1_qc_lang1(G,F) & v1_cqc_lang(G,F) -> (all H (m2_subset_1(H,k5_qc_lang1,k7_qc_lang1(F)) -> f5_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,k10_cqc_lang(C)) & 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)) & 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)) & f4_s4_cqc_lang(F,H,G) = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,k8_cqc_lang(F,H,G)))))))))))))) & m2_relset_1(B,k7_cqc_lang,f1_s4_cqc_lang))) & m1_subset_1(A,f1_s4_cqc_lang))) # label(s4_cqc_lang_AndLHS) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 4984 (all A (m1_subset_1(A,f1_s4_cqc_lang) -> (all B (m1_subset_1(B,f1_s4_cqc_lang) -> -((exists 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) = B & 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 (m1_qc_lang1(H,G) & v1_cqc_lang(H,G) -> (all I (m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G)) -> 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)) & 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)) & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s4_cqc_lang(G,I,H) & 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)))))))))))))) & m2_relset_1(C,k7_cqc_lang,f1_s4_cqc_lang) & v1_funct_1(C))) & (exists C (v1_funct_1(C) & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,f2_s4_cqc_lang) = A & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k9_cqc_lang) = f3_s4_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_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)) & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s4_cqc_lang(G,I,H))))))))))))) & m2_relset_1(C,k7_cqc_lang,f1_s4_cqc_lang) & v1_funct_2(C,k7_cqc_lang,f1_s4_cqc_lang))) & A != B))))) # label(s4_cqc_lang_AndRHS) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 4985 (all A all B all C (m1_subset_1(A,k5_numbers) & m1_relset_1(C,k4_qc_lang1,k1_qc_lang1) & v1_funct_1(C) & m1_qc_lang1(B,A) -> k4_cqc_lang(B,C) = k5_cqc_lang(A,B,C))) # label(redefinition_k5_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 4986 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (k5_qc_lang3(B) = k1_xboole_0 -> k17_cqc_lang(B,A) = B))))) # label(t39_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 4987 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) & m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) <-> m2_subset_1(k13_qc_lang1(A,B),k8_qc_lang1,k7_cqc_lang)))))) # label(t19_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 4988 $T # label(t27_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 4989 (all A (m1_subset_1(A,k5_numbers) -> (exists B (m1_qc_lang1(B,A) & v1_funct_1(B) & v1_relat_1(B) & v1_cqc_lang(B,A) & v1_finseq_1(B))))) # label(rc1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 4990 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k4_qc_lang1) -> v1_funct_1(k3_cqc_lang(B,A)) & m2_relset_1(k3_cqc_lang(B,A),k4_qc_lang1,k1_qc_lang1))))) # label(t10_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 4991 (all A all B (k2_relat_1(k3_cqc_lang(A,B)) = k1_tarski(B) & k1_tarski(A) = k1_relat_1(k3_cqc_lang(A,B)))) # label(t5_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 4992 (all A all B (m1_subset_1(A,k4_qc_lang1) & m1_subset_1(B,k2_qc_lang1) -> k3_cqc_lang(A,B) = k6_cqc_lang(A,B))) # label(redefinition_k6_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 4993 (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) & r1_xreal_0(A,k3_finseq_1(E)) & k4_cqc_lang(E,F) = D & r1_xreal_0(np__1,A) -> (C = k1_funct_1(E,A) -> B = k1_funct_1(D,A)) & (C != k1_funct_1(E,A) -> k1_funct_1(D,A) = k1_funct_1(E,A))))))))))))))) # label(t11_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 4994 $T # label(t2_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 4995 (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]. 56.98/55.99 4996 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r4_pboole(A,B,C) & r2_pboole(A,B,D) -> r4_pboole(A,B,k3_pboole(A,C,D))))))))) # label(t112_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 4997 (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]. 56.98/55.99 4998 (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]. 56.98/55.99 4999 (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]. 56.98/55.99 5000 (exists A ((all B (r2_hidden(B,f1_s4_pboole) -> f2_s4_pboole(B) = k1_funct_1(A,B))) & m1_pboole(A,f1_s4_pboole))) # label(s4_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 5001 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (m3_pboole(D,A,B,C) <-> (all E (r2_hidden(E,A) -> v1_funct_1(k1_funct_1(D,E)) & m2_relset_1(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E)) & v1_funct_2(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E))))))))))) # label(d18_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 5002 (all A k1_pboole(A) = k2_funcop_1(A,k1_xboole_0)) # label(d6_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 5003 (all A exists B (v1_funcop_1(B) & v1_funct_1(B) & m1_pboole(B,A) & v1_relat_1(B))) # label(rc4_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 5004 (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]. 56.98/55.99 5005 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> r2_pboole(A,B,B))) # label(reflexivity_r2_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 5006 (all A all B (m1_pboole(B,A) -> r6_pboole(A,k2_pboole(A,B,k1_pboole(A)),B) & r6_pboole(A,k2_pboole(A,k1_pboole(A),B),B))) # label(t53_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 5007 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,k3_pboole(A,C,D)) -> r2_pboole(A,B,C) & r2_pboole(A,B,D)))))))) # label(t44_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 5008 (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]. 56.98/55.99 5009 (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]. 56.98/55.99 5010 (all A all B (m1_pboole(B,A) -> r2_pboole(A,k1_pboole(A),B))) # label(t49_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/55.99 5011 (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]. 56.98/56.00 5012 (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]. 56.98/56.00 5013 (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]. 56.98/56.00 5014 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r4_pboole(A,B,C) & r2_pboole(A,B,D) -> r4_pboole(A,D,C)))))))) # label(t109_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5015 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> k3_pboole(A,C,B) = k3_pboole(A,B,C))) # label(commutativity_k3_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5016 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> (r5_pboole(A,B,C) -> r5_pboole(A,C,B)))) # label(symmetry_r5_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5017 (all A all B all C all D (m1_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) & -v1_xboole_0(B) & m1_pboole(D,B) -> m1_pboole(k7_pboole(A,B,C,D),A))) # label(dt_k7_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5018 (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]. 56.98/56.00 5019 (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]. 56.98/56.00 5020 (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]. 56.98/56.00 5021 (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]. 56.98/56.00 5022 (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]. 56.98/56.00 5023 (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]. 56.98/56.00 5024 (all A all B all C all D (m1_pboole(D,B) & -v1_xboole_0(B) & v1_funct_1(C) & v2_relat_1(D) & m1_relset_1(C,A,B) & v1_funct_2(C,A,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]. 56.98/56.00 5025 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> k2_pboole(A,C,B) = k2_pboole(A,B,C))) # label(commutativity_k2_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5026 (all A -(r2_hidden(A,f1_s1_pboole) & f2_s1_pboole(A) = k1_xboole_0)) -> (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]. 56.98/56.00 5027 (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]. 56.98/56.00 5028 (all A all B (m1_pboole(B,A) -> -(r5_pboole(A,B,B) & B != k1_pboole(A)))) # label(t122_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5029 (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]. 56.98/56.00 5030 (all A all B k10_pboole(A,B) = k2_funcop_1(A,B)) # label(redefinition_k10_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5031 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,k3_finseq_2(A)) -> ((all D (m2_finseq_2(D,A,k3_finseq_2(A)) -> k1_funct_1(C,D) = k4_card_3(k5_relat_1(D,B)))) <-> k6_pboole(A,B) = C))))) # label(d19_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5032 (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,B,D) & r2_pboole(A,C,D)))))))) # label(t43_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5033 (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]. 56.98/56.00 5034 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,D,C) & r2_pboole(A,B,C) -> r2_pboole(A,k2_pboole(A,B,D),C)))))))) # label(t18_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5035 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r4_pboole(A,B,k3_pboole(A,C,D)) -> r4_pboole(A,B,D) & r4_pboole(A,B,C)))))))) # label(t111_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5036 (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_1(D,E) = k1_funct_2(k1_funct_1(B,E),k1_funct_1(C,E)))) <-> k12_pboole(A,B,C) = D))))))) # label(d22_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5037 (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]. 56.98/56.00 5038 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) & v1_funcop_1(C) -> m1_pboole(k14_pboole(A,B,C),A))) # label(dt_k14_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5039 (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]. 56.98/56.00 5040 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> (all C (m1_subset_1(C,k2_relat_1(B)) -> (exists D (r2_hidden(D,A) & k1_funct_1(B,D) = C)))))))) # label(t150_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5041 (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]. 56.98/56.00 5042 (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]. 56.98/56.00 5043 (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,B,k4_pboole(A,C,B))) & r6_pboole(A,C,k2_pboole(A,k4_pboole(A,C,B),B))))))) # label(t72_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5044 (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]. 56.98/56.00 5045 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,k2_pboole(A,C,D)) & r6_pboole(A,k3_pboole(A,B,D),k1_pboole(A)) -> r2_pboole(A,B,C)))))))) # label(t56_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5046 (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]. 56.98/56.00 5047 (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]. 56.98/56.00 5048 (exists A (m1_pboole(A,f1_s2_pboole) & (all B (r2_hidden(B,f1_s2_pboole) -> (all C (r2_hidden(C,k1_funct_1(A,B)) <-> r2_hidden(C,k1_funct_1(f2_s2_pboole,B)) & p1_s2_pboole(B,C))))))) # label(s2_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5049 $T # label(t131_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5050 (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]. 56.98/56.00 5051 (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]. 56.98/56.00 5052 (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]. 56.98/56.00 5053 (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]. 56.98/56.00 5054 (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]. 56.98/56.00 5055 (all A -((all B -p1_s3_pboole(A,B)) & r2_hidden(A,f1_s3_pboole))) -> (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]. 56.98/56.00 5056 (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]. 56.98/56.00 5057 (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,B,C)),B) & r6_pboole(A,k2_pboole(A,k3_pboole(A,C,B),B),B) & r6_pboole(A,k2_pboole(A,B,k3_pboole(A,C,B)),B))))) # label(t37_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5058 (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]. 56.98/56.00 5059 (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]. 56.98/56.00 5060 (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]. 56.98/56.00 5061 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) & v2_relat_1(D) -> ((all E (m1_pboole(E,A) -> (r1_pboole(A,E,D) <-> r1_pboole(A,E,B) & r1_pboole(A,E,C)))) -> r6_pboole(A,D,k3_pboole(A,B,C))))))))) # label(t148_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5062 $T # label(t31_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5063 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r6_pboole(A,k3_pboole(A,B,C),k1_pboole(A)) <-> r6_pboole(A,k4_pboole(A,B,C),B)))))) # label(t77_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5064 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) & -v1_xboole_0(A) -> (r3_pboole(A,B,C) <-> r1_pboole(A,B,C)))) # label(redefinition_r3_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5065 (all A all B (v1_funct_1(B) & v1_funcop_1(B) & v1_relat_1(A) & v1_funcop_1(A) & v1_relat_1(B) & v1_funct_1(A) -> v1_relat_1(k13_pboole(A,B)) & v1_funct_1(k13_pboole(A,B)) & v1_funcop_1(k13_pboole(A,B)))) # label(dt_k13_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5066 (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]. 56.98/56.00 5067 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) & -v1_xboole_0(A) -> (r3_pboole(A,B,C) -> -r3_pboole(A,C,B)))) # label(antisymmetry_r3_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5068 (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) -> k2_zfmisc_1(k1_funct_1(B,E),k1_funct_1(C,E)) = k1_funct_1(D,E))) <-> k11_pboole(A,B,C) = D))))))) # label(d21_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5069 (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]. 56.98/56.00 5070 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) & r6_pboole(A,k3_pboole(A,C,D),k1_pboole(A)) -> r6_pboole(A,k3_pboole(A,B,D),k1_pboole(A))))))))) # label(t52_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5071 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (r2_hidden(D,A) -> k5_xboole_0(k1_funct_1(B,D),k1_funct_1(C,D)) = k1_funct_1(k5_pboole(A,B,C),D))))))) # label(t4_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5072 (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]. 56.98/56.00 5073 (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]. 56.98/56.00 5074 (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]. 56.98/56.00 5075 (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]. 56.98/56.00 5076 $T # label(t14_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5077 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k3_pboole(A,k4_pboole(A,B,C),C),k1_pboole(A)) & r6_pboole(A,k3_pboole(A,C,k4_pboole(A,B,C)),k1_pboole(A)))))) # label(t69_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5078 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> -(r3_pboole(A,B,D) & r3_pboole(A,B,C) & k3_pboole(A,C,D) = k1_pboole(A)))))))))) # label(t137_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5079 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> (r6_pboole(A,B,C) -> r6_pboole(A,C,B)))) # label(symmetry_r6_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5080 (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]. 56.98/56.00 5081 (exists A (v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A))) # label(rc1_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5082 (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]. 56.98/56.00 5083 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> (r6_pboole(A,B,C) <-> B = C))) # label(redefinition_r6_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5084 (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]. 56.98/56.00 5085 (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]. 56.98/56.00 5086 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v3_relat_1(A) <-> k1_tarski(k1_xboole_0) = k2_relat_1(A) | A = k1_xboole_0))) # label(t2_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5087 (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]. 56.98/56.00 5088 (all A all B (v2_relat_1(B) & m1_pboole(B,A) -> (exists C (r1_pboole(A,C,B) & m1_pboole(C,A))))) # label(t146_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5089 (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) -> (r4_pboole(A,B,D) & r2_pboole(A,D,E) & r2_pboole(A,B,C) -> r4_pboole(A,C,E)))))))))) # label(t110_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5090 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> -r4_pboole(A,B,k1_pboole(A)) & -r4_pboole(A,k1_pboole(A),B))))) # label(t138_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5091 (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]. 56.98/56.00 5092 (all A all B (m1_pboole(B,A) -> r6_pboole(A,k5_pboole(A,k1_pboole(A),B),B) & r6_pboole(A,k5_pboole(A,B,k1_pboole(A)),B))) # label(t91_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5093 (exists A ((all B (m1_subset_1(B,f1_s5_pboole) -> f2_s5_pboole(B) = k1_funct_1(A,B))) & m1_pboole(A,f1_s5_pboole))) # label(s5_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5094 (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]. 56.98/56.00 5095 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k3_pboole(A,k2_pboole(A,B,C),B),B) & r6_pboole(A,k3_pboole(A,B,k2_pboole(A,B,C)),B) & 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))))) # label(t36_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5096 (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]. 56.98/56.00 5097 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r6_pboole(A,B,k3_pboole(A,C,D)) <-> (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) & r2_pboole(A,B,C)))))))) # label(t29_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5098 (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]. 56.98/56.00 5099 (all A exists B (v1_funct_1(B) & v2_relat_1(B) & v1_relat_1(B) & m1_pboole(B,A))) # label(rc3_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5100 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_relat_1(A) -> v1_setfam_1(k2_relat_1(A))))) # label(t1_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5101 (all A all B (m2_relset_1(k10_pboole(A,B),A,k1_tarski(B)) & v1_funct_2(k10_pboole(A,B),A,k1_tarski(B)) & v1_funct_1(k10_pboole(A,B)))) # label(dt_k10_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5102 (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]. 56.98/56.00 5103 (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,C,E) -> r2_pboole(A,B,E)))) & r2_pboole(A,D,B) & r2_pboole(A,C,B) <-> r6_pboole(A,B,k2_pboole(A,C,D))))))))) # label(t28_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5104 (all A all B (m1_pboole(B,A) -> (v2_relat_1(B) <-> (all C -(r2_hidden(C,A) & v1_xboole_0(k1_funct_1(B,C))))))) # label(d16_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5105 (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]. 56.98/56.00 5106 (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]. 56.98/56.00 5107 $T # label(t107_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5108 (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) -> k2_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E)) = k1_funct_1(D,E))) <-> k2_pboole(A,B,C) = D))))))) # label(d7_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5109 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,C,B) & v3_relat_1(B) -> v3_relat_1(C)))))) # label(t142_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5110 (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]. 56.98/56.00 5111 $T # label(t125_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5112 (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]. 56.98/56.00 5113 (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]. 56.98/56.00 5114 $T # label(t93_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5115 (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]. 56.98/56.00 5116 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> m1_pboole(k4_pboole(A,B,C),A))) # label(dt_k4_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5117 (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]. 56.98/56.00 5118 (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]. 56.98/56.00 5119 (all A all B all C all D (v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_pboole(D,B) & v1_funct_1(C) & -v1_xboole_0(B) -> k7_pboole(A,B,C,D) = k5_relat_1(C,D))) # label(redefinition_k7_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5120 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> (all D (m3_pboole(D,A,B,C) -> v1_funcop_1(D))))) # label(cc3_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5121 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> B = k3_pboole(A,B,B))) # label(idempotence_k3_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5122 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) & v2_relat_1(C) -> ((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]. 56.98/56.00 5123 (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]. 56.98/56.00 5124 (all A all B (m1_pboole(B,A) -> v1_funct_1(B) & v1_relat_1(B))) # label(dt_m1_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.00 5125 (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]. 56.98/56.00 5126 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> -(-r4_pboole(A,B,C) & r4_pboole(A,k3_pboole(A,D,B),k3_pboole(A,D,C))))))))) # label(t114_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.01 5127 $T # label(d1_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.01 5128 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) -> r6_pboole(A,k3_pboole(A,C,B),B) & r6_pboole(A,k3_pboole(A,B,C),B)))))) # label(t25_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.01 5129 $T # label(t32_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.01 5130 (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]. 56.98/56.01 5131 (all A all B (v1_funct_1(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))) -> (B = k9_pboole(A) <-> (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)))))) # label(d20_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.01 5132 (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]. 56.98/56.01 5133 (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]. 56.98/56.01 5134 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,k4_pboole(A,B,C),D) & r2_pboole(A,k4_pboole(A,C,B),D) -> r2_pboole(A,k5_pboole(A,B,C),D)))))))) # label(t99_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.01 5135 (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]. 56.98/56.01 5136 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> r6_pboole(A,B,B))) # label(reflexivity_r6_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.01 5137 (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]. 56.98/56.01 5138 (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]. 56.98/56.01 5139 (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,C,D),B),k3_pboole(A,k2_pboole(A,C,B),k2_pboole(A,D,B))) & 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))))))))) # label(t39_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.01 5140 (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]. 56.98/56.01 5141 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r2_pboole(A,B,C) & r2_pboole(A,D,E) -> r2_pboole(A,k3_pboole(A,B,D),k3_pboole(A,C,E))))))))))) # label(t23_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.01 5142 (all A all B all C (m1_subset_1(C,A) & -v1_xboole_0(A) & v2_relat_1(B) & m1_pboole(B,A) -> -v1_xboole_0(k1_funct_1(B,C)))) # label(fc2_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.01 5143 (all A m1_pboole(k1_pboole(A),A)) # label(dt_k1_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.01 5144 (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]. 56.98/56.01 5145 (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]. 56.98/56.01 5146 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (v2_relat_1(B) & r2_pboole(A,B,C) -> v2_relat_1(C)))))) # label(t143_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.01 5147 (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]. 56.98/56.01 5148 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,C,D) & r2_pboole(A,B,C) -> r2_pboole(A,B,D)))))))) # label(t15_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.01 5149 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r7_pboole(A,B,C) & v2_relat_1(B) -> r2_pboole(A,B,C)))))) # label(t144_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.01 5150 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> m1_pboole(k11_pboole(A,B,C),A))) # label(dt_k11_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.01 5151 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> m1_pboole(k5_pboole(A,B,C),A))) # label(dt_k5_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.01 5152 $T # label(t13_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.01 5153 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (k3_pboole(A,B,C) = D <-> (all E (r2_hidden(E,A) -> k1_funct_1(D,E) = k3_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E))))))))))) # label(d8_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.01 5154 (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]. 56.98/56.01 5155 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) & v1_funcop_1(C) -> (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]. 56.98/56.01 5156 (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]. 56.98/56.01 5157 $T # label(d2_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.01 5158 (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]. 56.98/56.01 5159 (all A (m1_pboole(A,k1_xboole_0) -> A = k1_xboole_0)) # label(t134_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.01 5160 (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]. 56.98/56.01 5161 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> m1_pboole(k12_pboole(A,B,C),A))) # label(dt_k12_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.01 5162 (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) & r6_pboole(A,k2_pboole(A,B,C),k2_pboole(A,D,E)) & r5_pboole(A,D,B) -> r6_pboole(A,E,B) & r6_pboole(A,D,C)))))))))) # label(t124_pboole) # label(axiom) # label(non_clause). [assumption]. 56.98/56.01 5163 (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]. 56.98/56.01 5164 (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]. 56.98/56.01 5165 (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]. 57.05/56.01 5166 (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]. 57.05/56.01 5167 (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]. 57.05/56.01 5168 (all A all B (m1_pboole(B,A) -> (v3_relat_1(B) <-> v1_pboole(B,A)))) # label(redefinition_v1_pboole) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5169 (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]. 57.05/56.01 5170 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k2_pboole(A,k4_pboole(A,C,B),B),k2_pboole(A,C,B)) & r6_pboole(A,k2_pboole(A,B,k4_pboole(A,C,B)),k2_pboole(A,B,C)))))) # label(t73_pboole) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5171 (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]. 57.05/56.01 5172 (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]. 57.05/56.01 5173 (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,k2_pboole(A,B,D),k2_pboole(A,C,D))) & 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))))))))) # label(t45_pboole) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5174 (all A (v1_funct_1(k9_pboole(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))))) # label(dt_k9_pboole) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5175 (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_1(D,E) = k4_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E)))) <-> D = k4_pboole(A,B,C)))))))) # label(d9_pboole) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5176 (all A all B k1_funct_1(k1_pboole(B),A) = k1_xboole_0) # label(t5_pboole) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5177 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r4_pboole(A,B,C) & r2_pboole(A,C,D) -> r4_pboole(A,B,D)))))))) # label(t108_pboole) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5178 (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]. 57.05/56.01 5179 (all A all B (m1_pboole(B,A) -> ((all C (r2_hidden(C,A) -> k1_funct_1(B,C) = k1_xboole_0)) -> B = k1_pboole(A)))) # label(t6_pboole) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5180 (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)) & v1_relat_1(k6_pboole(A,B)) & v2_relat_1(k6_pboole(A,B)))) # label(fc1_pboole) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5181 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k4_pboole(A,B,k3_pboole(A,B,C)),k4_pboole(A,B,C)) & r6_pboole(A,k4_pboole(A,B,k3_pboole(A,C,B)),k4_pboole(A,B,C)))))) # label(t76_pboole) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5182 (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]. 57.05/56.01 5183 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B all C k2_finseq_2(A,C) = k5_relat_1(k2_finseq_2(A,B),k2_funcop_1(k1_tarski(B),C))))) # label(t152_pboole) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5184 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r6_pboole(A,k4_pboole(A,B,C),k1_pboole(A)) <-> r2_pboole(A,B,C)))))) # label(t58_pboole) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5185 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> (all D (m3_pboole(D,A,B,C) -> m1_pboole(D,A))))) # label(dt_m3_pboole) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5186 (all A all B (m1_pboole(B,A) & v2_relat_1(B) -> (exists C (v1_relat_1(C) & v1_funct_1(C) & m4_pboole(C,A,B) & v2_relat_1(C))))) # label(rc5_pboole) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5187 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> r7_pboole(A,B,B))) # label(reflexivity_r7_pboole) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5188 (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]. 57.05/56.01 5189 (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]. 57.05/56.01 5190 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_funcop_1(B) -> (all C (v1_funcop_1(C) & v1_relat_1(C) & v1_funct_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))) & k1_relat_1(C) = k3_xboole_0(k1_relat_1(A),k1_relat_1(B)) <-> C = k13_pboole(A,B)))))))) # label(d24_pboole) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5191 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r2_pboole(A,B,C) & r2_pboole(A,D,E) -> r2_pboole(A,k2_pboole(A,B,D),k2_pboole(A,C,E))))))))))) # label(t22_pboole) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5192 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> -(r4_pboole(A,B,B) & B = k1_pboole(A)))))) # label(t140_pboole) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5193 (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]. 57.05/56.01 5194 (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,C) & r5_pboole(A,B,D)))))))) # label(t116_pboole) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5195 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> k2_pboole(A,B,B) = B)) # label(idempotence_k2_pboole) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5196 (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]. 57.05/56.01 5197 $T # label(t117_pboole) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5198 $T # label(t30_pboole) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5199 (all A exists B (v3_relat_1(B) & v1_funct_1(B) & m1_pboole(B,A) & v1_relat_1(B))) # label(rc2_pboole) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5200 (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]. 57.05/56.01 5201 (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]. 57.05/56.01 5202 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r4_pboole(A,B,C) <-> (all D -(r1_xboole_0(k1_funct_1(B,D),k1_funct_1(C,D)) & r2_hidden(D,A)))))))) # label(d10_pboole) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5203 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> k5_pboole(A,B,C) = k2_pboole(A,k4_pboole(A,B,C),k4_pboole(A,C,B)))))) # label(d12_pboole) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5204 (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]. 57.05/56.01 5205 (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]. 57.05/56.01 5206 (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]. 57.05/56.01 5207 (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]. 57.05/56.01 5208 (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]. 57.05/56.01 5209 (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]. 57.05/56.01 5210 (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]. 57.05/56.01 5211 (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]. 57.05/56.01 5212 (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,D) & r2_pboole(A,B,C) -> r6_pboole(A,B,k1_pboole(A))))))))) # label(t51_pboole) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5213 (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]. 57.05/56.01 5214 $T # label(t90_pboole) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5215 (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]. 57.05/56.01 5216 (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]. 57.05/56.01 5217 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> (r4_pboole(A,B,C) -> r4_pboole(A,C,B)))) # label(symmetry_r4_pboole) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5218 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) & r6_pboole(A,k3_pboole(A,C,B),k1_pboole(A)) -> r6_pboole(A,B,k1_pboole(A))))))) # label(t57_pboole) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5219 (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]. 57.05/56.01 5220 (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]. 57.05/56.01 5221 $T # label(t33_pboole) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5222 (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]. 57.05/56.01 5223 (all A exists B m1_pboole(B,A)) # label(existence_m1_pboole) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5224 (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]. 57.05/56.01 5225 (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]. 57.05/56.01 5226 (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]. 57.05/56.01 5227 (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]. 57.05/56.01 5228 (all A all B all C all D (-v1_xboole_0(B) & v2_relat_1(D) & m1_relset_1(C,A,B) & v1_funct_1(C) & m1_pboole(D,B) & v1_funct_2(C,A,B) -> k5_relat_1(C,D) = k8_pboole(A,B,C,D))) # label(redefinition_k8_pboole) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5229 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(B) = A <-> m1_pboole(B,A)))) # label(d3_pboole) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5230 (all A (v1_funct_2(A,k5_numbers,k1_numbers) & v1_funct_1(A) & m2_relset_1(A,k5_numbers,k1_numbers) -> (v4_seq_2(A) <-> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(B,np__0) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (exists D (m2_subset_1(D,k1_numbers,k5_numbers) & r1_xreal_0(C,D) & r1_xreal_0(B,k18_complex1(k5_real_1(k8_funct_2(k5_numbers,k1_numbers,A,D),k8_funct_2(k5_numbers,k1_numbers,A,C)))))))))))))) # label(t58_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5231 (all A (-v1_xboole_0(A) & v2_membered(A) -> (all B (v1_xreal_0(B) -> ((all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r1_xreal_0(C,B)))) & (all C (v1_xreal_0(C) -> ((all D (v1_xreal_0(D) -> (r2_hidden(D,A) -> r1_xreal_0(D,C)))) -> r1_xreal_0(B,C)))) -> k2_seq_4(A) = B))))) # label(t63_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5232 (all A (v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> (v3_seq_2(A) & v6_seqm_3(A) -> v4_seq_2(A)))) # label(t53_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5233 (all A (v1_xreal_0(A) -> k1_seq_4(A) = k1_tarski(A))) # label(redefinition_k1_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5234 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> m1_subset_1(k4_seq_4(A),k1_numbers))) # label(dt_k4_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5235 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (m2_relset_1(C,k5_numbers,k1_numbers) & v1_funct_1(C) & v1_funct_2(C,k5_numbers,k1_numbers) -> ((all D (m2_subset_1(D,k1_numbers,k5_numbers) -> k7_xcmplx_0(B,k2_xcmplx_0(D,A)) = k8_funct_2(k5_numbers,k1_numbers,C,D))) -> np__0 = k2_seq_2(C) & v4_seq_2(C) | r1_xreal_0(A,np__0)))))))) # label(t46_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5236 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k5_numbers,k1_numbers) & v1_funct_2(C,k5_numbers,k1_numbers) -> ((all D (m2_subset_1(D,k1_numbers,k5_numbers) -> k7_xcmplx_0(B,k2_xcmplx_0(k2_nat_1(D,D),A)) = k8_funct_2(k5_numbers,k1_numbers,C,D))) -> k2_seq_2(C) = np__0 & v4_seq_2(C) | r1_xreal_0(A,np__0)))))))) # label(t50_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5237 (all A (v2_membered(A) -> v1_xreal_0(k2_seq_4(A)))) # label(dt_k2_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5238 (all A (m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) -> (v1_seq_2(A) & v3_seqm_3(A) -> v4_seq_2(A)))) # label(t51_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5239 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> k4_seq_4(A) = k2_seq_4(A))) # label(redefinition_k4_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.01 5240 (all A (v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) -> (v4_seq_2(A) -> k18_complex1(k2_seq_2(A)) = k2_seq_2(k22_seq_1(A))))) # label(t27_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5241 (all A (v1_funct_2(A,k5_numbers,k1_numbers) & v1_funct_1(A) & m2_relset_1(A,k5_numbers,k1_numbers) -> (all B (m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_numbers) -> (m1_seqm_3(A,B) & v4_seq_2(B) -> k2_seq_2(A) = k2_seq_2(B)))))) # label(t30_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5242 (all A (v2_membered(A) -> -((all B (v1_xreal_0(B) -> -((all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r1_xreal_0(B,C)))) & (all C (v1_xreal_0(C) -> -((all D (v1_xreal_0(D) -> -(r2_hidden(D,A) & -r1_xreal_0(k2_xcmplx_0(B,C),D)))) & -r1_xreal_0(C,np__0))))))) & v2_seq_4(A) & -v1_xboole_0(A)))) # label(t18_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5243 (all A (v2_membered(A) -> v1_xreal_0(k3_seq_4(A)))) # label(dt_k3_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5244 (all A (v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> (v5_seqm_3(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k8_funct_2(k5_numbers,k1_numbers,A,B) = k2_seq_2(A)))))) # label(t41_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5245 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_numbers)) -> -((all C (v1_xreal_0(C) -> (exists D ((exists E (v1_xreal_0(E) & r2_hidden(D,A) & r2_hidden(E,B) & -(r1_xreal_0(D,C) & r1_xreal_0(C,E)))) & v1_xreal_0(D))))) & (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(r2_hidden(C,A) & r1_xreal_0(D,C) & r2_hidden(D,B))))))))))) # label(t8_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5246 (all A (v1_xreal_0(A) -> (all B (v2_membered(B) & -v1_xboole_0(B) -> ((all C (v1_xreal_0(C) -> ((all D (v1_xreal_0(D) -> (r2_hidden(D,B) -> r1_xreal_0(C,D)))) -> r1_xreal_0(C,A)))) & (all C (v1_xreal_0(C) -> (r2_hidden(C,B) -> r1_xreal_0(A,C)))) -> k3_seq_4(B) = A))))) # label(t61_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5247 (all A (v2_membered(A) & -v1_xboole_0(A) -> (all B (v1_xreal_0(B) -> ((all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r1_xreal_0(B,C)))) -> r1_xreal_0(B,k3_seq_4(A))))))) # label(t60_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5248 (all A (v1_xreal_0(A) -> -(all B (m2_subset_1(B,k1_numbers,k5_numbers) -> r1_xreal_0(B,A))))) # label(t10_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5249 (all A (v1_funct_1(A) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_2(A,k5_numbers,k1_numbers) -> (v2_seq_2(A) & v4_seqm_3(A) -> v4_seq_2(A)))) # label(t52_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5250 (all A (-v1_xboole_0(A) & v2_membered(A) -> (all B (v2_membered(B) -> (v2_seq_4(B) & r1_tarski(A,B) -> r1_xreal_0(k3_seq_4(B),k3_seq_4(A))))))) # label(t64_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5251 (all A (v1_xreal_0(A) -> k5_seq_4(k1_seq_4(A)) = k4_seq_4(k1_seq_4(A)))) # label(t23_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5252 (all A (v2_membered(A) -> ((exists B ((all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r1_xreal_0(C,B)))) & v1_xreal_0(B))) <-> v1_seq_4(A)))) # label(d1_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5253 $T # label(t12_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5254 (all A (m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_2(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> -((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> -v2_relat_1(k1_seqm_3(A,B)))) & np__0 != k2_seq_2(A) & v4_seq_2(A)))) # label(t37_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5255 $T # label(t1_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5256 (all A (v1_xreal_0(A) -> k5_seq_4(k1_seq_4(A)) = A & k4_seq_4(k1_seq_4(A)) = A)) # label(t22_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5257 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v2_membered(C) -> ((all D (v1_xreal_0(D) -> (r2_hidden(D,C) -> r1_xreal_0(D,B)))) & (all D (v1_xreal_0(D) -> (r2_hidden(D,C) -> r1_xreal_0(D,A)))) & (all D (v1_xreal_0(D) -> -(-r1_xreal_0(D,np__0) & (all E (v1_xreal_0(E) -> -(r2_hidden(E,C) & -r1_xreal_0(E,k6_xcmplx_0(A,D)))))))) & (all D (v1_xreal_0(D) -> -(-r1_xreal_0(D,np__0) & (all E (v1_xreal_0(E) -> -(-r1_xreal_0(E,k6_xcmplx_0(B,D)) & r2_hidden(E,C))))))) -> B = A))))))) # label(t17_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5258 (all A (v2_membered(A) -> (v1_seq_4(A) -> (all B (v1_xreal_0(B) -> (B = k2_seq_4(A) <-> (all C (v1_xreal_0(C) -> -(-r1_xreal_0(C,np__0) & (all D (v1_xreal_0(D) -> -(-r1_xreal_0(D,k6_xcmplx_0(B,C)) & r2_hidden(D,A))))))) & (all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r1_xreal_0(C,B))))))) | v1_xboole_0(A)))) # label(d4_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5259 (all A (v1_funct_1(A) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_2(A,k5_numbers,k1_numbers) -> (exists B (v1_seqm_3(B) & v6_seqm_3(k3_seqm_3(B,A)) & m2_relset_1(B,k5_numbers,k1_numbers) & v7_seqm_3(B) & v1_funct_2(B,k5_numbers,k1_numbers) & v1_funct_1(B))))) # label(t56_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5260 $T # label(t13_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5261 (all A (v1_funct_1(A) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_2(A,k5_numbers,k1_numbers) -> (v2_seq_2(A) & v4_seqm_3(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> r1_xreal_0(k2_seq_2(A),k8_funct_2(k5_numbers,k1_numbers,A,B))))))) # label(t55_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5262 (all A (v1_xreal_0(A) -> (all B (m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_numbers) -> ((exists C (A = k8_funct_2(k5_numbers,k1_numbers,B,C) & m2_subset_1(C,k1_numbers,k5_numbers))) & v5_seqm_3(B) | v5_seqm_3(B) & r2_hidden(A,k2_relat_1(B)) -> A = k2_seq_2(B)))))) # label(t40_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5263 (all A (v1_xreal_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_numbers) & m2_relset_1(B,k5_numbers,k1_numbers) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k8_funct_2(k5_numbers,k1_numbers,B,C) = k7_xcmplx_0(np__1,k2_xcmplx_0(k2_nat_1(C,C),A)))) -> v4_seq_2(B) | r1_xreal_0(A,np__0)))))) # label(t47_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5264 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> (v3_seq_4(A) -> r1_xreal_0(k5_seq_4(A),k4_seq_4(A)) | v1_xboole_0(A)))) # label(t24_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5265 (all A (v2_membered(A) -> (v2_seq_4(A) <-> (exists B ((all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r1_xreal_0(B,C)))) & v1_xreal_0(B)))))) # label(d2_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5266 (all A (v1_xreal_0(A) -> (all B (m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_2(B,k5_numbers,k1_numbers) & v1_funct_1(B) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k7_xcmplx_0(np__1,k2_xcmplx_0(k2_nat_1(C,C),A)) = k8_funct_2(k5_numbers,k1_numbers,B,C))) -> k2_seq_2(B) = np__0 | r1_xreal_0(A,np__0)))))) # label(t48_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5267 $T # label(t21_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5268 (all A (v1_funct_2(A,k5_numbers,k1_numbers) & v1_funct_1(A) & m2_relset_1(A,k5_numbers,k1_numbers) -> (v4_seq_2(A) -> v4_seq_2(k22_seq_1(A))))) # label(t26_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5269 $T # label(t7_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5270 (all A (v1_funct_1(A) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_2(A,k5_numbers,k1_numbers) -> (all B (m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_numbers) -> (v4_seq_2(A) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> A != k1_seqm_3(B,C))) | v4_seq_2(B)))))) # label(t35_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5271 (all A (v1_xreal_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_numbers)) -> ((all C (v1_xreal_0(C) -> (r2_hidden(C,B) -> r2_hidden(k2_xcmplx_0(C,A),B)))) -> r1_xreal_0(A,np__0) | (all C (v1_xreal_0(C) -> (exists D (v1_xreal_0(D) & -r1_xreal_0(D,C) & r2_hidden(D,B))))) | (all C (v1_xreal_0(C) -> -r2_hidden(C,B)))))))) # label(t9_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5272 (all A (v1_xreal_0(A) -> (all B (v1_funct_2(B,k5_numbers,k1_numbers) & v1_funct_1(B) & m2_relset_1(B,k5_numbers,k1_numbers) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k7_xcmplx_0(np__1,k2_xcmplx_0(C,A)) = k8_funct_2(k5_numbers,k1_numbers,B,C))) -> r1_xreal_0(A,np__0) | np__0 = k2_seq_2(B)))))) # label(t44_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5273 (all A (m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) -> (all B (m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_2(B,k5_numbers,k1_numbers) & v1_funct_1(B) -> (v4_seq_2(A) -> k2_seq_2(A) = k2_seq_2(B) | (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k1_seqm_3(B,C) != A))))))) # label(t36_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5274 (all A (v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> (v1_seq_2(A) & v3_seqm_3(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> r1_xreal_0(k8_funct_2(k5_numbers,k1_numbers,A,B),k2_seq_2(A))))))) # label(t54_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5275 (all A (-v1_xboole_0(A) & v2_membered(A) -> (all B (v2_membered(B) -> (r1_tarski(A,B) & v1_seq_4(B) -> r1_xreal_0(k2_seq_4(A),k2_seq_4(B))))))) # label(t65_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5276 (all A (m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) -> (v5_seqm_3(A) -> v4_seq_2(A)))) # label(t39_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5277 (all A (v1_xreal_0(A) -> m1_subset_1(k1_seq_4(A),k1_zfmisc_1(k1_numbers)))) # label(dt_k1_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5278 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> (v2_seq_4(A) & v1_seq_4(A) <-> v3_seq_4(A)))) # label(d3_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5279 (all A (v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) -> (all B (v1_funct_2(B,k5_numbers,k1_numbers) & v1_funct_1(B) & m2_relset_1(B,k5_numbers,k1_numbers) -> (m1_seqm_3(A,B) & v4_seq_2(B) -> v4_seq_2(A)))))) # label(t29_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5280 (all A (m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) -> (all B (m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_numbers) -> (v4_seq_2(A) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (exists D (m2_subset_1(D,k1_numbers,k5_numbers) & r1_xreal_0(C,D) & k8_funct_2(k5_numbers,k1_numbers,A,D) != k8_funct_2(k5_numbers,k1_numbers,B,D))))) | k2_seq_2(A) = k2_seq_2(B)))))) # label(t32_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5281 $T # label(t4_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5282 (all A (m1_relset_1(A,k5_numbers,k1_numbers) -> (v5_seqm_3(A) & v1_funct_2(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> v1_seq_1(A) & v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & v4_seq_2(A)))) # label(cc1_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5283 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v2_membered(C) -> ((all D (v1_xreal_0(D) -> -(-r1_xreal_0(D,np__0) & (all E (v1_xreal_0(E) -> -(-r1_xreal_0(k2_xcmplx_0(B,D),E) & r2_hidden(E,C))))))) & (all D (v1_xreal_0(D) -> (r2_hidden(D,C) -> r1_xreal_0(B,D)))) & (all D (v1_xreal_0(D) -> -((all E (v1_xreal_0(E) -> -(r2_hidden(E,C) & -r1_xreal_0(k2_xcmplx_0(A,D),E)))) & -r1_xreal_0(D,np__0)))) & (all D (v1_xreal_0(D) -> (r2_hidden(D,C) -> r1_xreal_0(A,D)))) -> A = B))))))) # label(t19_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5284 $T # label(t11_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5285 $T # label(t6_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5286 (all A (v2_membered(A) -> -((all B (v1_xreal_0(B) -> -((all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r1_xreal_0(C,B)))) & (all C (v1_xreal_0(C) -> -((all D (v1_xreal_0(D) -> -(-r1_xreal_0(D,k6_xcmplx_0(B,C)) & r2_hidden(D,A)))) & -r1_xreal_0(C,np__0))))))) & -v1_xboole_0(A) & v1_seq_4(A)))) # label(t16_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5287 (all A (m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_2(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> -(v4_seq_2(A) & (all B (v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_numbers) & m2_relset_1(B,k5_numbers,k1_numbers) -> -(v2_relat_1(B) & m1_seqm_3(B,A)))) & k2_seq_2(A) != np__0))) # label(t38_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5288 (all A (-v1_xboole_0(A) & v2_membered(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> ((all D (v1_xreal_0(D) -> (r2_hidden(D,A) -> r1_xreal_0(D,C)))) -> r1_xreal_0(k2_seq_4(A),C)))))))) # label(t62_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5289 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> k3_seq_4(A) = k5_seq_4(A))) # label(redefinition_k5_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5290 (all A (v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) -> (v4_seq_2(k22_seq_1(A)) & k2_seq_2(k22_seq_1(A)) = np__0 -> v4_seq_2(A) & k2_seq_2(A) = np__0))) # label(t28_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5291 (all A (v1_funct_2(A,k5_numbers,k1_numbers) & v1_funct_1(A) & m2_relset_1(A,k5_numbers,k1_numbers) -> ((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k8_funct_2(k5_numbers,k1_numbers,A,B) = k6_real_1(np__1,k1_nat_1(B,np__1)))) -> v4_seq_2(A) & np__0 = k2_seq_2(A)))) # label(t45_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5292 (all A (m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) -> -(v3_seq_2(A) & (all B (m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_numbers) -> -(m1_seqm_3(B,A) & v4_seq_2(B))))))) # label(t57_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5293 $T # label(t34_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5294 (all A (v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) -> (v4_seq_2(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_numbers) & m2_relset_1(B,k5_numbers,k1_numbers) -> (v2_relat_1(B) & m1_seqm_3(B,A) -> k2_seq_2(k18_seq_1(B)) = k2_real_1(k2_seq_2(A))))) | k2_seq_2(A) = np__0))) # label(t42_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5295 (all A (v1_funct_2(A,k5_numbers,k1_numbers) & v1_funct_1(A) & m2_relset_1(A,k5_numbers,k1_numbers) -> (all B (v1_funct_2(B,k5_numbers,k1_numbers) & m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_1(B) -> (v4_seq_2(A) -> v4_seq_2(B) | (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (exists D (k8_funct_2(k5_numbers,k1_numbers,A,D) != k8_funct_2(k5_numbers,k1_numbers,B,D) & r1_xreal_0(C,D) & m2_subset_1(D,k1_numbers,k5_numbers)))))))))) # label(t31_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5296 $T # label(t5_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5297 (all A (v1_xreal_0(A) -> v3_seq_4(k1_seq_4(A)))) # label(t15_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5298 $T # label(t3_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5299 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> m1_subset_1(k5_seq_4(A),k1_numbers))) # label(dt_k5_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5300 $T # label(t2_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5301 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> (v3_seq_4(A) -> v1_xboole_0(A) | -(r1_xreal_0(k4_seq_4(A),k5_seq_4(A)) & (exists B ((exists C (r2_hidden(B,A) & r2_hidden(C,A) & v1_xreal_0(C) & B != C)) & v1_xreal_0(B)))) & -((all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(C != B & r2_hidden(C,A) & r2_hidden(B,A)))))) & -r1_xreal_0(k4_seq_4(A),k5_seq_4(A)))))) # label(t25_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5302 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_2(B,k5_numbers,k1_numbers) & v1_funct_1(B) -> (v4_seq_2(B) -> k2_seq_2(k1_seqm_3(B,A)) = k2_seq_2(B) & v4_seq_2(k1_seqm_3(B,A))))))) # label(t33_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5303 $T # label(t20_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5304 (all A (v1_xreal_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_2(B,k5_numbers,k1_numbers) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k8_funct_2(k5_numbers,k1_numbers,B,C) = k7_xcmplx_0(np__1,k2_xcmplx_0(C,A)))) -> v4_seq_2(B) | r1_xreal_0(A,np__0)))))) # label(t43_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5305 (all A (v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_numbers) & m2_relset_1(B,k5_numbers,k1_numbers) -> (v4_seq_2(B) & v5_seqm_3(A) -> k3_real_1(k8_funct_2(k5_numbers,k1_numbers,A,np__0),k2_seq_2(B)) = k2_seq_2(k9_seq_1(A,B)) & k5_real_1(k2_seq_2(B),k8_funct_2(k5_numbers,k1_numbers,A,np__0)) = k2_seq_2(k10_seq_1(B,A)) & k2_seq_2(k11_seq_1(A,B)) = k4_real_1(k8_funct_2(k5_numbers,k1_numbers,A,np__0),k2_seq_2(B)) & k2_seq_2(k10_seq_1(A,B)) = k5_real_1(k8_funct_2(k5_numbers,k1_numbers,A,np__0),k2_seq_2(B))))))) # label(t59_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5306 (all A (v2_membered(A) -> (v2_seq_4(A) -> (all B (v1_xreal_0(B) -> (k3_seq_4(A) = B <-> (all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r1_xreal_0(B,C)))) & (all C (v1_xreal_0(C) -> -(-r1_xreal_0(C,np__0) & (all D (v1_xreal_0(D) -> -(r2_hidden(D,A) & -r1_xreal_0(k2_xcmplx_0(B,C),D)))))))))) | v1_xboole_0(A)))) # label(d5_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5307 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> (v3_seq_4(A) <-> (exists B ((all C (v1_xreal_0(C) -> -(r2_hidden(C,A) & r1_xreal_0(B,k18_complex1(C))))) & -r1_xreal_0(B,np__0) & v1_xreal_0(B)))))) # label(t14_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5308 (all A (v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> ((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k6_real_1(np__1,k1_nat_1(k2_nat_1(B,B),np__1)) = k8_funct_2(k5_numbers,k1_numbers,A,B))) -> v4_seq_2(A) & k2_seq_2(A) = np__0))) # label(t49_seq_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5309 (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_2(F,k4_zfmisc_1(A,B,C,D),E) & v1_funct_1(F) & 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)))))))))) -> F = G))))))))))))))) # label(t7_multop_1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5310 $T # label(t5_multop_1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5311 (all A all B all C all D all E all F all G all H (-v1_xboole_0(B) & m1_subset_1(F,A) & -v1_xboole_0(D) & -v1_xboole_0(C) & -v1_xboole_0(A) & v1_funct_1(E) & m1_subset_1(H,C) & m1_subset_1(G,B) & m1_relset_1(E,k3_zfmisc_1(A,B,C),D) & v1_funct_2(E,k3_zfmisc_1(A,B,C),D) -> 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]. 57.05/56.02 5312 (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,E,k4_domain_1(A,B,C,G,H,I)) = k8_funct_2(k3_zfmisc_1(A,B,C),D,F,k4_domain_1(A,B,C,G,H,I)))))))) -> F = E))))))))))))) # label(t3_multop_1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.02 5313 (exists A ((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_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) & 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]. 57.05/56.03 5314 (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 (v1_funct_1(G) & v1_funct_2(G,k4_zfmisc_1(B,C,D,E),A) & m2_relset_1(G,k4_zfmisc_1(B,C,D,E),A) -> ((all H all I all J all K (r2_hidden(K,E) & r2_hidden(J,D) & r2_hidden(I,C) & r2_hidden(H,B) -> k1_funct_1(G,k4_mcart_1(H,I,J,K)) = k1_funct_1(F,k4_mcart_1(H,I,J,K)))) -> G = F))))))) # label(t6_multop_1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5315 (all A all B all C all D all E all F all G all H (-v1_xboole_0(B) & m1_subset_1(H,C) & m1_subset_1(G,B) & m1_relset_1(E,k3_zfmisc_1(A,B,C),D) & -v1_xboole_0(D) & -v1_xboole_0(A) & -v1_xboole_0(C) & v1_funct_2(E,k3_zfmisc_1(A,B,C),D) & m1_subset_1(F,A) & v1_funct_1(E) -> 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]. 57.05/56.03 5316 (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 (m1_subset_1(E,f1_s6_multop_1) & p1_s6_multop_1(A,B,C,D,E))))))))))) -> (exists A ((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_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) & 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]. 57.05/56.03 5317 (all A all B all C all D all E all F all G all H all I all J (-v1_xboole_0(C) & -v1_xboole_0(E) & m1_relset_1(F,k4_zfmisc_1(A,B,C,D),E) & m1_subset_1(J,D) & m1_subset_1(I,C) & m1_subset_1(H,B) & m1_subset_1(G,A) & -v1_xboole_0(A) & -v1_xboole_0(B) & v1_funct_2(F,k4_zfmisc_1(A,B,C,D),E) & v1_funct_1(F) & -v1_xboole_0(D) -> 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]. 57.05/56.03 5318 (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_2(A,k3_zfmisc_1(f1_s2_multop_1,f1_s2_multop_1,f1_s2_multop_1),f1_s2_multop_1) & m2_relset_1(A,k3_zfmisc_1(f1_s2_multop_1,f1_s2_multop_1,f1_s2_multop_1),f1_s2_multop_1) & (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)))))))) & v1_funct_1(A))) # label(s2_multop_1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5319 $T # label(dt_k3_multop_1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5320 (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 (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) -> k2_multop_1(A,B,C,D,E,G,H,I) = k2_multop_1(A,B,C,D,F,G,H,I))))))) -> F = E))))))))))))) # label(t4_multop_1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5321 $T # label(dt_k1_multop_1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5322 (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_1(E) & v1_funct_2(E,k3_zfmisc_1(B,C,D),A) -> (all F (v1_funct_2(F,k3_zfmisc_1(B,C,D),A) & m2_relset_1(F,k3_zfmisc_1(B,C,D),A) & v1_funct_1(F) -> ((all G all H all I (r2_hidden(I,D) & r2_hidden(G,B) & r2_hidden(H,C) -> k1_funct_1(F,k3_mcart_1(G,H,I)) = k1_funct_1(E,k3_mcart_1(G,H,I)))) -> E = F))))))) # label(t2_multop_1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5323 (exists A (v1_funct_1(A) & (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)))))))))) & 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))) # label(s7_multop_1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5324 (exists A (v1_funct_1(A) & 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) & 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) -> 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) = f2_s8_multop_1(B,C,D,E))))))))))) # label(s8_multop_1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5325 (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]. 57.05/56.03 5326 (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_2(F,k4_zfmisc_1(A,B,C,D),E) & m2_relset_1(F,k4_zfmisc_1(A,B,C,D),E) & v1_funct_1(F) -> (all G (m2_relset_1(G,k4_zfmisc_1(A,B,C,D),E) & v1_funct_1(G) & 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) -> k4_multop_1(A,B,C,D,E,G,H,I,J,K) = k4_multop_1(A,B,C,D,E,F,H,I,J,K))))))))) -> G = F))))))))))))))) # label(t8_multop_1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5327 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C all D all E k1_funct_1(A,k4_mcart_1(B,C,D,E)) = k3_multop_1(A,B,C,D,E)))) # label(d2_multop_1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5328 (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) & v1_funct_2(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) -> k2_multop_1(f1_s4_multop_1,f2_s4_multop_1,f3_s4_multop_1,f4_s4_multop_1,A,B,C,D) = f5_s4_multop_1(B,C,D))))))))) # label(s4_multop_1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5329 (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 (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_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))))))))) & 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]. 57.05/56.03 5330 (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_1(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) & 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) & (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))))))))))))) # label(s5_multop_1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5331 $T # label(t1_multop_1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5332 (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(E) & m1_subset_1(I,C) & m1_subset_1(J,D) & m1_subset_1(H,B) & m1_relset_1(F,k4_zfmisc_1(A,B,C,D),E) & v1_funct_1(F) & -v1_xboole_0(B) & -v1_xboole_0(D) & m1_subset_1(G,A) & v1_funct_2(F,k4_zfmisc_1(A,B,C,D),E) & -v1_xboole_0(C) -> 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]. 57.05/56.03 5333 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (m1_realset1(C,A,B) <-> (all D (r2_hidden(D,k2_zfmisc_1(C,C)) -> r2_hidden(k1_funct_1(B,D),C)))))))) # label(d2_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5334 (all A all B (m1_subset_1(B,A) -> (exists C ((all D (r2_hidden(D,k2_zfmisc_1(k4_xboole_0(A,k1_tarski(B)),k4_xboole_0(A,k1_tarski(B)))) -> r2_hidden(k1_funct_1(C,D),k4_xboole_0(A,k1_tarski(B))))) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A))))) # label(t10_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5335 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m2_realset1(C,A,B) -> v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A))))) # label(dt_m2_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5336 $T # label(dt_m4_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5337 (all A all B (m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_realset1(C,A,B) -> m1_subset_1(C,k1_zfmisc_1(A)))))) # label(dt_m1_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5338 (all A (-v1_realset1(A) -> (exists B (-v1_xboole_0(B) & m4_realset1(B,A))))) # label(rc3_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5339 $T # label(dt_k1_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5340 (all A all B (m1_subset_1(B,A) & -v1_realset1(A) -> k1_tarski(B) = k5_realset1(A,B))) # label(redefinition_k5_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5341 (all A (-v1_realset1(A) -> (exists B m4_realset1(B,A)))) # label(existence_m4_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5342 (all A (-v1_realset1(A) -> (all B (m4_realset1(B,A) -> -v1_xboole_0(k4_xboole_0(A,B)))))) # label(t12_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5343 (exists A (-v1_xboole_0(A) & v1_realset1(A))) # label(rc1_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5344 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> ((all D (r2_hidden(D,k2_zfmisc_1(B,B)) -> r2_hidden(k1_funct_1(C,D),B))) <-> m2_realset1(C,A,B)))))) # label(d6_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5345 (all A all B (m1_subset_1(B,A) -> (all C (m3_realset1(C,A,B) -> v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C))))) # label(dt_m3_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5346 (all A all B (v1_relat_1(A) -> v1_relat_1(k1_realset1(A,B)))) # label(fc1_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5347 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (exists C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & (all D (r2_hidden(D,k2_zfmisc_1(B,B)) -> r2_hidden(k1_funct_1(C,D),B))))))) # label(t8_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5348 (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) -> (exists C m1_realset1(C,A,B)))) # label(existence_m1_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5349 (all A (-v1_xboole_0(A) -> ((all B -v1_xboole_0(k4_xboole_0(A,k1_tarski(B)))) <-> -v1_realset1(A)))) # label(t4_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5350 (exists A (-v1_xboole_0(A) & -v1_realset1(A))) # label(rc2_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5351 (all A (-v1_realset1(A) -> -v1_xboole_0(A))) # label(cc1_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5352 (all A (-v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) & v1_realset1(k1_tarski(A)))) # label(fc3_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5353 (all A (-v1_realset1(A) -> (all B (m1_subset_1(B,A) -> (all C (m3_realset1(C,A,B) -> k4_realset1(A,B,C) = k1_realset1(C,k4_xboole_0(A,k1_tarski(B))))))))) # label(d9_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5354 (all A (-v1_xboole_0(A) -> -(v1_realset1(A) & (all B (m1_subset_1(B,A) -> -v1_xboole_0(k4_xboole_0(A,k1_tarski(B)))))))) # label(t6_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5355 (all A (-v1_realset1(A) -> (all B ((exists C (m1_subset_1(C,A) & B = k1_tarski(C))) <-> m4_realset1(B,A))))) # label(d10_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5356 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> -(v1_realset1(B) & (exists C ((exists D (D != C & r2_hidden(D,B) & r2_hidden(C,B) & m1_subset_1(D,A))) & m1_subset_1(C,A)))) & -((all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> -(C != D & r2_hidden(D,B) & r2_hidden(C,B)))))) & -v1_realset1(B)))) # label(t15_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5357 (all A (v1_finset_1(A) -> (-r1_xreal_0(np__2,k4_card_1(A)) <-> v1_realset1(A)))) # label(t13_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5358 (all A all B (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k1_realset1(A,B)) & v1_funct_1(k1_realset1(A,B)))) # label(fc2_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5359 (all A (v1_relat_1(A) -> (all B k7_relat_1(A,k2_zfmisc_1(B,B)) = k1_realset1(A,B)))) # label(d3_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5360 (all A all B (m1_subset_1(B,A) -> (exists C m3_realset1(C,A,B)))) # label(existence_m3_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5361 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (exists C (m1_subset_1(C,k1_zfmisc_1(A)) & (all D (r2_hidden(D,k2_zfmisc_1(C,C)) -> r2_hidden(k1_funct_1(B,D),C))))))) # label(t2_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5362 (all A (-(-v1_xboole_0(A) & (all B k1_tarski(B) != A)) <-> v1_realset1(A))) # label(d4_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5363 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m1_realset1(C,A,B) -> v1_funct_1(k1_realset1(B,C)) & v1_funct_2(k1_realset1(B,C),k2_zfmisc_1(C,C),C) & m2_relset_1(k1_realset1(B,C),k2_zfmisc_1(C,C),C))))) # label(t3_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5364 (all A all B (m1_subset_1(B,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (m3_realset1(C,A,B) <-> (all D (r2_hidden(D,k2_zfmisc_1(k4_xboole_0(A,k1_tarski(B)),k4_xboole_0(A,k1_tarski(B)))) -> r2_hidden(k1_funct_1(C,D),k4_xboole_0(A,k1_tarski(B)))))))))) # label(d8_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5365 (exists A ((all B (m1_subset_1(B,A) -> -v1_xboole_0(k4_xboole_0(A,k1_tarski(B))))) & -v1_xboole_0(A))) # label(t5_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5366 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m2_realset1(C,A,B) -> k3_realset1(A,B,C) = k1_realset1(C,B))))) # label(d7_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5367 (all A all B all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (r2_hidden(B,k2_zfmisc_1(A,A)) -> r2_hidden(k1_funct_1(C,B),A)))) # label(t1_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5368 (all A all B (m4_realset1(B,A) & -v1_realset1(A) -> -v1_xboole_0(k4_xboole_0(A,B)))) # label(fc4_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5369 (all A (-v1_realset1(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> (r2_realset1(A,B,C) <-> v1_funct_1(k4_xboole_0(k1_realset1(B,A),k1_tarski(C))) & m1_realset1(k4_xboole_0(A,k1_tarski(C)),A,B) & m2_relset_1(k4_xboole_0(k1_realset1(B,A),k1_tarski(C)),k2_zfmisc_1(k4_xboole_0(A,k1_tarski(C)),k4_xboole_0(A,k1_tarski(C))),k4_xboole_0(A,k1_tarski(C))) & v1_funct_2(k4_xboole_0(k1_realset1(B,A),k1_tarski(C)),k2_zfmisc_1(k4_xboole_0(A,k1_tarski(C)),k4_xboole_0(A,k1_tarski(C))),k4_xboole_0(A,k1_tarski(C)))))))))) # label(d5_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5370 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> -v1_xboole_0(k4_xboole_0(A,k1_tarski(B))))) -> -v1_realset1(A)))) # label(t7_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5371 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m2_realset1(C,A,B) -> m2_relset_1(k1_realset1(C,B),k2_zfmisc_1(B,B),B) & v1_funct_1(k1_realset1(C,B)) & v1_funct_2(k1_realset1(C,B),k2_zfmisc_1(B,B),B))))) # label(t9_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5372 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m2_realset1(C,A,B) -> m2_relset_1(k3_realset1(A,B,C),k2_zfmisc_1(B,B),B) & v1_funct_2(k3_realset1(A,B,C),k2_zfmisc_1(B,B),B) & v1_funct_1(k3_realset1(A,B,C)))) # label(dt_k3_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5373 (all A (-v1_realset1(A) -> (all B (m1_subset_1(B,A) -> (all C (m3_realset1(C,A,B) -> m2_relset_1(k1_realset1(C,k4_xboole_0(A,k1_tarski(B))),k2_zfmisc_1(k4_xboole_0(A,k1_tarski(B)),k4_xboole_0(A,k1_tarski(B))),k4_xboole_0(A,k1_tarski(B))) & v1_funct_2(k1_realset1(C,k4_xboole_0(A,k1_tarski(B))),k2_zfmisc_1(k4_xboole_0(A,k1_tarski(B)),k4_xboole_0(A,k1_tarski(B))),k4_xboole_0(A,k1_tarski(B))) & v1_funct_1(k1_realset1(C,k4_xboole_0(A,k1_tarski(B)))))))))) # label(t11_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5374 (all A all B (m1_subset_1(B,A) & -v1_realset1(A) -> m4_realset1(k5_realset1(A,B),A))) # label(dt_k5_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5375 (all A (-((all B all C -(r2_hidden(B,A) & B != C & r2_hidden(C,A))) & -v1_realset1(A)) & -(v1_realset1(A) & (exists B exists C (r2_hidden(B,A) & r2_hidden(C,A) & C != B))))) # label(t14_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5376 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (exists C m2_realset1(C,A,B)))) # label(existence_m2_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5377 (all A all B all C (v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & m1_realset1(C,A,B) -> v1_funct_1(k2_realset1(A,B,C)) & v1_funct_2(k2_realset1(A,B,C),k2_zfmisc_1(C,C),C) & m2_relset_1(k2_realset1(A,B,C),k2_zfmisc_1(C,C),C))) # label(dt_k2_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5378 (all A all B all C (m3_realset1(C,A,B) & m1_subset_1(B,A) & -v1_realset1(A) -> v1_funct_1(k4_realset1(A,B,C)) & v1_funct_2(k4_realset1(A,B,C),k2_zfmisc_1(k4_xboole_0(A,k1_tarski(B)),k4_xboole_0(A,k1_tarski(B))),k4_xboole_0(A,k1_tarski(B))) & m2_relset_1(k4_realset1(A,B,C),k2_zfmisc_1(k4_xboole_0(A,k1_tarski(B)),k4_xboole_0(A,k1_tarski(B))),k4_xboole_0(A,k1_tarski(B))))) # label(dt_k4_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5379 (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,k1_zfmisc_1(A)) -> ((all D (r2_hidden(D,k2_zfmisc_1(C,C)) -> r2_hidden(k1_funct_1(B,D),C))) <-> r1_realset1(A,B,C)))))) # label(d1_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5380 (all A all B all C (v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & m1_realset1(C,A,B) & m1_relset_1(B,k2_zfmisc_1(A,A),A) -> k2_realset1(A,B,C) = k1_realset1(B,C))) # label(redefinition_k2_realset1) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5381 (all A all B (k2_xboole_0(A,B) = k3_card_3(k10_finseq_1(A,B)) & k4_funct_6(k10_finseq_1(A,B)) = k3_xboole_0(A,B))) # label(t40_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5382 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(A,k1_relat_1(B)) -> k5_funct_6(k10_finseq_1(C,B),np__2,A) = k1_funct_1(B,A) & k1_funct_1(B,A) = k5_funct_6(k11_finseq_1(C,B,D),np__2,A)))))))) # label(t46_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5383 (all A all B all C all D all E all F (v1_relat_1(F) & v1_funct_1(F) -> (r1_tarski(k1_relat_1(F),k2_zfmisc_1(D,E)) -> -r2_hidden(k5_funct_5(F),k4_partfun1(B,k4_partfun1(A,C))) & -r2_hidden(k3_funct_5(F),k4_partfun1(A,k4_partfun1(B,C))) | r2_hidden(F,k4_partfun1(k2_zfmisc_1(A,B),C))))) # label(t25_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5384 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(D,k1_funct_2(A,k1_funct_2(B,C))) -> A = k1_xboole_0 | k10_funct_6(k10_funct_6(D)) = D | k1_xboole_0 = B))) # label(t87_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5385 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (C = k1_funct_1(B,A) & r2_hidden(A,k1_relat_1(B)) -> r2_hidden(A,k1_relat_1(k2_funct_6(B))) & k1_relat_1(C) = k1_funct_1(k2_funct_6(B),A) & r2_hidden(A,k1_relat_1(k3_funct_6(B))) & k2_relat_1(C) = k1_funct_1(k3_funct_6(B),A)))))) # label(t31_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5386 (all A (v1_relat_1(A) & v1_funct_1(A) -> k9_funct_6(k1_xboole_0,A) = k2_funcop_1(k1_relat_1(A),k1_tarski(k1_xboole_0)))) # label(t78_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5387 (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) = k1_relat_1(B) & (all D (r2_hidden(D,k1_relat_1(B)) -> k1_funct_2(A,k1_funct_1(B,D)) = k1_funct_1(C,D))) <-> C = k9_funct_6(A,B)))))) # label(d9_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5388 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(D,k1_funct_2(k2_zfmisc_1(A,B),C)) -> r2_hidden(k5_funct_5(D),k1_funct_2(B,k1_funct_2(A,C))) & r2_hidden(k3_funct_5(D),k1_funct_2(A,k1_funct_2(B,C))) | k1_xboole_0 = k2_zfmisc_1(A,B)))) # label(t19_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5389 $T # label(d11_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5390 (all A all B all C k9_funct_6(A,k2_funcop_1(B,C)) = k2_funcop_1(B,k1_funct_2(A,C))) # label(t82_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5391 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> a_3_0_funct_6(A,B,C) = k4_card_3(k11_finseq_1(A,B,C)))))))) # label(t7_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5392 (all A all B (B = k1_funct_6(A) <-> (all C (r2_hidden(C,B) <-> r2_hidden(C,A) & v1_funct_1(C) & v1_relat_1(C))))) # label(d1_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5393 (all A all B k9_finseq_1(k1_funct_2(A,B)) = k9_funct_6(A,k9_finseq_1(B))) # label(t80_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.03 5394 (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(B,k1_relat_1(D)) & r2_hidden(A,k1_relat_1(C)) -> (all E all F (k10_finseq_1(E,F) = k1_funct_1(k7_funct_6(k10_finseq_1(C,D)),k10_finseq_1(A,B)) <-> k4_tarski(E,F) = k1_funct_1(k15_funct_3(C,D),k4_tarski(A,B))))))))) # label(t68_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5395 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (B = k2_funct_6(A) <-> k1_relat_1(B) = k10_relat_1(A,k1_funct_6(k2_relat_1(A))) & (all C (r2_hidden(C,k10_relat_1(A,k1_funct_6(k2_relat_1(A)))) -> k1_funct_1(B,C) = k1_funct_5(k1_funct_1(A,C))))))))) # label(d2_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5396 (all A all B all C (k4_funct_5(k2_funcop_1(A,k2_funcop_1(B,C))) = k2_funcop_1(k2_zfmisc_1(A,B),C) & k6_funct_5(k2_funcop_1(A,k2_funcop_1(B,C))) = k2_funcop_1(k2_zfmisc_1(B,A),C))) # label(t15_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5397 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k6_funct_6(A)) & v1_relat_1(k6_funct_6(A)))) # label(dt_k6_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5398 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (r2_hidden(C,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k10_finseq_1(k1_funct_1(A,C),k1_funct_1(B,C)) = k1_funct_1(k6_funct_6(k10_finseq_1(A,B)),C))) & k1_relat_1(k6_funct_6(k10_finseq_1(A,B))) = k3_xboole_0(k1_relat_1(A),k1_relat_1(B)))))) # label(t62_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5399 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (C = k1_funct_1(k6_funct_6(B),A) & r2_hidden(A,k1_relat_1(k6_funct_6(B))) -> (all D (r2_hidden(D,k1_relat_1(C)) -> k1_funct_1(k4_funct_5(B),k4_tarski(D,A)) = k1_funct_1(C,D) & r2_hidden(k4_tarski(D,A),k1_relat_1(k4_funct_5(B))))) & k1_relat_1(C) = k10_relat_1(B,k1_funct_6(k2_relat_1(B)))))))) # label(t51_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5400 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> k1_funct_2(A,k2_relat_1(B)) = k2_relat_1(k7_funct_6(k2_funcop_1(A,B))) & (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(C,k1_funct_2(A,k1_relat_1(B))) -> k1_funct_1(k7_funct_6(k2_funcop_1(A,B)),C) = k5_relat_1(C,B)))) & k1_relat_1(k7_funct_6(k2_funcop_1(A,B))) = k1_funct_2(A,k1_relat_1(B)))) # label(t66_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5401 (all A (-v1_xboole_0(A) -> k4_card_3(k10_finseq_1(A,A)) = k4_finseq_2(np__2,A))) # label(t6_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5402 (all A all B all C all D (r2_hidden(A,k4_card_3(k11_finseq_1(B,C,D))) <-> (exists E exists F exists G (r2_hidden(E,B) & r2_hidden(F,C) & r2_hidden(G,D) & k11_finseq_1(E,F,G) = A)))) # label(t3_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5403 (all A all B all C all D all E all F (v1_funct_1(F) & v1_relat_1(F) -> (r1_tarski(k2_relat_1(F),k4_partfun1(D,E)) & r1_tarski(k1_relat_1(F),A) -> -r2_hidden(k4_funct_5(F),k4_partfun1(k2_zfmisc_1(A,B),C)) & -r2_hidden(k6_funct_5(F),k4_partfun1(k2_zfmisc_1(B,A),C)) | r2_hidden(F,k4_partfun1(A,k4_partfun1(B,C)))))) # label(t26_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5404 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (B = k7_funct_6(A) <-> k4_card_3(k2_funct_6(A)) = k1_relat_1(B) & (all C (v1_funct_1(C) & v1_relat_1(C) -> -((all D (v1_relat_1(D) & v1_funct_1(D) -> -((all E (r2_hidden(E,k1_relat_1(D)) -> k1_funct_1(k4_funct_5(A),k4_tarski(E,k1_funct_1(C,E))) = k1_funct_1(D,E))) & D = k1_funct_1(B,C) & k10_relat_1(A,k1_funct_6(k2_relat_1(A))) = k1_relat_1(D)))) & r2_hidden(C,k4_card_3(k2_funct_6(A))))))))))) # label(d7_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5405 $T # label(d10_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5406 (all A k1_xboole_0 = k8_funct_6(k1_xboole_0,A)) # label(t73_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5407 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(D,k1_funct_2(A,k1_funct_2(B,C))) -> (all E (v1_funct_1(E) & v1_relat_1(E) -> (all F (v1_funct_1(F) & v1_relat_1(F) -> (all G all H (r2_hidden(G,A) & r2_hidden(H,B) & k1_funct_1(k10_funct_6(D),H) = F & E = k1_funct_1(D,G) -> k1_relat_1(E) = B & r1_tarski(k2_relat_1(F),C) & k1_relat_1(F) = A & k1_funct_1(F,G) = k1_funct_1(E,H) & r1_tarski(k2_relat_1(E),C))))))) | k1_xboole_0 = A | B = k1_xboole_0))) # label(t86_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5408 (all A all B k8_funct_6(k9_finseq_1(A),B) = k9_finseq_1(k1_funct_2(A,B))) # label(t74_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5409 (all A all B all C (k3_card_3(k11_finseq_1(A,B,C)) = k2_xboole_0(k2_xboole_0(A,B),C) & k4_funct_6(k11_finseq_1(A,B,C)) = k3_xboole_0(k3_xboole_0(A,B),C))) # label(t41_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5410 (all A (v1_funct_1(A) & v1_relat_1(A) -> (-r2_hidden(k1_xboole_0,k2_relat_1(A)) -> k2_funcop_1(k1_relat_1(A),k1_xboole_0) = k8_funct_6(A,k1_xboole_0)))) # label(t72_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5411 (all A all B (v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k8_funct_6(A,B)) & v1_funct_1(k8_funct_6(A,B)))) # label(dt_k8_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5412 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(C) = k1_relat_1(A) & (all D (r2_hidden(D,k1_relat_1(A)) -> k1_funct_1(C,D) = k1_funct_2(k1_funct_1(A,D),B))) <-> C = k8_funct_6(A,B)))))) # label(d8_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5413 (all A (A = k4_funct_6(k9_finseq_1(A)) & A = k3_card_3(k9_finseq_1(A)))) # label(t39_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5414 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> k2_zfmisc_1(A,k1_relat_1(B)) = k1_relat_1(k4_funct_5(k2_funcop_1(A,B))) & r1_tarski(k2_relat_1(k6_funct_5(k2_funcop_1(A,B))),k2_relat_1(B)) & r1_tarski(k2_relat_1(k4_funct_5(k2_funcop_1(A,B))),k2_relat_1(B)) & k1_relat_1(k6_funct_5(k2_funcop_1(A,B))) = k2_zfmisc_1(k1_relat_1(B),A))) # label(t17_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5415 (all A all B all C all D all E all F (v1_funct_1(F) & v1_relat_1(F) -> (r1_tarski(k1_relat_1(F),k2_zfmisc_1(D,E)) -> -r2_hidden(k5_funct_5(F),k1_funct_2(B,k1_funct_2(A,C))) & -r2_hidden(k3_funct_5(F),k1_funct_2(A,k1_funct_2(B,C))) | r2_hidden(F,k1_funct_2(k2_zfmisc_1(A,B),C))))) # label(t21_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5416 (all A (v1_relat_1(A) & v1_funct_1(A) -> k3_funct_6(k9_finseq_1(A)) = k9_finseq_1(k2_relat_1(A)) & k2_funct_6(k9_finseq_1(A)) = k9_finseq_1(k1_relat_1(A)))) # label(t33_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5417 (all A (k3_card_3(k2_funcop_1(k1_xboole_0,A)) = k1_xboole_0 & k4_funct_6(k2_funcop_1(k1_xboole_0,A)) = k1_xboole_0)) # label(t42_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5418 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> k1_relat_1(k7_funct_6(k10_finseq_1(A,B))) = k4_card_3(k10_finseq_1(k1_relat_1(A),k1_relat_1(B))) & k4_card_3(k10_finseq_1(k2_relat_1(A),k2_relat_1(B))) = k2_relat_1(k7_funct_6(k10_finseq_1(A,B))) & (all C all D (r2_hidden(D,k1_relat_1(B)) & r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(k7_funct_6(k10_finseq_1(A,B)),k10_finseq_1(C,D)) = k10_finseq_1(k1_funct_1(A,C),k1_funct_1(B,D)))))))) # label(t65_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5419 (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) -> k11_finseq_1(k2_relat_1(A),k2_relat_1(B),k2_relat_1(C)) = k3_funct_6(k11_finseq_1(A,B,C)) & k11_finseq_1(k1_relat_1(A),k1_relat_1(B),k1_relat_1(C)) = k2_funct_6(k11_finseq_1(A,B,C)))))))) # label(t35_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5420 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(B)) & v1_relat_1(k1_funct_1(B,A)) & v1_funct_1(k1_funct_1(B,A)) <-> r2_hidden(A,k10_relat_1(B,k1_funct_6(k2_relat_1(B))))))) # label(t28_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5421 (all A all B all C (r2_hidden(A,k4_card_3(k10_finseq_1(B,C))) <-> (exists D exists E (r2_hidden(E,C) & r2_hidden(D,B) & A = k10_finseq_1(D,E))))) # label(t2_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5422 (all A all B (k1_xboole_0 != A -> k4_funct_6(k2_funcop_1(A,B)) = B & B = k3_card_3(k2_funcop_1(A,B)))) # label(t43_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5423 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(D,k4_partfun1(A,k4_partfun1(B,C))) -> r2_hidden(k4_funct_5(D),k4_partfun1(k2_zfmisc_1(A,B),C)) & r2_hidden(k6_funct_5(D),k4_partfun1(k2_zfmisc_1(B,A),C))))) # label(t24_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5424 (all A (-v1_xboole_0(A) -> k4_card_3(k9_finseq_1(A)) = k4_finseq_2(np__1,A))) # label(t4_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5425 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> k4_card_3(k2_finseq_2(A,B)) = k4_finseq_2(A,B))))) # label(t9_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5426 (all A (v1_funct_1(A) & v1_relat_1(A) -> r1_tarski(k2_relat_1(k6_funct_6(A)),k4_card_3(k3_funct_6(A))) & k4_funct_6(k2_funct_6(A)) = k1_relat_1(k6_funct_6(A)))) # label(t49_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5427 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funcop_1(k10_funct_6(A)) & v1_funct_1(k10_funct_6(A)) & v1_relat_1(k10_funct_6(A)))) # label(dt_k10_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5428 (all A (v1_funct_1(A) & v1_relat_1(A) -> k1_relat_1(A) = k1_relat_1(k6_funct_6(k9_finseq_1(A))) & (all B (r2_hidden(B,k1_relat_1(A)) -> k9_finseq_1(k1_funct_1(A,B)) = k1_funct_1(k6_funct_6(k9_finseq_1(A)),B))))) # label(t61_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5429 (all A all B (r2_hidden(A,k4_card_3(k9_finseq_1(B))) <-> (exists C (k9_finseq_1(C) = A & r2_hidden(C,B))))) # label(t1_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5430 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k3_funct_6(A)) & v1_relat_1(k3_funct_6(A)))) # label(dt_k3_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5431 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k1_relat_1(k6_funct_6(C))) & v1_relat_1(k1_funct_1(C,A)) & v1_funct_1(k1_funct_1(C,A)) & r2_hidden(A,k1_relat_1(C)) -> k5_funct_6(C,A,B) = k5_funct_6(k6_funct_6(C),B,A)))) # label(t55_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5432 (all A (v1_relat_1(A) & v1_funct_1(A) -> k3_funct_5(k7_relat_1(k6_funct_5(A),k2_zfmisc_1(k4_funct_6(k2_funct_6(A)),k1_relat_1(A)))) = k6_funct_6(A))) # label(d6_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5433 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (A != k1_xboole_0 -> k2_relat_1(B) = k2_relat_1(k6_funct_5(k2_funcop_1(A,B))) & k2_relat_1(B) = k2_relat_1(k4_funct_5(k2_funcop_1(A,B)))))) # label(t18_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5434 $T # label(dt_k5_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5435 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r2_wellord2(k4_card_3(k9_funct_6(A,B)),k1_funct_2(A,k4_card_3(B))))) # label(t83_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5436 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (C = k1_funct_1(B,A) & r2_hidden(A,k1_relat_1(B)) -> r1_tarski(k2_relat_1(C),k2_relat_1(k6_funct_5(B))) & r1_tarski(k2_relat_1(C),k2_relat_1(k4_funct_5(B)))))))) # label(t16_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5437 (all A (v1_relat_1(A) & v1_funct_1(A) -> r1_tarski(k4_card_3(A),k1_funct_2(k1_relat_1(A),k3_card_3(A))))) # label(t10_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5438 (all A all B all C all D all E all F (v1_relat_1(F) & v1_funct_1(F) -> (r1_tarski(k2_relat_1(F),k4_partfun1(D,E)) & A = k1_relat_1(F) -> -r2_hidden(k6_funct_5(F),k1_funct_2(k2_zfmisc_1(B,A),C)) & -r2_hidden(k4_funct_5(F),k1_funct_2(k2_zfmisc_1(A,B),C)) | r2_hidden(F,k1_funct_2(A,k1_funct_2(B,C)))))) # label(t22_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5439 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> k4_card_3(k10_finseq_1(A,B)) = a_2_0_funct_6(A,B))))) # label(t5_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5440 (all A (v1_funcop_1(A) & v1_funct_1(A) & v1_relat_1(A) -> k1_relat_1(A) = k1_relat_1(k3_funct_6(A)))) # label(t90_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5441 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,A) & v3_funct_2(C,A,A) & m2_relset_1(C,A,A) -> (k1_relat_1(B) = A -> r2_wellord2(k4_card_3(B),k4_card_3(k5_relat_1(C,B)))))))) # label(t71_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5442 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (r2_hidden(B,k1_relat_1(A)) -> k1_funct_1(k7_funct_6(k9_finseq_1(A)),k9_finseq_1(B)) = k9_finseq_1(k1_funct_1(A,B)))) & k4_card_3(k9_finseq_1(k1_relat_1(A))) = k1_relat_1(k7_funct_6(k9_finseq_1(A))) & k4_card_3(k9_finseq_1(k2_relat_1(A))) = k2_relat_1(k7_funct_6(k9_finseq_1(A))))) # label(t64_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5443 (all A all B all C (-v1_xboole_0(C) & -v1_xboole_0(B) -> (r2_hidden(A,a_2_0_funct_6(B,C)) <-> (exists D exists E (m1_subset_1(E,C) & m1_subset_1(D,B) & A = k10_finseq_1(D,E)))))) # label(fraenkel_a_2_0_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5444 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> k2_funct_6(k10_finseq_1(A,B)) = k10_finseq_1(k1_relat_1(A),k1_relat_1(B)) & k10_finseq_1(k2_relat_1(A),k2_relat_1(B)) = k3_funct_6(k10_finseq_1(A,B)))))) # label(t34_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5445 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (all E (v1_funct_1(E) & v1_relat_1(E) -> (D = k1_funct_1(C,A) & r2_hidden(B,k1_relat_1(k6_funct_6(C))) & r2_hidden(A,k1_relat_1(C)) & E = k1_funct_1(k6_funct_6(C),B) -> k1_funct_1(D,B) = k1_funct_1(E,A)))))))) # label(t54_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5446 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (A != k1_xboole_0 -> k1_relat_1(k6_funct_6(k2_funcop_1(A,B))) = k1_relat_1(B) & (all C (r2_hidden(C,k1_relat_1(B)) -> k2_funcop_1(A,k1_funct_1(B,C)) = k1_funct_1(k6_funct_6(k2_funcop_1(A,B)),C)))))) # label(t63_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5447 $T # label(dt_k4_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5448 (all A all B all C all D (-v1_xboole_0(C) & -v1_xboole_0(B) & -v1_xboole_0(D) -> (r2_hidden(A,a_3_0_funct_6(B,C,D)) <-> (exists E exists F exists G (m1_subset_1(G,D) & m1_subset_1(E,B) & A = k11_finseq_1(E,F,G) & m1_subset_1(F,C)))))) # label(fraenkel_a_3_0_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5449 (all A all B all C k9_funct_6(A,k10_finseq_1(B,C)) = k10_finseq_1(k1_funct_2(A,B),k1_funct_2(A,C))) # label(t81_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5450 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(k6_funct_6(B))) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(C,k2_relat_1(B)) -> r2_hidden(A,k1_relat_1(C)))))))) # label(t52_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5451 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(D,k1_funct_2(A,k1_funct_2(B,C))) -> r2_hidden(k4_funct_5(D),k1_funct_2(k2_zfmisc_1(A,B),C)) & r2_hidden(k6_funct_5(D),k1_funct_2(k2_zfmisc_1(B,A),C))))) # label(t20_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5452 (all A all B all C k2_funcop_1(A,k1_funct_2(B,C)) = k8_funct_6(k2_funcop_1(A,B),C)) # label(t76_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5453 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> ((all D (r2_hidden(D,A) -> r2_wellord2(k1_funct_1(B,D),k1_funct_1(C,D)))) & A = k1_relat_1(C) & A = k1_relat_1(B) -> r2_wellord2(k4_card_3(B),k4_card_3(C))))))) # label(t69_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5454 (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(B,k1_relat_1(D)) & D = k1_funct_1(C,A) & r2_hidden(A,k1_relat_1(C)) -> k1_funct_1(D,B) = k5_funct_6(C,A,B)))))) # label(t44_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5455 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C k5_funct_6(A,B,C) = k1_funct_1(k4_funct_5(A),k4_tarski(B,C))))) # label(d5_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5456 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(B)) & r2_hidden(A,k1_relat_1(C)) -> (all D all E (k4_tarski(D,E) = k1_funct_1(k13_funct_3(B,C),A) <-> k10_finseq_1(D,E) = k1_funct_1(k6_funct_6(k10_finseq_1(B,C)),A)))))))) # label(t67_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5457 (all A (v1_relat_1(A) & v1_funct_1(A) -> k4_card_3(k3_funct_6(A)) = k2_relat_1(k7_funct_6(A)))) # label(t58_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5458 (all A (v1_relat_1(A) & v1_funct_1(A) -> k1_setfam_1(k2_relat_1(A)) = k4_funct_6(A))) # label(d4_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5459 (all A k9_funct_6(A,k1_xboole_0) = k1_xboole_0) # label(t79_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5460 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> v1_relat_1(k9_funct_6(A,B)) & v1_funct_1(k9_funct_6(A,B)))) # label(dt_k9_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5461 (all A (v1_relat_1(A) & v1_funct_1(A) -> (-r2_hidden(k1_xboole_0,k2_relat_1(A)) -> ((all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(B,k2_relat_1(A)) -> v2_funct_1(B)))) <-> v2_funct_1(k7_funct_6(A)))))) # label(t59_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5462 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> ((all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(D,k2_relat_1(C)) -> r2_hidden(A,k1_relat_1(D))))) & r2_hidden(B,k2_relat_1(C)) -> r2_hidden(A,k1_relat_1(k6_funct_6(C)))))))) # label(t53_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5463 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_xboole_0 != B -> ((all C (r2_hidden(C,k1_relat_1(B)) -> r2_hidden(A,k1_funct_1(B,C)))) <-> r2_hidden(A,k4_funct_6(B)))))) # label(t37_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5464 (all A all B all C k8_funct_6(k10_finseq_1(A,B),C) = k10_finseq_1(k1_funct_2(A,C),k1_funct_2(B,C))) # label(t75_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5465 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(A,B) & r2_hidden(C,k1_relat_1(D)) -> k5_funct_6(k2_funcop_1(B,D),A,C) = k1_funct_1(D,C)))) # label(t48_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5466 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k2_funct_6(A)) & v1_funct_1(k2_funct_6(A)))) # label(dt_k2_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5467 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (r2_hidden(B,k1_relat_1(k10_funct_6(A))) -> v1_funct_1(k1_funct_1(k10_funct_6(A),B)) & v1_relat_1(k1_funct_1(k10_funct_6(A),B)))))) # label(t84_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5468 (all A r1_tarski(k1_funct_6(A),A)) # label(t27_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5469 $T # label(dt_k1_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5470 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r2_wellord2(k1_funct_2(k3_card_3(k2_card_3(B)),A),k4_card_3(k8_funct_6(B,A))))) # label(t77_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5471 (all A all B (r1_tarski(A,k1_funct_6(B)) -> A = k1_funct_6(A))) # label(t30_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5472 (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) -> k1_funct_6(k1_enumset1(A,B,C)) = k1_enumset1(A,B,C) & k1_funct_6(k1_xboole_0) = k1_xboole_0 & k2_tarski(A,B) = k1_funct_6(k2_tarski(A,B)) & k1_tarski(A) = k1_funct_6(k1_tarski(A)))))))) # label(t29_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5473 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> ((all D (r2_hidden(D,k1_relat_1(B)) -> r2_wellord2(k1_funct_1(A,D),k1_funct_1(C,k1_funct_1(B,D))))) & v2_funct_1(B) & k2_relat_1(B) = k1_relat_1(C) & k1_relat_1(B) = k1_relat_1(A) -> r2_wellord2(k4_card_3(A),k4_card_3(C))))))))) # label(t70_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5474 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k10_relat_1(A,k1_funct_6(k2_relat_1(A))) = k1_relat_1(B) & (all C (r2_hidden(C,k10_relat_1(A,k1_funct_6(k2_relat_1(A)))) -> k2_funct_5(k1_funct_1(A,C)) = k1_funct_1(B,C))) <-> B = k3_funct_6(A)))))) # label(d3_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5475 (all A (v1_relat_1(A) & v1_funct_1(A) -> k10_funct_6(A) = k5_funct_5(k4_funct_5(A)))) # label(d12_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.04 5476 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> -(r2_hidden(A,k1_relat_1(k2_funct_4(B))) & (all C all D k4_tarski(C,D) != A)))) # label(t11_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5477 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> k2_funct_6(k2_funcop_1(A,B)) = k2_funcop_1(A,k1_relat_1(B)) & k2_funcop_1(A,k2_relat_1(B)) = k3_funct_6(k2_funcop_1(A,B)))) # label(t36_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5478 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k7_funct_6(A)) & v1_funct_1(k7_funct_6(A)))) # label(dt_k7_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5479 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(k6_funct_6(B))) -> v1_funct_1(k1_funct_1(k6_funct_6(B),A)) & v1_relat_1(k1_funct_1(k6_funct_6(B),A))))) # label(t50_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5480 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(B,A) = k5_funct_6(k11_finseq_1(C,D,B),np__3,A)))))))) # label(t47_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5481 (all A all B all C (k2_zfmisc_1(A,B) != k1_xboole_0 -> k2_funcop_1(B,k2_funcop_1(A,C)) = k5_funct_5(k2_funcop_1(k2_zfmisc_1(A,B),C)) & k2_funcop_1(A,k2_funcop_1(B,C)) = k3_funct_5(k2_funcop_1(k2_zfmisc_1(A,B),C)))) # label(t14_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5482 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(B)) & r2_hidden(B,k4_card_3(k2_funct_6(C))) -> k5_funct_6(C,A,k1_funct_1(B,A)) = k5_funct_6(k7_funct_6(C),B,A)))))) # label(t56_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5483 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(B,A) = k5_funct_6(k9_finseq_1(B),np__1,A) & k5_funct_6(k11_finseq_1(B,C,D),np__1,A) = k1_funct_1(B,A) & k1_funct_1(B,A) = k5_funct_6(k10_finseq_1(B,C),np__1,A)))))))) # label(t45_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5484 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(D,k1_funct_2(A,k1_funct_2(B,C))) -> r2_hidden(k10_funct_6(D),k1_funct_2(B,k1_funct_2(A,C))) | B = k1_xboole_0 | A = k1_xboole_0))) # label(t85_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5485 (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) -> (all E (v1_funct_1(E) & v1_relat_1(E) -> (r2_hidden(D,k4_card_3(k2_funct_6(B))) & r2_hidden(A,k1_relat_1(B)) & E = k1_funct_1(k7_funct_6(B),D) & C = k1_funct_1(B,A) -> r2_hidden(k1_funct_1(D,A),k1_relat_1(C)) & k1_funct_1(E,A) = k1_funct_1(C,k1_funct_1(D,A)) & r2_hidden(E,k4_card_3(k3_funct_6(B)))))))))))) # label(t57_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5486 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) -> k1_relat_1(k2_funct_6(A)) = k1_relat_1(A))) # label(t89_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5487 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(D,k4_partfun1(k2_zfmisc_1(A,B),C)) -> r2_hidden(k3_funct_5(D),k4_partfun1(A,k4_partfun1(B,C))) & r2_hidden(k5_funct_5(D),k4_partfun1(B,k4_partfun1(A,C)))))) # label(t23_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5488 (all A (-v1_xboole_0(A) -> k4_card_3(k11_finseq_1(A,A,A)) = k4_finseq_2(np__3,A))) # label(t8_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5489 (all A (v1_funct_1(A) & v1_relat_1(A) -> k5_funct_5(k2_funct_4(A)) = k3_funct_5(A) & k4_funct_5(A) = k2_funct_4(k6_funct_5(A)))) # label(t13_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5490 (all A all B all C k2_funct_4(k2_funcop_1(k2_zfmisc_1(A,B),C)) = k2_funcop_1(k2_zfmisc_1(B,A),C)) # label(t12_funct_6) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5491 $T # label(t23_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5492 (all A all B (v1_relat_1(B) -> (r1_tarski(k6_relat_1(A),B) & k1_xboole_0 = k5_relat_1(k6_relat_1(A),k4_xboole_0(B,k6_relat_1(A))) -> k7_relat_1(B,A) = k6_relat_1(A)) & (r1_tarski(k6_relat_1(A),B) & k1_xboole_0 = k5_relat_1(k4_xboole_0(B,k6_relat_1(A)),k6_relat_1(A)) -> k6_relat_1(A) = k8_relat_1(A,B)))) # label(t54_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5493 (all A all B all C (v1_relat_1(C) -> (r1_xboole_0(A,B) -> r1_xboole_0(k1_relat_1(k3_xboole_0(k4_relat_1(C),k2_zfmisc_1(A,B))),k2_relat_1(k3_xboole_0(k4_relat_1(C),k2_zfmisc_1(A,B)))) & r1_xboole_0(k1_relat_1(k3_xboole_0(C,k2_zfmisc_1(A,B))),k2_relat_1(k3_xboole_0(C,k2_zfmisc_1(A,B))))))) # label(t14_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5494 $T # label(t17_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5495 (all A (v1_relat_1(A) -> (k1_xboole_0 = k5_relat_1(A,k4_xboole_0(A,k6_relat_1(k1_relat_1(A)))) -> k1_xboole_0 = k5_relat_1(k6_relat_1(k1_relat_1(k1_sysrel(A))),k4_xboole_0(A,k6_relat_1(k1_relat_1(k1_sysrel(A)))))) & (k5_relat_1(k4_xboole_0(A,k6_relat_1(k1_relat_1(A))),A) = k1_xboole_0 -> k1_xboole_0 = k5_relat_1(k4_xboole_0(A,k6_relat_1(k1_relat_1(k1_sysrel(A)))),k6_relat_1(k1_relat_1(k1_sysrel(A))))))) # label(t56_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5496 (all A (v1_relat_1(A) -> (k1_xboole_0 = k5_relat_1(k4_xboole_0(A,k6_relat_1(k1_relat_1(A))),A) & r1_tarski(A,k5_relat_1(A,A)) -> r1_tarski(k6_relat_1(k1_relat_1(A)),A)) & (r1_tarski(A,k5_relat_1(A,A)) & k1_xboole_0 = k5_relat_1(A,k4_xboole_0(A,k6_relat_1(k2_relat_1(A)))) -> r1_tarski(k6_relat_1(k2_relat_1(A)),A)))) # label(t40_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5497 (all A all B v1_relat_1(k2_zfmisc_1(A,B))) # label(fc1_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5498 (all A (v1_relat_1(A) -> r1_tarski(k6_relat_1(k2_relat_1(k1_sysrel(A))),k6_relat_1(k1_relat_1(A))) & r1_tarski(k6_relat_1(k1_relat_1(k1_sysrel(A))),k6_relat_1(k1_relat_1(A))))) # label(t52_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5499 (all A all B (r1_tarski(A,B) -> r1_tarski(k6_relat_1(A),k6_relat_1(B)))) # label(t33_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5500 $T # label(t6_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5501 (all A all B all C all D all E (v1_relat_1(E) -> (A = k2_xboole_0(C,D) & r1_tarski(E,k2_zfmisc_1(A,B)) -> k2_xboole_0(k7_relat_1(E,C),k7_relat_1(E,D)) = E))) # label(t25_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5502 (all A all B all C (v1_relat_1(C) -> (k1_xboole_0 = k5_relat_1(k4_xboole_0(C,k1_sysrel(C)),C) & r2_hidden(k4_tarski(A,B),C) & C = k5_relat_1(C,C) -> B = A | r2_hidden(A,k1_relat_1(k1_sysrel(C))) & r2_hidden(B,k4_xboole_0(k2_relat_1(C),k1_relat_1(k1_sysrel(C))))) & (k5_relat_1(C,C) = C & r2_hidden(k4_tarski(A,B),C) & k5_relat_1(C,k4_xboole_0(C,k1_sysrel(C))) = k1_xboole_0 -> r2_hidden(B,k1_relat_1(k1_sysrel(C))) & r2_hidden(A,k4_xboole_0(k1_relat_1(C),k1_relat_1(k1_sysrel(C)))) | B = A))) # label(t48_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5503 $T # label(t8_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5504 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k2_xboole_0(k5_relat_1(A,C),k5_relat_1(B,C)) = k5_relat_1(k2_xboole_0(A,B),C) & k5_relat_1(A,k2_xboole_0(B,C)) = k2_xboole_0(k5_relat_1(A,B),k5_relat_1(A,C)))))))) # label(t20_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5505 $T # label(t28_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5506 (all A (v1_relat_1(A) -> k1_sysrel(A) = k6_relat_1(k1_relat_1(k1_sysrel(A))))) # label(t47_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5507 (all A (v1_relat_1(A) -> v1_relat_1(k1_sysrel(A)))) # label(dt_k1_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5508 $T # label(t2_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5509 (all A (v1_relat_1(A) -> (r1_tarski(A,k6_relat_1(k1_relat_1(A))) -> A = k6_relat_1(k1_relat_1(A))))) # label(t35_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5510 (all A k6_relat_1(k1_tarski(A)) = k1_tarski(k4_tarski(A,A))) # label(t30_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5511 (all A (v1_relat_1(A) -> k1_relat_1(k1_sysrel(A)) = k2_relat_1(k1_sysrel(A)))) # label(t45_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5512 $T # label(t4_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5513 (all A all B (k2_xboole_0(k6_relat_1(A),k6_relat_1(B)) = k6_relat_1(k2_xboole_0(A,B)) & k6_relat_1(k3_xboole_0(A,B)) = k3_xboole_0(k6_relat_1(A),k6_relat_1(B)) & k4_xboole_0(k6_relat_1(A),k6_relat_1(B)) = k6_relat_1(k4_xboole_0(A,B)))) # label(t32_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5514 (all A all B k4_relat_1(k2_zfmisc_1(A,B)) = k2_zfmisc_1(B,A)) # label(t18_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5515 $T # label(t7_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5516 (all A (v1_relat_1(A) -> (k1_xboole_0 = k5_relat_1(k4_xboole_0(A,k6_relat_1(k1_relat_1(A))),A) & k5_relat_1(A,A) = A -> k2_relat_1(k1_sysrel(A)) = k1_relat_1(A) & k1_relat_1(k1_sysrel(A)) = k1_relat_1(A)) & (A = k5_relat_1(A,A) & k5_relat_1(A,k4_xboole_0(A,k6_relat_1(k1_relat_1(A)))) = k1_xboole_0 -> k1_relat_1(k1_sysrel(A)) = k2_relat_1(A) & k2_relat_1(A) = k2_relat_1(k1_sysrel(A))))) # label(t50_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5517 (all A all B all C (v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),k1_sysrel(C)) -> r2_hidden(A,k1_relat_1(k1_sysrel(C))) & B = A))) # label(t44_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5518 $T # label(t3_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5519 $T # label(t9_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5520 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (k5_relat_1(A,B) = A & k5_relat_1(B,k4_xboole_0(B,k6_relat_1(k1_relat_1(B)))) = k1_xboole_0 & B = k5_relat_1(B,A) & k1_xboole_0 = k5_relat_1(A,k4_xboole_0(A,k6_relat_1(k1_relat_1(A)))) -> k1_sysrel(A) = k1_sysrel(B)) & (k5_relat_1(B,A) = A & k5_relat_1(A,B) = B & k5_relat_1(k4_xboole_0(A,k6_relat_1(k1_relat_1(A))),A) = k1_xboole_0 & k1_xboole_0 = k5_relat_1(k4_xboole_0(B,k6_relat_1(k1_relat_1(B))),B) -> k1_sysrel(B) = k1_sysrel(A)))))) # label(t59_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5521 $T # label(t1_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5522 (all A k6_relat_1(A) = k5_relat_1(k6_relat_1(A),k6_relat_1(A))) # label(t29_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5523 (all A all B k1_xboole_0 = k4_xboole_0(k6_relat_1(k4_xboole_0(A,B)),k6_relat_1(A))) # label(t34_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5524 (all A all B -(-(k2_relat_1(k2_zfmisc_1(A,B)) = B & k1_relat_1(k2_zfmisc_1(A,B)) = A) & A != k1_xboole_0 & k1_xboole_0 != B)) # label(t12_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5525 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (k5_relat_1(k4_xboole_0(B,k6_relat_1(k1_relat_1(B))),B) = k1_xboole_0 & k5_relat_1(B,A) = A -> k1_xboole_0 = k5_relat_1(k4_xboole_0(B,k6_relat_1(k1_relat_1(B))),A)) & (k5_relat_1(A,B) = A & k1_xboole_0 = k5_relat_1(B,k4_xboole_0(B,k6_relat_1(k1_relat_1(B)))) -> k5_relat_1(A,k4_xboole_0(B,k6_relat_1(k1_relat_1(B)))) = k1_xboole_0))))) # label(t57_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5526 (all A all B all C (v1_relat_1(C) -> r1_tarski(k1_relat_1(k3_xboole_0(C,k2_zfmisc_1(A,B))),A) & r1_tarski(k2_relat_1(k3_xboole_0(C,k2_zfmisc_1(A,B))),B))) # label(t13_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5527 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(A,B) -> r1_tarski(k4_relat_1(A),k4_relat_1(B))))))) # label(t27_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5528 (all A all B (v1_relat_1(B) -> (r2_hidden(A,k2_relat_1(k1_sysrel(B))) -> r2_hidden(A,k1_relat_1(B)) & r2_hidden(k4_tarski(A,A),B)) & (r2_hidden(k4_tarski(A,A),B) & r2_hidden(A,k2_relat_1(B)) -> r2_hidden(A,k1_relat_1(k1_sysrel(B)))) & (r2_hidden(A,k2_relat_1(B)) & r2_hidden(k4_tarski(A,A),B) -> r2_hidden(A,k2_relat_1(k1_sysrel(B)))) & (r2_hidden(k4_tarski(A,A),B) & r2_hidden(A,k1_relat_1(B)) -> r2_hidden(A,k1_relat_1(k1_sysrel(B)))) & (r2_hidden(A,k1_relat_1(k1_sysrel(B))) -> r2_hidden(A,k1_relat_1(B)) & r2_hidden(k4_tarski(A,A),B)) & (r2_hidden(k4_tarski(A,A),B) & r2_hidden(A,k1_relat_1(B)) -> r2_hidden(A,k2_relat_1(k1_sysrel(B)))) & (r2_hidden(A,k1_relat_1(k1_sysrel(B))) -> r2_hidden(k4_tarski(A,A),B) & r2_hidden(A,k2_relat_1(B))) & (r2_hidden(A,k2_relat_1(k1_sysrel(B))) -> r2_hidden(k4_tarski(A,A),B) & r2_hidden(A,k2_relat_1(B))))) # label(t46_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5529 (all A all B all C (r2_hidden(k4_tarski(B,A),k6_relat_1(C)) <-> r2_hidden(k4_tarski(A,B),k6_relat_1(C)))) # label(t31_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5530 (all A all B (v1_relat_1(B) -> (k1_xboole_0 = k5_relat_1(k4_xboole_0(B,k6_relat_1(A)),k6_relat_1(A)) -> k4_xboole_0(k2_relat_1(B),k2_relat_1(k6_relat_1(A))) = k2_relat_1(k4_xboole_0(B,k6_relat_1(A)))) & (k1_xboole_0 = k5_relat_1(k6_relat_1(A),k4_xboole_0(B,k6_relat_1(A))) -> k1_relat_1(k4_xboole_0(B,k6_relat_1(A))) = k4_xboole_0(k1_relat_1(B),k1_relat_1(k6_relat_1(A)))))) # label(t39_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5531 (all A all B all C (v1_relat_1(C) -> (r1_tarski(C,k2_zfmisc_1(A,B)) -> r1_tarski(k2_relat_1(C),B) & r1_tarski(k1_relat_1(C),A)))) # label(t15_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5532 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (k1_xboole_0 = k5_relat_1(B,k4_xboole_0(B,k6_relat_1(k1_relat_1(B)))) & A = k5_relat_1(A,B) -> r1_tarski(k1_sysrel(A),k1_sysrel(B))) & (k5_relat_1(B,A) = A & k5_relat_1(k4_xboole_0(B,k6_relat_1(k1_relat_1(B))),B) = k1_xboole_0 -> r1_tarski(k1_sysrel(A),k1_sysrel(B))))))) # label(t58_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5533 (all A (v1_relat_1(A) -> r1_tarski(k1_sysrel(A),k6_relat_1(k1_relat_1(A))) & r1_tarski(k1_sysrel(A),A))) # label(t43_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5534 $T # label(t11_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5535 $T # label(t21_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5536 (all A all B (v1_relat_1(B) -> (k1_xboole_0 = k5_relat_1(B,k4_xboole_0(B,k6_relat_1(A))) & r1_tarski(k2_relat_1(B),A) -> k5_relat_1(B,k4_xboole_0(B,k6_relat_1(k2_relat_1(B)))) = k1_xboole_0) & (k5_relat_1(k4_xboole_0(B,k6_relat_1(A)),B) = k1_xboole_0 & r1_tarski(k1_relat_1(B),A) -> k5_relat_1(k4_xboole_0(B,k6_relat_1(k1_relat_1(B))),B) = k1_xboole_0))) # label(t42_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5537 $T # label(t19_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5538 $T # label(t10_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5539 (all A (v1_relat_1(A) -> r1_tarski(k1_relat_1(k1_sysrel(A)),k1_relat_1(A)) & r1_tarski(k2_relat_1(k1_sysrel(A)),k1_relat_1(A)) & r1_tarski(k1_relat_1(k1_sysrel(A)),k2_relat_1(A)) & r1_tarski(k2_relat_1(k1_sysrel(A)),k2_relat_1(A)))) # label(t51_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5540 (all A (v1_relat_1(A) -> r1_tarski(k6_relat_1(k2_relat_1(k1_sysrel(A))),A) & r1_tarski(k6_relat_1(k1_relat_1(k1_sysrel(A))),A))) # label(t53_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5541 (all A all B all C (v1_relat_1(C) -> (r1_tarski(C,k2_zfmisc_1(A,B)) -> r1_tarski(k4_relat_1(C),k2_zfmisc_1(B,A))))) # label(t16_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5542 $T # label(t5_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5543 (all A all B (v1_relat_1(B) -> (r1_tarski(k6_relat_1(A),B) -> r1_tarski(k6_relat_1(A),k4_relat_1(B))))) # label(t37_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5544 (all A all B (v1_relat_1(B) -> (r1_tarski(k6_relat_1(A),k2_xboole_0(B,k4_relat_1(B))) -> r1_tarski(k6_relat_1(A),B) & r1_tarski(k6_relat_1(A),k4_relat_1(B))))) # label(t36_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5545 (all A all B all C all D all E (v1_relat_1(E) -> (r1_tarski(E,k2_xboole_0(k2_zfmisc_1(A,B),k2_zfmisc_1(B,A))) & r1_xboole_0(A,B) & r2_hidden(D,B) & r2_hidden(k4_tarski(C,D),E) -> -r2_hidden(D,A) & r2_hidden(C,A) & -r2_hidden(C,B)) & (r2_hidden(k4_tarski(C,D),E) & r1_tarski(E,k2_xboole_0(k2_zfmisc_1(A,B),k2_zfmisc_1(B,A))) & r1_xboole_0(A,B) & r2_hidden(C,B) -> -r2_hidden(D,B) & -r2_hidden(C,A) & r2_hidden(D,A)) & (r2_hidden(C,A) & r1_xboole_0(A,B) & r1_tarski(E,k2_xboole_0(k2_zfmisc_1(A,B),k2_zfmisc_1(B,A))) & r2_hidden(k4_tarski(C,D),E) -> -r2_hidden(D,A) & -r2_hidden(C,B) & r2_hidden(D,B)) & (r1_tarski(E,k2_xboole_0(k2_zfmisc_1(A,B),k2_zfmisc_1(B,A))) & r1_xboole_0(A,B) & r2_hidden(D,A) & r2_hidden(k4_tarski(C,D),E) -> -r2_hidden(D,B) & -r2_hidden(C,A) & r2_hidden(C,B)))) # label(t22_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5546 (all A all B all C (v1_relat_1(C) -> (k1_xboole_0 = k5_relat_1(k4_xboole_0(C,k6_relat_1(k1_relat_1(C))),C) & C = k5_relat_1(C,C) & r2_hidden(k4_tarski(A,B),C) -> r2_hidden(B,k4_xboole_0(k2_relat_1(C),k1_relat_1(k1_sysrel(C)))) & r2_hidden(A,k1_relat_1(k1_sysrel(C))) | A = B) & (C = k5_relat_1(C,C) & k1_xboole_0 = k5_relat_1(C,k4_xboole_0(C,k6_relat_1(k1_relat_1(C)))) & r2_hidden(k4_tarski(A,B),C) -> r2_hidden(B,k1_relat_1(k1_sysrel(C))) & r2_hidden(A,k4_xboole_0(k1_relat_1(C),k1_relat_1(k1_sysrel(C)))) | B = A))) # label(t49_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5547 (all A all B all C all D (v1_relat_1(D) -> (r1_tarski(C,A) & r1_tarski(D,k2_zfmisc_1(A,B)) -> k7_relat_1(D,C) = k3_xboole_0(D,k2_zfmisc_1(C,B))) & (r1_tarski(D,k2_zfmisc_1(A,B)) & r1_tarski(C,B) -> k3_xboole_0(D,k2_zfmisc_1(A,C)) = k8_relat_1(C,D)))) # label(t24_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5548 (all A (v1_relat_1(A) -> k3_xboole_0(A,k6_relat_1(k1_relat_1(A))) = k1_sysrel(A))) # label(d1_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5549 (all A all B all C (v1_relat_1(C) -> (r1_tarski(C,k2_xboole_0(k2_zfmisc_1(A,B),k2_zfmisc_1(B,A))) & r1_xboole_0(A,B) -> r1_tarski(k7_relat_1(C,A),k2_zfmisc_1(A,B))))) # label(t26_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5550 (all A (v1_relat_1(A) -> (k5_relat_1(k4_xboole_0(A,k6_relat_1(k2_relat_1(k1_sysrel(A)))),k6_relat_1(k2_relat_1(k1_sysrel(A)))) = k1_xboole_0 -> k6_relat_1(k1_relat_1(k1_sysrel(A))) = k8_relat_1(k1_relat_1(k1_sysrel(A)),A) & k6_relat_1(k2_relat_1(k1_sysrel(A))) = k8_relat_1(k2_relat_1(k1_sysrel(A)),A)) & (k5_relat_1(k6_relat_1(k1_relat_1(k1_sysrel(A))),k4_xboole_0(A,k6_relat_1(k1_relat_1(k1_sysrel(A))))) = k1_xboole_0 -> k6_relat_1(k1_relat_1(k1_sysrel(A))) = k7_relat_1(A,k1_relat_1(k1_sysrel(A))) & k7_relat_1(A,k2_relat_1(k1_sysrel(A))) = k6_relat_1(k1_relat_1(k1_sysrel(A)))))) # label(t55_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5551 (all A (v1_relat_1(A) -> (r1_tarski(A,k5_relat_1(A,A)) & k5_relat_1(A,k4_xboole_0(A,k6_relat_1(k2_relat_1(A)))) = k1_xboole_0 -> k3_xboole_0(A,k6_relat_1(k2_relat_1(A))) = k6_relat_1(k2_relat_1(A))) & (k1_xboole_0 = k5_relat_1(k4_xboole_0(A,k6_relat_1(k1_relat_1(A))),A) & r1_tarski(A,k5_relat_1(A,A)) -> k6_relat_1(k1_relat_1(A)) = k3_xboole_0(A,k6_relat_1(k1_relat_1(A)))))) # label(t41_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5552 (all A all B (v1_relat_1(B) -> (r1_tarski(B,k2_zfmisc_1(A,A)) -> k4_xboole_0(B,k6_relat_1(A)) = k4_xboole_0(B,k6_relat_1(k1_relat_1(B))) & k4_xboole_0(B,k6_relat_1(A)) = k4_xboole_0(B,k6_relat_1(k2_relat_1(B)))))) # label(t38_sysrel) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5553 (all A (v1_card_4(A) <-> (exists B (v1_relat_1(B) & v1_funct_1(B) & k1_relat_1(B) = k5_numbers & r1_tarski(A,k2_relat_1(B)))))) # label(t45_card_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5554 (all A (v1_card_1(A) -> r1_tarski(np__0,A))) # label(t19_card_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5555 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> -(-(r1_tarski(k2_card_2(A,B),A) & r1_tarski(k2_card_2(B,A),A)) & (r2_hidden(B,A) | r1_tarski(B,A)) & -v1_finset_1(A)))))) # label(t79_card_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5556 (all A all B (v1_finset_1(A) -> k1_card_1(B) = k2_card_2(k1_card_1(B),k1_card_1(A)) | A = k1_xboole_0 | v1_finset_1(B))) # label(t85_card_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5557 (all A (v3_ordinal1(A) -> (exists B (m2_subset_1(B,k1_numbers,k5_numbers) & k15_ordinal2(A,k1_ordinal1(k4_ordinal2)) = k14_ordinal2(A,B))))) # label(t29_card_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5558 (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) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (k2_nat_1(k1_card_4(np__2,A),k1_nat_1(k2_nat_1(np__2,B),np__1)) = k2_nat_1(k1_card_4(np__2,C),k1_nat_1(k2_nat_1(np__2,D),np__1)) -> C = A & D = B))))))))) # label(t52_card_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5559 (all A (k1_xboole_0 = A <-> np__0 = k1_card_1(A))) # label(t17_card_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5560 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v1_card_4(k1_relat_1(A)) & (all B (r2_hidden(B,k1_relat_1(A)) -> v1_card_4(k1_funct_1(A,B)))) -> v1_card_4(k3_card_3(A))))) # label(t61_card_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5561 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_card_1(C) -> (all D (v1_card_1(D) -> (r2_hidden(C,D) & r2_hidden(A,B) -> r2_hidden(k1_card_2(A,C),k1_card_2(B,D)) & r2_hidden(k1_card_2(C,A),k1_card_2(B,D))))))))))) # label(t74_card_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5562 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_card_1(C) -> (all D (v1_card_1(D) -> (-(-(r2_hidden(A,B) & r1_tarski(C,D)) & -(r1_tarski(C,D) & r1_tarski(A,B)) & -(r1_tarski(A,B) & r2_hidden(C,D)) & -(r2_hidden(A,B) & r2_hidden(C,D))) -> r1_tarski(k1_card_2(C,A),k1_card_2(B,D)) & r1_tarski(k1_card_2(A,C),k1_card_2(B,D))))))))))) # label(t41_card_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5563 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (v1_finset_1(A) -> v1_finset_1(B) | -r2_hidden(B,A) & -r1_tarski(B,A)))))) # label(t26_card_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5564 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_card_1(C) -> (all D (v1_card_1(D) -> -(-(-(r1_tarski(C,D) & r2_hidden(A,B)) & -(r1_tarski(C,D) & r1_tarski(A,B)) & -(r2_hidden(A,B) & r2_hidden(C,D)) & -(r2_hidden(C,D) & r1_tarski(A,B))) & -r1_tarski(k3_card_2(A,C),k3_card_2(B,D)) & A != np__0))))))))) # label(t70_card_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5565 (all A all B (k1_card_1(A) = k1_card_1(B) <-> k2_card_1(B) = k2_card_1(A))) # label(t20_card_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5566 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> k1_card_4(A,B) = k2_newton(A,B))) # label(redefinition_k1_card_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5567 (all A (-v1_xboole_0(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (v1_card_4(A) -> v1_card_4(k4_finseq_2(B,A))))))) # label(t58_card_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5568 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (r2_hidden(np__0,B) -> v1_finset_1(A) | -r1_tarski(B,A) & -r2_hidden(B,A) | A = k2_card_2(B,A) & k2_card_2(A,B) = A))))) # label(t78_card_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5569 (all A (-v1_xboole_0(A) -> r2_wellord2(k4_finseq_2(np__1,A),A) & k1_card_1(A) = k1_card_1(k4_finseq_2(np__1,A)))) # label(t56_card_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5570 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> -(-(k1_card_2(B,A) = A & A = k1_card_2(A,B)) & (r1_tarski(B,A) | r2_hidden(B,A)) & -v1_finset_1(A)))))) # label(t34_card_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5571 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_card_1(C) -> (all D (v1_card_1(D) -> (r2_hidden(C,D) & r2_hidden(A,B) -> r2_hidden(k2_card_2(A,C),k2_card_2(B,D)) & r2_hidden(k2_card_2(C,A),k2_card_2(B,D))))))))))) # label(t82_card_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5572 (all A all B (v1_card_1(B) -> (all C (v1_card_1(C) -> ((all D (r2_hidden(D,A) -> r1_tarski(k1_card_1(D),C))) & r1_tarski(k1_card_1(A),B) -> r1_tarski(k1_card_1(k3_tarski(A)),k2_card_2(B,C))))))) # label(t60_card_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5573 (all A (v1_card_1(A) -> (-v1_finset_1(A) <-> r1_ordinal1(k3_card_1(np__0),A)))) # label(t11_card_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5574 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v3_ordinal1(B) -> (r2_wellord2(B,A) -> A = B))))) # label(t6_card_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5575 (all A (-v1_finset_1(A) -> k1_card_1(A) = k2_card_2(k3_card_1(np__0),k1_card_1(A)))) # label(t84_card_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5576 (all A all B (v1_finset_1(B) -> k1_card_1(A) = k1_card_1(k2_xboole_0(A,B)) & r2_wellord2(k2_xboole_0(A,B),A) | v1_finset_1(A))) # label(t36_card_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5577 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_card_1(C) -> (all D (v1_card_1(D) -> (-(-(r1_tarski(A,B) & r2_hidden(C,D)) & -(r2_hidden(C,D) & r2_hidden(A,B)) & -(r2_hidden(A,B) & r1_tarski(C,D)) & -(r1_tarski(C,D) & r1_tarski(A,B))) -> r1_tarski(k2_card_2(A,C),k2_card_2(B,D)) & r1_tarski(k2_card_2(C,A),k2_card_2(B,D))))))))))) # label(t68_card_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5578 (all A (r2_hidden(A,a_0_2_card_4) <-> (exists B exists C exists D (m2_subset_1(B,k1_numbers,k5_numbers) & A = f1_s3_card_4(B,C,D) & p1_s3_card_4(B,C,D) & m2_subset_1(D,k1_numbers,k5_numbers) & m2_subset_1(C,k1_numbers,k5_numbers))))) # label(fraenkel_a_0_2_card_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5579 (all A (v3_ordinal1(A) -> (r1_ordinal1(k5_ordinal2,A) -> k14_ordinal2(k4_ordinal2,A) = A))) # label(t31_card_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5580 (all A (r2_hidden(k1_card_1(A),k3_card_1(np__0)) <-> v1_finset_1(A))) # label(t2_card_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5581 (all A all B (v1_card_4(B) & v1_card_4(A) -> v1_card_4(k2_zfmisc_1(A,B)))) # label(t55_card_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5582 (all A (v1_card_1(A) -> (r2_hidden(np__0,A) <-> r1_tarski(np__1,A)))) # label(t24_card_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5583 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_card_1(C) -> (r2_hidden(k1_card_2(A,B),k1_card_2(A,C)) -> r2_hidden(B,C)))))))) # label(t75_card_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5584 (all A (-v1_xboole_0(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k1_card_1(k2_zfmisc_1(k4_finseq_2(B,A),k4_finseq_2(C,A))) = k1_card_1(k4_finseq_2(k1_nat_1(B,C),A)) & r2_wellord2(k2_zfmisc_1(k4_finseq_2(B,A),k4_finseq_2(C,A)),k4_finseq_2(k1_nat_1(B,C),A)))))))) # label(t57_card_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5585 (all A (-v1_finset_1(A) -> r2_wellord2(k2_zfmisc_1(A,A),A) & k1_card_1(A) = k1_card_1(k2_zfmisc_1(A,A)))) # label(t80_card_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5586 $T # label(t12_card_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5587 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> m2_subset_1(k1_card_4(A,B),k1_numbers,k5_numbers))) # label(dt_k1_card_4) # label(axiom) # label(non_clause). [assumption]. 57.05/56.05 5588 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v3_ordinal1(B) -> k14_ordinal2(k1_ordinal1(B),A) = k14_ordinal2(B,k1_nat_1(A,np__1)) & k14_ordinal2(k1_ordinal1(B),A) = k14_ordinal2(B,k1_ordinal1(A)))))) # label(t28_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5589 (all A all B (v1_card_4(A) -> v1_card_4(k3_xboole_0(B,A)) & v1_card_4(k3_xboole_0(A,B)))) # label(t48_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5590 (all A (v1_card_1(A) & v1_finset_1(A) -> (all B (v1_card_1(B) & v1_finset_1(B) -> v1_finset_1(k1_card_2(A,B)))))) # label(t38_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5591 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_card_1(C) -> (r2_hidden(A,B) | r1_tarski(A,B) -> r1_tarski(k2_card_2(A,C),k2_card_2(B,C)) & r1_tarski(k2_card_2(C,A),k2_card_2(C,B)) & r1_tarski(k2_card_2(C,A),k2_card_2(B,C)) & r1_tarski(k2_card_2(A,C),k2_card_2(C,B))))))))) # label(t69_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5592 (all A (r2_hidden(A,a_0_0_card_4) <-> (exists B (p1_s1_card_4(B) & f1_s1_card_4(B) = A & m2_subset_1(B,k1_numbers,k5_numbers))))) # label(fraenkel_a_0_0_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5593 (all A all B -(-v1_finset_1(A) & -(k1_card_1(k2_xboole_0(A,B)) = k1_card_1(A) & r2_wellord2(k2_xboole_0(A,B),A)) & (r1_tarski(k1_card_1(B),k1_card_1(A)) | r2_hidden(k1_card_1(B),k1_card_1(A))))) # label(t37_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5594 (all A all B (r2_hidden(k1_card_1(B),k1_card_1(A)) & k1_card_1(A) = k1_card_2(k1_card_1(A),k1_card_1(B)) -> k1_card_1(k4_xboole_0(A,B)) = k1_card_1(A))) # label(t76_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5595 (all A (v1_card_1(A) -> (-v1_finset_1(A) -> v4_ordinal1(A)))) # label(t32_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5596 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> r1_tarski(k2_card_2(k1_card_1(A),k3_card_1(np__0)),k3_card_1(np__0)) & r1_tarski(k2_card_2(k3_card_1(np__0),k1_card_1(A)),k3_card_1(np__0)))) # label(t67_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5597 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (r1_tarski(A,B) <-> r2_hidden(A,k2_card_1(B))))))) # label(t23_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5598 (all A (v3_ordinal1(A) -> (v1_finset_1(A) <-> r2_hidden(A,k5_ordinal2)))) # label(t7_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5599 (all A (v1_finset_1(A) <-> (exists B (m2_subset_1(B,k1_numbers,k5_numbers) & k1_card_1(A) = k1_card_1(B))))) # label(t4_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5600 $T # label(t18_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5601 (all A (-((all B -(k3_card_1(np__0) = k1_card_1(B) & r1_tarski(B,A))) & -v1_finset_1(A)) & -(v1_finset_1(A) & (exists B (r1_tarski(B,A) & k1_card_1(B) = k3_card_1(np__0)))))) # label(t14_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5602 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B (r2_hidden(B,k1_relat_1(A)) -> v1_finset_1(k1_funct_1(A,B)))) & v1_finset_1(k1_relat_1(A)) -> v1_finset_1(k3_card_3(A))))) # label(t63_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5603 (all A all B (v1_finset_1(B) -> r2_wellord2(k2_zfmisc_1(A,B),A) & k1_card_1(A) = k1_card_1(k2_zfmisc_1(A,B)) | B = k1_xboole_0 | v1_finset_1(A))) # label(t81_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5604 (all A (v3_ordinal1(A) -> (v4_ordinal1(A) <-> (all B (v3_ordinal1(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(B,A) -> r2_hidden(k14_ordinal2(B,C),A))))))))) # label(t27_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5605 (all A (r2_hidden(A,a_0_1_card_4) <-> (exists B exists C (A = f1_s2_card_4(B,C) & m2_subset_1(C,k1_numbers,k5_numbers) & p1_s2_card_4(B,C) & m2_subset_1(B,k1_numbers,k5_numbers))))) # label(fraenkel_a_0_1_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5606 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (-v1_finset_1(A) -> -v1_finset_1(k1_card_2(A,B)) & -v1_finset_1(k1_card_2(B,A))))))) # label(t39_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5607 $T # label(t10_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5608 $T # label(t16_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5609 (all A (r1_tarski(k1_card_1(A),k3_card_1(np__0)) <-> v1_card_4(A))) # label(d1_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5610 (all A (v1_finset_1(A) <-> v1_finset_1(k1_card_1(A)))) # label(t1_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5611 (all A (v1_card_4(A) & (all B (r2_hidden(B,A) -> v1_card_4(B))) -> v1_card_4(k3_tarski(A)))) # label(t62_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5612 (all A all B -(-(r2_wellord2(k2_xboole_0(A,B),A) & k1_card_1(k2_xboole_0(A,B)) = k1_card_1(A)) & (r2_wellord2(A,B) | r2_wellord2(B,A)) & -v1_finset_1(A))) # label(t35_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5613 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (k2_card_1(B) = k2_card_1(A) <-> A = B))))) # label(t21_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5614 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_card_1(C) -> -(np__0 != C & (r2_hidden(A,B) | r1_tarski(A,B)) & -(r1_tarski(k3_card_2(C,A),k3_card_2(C,B)) & r1_tarski(k3_card_2(A,C),k3_card_2(B,C)))))))))) # label(t71_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5615 (all A (v1_card_1(A) -> (-v1_finset_1(A) -> k1_card_2(A,A) = A))) # label(t33_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5616 (all A (-v1_xboole_0(A) -> (v1_card_4(A) -> v1_card_4(k3_finseq_2(A))))) # label(t65_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5617 (all A all B (v1_card_4(B) & v1_card_4(A) -> v1_card_4(k2_xboole_0(A,B)))) # label(t47_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5618 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_card_1(C) -> (r2_hidden(k2_card_2(A,B),k2_card_2(A,C)) -> r2_hidden(B,C)))))))) # label(t83_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5619 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> -(np__0 != A & np__0 = B & np__0 != k3_newton(B,A)) & -(-(A != np__0 & B = np__0) & k3_newton(B,A) = np__0))))) # label(t51_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5620 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (np__0 != A -> r1_tarski(B,k2_card_2(B,A)) & r1_tarski(B,k2_card_2(A,B))))))) # label(t73_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5621 (all A all B (v1_card_4(A) -> v1_card_4(k4_xboole_0(A,B)))) # label(t49_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5622 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> r1_tarski(B,k1_card_2(A,B)) & r1_tarski(A,k1_card_2(A,B)))))) # label(t72_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5623 (all A (v3_ordinal1(A) -> (v4_ordinal1(A) -> A = k15_ordinal2(A,k1_ordinal1(k4_ordinal2))))) # label(t30_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5624 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_card_1(C) -> (r2_hidden(A,B) | r1_tarski(A,B) -> r1_tarski(k1_card_2(C,A),k1_card_2(C,B)) & r1_tarski(k1_card_2(A,C),k1_card_2(B,C)) & r1_tarski(k1_card_2(A,C),k1_card_2(C,B)) & r1_tarski(k1_card_2(C,A),k1_card_2(B,C))))))))) # label(t42_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5625 (all A (v3_ordinal1(A) -> (r1_ordinal1(k5_ordinal2,A) <-> -v1_finset_1(A)))) # label(t8_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5626 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (r1_tarski(k2_card_1(A),B) <-> r2_hidden(A,B)))))) # label(t22_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5627 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (v1_finset_1(A) -> r2_hidden(A,B) & r1_tarski(A,B) | v1_finset_1(B)))))) # label(t13_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5628 (all A (-v1_xboole_0(A) -> (-v1_finset_1(A) -> k1_card_1(A) = k1_card_1(k3_finseq_2(A))))) # label(t87_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5629 (all A all B (r1_tarski(A,B) & v1_card_4(B) -> v1_card_4(A))) # label(t46_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5630 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k1_card_1(k1_relat_1(C)),A) & (all D (r2_hidden(D,k1_relat_1(C)) -> r1_tarski(k1_card_1(k1_funct_1(C,D)),B))) -> r1_tarski(k1_card_1(k3_card_3(C)),k2_card_2(A,B))))))))) # label(t59_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5631 (all A (v1_finset_1(A) -> v1_card_4(A))) # label(t43_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5632 (all A (v1_card_1(A) -> (v1_finset_1(A) <-> r2_hidden(A,k3_card_1(np__0))))) # label(t9_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5633 (all A (-v1_xboole_0(A) -> r1_tarski(k3_card_1(np__0),k1_card_1(k3_finseq_2(A))))) # label(t66_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5634 (all A (-v1_xboole_0(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> -(B != np__0 & -v1_finset_1(A) & -(k1_card_1(k4_finseq_2(B,A)) = k1_card_1(A) & r2_wellord2(k4_finseq_2(B,A),A))))))) # label(t86_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5635 (all A (v1_card_1(A) -> (r1_tarski(np__2,A) <-> r2_hidden(np__1,A)))) # label(t25_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5636 (all A (v3_ordinal1(A) -> A = k4_xboole_0(k1_ordinal1(A),k1_tarski(A)))) # label(t5_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5637 (all A (v1_card_1(A) -> (-v1_finset_1(A) -> k2_card_2(A,A) = A))) # label(t77_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5638 (all A (v1_card_1(A) & v1_finset_1(A) -> (all B (v1_finset_1(B) & v1_card_1(B) -> v1_finset_1(k2_card_2(A,B)))))) # label(t40_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5639 (all A all B (v1_card_4(A) & v1_card_4(B) -> v1_card_4(k5_xboole_0(A,B)))) # label(t50_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5640 (all A (v1_finset_1(A) -> r2_hidden(k1_card_1(A),k3_card_1(np__0)) & r2_hidden(k1_card_1(A),k5_ordinal2))) # label(t3_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5641 $T # label(t64_card_4) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5642 $T # label(t14_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5643 $T # label(t18_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5644 (all A all B (v1_partfun1(B,A,A) & v3_relat_2(B) & v1_relat_2(B) & m2_relset_1(B,A,A) -> (all C (r2_hidden(C,A) -> m1_toler_1(k1_tarski(C),A,B))))) # label(t41_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5645 (all A all B all C (v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v1_relat_2(C) -> (r2_hidden(k4_tarski(B,B),C) <-> r2_hidden(B,A)))) # label(t27_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5646 (all A v6_relat_2(k1_eqrel_1(A))) # label(t21_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5647 $T # label(t37_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5648 (all A all B (v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v3_relat_2(B) & v1_relat_2(B) -> r1_tarski(B,k7_relset_1(A,A,A,A,B,B)))) # label(t74_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5649 $T # label(dt_k4_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5650 (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 all D -((all E (m1_toler_1(E,A,B) & v1_toler_1(E,A,B) -> -(r2_hidden(D,E) & r2_hidden(C,E)))) & r2_hidden(k4_tarski(C,D),B))))) # label(t46_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5651 (all A all B (v1_partfun1(B,A,A) & v1_relat_2(B) & v3_relat_2(B) & m2_relset_1(B,A,A) -> k3_tarski(k4_toler_1(A,B)) = A)) # label(t66_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5652 (all A all B (v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v1_relat_2(B) -> (v8_relat_2(B) -> (all C (r2_hidden(C,A) -> m1_toler_1(k6_eqrel_1(A,B,C),A,B) & v1_toler_1(k6_eqrel_1(A,B,C),A,B)))))) # label(t69_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5653 $T # label(t55_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5654 $T # label(t35_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5655 (all A all B (v1_partfun1(B,A,A) & v3_relat_2(B) & m2_relset_1(B,A,A) & v1_relat_2(B) -> (all C (m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v1_relat_2(C) & v3_relat_2(C) -> (k4_toler_1(A,C) = k4_toler_1(A,B) -> C = B))))) # label(t65_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5656 (all A all B (v1_relat_2(B) & v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> (all C (m1_toler_1(C,A,B) -> (exists D (m1_toler_1(D,A,B) & v1_toler_1(D,A,B) & r1_tarski(C,D))))))) # label(t45_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5657 $T # label(t36_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5658 (all A all B all C (v1_relat_2(B) & v3_relat_2(B) & m1_relset_1(B,A,A) & m1_subset_1(C,k1_zfmisc_1(A)) & v1_partfun1(B,A,A) -> m2_relset_1(k2_toler_1(A,B,C),C,C) & v3_relat_2(k2_toler_1(A,B,C)) & v1_relat_2(k2_toler_1(A,B,C)) & v1_partfun1(k2_toler_1(A,B,C),C,C))) # label(dt_k2_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5659 $T # label(t44_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5660 (all A all B (m2_relset_1(B,A,A) & v1_relat_2(B) & v1_partfun1(B,A,A) & v3_relat_2(B) -> (all C -((all D (m1_toler_1(D,A,B) & v1_toler_1(D,A,B) -> -r2_hidden(C,D))) & r2_hidden(C,A))))) # label(t47_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5661 (all A all B (v1_relat_1(A) -> k1_toler_1(A,B) = k2_wellord1(A,B))) # label(redefinition_k1_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5662 (all A all B all C all D (m2_relset_1(D,A,B) -> (v3_relat_2(D) -> v3_relat_2(k1_toler_1(D,C))))) # label(t32_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5663 (all A all B (v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v1_relat_2(B) -> (all C all D (r2_hidden(k4_tarski(C,D),B) -> m1_toler_1(k2_tarski(C,D),A,B))))) # label(t40_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5664 (all A A = k5_relset_1(A,A,k1_eqrel_1(A))) # label(t13_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5665 $T # label(t31_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5666 $T # label(t11_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5667 $T # label(t20_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5668 $T # label(t63_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5669 (all A all B (v1_relat_2(B) & m2_relset_1(B,A,A) & v3_relat_2(B) & v1_partfun1(B,A,A) -> k5_relset_1(A,A,B) = A)) # label(t25_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5670 (all A all B (v3_relat_2(B) & v1_relat_2(B) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) -> (exists C m1_toler_1(C,A,B)))) # label(existence_m1_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5671 (all A all B (v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v3_relat_2(B) & v1_relat_2(B) -> (all C (v1_relat_2(C) & v3_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) -> ((all D (v1_toler_1(D,A,B) & m1_toler_1(D,A,B) <-> v1_toler_1(D,A,C) & m1_toler_1(D,A,C))) -> C = B))))) # label(t53_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5672 (all A all B all C (m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v3_relat_2(C) & v1_relat_2(C) -> (all D (r2_hidden(k4_tarski(B,D),C) <-> r2_hidden(D,k6_eqrel_1(A,C,B)))))) # label(t54_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5673 (all A all B all C (m1_relset_1(B,A,A) & v1_relat_2(B) & m1_subset_1(C,k1_zfmisc_1(A)) & v1_partfun1(B,A,A) & v3_relat_2(B) -> k2_toler_1(A,B,C) = k2_wellord1(B,C))) # label(redefinition_k2_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5674 $T # label(t12_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5675 (all A all B (m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) & v1_relat_2(B) -> (exists C (m1_toler_1(C,A,B) & v1_toler_1(C,A,B))))) # label(rc1_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5676 (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 ((all D all E (r2_hidden(E,C) & r2_hidden(D,C) -> r2_hidden(k4_tarski(D,E),B))) <-> m1_toler_1(C,A,B))))) # label(d3_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5677 (all A all B all C (r2_hidden(B,A) & r2_hidden(C,A) -> r2_hidden(k4_tarski(B,C),k1_eqrel_1(A)))) # label(t15_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5678 (all A all B (v1_partfun1(B,A,A) & v1_relat_2(B) & v3_relat_2(B) & m2_relset_1(B,A,A) -> r3_relat_2(B,A))) # label(t29_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5679 $T # label(dt_k3_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5680 (all A all B (v1_partfun1(B,A,A) & v3_relat_2(B) & m2_relset_1(B,A,A) & v1_relat_2(B) -> (all C (v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v3_relat_2(C) & v1_relat_2(C) -> (r1_tarski(B,C) <-> r1_tarski(k3_toler_1(A,B),k3_toler_1(A,C))))))) # label(t71_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5681 (all A all B (v1_relat_1(A) -> m2_relset_1(k1_toler_1(A,B),B,B))) # label(dt_k1_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5682 $T # label(t23_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5683 $T # label(t56_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5684 (all A all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v1_relat_2(B) & v3_relat_2(B) -> r1_tarski(B,k1_eqrel_1(A)))) # label(t49_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5685 (all A all B (m2_relset_1(B,A,A) & v1_relat_2(B) & v1_partfun1(B,A,A) & v3_relat_2(B) -> r1_relat_2(B,A))) # label(t28_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5686 (all A all B (v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v1_relat_2(B) & v3_relat_2(B) -> (all C ((all D (v1_toler_1(D,A,B) & m1_toler_1(D,A,B) <-> r2_hidden(D,C))) <-> C = k4_toler_1(A,B))))) # label(d7_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5687 $T # label(t61_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5688 (all A v7_relat_2(k1_eqrel_1(A))) # label(t19_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5689 (all A all B (v1_relat_2(B) & v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) -> (all C (v3_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v1_relat_2(C) -> (r1_tarski(k4_toler_1(A,B),k4_toler_1(A,C)) -> r1_tarski(B,C)))))) # label(t64_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5690 $T # label(t60_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5691 (all A all B all C (v3_relat_2(C) & v1_partfun1(C,B,B) & m2_relset_1(C,B,B) & v1_relat_2(C) -> (r1_tarski(A,B) -> v3_relat_2(k1_toler_1(C,A)) & m2_relset_1(k1_toler_1(C,A),A,A) & v1_partfun1(k1_toler_1(C,A),A,A) & v1_relat_2(k1_toler_1(C,A))))) # label(t33_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5692 $T # label(t30_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5693 (all A all B (v1_relat_2(B) & m2_relset_1(B,A,A) & v3_relat_2(B) & v1_partfun1(B,A,A) -> m1_toler_1(k1_xboole_0,A,B))) # label(t34_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5694 (all A all B (v1_relat_2(B) & v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) -> (all C all D (m1_toler_1(C,A,B) & m1_toler_1(D,A,B) -> m1_toler_1(k3_xboole_0(C,D),A,B))))) # label(t42_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5695 (all A all B (m2_relset_1(B,k3_tarski(A),k3_tarski(A)) & v1_partfun1(B,k3_tarski(A),k3_tarski(A)) & v3_relat_2(B) & v1_relat_2(B) -> (all C (m2_relset_1(C,k3_tarski(A),k3_tarski(A)) & v1_partfun1(C,k3_tarski(A),k3_tarski(A)) & v3_relat_2(C) & v1_relat_2(C) -> ((all D all E (r2_hidden(k4_tarski(D,E),B) <-> (exists F (r2_hidden(F,A) & r2_hidden(D,F) & r2_hidden(E,F))))) & (all D all E (r2_hidden(k4_tarski(D,E),C) <-> (exists F (r2_hidden(D,F) & r2_hidden(E,F) & r2_hidden(F,A))))) -> C = B))))) # label(t52_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5696 (all A all B (r2_hidden(A,f1_s1_toler_1) & r2_hidden(B,f1_s1_toler_1) & p1_s1_toler_1(A,B) -> p1_s1_toler_1(B,A))) & (all A (r2_hidden(A,f1_s1_toler_1) -> p1_s1_toler_1(A,A))) -> (exists A (v1_relat_2(A) & v1_partfun1(A,f1_s1_toler_1,f1_s1_toler_1) & m2_relset_1(A,f1_s1_toler_1,f1_s1_toler_1) & (all B all C (r2_hidden(C,f1_s1_toler_1) & r2_hidden(B,f1_s1_toler_1) -> (p1_s1_toler_1(B,C) <-> r2_hidden(k4_tarski(B,C),A)))) & v3_relat_2(A))) # label(s1_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5697 (all A all B (v1_relat_2(B) & v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> (all C all D (v1_toler_1(D,A,B) & m1_toler_1(D,A,B) -> (r2_hidden(C,D) -> r1_tarski(D,k6_eqrel_1(A,B,C))))))) # label(t70_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5698 $T # label(t17_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5699 (all A all B all C (v1_relat_2(C) & v3_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) -> (all D ((all E (r2_hidden(E,D) <-> m1_toler_1(E,A,C) & r2_hidden(B,E))) -> k3_tarski(D) = k6_eqrel_1(A,C,B))))) # label(t59_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5700 (all A all B all C (v3_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v1_relat_2(C) -> (all D ((all E (r2_hidden(E,D) <-> v1_toler_1(E,A,C) & r2_hidden(B,E) & m1_toler_1(E,A,C))) -> k3_tarski(D) = k6_eqrel_1(A,C,B))))) # label(t58_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5701 (all A all B (m2_relset_1(B,A,A) & v3_relat_2(B) & v1_relat_2(B) & v1_partfun1(B,A,A) -> (m1_toler_1(k1_xboole_0,A,B) & v1_toler_1(k1_xboole_0,A,B) -> B = k1_xboole_0))) # label(t38_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5702 $T # label(d5_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5703 (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 (v3_relat_2(C) & v1_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) -> ((all D (r2_hidden(D,A) -> r1_tarski(k6_eqrel_1(A,B,D),k6_eqrel_1(A,C,D)))) -> r1_tarski(B,C)))))) # label(t73_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5704 $T # label(t26_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5705 $T # label(d2_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5706 $T # label(t10_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5707 (all A exists B ((all C (r2_hidden(C,A) -> m1_toler_1(C,k3_tarski(A),B))) & v3_relat_2(B) & v1_relat_2(B) & v1_partfun1(B,k3_tarski(A),k3_tarski(A)) & m2_relset_1(B,k3_tarski(A),k3_tarski(A)))) # label(t51_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5708 $T # label(t57_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5709 (all A all B (v1_partfun1(B,A,A) & v3_relat_2(B) & v1_relat_2(B) & m2_relset_1(B,A,A) -> (all C (C = k3_toler_1(A,B) <-> (all D (m1_toler_1(D,A,B) <-> r2_hidden(D,C))))))) # label(d6_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5710 $T # label(t24_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5711 (all A all B (v1_partfun1(B,A,A) & v1_relat_2(B) & v3_relat_2(B) & m2_relset_1(B,A,A) -> ((all C (r2_hidden(C,A) -> m1_toler_1(k6_eqrel_1(A,B,C),A,B))) -> v8_relat_2(B)))) # label(t68_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5712 (all A all B all C (m2_relset_1(C,B,B) & v1_partfun1(C,B,B) & v3_relat_2(C) & v1_relat_2(C) -> (m1_toler_1(A,B,C) -> r1_tarski(A,B)))) # label(t43_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5713 (all A all B all C (r2_hidden(B,k3_relat_1(k1_eqrel_1(A))) & r2_hidden(C,k3_relat_1(k1_eqrel_1(A))) -> r2_hidden(k4_tarski(B,C),k1_eqrel_1(A)))) # label(t16_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5714 (all A all B (v3_relat_2(B) & v1_partfun1(B,A,A) & v1_relat_2(B) & m2_relset_1(B,A,A) -> r1_tarski(k4_toler_1(A,B),k3_toler_1(A,B)))) # label(t72_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5715 $T # label(t48_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5716 (all A all B (v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v3_relat_2(B) & v1_relat_2(B) -> r1_tarski(k6_partfun1(A),B))) # label(t50_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5717 $T # label(d1_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.06 5718 (all A all B (v1_partfun1(B,A,A) & v1_relat_2(B) & m2_relset_1(B,A,A) & v3_relat_2(B) -> k3_tarski(k3_toler_1(A,B)) = A)) # label(t67_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5719 $T # label(t62_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5720 (all A all B (m2_relset_1(B,A,A) & v3_relat_2(B) & v1_relat_2(B) & v1_partfun1(B,A,A) -> (all C (m1_toler_1(C,A,B) -> (v1_toler_1(C,A,B) <-> (all D -(r2_hidden(D,A) & -r2_hidden(D,C) & (all E -(-r2_hidden(k4_tarski(D,E),B) & r2_hidden(E,C)))))))))) # label(d4_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5721 $T # label(dt_m1_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5722 $T # label(t22_toler_1) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5723 (all A (m2_finseq_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (B = k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(C,np__1)) & k3_finseq_1(A) = k1_nat_1(C,np__2) -> k8_finseq_1(k1_numbers,k16_finseq_1(k1_numbers,k2_rfinseq(A),C),k12_finseq_1(k1_numbers,B)) = k2_rfinseq(k16_finseq_1(k1_numbers,A,k1_nat_1(C,np__1)))))))))) # label(t23_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5724 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> k2_finseq_4(k1_numbers,k5_real_1(A,B),B) = k2_rfinseq(k2_finseq_4(k1_numbers,A,B)))))) # label(t27_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5725 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_rfinseq(A,B) -> k1_card_1(k1_relat_1(B)) = k1_card_1(k1_relat_1(A))))))) # label(t7_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5726 (all A (m2_finseq_1(A,k1_numbers) -> (v1_rfinseq(A) <-> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(B,k4_finseq_1(A)) & r2_hidden(C,k4_finseq_1(A)) -> r1_xreal_0(C,B) | r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,C),k2_seq_1(k5_numbers,k1_numbers,A,B)))))))))) # label(t32_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5727 (all A all B all C (m1_finseq_1(B,A) & m1_subset_1(C,k5_numbers) -> m2_finseq_1(k1_rfinseq(A,B,C),A))) # label(dt_k1_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5728 (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) -> (r1_rfinseq(A,B) <-> (exists C (v1_funct_2(C,k1_relat_1(A),k1_relat_1(A)) & v3_funct_2(C,k1_relat_1(A),k1_relat_1(A)) & m2_relset_1(C,k1_relat_1(A),k1_relat_1(A)) & v1_funct_1(C) & A = k5_relat_1(C,B))))))))) # label(t6_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5729 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_relat_1(C),A) & r1_tarski(k2_relat_1(B),A) -> (r1_rfinseq(B,C) <-> (all D (m1_subset_1(D,A) -> k1_card_1(k10_relat_1(C,k1_tarski(D))) = k1_card_1(k10_relat_1(B,k1_tarski(D))))))))))))) # label(t5_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5730 (all A (m2_finseq_1(A,k1_numbers) -> (exists B (r1_rfinseq(A,B) & m2_finseq_1(B,k1_numbers) & v1_rfinseq(B))))) # label(t35_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5731 (all A all B (v1_relat_1(A) & v1_relat_1(B) -> (r1_rfinseq(A,B) -> r1_rfinseq(B,A)))) # label(symmetry_r1_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5732 (all A (v1_funct_1(A) & v1_relat_1(A) & v1_finset_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) & v1_finset_1(B) -> ((all C k4_card_1(k10_relat_1(B,C)) = k4_card_1(k10_relat_1(A,C))) <-> r1_rfinseq(A,B)))))) # label(t9_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5733 (all A (m2_finseq_1(A,k1_numbers) & v1_rfinseq(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> m2_finseq_1(k1_rfinseq(k1_numbers,A,B),k1_numbers) & v1_rfinseq(k1_rfinseq(k1_numbers,A,B)))))) # label(t34_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5734 (all A (m2_finseq_1(A,k1_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,B) -> r1_xreal_0(k3_finseq_1(A),B) | k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(B,np__1)) = k15_rvsum_1(k2_rfinseq(k1_rfinseq(k1_numbers,A,B)))))))) # label(t30_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5735 $T # label(t12_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5736 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> B = k8_finseq_1(A,k16_finseq_1(A,B,C),k1_rfinseq(A,B,C)))))))) # label(t21_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5737 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C k1_card_1(k10_relat_1(B,C)) = k1_card_1(k10_relat_1(A,C))) <-> r1_rfinseq(A,B)))))) # label(t4_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5738 (all A (m2_finseq_1(A,k1_numbers) & v1_rfinseq(A) -> (all B (m2_finseq_1(B,k1_numbers) & v1_rfinseq(B) -> (r1_rfinseq(A,B) -> A = B))))) # label(t36_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5739 (all A (m2_finseq_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (B != np__0 -> k3_funct_2(k5_numbers,k1_numbers,A,k1_tarski(k6_real_1(C,B))) = k3_funct_2(k5_numbers,k1_numbers,k9_rvsum_1(B,A),k1_tarski(C))))))))) # label(t37_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5740 (all A all B (v1_relat_1(B) & v1_relat_1(A) -> r1_rfinseq(A,A))) # label(reflexivity_r1_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5741 (all A (m2_finseq_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (B = k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(D,np__1)) & C = k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(D,np__2)) & k1_nat_1(D,np__2) = k3_finseq_1(A) -> k8_finseq_1(k1_numbers,k16_finseq_1(k1_numbers,k2_rfinseq(A),D),k2_finseq_4(k1_numbers,k5_real_1(B,C),C)) = k2_rfinseq(A)))))))))) # label(t24_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5742 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (k1_funct_1(B,k1_nat_1(C,np__1)) = D & k1_nat_1(C,np__1) = k3_finseq_1(B) -> B = k7_finseq_1(k16_finseq_1(A,B,C),k9_finseq_1(D)))))))))) # label(t20_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5743 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_rfinseq(A,B) -> k2_relat_1(A) = k2_relat_1(B)))))) # label(t1_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5744 (all A (m2_finseq_1(A,k1_numbers) -> ((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(k1_nat_1(B,np__1),k4_finseq_1(A)) & r2_hidden(B,k4_finseq_1(A)) -> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(B,np__1)),k2_seq_1(k5_numbers,k1_numbers,A,B))))) <-> v1_rfinseq(A)))) # label(d4_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5745 (all A (m1_subset_1(A,k1_numbers) -> k12_finseq_1(k1_numbers,A) = k2_rfinseq(k12_finseq_1(k1_numbers,A)))) # label(t26_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5746 (all A (v1_finset_1(A) & v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_finset_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (r1_rfinseq(A,B) -> k4_card_1(k1_relat_1(A)) = k4_card_1(k1_relat_1(B))))))) # label(t10_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5747 (all A (m2_finseq_1(A,k1_numbers) -> (all B (m2_finseq_1(B,k1_numbers) -> (k2_rfinseq(A) = B <-> k3_finseq_1(A) = k3_finseq_1(B) & k2_seq_1(k5_numbers,k1_numbers,B,k3_finseq_1(B)) = k2_seq_1(k5_numbers,k1_numbers,A,k3_finseq_1(A)) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,C) & r1_xreal_0(C,k5_real_1(k3_finseq_1(B),np__1)) -> k5_real_1(k2_seq_1(k5_numbers,k1_numbers,A,C),k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(C,np__1))) = k2_seq_1(k5_numbers,k1_numbers,B,C))))))))) # label(d3_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5748 (all A (v1_funct_1(A) & v1_relat_1(A) & v1_finseq_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (r1_rfinseq(A,B) -> k3_finseq_1(A) = k3_finseq_1(B) & k4_finseq_1(A) = k4_finseq_1(B)))))) # label(t16_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5749 (all A (m2_finseq_1(A,k1_numbers) -> (all B (m2_finseq_1(B,k1_numbers) -> (r1_rfinseq(A,B) -> k15_rvsum_1(B) = k15_rvsum_1(A)))))) # label(t22_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5750 (all A (m1_finseq_1(A,k1_numbers) -> m2_finseq_1(k2_rfinseq(A),k1_numbers))) # label(dt_k2_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5751 (all A (m2_finseq_1(A,k1_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k1_rfinseq(k1_numbers,k2_rfinseq(A),B) = k2_rfinseq(k1_rfinseq(k1_numbers,A,B)))))) # label(t28_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5752 (all A (m2_finseq_1(A,k1_numbers) -> (k3_finseq_1(A) != np__0 -> k2_seq_1(k5_numbers,k1_numbers,A,np__1) = k15_rvsum_1(k2_rfinseq(A))))) # label(t29_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5753 (exists A (v1_finset_1(A) & m1_finseq_1(A,k1_numbers) & v1_funct_1(A) & v1_finseq_1(A) & v1_rfinseq(A) & v1_relat_1(A))) # label(rc1_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5754 (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) -> (r1_rfinseq(A,B) <-> (exists C (v3_funct_2(C,k4_finseq_1(B),k4_finseq_1(B)) & v1_funct_2(C,k4_finseq_1(B),k4_finseq_1(B)) & v1_funct_1(C) & m2_relset_1(C,k4_finseq_1(B),k4_finseq_1(B)) & k5_relat_1(C,B) = A))))))) # label(t17_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5755 $T # label(t8_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5756 (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 k4_card_1(k10_relat_1(B,C)) = k4_card_1(k10_relat_1(A,C))) <-> r1_rfinseq(A,B)))))) # label(t13_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5757 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((exists C (k1_relat_1(A) = k1_relat_1(C) & k2_relat_1(C) = k1_relat_1(B) & v1_relat_1(C) & v1_funct_1(C) & v2_funct_1(C) & A = k5_relat_1(C,B))) <-> r1_rfinseq(A,B)))))) # label(t3_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5758 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_finset_1(B) -> (exists C (v1_relat_1(C) & r1_rfinseq(k7_relat_1(A,B),C) & v1_funct_1(C) & v1_finseq_1(C))))))) # label(t18_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5759 (all A all B (v1_relat_1(A) & v1_finset_1(B) & v1_funct_1(A) -> v1_finset_1(k7_relat_1(A,B)) & v1_relat_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)))) # label(fc1_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5760 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_rfinseq(A,B) <-> (all C k1_card_1(k10_relat_1(B,k1_tarski(C))) = k1_card_1(k10_relat_1(A,k1_tarski(C))))))))) # label(d1_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5761 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(C,k4_finseq_1(B)) & r2_hidden(D,k2_finseq_1(C)) -> r2_hidden(D,k4_finseq_1(B)) & k1_funct_1(k16_finseq_1(A,B,C),D) = k1_funct_1(B,D)))))))))) # label(t19_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5762 (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_rfinseq(A,B) & r1_rfinseq(A,C) -> r1_rfinseq(B,C)))))))) # label(t2_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5763 (all A (v1_rfinseq(A) & m2_finseq_1(A,k1_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> v1_rfinseq(k16_finseq_1(k1_numbers,A,B)) & m2_finseq_1(k16_finseq_1(k1_numbers,A,B),k1_numbers))))) # label(t33_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5764 (all A all B (m2_finseq_1(B,A) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_finseq_1(D,A) -> (r1_xreal_0(C,k3_finseq_1(B)) -> ((all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (r2_hidden(E,k4_finseq_1(D)) -> k1_funct_1(D,E) = k1_funct_1(B,k1_nat_1(E,C))))) & k3_finseq_1(D) = k5_real_1(k3_finseq_1(B),C) <-> k1_rfinseq(A,B,C) = D)) & (-r1_xreal_0(C,k3_finseq_1(B)) -> (D = k6_finseq_1(A) <-> D = k1_rfinseq(A,B,C))))))))) # label(d2_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5765 (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) -> r1_rfinseq(k7_finseq_1(A,B),k7_finseq_1(B,A)))))) # label(t15_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5766 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_finset_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_finset_1(C) & v1_relat_1(C) -> (r1_tarski(k2_relat_1(B),A) & r1_tarski(k2_relat_1(C),A) -> (r1_rfinseq(B,C) <-> (all D (m1_subset_1(D,A) -> k4_card_1(k10_relat_1(B,k1_tarski(D))) = k4_card_1(k10_relat_1(C,k1_tarski(D))))))))))))) # label(t11_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5767 (all A (m2_finseq_1(A,k1_numbers) -> (np__1 = k3_finseq_1(A) | np__0 = k3_finseq_1(A) -> v1_rfinseq(A)))) # label(t31_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5768 (all A (m2_finseq_1(A,k1_numbers) -> k4_finseq_1(A) = k3_funct_2(k5_numbers,k1_numbers,k9_rvsum_1(np__0,A),k1_tarski(np__0)))) # label(t38_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5769 (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 (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (r1_rfinseq(A,B) <-> r1_rfinseq(k7_finseq_1(A,C),k7_finseq_1(B,C))))))))) # label(t14_rfinseq) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5770 (all A (-v1_finset_1(A) -> m1_card_fil(k5_card_fil(A),A))) # label(dt_k5_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5771 (all A (-v1_finset_1(A) & v1_card_1(A) -> (v7_card_fil(A) -> v4_card_fil(A)))) # label(t39_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5772 (all A (v1_card_1(A) & -v1_finset_1(A) -> (v7_card_fil(A) -> v1_card_5(A)))) # label(t33_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5773 (all A (-v1_xboole_0(A) -> (all B (m1_card_fil(B,A) -> (all C (-v1_xboole_0(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(k3_subset_1(A,D),B)))) -> -r2_hidden(A,C) & (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (all E (m1_subset_1(E,k1_zfmisc_1(A)) -> (r2_hidden(E,C) & r2_hidden(D,C) -> r2_hidden(k4_subset_1(A,D,E),C)) & (r2_hidden(D,C) & r1_tarski(E,D) -> r2_hidden(E,C))))))))))))) # label(t7_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5774 (all A (-v1_xboole_0(A) -> (exists B m2_card_fil(B,A)))) # label(existence_m2_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5775 (all A (-v1_xboole_0(A) -> (all B (m1_card_fil(B,A) -> (exists C (v3_card_fil(C,A) & r1_tarski(B,C) & m1_card_fil(C,A))))))) # label(t17_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5776 (all A (v4_card_fil(A) & -v1_finset_1(A) & v1_card_1(A) -> v2_ordinal1(A) & v3_ordinal1(A) & -v1_xboole_0(A) & v1_card_5(A) & -v1_finset_1(A) & v2_card_1(A) & v1_card_1(A) & v1_ordinal1(A))) # label(cc2_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5777 (all A (-v1_finset_1(A) -> m2_card_fil(k6_card_fil(A),A))) # label(dt_k6_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5778 (all A (v1_card_1(A) & -v2_card_1(A) -> v1_card_1(k7_card_fil(A)))) # label(dt_k7_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5779 (all A (-v1_xboole_0(A) -> -r2_hidden(k1_xboole_0,k1_tarski(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) & r2_hidden(B,k1_tarski(A)) -> r2_hidden(C,k1_tarski(A))) & (r2_hidden(C,k1_tarski(A)) & r2_hidden(B,k1_tarski(A)) -> r2_hidden(k5_subset_1(A,B,C),k1_tarski(A))))))) & m1_subset_1(k1_tarski(A),k1_zfmisc_1(k1_zfmisc_1(A))) & -v1_xboole_0(k1_tarski(A)))) # label(t2_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5780 (all A (-v1_finset_1(A) & v1_card_1(A) -> ((exists B (-v2_card_fil(B,A) & v3_card_fil(B,A) & r1_card_fil(A,A,B) & m1_card_fil(B,A))) <-> v7_card_fil(A)))) # label(d16_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5781 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(D,k1_zfmisc_1(B)) & m1_card_fil(C,B) -> ((exists E (r2_hidden(E,C) & A = k5_subset_1(B,E,D) & m1_subset_1(E,k1_zfmisc_1(B)))) <-> r2_hidden(A,a_3_1_card_fil(B,C,D))))) # label(fraenkel_a_3_1_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5782 (all A (-v1_xboole_0(A) -> (all B (m1_card_fil(B,A) -> (v1_card_fil(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r2_hidden(C,B) -> k1_card_1(A) = k1_card_1(C))))))))) # label(d5_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5783 (all A (v1_card_1(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) & -v1_xboole_0(C) -> (r1_card_fil(B,A,C) -> r2_card_fil(B,A,k7_setfam_1(B,C))))))))) # label(t12_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5784 (all A (-v1_xboole_0(A) -> m1_subset_1(k4_card_fil(A),k1_zfmisc_1(k1_zfmisc_1(k1_zfmisc_1(A)))) & -v1_xboole_0(k4_card_fil(A)))) # label(dt_k4_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5785 (all A (v1_card_1(A) -> r1_tarski(k2_card_1(A),k3_card_2(np__2,A)))) # label(t24_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5786 (all A (v1_card_1(A) & -v1_finset_1(A) -> (v1_card_5(A) & v2_card_1(A) <-> v4_card_fil(A)))) # label(d13_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5787 (all A all B (-v1_xboole_0(B) -> ((exists C (m1_card_fil(C,B) & C = A & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))))) <-> r2_hidden(A,a_1_0_card_fil(B))))) # label(fraenkel_a_1_0_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5788 (all A (-v1_finset_1(A) & v1_card_1(A) & -v2_card_1(A) -> (all B (m2_card_fil(B,A) -> -(r1_tarski(k6_card_fil(A),B) & (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> -((all D -(r2_hidden(D,B) & r2_hidden(D,C))) & A = k1_card_1(C) & (all D all E (r2_hidden(D,C) & r2_hidden(E,C) -> r1_xboole_0(D,E) | E = D))))) & r2_card_fil(A,A,B)))))) # label(t35_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5789 (all A all B k1_card_fil(A,B) = k4_xboole_0(A,B)) # label(redefinition_k1_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5790 (all A (v1_card_1(A) & -v1_finset_1(A) -> (v7_card_fil(A) -> v5_card_fil(A)))) # label(t40_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5791 (all A all B (v1_card_1(B) -> -((all C -(k1_card_1(C) = B & r1_tarski(C,A))) & r1_tarski(B,k1_card_1(A))))) # label(t36_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5792 (all A (v1_card_1(A) & v6_card_fil(A) & -v1_finset_1(A) -> v1_ordinal1(A) & v2_ordinal1(A) & v1_card_5(A) & v3_ordinal1(A) & v1_card_1(A) & v2_card_1(A) & v5_card_fil(A) & -v1_finset_1(A) & -v1_xboole_0(A))) # label(cc4_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5793 (all A all B (m1_card_fil(B,A) & -v1_xboole_0(A) -> k2_card_fil(A,k2_card_fil(A,B)) = B)) # label(involutiveness_k2_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5794 (all A all B (-v1_finset_1(B) -> ((exists C (m1_subset_1(C,k1_zfmisc_1(B)) & r2_hidden(k1_card_1(k1_card_fil(B,C)),k1_card_1(B)) & A = C)) <-> r2_hidden(A,a_1_1_card_fil(B))))) # label(fraenkel_a_1_1_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5795 (all A all B (-v1_finset_1(B) -> r2_hidden(k1_card_1(k1_tarski(A)),k1_card_1(B)))) # label(t1_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5796 (all A (v1_card_1(A) & -v1_finset_1(A) -> (v5_card_fil(A) & v1_card_5(A) <-> v6_card_fil(A)))) # label(d15_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5797 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_card_fil(B,A) & -v1_xboole_0(A) -> m1_subset_1(k3_card_fil(A,B,C),k1_zfmisc_1(k1_zfmisc_1(A))) & -v1_xboole_0(k3_card_fil(A,B,C)))) # label(dt_k3_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.07 5798 (all A (-v1_finset_1(A) -> (exists B (-v1_xboole_0(B) & v3_card_fil(B,A) & m1_card_fil(B,A) & -v2_card_fil(B,A))))) # label(rc1_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.08 5799 (all A (-v1_xboole_0(A) -> a_1_0_card_fil(A) = k4_card_fil(A))) # label(d9_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.08 5800 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> a_2_1_card_fil(A,B) = k7_setfam_1(A,B))))) # label(t9_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.08 5801 (all A (-v1_finset_1(A) & -v2_card_1(A) & v1_card_1(A) -> v1_ordinal1(k7_card_fil(A)) & -v1_xboole_0(k7_card_fil(A)) & v2_ordinal1(k7_card_fil(A)) & v1_card_1(k7_card_fil(A)) & -v1_finset_1(k7_card_fil(A)) & v3_ordinal1(k7_card_fil(A)))) # label(fc4_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.08 5802 (all A (-v1_xboole_0(A) -> (all B (m1_card_fil(B,A) -> r2_hidden(A,B))))) # label(t5_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.08 5803 (all A (v1_card_1(A) & -v1_finset_1(A) & -v2_card_1(A) -> (exists B (m2_relset_1(B,k2_zfmisc_1(k7_card_fil(A),A),k1_zfmisc_1(A)) & v1_funct_2(B,k2_zfmisc_1(k7_card_fil(A),A),k1_zfmisc_1(A)) & r4_card_fil(A,B) & v1_funct_1(B))))) # label(t34_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.08 5804 (all A (-v1_finset_1(A) -> k6_card_fil(A) = k2_card_fil(A,k5_card_fil(A)))) # label(d11_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.08 5805 (all A (-v1_finset_1(A) -> (all B (m1_card_fil(B,A) -> (v3_card_fil(B,A) & r1_card_fil(A,k1_card_1(A),B) -> v2_card_fil(B,A) | v1_card_fil(B,A)))))) # label(t23_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.08 5806 (all A (-v1_finset_1(A) -> k5_card_fil(A) = a_1_1_card_fil(A))) # label(d10_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.08 5807 (all A (r2_hidden(A,a_0_0_card_fil) <-> (exists B (p1_s1_card_fil(B) & B = A & m1_subset_1(B,f1_s1_card_fil))))) # label(fraenkel_a_0_0_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.08 5808 (all A (-v1_xboole_0(A) -> (all B (m2_card_fil(B,A) -> r2_hidden(k1_xboole_0,B))))) # label(t11_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.08 5809 (all A (-v1_xboole_0(A) -> (all B (m2_card_fil(B,A) -> m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) & -v1_xboole_0(B))))) # label(dt_m2_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.08 5810 (all A (-v1_finset_1(A) & v1_card_1(A) & v6_card_fil(A) -> v3_ordinal1(A) & v4_card_fil(A) & v1_card_5(A) & v1_card_1(A) & -v1_finset_1(A) & -v1_xboole_0(A) & v2_ordinal1(A) & v1_ordinal1(A) & v2_card_1(A))) # label(cc5_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.08 5811 (all A (v1_card_1(A) & -v1_finset_1(A) -> (v6_card_fil(A) -> v4_card_fil(A)))) # label(t30_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.08 5812 (all A (-v1_finset_1(A) -> (all B (m1_card_fil(B,A) -> (r1_tarski(k5_card_fil(A),B) -> v1_card_fil(B,A)))))) # label(t20_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.08 5813 (all A all B all C all D (m2_relset_1(C,k2_zfmisc_1(k7_card_fil(B),B),k1_zfmisc_1(B)) & v1_funct_1(C) & -v1_finset_1(B) & -v2_card_1(B) & m1_subset_1(D,k7_card_fil(B)) & v1_funct_2(C,k2_zfmisc_1(k7_card_fil(B),B),k1_zfmisc_1(B)) & v1_card_1(B) -> (r2_hidden(A,a_3_2_card_fil(B,C,D)) <-> (exists E (m1_subset_1(E,B) & r2_hidden(E,B) & A = k2_binop_1(k7_card_fil(B),B,k1_zfmisc_1(B),C,D,E)))))) # label(fraenkel_a_3_2_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.08 5814 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) & -v1_xboole_0(B) & -v1_xboole_0(C) -> ((exists D (r2_hidden(k3_subset_1(B,D),C) & D = A & m1_subset_1(D,k1_zfmisc_1(B)))) <-> r2_hidden(A,a_2_0_card_fil(B,C))))) # label(fraenkel_a_2_0_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.08 5815 (all A (-v1_finset_1(A) & v1_card_1(A) -> (v5_card_fil(A) -> v2_card_1(A)))) # label(t27_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.08 5816 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_card_fil(C,A) -> ((all D (m1_subset_1(D,k1_zfmisc_1(A)) -> -(r1_xboole_0(D,B) & r2_hidden(D,C)))) -> r2_hidden(B,k3_card_fil(A,C,B)) & r1_tarski(C,k3_card_fil(A,C,B)) & m1_card_fil(k3_card_fil(A,C,B),A)))))))) # label(t14_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5817 (all A (-v1_finset_1(A) -> -v1_xboole_0(k1_card_1(A)) & v3_ordinal1(k1_card_1(A)) & v2_ordinal1(k1_card_1(A)) & v1_ordinal1(k1_card_1(A)) & v1_card_1(k1_card_1(A)) & -v1_finset_1(k1_card_1(A)))) # label(fc1_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5818 (all A (-v1_xboole_0(A) -> m1_card_fil(k1_tarski(A),A))) # label(t4_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5819 (all A all B all C all D (m1_card_fil(C,B) & -v1_xboole_0(B) & m1_subset_1(D,k1_zfmisc_1(B)) -> ((exists E (m1_subset_1(E,k1_zfmisc_1(B)) & A = E & (exists F (r2_hidden(F,a_3_1_card_fil(B,C,D)) & r1_tarski(F,E) & m1_subset_1(F,k1_zfmisc_1(B)))))) <-> r2_hidden(A,a_3_0_card_fil(B,C,D))))) # label(fraenkel_a_3_0_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5820 (all A (-v2_card_1(A) & -v1_finset_1(A) & v1_card_1(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(k7_card_fil(A),A),k1_zfmisc_1(A)) & m2_relset_1(B,k2_zfmisc_1(k7_card_fil(A),A),k1_zfmisc_1(A)) -> ((all C (m1_subset_1(C,k7_card_fil(A)) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (E != D -> v1_xboole_0(k5_subset_1(A,k2_binop_1(k7_card_fil(A),A,k1_zfmisc_1(A),B,C,D),k2_binop_1(k7_card_fil(A),A,k1_zfmisc_1(A),B,C,E)))))))))) & (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,k7_card_fil(A)) -> (all E (m1_subset_1(E,k7_card_fil(A)) -> (E != D -> v1_xboole_0(k5_subset_1(A,k2_binop_1(k7_card_fil(A),A,k1_zfmisc_1(A),B,D,C),k2_binop_1(k7_card_fil(A),A,k1_zfmisc_1(A),B,E,C)))))))))) & (all C (m1_subset_1(C,A) -> r1_tarski(k1_card_1(k1_card_fil(A,k3_tarski(a_3_3_card_fil(A,B,C)))),k7_card_fil(A)))) & (all C (m1_subset_1(C,k7_card_fil(A)) -> r1_tarski(k1_card_1(k1_card_fil(A,k3_tarski(a_3_2_card_fil(A,B,C)))),k7_card_fil(A)))) <-> r4_card_fil(A,B)))))) # label(d18_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5821 (all A (-v1_xboole_0(A) -> (all B (v1_card_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) & -v1_xboole_0(C) -> ((all D (-v1_xboole_0(D) -> (r1_tarski(D,C) & r2_hidden(k1_card_1(D),B) -> r2_hidden(k3_tarski(D),C)))) <-> r2_card_fil(A,B,C)))))))) # label(d4_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5822 (all A (v1_card_1(A) & -v2_card_1(A) -> (all B (v1_card_1(B) -> (k7_card_fil(A) = B <-> k2_card_1(B) = A))))) # label(d17_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5823 (all A (-v1_xboole_0(A) -> (all B (m1_card_fil(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> a_3_0_card_fil(A,B,C) = k3_card_fil(A,B,C))))))) # label(d8_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5824 (all A (-v2_card_1(A) & -v1_finset_1(A) & v1_card_1(A) -> (all B (m1_card_fil(B,A) -> -(v3_card_fil(B,A) & v1_card_fil(B,A) & r1_card_fil(A,A,B)))))) # label(t37_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5825 (all A all B all C (-v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) -> ((exists D (m1_subset_1(D,k1_zfmisc_1(B)) & r2_hidden(D,C) & k3_subset_1(B,D) = A)) <-> r2_hidden(A,a_2_1_card_fil(B,C))))) # label(fraenkel_a_2_1_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5826 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_card_fil(C,A) -> -(r2_hidden(B,C) & r2_hidden(k1_card_fil(A,B),C)))))))) # label(t6_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5827 (all A (-v1_finset_1(A) -> (all B (v3_card_fil(B,A) & m1_card_fil(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (-r2_hidden(C,k2_card_fil(A,B)) <-> r2_hidden(C,B)))))))) # label(t22_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5828 (all A (-v1_xboole_0(A) -> (all B (v1_card_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) & -v1_xboole_0(C) -> ((all D (-v1_xboole_0(D) -> (r2_hidden(k1_card_1(D),B) & r1_tarski(D,C) -> r2_hidden(k1_setfam_1(D),C)))) <-> r1_card_fil(A,B,C)))))))) # label(d3_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5829 (all A (v1_card_1(A) & -v1_finset_1(A) -> -v1_finset_1(k2_card_1(A)) & v1_card_1(k2_card_1(A)) & v2_ordinal1(k2_card_1(A)) & v1_ordinal1(k2_card_1(A)) & -v1_xboole_0(k2_card_1(A)) & -v2_card_1(k2_card_1(A)) & v3_ordinal1(k2_card_1(A)))) # label(fc3_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5830 (all A (-v1_xboole_0(A) -> (all B (r2_hidden(B,k4_card_fil(A)) <-> m1_card_fil(B,A))))) # label(t15_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5831 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_card_fil(C,A) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((exists E (r1_tarski(k5_subset_1(A,E,B),D) & m1_subset_1(E,k1_zfmisc_1(A)) & r2_hidden(E,C))) <-> r2_hidden(D,k3_card_fil(A,C,B))))))))))) # label(t13_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5832 (all A (-v1_finset_1(A) & v1_card_1(A) -> (v7_card_fil(A) -> v2_card_1(A)))) # label(t38_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5833 (all A (-v1_finset_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (r2_hidden(k1_card_1(k1_card_fil(A,B)),k1_card_1(A)) <-> r2_hidden(B,k5_card_fil(A))))))) # label(t18_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5834 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) & -v1_xboole_0(A) & -v1_xboole_0(B) -> -v1_xboole_0(k7_setfam_1(A,B)))) # label(fc2_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5835 (exists A (v2_ordinal1(A) & -v1_finset_1(A) & v1_card_1(A) & -v2_card_1(A) & v1_ordinal1(A) & v3_ordinal1(A) & -v1_xboole_0(A))) # label(rc2_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5836 (all A (-v1_xboole_0(A) -> (all B (m1_card_fil(B,A) -> m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) & -v1_xboole_0(B))))) # label(dt_m1_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5837 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> a_2_0_card_fil(A,B) = k7_setfam_1(A,B))))) # label(t8_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5838 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(D,B) & r2_hidden(C,B) -> r2_hidden(k4_subset_1(A,C,D),B)) & (r1_tarski(D,C) & r2_hidden(C,B) -> r2_hidden(D,B)))))) & -r2_hidden(A,B) <-> m2_card_fil(B,A)))))) # label(d2_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5839 (all A (v1_card_1(A) & -v1_finset_1(A) -> (r3_card_fil & v4_card_fil(A) -> v6_card_fil(A)))) # label(t31_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5840 r2_hidden(f2_s1_card_fil,a_0_0_card_fil) -> p1_s1_card_fil(f2_s1_card_fil) # label(s1_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5841 (all A (v3_ordinal1(A) & v4_ordinal1(A) -> (all B (k7_ordinal2(B) = A & r1_tarski(B,A) -> k3_tarski(B) = A)))) # label(t32_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5842 (all A all B m1_subset_1(k1_card_fil(A,B),k1_zfmisc_1(A))) # label(dt_k1_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5843 (all A all B (m1_card_fil(B,A) & -v1_xboole_0(A) -> k7_setfam_1(A,B) = k2_card_fil(A,B))) # label(redefinition_k2_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5844 (all A all B (m1_card_fil(B,A) & -v1_xboole_0(A) -> m2_card_fil(k2_card_fil(A,B),A))) # label(dt_k2_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5845 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k4_card_fil(A))) -> (v6_ordinal1(B) -> m1_card_fil(k3_tarski(B),A)))))) # label(t16_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5846 r3_card_fil <-> (all A (v1_card_1(A) & -v1_finset_1(A) -> k2_card_1(A) = k3_card_2(np__2,A))) # label(d12_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5847 (all A (v1_card_1(A) & -v1_finset_1(A) -> (r3_card_fil & v2_card_1(A) -> v5_card_fil(A)))) # label(t28_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5848 (all A (v1_card_1(A) & -v1_finset_1(A) & -v2_card_1(A) -> -v1_finset_1(A) & v2_ordinal1(A) & v1_ordinal1(A) & -v1_xboole_0(A) & v1_card_5(A) & v1_card_1(A) & v3_ordinal1(A))) # label(cc6_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5849 (all A (-v1_xboole_0(A) -> (exists B m1_card_fil(B,A)))) # label(existence_m1_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5850 (all A (-v1_finset_1(A) -> (all B (m1_card_fil(B,A) -> (v1_card_fil(B,A) & v3_card_fil(B,A) -> r1_tarski(k5_card_fil(A),B)))))) # label(t21_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5851 (all A (-v1_xboole_0(A) -> (all B (m1_card_fil(B,A) -> ((exists 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) -> r1_tarski(C,D)))))) <-> v2_card_fil(B,A)))))) # label(d6_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5852 (all A (-v1_finset_1(A) & v1_card_1(A) -> (v7_card_fil(A) -> v6_card_fil(A)))) # label(t41_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5853 (all A (v5_card_fil(A) & v1_card_1(A) & -v1_finset_1(A) -> v2_card_1(A) & v3_ordinal1(A) & v1_ordinal1(A) & v2_ordinal1(A) & -v1_xboole_0(A) & v1_card_1(A) & -v1_finset_1(A))) # label(cc3_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5854 (all A all B all C all D (-v1_finset_1(B) & v1_funct_2(C,k2_zfmisc_1(k7_card_fil(B),B),k1_zfmisc_1(B)) & v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(k7_card_fil(B),B),k1_zfmisc_1(B)) & m1_subset_1(D,B) & -v2_card_1(B) & v1_card_1(B) -> (r2_hidden(A,a_3_3_card_fil(B,C,D)) <-> (exists E (m1_subset_1(E,k7_card_fil(B)) & r2_hidden(E,k7_card_fil(B)) & A = k2_binop_1(k7_card_fil(B),B,k1_zfmisc_1(B),C,E,D)))))) # label(fraenkel_a_3_3_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5855 (all A (-v1_xboole_0(A) -> (all B (m1_card_fil(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r1_tarski(C,D) & r2_hidden(C,B) -> r2_hidden(D,B)) & (r2_hidden(C,B) & r2_hidden(D,B) -> r2_hidden(k5_subset_1(A,C,D),B)))))) & -v1_xboole_0(B) & -r2_hidden(k1_xboole_0,B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))))))) # label(t3_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5856 (all A (-v1_finset_1(A) -> (all B (m1_card_fil(B,A) -> (v3_card_fil(B,A) & v1_card_fil(B,A) -> -v2_card_fil(B,A)))))) # label(cc1_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5857 (all A (-v1_xboole_0(A) -> (all B (m1_card_fil(B,A) -> (all C (m2_card_fil(C,A) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> -(r2_hidden(D,B) & r2_hidden(D,k2_card_fil(A,B))))) & (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> -(r2_hidden(D,C) & r2_hidden(D,k7_setfam_1(A,C))))))))))) # label(t10_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5858 (all A (-v1_finset_1(A) & v1_card_1(A) -> (v5_card_fil(A) <-> (all B (v1_card_1(B) -> (r2_hidden(B,A) -> r2_hidden(k3_card_2(np__2,B),A))))))) # label(d14_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5859 (all A (-v1_xboole_0(A) -> (all B (m1_card_fil(B,A) -> (v3_card_fil(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> r2_hidden(C,B) | r2_hidden(k1_card_fil(A,C),B)))))))) # label(d7_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5860 (all A (-v1_finset_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (r2_hidden(k1_card_1(B),k1_card_1(A)) <-> r2_hidden(B,k6_card_fil(A))))))) # label(t19_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5861 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (m1_card_fil(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(C,B) & r1_tarski(C,D) -> r2_hidden(D,B)) & (r2_hidden(C,B) & r2_hidden(D,B) -> r2_hidden(k5_subset_1(A,C,D),B)))))) & -r2_hidden(k1_xboole_0,B)))))) # label(d1_card_fil) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5862 (all A all B (m1_pboole(B,A) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(C,k4_card_3(B)) -> r2_hidden(k5_relat_1(D,C),k4_card_3(k5_relat_1(D,B)))))))))) # label(t11_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5863 (all A all B all C (m1_pboole(B,A) & m1_subset_1(C,k1_zfmisc_1(A)) -> k7_relat_1(B,C) = k3_pre_circ(A,B,C))) # label(redefinition_k3_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5864 (all A all B (v1_relat_1(A) & v1_finset_1(A) & v3_trees_2(A) & m1_subset_1(B,k1_relat_1(A)) & v1_funct_1(A) -> v1_relat_1(k5_trees_2(A,B)) & v3_trees_2(k5_trees_2(A,B)) & v1_funct_1(k5_trees_2(A,B)) & v1_finset_1(k5_trees_2(A,B)))) # label(fc4_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5865 (all A (v1_funct_1(k1_trees_4(A)) & v3_trees_2(k1_trees_4(A)) & v1_finset_1(k1_trees_4(A)) & v1_relat_1(k1_trees_4(A)))) # label(fc6_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5866 (all A all B (m1_pboole(B,A) & v2_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (m1_subset_1(D,k4_card_3(B)) -> ((all E (r2_hidden(E,k1_relat_1(C)) -> r2_hidden(k1_funct_1(C,E),k1_funct_1(B,E)))) & r1_tarski(k1_relat_1(C),k1_relat_1(B)) -> m1_subset_1(k1_funct_4(D,C),k4_card_3(B))))))))) # label(t9_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5867 (all A (m1_subset_1(A,f1_s4_pre_circ) -> (r2_hidden(A,f2_s4_pre_circ) -> v1_funct_1(f5_s4_pre_circ(A)) & m2_relset_1(f5_s4_pre_circ(A),k1_funct_1(f3_s4_pre_circ,A),k1_funct_1(f4_s4_pre_circ,A)) & v1_funct_2(f5_s4_pre_circ(A),k1_funct_1(f3_s4_pre_circ,A),k1_funct_1(f4_s4_pre_circ,A))))) -> (exists A (m3_pboole(A,f2_s4_pre_circ,f3_s4_pre_circ,f4_s4_pre_circ) & (all B (m1_subset_1(B,f1_s4_pre_circ) -> (r2_hidden(B,f2_s4_pre_circ) -> f5_s4_pre_circ(B) = k1_funct_1(A,B)))))) # label(s4_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5868 (all A (-v1_xboole_0(A) -> (all B all C (m1_pboole(C,A) & v2_relat_1(C) -> (all D (m3_pboole(D,A,k2_pre_circ(A,B),C) -> k1_relat_1(k10_funct_6(D)) = B)))))) # label(t8_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5869 $T # label(d2_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5870 (all A all B k2_funcop_1(A,B) = k2_pre_circ(A,B)) # label(redefinition_k2_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5871 (all A (v1_trees_1(A) & v1_finset_1(A) & -v1_xboole_0(A) -> (all B (m1_trees_1(B,A) -> -(r1_xreal_0(k4_card_1(A),k4_card_1(k4_trees_1(A,B))) & k1_xboole_0 != B))))) # label(t20_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5872 (all A all B (v2_relat_1(A) & v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k7_relat_1(A,B)) & v2_relat_1(k7_relat_1(A,B)) & v1_relat_1(k7_relat_1(A,B)))) # label(fc2_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5873 (all A k4_card_1(k1_trees_4(A)) = np__1) # label(t24_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5874 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) & v6_trees_3(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(k1_nat_1(B,np__1),k4_finseq_1(A)) -> r2_hidden(k12_finseq_1(k5_numbers,B),k13_trees_3(k2_funct_6(A)))))))) # label(t17_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5875 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_pboole(C,A) & v2_relat_1(C) -> (all D (m3_pboole(D,A,k2_pre_circ(A,B),C) -> (all E (m1_subset_1(E,B) -> (exists F (m1_pboole(F,A) & r3_pboole(A,F,C) & F = k1_funct_1(k10_funct_6(D),E))))))))))))) # label(t10_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5876 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k1_funct_4(A,C),k1_funct_4(B,C))))))))) # label(t3_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5877 (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_xboole_0(k1_relat_1(A),k1_relat_1(C)) & r1_tarski(A,B) -> r1_tarski(A,k1_funct_4(B,C))))))))) # label(t4_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5878 (all A all B all C (m1_trees_1(C,B) & v1_trees_1(B) & -v1_xboole_0(B) & v1_finset_1(B) -> (r2_hidden(A,a_2_1_pre_circ(B,C)) <-> (exists D (m1_trees_1(D,B) & D = A & -r1_tarski(C,D)))))) # label(fraenkel_a_2_1_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5879 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (k1_relat_1(A) = k1_tarski(B) & k2_relat_1(A) = k1_tarski(C) -> k1_tarski(k4_tarski(B,C)) = A)))) # label(t2_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5880 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) & v2_relat_1(B) -> -v1_xboole_0(k3_tarski(k2_relat_1(B))))))) # label(t6_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5881 (all A (-v1_xboole_0(A) & v1_trees_1(A) & v1_finset_1(A) -> (all B (-v1_xboole_0(B) & v1_finset_1(B) & v1_trees_1(B) -> (all C (m1_trees_1(C,A) -> k5_trees_1(A,C,B) = k2_xboole_0(a_2_1_pre_circ(A,C),a_3_0_pre_circ(A,B,C)))))))) # label(t14_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5882 (all A (-v1_xboole_0(A) & v5_membered(A) & v1_finset_1(A) -> v1_xreal_0(k2_seq_4(A)) & v4_ordinal2(k2_seq_4(A)) & v1_xcmplx_0(k2_seq_4(A)))) # label(fc1_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5883 (all A (v1_funct_1(A) & v1_relat_1(A) -> k1_card_1(k1_relat_1(A)) = k1_card_1(A))) # label(t21_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5884 (all A (-v1_xboole_0(A) & v2_membered(A) & v1_finset_1(A) -> (all B (v1_xreal_0(B) -> (r2_hidden(B,A) & (all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r1_xreal_0(C,B)))) <-> k1_pre_circ(A) = B))))) # label(d1_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5885 (exists A (v2_membered(A) & v3_membered(A) & v4_membered(A) & v1_membered(A) & -v1_xboole_0(A) & v5_membered(A) & v1_finset_1(A))) # label(rc1_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5886 (all A (v1_trees_1(A) & -v1_xboole_0(A) & v1_finset_1(A) -> (all B (m1_trees_1(B,A) -> r2_tarski(k4_trees_1(A,B),a_2_0_pre_circ(A,B)))))) # label(t13_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5887 (exists A ((all B (m1_subset_1(B,f1_s2_pre_circ) -> (r2_hidden(B,f1_s2_pre_circ) -> (-p1_s2_pre_circ(B) -> f3_s2_pre_circ(B) = k1_funct_1(A,B)) & (p1_s2_pre_circ(B) -> f2_s2_pre_circ(B) = k1_funct_1(A,B))))) & m1_pboole(A,f1_s2_pre_circ))) # label(s2_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5888 (all A (-v1_xboole_0(A) & v1_trees_1(A) & v1_finset_1(A) -> (all B (v1_finset_1(B) & -v1_xboole_0(B) & v1_trees_1(B) -> (all C (m1_trees_1(C,A) -> k1_nat_1(k4_card_1(A),k4_card_1(B)) = k1_nat_1(k4_card_1(k5_trees_1(A,C,B)),k4_card_1(k4_trees_1(A,C))))))))) # label(t22_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5889 (all A ((exists B (m1_subset_1(B,f1_s1_pre_circ) & A = f2_s1_pre_circ(B) & p1_s1_pre_circ(B))) <-> r2_hidden(A,a_0_0_pre_circ))) # label(fraenkel_a_0_0_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5890 (all A (v1_funct_1(A) & v3_trees_2(A) & v1_relat_1(A) & v1_finset_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v3_trees_2(B) -> (all C (m1_trees_1(C,k1_relat_1(A)) -> k1_nat_1(k4_card_1(A),k4_card_1(B)) = k1_nat_1(k4_card_1(k8_trees_2(A,C,B)),k4_card_1(k5_trees_2(A,C))))))))) # label(t23_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5891 (all A (-v1_xboole_0(A) & v2_membered(A) & v1_finset_1(A) -> k1_pre_circ(A) = k2_seq_4(A))) # label(redefinition_k1_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.09 5892 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v3_trees_2(A) -> (all B (v1_finset_1(B) & v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) -> (all C all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (v1_relat_1(E) & v1_finseq_1(E) & v6_trees_3(E) & v1_funct_1(E) -> -(r2_hidden(k12_finseq_1(k5_numbers,D),k1_relat_1(A)) & k4_trees_4(C,E) = A & (all F (v1_relat_1(F) & v1_finseq_1(F) & v6_trees_3(F) & v1_funct_1(F) -> -(k4_trees_4(C,F) = k8_trees_2(A,k12_finseq_1(k5_numbers,D),B) & (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (r2_hidden(G,k4_finseq_1(E)) -> G = k1_nat_1(D,np__1) | k1_funct_1(E,G) = k1_funct_1(F,G)))) & k1_funct_1(F,k1_nat_1(D,np__1)) = B & k3_finseq_1(E) = k3_finseq_1(F))))))))))))) # label(t19_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.10 5893 (all A (v1_finset_1(A) & v2_membered(A) & -v1_xboole_0(A) -> v1_xreal_0(k1_pre_circ(A)))) # label(dt_k1_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.10 5894 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_trees_3(A)) -> v1_finset_1(B))))) # label(cc1_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.10 5895 $T # label(t1_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.10 5896 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B k1_tarski(k2_finseq_2(A,B)) = k4_card_3(k2_finseq_2(A,k1_tarski(B)))))) # label(t12_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.10 5897 (all A all B (v1_funct_1(A) & v1_relat_1(A) & v1_funct_1(B) & v1_relat_1(B) & v2_relat_1(A) -> v1_funct_1(k5_relat_1(B,A)) & v1_relat_1(k5_relat_1(B,A)) & v2_relat_1(k5_relat_1(B,A)))) # label(fc3_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.10 5898 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_pboole(B,A) -> m1_pboole(k3_pre_circ(A,B,C),C))) # label(dt_k3_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.10 5899 (all A (v1_finseq_1(A) & v1_relat_1(A) & v4_trees_3(A) & v1_funct_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(k1_nat_1(B,np__1),k4_finseq_1(A)) -> k1_funct_1(A,k1_nat_1(B,np__1)) = k4_trees_1(k13_trees_3(A),k12_finseq_1(k5_numbers,B))))))) # label(t16_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.10 5900 (all A all B all C (v1_funct_1(A) & m1_subset_1(B,k1_relat_1(A)) & v1_funct_1(C) & v3_trees_2(C) & v3_trees_2(A) & v1_finset_1(C) & v1_relat_1(C) & v1_finset_1(A) & v1_relat_1(A) -> v1_finset_1(k8_trees_2(A,B,C)) & v1_relat_1(k8_trees_2(A,B,C)) & v1_funct_1(k8_trees_2(A,B,C)) & v3_trees_2(k8_trees_2(A,B,C)))) # label(fc5_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.10 5901 (all A k1_xboole_0 = k4_funct_5(k2_pre_circ(A,k1_xboole_0))) # label(t7_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.10 5902 (all A exists B (v1_funct_1(B) & v1_pre_circ(B,A) & v2_relat_1(B) & m1_pboole(B,A) & v1_relat_1(B))) # label(rc2_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.10 5903 (all A (v1_relat_1(A) & v4_trees_3(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_funct_1(B) & v4_trees_3(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (k3_finseq_1(B) = k3_finseq_1(A) & r2_hidden(k1_nat_1(C,np__1),k4_finseq_1(A)) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(A)) -> k1_nat_1(C,np__1) = D | k1_funct_1(A,D) = k1_funct_1(B,D)))) -> (all D (v1_trees_1(D) & -v1_xboole_0(D) -> (k1_funct_1(B,k1_nat_1(C,np__1)) = D -> k13_trees_3(B) = k5_trees_1(k13_trees_3(A),k12_finseq_1(k5_numbers,C),D))))))))))) # label(t18_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.10 5904 (all A all B all C all D (-v1_xboole_0(C) & v1_finset_1(C) & v1_trees_1(C) & -v1_xboole_0(B) & v1_finset_1(B) & v1_trees_1(B) & m1_trees_1(D,B) -> (r2_hidden(A,a_3_0_pre_circ(B,C,D)) <-> (exists E (m1_trees_1(E,C) & A = k8_finseq_1(k5_numbers,D,E)))))) # label(fraenkel_a_3_0_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.10 5905 (exists A ((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k8_funct_2(k5_numbers,f1_s3_pre_circ,A,k1_nat_1(B,np__1)) = f3_s3_pre_circ(B,k8_funct_2(k5_numbers,f1_s3_pre_circ,A,B)))) & v1_funct_1(A) & m2_relset_1(A,k5_numbers,f1_s3_pre_circ) & f2_s3_pre_circ = k8_funct_2(k5_numbers,f1_s3_pre_circ,A,np__0) & v1_funct_2(A,k5_numbers,f1_s3_pre_circ))) # label(s3_pre_circ_AndLHS) # label(axiom) # label(non_clause). [assumption]. 57.11/56.10 5906 (all A (v1_funct_2(A,k5_numbers,f1_s3_pre_circ) & v1_funct_1(A) & m2_relset_1(A,k5_numbers,f1_s3_pre_circ) -> (all B (v1_funct_1(B) & m2_relset_1(B,k5_numbers,f1_s3_pre_circ) & v1_funct_2(B,k5_numbers,f1_s3_pre_circ) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k8_funct_2(k5_numbers,f1_s3_pre_circ,A,k1_nat_1(C,np__1)) = f3_s3_pre_circ(C,k8_funct_2(k5_numbers,f1_s3_pre_circ,A,C)))) & f2_s3_pre_circ = k8_funct_2(k5_numbers,f1_s3_pre_circ,B,np__0) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k8_funct_2(k5_numbers,f1_s3_pre_circ,B,k1_nat_1(C,np__1)) = f3_s3_pre_circ(C,k8_funct_2(k5_numbers,f1_s3_pre_circ,B,C)))) & f2_s3_pre_circ = k8_funct_2(k5_numbers,f1_s3_pre_circ,A,np__0) -> A = B))))) # label(s3_pre_circ_AndRHS) # label(axiom) # label(non_clause). [assumption]. 57.11/56.10 5907 (all A all B all C (m1_trees_1(C,B) & -v1_xboole_0(B) & v1_trees_1(B) & v1_finset_1(B) -> ((exists D (m1_trees_1(D,B) & D = A & r1_tarski(C,D))) <-> r2_hidden(A,a_2_0_pre_circ(B,C))))) # label(fraenkel_a_2_0_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.10 5908 (all A all B (m1_pboole(B,A) -> k1_tarski(k1_xboole_0) = k1_funct_1(k6_pboole(A,B),k6_finseq_1(A)))) # label(t5_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.10 5909 (all A all B m1_pboole(k2_pre_circ(A,B),A)) # label(dt_k2_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.10 5910 (all A (v1_trees_1(A) & v1_finset_1(A) & -v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & v1_finset_1(B) & v1_trees_1(B) -> (all C (m1_trees_1(C,A) -> (all D (m2_finseq_1(D,k5_numbers) -> -(r1_tarski(C,D) & (all E (m1_trees_1(E,B) -> k8_finseq_1(k5_numbers,C,E) != D)) & r2_hidden(D,k5_trees_1(A,C,B))))))))))) # label(t15_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.10 5911 (all A all B (m1_pboole(B,A) -> ((all C (r2_hidden(C,A) -> v1_finset_1(k1_funct_1(B,C)))) <-> v1_pre_circ(B,A)))) # label(d3_pre_circ) # label(axiom) # label(non_clause). [assumption]. 57.11/56.10 5912 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) & v2_relat_1(C) -> ((all D (m1_pboole(D,A) -> (r1_pboole(A,D,C) -> r6_pboole(A,k3_pboole(A,D,B),k1_pboole(A))))) -> r6_pboole(A,k3_pboole(A,k2_mboolean(A,C),B),k1_pboole(A))))))) # label(t34_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.11/56.10 5913 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> ((all D (r2_hidden(D,A) -> k1_funct_1(C,D) = k3_tarski(k1_funct_1(B,D)))) <-> k2_mboolean(A,B) = C))))) # label(d2_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.11/56.10 5914 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,k4_pboole(A,C,D)) <-> r5_pboole(A,B,D) & r2_pboole(A,B,C)))))))) # label(t11_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.11/56.10 5915 (all A r6_pboole(A,k1_mboolean(A,k1_pboole(A)),k2_pre_circ(A,k1_tarski(k1_xboole_0)))) # label(t2_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.11/56.10 5916 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) -> r2_pboole(A,k2_mboolean(A,B),k2_mboolean(A,C))))))) # label(t27_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.11/56.10 5917 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k2_mboolean(A,k2_pboole(A,B,C)),k2_pboole(A,k2_mboolean(A,B),k2_mboolean(A,C))))))) # label(t28_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.11/56.10 5918 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (v2_relat_1(k2_pboole(A,B,C)) & (all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r1_pboole(A,D,k2_pboole(A,B,C)) & r1_pboole(A,E,k2_pboole(A,B,C)) -> E = D | r6_pboole(A,k3_pboole(A,D,E),k1_pboole(A))))))) -> r6_pboole(A,k2_mboolean(A,k3_pboole(A,B,C)),k3_pboole(A,k2_mboolean(A,B),k2_mboolean(A,C)))))))) # label(t35_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.11/56.10 5919 $T # label(t14_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.11/56.10 5920 (all A all B (m1_pboole(B,A) -> r6_pboole(A,k2_mboolean(A,k1_mboolean(A,B)),B))) # label(t30_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.11/56.10 5921 (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,k5_pboole(A,B,D),C)))))))) # label(t17_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.11/56.10 5922 (all A all B (m1_pboole(B,A) -> (all C (v2_relat_1(C) & m1_pboole(C,A) -> ((all D (m1_pboole(D,A) -> (r1_pboole(A,D,C) -> r2_pboole(A,D,B)))) -> r2_pboole(A,k2_mboolean(A,C),B)))))) # label(t33_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5923 (all A all B r6_pboole(A,k1_mboolean(A,k2_pre_circ(A,k1_tarski(B))),k2_pre_circ(A,k2_tarski(k1_xboole_0,k1_tarski(B))))) # label(t4_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5924 (all A all B all C r6_pboole(A,k2_mboolean(A,k2_pre_circ(A,k2_tarski(k1_tarski(B),k1_tarski(C)))),k2_pre_circ(A,k2_tarski(B,C)))) # label(t25_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5925 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) & v2_relat_1(D) -> (r2_pboole(A,C,k2_mboolean(A,k2_pboole(A,B,D))) & (all E (m1_pboole(E,A) -> (r1_pboole(A,E,D) -> r6_pboole(A,k3_pboole(A,E,C),k1_pboole(A))))) -> r2_pboole(A,C,k2_mboolean(A,B))))))))) # label(t36_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5926 (all A all B (m1_pboole(B,A) -> v1_relat_1(k1_mboolean(A,B)) & v2_relat_1(k1_mboolean(A,B)) & v1_funct_1(k1_mboolean(A,B)))) # label(fc1_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5927 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) -> r2_pboole(A,k4_pboole(A,B,D),C)))))))) # label(t16_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5928 (all A (v3_relat_1(k2_mboolean(A,k1_pboole(A))) & v1_funct_1(k2_mboolean(A,k1_pboole(A))) & v1_relat_1(k2_mboolean(A,k1_pboole(A))))) # label(fc2_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5929 (all A all B (m1_pboole(B,A) & v2_relat_1(B) & v1_pre_circ(B,A) -> ((all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> -(r1_pboole(A,D,B) & -r2_pboole(A,D,C) & -r2_pboole(A,C,D) & r1_pboole(A,C,B)))))) -> r1_pboole(A,k2_mboolean(A,B),B)))) # label(t37_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5930 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r5_pboole(A,B,k3_pboole(A,C,D)) & r2_pboole(A,B,k2_pboole(A,C,D)) <-> r2_pboole(A,B,k5_pboole(A,C,D))))))))) # label(t13_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5931 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r2_pboole(A,k2_pboole(A,k1_mboolean(A,k4_pboole(A,B,C)),k1_mboolean(A,k4_pboole(A,C,B))),k1_mboolean(A,k5_pboole(A,B,C))))))) # label(t12_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5932 (all A all B (m1_pboole(B,A) -> r2_pboole(A,B,k1_mboolean(A,k2_mboolean(A,B))))) # label(t31_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5933 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r6_pboole(A,k2_pboole(A,k1_mboolean(A,B),k1_mboolean(A,C)),k1_mboolean(A,k2_pboole(A,B,C))) -> (all D (r2_hidden(D,A) -> r3_xboole_0(k1_funct_1(B,D),k1_funct_1(C,D))))))))) # label(t8_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5934 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r2_pboole(A,k1_mboolean(A,k4_pboole(A,B,C)),k2_pboole(A,k2_pre_circ(A,k1_tarski(k1_xboole_0)),k4_pboole(A,k1_mboolean(A,B),k1_mboolean(A,C)))))))) # label(t10_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5935 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r2_pboole(A,k11_pboole(A,B,C),k1_mboolean(A,k1_mboolean(A,k2_pboole(A,B,C)))))))) # label(t18_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5936 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r1_pboole(A,B,k1_mboolean(A,C)) <-> r2_pboole(A,B,C)))))) # label(t19_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5937 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r1_pboole(A,D,B) & r2_pboole(A,k2_mboolean(A,B),C) -> r2_pboole(A,D,C)))))))) # label(t32_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5938 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r2_pboole(A,k2_pboole(A,k1_mboolean(A,B),k1_mboolean(A,C)),k1_mboolean(A,k2_pboole(A,B,C))))))) # label(t7_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5939 (all A all B (m1_pboole(B,A) -> m1_pboole(k2_mboolean(A,B),A))) # label(dt_k2_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5940 (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_zfmisc_1(k1_funct_1(B,D)))) <-> k1_mboolean(A,B) = C))))) # label(d1_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5941 (all A all B (m1_pboole(B,A) -> m1_pboole(k1_mboolean(A,B),A))) # label(dt_k1_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5942 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k1_mboolean(A,k3_pboole(A,B,C)),k3_pboole(A,k1_mboolean(A,B),k1_mboolean(A,C))))))) # label(t9_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5943 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> ((exists D (r1_pboole(A,B,D) & m1_pboole(D,A) & r1_pboole(A,D,C))) <-> r1_pboole(A,B,k2_mboolean(A,C))))))) # label(t21_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5944 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r2_pboole(A,k2_mboolean(A,k3_pboole(A,B,C)),k3_pboole(A,k2_mboolean(A,B),k2_mboolean(A,C))))))) # label(t29_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5945 (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,k3_pboole(A,B,D),C)))))))) # label(t15_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5946 (all A all B r6_pboole(A,k2_mboolean(A,k2_pre_circ(A,B)),k2_pre_circ(A,k3_tarski(B)))) # label(t23_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5947 (all A r6_pboole(A,k2_mboolean(A,k1_pboole(A)),k1_pboole(A))) # label(t22_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5948 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) -> r2_pboole(A,k1_mboolean(A,B),k1_mboolean(A,C))))))) # label(t6_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5949 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r2_pboole(A,k12_pboole(A,B,C),k1_mboolean(A,k11_pboole(A,B,C))))))) # label(t20_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5950 (all A all B r6_pboole(A,k2_mboolean(A,k2_pre_circ(A,k1_tarski(B))),k2_pre_circ(A,B))) # label(t24_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5951 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r1_pboole(A,B,C) -> r2_pboole(A,B,k2_mboolean(A,C))))))) # label(t26_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5952 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> ((all D (m1_pboole(D,A) -> (r2_pboole(A,D,C) <-> r1_pboole(A,D,B)))) <-> r6_pboole(A,B,k1_mboolean(A,C))))))) # label(t1_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5953 (all A all B r6_pboole(A,k1_mboolean(A,k2_pre_circ(A,B)),k2_pre_circ(A,k1_zfmisc_1(B)))) # label(t3_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5954 (all A all B (m1_pboole(B,A) -> r2_pboole(A,k1_pboole(A),B))) # label(t5_mboolean) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5955 (all A all B (m1_pboole(B,A) & v2_relat_1(B) -> (v1_pre_circ(B,A) & (all C (m1_pboole(C,A) -> (r1_pboole(A,C,B) -> v1_pre_circ(C,A)))) -> v1_pre_circ(k2_mboolean(A,B),A)))) # label(t22_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5956 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (v2_relat_1(B) & v1_pre_circ(k11_pboole(A,B,C),A) -> v1_pre_circ(C,A)))))) # label(t20_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5957 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (all D (m4_pboole(D,A,k1_mboolean(A,B)) -> (all E (m4_pboole(E,A,k1_mboolean(A,B)) -> (r6_pboole(A,C,k2_pboole(A,D,E)) -> r6_pboole(A,k6_mssubfam(A,B,C),k3_pboole(A,k6_mssubfam(A,B,D),k6_mssubfam(A,B,E)))))))))))) # label(t49_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5958 (all A all B all C (m1_pboole(C,B) -> (all D (m4_pboole(D,B,k1_mboolean(B,C)) -> (r2_hidden(A,B) -> m1_subset_1(k1_funct_1(D,A),k1_zfmisc_1(k1_zfmisc_1(k1_funct_1(C,A))))))))) # label(t32_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5959 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> ((all D (r2_hidden(D,C) -> r1_tarski(B,D))) -> C = k1_xboole_0 | r1_tarski(B,k8_setfam_1(A,C))))) # label(t5_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5960 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r1_tarski(B,C) & r2_hidden(B,D) -> r1_tarski(k8_setfam_1(A,D),C)))) # label(t6_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5961 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (v2_relat_1(B) & v1_pre_circ(k11_pboole(A,C,B),A) -> v1_pre_circ(C,A)))))) # label(t19_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5962 (all A all B all C (m1_pboole(B,A) & v1_pre_circ(B,A) & v1_pre_circ(C,A) & m1_pboole(C,A) -> v1_pre_circ(k11_pboole(A,B,C),A) & v1_relat_1(k11_pboole(A,B,C)) & v1_funct_1(k11_pboole(A,B,C)))) # label(fc7_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5963 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r2_hidden(B,C) -> r1_tarski(k8_setfam_1(A,C),B)))) # label(t2_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5964 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (all D (m4_pboole(D,A,k1_mboolean(A,B)) -> m4_pboole(k3_pboole(A,C,D),A,k1_mboolean(A,B)))))))) # label(t35_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5965 (all A all B all C (m1_pboole(B,A) & v1_pre_circ(C,A) & m1_pboole(C,A) -> v1_pre_circ(k4_pboole(A,C,B),A) & v1_relat_1(k4_pboole(A,C,B)) & v1_funct_1(k4_pboole(A,C,B)))) # label(fc5_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5966 (all A all B all C (m1_pboole(C,A) & v1_pre_circ(B,A) & m1_pboole(B,A) & v1_pre_circ(C,A) -> v1_funct_1(k12_pboole(A,B,C)) & v1_pre_circ(k12_pboole(A,B,C),A) & v1_relat_1(k12_pboole(A,B,C)))) # label(fc9_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5967 (all A all B (m1_pboole(B,A) & v1_pre_circ(B,A) -> v2_relat_1(k1_mboolean(A,B)) & v1_relat_1(k1_mboolean(A,B)) & v1_pre_circ(k1_mboolean(A,B),A) & v1_funct_1(k1_mboolean(A,B)))) # label(fc8_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5968 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (v6_mssubfam(C,A,B) -> v2_relat_1(C)))))) # label(cc8_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5969 (all A all B (m1_pboole(B,A) -> (exists C (m4_pboole(C,A,k1_mboolean(A,B)) & v1_funct_1(C) & v3_relat_1(C) & v1_pre_circ(C,A) & v1_relat_1(C))))) # label(rc3_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5970 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r1_pboole(A,B,C) -> m2_pboole(B,A,C)))))) # label(t11_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5971 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (v2_mssubfam(C,A,B) -> v6_mssubfam(C,A,B)))))) # label(cc7_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5972 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (all D (m4_pboole(D,A,k1_mboolean(A,B)) -> m4_pboole(k2_pboole(A,C,D),A,k1_mboolean(A,B)))))))) # label(t34_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5973 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> -(r2_pboole(A,B,k11_pboole(A,C,D)) & (all E (m1_pboole(E,A) -> (all F (m1_pboole(F,A) -> -(r2_pboole(A,E,C) & r2_pboole(A,F,D) & r2_pboole(A,B,k11_pboole(A,E,F)) & v1_pre_circ(E,A) & v1_pre_circ(F,A)))))) & v1_pre_circ(B,A)))))))) # label(t26_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5974 (all A all B (v1_funcop_1(B) & m1_pboole(B,A) -> k1_mssubfam(A,B) = k2_funct_6(B))) # label(redefinition_k1_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5975 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (r2_hidden(D,B) -> r1_tarski(C,D))) -> r1_tarski(C,k8_setfam_1(A,B))))))) # label(t4_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5976 (all A all B all C (m1_pboole(B,A) & m4_pboole(C,A,k1_mboolean(A,B)) -> k5_mssubfam(A,B,C) = k6_mssubfam(A,B,C))) # label(redefinition_k6_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5977 (all A (v1_pre_circ(k1_pboole(A),A) & v3_relat_1(k1_pboole(A)) & v1_funct_1(k1_pboole(A)) & v1_relat_1(k1_pboole(A)))) # label(fc1_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5978 (all A all B (m1_pboole(B,A) -> (all C (v2_relat_1(C) & m4_pboole(C,A,k1_mboolean(A,B)) -> r2_pboole(A,k6_mssubfam(A,B,C),k2_mboolean(A,C)))))) # label(t42_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5979 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (v1_pre_circ(C,A) & r2_pboole(A,B,C) -> v1_pre_circ(B,A)))))) # label(t18_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5980 (all A all B (m1_pboole(B,A) -> m4_pboole(k1_pboole(A),A,k1_mboolean(A,B)) & v3_relat_1(k1_pboole(A)) & v1_pre_circ(k1_pboole(A),A))) # label(t31_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5981 (all A all B (v2_relat_1(B) & m1_pboole(B,A) -> (all C (m3_pboole(C,A,B,k1_pboole(A)) -> r6_pboole(A,C,k1_pboole(A)))))) # label(t16_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5982 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (r1_pboole(A,k1_pboole(A),C) -> r6_pboole(A,k6_mssubfam(A,B,C),k1_pboole(A))))))) # label(t44_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5983 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (v4_mssubfam(C,A,B) <-> (all D (m4_pboole(D,A,k1_mboolean(A,B)) -> (r2_pboole(A,D,C) -> r1_pboole(A,k6_mssubfam(A,B,D),C))))))))) # label(d6_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5984 (all A all B all C (m1_pboole(B,A) & m4_pboole(C,A,k1_mboolean(A,B)) -> m1_pboole(k5_mssubfam(A,B,C),A))) # label(dt_k5_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5985 (all A all B (v1_pre_circ(B,A) & m1_pboole(B,A) -> (all C (m4_pboole(C,A,B) -> v1_pre_circ(C,A))))) # label(cc2_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5986 (all A all B (m1_pboole(B,A) -> (v1_pre_circ(k2_mboolean(A,B),A) -> v1_pre_circ(B,A) & (all C (m1_pboole(C,A) -> (r1_pboole(A,C,B) -> v1_pre_circ(C,A))))))) # label(t23_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5987 (all A all B all C (m1_pboole(C,A) & v1_pre_circ(C,A) & m1_pboole(B,A) -> v1_funct_1(k3_pboole(A,B,C)) & v1_relat_1(k3_pboole(A,B,C)) & v1_pre_circ(k3_pboole(A,B,C),A))) # label(fc3_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5988 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (v1_mssubfam(C,A,B) <-> (all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r1_pboole(A,D,C) & r1_pboole(A,E,C) -> r1_pboole(A,k2_pboole(A,D,E),C))))))))))) # label(d3_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5989 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (all D (m4_pboole(D,A,B) -> (all E (m4_pboole(E,A,B) -> (r6_pboole(A,C,k2_pzfmisc1(A,D,E)) -> r6_pboole(A,k6_mssubfam(A,B,C),k3_pboole(A,D,E))))))))))) # label(t51_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5990 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r2_hidden(k1_xboole_0,B) -> k8_setfam_1(A,B) = k1_xboole_0))) # label(t3_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5991 (all A all B (m1_pboole(B,A) -> k7_mssubfam(A,B) = k1_mboolean(A,B))) # label(redefinition_k7_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5992 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m4_pboole(D,A,k1_mboolean(A,B)) -> (r1_pboole(A,C,k6_mssubfam(A,B,D)) -> (all E (m1_pboole(E,A) -> (r1_pboole(A,E,D) -> r1_pboole(A,C,E))))))))))) # label(t52_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5993 (all A all B (v1_funcop_1(B) & m1_pboole(B,A) -> (v1_pre_circ(k1_mssubfam(A,B),A) -> v1_pre_circ(k2_mssubfam(A,B),A)))) # label(t24_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5994 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (v2_mssubfam(C,A,B) -> v1_mssubfam(C,A,B)))))) # label(cc3_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5995 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (v4_mssubfam(C,A,B) -> v5_mssubfam(C,A,B)))))) # label(cc5_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5996 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (v4_mssubfam(C,A,B) -> v3_mssubfam(C,A,B)))))) # label(cc4_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5997 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (all D (m1_pboole(D,A) -> (D = k5_mssubfam(A,B,C) <-> (all E -(r2_hidden(E,A) & (all F (m1_subset_1(F,k1_zfmisc_1(k1_zfmisc_1(k1_funct_1(B,E)))) -> -(k1_funct_1(D,E) = k8_setfam_1(k1_funct_1(B,E),F) & k1_funct_1(C,E) = F)))))))))))) # label(d2_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5998 (all A all B all C (m1_pboole(C,B) & v1_funcop_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k1_funct_1(C,A) = D & r2_hidden(A,B) -> k1_funct_1(k2_mssubfam(B,C),A) = k2_relat_1(D)))))) # label(t13_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 5999 (all A all B all C (m1_pboole(B,A) & v1_pre_circ(C,A) & m1_pboole(C,A) -> v1_funct_1(k3_pboole(A,C,B)) & v1_relat_1(k3_pboole(A,C,B)) & v1_pre_circ(k3_pboole(A,C,B),A))) # label(fc4_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 6000 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> ((all D (m4_pboole(D,A,k1_mboolean(A,B)) -> (r2_pboole(A,D,C) -> r1_pboole(A,k2_mboolean(A,D),C)))) <-> v2_mssubfam(C,A,B)))))) # label(d4_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 6001 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m4_pboole(D,A,k1_mboolean(A,B)) -> (r1_pboole(A,C,D) -> r2_pboole(A,k6_mssubfam(A,B,D),C)))))))) # label(t43_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 6002 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) & v1_funcop_1(D) -> (m3_pboole(D,A,B,C) & r1_pzfmisc1(A,B,C) -> r2_pboole(A,k2_mssubfam(A,D),C) & r6_pboole(A,k1_mssubfam(A,D),B)))))))) # label(t17_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 6003 (all A (r2_hidden(A,f1_s1_mssubfam) -> (all B -((all C -(r2_hidden(C,k1_funct_1(f3_s1_mssubfam,A)) & p1_s1_mssubfam(C,B,A))) & r2_hidden(B,k1_funct_1(f2_s1_mssubfam,A)))))) -> (exists A (m3_pboole(A,f1_s1_mssubfam,f2_s1_mssubfam,f3_s1_mssubfam) & (all B -(r2_hidden(B,f1_s1_mssubfam) & (all C (v1_funct_1(C) & m2_relset_1(C,k1_funct_1(f2_s1_mssubfam,B),k1_funct_1(f3_s1_mssubfam,B)) & v1_funct_2(C,k1_funct_1(f2_s1_mssubfam,B),k1_funct_1(f3_s1_mssubfam,B)) -> -(k1_funct_1(A,B) = C & (all D (r2_hidden(D,k1_funct_1(f2_s1_mssubfam,B)) -> p1_s1_mssubfam(k1_funct_1(C,D),D,B)))))))))) # label(s1_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 6004 (all A all B (m1_pboole(B,A) -> k1_mboolean(A,B) = k3_mssubfam(A,B))) # label(redefinition_k3_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 6005 (all A all B (m1_pboole(B,A) & v1_funcop_1(B) -> m1_pboole(k2_mssubfam(A,B),A))) # label(dt_k2_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 6006 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (v2_relat_1(D) & m4_pboole(D,A,k1_mboolean(A,C)) -> ((all E (m1_pboole(E,A) -> (r1_pboole(A,E,D) -> r2_pboole(A,B,E)))) -> r2_pboole(A,B,k6_mssubfam(A,C,D))))))))) # label(t45_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 6007 (all A all B (m1_pboole(B,A) -> (exists C (m4_pboole(C,A,k1_mboolean(A,B)) & v2_relat_1(C) & v1_relat_1(C) & v1_funct_1(C))))) # label(rc2_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 6008 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (all D (m4_pboole(D,A,B) -> (r6_pboole(A,C,k1_pzfmisc1(A,D)) -> r6_pboole(A,k6_mssubfam(A,B,C),D)))))))) # label(t50_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.10 6009 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (all D (m4_pboole(D,A,k1_mboolean(A,B)) -> (r2_pboole(A,C,D) -> r2_pboole(A,k6_mssubfam(A,B,D),k6_mssubfam(A,B,C))))))))) # label(t46_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6010 (all A all B (v1_funcop_1(B) & m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> -(r2_pboole(A,C,k2_mssubfam(A,B)) & v1_pre_circ(C,A) & (all D (m1_pboole(D,A) -> -(r6_pboole(A,k14_pboole(A,D,B),C) & v1_pre_circ(D,A) & r2_pboole(A,D,k1_mssubfam(A,B)))))))))) # label(t30_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6011 (all A all B (v2_relat_1(B) & m1_pboole(B,A) & v1_pre_circ(B,A) -> -((all C (m1_pboole(C,A) -> -(r1_pboole(A,C,B) & (all D (m1_pboole(D,A) -> (r1_pboole(A,D,B) -> r2_pboole(A,D,C))))))) & (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> -(-r2_pboole(A,D,C) & -r2_pboole(A,C,D) & r1_pboole(A,D,B) & r1_pboole(A,C,B))))))))) # label(t29_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6012 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (all E (m4_pboole(E,A,k1_mboolean(A,B)) -> (r1_pboole(A,C,E) & r6_pboole(A,k3_pboole(A,C,D),k1_pboole(A)) -> r6_pboole(A,k3_pboole(A,k6_mssubfam(A,B,E),D),k1_pboole(A))))))))))) # label(t48_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6013 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m4_pboole(D,A,k1_mboolean(A,C)) -> m4_pboole(k4_pboole(A,D,B),A,k1_mboolean(A,C)))))))) # label(t36_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6014 $T # label(d1_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6015 (all A all B (m1_pboole(B,A) & v1_funcop_1(B) -> k3_funct_6(B) = k2_mssubfam(A,B))) # label(redefinition_k2_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6016 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (v3_mssubfam(C,A,B) <-> (all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r1_pboole(A,D,C) & r1_pboole(A,E,C) -> r1_pboole(A,k3_pboole(A,D,E),C))))))))))) # label(d5_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6017 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (all D (m4_pboole(D,A,k1_mboolean(A,B)) -> m4_pboole(k5_pboole(A,C,D),A,k1_mboolean(A,B)))))))) # label(t37_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6018 (all A all B all C all D (-v1_xboole_0(A) & m1_pboole(B,A) & m1_subset_1(D,A) & m4_pboole(C,A,k1_mboolean(A,B)) -> k4_mssubfam(A,B,C,D) = k1_funct_1(C,D))) # label(redefinition_k4_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6019 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> r2_pboole(A,k2_mboolean(A,C),B))))) # label(t40_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6020 (all A all B (m1_pboole(B,A) -> (v3_relat_1(B) -> v1_pre_circ(B,A)))) # label(cc1_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6021 (all A all B all C (m1_pboole(B,A) & m4_pboole(C,A,k1_mboolean(A,B)) -> m4_pboole(k6_mssubfam(A,B,C),A,B))) # label(dt_k6_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6022 (all A all B (v1_funcop_1(B) & m1_pboole(B,A) -> (all C (m1_pboole(C,A) & v1_funcop_1(C) -> m1_pboole(k13_pboole(B,C),A) & v1_funcop_1(k13_pboole(B,C)))))) # label(t15_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6023 (all A all B (m1_pboole(B,A) -> v6_mssubfam(k7_mssubfam(A,B),A,B) & v4_mssubfam(k7_mssubfam(A,B),A,B) & v3_mssubfam(k7_mssubfam(A,B),A,B) & v1_mssubfam(k7_mssubfam(A,B),A,B) & v2_mssubfam(k7_mssubfam(A,B),A,B) & v5_mssubfam(k7_mssubfam(A,B),A,B) & m4_pboole(k7_mssubfam(A,B),A,k1_mboolean(A,B)))) # label(dt_k7_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6024 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (all E (m4_pboole(E,A,k1_mboolean(A,B)) -> (r1_pboole(A,C,E) & r2_pboole(A,C,D) -> r2_pboole(A,k6_mssubfam(A,B,E),D)))))))))) # label(t47_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6025 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (k1_tarski(C) = B -> k8_setfam_1(A,B) = C))))) # label(t9_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6026 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r1_xboole_0(B,C) & r2_hidden(B,D) -> r1_xboole_0(k8_setfam_1(A,D),C)))) # label(t7_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6027 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (r6_pboole(A,C,k1_pboole(A)) -> r6_pboole(A,k6_mssubfam(A,B,C),B)))))) # label(t41_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6028 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m4_pboole(D,A,k1_mboolean(A,C)) -> (r1_pboole(A,B,D) -> m4_pboole(B,A,C)))))))) # label(t33_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6029 (all A all B all C all D (m1_pboole(B,A) & m4_pboole(C,A,k1_mboolean(A,B)) & m1_subset_1(D,A) & -v1_xboole_0(A) -> m1_subset_1(k4_mssubfam(A,B,C,D),k1_zfmisc_1(k1_zfmisc_1(k1_funct_1(B,D)))))) # label(dt_k4_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6030 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (v6_mssubfam(C,A,B) <-> r1_pboole(A,k1_pboole(A),C)))))) # label(d8_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6031 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (B != k1_xboole_0 -> r1_tarski(k8_setfam_1(A,B),k5_setfam_1(A,B))))) # label(t1_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6032 (all A all B (m1_pboole(B,A) -> (exists C (v1_relat_1(C) & v1_funct_1(C) & v4_mssubfam(C,A,B) & v1_mssubfam(C,A,B) & v3_mssubfam(C,A,B) & v5_mssubfam(C,A,B) & v6_mssubfam(C,A,B) & v2_mssubfam(C,A,B) & v2_relat_1(C) & m4_pboole(C,A,k1_mboolean(A,B)))))) # label(rc5_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6033 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> -(v1_pre_circ(B,A) & (all E (m1_pboole(E,A) -> -(r2_pboole(A,E,D) & r2_pboole(A,B,k11_pboole(A,E,C)) & v1_pre_circ(E,A)))) & r2_pboole(A,B,k11_pboole(A,D,C)) & v1_pre_circ(C,A)))))))) # label(t27_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6034 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (v5_mssubfam(C,A,B) -> v2_relat_1(C)))))) # label(cc6_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6035 (all A all B (m1_pboole(B,A) -> m4_pboole(k3_mssubfam(A,B),A,k1_mboolean(A,B)))) # label(dt_k3_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6036 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) & v2_relat_1(C) -> (m2_pboole(B,A,C) -> r1_pboole(A,B,C)))))) # label(t12_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6037 (all A all B (v1_pre_circ(B,A) & m1_pboole(B,A) -> (exists C (m4_pboole(C,A,k1_mboolean(A,B)) & v1_relat_1(C) & v1_pre_circ(C,A) & v2_relat_1(C) & v1_funct_1(C))))) # label(rc4_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6038 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (r1_pboole(A,B,C) <-> v5_mssubfam(C,A,B)))))) # label(d7_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6039 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (B = k2_tarski(C,D) -> k8_setfam_1(A,B) = k5_subset_1(A,C,D)))))))) # label(t10_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6040 (all A all B (m1_pboole(B,A) & v1_funcop_1(B) -> m1_pboole(k1_mssubfam(A,B),A))) # label(dt_k1_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6041 (all A all B all C (v1_funcop_1(C) & m1_pboole(C,B) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(A,B) & D = k1_funct_1(C,A) -> k1_funct_1(k1_mssubfam(B,C),A) = k1_relat_1(D)))))) # label(t14_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6042 (all A all B all C (v1_pre_circ(C,A) & m1_pboole(B,A) & v1_funcop_1(B) & m1_pboole(C,A) -> v1_relat_1(k14_pboole(A,C,B)) & v1_funct_1(k14_pboole(A,C,B)) & v1_pre_circ(k14_pboole(A,C,B),A))) # label(fc6_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6043 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) -> m4_pboole(k1_pzfmisc1(A,B),A,k1_mboolean(A,C))))))) # label(t38_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6044 (all A all B (v1_pre_circ(B,A) & v2_relat_1(B) & m1_pboole(B,A) -> -((all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> -(r1_pboole(A,C,B) & -r2_pboole(A,D,C) & -r2_pboole(A,C,D) & r1_pboole(A,D,B)))))) & (all C (m1_pboole(C,A) -> -(r1_pboole(A,C,B) & (all D (m1_pboole(D,A) -> (r1_pboole(A,D,B) -> r2_pboole(A,C,D)))))))))) # label(t28_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6045 (all A all B all C (v1_pre_circ(C,A) & v1_pre_circ(B,A) & m1_pboole(B,A) & m1_pboole(C,A) -> v1_pre_circ(k5_pboole(A,B,C),A) & v1_funct_1(k5_pboole(A,B,C)) & v1_relat_1(k5_pboole(A,B,C)))) # label(fc10_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6046 (all A all B all C (m1_pboole(C,A) & v1_pre_circ(C,A) & m1_pboole(B,A) & v1_pre_circ(B,A) -> v1_relat_1(k2_pboole(A,B,C)) & v1_pre_circ(k2_pboole(A,B,C),A) & v1_funct_1(k2_pboole(A,B,C)))) # label(fc2_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6047 (all A all B (m1_pboole(B,A) -> (v1_pre_circ(k1_mboolean(A,B),A) <-> v1_pre_circ(B,A)))) # label(t21_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6048 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) -> (B = k4_subset_1(k1_zfmisc_1(A),C,D) -> k8_setfam_1(A,B) = k5_subset_1(A,k8_setfam_1(A,C),k8_setfam_1(A,D))))))))) # label(t8_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6049 (all A all B (m1_pboole(B,A) -> (exists C (v1_funct_1(C) & v1_pre_circ(C,A) & v1_relat_1(C) & v3_relat_1(C) & m4_pboole(C,A,B))))) # label(rc1_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6050 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,D,C) & r2_pboole(A,B,C) -> m4_pboole(k2_pzfmisc1(A,B,D),A,k1_mboolean(A,C))))))))) # label(t39_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6051 (all A all B (m1_pboole(B,A) -> (all C (v1_funcop_1(C) & m1_pboole(C,A) -> ((all D all E (v1_relat_1(E) & v1_funct_1(E) -> (E = k1_funct_1(C,D) & r2_hidden(D,A) -> v1_finset_1(k10_relat_1(E,k1_funct_1(B,D)))))) & r2_pboole(A,B,k2_mssubfam(A,C)) -> v1_pre_circ(B,A)))))) # label(t25_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6052 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (v2_relat_1(D) & m4_pboole(D,A,k1_mboolean(A,C)) -> (r1_pboole(A,B,C) & (all E (m1_pboole(E,A) -> (r1_pboole(A,E,D) -> r1_pboole(A,B,E)))) -> r1_pboole(A,B,k6_mssubfam(A,C,D))))))))) # label(t53_mssubfam) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6053 (all A (m1_subset_1(A,f2_s2_funct_7) -> (all B (m1_subset_1(B,f2_s2_funct_7) -> (f4_s2_funct_7(A) = f4_s2_funct_7(B) -> B = A))))) & v1_finset_1(f1_s2_funct_7) -> v1_finset_1(a_0_0_funct_7) # label(s2_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6054 (all A (v1_funct_7(A) & v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k7_funct_7(A),k1_relat_1(B)) -> v1_relat_1(k7_finseq_1(A,k9_finseq_1(B))) & v1_funct_1(k7_finseq_1(A,k9_finseq_1(B))) & v1_funct_7(k7_finseq_1(A,k9_finseq_1(B))) & v1_finseq_1(k7_finseq_1(A,k9_finseq_1(B)))))))) # label(t66_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6055 (all A all B ((v1_xboole_0(B) -> v1_xboole_0(A)) -> (all C (v1_funct_1(C) & v1_funct_7(C) & v1_finseq_1(C) & v1_relat_1(C) -> (m1_funct_7(C,A,B) <-> r1_tarski(k7_funct_7(C),B) & A = k6_funct_7(C)))))) # label(d9_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6056 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C k1_relat_1(A) = k1_relat_1(k2_funct_7(A,C,B))))) # label(t32_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6057 (all A all B all C -(B != A & r2_hidden(A,k2_relat_1(k1_funct_4(k6_partfun1(C),k3_cqc_lang(A,B)))))) # label(t14_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6058 (all A all B exists C m1_funct_7(C,A,B)) # label(existence_m1_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6059 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> k9_funct_7(B,np__0) = k6_partfun1(A))) # label(t86_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6060 (all A (-v1_xboole_0(A) & v1_finseq_1(A) & v2_relat_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (m2_funct_7(B,A) -> v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B))))) # label(dt_m2_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6061 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (r1_tarski(k2_relat_1(A),B) -> A = k5_relat_1(A,k6_partfun1(B)))))) # label(t1_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6062 (all A all B all C (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k2_funct_7(A,B,C)) & v1_relat_1(k2_funct_7(A,B,C)))) # label(dt_k2_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6063 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C all D k2_funct_7(k2_funct_7(A,D,B),D,C) = k2_funct_7(A,D,C)))) # label(t36_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6064 (all A (m1_subset_1(A,f2_s3_funct_7) -> (all B (m1_subset_1(B,f2_s3_funct_7) -> (f3_s3_funct_7(B) = f3_s3_funct_7(A) -> A = B))))) & (all A -(r2_hidden(A,f1_s3_funct_7) & (all B (m1_subset_1(B,f2_s3_funct_7) -> A != f3_s3_funct_7(B))))) -> r2_tarski(f1_s3_funct_7,a_0_1_funct_7) # label(s3_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6065 (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 (r1_funct_7(B,C,D) & r1_funct_7(A,B,D) -> r1_funct_7(A,C,D))))))))) # label(t29_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6066 (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_xboole_0(k2_relat_1(A),k1_relat_1(B)) -> k5_relat_1(A,C) = k5_relat_1(A,k1_funct_4(C,B))))))))) # label(t12_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6067 (all A all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k9_funct_7(k6_partfun1(A),B) = k6_partfun1(A))) # label(t83_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6068 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (-(-r1_tarski(k1_relat_1(k5_relat_1(B,C)),A) & -r1_tarski(k1_relat_1(k5_relat_1(B,k5_relat_1(C,D))),A) & -r1_tarski(k1_relat_1(B),A)) -> k4_funct_7(A,k11_finseq_1(B,C,D)) = k5_relat_1(B,k5_relat_1(C,D))))))))) # label(t57_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6069 (all A k9_finseq_1(A) = k5_funct_7(k1_xboole_0,A)) # label(t42_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6070 $T # label(dt_k7_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6071 $T # label(dt_k6_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6072 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(B)) -> C = k4_finseq_4(k5_numbers,A,k3_funct_7(A,B,D,C),D)))))))))) # label(t38_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6073 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> k5_funct_7(k9_finseq_1(B),A) = k10_finseq_1(A,k1_funct_1(B,A)))) # label(t49_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6074 (all A all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (v1_funct_2(C,A,A) & v1_funct_1(C) & m2_relset_1(C,A,A) -> v1_funct_2(k9_funct_7(C,B),A,A) & v1_funct_1(k9_funct_7(C,B)) & m2_relset_1(k9_funct_7(C,B),A,A))))) # label(t85_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6075 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k5_finseq_1(A)) & v1_funcop_1(k5_finseq_1(A)) & -v1_xboole_0(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_relat_1(k5_finseq_1(A)))) # label(fc4_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6076 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (B != np__0 -> k9_funct_7(k9_funct_7(A,C),B) = k9_funct_7(A,k2_nat_1(C,B))))))))) # label(t80_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6077 (all A all B all C (m1_funct_7(C,B,A) & -v1_xboole_0(A) -> k4_funct_7(B,C) = k8_funct_7(A,B,C))) # label(redefinition_k8_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6078 (all A (v1_finseq_1(A) & v1_relat_1(A) & v1_funct_1(A) -> (v1_funct_7(A) <-> (exists B (v1_relat_1(B) & k1_nat_1(k3_finseq_1(A),np__1) = k3_finseq_1(B) & v1_funct_1(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),k1_funct_2(k1_funct_1(B,C),k1_funct_1(B,k1_nat_1(C,np__1))))))) & v1_finseq_1(B)))))) # label(d8_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6079 (all A all B (v1_funct_1(A) & v1_finseq_1(A) & v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) & v1_funcop_1(A) & v1_funcop_1(B) & v1_relat_1(A) -> v1_relat_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_funcop_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)))) # label(fc8_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6080 (all A (v1_relat_1(A) & v1_funct_1(A) -> k9_funct_7(A,np__1) = A)) # label(t72_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6081 (all A all B all C (v1_relat_1(A) & v1_funct_1(B) & v1_funct_1(C) & v1_relat_1(C) & v1_funct_1(A) & v1_relat_1(B) -> v1_relat_1(k11_finseq_1(A,B,C)) & v1_finset_1(k11_finseq_1(A,B,C)) & v1_finseq_1(k11_finseq_1(A,B,C)) & v1_funcop_1(k11_finseq_1(A,B,C)) & v1_funct_1(k11_finseq_1(A,B,C)))) # label(fc6_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6082 (all A all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (v1_funct_2(D,A,A) & v1_funct_1(D) & m2_relset_1(D,A,A) -> k9_funct_7(k9_funct_7(D,B),C) = k9_funct_7(D,k2_nat_1(B,C)))))))) # label(t87_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6083 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k5_relat_1(k9_funct_7(A,C),k9_funct_7(A,B)) = k9_funct_7(A,k1_nat_1(B,C)))))))) # label(t79_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6084 (all A (v1_funct_1(A) & v1_finseq_1(A) & -v1_xboole_0(A) & v2_relat_1(A) & v1_relat_1(A) -> (exists B m2_funct_7(B,A)))) # label(existence_m2_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6085 (all A all B (v1_funcop_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> k7_finseq_1(k9_finseq_1(A),k5_funct_7(B,k1_funct_1(C,A))) = k5_funct_7(k7_finseq_1(k9_finseq_1(C),B),A))))) # label(t46_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6086 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r1_tarski(k2_relat_1(A),k1_relat_1(A)) -> r1_tarski(k2_relat_1(k9_funct_7(A,B)),k1_relat_1(A)) & k1_relat_1(A) = k1_relat_1(k9_funct_7(A,B))))))) # label(t76_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6087 (all A all B (v1_funct_1(B) & v1_funcop_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_funcop_1(C) & v1_finseq_1(C) -> k1_rewrite1(k5_funct_7(B,A),k5_funct_7(C,k1_funct_1(k5_funct_7(B,A),k1_nat_1(k3_finseq_1(B),np__1)))) = k5_funct_7(k7_finseq_1(B,C),A))))) # label(t52_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6088 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (r2_hidden(E,k4_finseq_1(B)) -> k4_finseq_4(k5_numbers,A,k3_funct_7(A,B,D,C),E) = k4_finseq_4(k5_numbers,A,B,E) | D = E))))))))))) # label(t39_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.11 6089 (all A (v1_funcop_1(A) & v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (C = k5_funct_7(A,B) <-> k3_finseq_1(C) = k1_nat_1(k3_finseq_1(A),np__1) & k1_funct_1(C,np__1) = B & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (v1_relat_1(E) & v1_funct_1(E) -> (r2_hidden(D,k4_finseq_1(A)) & E = k1_funct_1(A,D) -> k1_funct_1(E,k1_funct_1(C,D)) = k1_funct_1(C,k1_nat_1(D,np__1)))))))))))) # label(d5_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6090 (all A all B all C (m1_funct_7(C,B,A) & -v1_xboole_0(A) -> v1_funct_2(k8_funct_7(A,B,C),B,A) & m2_relset_1(k8_funct_7(A,B,C),B,A) & v1_funct_1(k8_funct_7(A,B,C)))) # label(dt_k8_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6091 (exists A (v1_funct_1(A) & v1_finseq_1(A) & -v1_xboole_0(A) & v1_relat_1(A) & v2_relat_1(A) & v1_funcop_1(A) & v1_finset_1(A))) # label(rc1_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6092 (all A all B (m1_subset_1(B,k5_numbers) & v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k9_funct_7(A,B)) & v1_funct_1(k9_funct_7(A,B)))) # label(dt_k9_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6093 (all A all B all C all D (m1_subset_1(D,A) & m1_subset_1(C,k5_numbers) & m1_finseq_1(B,A) -> k2_funct_7(B,C,D) = k3_funct_7(A,B,C,D))) # label(redefinition_k3_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6094 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k9_funct_7(k1_xboole_0,A) = k1_xboole_0)) # label(t82_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6095 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (np__0 != B -> r1_tarski(k1_relat_1(k9_funct_7(A,B)),k1_relat_1(A)) & r1_tarski(k2_relat_1(k9_funct_7(A,B)),k2_relat_1(A))))))) # label(t75_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6096 (all A ((exists B (m1_subset_1(B,f2_s2_funct_7) & r2_hidden(f4_s2_funct_7(B),f1_s2_funct_7) & A = f3_s2_funct_7(B))) <-> r2_hidden(A,a_0_0_funct_7))) # label(fraenkel_a_0_0_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6097 (all A (v2_relat_1(A) & v1_funct_1(A) & -v1_xboole_0(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (m2_funct_7(B,A) -> r1_tarski(k2_relat_1(k4_funct_7(k1_funct_1(A,np__1),B)),k1_funct_1(A,k3_finseq_1(A))) & k1_funct_1(A,np__1) = k1_relat_1(k4_funct_7(k1_funct_1(A,np__1),B)))))) # label(t69_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6098 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> k5_relat_1(k6_partfun1(A),k5_relat_1(B,C)) = k4_funct_7(A,k10_finseq_1(B,C)))))) # label(t53_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6099 (all A (v1_finseq_1(A) & v1_relat_1(A) & v1_funct_1(A) -> (all B ((v1_xboole_0(A) -> (v1_xboole_0(B) <-> k7_funct_7(A) = B)) & (-v1_xboole_0(A) -> (B = k7_funct_7(A) <-> B = k2_funct_5(k1_funct_1(A,k3_finseq_1(A))))))))) # label(d7_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6100 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_funct_7(k5_finseq_1(A)) & -v1_xboole_0(k5_finseq_1(A)) & v1_funcop_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)))) # label(fc10_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6101 (all A k6_partfun1(A) = k4_funct_7(A,k1_xboole_0)) # label(t41_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6102 (all A all B (r1_tarski(k3_finseq_2(A),k3_finseq_2(B)) -> r1_tarski(A,B))) # label(t21_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6103 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k1_relat_1(B),A) | r1_tarski(k1_relat_1(k5_relat_1(B,C)),A) -> k4_funct_7(A,k10_finseq_1(B,C)) = k5_relat_1(B,C)))))) # label(t54_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6104 (all A all B all C (m1_subset_1(B,k5_numbers) & v1_finseq_1(A) & v1_relat_1(A) & v1_funct_1(A) -> v1_finseq_1(k2_funct_7(A,B,C)) & v1_funct_1(k2_funct_7(A,B,C)) & v1_finset_1(k2_funct_7(A,B,C)) & v1_relat_1(k2_funct_7(A,B,C)))) # label(fc9_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6105 (all A all B (v1_funcop_1(B) & v1_funct_1(B) & v1_relat_1(B) & v1_finseq_1(B) -> v1_relat_1(k4_funct_7(A,B)) & v1_funct_1(k4_funct_7(A,B)))) # label(dt_k4_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6106 (all A all B (v1_funct_1(B) & v1_relat_1(B) & m1_subset_1(A,k5_numbers) -> v1_funcop_1(k2_finseq_2(A,B)) & v1_finset_1(k2_finseq_2(A,B)) & v1_relat_1(k2_finseq_2(A,B)) & v1_finseq_1(k2_finseq_2(A,B)) & v1_funct_1(k2_finseq_2(A,B)))) # label(fc7_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6107 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (r1_funct_7(A,B,C) -> k4_xboole_0(k1_relat_1(A),C) = k4_xboole_0(k1_relat_1(B),C))))))) # label(t30_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6108 (all A all B (-v1_xboole_0(k3_cqc_lang(A,B)) & v1_relat_1(k3_cqc_lang(A,B)) & v1_funct_1(k3_cqc_lang(A,B)))) # label(fc1_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6109 (exists A (-v1_xboole_0(A) & v1_finset_1(A) & v1_funct_1(A) & v2_relat_1(A) & v1_funct_7(A) & v1_funcop_1(A) & v1_finseq_1(A) & v1_relat_1(A))) # label(rc2_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6110 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k9_funct_7(A,B) = k5_relat_1(k9_funct_7(A,B),k6_partfun1(k2_xboole_0(k1_relat_1(A),k2_relat_1(A)))))))) # label(t78_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6111 (all A all B all C (-r1_xboole_0(A,k2_relat_1(k1_funct_4(k6_partfun1(B),k2_funcop_1(A,C)))) -> r2_hidden(C,A))) # label(t13_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6112 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_funct_7(A) & v1_relat_1(A) -> v1_finset_1(A) & v1_funcop_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A))) # label(cc1_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6113 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(C) = k2_xboole_0(A,k1_tarski(B)) -> C = k1_funct_4(k7_relat_1(C,A),k3_cqc_lang(B,k1_funct_1(C,B)))))) # label(t15_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6114 (all A all B all C all D (v1_funct_1(k4_funct_4(A,B,C,D)) & -v1_xboole_0(k4_funct_4(A,B,C,D)) & v1_relat_1(k4_funct_4(A,B,C,D)))) # label(fc2_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6115 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_funct_7(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),k6_funct_7(A)) -> v1_finseq_1(k7_finseq_1(k9_finseq_1(B),A)) & v1_relat_1(k7_finseq_1(k9_finseq_1(B),A)) & v1_funct_7(k7_finseq_1(k9_finseq_1(B),A)) & v1_funct_1(k7_finseq_1(k9_finseq_1(B),A))))))) # label(t65_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6116 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(k2_funct_7(A,C,B),C) = B)))) # label(t33_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6117 (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) -> (v1_funct_7(k7_finseq_1(A,B)) -> v1_funct_7(A) & v1_funct_7(B)))))) # label(t62_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6118 (all A all B all C (m1_funct_7(C,A,B) -> v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & v1_funct_7(C))) # label(dt_m1_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6119 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(k1_relat_1(B),A) -> B = k4_funct_7(A,k9_finseq_1(B))))) # label(t48_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6120 (all A all B (v1_finseq_1(B) & v1_relat_1(B) & v1_funcop_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> k4_funct_7(A,k7_finseq_1(B,k9_finseq_1(C))) = k5_relat_1(k4_funct_7(A,B),C))))) # label(t43_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6121 (all A (v1_finset_1(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (exists C ((all D (m2_subset_1(D,k1_zfmisc_1(A),B) -> (r1_tarski(D,C) -> C = D))) & m2_subset_1(C,k1_zfmisc_1(A),B))))))) # label(t23_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6122 (all A all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,A,B) & v1_funct_1(C) & m2_relset_1(C,A,B) -> (v2_funct_1(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (all E (m1_subset_1(E,k1_zfmisc_1(B)) -> (r1_tarski(E,k2_funct_2(A,B,C,D)) -> r1_tarski(k3_funct_2(A,B,C,E),D))))))))))) # label(t2_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6123 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> k4_funct_7(A,k9_finseq_1(B)) = k5_relat_1(k6_partfun1(A),B))) # label(t47_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6124 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> r1_tarski(k2_relat_1(k9_funct_7(A,B)),k2_xboole_0(k1_relat_1(A),k2_relat_1(A))) & r1_tarski(k1_relat_1(k9_funct_7(A,B)),k2_xboole_0(k1_relat_1(A),k2_relat_1(A))))))) # label(t74_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6125 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_funcop_1(A) -> v1_funct_1(k5_funct_7(A,B)) & v1_finseq_1(k5_funct_7(A,B)) & v1_relat_1(k5_funct_7(A,B)))) # label(dt_k5_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6126 (all A all B all C (v1_funct_1(C) & v1_finseq_1(C) & v1_funct_7(C) & v1_relat_1(C) -> (r2_hidden(A,k6_funct_7(C)) & r2_hidden(A,B) -> k1_funct_1(k5_funct_7(C,A),k1_nat_1(k3_finseq_1(C),np__1)) = k1_funct_1(k4_funct_7(B,C),A)))) # label(t67_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6127 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (r1_funct_7(A,B,C) -> r1_funct_7(B,A,C))))))) # label(t28_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6128 (all A all B (v1_funct_1(B) & v1_funct_1(A) & v1_relat_1(A) & v1_relat_1(B) -> v1_funcop_1(k10_finseq_1(A,B)) & v1_relat_1(k10_finseq_1(A,B)) & v1_finseq_1(k10_finseq_1(A,B)) & v1_finset_1(k10_finseq_1(A,B)) & v1_funct_1(k10_finseq_1(A,B)))) # label(fc5_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6129 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(A,B) & k2_funcop_1(B,A) = C -> np__0 = D | C = k9_funct_7(C,D)))))) # label(t89_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6130 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (r2_hidden(B,k1_relat_1(A)) -> k7_relat_1(A,k1_tarski(B)) = k3_cqc_lang(B,k1_funct_1(A,B)))))) # label(t6_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6131 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> k7_finseq_1(k9_finseq_1(A),k11_finseq_1(k1_funct_1(B,A),k1_funct_1(C,k1_funct_1(B,A)),k1_funct_1(D,k1_funct_1(C,k1_funct_1(B,A))))) = k5_funct_7(k11_finseq_1(B,C,D),A))))))) # label(t58_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6132 p1_s5_funct_7(k1_xboole_0) & (all A (v1_funct_1(A) & v1_relat_1(A) & v1_finseq_1(A) & v1_funcop_1(A) -> (p1_s5_funct_7(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> p1_s5_funct_7(k7_finseq_1(A,k9_finseq_1(B)))))))) -> (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_funcop_1(A) & v1_relat_1(A) -> p1_s5_funct_7(A))) # label(s5_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6133 (all A (v2_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) & -v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (k1_nat_1(k3_finseq_1(B),np__1) = k3_finseq_1(A) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(C,k4_finseq_1(B)) -> r2_hidden(k1_funct_1(B,C),k1_funct_2(k1_funct_1(A,C),k1_funct_1(A,k1_nat_1(C,np__1))))))) <-> m2_funct_7(B,A)))))) # label(d10_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6134 (all A (v1_relat_1(A) & v1_funct_1(A) -> k9_funct_7(A,np__0) = k6_partfun1(k2_xboole_0(k1_relat_1(A),k2_relat_1(A))))) # label(t70_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6135 (all A all B all C (v1_finseq_1(C) & v1_funcop_1(C) & v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_funcop_1(D) & v1_relat_1(D) & v1_finseq_1(D) -> (r1_tarski(k2_relat_1(k4_funct_7(A,C)),B) -> k5_relat_1(k4_funct_7(A,C),k4_funct_7(B,D)) = k4_funct_7(A,k7_finseq_1(C,D))))))) # label(t50_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6136 (all A (v1_relat_1(A) & -v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_relat_1(A) -> (all B (m2_funct_7(B,A) -> (B != k1_xboole_0 -> k1_funct_1(A,np__1) = k6_funct_7(B) & r1_tarski(k7_funct_7(B),k1_funct_1(A,k3_finseq_1(A)))))))) # label(t68_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6137 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C all D k1_funct_4(k1_funct_4(A,k2_funcop_1(B,C)),k2_funcop_1(B,D)) = k1_funct_4(A,k2_funcop_1(B,D))))) # label(t16_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6138 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> B = k3_funct_7(A,B,E,k4_finseq_4(k5_numbers,A,B,E)))))))))))) # label(t40_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6139 (all A all B (r2_hidden(A,B) -> k1_funct_7(A,B) = A)) # label(d1_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6140 (all A all B all C all D (m1_finseq_1(B,A) & m1_subset_1(D,A) & m1_subset_1(C,k5_numbers) -> m2_finseq_1(k3_funct_7(A,B,C,D),A))) # label(dt_k3_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6141 (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) -> (v1_funcop_1(k7_finseq_1(A,B)) -> v1_funcop_1(B) & v1_funcop_1(A)))))) # label(t25_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6142 (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) -> k5_relat_1(A,k1_funct_4(B,C)) = k1_funct_4(k5_relat_1(A,B),k5_relat_1(A,C)))))))) # label(t11_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6143 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C ((r2_hidden(B,k1_relat_1(A)) -> k1_funct_4(A,k3_cqc_lang(B,C)) = k2_funct_7(A,B,C)) & (-r2_hidden(B,k1_relat_1(A)) -> A = k2_funct_7(A,B,C)))))) # label(d3_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6144 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k5_relat_1(k9_funct_7(A,B),A) = k9_funct_7(A,k1_nat_1(B,np__1)))))) # label(t73_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6145 (all A all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,A) -> v1_funct_1(k9_funct_7(C,B)) & m2_relset_1(k9_funct_7(C,B),A,A))))) # label(t88_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6146 (all A ((exists B (r2_hidden(f3_s3_funct_7(B),f1_s3_funct_7) & A = B & m1_subset_1(B,f2_s3_funct_7))) <-> r2_hidden(A,a_0_1_funct_7))) # label(fraenkel_a_0_1_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6147 $T # label(t17_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6148 (all A (m1_subset_1(A,k1_zfmisc_1(k5_numbers)) -> ((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(B,A) -> r2_hidden(C,A) | r1_xreal_0(B,C)))))) -> v1_card_1(A)))) # label(t22_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6149 (all A all B (v1_relat_1(B) & v1_funcop_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_finseq_1(C) & v1_relat_1(C) & v1_funct_1(C) & v1_funcop_1(C) -> k1_funct_1(k5_funct_7(k7_finseq_1(B,C),A),k1_nat_1(k3_finseq_1(k7_finseq_1(B,C)),np__1)) = k1_funct_1(k5_funct_7(C,k1_funct_1(k5_funct_7(B,A),k1_nat_1(k3_finseq_1(B),np__1))),k1_nat_1(k3_finseq_1(C),np__1)))))) # label(t51_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6150 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C all D (D != C -> k1_funct_1(A,D) = k1_funct_1(k2_funct_7(A,C,B),D))))) # label(t34_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6151 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_funcop_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> k7_finseq_1(k5_funct_7(B,A),k9_finseq_1(k1_funct_1(C,k1_funct_1(k5_funct_7(B,A),k1_nat_1(k3_finseq_1(B),np__1))))) = k5_funct_7(k7_finseq_1(B,k9_finseq_1(C)),A))))) # label(t44_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6152 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> ((exists D (k6_partfun1(k2_xboole_0(k1_relat_1(A),k2_relat_1(A))) = k8_funct_2(k5_numbers,k4_partfun1(k2_xboole_0(k1_relat_1(A),k2_relat_1(A)),k2_xboole_0(k1_relat_1(A),k2_relat_1(A))),D,np__0) & k8_funct_2(k5_numbers,k4_partfun1(k2_xboole_0(k1_relat_1(A),k2_relat_1(A)),k2_xboole_0(k1_relat_1(A),k2_relat_1(A))),D,B) = C & v1_funct_1(D) & m2_relset_1(D,k5_numbers,k4_partfun1(k2_xboole_0(k1_relat_1(A),k2_relat_1(A)),k2_xboole_0(k1_relat_1(A),k2_relat_1(A)))) & (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (exists F (v1_funct_1(F) & k8_funct_2(k5_numbers,k4_partfun1(k2_xboole_0(k1_relat_1(A),k2_relat_1(A)),k2_xboole_0(k1_relat_1(A),k2_relat_1(A))),D,E) = F & k8_funct_2(k5_numbers,k4_partfun1(k2_xboole_0(k1_relat_1(A),k2_relat_1(A)),k2_xboole_0(k1_relat_1(A),k2_relat_1(A))),D,k1_nat_1(E,np__1)) = k5_relat_1(A,F) & v1_relat_1(F))))) & v1_funct_2(D,k5_numbers,k4_partfun1(k2_xboole_0(k1_relat_1(A),k2_relat_1(A)),k2_xboole_0(k1_relat_1(A),k2_relat_1(A)))))) <-> k9_funct_7(A,B) = C))))))) # label(d11_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6153 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) & v1_finseq_1(B) -> (k1_nat_1(k3_finseq_1(B),np__1) = k3_finseq_1(A) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(C,k4_finseq_1(B)) <-> r2_hidden(C,k4_finseq_1(A)) & r2_hidden(k1_nat_1(C,np__1),k4_finseq_1(A)))))))))) # label(t24_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6154 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k9_funct_7(A,k1_nat_1(B,np__1)) = k5_relat_1(A,k9_funct_7(A,B)))))) # label(t71_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6155 r1_tarski(f1_s4_funct_7,f2_s4_funct_7) & (all A (m1_subset_1(A,f2_s4_funct_7) -> (all B (m1_subset_1(B,f2_s4_funct_7) -> (f3_s4_funct_7(B) = f3_s4_funct_7(A) -> A = B))))) -> r2_tarski(f1_s4_funct_7,a_0_2_funct_7) # label(s4_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6156 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (k7_relat_1(A,k4_xboole_0(k1_relat_1(A),C)) = k7_relat_1(B,k4_xboole_0(k1_relat_1(B),C)) <-> r1_funct_7(A,B,C))))))) # label(d2_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6157 (all A (-v1_xboole_0(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) -> (v2_funct_1(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,k1_zfmisc_1(A)) -> (r2_hidden(k8_funct_2(A,B,C,D),k2_funct_2(A,B,C,E)) -> r2_hidden(D,E))))))))))))) # label(t3_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6158 (all A (r2_hidden(A,a_0_2_funct_7) <-> (exists B (r2_hidden(B,f1_s4_funct_7) & f3_s4_funct_7(B) = A & m1_subset_1(B,f2_s4_funct_7))))) # label(fraenkel_a_0_2_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6159 (all A all B (m1_pboole(B,A) -> (all C (r2_hidden(C,A) -> k7_relat_1(B,k1_tarski(C)) = k3_cqc_lang(C,k1_funct_1(B,C)))))) # label(t7_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6160 (all A (v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & -v1_xboole_0(A) & v1_finseq_1(A) -> (all B (m2_funct_7(B,A) -> v1_funct_7(B) & v2_relat_1(B))))) # label(cc3_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6161 (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) -> (v2_funct_1(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,k1_zfmisc_1(A)) -> (all F (m1_subset_1(F,k1_zfmisc_1(B)) -> (r2_hidden(k8_funct_2(A,B,C,D),k6_subset_1(B,k2_funct_2(A,B,C,E),F)) -> r2_hidden(D,k6_subset_1(A,E,k3_funct_2(A,B,C,F))))))))))))))))) # label(t4_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6162 (all A (v1_funct_1(A) & v1_relat_1(A) -> (r1_xboole_0(k2_relat_1(A),k1_relat_1(A)) -> k1_xboole_0 = k9_funct_7(A,np__2)))) # label(t84_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6163 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B r1_funct_7(A,A,B)))) # label(t27_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6164 (all A all B (r2_hidden(A,B) <-> r2_hidden(k9_finseq_1(A),k3_finseq_2(B)))) # label(t20_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6165 (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(k2_relat_1(C),k1_relat_1(A)) & r1_tarski(k2_relat_1(B),k1_relat_1(A)) -> k1_funct_4(k5_relat_1(B,A),k5_relat_1(C,A)) = k5_relat_1(k1_funct_4(B,C),A)))))))) # label(t10_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6166 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_tarski(k2_relat_1(A),k1_relat_1(A)) -> k9_funct_7(k9_funct_7(A,B),C) = k9_funct_7(A,k2_nat_1(B,C))))))))) # label(t81_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6167 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> k6_funct_7(k7_finseq_1(k9_finseq_1(A),B)) = k1_relat_1(A) & k2_relat_1(A) = k7_funct_7(k7_finseq_1(B,k9_finseq_1(A))))))) # label(t60_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6168 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,A,B) & v1_funct_1(C) & m2_relset_1(C,A,B) -> (v2_funct_1(C) -> (all D (m1_subset_1(D,B) -> (all E (m1_subset_1(E,k1_zfmisc_1(A)) -> (all F (m1_subset_1(F,k1_zfmisc_1(B)) -> (r2_hidden(D,k6_subset_1(B,k2_funct_2(A,B,C,E),F)) -> r2_hidden(k1_funct_1(k2_funct_1(C),D),k6_subset_1(A,E,k3_funct_2(A,B,C,F))))))))))))))))) # label(t5_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6169 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C all D all E (D != E -> k2_funct_7(k2_funct_7(A,E,C),D,B) = k2_funct_7(k2_funct_7(A,D,B),E,C))))) # label(t35_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6170 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_funcop_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (C = k4_funct_7(A,B) <-> (exists D (k6_partfun1(A) = k1_funct_1(D,np__0) & m1_pboole(D,k5_numbers) & (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (r2_hidden(k1_nat_1(E,np__1),k4_finseq_1(B)) -> (all F (v1_funct_1(F) & v1_relat_1(F) -> (all G (v1_funct_1(G) & v1_relat_1(G) -> (k1_funct_1(B,k1_nat_1(E,np__1)) = G & k1_funct_1(D,E) = F -> k5_relat_1(F,G) = k1_funct_1(D,k1_nat_1(E,np__1)))))))))) & C = k1_funct_1(D,k3_finseq_1(B)) & v1_funcop_1(D)))))))) # label(d4_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6171 (all A (v1_xboole_0(A) & v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> v1_finseq_1(A) & v1_funcop_1(A) & v1_funct_1(A) & v1_relat_1(A) & v1_finset_1(A) & v1_funct_7(A))) # label(cc2_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6172 (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(B),C) -> r1_funct_7(A,k1_funct_4(A,B),C))))))) # label(t31_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6173 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B k2_funct_7(A,B,k1_funct_1(A,B)) = A))) # label(t37_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6174 (all A all B m1_subset_1(k1_funct_7(A,B),B)) # label(dt_k1_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6175 (all A all B (v1_funct_1(B) & v1_funct_7(B) & v1_relat_1(B) & v1_finseq_1(B) -> (k1_xboole_0 != B -> k1_relat_1(k4_funct_7(A,B)) = k3_xboole_0(k6_funct_7(B),A)))) # label(t63_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6176 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> k11_finseq_1(A,k1_funct_1(B,A),k1_funct_1(C,k1_funct_1(B,A))) = k5_funct_7(k10_finseq_1(B,C),A))))) # label(t55_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.12 6177 $T # label(t9_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6178 (all A all B (v1_funct_1(B) & v1_relat_1(B) & v1_finseq_1(B) & v1_funcop_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> k5_relat_1(k7_relat_1(C,A),k4_funct_7(k9_relat_1(C,A),B)) = k4_funct_7(A,k7_finseq_1(k9_finseq_1(C),B)))))) # label(t45_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6179 (all A all B all C (r2_hidden(A,k3_xboole_0(B,C)) -> k1_funct_7(A,B) = k1_funct_7(A,C))) # label(t26_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6180 (all A all B all C (m1_pboole(C,k2_zfmisc_1(A,B)) -> (all D all E (r2_hidden(D,A) & r2_hidden(E,B) -> k7_relat_1(C,k2_zfmisc_1(k1_tarski(D),k1_tarski(E))) = k9_funct_2(D,E,k1_binop_1(C,D,E)))))) # label(t8_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6181 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k4_funct_7(k2_xboole_0(k1_relat_1(A),k2_relat_1(A)),k2_finseq_2(B,A)) = k9_funct_7(A,B))))) # label(t90_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6182 (all A all B (v1_funcop_1(B) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (k1_xboole_0 != B -> r1_tarski(k2_relat_1(k4_funct_7(A,B)),k7_funct_7(B))))) # label(t61_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6183 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> k4_funct_7(A,k11_finseq_1(B,C,D)) = k5_relat_1(k6_partfun1(A),k5_relat_1(B,k5_relat_1(C,D))))))))) # label(t56_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6184 (all A (m1_subset_1(A,f1_s1_funct_7) -> (all B (m1_subset_1(B,f2_s1_funct_7) -> r2_hidden(f4_s1_funct_7(A,B),f3_s1_funct_7))))) -> (exists A (v1_funct_2(A,k2_zfmisc_1(f1_s1_funct_7,f2_s1_funct_7),f3_s1_funct_7) & (all B (m1_subset_1(B,f1_s1_funct_7) -> (all C (m1_subset_1(C,f2_s1_funct_7) -> f4_s1_funct_7(B,C) = k8_funct_2(k2_zfmisc_1(f1_s1_funct_7,f2_s1_funct_7),f3_s1_funct_7,A,k1_domain_1(f1_s1_funct_7,f2_s1_funct_7,B,C)))))) & m2_relset_1(A,k2_zfmisc_1(f1_s1_funct_7,f2_s1_funct_7),f3_s1_funct_7) & v1_funct_1(A))) # label(s1_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6185 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B ((-v1_xboole_0(A) -> (k1_funct_5(k1_funct_1(A,np__1)) = B <-> k6_funct_7(A) = B)) & (v1_xboole_0(A) -> (B = k6_funct_7(A) <-> v1_xboole_0(B))))))) # label(d6_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6186 (all A (v1_relat_1(A) & v1_funct_7(A) & v1_funct_1(A) & v1_finseq_1(A) -> k1_relat_1(k4_funct_7(k6_funct_7(A),A)) = k6_funct_7(A))) # label(t64_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6187 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k9_funct_7(A,B) = k5_relat_1(k6_partfun1(k2_xboole_0(k1_relat_1(A),k2_relat_1(A))),k9_funct_7(A,B)))))) # label(t77_funct_7) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6188 (all A (l1_struct_0(A) -> (v1_struct_0(A) -> A = g1_struct_0(u1_struct_0(A))))) # label(abstractness_v1_struct_0) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6189 (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]. 57.14/56.13 6190 (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]. 57.14/56.13 6191 (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]. 57.14/56.13 6192 (all A (-v3_struct_0(A) & l1_struct_0(A) -> -v1_xboole_0(u1_struct_0(A)))) # label(fc1_struct_0) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6193 (all A all B (-v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & l1_struct_0(A) -> k1_struct_0(A,B) = k1_tarski(B))) # label(redefinition_k1_struct_0) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6194 (all A (l2_struct_0(A) -> l1_struct_0(A))) # label(dt_l2_struct_0) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6195 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & l1_struct_0(A) & -v3_struct_0(A) -> (all C (m1_subset_1(C,B) <-> m1_struct_0(C,A,B))))) # label(redefinition_m1_struct_0) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6196 (exists A l2_struct_0(A)) # label(existence_l2_struct_0) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6197 (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]. 57.14/56.13 6198 (exists A (l2_struct_0(A) & v2_struct_0(A))) # label(rc2_struct_0) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6199 (exists A (l1_struct_0(A) & -v3_struct_0(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6200 (exists A l1_struct_0(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6201 (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]. 57.14/56.13 6202 (exists A (v1_struct_0(A) & l1_struct_0(A))) # label(rc1_struct_0) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6203 (all A all B all C (-v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> m1_subset_1(k2_struct_0(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k2_struct_0) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6204 (all A all B all C (-v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> k2_tarski(B,C) = k2_struct_0(A,B,C))) # label(redefinition_k2_struct_0) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6205 (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]. 57.14/56.13 6206 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6207 (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]. 57.14/56.13 6208 (all A (l1_struct_0(A) & -v3_struct_0(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B))))) # label(rc5_struct_0) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6209 (all A all B all C (m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_struct_0(A) & -v3_struct_0(A) -> k2_struct_0(A,B,C) = k2_struct_0(A,C,B))) # label(commutativity_k2_struct_0) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6210 (all A all B (m1_subset_1(B,A) -> (all C all D (g2_struct_0(C,D) = g2_struct_0(A,B) -> C = A & B = D)))) # label(free_g2_struct_0) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6211 (all A all B (-v1_xboole_0(B) & -v3_struct_0(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_struct_0(A) -> (exists C m1_struct_0(C,A,B)))) # label(existence_m1_struct_0) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6212 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6213 (all A (l1_struct_0(A) -> (v3_struct_0(A) <-> v1_xboole_0(u1_struct_0(A))))) # label(d1_struct_0) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6214 (exists A (l2_struct_0(A) & -v3_struct_0(A))) # label(rc4_struct_0) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6215 (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]. 57.14/56.13 6216 (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 -> D = k9_cat_1(A,B,C,C,D,k10_cat_1(A,C))))))))))) # label(t57_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6217 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (v7_cat_1(B,A) <-> (all C (m1_subset_1(C,u1_cat_1(A)) -> k6_cat_1(A,B,C) != k1_xboole_0 & (exists D (m1_cat_1(D,A,B,C) & (all E (m1_cat_1(E,A,B,C) -> E = D))))))))))) # label(d16_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6218 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_1(C) & m2_relset_1(C,u2_cat_1(A),u2_cat_1(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,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_2(D,u1_cat_1(A),u1_cat_1(B)) & m2_relset_1(D,u1_cat_1(A),u1_cat_1(B)) & v1_funct_1(D) -> (k12_cat_1(A,B,C) = D <-> (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))))))))))))))) # label(d19_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6219 $T # label(t80_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6220 (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)) -> (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,F) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,G) -> F = G)))))))))) <-> v10_cat_1(C,A,B)))))))) # label(d24_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6221 (all A all B all C (l1_cat_1(A) & v1_funct_1(C) & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & v2_cat_1(B) & v2_cat_1(A) & l1_cat_1(B) & m1_relset_1(C,u2_cat_1(A),u2_cat_1(B)) -> 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]. 57.14/56.13 6222 (all A all B (m1_subset_1(B,u2_cat_1(A)) & l1_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]. 57.14/56.13 6223 (all A all B all C all D all E all F (v2_cat_1(A) & 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)) -> 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]. 57.14/56.13 6224 (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]. 57.14/56.13 6225 (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) -> (v5_cat_1(D,A) -> k1_xboole_0 = k6_cat_1(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) & k9_cat_1(A,B,C,B,D,E) = k10_cat_1(A,B) <-> k11_cat_1(A,B,C,D) = E)))))))))))) # label(d14_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6226 (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)) -> -(k6_cat_1(A,C,D) != k1_xboole_0 & k1_xboole_0 = k6_cat_1(A,B,D) & k6_cat_1(A,B,C) != k1_xboole_0))))))))) # label(t52_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6227 (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,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))))) <-> v6_cat_1(B,A)))))) # label(d15_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6228 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> k3_cat_1(A,B) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),B))))) # label(d3_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.14/56.13 6229 $T # label(t14_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.62 6230 (exists A (l1_cat_1(A) & v2_cat_1(A))) # label(rc2_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.62 6231 (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) -> D = E))))))))))) # label(t25_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.62 6232 $T # label(t79_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.62 6233 (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)) -> (k5_cat_1(A,C) = k5_cat_1(A,B) -> B = C))))))) # label(t45_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.62 6234 (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)) -> (k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C) = B -> 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))) & (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))) & 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 & 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)))) & (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),u3_cat_1(A),C) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),B) <-> r2_hidden(k4_tarski(C,B),k1_relat_1(u5_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)) -> (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),u4_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(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))))))))))) & (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) -> k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),B) = 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),u4_cat_1(A),C) = k1_funct_1(u4_cat_1(A),k1_funct_1(u5_cat_1(A),k4_tarski(C,B))))))))))) # label(d8_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.62 6235 $T # label(t2_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.62 6236 (all A (v2_cat_1(A) & l1_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]. 57.65/56.62 6237 (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]. 57.65/56.62 6238 $T # label(t28_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.62 6239 (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,k2_cat_1(A,D)) = k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)) & 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)))))))))) # label(t109_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.62 6240 (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]. 57.65/56.62 6241 (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)) -> 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]. 57.65/56.62 6242 (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]. 57.65/56.62 6243 (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)) -> k16_cat_1(A,B,C,D,E) = k2_partfun1(u2_cat_1(A),u2_cat_1(B),C,k6_cat_1(A,D,E)))))))))))) # label(d25_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.62 6244 (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 (v5_cat_1(D,A) & m1_cat_1(D,A,B,C))) & k1_xboole_0 != k6_cat_1(A,B,C) <-> r1_cat_1(A,B,C)))))))) # label(d17_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.62 6245 $T # label(t3_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.62 6246 (all A all B (l1_cat_1(A) & m1_subset_1(B,u2_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]. 57.65/56.62 6247 $T # label(t121_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.62 6248 $T # label(t53_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.62 6249 (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) -> r1_cat_1(A,C,B)))))))) # label(t92_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.62 6250 (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]. 57.65/56.62 6251 (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)) <-> C = k3_cat_1(A,D) & B = k2_cat_1(A,D)))))))))) # label(t18_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.62 6252 (all A all B all C all D (v2_cat_1(B) & m1_subset_1(D,u1_cat_1(A)) & m2_cat_1(C,A,B) & l1_cat_1(B) & v2_cat_1(A) & l1_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]. 57.65/56.62 6253 $T # label(dt_l1_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.62 6254 $T # label(t130_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.62 6255 $T # label(t12_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.62 6256 (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) -> (v5_cat_1(D,A) -> v5_cat_1(k11_cat_1(A,B,C,D),A) | k6_cat_1(A,B,C) = k1_xboole_0))))))))) # label(t76_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.62 6257 (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]. 57.65/56.62 6258 $T # label(t30_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.62 6259 (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) -> 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]. 57.65/56.62 6260 (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,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]. 57.65/56.62 6261 (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)) -> -(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]. 57.65/56.62 6262 (all A all B all C all D (v2_cat_1(A) & m1_cat_1(D,A,B,C) & m1_subset_1(C,u1_cat_1(A)) & l1_cat_1(A) & m1_subset_1(B,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]. 57.65/56.62 6263 (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)) & (all G (m1_cat_1(G,A,D,E) -> k1_tarski(G) != k6_cat_1(A,D,E))) & k6_cat_1(A,B,C) = k1_tarski(F)))))))))))))) # label(t27_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.62 6264 (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)) -> (exists D (m1_cat_1(D,A,C,B) & k6_cat_1(A,C,B) = k1_tarski(D)))))))))) # label(t86_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.62 6265 (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)) -> 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))) & 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))))))))))) # label(t98_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.62 6266 (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)) -> a_3_0_cat_1(A,B,C) = k6_cat_1(A,B,C))))))) # label(d6_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.62 6267 (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]. 57.65/56.62 6268 (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) <-> 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) & k10_cat_1(A,B) = k9_cat_1(A,B,C,B,D,E) & m1_cat_1(E,A,C,B))) & m1_cat_1(D,A,B,C))) & k1_xboole_0 != k6_cat_1(A,C,B)))))))) # label(t81_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.62 6269 (all A (v2_cat_1(A) & l1_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_1(C) & 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)) & k10_cat_1(B,E) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)))))) & (all D (m1_subset_1(D,u2_cat_1(A)) -> 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))) & 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))))) & (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))))))) -> m2_cat_1(C,A,B)))))))) # label(t96_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.62 6270 $T # label(t94_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.62 6271 (all A all B all C (m1_subset_1(B,u2_cat_1(A)) & m1_subset_1(C,u2_cat_1(A)) & l1_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]. 57.65/56.62 6272 (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]. 57.65/56.62 6273 $T # label(t10_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6274 (all A all B all C all D (l1_cat_1(B) & m1_subset_1(C,u1_cat_1(B)) & m1_subset_1(D,u1_cat_1(B)) -> ((exists E (k3_cat_1(B,E) = D & E = A & k2_cat_1(B,E) = C & m1_subset_1(E,u2_cat_1(B)))) <-> r2_hidden(A,a_3_0_cat_1(B,C,D))))) # label(fraenkel_a_3_0_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6275 (all A (v2_cat_1(A) & l1_cat_1(A) -> m2_cat_1(k15_cat_1(A),A,A))) # label(dt_k15_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6276 (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]. 57.65/56.63 6277 $T # label(t13_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6278 (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) -> k1_funct_1(k16_cat_1(A,B,C,D,E),F) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,F)))))))))))))) # label(t131_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6279 (all A all B all C (m1_subset_1(C,u1_cat_1(A)) & l1_cat_1(A) & m1_subset_1(B,u1_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]. 57.65/56.63 6280 (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)) -> (k4_cat_1(A,C,B) = k4_cat_1(A,D,B) & k3_cat_1(A,C) = k2_cat_1(A,B) & k2_cat_1(A,B) = k3_cat_1(A,D) & k2_cat_1(A,D) = k2_cat_1(A,C) -> C = D))))) <-> v3_cat_1(B,A)))))) # label(d10_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6281 (all A (v2_cat_1(A) & l1_cat_1(A) -> v8_cat_1(k15_cat_1(A),A,A))) # label(t122_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6282 $T # label(t78_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6283 $T # label(t106_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6284 (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) -> 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]. 57.65/56.63 6285 (all A all B k7_cat_1(A,B) = k3_cqc_lang(A,B)) # label(redefinition_k7_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6286 (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]. 57.65/56.63 6287 (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,C) = k2_cat_1(A,B) -> 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]. 57.65/56.63 6288 (exists A (l1_cat_1(A) & v2_cat_1(A) & v1_cat_1(A))) # label(rc3_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6289 (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]. 57.65/56.63 6290 (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(F,A) & v5_cat_1(E,A) -> k1_xboole_0 = k6_cat_1(A,B,C) | k6_cat_1(A,C,D) = k1_xboole_0 | v5_cat_1(k9_cat_1(A,B,C,D,E,F),A)))))))))))))) # label(t75_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6291 $T # label(t49_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6292 (all A all B all C all D all E (v2_cat_1(A) & l1_cat_1(B) & l1_cat_1(C) & m2_cat_1(E,B,C) & m2_cat_1(D,A,B) & v2_cat_1(C) & v2_cat_1(B) & l1_cat_1(A) -> k5_relat_1(D,E) = k14_cat_1(A,B,C,D,E))) # label(redefinition_k14_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6293 $T # label(t31_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6294 (all A all B all C all D all E (l1_cat_1(B) & m2_cat_1(C,A,B) & v2_cat_1(A) & l1_cat_1(A) & m1_subset_1(D,u1_cat_1(A)) & m1_subset_1(E,u1_cat_1(A)) & v2_cat_1(B) -> 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))) & 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_1(k16_cat_1(A,B,C,D,E)))) # label(dt_k16_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6295 (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) -> (v4_cat_1(k9_cat_1(A,B,C,D,E,F),A) -> v4_cat_1(F,A) | k1_xboole_0 = k6_cat_1(A,C,D) | k6_cat_1(A,B,C) = k1_xboole_0))))))))))))) # label(t67_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6296 (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) -> (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]. 57.65/56.63 6297 (all A (l1_cat_1(A) -> -v1_xboole_0(u2_cat_1(A)))) # label(dt_u2_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6298 $T # label(t114_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6299 (all A all B all C all D (-v1_xboole_0(D) -> (all E (v1_funct_2(E,A,D) & m2_relset_1(E,A,D) & v1_funct_1(E) -> (r1_tarski(B,A) & r1_tarski(k2_funct_2(A,D,E,B),C) -> m2_relset_1(k2_partfun1(A,D,E,B),B,C) & v1_funct_2(k2_partfun1(A,D,E,B),B,C) & v1_funct_1(k2_partfun1(A,D,E,B))))))) # label(t4_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6300 (all A (v2_cat_1(A) & l1_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]. 57.65/56.63 6301 (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) -> (u1_cat_1(B) = k2_relat_1(k12_cat_1(A,B,C)) & u2_cat_1(B) = k2_relat_1(C) & v2_funct_1(C) <-> v8_cat_1(C,A,B)))))))) # label(d22_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6302 (all A all B (v2_cat_1(B) & v2_cat_1(A) & l1_cat_1(B) & l1_cat_1(A) -> (exists C m2_cat_1(C,A,B)))) # label(existence_m2_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6303 (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]. 57.65/56.63 6304 (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 = k2_cat_1(A,C) -> C = k4_cat_1(A,k5_cat_1(A,B),C)))))))) # label(t47_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6305 (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)) -> (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]. 57.65/56.63 6306 $T # label(t50_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6307 (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,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]. 57.65/56.63 6308 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> k13_cat_1(A,A,k15_cat_1(A),B) = B)))) # label(t118_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6309 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> B = k8_funct_2(u2_cat_1(A),u2_cat_1(A),k15_cat_1(A),B))))) # label(t115_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6310 $T # label(t1_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6311 $T # label(t16_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6312 (all A (l1_cat_1(A) -> v1_funct_2(u3_cat_1(A),u2_cat_1(A),u1_cat_1(A)) & v1_funct_1(u3_cat_1(A)) & m2_relset_1(u3_cat_1(A),u2_cat_1(A),u1_cat_1(A)))) # label(dt_u3_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6313 (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) -> (v9_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)) -> (all F (m1_cat_1(F,B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)) -> (exists G (m1_cat_1(G,A,D,E) & k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,G) = F)) & k1_xboole_0 != k6_cat_1(A,D,E))))))))))))))) # label(d23_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6314 (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),u3_cat_1(A),B) = k2_cat_1(A,B))))) # label(d2_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6315 (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]. 57.65/56.63 6316 (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]. 57.65/56.63 6317 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> k2_cat_1(A,k5_cat_1(A,B)) = B & k3_cat_1(A,k5_cat_1(A,B)) = B)))) # label(t44_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6318 (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) -> -(k1_xboole_0 != k6_cat_1(A,B,C) & (exists E (m1_cat_1(E,A,C,B) & (exists F (k10_cat_1(A,C) = k9_cat_1(A,C,B,C,E,D) & m1_cat_1(F,A,C,B) & E != F & k9_cat_1(A,B,C,B,D,F) = k10_cat_1(A,B))))) & k6_cat_1(A,C,B) != k1_xboole_0))))))))) # label(t71_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6319 (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_subset_1(C,u1_cat_1(A)) -> (exists D (m1_cat_1(D,A,B,C) & k6_cat_1(A,B,C) = k1_tarski(D)))))))))) # label(t82_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6320 (exists A l1_cat_1(A)) # label(existence_l1_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6321 (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)) & k3_cat_1(A,B) = k2_cat_1(A,C) & k4_cat_1(A,B,C) = k5_cat_1(A,k2_cat_1(A,B)) & k5_cat_1(A,k3_cat_1(A,B)) = k4_cat_1(A,C,B) & k2_cat_1(A,B) = k3_cat_1(A,C))) <-> v5_cat_1(B,A)))))) # label(d12_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6322 (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]. 57.65/56.63 6323 (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]. 57.65/56.63 6324 (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]. 57.65/56.63 6325 (all A all B all C all D all E all F (m1_relset_1(C,B,A) & v1_funct_1(D) & m1_relset_1(E,k2_zfmisc_1(B,B),B) & v1_funct_2(F,A,B) & v1_funct_2(D,B,A) & v1_funct_2(C,B,A) & v1_funct_1(C) & -v1_xboole_0(B) & m1_relset_1(D,B,A) & v1_funct_1(E) & v1_funct_1(F) & m1_relset_1(F,A,B) & -v1_xboole_0(A) -> (all G all H all I all J all K all L (g1_cat_1(G,H,I,J,K,L) = g1_cat_1(A,B,C,D,E,F) -> K = E & F = L & B = H & J = D & C = I & A = G)))) # label(free_g1_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6326 (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,B,C) != k1_xboole_0 & k9_cat_1(A,B,C,D,E,F) != k4_cat_1(A,E,F) & k6_cat_1(A,C,D) != k1_xboole_0))))))))))))) # label(d13_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6327 $T # label(t48_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6328 (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]. 57.65/56.63 6329 $T # label(t11_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6330 $T # label(t17_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6331 (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) -> k10_cat_1(A,B) = C))))))) # label(t87_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6332 (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) -> (k1_xboole_0 != k6_cat_1(A,B,C) -> (v5_cat_1(D,A) <-> (exists E (k10_cat_1(A,B) = k9_cat_1(A,B,C,B,D,E) & k9_cat_1(A,C,B,C,E,D) = k10_cat_1(A,C) & m1_cat_1(E,A,C,B))) & k6_cat_1(A,C,B) != k1_xboole_0)))))))))) # label(t70_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6333 (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]. 57.65/56.63 6334 (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)) -> 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]. 57.65/56.63 6335 (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) -> (k10_cat_1(A,C) = k9_cat_1(A,C,B,C,E,D) -> k1_xboole_0 = k6_cat_1(A,B,C) | k1_xboole_0 = k6_cat_1(A,C,B) | v4_cat_1(D,A)))))))))))) # label(t68_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6336 (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)) -> (r2_hidden(k4_tarski(B,C),k1_relat_1(u5_cat_1(A))) <-> k3_cat_1(A,C) = k2_cat_1(A,B)))))))) # label(t40_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6337 (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]. 57.65/56.63 6338 (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 -> (v3_cat_1(D,A) <-> (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,F,D) = k9_cat_1(A,E,B,C,G,D) -> F = G | k1_xboole_0 = k6_cat_1(A,E,B)))))))))))))))))) # label(t60_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6339 (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) -> 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]. 57.65/56.63 6340 $T # label(t120_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6341 (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]. 57.65/56.63 6342 (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) -> ((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,G) = k9_cat_1(A,B,C,E,D,F) -> F = G | k6_cat_1(A,C,E) = k1_xboole_0))))))) <-> v4_cat_1(D,A))))))))))) # label(t65_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6343 (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 -> D = k9_cat_1(A,B,B,C,k10_cat_1(A,B),D)))))))))) # label(t58_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6344 (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)) -> (exists 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)))))))))))) # label(t97_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6345 (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_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) -> -(k6_cat_1(A,C,D) != k1_xboole_0 & 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)))))))))))))))))) # label(t54_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6346 (all A all B (v2_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) & l1_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]. 57.65/56.63 6347 (all A (l1_cat_1(A) -> (v1_cat_1(A) -> 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))))) # label(abstractness_v1_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6348 (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]. 57.65/56.63 6349 (all A (l1_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)) & v1_funct_1(u5_cat_1(A)))) # label(dt_u5_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6350 (all A (v2_cat_1(A) & l1_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 (v1_funct_2(D,u1_cat_1(A),u1_cat_1(B)) & m2_relset_1(D,u1_cat_1(A),u1_cat_1(B)) & v1_funct_1(D) -> ((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) -> k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k4_cat_1(A,E,F)) = 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))))))) & (all E (m1_subset_1(E,u2_cat_1(A)) -> k2_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)) & 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)))) & (all E (m1_subset_1(E,u1_cat_1(A)) -> k10_cat_1(B,k8_funct_2(u1_cat_1(A),u1_cat_1(B),D,E)) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,E)))) -> m2_cat_1(C,A,B)))))))))) # label(t100_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.63 6351 (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)) -> (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]. 57.65/56.64 6352 (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,u2_cat_1(A)) -> 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)) & k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),k2_cat_1(A,D)) = k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)))))))))) # label(t105_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.64 6353 (all A all B all C all D all E (l1_cat_1(A) & l1_cat_1(B) & l1_cat_1(C) & v2_cat_1(C) & v2_cat_1(A) & v2_cat_1(B) & m2_cat_1(D,A,B) & m2_cat_1(E,B,C) -> m2_cat_1(k14_cat_1(A,B,C,D,E),A,C))) # label(dt_k14_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.64 6354 $T # label(t119_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.64 6355 (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(B,A) & r1_cat_1(A,C,B) -> v6_cat_1(C,A)))))))) # label(t89_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.64 6356 (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) & v6_cat_1(C,A) -> r1_cat_1(A,B,C)))))))) # label(t88_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.64 6357 (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]. 57.65/56.64 6358 (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) -> -(k1_xboole_0 != k6_cat_1(A,B,C) & -r2_hidden(k4_cat_1(A,E,F),k6_cat_1(A,B,D)) & k6_cat_1(A,C,D) != k1_xboole_0))))))))))))) # label(t51_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.64 6359 (all A (l1_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)) & v1_funct_1(u6_cat_1(A)))) # label(dt_u6_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.64 6360 (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 (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,B,C) -> (v10_cat_1(E,B,C) & v10_cat_1(D,A,B) -> v10_cat_1(k14_cat_1(A,B,C,D,E),A,C)))))))))))) # label(t128_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.64 6361 (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]. 57.65/56.64 6362 (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]. 57.65/56.64 6363 (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) -> k11_cat_1(A,B,D,k9_cat_1(A,B,C,D,E,F)) = k9_cat_1(A,D,C,B,k11_cat_1(A,C,D,F),k11_cat_1(A,B,C,E)) | k6_cat_1(A,C,D) = k1_xboole_0 | k1_xboole_0 = k6_cat_1(A,B,C)))))))))))))) # label(t77_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.64 6364 $T # label(t5_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.64 6365 (all A all B all C all D all E all F (v1_funct_1(C) & v1_funct_1(D) & v1_funct_2(D,B,A) & -v1_xboole_0(B) & -v1_xboole_0(A) & v1_funct_2(C,B,A) & m1_relset_1(D,B,A) & 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) & v1_funct_1(E) & m1_relset_1(C,B,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]. 57.65/56.64 6366 $T # label(t101_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.64 6367 (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) -> v3_cat_1(E,A) | k6_cat_1(A,C,D) = k1_xboole_0 | k1_xboole_0 = k6_cat_1(A,B,C)))))))))))))) # label(t62_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.64 6368 (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)) -> 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]. 57.65/56.64 6369 (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]. 57.65/56.64 6370 (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) & v7_cat_1(B,A) -> v7_cat_1(C,A)))))))) # label(t85_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.64 6371 $T # label(t20_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.64 6372 (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) -> D = E)) -> k1_tarski(D) = k6_cat_1(A,B,C) | k1_xboole_0 = k6_cat_1(A,B,C)))))))))) # label(t26_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.64 6373 (exists A (v1_cat_1(A) & l1_cat_1(A))) # label(rc1_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.64 6374 (all A all B (m1_subset_1(B,u1_cat_1(A)) & l1_cat_1(A) & v2_cat_1(A) -> k10_cat_1(A,B) = k5_cat_1(A,B))) # label(redefinition_k10_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.64 6375 (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 (m1_subset_1(D,u2_cat_1(A)) -> (k2_cat_1(A,D) = k3_cat_1(A,C) & k2_cat_1(A,C) = k3_cat_1(A,B) -> k4_cat_1(A,B,k4_cat_1(A,C,D)) = k4_cat_1(A,k4_cat_1(A,B,C),D)))))))))) # label(t43_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.64 6376 (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,B) = k2_cat_1(A,C) -> k3_cat_1(A,C) = k3_cat_1(A,k4_cat_1(A,B,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]. 57.65/56.64 6377 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> k1_xboole_0 != k6_cat_1(A,k2_cat_1(A,B),k3_cat_1(A,B)))))) # label(t19_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.64 6378 (all A (l1_cat_1(A) -> -v1_xboole_0(u1_cat_1(A)))) # label(dt_u1_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.64 6379 (all A all B (m1_subset_1(B,u1_cat_1(A)) & l1_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]. 57.65/56.64 6380 (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(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]. 57.65/56.64 6381 (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) -> k4_cat_1(A,C,k5_cat_1(A,B)) = C))))))) # label(t46_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.65/56.64 6382 (all A all 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)) & v1_funct_1(k7_cat_1(A,B)))) # label(dt_k7_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.83/56.80 6383 $T # label(t6_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.83/56.80 6384 (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)) -> (k3_cat_1(A,B) = k2_cat_1(A,C) -> k2_cat_1(A,k4_cat_1(A,B,C)) = k2_cat_1(A,B) & k3_cat_1(A,C) = k3_cat_1(A,k4_cat_1(A,B,C))))))) & (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))) <-> k2_cat_1(A,C) = k3_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)) -> (k3_cat_1(A,B) = k2_cat_1(A,C) & k3_cat_1(A,C) = k2_cat_1(A,D) -> k4_cat_1(A,B,k4_cat_1(A,C,D)) = k4_cat_1(A,k4_cat_1(A,B,C),D)))))))) & (all B (m1_subset_1(B,u1_cat_1(A)) -> B = k2_cat_1(A,k5_cat_1(A,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))))) & k3_cat_1(A,k5_cat_1(A,B)) = B)) -> v2_cat_1(A)))) # label(t29_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.83/56.80 6385 (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) -> E = k13_cat_1(A,B,C,D)))))))))))) # label(t107_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.83/56.80 6386 (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_1(C) & 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,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(t102_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.83/56.80 6387 (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)) -> 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]. 57.83/56.80 6388 (all A all B (v2_cat_1(B) & v2_cat_1(A) & l1_cat_1(A) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_1(C) & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)))))) # label(dt_m2_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.83/56.80 6389 $T # label(t72_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.83/56.80 6390 $T # label(t95_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.83/56.80 6391 (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)) -> (all E (m1_subset_1(E,u2_cat_1(A)) -> (k3_cat_1(A,D) = k2_cat_1(A,E) -> 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,E)) & 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))))))))))))) # label(t99_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.83/56.80 6392 (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) -> (exists D m1_cat_1(D,A,B,C)))) # label(existence_m1_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.83/56.80 6393 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> k10_cat_1(A,B) = k9_cat_1(A,B,B,B,k10_cat_1(A,B),k10_cat_1(A,B)))))) # label(t59_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.83/56.80 6394 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (v4_cat_1(B,A) <-> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (k4_cat_1(A,B,C) = k4_cat_1(A,B,D) & k2_cat_1(A,C) = k3_cat_1(A,B) & k2_cat_1(A,D) = k3_cat_1(A,B) & k3_cat_1(A,C) = k3_cat_1(A,D) -> D = C)))))))))) # label(d11_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.83/56.80 6395 (all A (v2_cat_1(A) & l1_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]. 57.83/56.80 6396 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> k1_xboole_0 != k6_cat_1(A,B,B))))) # label(t56_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.83/56.80 6397 (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) -> k3_cat_1(A,D) = C & k2_cat_1(A,D) = B))))))))) # label(t23_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.83/56.80 6398 (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) -> E = k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D)))))))))))) # label(t103_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.83/56.80 6399 (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]. 57.83/56.80 6400 (all A (v2_cat_1(A) & l1_cat_1(A) -> k15_cat_1(A) = k6_partfun1(u2_cat_1(A)))) # label(d21_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.83/56.80 6401 (all A all B all C (m1_subset_1(C,u1_cat_1(A)) & l1_cat_1(A) & m1_subset_1(B,u1_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]. 57.83/56.80 6402 (all A (l1_cat_1(A) -> v1_funct_2(u4_cat_1(A),u2_cat_1(A),u1_cat_1(A)) & m2_relset_1(u4_cat_1(A),u2_cat_1(A),u1_cat_1(A)) & v1_funct_1(u4_cat_1(A)))) # label(dt_u4_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.83/56.80 6403 (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]. 57.83/56.80 6404 (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)) -> k10_cat_1(B,k13_cat_1(A,B,C,D)) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)))))))))) # label(t108_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.83/56.80 6405 $T # label(t15_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.83/56.80 6406 (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)) -> k10_cat_1(B,k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D)) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)))))))))) # label(t104_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.83/56.80 6407 (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) -> (v5_cat_1(D,A) -> k1_xboole_0 = k6_cat_1(A,B,C) | v4_cat_1(D,A) & v3_cat_1(D,A)))))))))) # label(t73_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.83/56.80 6408 (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 -> k1_xboole_0 = k6_cat_1(A,B,C) | E = C & B = D | k6_cat_1(A,D,E) = k1_xboole_0))))))))))))))) # label(t24_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.83/56.80 6409 (all A all B all C C = k1_funct_1(k1_cat_1(A,B,C),k4_tarski(A,B))) # label(t8_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.83/56.80 6410 (all A (v2_cat_1(A) & l1_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,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)))))) & (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(C,k1_funct_1(u5_cat_1(A),k4_tarski(E,D))) = 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)))))))) <-> m2_cat_1(C,A,B)))))))) # label(d18_cat_1) # label(axiom) # label(non_clause). [assumption]. 57.83/56.80 6411 (exists A (l1_lattices(A) & v1_lattices(A) & v7_lattices(A) & v6_lattices(A) & -v3_struct_0(A))) # label(rc8_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.80 6412 (all A (l1_lattices(A) -> l1_struct_0(A))) # label(dt_l1_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.80 6413 (all A (l1_lattices(A) & -v3_struct_0(A) -> ((exists B ((all C (m1_subset_1(C,u1_struct_0(A)) -> k2_lattices(A,C,B) = B & k2_lattices(A,B,C) = B)) & m1_subset_1(B,u1_struct_0(A)))) <-> v13_lattices(A)))) # label(d13_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.80 6414 (all A all B all C (-v3_struct_0(A) & l1_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_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]. 57.83/56.80 6415 (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]. 57.83/56.80 6416 $T # label(t8_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.80 6417 (all A all B all 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) & v1_funct_1(C) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & -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]. 57.83/56.80 6418 $T # label(t38_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.80 6419 (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)) -> B = k7_lattices(A,k7_lattices(A,B)))))) # label(t49_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.80 6420 $T # label(t37_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.80 6421 $T # label(t36_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.80 6422 (exists A (v1_lattices(A) & l1_lattices(A) & -v3_struct_0(A))) # label(rc5_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.80 6423 (all A all B all C (-v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & l1_lattices(A) & v6_lattices(A) & m1_subset_1(C,u1_struct_0(A)) -> k4_lattices(A,B,C) = k4_lattices(A,C,B))) # label(commutativity_k4_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.80 6424 (all A (l2_lattices(A) & -v3_struct_0(A) -> (v14_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (B = k6_lattices(A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_lattices(A,C,B) = B & k1_lattices(A,B,C) = B)))))))) # label(d17_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.80 6425 (all 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)) -> (r1_lattices(A,B,D) -> k1_lattices(A,B,k2_lattices(A,C,D)) = k2_lattices(A,k1_lattices(A,B,C),D)))))))) <-> v12_lattices(A)))) # label(d12_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6426 (all A (v10_lattices(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)) -> k4_lattices(A,k3_lattices(A,B,C),k3_lattices(A,B,D)) = k3_lattices(A,B,k4_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,B,k3_lattices(A,C,D)) = k3_lattices(A,k4_lattices(A,B,C),k4_lattices(A,B,D))))))))))) # label(t19_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6427 (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)) -> k6_lattices(A) = k3_lattices(A,k7_lattices(A,B),B))))) # label(t48_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6428 (exists A (v3_lattices(A) & v5_lattices(A) & v9_lattices(A) & v12_lattices(A) & v13_lattices(A) & v8_lattices(A) & v7_lattices(A) & v6_lattices(A) & -v3_struct_0(A) & v10_lattices(A) & v11_lattices(A) & v14_lattices(A) & v4_lattices(A) & l3_lattices(A))) # label(rc10_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6429 $T # label(t42_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6430 $T # label(t15_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6431 (all A all B all C (l1_lattices(A) & m1_subset_1(C,u1_struct_0(A)) & -v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & v6_lattices(A) -> k2_lattices(A,B,C) = k4_lattices(A,B,C))) # label(redefinition_k4_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6432 (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_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]. 57.83/56.81 6433 (all A (l1_lattices(A) -> v1_funct_2(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & m2_relset_1(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]. 57.83/56.81 6434 $T # label(t10_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6435 (all A (l3_lattices(A) -> l1_lattices(A) & l2_lattices(A))) # label(dt_l3_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6436 (all A (l3_lattices(A) -> (v10_lattices(A) & -v3_struct_0(A) -> v5_lattices(A) & v9_lattices(A) & v7_lattices(A) & v6_lattices(A) & v8_lattices(A) & v4_lattices(A) & -v3_struct_0(A)))) # label(cc1_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6437 (all A all B all C (-v3_struct_0(A) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> k3_lattices(A,B,C) = k1_lattices(A,B,C))) # label(redefinition_k3_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6438 (all A (-v3_struct_0(A) & l3_lattices(A) -> (v15_lattices(A) <-> v14_lattices(A) & v13_lattices(A)))) # label(d15_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6439 (all A (v17_lattices(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)) -> (k4_lattices(A,B,C) = k5_lattices(A) <-> r3_lattices(A,B,k7_lattices(A,C))))))))) # label(t52_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6440 (exists A (v4_lattices(A) & -v3_struct_0(A) & v2_lattices(A) & v5_lattices(A) & l2_lattices(A))) # label(rc7_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6441 (exists A l1_lattices(A)) # label(existence_l1_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6442 (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) -> (all C all D (g2_lattices(C,D) = g2_lattices(A,B) -> D = B & C = A)))) # label(free_g2_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6443 (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,k2_lattices(A,B,C),D) = k2_lattices(A,B,k2_lattices(A,C,D)))))))) <-> v7_lattices(A)))) # label(d7_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6444 (all A (-v3_struct_0(A) & l3_lattices(A) & v11_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)) -> 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)))))))))) # label(t34_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6445 $T # label(t5_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6446 (all A (l3_lattices(A) -> (v17_lattices(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v13_lattices(A) & v15_lattices(A) & v16_lattices(A) & v14_lattices(A) & v11_lattices(A)))) # label(cc5_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6447 (all A all B all C (-v3_struct_0(A) & l2_lattices(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & v4_lattices(A) -> k3_lattices(A,C,B) = k3_lattices(A,B,C))) # label(commutativity_k3_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6448 (all A (l3_lattices(A) -> (v3_lattices(A) -> g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = A))) # label(abstractness_v3_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6449 (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]. 57.83/56.81 6450 (all A (-v3_struct_0(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & v6_lattices(A) & v5_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,k1_lattices(A,B,C)))))))) # label(t22_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6451 (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)) -> (r2_lattices(A,B,C) <-> k6_lattices(A) = k1_lattices(A,C,B) & k5_lattices(A) = k2_lattices(A,B,C) & k5_lattices(A) = k2_lattices(A,C,B) & k6_lattices(A) = k1_lattices(A,B,C)))))))) # label(d18_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6452 (all A (v8_lattices(A) & v9_lattices(A) & -v3_struct_0(A) & l3_lattices(A) & v6_lattices(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]. 57.83/56.81 6453 (all A (l3_lattices(A) & -v3_struct_0(A) & v6_lattices(A) & v9_lattices(A) & v8_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k1_lattices(A,B,B))))) # label(t17_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6454 $T # label(t3_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6455 (all A all B all C (-v3_struct_0(A) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> m1_subset_1(k3_lattices(A,B,C),u1_struct_0(A)))) # label(dt_k3_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6456 (exists A (-v3_struct_0(A) & v3_lattices(A) & l3_lattices(A))) # label(rc6_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6457 (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)) -> k1_lattices(A,B,C) = k1_lattices(A,C,B))))) <-> v4_lattices(A)))) # label(d4_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6458 (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)) -> 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]. 57.83/56.81 6459 (all A (l3_lattices(A) & v11_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)) -> k4_lattices(A,k3_lattices(A,B,C),k3_lattices(A,B,D)) = k3_lattices(A,B,k4_lattices(A,C,D)))))))))) # label(t31_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6460 (all A (l3_lattices(A) -> (v15_lattices(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v13_lattices(A) & v14_lattices(A)))) # label(cc4_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6461 $T # label(t14_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6462 $T # label(t13_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6463 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) & v17_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]. 57.83/56.81 6464 (all A (v10_lattices(A) & -v3_struct_0(A) & l3_lattices(A) & v13_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]. 57.83/56.81 6465 (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]. 57.83/56.81 6466 (all A all B (m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C all D (g1_lattices(C,D) = g1_lattices(A,B) -> B = D & A = C)))) # label(free_g1_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6467 (all A (l2_lattices(A) & -v3_struct_0(A) -> (v5_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)))))))))) # label(d5_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6468 (all A (l2_lattices(A) -> (v2_lattices(A) -> A = g2_lattices(u1_struct_0(A),u2_lattices(A))))) # label(abstractness_v2_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6469 $T # label(t7_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6470 (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)) -> k1_lattices(A,k2_lattices(A,B,C),k2_lattices(A,B,D)) = k2_lattices(A,B,k1_lattices(A,C,D)))))))) <-> v11_lattices(A)))) # label(d11_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6471 (all A all B all C (-v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(C,u1_struct_0(A)) -> r3_lattices(A,B,B))) # label(reflexivity_r3_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6472 (all A (l3_lattices(A) & v11_lattices(A) & -v3_struct_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)) -> (k4_lattices(A,B,D) = k4_lattices(A,B,C) & k3_lattices(A,B,C) = k3_lattices(A,B,D) -> D = C))))))))) # label(t32_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6473 (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)) -> k2_lattices(A,B,k1_lattices(A,B,C)) = B))))))) # label(d9_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6474 (all A (-v3_struct_0(A) & l2_lattices(A) -> (v14_lattices(A) <-> (exists B ((all C (m1_subset_1(C,u1_struct_0(A)) -> k1_lattices(A,C,B) = B & k1_lattices(A,B,C) = B)) & m1_subset_1(B,u1_struct_0(A))))))) # label(d14_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6475 $T # label(t1_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6476 (all A (v17_lattices(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_lattices(A,B,C) -> r3_lattices(A,k7_lattices(A,C),k7_lattices(A,B))))))))) # label(t53_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6477 $T # label(t24_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6478 (all A all B (l3_lattices(A) & m1_subset_1(B,u1_struct_0(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]. 57.83/56.81 6479 (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]. 57.83/56.81 6480 (all A (l3_lattices(A) -> (v6_lattices(A) & v9_lattices(A) & v4_lattices(A) & v8_lattices(A) & v7_lattices(A) & v5_lattices(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v10_lattices(A)))) # label(cc2_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6481 (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]. 57.83/56.81 6482 (all A (v13_lattices(A) & v10_lattices(A) & -v3_struct_0(A) & l3_lattices(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]. 57.83/56.81 6483 (all A (l3_lattices(A) -> (v16_lattices(A) & v11_lattices(A) & -v3_struct_0(A) & v15_lattices(A) -> -v3_struct_0(A) & v17_lattices(A)))) # label(cc6_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6484 $T # label(t9_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6485 (exists A (l3_lattices(A) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v13_lattices(A) & v15_lattices(A) & v9_lattices(A) & -v3_struct_0(A) & v14_lattices(A) & v10_lattices(A) & v8_lattices(A) & v7_lattices(A) & v3_lattices(A))) # label(rc11_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6486 (all A all B (m1_relset_1(B,k2_zfmisc_1(A,A),A) & -v1_xboole_0(A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> -v3_struct_0(g1_lattices(A,B)) & v1_lattices(g1_lattices(A,B)))) # label(fc2_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6487 $T # label(t28_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6488 $T # label(t16_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6489 $T # label(t35_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6490 (all A (-v3_struct_0(A) & l3_lattices(A) -> (v15_lattices(A) & v11_lattices(A) & v16_lattices(A) <-> v17_lattices(A)))) # label(d20_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6491 (all A (v6_lattices(A) & v8_lattices(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)) -> r1_lattices(A,k4_lattices(A,B,C),B))))))) # label(t23_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6492 (exists A (v6_lattices(A) & v10_lattices(A) & v9_lattices(A) & v8_lattices(A) & v3_lattices(A) & -v3_struct_0(A) & v7_lattices(A) & v5_lattices(A) & v4_lattices(A) & l3_lattices(A))) # label(rc9_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6493 (exists A (l2_lattices(A) & v2_lattices(A))) # label(rc2_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6494 (all A (v10_lattices(A) & -v3_struct_0(A) & v14_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k4_lattices(A,k6_lattices(A),B) = B)))) # label(t43_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6495 (exists A (l3_lattices(A) & -v3_struct_0(A) & v3_lattices(A) & v5_lattices(A) & v6_lattices(A) & v15_lattices(A) & v14_lattices(A) & v4_lattices(A) & v9_lattices(A) & v13_lattices(A) & v16_lattices(A) & v10_lattices(A) & v8_lattices(A) & v7_lattices(A))) # label(rc12_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6496 (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]. 57.83/56.81 6497 (all A all B all C (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(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all D all E all F (g3_lattices(A,B,C) = g3_lattices(D,E,F) -> E = B & C = F & D = A)))) # label(free_g3_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6498 (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]. 57.83/56.81 6499 $T # label(t30_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6500 (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]. 57.83/56.81 6501 (all A (l2_lattices(A) -> m2_relset_1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_2(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]. 57.83/56.81 6502 (all A (l1_lattices(A) & -v3_struct_0(A) -> (v13_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k5_lattices(A) = B <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_lattices(A,B,C) = B & k2_lattices(A,C,B) = B)))))))) # label(d16_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6503 (all A (-v3_struct_0(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (l3_lattices(A) & v16_lattices(A) & v10_lattices(A) & v11_lattices(A) & -v3_struct_0(A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (C = k7_lattices(A,B) <-> r2_lattices(A,C,B))))))))) # label(d21_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6504 (exists A l2_lattices(A)) # label(existence_l2_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6505 $T # label(t11_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6506 (exists A (l3_lattices(A) & v5_lattices(A) & v17_lattices(A) & v15_lattices(A) & v13_lattices(A) & v10_lattices(A) & v9_lattices(A) & -v3_struct_0(A) & v4_lattices(A) & v6_lattices(A) & v7_lattices(A) & v16_lattices(A) & v14_lattices(A) & v11_lattices(A) & v8_lattices(A) & v3_lattices(A))) # label(rc13_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6507 $T # label(t6_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6508 (all A all B all C (v9_lattices(A) & v6_lattices(A) & v8_lattices(A) & l3_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(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]. 57.83/56.81 6509 (exists A (v3_lattices(A) & l3_lattices(A))) # label(rc3_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6510 (exists A (v1_lattices(A) & l1_lattices(A))) # label(rc1_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6511 (all A (-v3_struct_0(A) & v14_lattices(A) & v10_lattices(A) & l3_lattices(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]. 57.83/56.81 6512 $T # label(t33_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6513 (all A (l3_lattices(A) & -v3_struct_0(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]. 57.83/56.81 6514 (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)) -> k7_lattices(A,k3_lattices(A,B,C)) = k4_lattices(A,k7_lattices(A,B),k7_lattices(A,C)))))))) # label(t51_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6515 (all A (-v3_struct_0(A) & l3_lattices(A) & v8_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]. 57.83/56.81 6516 (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_lattices(g1_lattices(A,B)) & l1_lattices(g1_lattices(A,B)))) # label(dt_g1_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6517 (all A all B all C (v6_lattices(A) & m1_subset_1(C,u1_struct_0(A)) & -v3_struct_0(A) & l1_lattices(A) & m1_subset_1(B,u1_struct_0(A)) -> m1_subset_1(k4_lattices(A,B,C),u1_struct_0(A)))) # label(dt_k4_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6518 (all A (v7_lattices(A) & v9_lattices(A) & l3_lattices(A) & v8_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]. 57.83/56.81 6519 (all A (l3_lattices(A) & -v3_struct_0(A) -> (v16_lattices(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (exists C (r2_lattices(A,C,B) & m1_subset_1(C,u1_struct_0(A))))))))) # label(d19_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6520 (all A all B (-v1_xboole_0(A) & 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)) & -v3_struct_0(g2_lattices(A,B)))) # label(fc1_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6521 (all A all B all C (m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m1_relset_1(B,k2_zfmisc_1(A,A),A) -> l3_lattices(g3_lattices(A,B,C)) & v3_lattices(g3_lattices(A,B,C)))) # label(dt_g3_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6522 (exists A (l2_lattices(A) & v2_lattices(A) & -v3_struct_0(A))) # label(rc4_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6523 $T # label(t2_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6524 $T # label(t12_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6525 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & m1_relset_1(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]. 57.83/56.81 6526 (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]. 57.83/56.81 6527 (all A (v5_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)) -> (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]. 57.83/56.81 6528 (all A (l3_lattices(A) -> (v11_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v4_lattices(A) & v10_lattices(A) & v6_lattices(A) & v5_lattices(A) & v12_lattices(A) & v9_lattices(A) & v8_lattices(A) & v7_lattices(A)))) # label(cc7_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.81 6529 (all A (-v3_struct_0(A) & l3_lattices(A) -> (v4_lattices(A) & v7_lattices(A) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & v5_lattices(A) <-> v10_lattices(A)))) # label(d10_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6530 (all A (l2_lattices(A) -> l1_struct_0(A))) # label(dt_l2_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6531 $T # label(t46_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6532 $T # label(t20_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6533 (all A (v17_lattices(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)) -> k7_lattices(A,k4_lattices(A,B,C)) = k3_lattices(A,k7_lattices(A,B),k7_lattices(A,C)))))))) # label(t50_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6534 (all A (v10_lattices(A) & -v3_struct_0(A) & v13_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k3_lattices(A,k5_lattices(A),B))))) # label(t39_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6535 (exists A l3_lattices(A)) # label(existence_l3_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6536 $T # label(t4_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6537 (all A (l2_lattices(A) & v4_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) -> B = C))))))) # label(t26_lattices) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6538 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -((all C (m1_subset_1(C,u1_struct_0(A)) -> -r2_hidden(C,B))) & B != k1_pre_topc(A)))))) # label(t41_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6539 (all A all B all C all D (l1_struct_0(B) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) & l1_struct_0(A) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> m1_subset_1(k4_pre_topc(A,B,C,D),k1_zfmisc_1(u1_struct_0(B))))) # label(dt_k4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6540 (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]. 57.83/56.82 6541 (all A all B (l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> m1_pre_topc(k3_pre_topc(A,B),A) & v1_pre_topc(k3_pre_topc(A,B)))) # label(dt_k3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6542 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (exists B (v1_pre_topc(B) & -v3_struct_0(B) & m1_pre_topc(B,A))))) # label(rc4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6543 $T # label(d4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6544 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (r2_hidden(C,u1_struct_0(A)) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,D) & v4_pre_topc(D,A) -> r2_hidden(C,D)))) <-> r2_hidden(C,k6_pre_topc(A,B))))))))) # label(t45_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6545 (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]. 57.83/56.82 6546 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) -> k6_pre_topc(A,B) = B) & (B = k6_pre_topc(A,B) & v2_pre_topc(A) -> v4_pre_topc(B,A)))))) # label(t52_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6547 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) <-> v3_pre_topc(k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B),A)))))) # label(d6_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6548 $T # label(t10_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6549 (all A (l1_struct_0(A) -> v3_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) & v1_xboole_0(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)))) # label(fc1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6550 (all A (l1_struct_0(A) -> u1_struct_0(A) = k2_pre_topc(A))) # label(d3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6551 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) = C -> k4_subset_1(u1_struct_0(A),B,C) = k2_pre_topc(A)))))))) # label(t24_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6552 (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]. 57.83/56.82 6553 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C all D (g1_pre_topc(A,B) = g1_pre_topc(C,D) -> D = B & C = A)))) # label(free_g1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6554 (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]. 57.83/56.82 6555 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k6_pre_topc(A,k4_subset_1(u1_struct_0(A),B,C)) = k4_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,C)))))))) # label(t50_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6556 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> ((exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & C = k3_xboole_0(D,k2_pre_topc(B)) & v4_pre_topc(D,A))) <-> v4_pre_topc(C,B)))))))) # label(t43_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6557 $T # label(t33_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6558 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (v2_pre_topc(B) & v1_pre_topc(B) & m1_pre_topc(B,A))))) # label(rc5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6559 $T # label(d11_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6560 $T # label(t2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6561 $T # label(t4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6562 $T # label(t37_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6563 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> k6_pre_topc(A,k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B)) = k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B)) & (v2_pre_topc(A) & k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) = k6_pre_topc(A,k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B)) -> v3_pre_topc(B,A)))))) # label(t53_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6564 $T # label(t6_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6565 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) != k1_xboole_0 & k2_pre_topc(A) = B) & -(k1_xboole_0 = k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) & B != k2_pre_topc(A)))))) # label(t23_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6566 (all A (l1_struct_0(A) -> k2_pre_topc(A) = u1_struct_0(A))) # label(t12_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6567 (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]. 57.83/56.82 6568 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,k6_pre_topc(A,B)) <-> -v3_struct_0(A) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_hidden(C,D) & v3_pre_topc(D,A) & r1_xboole_0(B,D))))))))))) # label(t54_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6569 $T # label(t26_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6570 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> m1_subset_1(k6_pre_topc(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k6_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6571 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (exists C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,D) & v4_pre_topc(D,A) <-> r2_hidden(D,C)))) & k6_setfam_1(u1_struct_0(A),C) = k6_pre_topc(A,B))))))) # label(t46_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6572 $T # label(t28_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6573 (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]. 57.83/56.82 6574 (all A all B all C all D (l1_struct_0(B) & l1_struct_0(A) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> k5_pre_topc(A,B,C,D) = k10_relat_1(C,D))) # label(redefinition_k5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6575 $T # label(t19_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6576 (all A (l1_pre_topc(A) -> (exists B (v1_pre_topc(B) & m1_pre_topc(B,A))))) # label(rc3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6577 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_pre_topc(C,A) & v1_pre_topc(C) -> (k2_pre_topc(C) = B <-> C = k3_pre_topc(A,B)))))))) # label(d10_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6578 (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]. 57.83/56.82 6579 $T # label(t29_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6580 $T # label(t11_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6581 (all A (l1_struct_0(A) -> k1_pre_topc(A) = k1_xboole_0)) # label(d2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6582 (all A all B (l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v2_pre_topc(A) -> v1_pre_topc(k3_pre_topc(A,B)) & v2_pre_topc(k3_pre_topc(A,B)))) # label(fc4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6583 (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]. 57.83/56.82 6584 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) <-> r2_hidden(B,u1_pre_topc(A))))))) # label(d5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6585 (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]. 57.83/56.82 6586 $T # label(t8_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6587 (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]. 57.83/56.82 6588 $T # label(t21_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6589 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & v4_pre_topc(B,A))))) # label(rc7_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6590 $T # label(t3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6591 $T # label(d7_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6592 (all A (l1_pre_topc(A) -> (exists B m1_pre_topc(B,A)))) # label(existence_m1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6593 (exists A (l1_pre_topc(A) & -v3_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A))) # label(rc2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6594 (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]. 57.83/56.82 6595 (all A all B (l1_pre_topc(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v3_struct_0(A) -> v1_pre_topc(k3_pre_topc(A,B)) & -v3_struct_0(k3_pre_topc(A,B)))) # label(fc3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6596 (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]. 57.83/56.82 6597 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k6_subset_1(u1_struct_0(A),k2_pre_topc(A),k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B)) = B)))) # label(t22_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6598 $T # label(t9_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6599 $T # label(t38_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6600 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k4_subset_1(u1_struct_0(A),B,k3_subset_1(u1_struct_0(A),B)) = k2_pre_topc(A))))) # label(t18_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6601 $T # label(t32_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6602 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> v4_pre_topc(C,A)))) -> v4_pre_topc(k6_setfam_1(u1_struct_0(A),B),A)))))) # label(t44_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6603 $T # label(t1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6604 (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]. 57.83/56.82 6605 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> v4_pre_topc(k2_pre_topc(A),A))) # label(t42_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6606 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> ((exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & k3_xboole_0(D,k2_pre_topc(B)) = C & r2_hidden(D,u1_pre_topc(A)))) <-> r2_hidden(C,u1_pre_topc(B))))) & r1_tarski(k2_pre_topc(B),k2_pre_topc(A)) <-> m1_pre_topc(B,A)))))) # label(d9_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6607 (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]. 57.83/56.82 6608 (all A (l1_struct_0(A) & -v3_struct_0(A) -> -v1_xboole_0(k2_pre_topc(A)))) # label(fc2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6609 $T # label(t40_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6610 $T # label(t30_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6611 (all A (l1_pre_topc(A) -> l1_struct_0(A))) # label(dt_l1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6612 (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]. 57.83/56.82 6613 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (C = D -> k3_xboole_0(k6_pre_topc(A,C),k2_pre_topc(B)) = k6_pre_topc(B,D)))))))))) # label(t47_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6614 $T # label(t20_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6615 $T # label(t35_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6616 (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]. 57.83/56.82 6617 $T # label(t31_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6618 (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]. 57.83/56.82 6619 (exists A l1_pre_topc(A)) # label(existence_l1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6620 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k5_subset_1(u1_struct_0(A),B,k2_pre_topc(A)) = B)))) # label(t15_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6621 $T # label(t7_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6622 (exists A (v1_pre_topc(A) & l1_pre_topc(A))) # label(rc1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6623 $T # label(t36_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6624 (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]. 57.83/56.82 6625 (all A (l1_struct_0(A) -> k2_pre_topc(A) = k3_subset_1(u1_struct_0(A),k1_pre_topc(A)))) # label(t27_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6626 $T # label(t34_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6627 (all A all B all C all D (l1_struct_0(B) & v1_funct_1(C) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & l1_struct_0(A) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> k9_relat_1(C,D) = k4_pre_topc(A,B,C,D))) # label(redefinition_k4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6628 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (k6_pre_topc(A,B) = C <-> (all D (r2_hidden(D,u1_struct_0(A)) -> ((all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(E,A) & r1_xboole_0(B,E) & r2_hidden(D,E)))) <-> r2_hidden(D,C))))))))))) # label(d13_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6629 (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]. 57.83/56.82 6630 (all A all B all C all D (l1_struct_0(B) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & l1_struct_0(A) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> m1_subset_1(k5_pre_topc(A,B,C,D),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6631 (all A (l1_pre_topc(A) -> (r2_hidden(u1_struct_0(A),u1_pre_topc(A)) & (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,u1_pre_topc(A)) & r2_hidden(B,u1_pre_topc(A)) -> r2_hidden(k5_subset_1(u1_struct_0(A),B,C),u1_pre_topc(A))))))) & (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(B,u1_pre_topc(A)) -> r2_hidden(k5_setfam_1(u1_struct_0(A),B),u1_pre_topc(A))))) <-> v2_pre_topc(A)))) # label(d1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6632 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_xboole_0(B,C) & k4_subset_1(u1_struct_0(A),B,C) = k2_pre_topc(A) -> k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) = C))))))) # label(t25_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6633 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (v5_pre_topc(C,A,B) <-> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v4_pre_topc(D,B) -> v4_pre_topc(k5_pre_topc(A,B,C,D),A))))))))))) # label(d12_pre_topc) # label(axiom) # label(non_clause). [assumption]. 57.83/56.82 6634 (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]. 57.83/56.82 6635 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v4_tops_1(D,B) & v4_pre_topc(D,B) -> v5_tops_1(D,B)) & (v5_tops_1(C,A) -> v4_tops_1(C,A) & v4_pre_topc(C,A)))))))))) # label(t106_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.82 6636 (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]. 57.87/56.82 6637 $T # label(t16_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.82 6638 $T # label(t24_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.82 6639 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) -> v3_tops_1(k2_tops_1(A,B),A)))))) # label(t96_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.82 6640 $T # label(t78_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.82 6641 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (C = k1_tops_1(A,C) -> v3_pre_topc(C,A)) & (v3_pre_topc(D,B) -> D = k1_tops_1(B,D)))))))))) # label(t55_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.82 6642 $T # label(t28_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.82 6643 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (k1_tops_1(A,B) = k1_xboole_0 <-> v2_tops_1(B,A)))))) # label(t84_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.82 6644 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(C,A) & v3_tops_1(B,A) -> v3_tops_1(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t90_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.82 6645 $T # label(t12_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.82 6646 $T # label(t18_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.82 6647 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,D) & v3_pre_topc(D,A) -> -r1_xboole_0(B,D) & -r1_xboole_0(k3_subset_1(u1_struct_0(A),B),D)))) <-> r2_hidden(C,k2_tops_1(A,B))))))))) # label(t61_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.82 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))) -> (v4_pre_topc(B,A) & v4_pre_topc(C,A) -> v4_pre_topc(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t35_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.82 6649 $T # label(t4_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.82 6650 (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]. 57.87/56.82 6651 (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]. 57.87/56.82 6652 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_xboole_0(B) -> v4_pre_topc(B,A) & v3_pre_topc(B,A)))))) # label(cc1_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.82 6653 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_tops_1(B,A) -> k1_tops_1(A,k2_tops_1(A,B)) = k1_xboole_0))))) # label(t110_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.82 6654 (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]. 57.87/56.82 6655 $T # label(t1_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.82 6656 (all A all B (l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> m1_subset_1(k1_tops_1(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k1_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.82 6657 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_1(k3_subset_1(u1_struct_0(A),B),A) <-> v2_tops_1(B,A)))))) # label(d4_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.82 6658 $T # label(t13_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.82 6659 (all A all B (v2_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> v3_pre_topc(k1_tops_1(A,B),A))) # label(fc6_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.82 6660 (all A all B (l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> m1_subset_1(k2_tops_1(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k2_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.82 6661 (all A all B (v2_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> v4_pre_topc(k6_pre_topc(A,B),A))) # label(fc2_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.82 6662 (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]. 57.87/56.82 6663 $T # label(t23_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.82 6664 (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]. 57.87/56.82 6665 $T # label(t7_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.82 6666 (all A all B (l1_pre_topc(A) & v2_tops_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v1_membered(k1_tops_1(A,B)) & v2_membered(k1_tops_1(A,B)) & v5_membered(k1_tops_1(A,B)) & v4_membered(k1_tops_1(A,B)) & v1_xboole_0(k1_tops_1(A,B)) & v3_membered(k1_tops_1(A,B)) & v2_tops_1(k1_tops_1(A,B),A))) # label(fc10_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.82 6667 (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]. 57.87/56.82 6668 (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]. 57.87/56.82 6669 (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]. 57.87/56.82 6670 (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]. 57.87/56.82 6671 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,C)) = k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,C)))))))))) # label(t41_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.82 6672 (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]. 57.87/56.82 6673 (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]. 57.87/56.83 6674 (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]. 57.87/56.83 6675 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k1_tops_1(A,k6_subset_1(u1_struct_0(A),B,C)),k6_subset_1(u1_struct_0(A),k1_tops_1(A,B),k1_tops_1(A,C))))))))) # label(t50_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6676 $T # label(t100_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6677 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k1_tops_1(A,k5_subset_1(u1_struct_0(A),B,C)) = k5_subset_1(u1_struct_0(A),k1_tops_1(A,B),k1_tops_1(A,C)))))))) # label(t46_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6678 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(k1_tops_1(A,k6_pre_topc(A,B)),B) & r1_tarski(B,k6_pre_topc(A,k1_tops_1(A,B))) <-> v4_tops_1(B,A)))))) # label(d6_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6679 (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]. 57.87/56.83 6680 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(B,A))))) # label(rc1_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6681 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> v3_pre_topc(k1_pre_topc(A),A))) # label(t52_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6682 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v3_pre_topc(k1_tops_1(A,B),A))))) # label(t51_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6683 (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]. 57.87/56.83 6684 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v6_tops_1(C,A) -> v3_pre_topc(C,A) & v4_tops_1(C,A)) & (v3_pre_topc(D,B) & v4_tops_1(D,B) -> v6_tops_1(D,B)))))))))) # label(t107_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6685 $T # label(t17_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6686 (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]. 57.87/56.83 6687 $T # label(t6_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6688 $T # label(t9_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6689 (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]. 57.87/56.83 6690 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k2_tops_1(A,B) = k4_subset_1(u1_struct_0(A),k5_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B)),B),k6_subset_1(u1_struct_0(A),k6_pre_topc(A,B),B)))))) # label(t64_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6691 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(C,A) & v1_tops_1(C,A) & v1_tops_1(B,A) -> v1_tops_1(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t82_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6692 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k2_tops_1(A,k2_tops_1(A,k2_tops_1(A,B))) = k2_tops_1(A,k2_tops_1(A,B)))))) # label(t75_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6693 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(B,A) & v1_membered(B) & v3_pre_topc(B,A) & v2_membered(B) & v4_membered(B) & v5_membered(B) & v3_tops_1(B,A) & v2_tops_1(B,A) & v3_membered(B) & v1_xboole_0(B))))) # label(rc5_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6694 (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]. 57.87/56.83 6695 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k2_tops_1(A,k4_subset_1(u1_struct_0(A),B,C)),k4_subset_1(u1_struct_0(A),k2_tops_1(A,B),k2_tops_1(A,C))))))))) # label(t67_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6696 $T # label(t3_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6697 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> v2_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v4_pre_topc(k1_pre_topc(A),A) & v1_xboole_0(k1_pre_topc(A)))) # label(fc1_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6698 $T # label(t98_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6699 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) & v3_pre_topc(B,A) & v2_pre_topc(A) -> v2_tops_1(k2_tops_1(A,B),A) & v3_tops_1(k2_tops_1(A,B),A))) # label(fc12_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6700 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (k6_subset_1(u1_struct_0(A),k6_pre_topc(A,B),B) = k2_tops_1(A,B) <-> v3_pre_topc(B,A)))))) # label(t76_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6701 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v5_tops_1(C,A) & v5_tops_1(B,A) -> v5_tops_1(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t108_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6702 (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]. 57.87/56.83 6703 (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]. 57.87/56.83 6704 (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]. 57.87/56.83 6705 (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]. 57.87/56.83 6706 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k6_pre_topc(A,B) = k4_subset_1(u1_struct_0(A),B,k2_tops_1(A,B)))))) # label(t65_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6707 (all A (l1_pre_topc(A) -> k6_pre_topc(A,k2_pre_topc(A)) = k2_pre_topc(A))) # label(t27_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6708 (all A all B (l1_pre_topc(A) & v2_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(B,A) -> v3_pre_topc(k3_subset_1(u1_struct_0(A),B),A))) # label(fc3_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6709 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_tops_1(B,A) -> v4_tops_1(k1_tops_1(A,B),A) & v4_tops_1(k6_pre_topc(A,B),A)))))) # label(t111_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6710 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> v4_pre_topc(k1_pre_topc(A),A) & v3_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v1_xboole_0(k1_pre_topc(A)) & v3_pre_topc(k1_pre_topc(A),A) & v2_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)))) # label(fc7_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6711 (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]. 57.87/56.83 6712 (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]. 57.87/56.83 6713 $T # label(t25_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6714 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(C,A) & v4_pre_topc(B,A) -> k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,C)) = k5_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,C))))))))) # label(t34_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6715 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(C,A) & v2_tops_1(C,A) & v2_tops_1(B,A) -> v2_tops_1(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t85_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6716 (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]. 57.87/56.83 6717 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) & r1_tarski(C,B) -> r1_tarski(k6_pre_topc(A,C),B)))))))) # label(t31_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6718 (all A all B (l1_pre_topc(A) & v2_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(B,A) -> v2_tops_1(k2_tops_1(A,B),A) & v3_tops_1(k2_tops_1(A,B),A))) # label(fc13_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6719 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,k2_tops_1(A,B)) <-> v2_tops_1(B,A)))))) # label(t88_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6720 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(k3_subset_1(u1_struct_0(A),B),A) <-> v4_pre_topc(B,A)))))) # label(t29_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6721 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_1(B,A) <-> k6_pre_topc(A,B) = k2_pre_topc(A)))))) # label(d3_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6722 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(B,A) <-> v2_tops_1(k6_pre_topc(A,B),A)))))) # label(d5_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6723 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((exists D (r1_tarski(D,C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D,A) & r2_hidden(B,D))) <-> r2_hidden(B,k1_tops_1(A,C))))))) # label(t54_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6724 $T # label(t42_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6725 (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]. 57.87/56.83 6726 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(C,A) & v3_pre_topc(B,A) -> v3_pre_topc(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t38_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6727 (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]. 57.87/56.83 6728 $T # label(t89_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6729 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) & v4_pre_topc(B,A) -> (v5_tops_1(B,A) <-> v6_tops_1(B,A))))))) # label(t105_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6730 (all A (l1_pre_topc(A) -> (exists B (v1_membered(B) & v3_membered(B) & v5_membered(B) & v1_xboole_0(B) & v4_membered(B) & v2_tops_1(B,A) & v2_membered(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc4_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6731 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(B,A) & v3_pre_topc(B,A) -> k1_xboole_0 = B))))) # label(t97_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6732 (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]. 57.87/56.83 6733 (all A (l1_pre_topc(A) -> v1_membered(k1_tops_1(A,k1_pre_topc(A))) & v2_membered(k1_tops_1(A,k1_pre_topc(A))) & v5_membered(k1_tops_1(A,k1_pre_topc(A))) & v1_xboole_0(k1_tops_1(A,k1_pre_topc(A))) & v4_membered(k1_tops_1(A,k1_pre_topc(A))) & v3_membered(k1_tops_1(A,k1_pre_topc(A))))) # label(fc5_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6734 (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]. 57.87/56.83 6735 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tops_1(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(C,A) & r1_tarski(C,B) -> k1_xboole_0 = C)))))))) # label(t86_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6736 (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]. 57.87/56.83 6737 (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]. 57.87/56.83 6738 $T # label(t60_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6739 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k5_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B))) = k2_tops_1(A,B))))) # label(d2_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6740 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> v3_pre_topc(k2_pre_topc(A),A) & v4_pre_topc(k2_pre_topc(A),A))) # label(fc8_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6741 (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]. 57.87/56.83 6742 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(C,A) & v4_pre_topc(B,A) -> v4_pre_topc(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t36_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6743 (all A (v2_pre_topc(A) & -v3_struct_0(A) & l1_pre_topc(A) -> (exists B (-v1_xboole_0(B) & v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(B,A))))) # label(rc3_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6744 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,k6_pre_topc(A,B)) <-> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_hidden(C,D) & v3_pre_topc(D,A) & r1_xboole_0(B,D))))))))))) # label(t39_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6745 (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]. 57.87/56.83 6746 (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]. 57.87/56.83 6747 $T # label(t15_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6748 (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]. 57.87/56.83 6749 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(B,A) & v4_pre_topc(B,A))))) # label(rc2_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6750 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) & v3_pre_topc(C,A) -> v3_pre_topc(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t37_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6751 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(C,A) & C != k1_xboole_0 & r1_xboole_0(B,C)))) <-> v1_tops_1(B,A)))))) # label(t80_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6752 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> k6_pre_topc(A,B) = k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,B)))))))) # label(t59_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6753 (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]. 57.87/56.83 6754 (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]. 57.87/56.83 6755 (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]. 57.87/56.83 6756 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v6_tops_1(B,A) & v6_tops_1(C,A) -> v6_tops_1(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t109_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6757 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (k3_subset_1(u1_struct_0(A),B) = k3_subset_1(u1_struct_0(A),C) -> B = C))))))) # label(t21_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6758 $T # label(t14_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6759 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tops_1(B,A) & v4_pre_topc(B,A) -> v3_tops_1(B,A) & v2_tops_1(B,A)))))) # label(cc5_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6760 $T # label(t33_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6761 (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]. 57.87/56.83 6762 $T # label(t19_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6763 $T # label(t99_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6764 $T # label(t5_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6765 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) -> (B = k2_tops_1(A,B) <-> v3_tops_1(B,A))))))) # label(t94_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6766 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(B,A) & v3_pre_topc(B,A) -> v3_pre_topc(B,A) & v4_membered(B) & v2_tops_1(B,A) & v5_membered(B) & v4_pre_topc(B,A) & v2_membered(B) & v3_tops_1(B,A) & v3_membered(B) & v1_membered(B) & v1_xboole_0(B)))))) # label(cc6_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6767 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v6_tops_1(B,A) -> k2_tops_1(A,B) = k2_tops_1(A,k6_pre_topc(A,B)) & k2_tops_1(A,k6_pre_topc(A,B)) = k6_subset_1(u1_struct_0(A),k6_pre_topc(A,B),B)))))) # label(t104_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6768 (all A (l1_pre_topc(A) -> v1_tops_1(k2_pre_topc(A),A))) # label(fc9_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6769 $T # label(t83_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6770 $T # label(t11_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6771 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) -> (v2_tops_1(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(C,A) & C != k1_xboole_0 & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_xboole_0(B,D) & r1_tarski(D,C) & v3_pre_topc(D,A) & k1_xboole_0 != D)))))))))))) # label(t87_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6772 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k6_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,C)),k6_pre_topc(A,k6_subset_1(u1_struct_0(A),B,C))))))))) # label(t32_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6773 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) & v3_tops_1(B,A) & v2_pre_topc(A) -> v1_tops_1(k3_subset_1(u1_struct_0(A),B),A))) # label(fc11_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6774 $T # label(t10_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6775 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) <-> (all C ((exists D (r2_hidden(C,D) & r1_tarski(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D,A))) <-> r2_hidden(C,B)))))))) # label(t57_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6776 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k2_tops_1(A,k3_subset_1(u1_struct_0(A),B)) = k2_tops_1(A,B))))) # label(t62_tops_1) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6777 (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]. 57.87/56.83 6778 (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]. 57.87/56.83 6779 $T # label(t15_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.87/56.83 6780 (all A all B all C (l1_pre_topc(A) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> m1_subset_1(k1_tops_2(A,B,C),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,B))))))) # label(dt_k1_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6781 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) -> -((all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(v1_tops_2(D,A) & (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (E = k2_pre_topc(B) -> C = k1_tops_2(A,E,D))))))) & v1_tops_2(C,B)))))))) # label(t49_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6782 $T # label(t2_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6783 (all A (l1_struct_0(A) -> (all B (-v3_struct_0(B) & l1_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> k5_pre_topc(A,B,C,k2_pre_topc(B)) = k2_pre_topc(A))))))) # label(t52_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6784 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_finset_1(B) & v1_tops_2(B,A) -> v3_pre_topc(k6_setfam_1(u1_struct_0(A),B),A)))))) # label(t27_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6785 $T # label(t7_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6786 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k4_pre_topc(A,B,C,k6_pre_topc(A,D)),k6_pre_topc(B,k4_pre_topc(A,B,C,D))))) <-> v5_pre_topc(C,A,B)))))))) # label(t57_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6787 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (k2_pre_topc(A) = k1_relat_1(C) & k2_pre_topc(B) = k2_relat_1(C) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> k5_pre_topc(A,B,C,k6_pre_topc(B,D)) = k6_pre_topc(A,k5_pre_topc(A,B,C,D)))) & v2_funct_1(C) <-> v3_tops_2(C,A,B)))))))) # label(t73_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6788 $T # label(t4_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6789 $T # label(t9_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6790 (all A (l1_pre_topc(A) -> (all B (-v3_struct_0(B) & l1_pre_topc(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v3_tops_2(C,A,B) <-> k2_pre_topc(A) = k1_relat_1(C) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(D,A) <-> v4_pre_topc(k4_pre_topc(A,B,C,D),B)))) & v2_funct_1(C) & k2_pre_topc(B) = k2_relat_1(C)))))))) # label(t72_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6791 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_pre_topc(C,A) -> (v1_tops_2(B,A) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(C)))) -> (B = D -> v1_tops_2(D,C))))))))))) # label(t35_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6792 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (l1_pre_topc(B) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & l1_pre_topc(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) -> (all E (v1_funct_1(E) & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C)) -> (v3_tops_2(D,A,B) & v3_tops_2(E,B,C) -> v3_tops_2(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C)))))))))))) # label(t71_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6793 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & -v3_struct_0(B) & l1_pre_topc(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> k4_pre_topc(A,B,C,k6_pre_topc(A,D)) = k6_pre_topc(B,k4_pre_topc(A,B,C,D)))) & v2_funct_1(C) & k2_pre_topc(B) = k2_relat_1(C) & k2_pre_topc(A) = k1_relat_1(C) <-> v3_tops_2(C,A,B)))))))) # label(t74_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6794 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> r1_tarski(B,k1_zfmisc_1(k2_pre_topc(A))))))) # label(t1_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6795 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) & -v3_struct_0(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v3_pre_topc(D,B) -> v3_pre_topc(k5_pre_topc(A,B,C,D),A)))) <-> v5_pre_topc(C,A,B)))))))) # label(t55_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6796 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (l1_pre_topc(C) & -v3_struct_0(C) -> (all D (v1_funct_2(D,u1_struct_0(A),u1_struct_0(C)) & v1_funct_1(D) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(C)) -> (all E (m2_relset_1(E,u1_struct_0(C),u1_struct_0(B)) & v1_funct_2(E,u1_struct_0(C),u1_struct_0(B)) & v1_funct_1(E) -> (v5_pre_topc(E,C,B) & v5_pre_topc(D,A,C) -> v5_pre_topc(k7_funct_2(u1_struct_0(A),u1_struct_0(C),u1_struct_0(B),D,E),A,B)))))))))))) # label(t58_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6797 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) & -v3_struct_0(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> k2_pre_topc(A) = k1_relat_1(C) & r1_tarski(k2_relat_1(C),k2_pre_topc(B)))))))) # label(t51_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6798 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) -> (v5_pre_topc(C,A,B) & v2_tops_2(D,B) -> (all E (m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (E = k9_relat_1(k3_funct_3(C),D) -> v2_tops_2(E,A))))))))))))) # label(t60_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6799 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v2_tops_2(B,A) <-> v1_tops_2(k7_setfam_1(u1_struct_0(A),B),A)))))) # label(t16_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6800 (all A (-v3_struct_0(A) & l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(B = k1_xboole_0 & r1_pre_topc(A,B)))))) # label(t5_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6801 $T # label(t53_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6802 (all A (l1_struct_0(A) -> (all B (-v3_struct_0(B) & l1_struct_0(B) -> (all C (l1_struct_0(C) & -v3_struct_0(C) -> (all D (v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(D) -> (all E (v1_funct_2(E,u1_struct_0(B),u1_struct_0(C)) & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) & v1_funct_1(E) -> (v2_funct_1(E) & v2_funct_1(D) & k1_relat_1(D) = k2_pre_topc(A) & k2_relat_1(D) = k2_pre_topc(B) & k1_relat_1(E) = k2_pre_topc(B) & k2_pre_topc(C) = k2_relat_1(E) -> k7_funct_2(u1_struct_0(C),u1_struct_0(B),u1_struct_0(A),k2_tops_2(B,C,E),k2_tops_2(A,B,D)) = k2_tops_2(A,C,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E))))))))))))) # label(t66_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6803 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> r1_tarski(k6_pre_topc(A,k5_pre_topc(A,B,C,D)),k5_pre_topc(A,B,C,k6_pre_topc(B,D))))) <-> v5_pre_topc(C,A,B)))))))) # label(t56_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6804 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_pre_topc(C,A) -> (v2_tops_2(B,A) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(C)))) -> (B = D -> v2_tops_2(D,C))))))))))) # label(t36_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6805 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v2_tops_2(C,A) -> v2_tops_2(k1_tops_2(A,B,C),k3_pre_topc(A,B))))))))) # label(t48_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6806 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> r1_tarski(k5_setfam_1(u1_struct_0(k3_pre_topc(A,B)),k1_tops_2(A,B,C)),k5_setfam_1(u1_struct_0(A),C)))))))) # label(t44_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6807 $T # label(t39_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6808 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v2_tops_2(C,A) & v2_tops_2(B,A) -> v2_tops_2(k4_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C),A)))))))) # label(t23_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6809 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) & -v3_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) -> (v1_tops_2(D,B) & v5_pre_topc(C,A,B) -> (all E (m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (E = k9_relat_1(k3_funct_3(C),D) -> v1_tops_2(E,A))))))))))))) # label(t59_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6810 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (exists D (k2_relat_1(D) = k1_tops_2(A,B,C) & k1_relat_1(D) = C & v1_relat_1(D) & (all E (r2_hidden(E,C) -> (all F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) -> (F = E -> k1_funct_1(D,E) = k5_subset_1(u1_struct_0(A),F,B)))))) & v1_funct_1(D))))))))) # label(t50_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6811 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_finset_1(k7_setfam_1(u1_struct_0(A),B)) <-> v1_finset_1(B)))))) # label(t13_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6812 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (v2_funct_1(C) & k2_pre_topc(B) = k2_relat_1(C) -> v2_funct_1(k2_tops_2(A,B,C))))))))) # label(t63_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6813 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> -(B != k1_xboole_0 & k7_setfam_1(A,B) = k1_xboole_0) & -(B = k1_xboole_0 & k7_setfam_1(A,B) != k1_xboole_0))) # label(t10_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6814 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(C,D) -> r1_tarski(k1_tops_2(A,B,C),k1_tops_2(A,B,D))))))))))) # label(t40_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6815 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> v3_pre_topc(C,A)))) <-> v1_tops_2(B,A)))))) # label(d1_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6816 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k1_xboole_0 != B -> k6_setfam_1(A,k7_setfam_1(A,B)) = k3_subset_1(A,k5_setfam_1(A,B))))) # label(t11_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6817 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v2_tops_2(B,A) & v1_finset_1(B) -> v4_pre_topc(k5_setfam_1(u1_struct_0(A),B),A)))))) # label(t28_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6818 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> r1_tarski(k6_subset_1(u1_struct_0(A),k5_setfam_1(u1_struct_0(A),B),k5_setfam_1(u1_struct_0(A),C)),k5_setfam_1(u1_struct_0(A),k6_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C))))))))) # label(t6_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6819 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> v4_pre_topc(C,A)))) <-> v2_tops_2(B,A)))))) # label(d2_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6820 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) -> m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))))))) # label(t31_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6821 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(B,C) & v2_tops_2(C,A) -> v2_tops_2(B,A)))))))) # label(t19_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6822 $T # label(t37_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6823 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v2_tops_2(B,A) -> v2_tops_2(k5_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C),A)))))))) # label(t24_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6824 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (v2_funct_1(C) & k2_relat_1(C) = k2_pre_topc(B) -> k6_relat_1(k2_relat_1(C)) = k5_relat_1(k2_tops_2(A,B,C),C) & k5_relat_1(C,k2_tops_2(A,B,C)) = k6_relat_1(k1_relat_1(C))))))))) # label(t65_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6825 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_tops_2(B,A) -> v1_tops_2(k5_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C),A)))))))) # label(t21_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6826 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(B,C) & v1_tops_2(C,A) -> v1_tops_2(B,A)))))))) # label(t18_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6827 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (B != k1_xboole_0 -> k3_subset_1(A,k6_setfam_1(A,B)) = k5_setfam_1(A,k7_setfam_1(A,B))))) # label(t12_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6828 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_finset_1(C) -> v1_finset_1(k1_tops_2(A,B,C))))))))) # label(t46_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6829 (all A all B all C (l1_struct_0(A) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) -> v1_funct_2(k2_tops_2(A,B,C),u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(k2_tops_2(A,B,C),u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(k2_tops_2(A,B,C)))) # label(dt_k2_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6830 $T # label(t8_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6831 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(B,k5_setfam_1(u1_struct_0(k3_pre_topc(A,B)),k1_tops_2(A,B,C))) -> r1_tarski(B,k5_setfam_1(u1_struct_0(A),C))))))))) # label(t45_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6832 $T # label(t30_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6833 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_tops_2(B,A) -> v1_tops_2(k6_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C),A)))))))) # label(t22_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6834 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v3_tops_2(C,A,B) <-> k2_relat_1(C) = k2_pre_topc(B) & v2_funct_1(C) & v5_pre_topc(k2_tops_2(A,B,C),B,A) & k2_pre_topc(A) = k1_relat_1(C) & v5_pre_topc(C,A,B)))))))) # label(d5_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6835 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v2_funct_1(C) & k2_relat_1(C) = k2_pre_topc(B) -> k4_pre_topc(B,A,k2_tops_2(A,B,C),D) = k5_pre_topc(A,B,C,D)))))))))) # label(t68_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6836 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (r1_tarski(C,B) -> m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))))))) # label(t3_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6837 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(B,k5_setfam_1(u1_struct_0(A),C)) -> k5_setfam_1(u1_struct_0(k3_pre_topc(A,B)),k1_tops_2(A,B,C)) = B))))))) # label(t43_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6838 $T # label(t69_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6839 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_tops_2(B,A) -> v3_pre_topc(k5_setfam_1(u1_struct_0(A),B),A)))))) # label(t26_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6840 $T # label(t14_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6841 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v2_tops_2(B,A) -> v2_tops_2(k6_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C),A)))))))) # label(t25_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6842 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,B))))) -> (k1_tops_2(A,B,C) = D <-> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,B)))) -> ((exists F (k5_subset_1(u1_struct_0(A),F,B) = E & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) & r2_hidden(F,C))) <-> r2_hidden(E,D))))))))))))) # label(d3_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6843 $T # label(t61_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6844 (all A (l1_struct_0(A) -> (all B (-v3_struct_0(B) & l1_struct_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) -> m1_subset_1(k9_relat_1(k3_funct_3(C),D),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))))))))) # label(t54_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6845 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_tops_2(C,A) -> v1_tops_2(k1_tops_2(A,B,C),k3_pre_topc(A,B))))))))) # label(t47_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6846 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_pre_topc(C,A) -> (v4_pre_topc(B,A) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) -> (B = D -> v4_pre_topc(D,C))))))))))) # label(t34_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6847 (all A (l1_pre_topc(A) -> (all B (-v3_struct_0(B) & l1_pre_topc(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (v3_tops_2(C,A,B) -> v3_tops_2(k2_tops_2(A,B,C),B,A)))))))) # label(t70_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6848 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (v2_funct_1(C) & k2_relat_1(C) = k2_pre_topc(B) -> k5_pre_topc(B,A,k2_tops_2(A,B,C),D) = k4_pre_topc(A,B,C,D)))))))))) # label(t67_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6849 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_pre_topc(C,A) -> (v3_pre_topc(B,A) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) -> (D = B -> v3_pre_topc(D,C))))))))))) # label(t33_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6850 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(B,k5_setfam_1(u1_struct_0(A),D)) -> r1_tarski(k5_subset_1(u1_struct_0(A),B,C),k5_setfam_1(u1_struct_0(k3_pre_topc(A,C)),k1_tops_2(A,C,D)))))))))))) # label(t42_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6851 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_tops_2(B,A) <-> v2_tops_2(k7_setfam_1(u1_struct_0(A),B),A)))))) # label(t17_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6852 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r2_hidden(B,D) -> r2_hidden(k5_subset_1(u1_struct_0(A),B,C),k1_tops_2(A,C,D))))))))))) # label(t41_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6853 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> ((exists D (v3_pre_topc(D,A) & C = k3_xboole_0(D,k2_pre_topc(B)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))))) <-> v3_pre_topc(C,B)))))))) # label(t32_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6854 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> m1_subset_1(k5_subset_1(u1_struct_0(A),B,C),k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,C)))))))))) # label(t38_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6855 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_tops_2(B,A) & v1_tops_2(C,A) -> v1_tops_2(k4_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C),A)))))))) # label(t20_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6856 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v2_tops_2(B,A) -> v4_pre_topc(k6_setfam_1(u1_struct_0(A),B),A)))))) # label(t29_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6857 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (k2_relat_1(C) = k2_pre_topc(B) & v2_funct_1(C) -> k2_pre_topc(A) = k2_relat_1(k2_tops_2(A,B,C)) & k1_relat_1(k2_tops_2(A,B,C)) = k2_pre_topc(B)))))))) # label(t62_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6858 (all A (l1_struct_0(A) -> (all B (-v3_struct_0(B) & l1_struct_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (k2_pre_topc(B) = k2_relat_1(C) & v2_funct_1(C) -> k2_tops_2(B,A,k2_tops_2(A,B,C)) = C))))))) # label(t64_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6859 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (v2_funct_1(C) & k2_pre_topc(B) = k2_relat_1(C) -> k2_funct_1(C) = k2_tops_2(A,B,C)))))))) # label(d4_tops_2) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6860 $T # label(t4_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6861 $T # label(t52_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6862 (all A (v5_rlvect_1(A) & v4_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)) -> k5_rlvect_1(A,k2_rlvect_1(A,B,C)) = k2_rlvect_1(A,k5_rlvect_1(A,C),k5_rlvect_1(A,B)))))))) # label(t45_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6863 (exists A l2_rlvect_1(A)) # label(existence_l2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6864 (all A (v6_rlvect_1(A) & v4_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)) -> (B = k2_rlvect_1(A,B,C) | k2_rlvect_1(A,C,B) = B -> C = k1_rlvect_1(A)))))))) # label(t22_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6865 (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)) -> k6_rlvect_1(A,k1_rlvect_1(A),B) = k5_rlvect_1(A,B))))) # label(t27_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6866 (all A (v5_rlvect_1(A) & l1_rlvect_1(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k6_rlvect_1(A,B,k6_rlvect_1(A,C,D)) = k4_rlvect_1(A,k6_rlvect_1(A,B,C),D))))))))) # label(t43_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6867 (all A (-v3_struct_0(A) & l1_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 (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]. 57.88/56.84 6868 (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,C) = k2_rlvect_1(A,C,B))))) <-> v3_rlvect_1(A)))) # label(d5_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6869 (all A (l2_rlvect_1(A) -> m2_relset_1(u2_rlvect_1(A),k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(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)))) # label(dt_u2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6870 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & -v3_struct_0(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,k1_numbers) -> k1_rlvect_1(A) = k3_rlvect_1(A,k9_rlvect_1(A,k6_finseq_1(u1_struct_0(A))),B))))) # label(t64_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.84 6871 (all A (-v3_struct_0(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)) -> 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]. 57.88/56.84 6872 (all A (-v3_struct_0(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_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)) -> (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]. 57.88/56.84 6873 (all A all B all C all D (v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A) & m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & m1_subset_1(B,A) & v1_funct_1(D) & v1_funct_2(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]. 57.88/56.85 6874 (all A (v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) & v5_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)) -> (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]. 57.88/56.85 6875 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (l2_rlvect_1(C) & v7_rlvect_1(C) & v3_rlvect_1(C) & -v3_struct_0(C) & v6_rlvect_1(C) & v5_rlvect_1(C) & v4_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]. 57.88/56.85 6876 (all A (v5_rlvect_1(A) & v4_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)) -> B = k2_rlvect_1(A,B,k1_rlvect_1(A)) & k2_rlvect_1(A,k1_rlvect_1(A),B) = B)))) # label(t10_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6877 (all A all B all C all D (m1_subset_1(B,A) & v1_funct_1(D) & v1_funct_1(C) & m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A) & v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (all E all F all G all H (g2_rlvect_1(A,B,C,D) = g2_rlvect_1(E,F,G,H) -> G = C & H = D & B = F & E = A)))) # label(free_g2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6878 $T # label(t32_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6879 (all A (v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) & v3_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v4_rlvect_1(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)) -> k3_rlvect_1(A,k9_rlvect_1(A,k7_rlvect_1(A,C,D)),B) = k4_rlvect_1(A,k3_rlvect_1(A,C,B),k3_rlvect_1(A,D,B)))))))))) # label(t66_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6880 (all A (m1_subset_1(A,k1_numbers) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k6_rlvect_1(B,k3_rlvect_1(B,C,A),k3_rlvect_1(B,D,A)) = k3_rlvect_1(B,k6_rlvect_1(B,C,D),A))))))))) # label(t48_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6881 (all A (v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(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,k8_rlvect_1(A,k1_rlvect_1(A),B,C)) = k2_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]. 57.88/56.85 6882 (all A (m1_subset_1(A,k1_numbers) -> (all B (v7_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) & v3_rlvect_1(B) & v6_rlvect_1(B) & l2_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (np__0 = A | C = k1_rlvect_1(B) -> k3_rlvect_1(B,C,A) = k1_rlvect_1(B)))))))) # label(t23_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6883 $T # label(t12_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6884 (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) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_rlvect_1(A),B,C))))))) # label(t5_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6885 $T # label(t6_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6886 $T # label(t53_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6887 (all A (v5_rlvect_1(A) & -v3_struct_0(A) & v4_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)) -> 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]. 57.88/56.85 6888 $T # label(t15_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6889 (all A (v5_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) & v6_rlvect_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (k3_finseq_1(B) = np__3 & k1_funct_1(B,np__3) = E & k1_funct_1(B,np__2) = D & k1_funct_1(B,np__1) = C -> 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]. 57.88/56.85 6890 (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) -> (all D all E all F (g1_rlvect_1(D,E,F) = g1_rlvect_1(A,B,C) -> B = E & F = C & A = D)))) # label(free_g1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6891 (all A (l2_struct_0(A) -> u2_struct_0(A) = k1_rlvect_1(A))) # label(d2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6892 (all A all B all C (m1_subset_1(B,u1_struct_0(A)) & l1_rlvect_1(A) & -v3_struct_0(A) & m1_subset_1(C,u1_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]. 57.88/56.85 6893 (all A (v3_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) & v5_rlvect_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> (k2_relat_1(C) = k2_relat_1(B) & v2_funct_1(B) & v2_funct_1(C) -> k9_rlvect_1(A,B) = k9_rlvect_1(A,C)))))))) # label(t59_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6894 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) & v4_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,E,B) = k2_rlvect_1(A,D,B) | k2_rlvect_1(A,B,E) = k2_rlvect_1(A,B,D) -> E = D))))))))))) # label(t21_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6895 (all A (v6_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(A) & v5_rlvect_1(A) & v4_rlvect_1(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)) & k1_rlvect_1(A) = k2_rlvect_1(A,k5_rlvect_1(A,B),B))))) # label(t16_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6896 (all A (l1_rlvect_1(A) & -v3_struct_0(A) & v4_rlvect_1(A) & v5_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)) -> 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]. 57.88/56.85 6897 (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]. 57.88/56.85 6898 (all A (l1_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)) = k9_rlvect_1(A,k8_rlvect_1(A,C,D,B)))))))))) # label(t85_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6899 (all A all B all C (m1_subset_1(C,u1_struct_0(A)) & -v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_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]. 57.88/56.85 6900 (all A (-v3_struct_0(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)) -> 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]. 57.88/56.85 6901 (all A (v6_rlvect_1(A) & -v3_struct_0(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(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]. 57.88/56.85 6902 (all A (l1_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_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) -> k9_rlvect_1(A,B) = k2_rlvect_1(A,C,D)))))))))) # label(t96_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6903 (all A (v5_rlvect_1(A) & v4_rlvect_1(A) & v3_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,u1_struct_0(A)) -> k5_rlvect_1(A,B) = k3_rlvect_1(A,B,k1_real_1(np__1)))))) # label(t29_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6904 (all A all B all C all D (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & -v1_xboole_0(A) & 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) & m1_subset_1(B,A) -> -v3_struct_0(g2_rlvect_1(A,B,C,D)) & v2_rlvect_1(g2_rlvect_1(A,B,C,D)))) # label(fc1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6905 (all A (l1_rlvect_1(A) -> l2_struct_0(A))) # label(dt_l1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6906 (all A (v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v4_rlvect_1(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]. 57.88/56.85 6907 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v5_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)) -> 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]. 57.88/56.85 6908 (all A all B all C all D (-v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(A)) & l1_struct_0(A) & m1_subset_1(C,u1_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]. 57.88/56.85 6909 (all A (-v3_struct_0(A) & v3_rlvect_1(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)) -> k6_rlvect_1(A,k5_rlvect_1(A,C),B) = k6_rlvect_1(A,k5_rlvect_1(A,B),C))))))) # label(t46_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6910 $T # label(t1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6911 (all A (-v3_struct_0(A) & v7_rlvect_1(A) & v3_rlvect_1(A) & l2_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)) -> 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]. 57.88/56.85 6912 (all A (l2_rlvect_1(A) -> l1_rlvect_1(A))) # label(dt_l2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6913 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) & v4_rlvect_1(A) & l1_rlvect_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (k3_finseq_1(B) = np__1 -> k9_rlvect_1(A,B) = k1_funct_1(B,np__1)))))) # label(t95_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6914 $T # label(t2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6915 (all A all B all C (m1_subset_1(B,u1_struct_0(A)) & l1_struct_0(A) & -v3_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]. 57.88/56.85 6916 (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)) -> (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]. 57.88/56.85 6917 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> ((exists D (v1_funct_2(D,k5_numbers,u1_struct_0(A)) & (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (all F (m1_subset_1(F,u1_struct_0(A)) -> (F = k1_funct_1(B,k1_nat_1(E,np__1)) -> k2_rlvect_1(A,k8_funct_2(k5_numbers,u1_struct_0(A),D,E),F) = k8_funct_2(k5_numbers,u1_struct_0(A),D,k1_nat_1(E,np__1)) | r1_xreal_0(k3_finseq_1(B),E)))))) & k8_funct_2(k5_numbers,u1_struct_0(A),D,np__0) = k1_rlvect_1(A) & m2_relset_1(D,k5_numbers,u1_struct_0(A)) & C = k8_funct_2(k5_numbers,u1_struct_0(A),D,k3_finseq_1(B)) & v1_funct_1(D))) <-> k9_rlvect_1(A,B) = C))))))) # label(d12_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6918 $T # label(t14_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6919 (all A (m1_subset_1(A,k1_numbers) -> (all B (v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) & v4_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,D,A) = k3_rlvect_1(B,C,A) -> np__0 = A | C = D))))))))) # label(t50_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6920 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(A) -> k5_rlvect_1(A,k1_rlvect_1(A)) = k1_rlvect_1(A))) # label(t25_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6921 (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)) -> 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)) = k2_rlvect_1(A,B,C))))))) # label(d3_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6922 (all A (l1_rlvect_1(A) & v6_rlvect_1(A) & v4_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)) -> 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]. 57.88/56.85 6923 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (v3_rlvect_1(C) & v5_rlvect_1(C) & l2_rlvect_1(C) & v4_rlvect_1(C) & v6_rlvect_1(C) & v7_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) -> A = B | D = k1_rlvect_1(C)))))))))) # label(t51_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6924 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) & v4_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)) -> 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]. 57.88/56.85 6925 (exists A (v1_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(A))) # label(rc4_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6926 (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 (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]. 57.88/56.85 6927 $T # label(t17_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6928 (all A all B all C (m1_subset_1(C,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) -> v1_rlvect_1(g1_rlvect_1(A,B,C)) & l1_rlvect_1(g1_rlvect_1(A,B,C)))) # label(dt_g1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6929 (all A (v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(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,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]. 57.88/56.85 6930 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (C = k5_rlvect_1(A,B) <-> k1_rlvect_1(A) = k2_rlvect_1(A,B,C))))))))) # label(d10_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6931 (exists A (-v3_struct_0(A) & l2_rlvect_1(A))) # label(rc3_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6932 (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,k7_rlvect_1(A,k1_rlvect_1(A),k1_rlvect_1(A))) = k1_rlvect_1(A))) # label(t74_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6933 (all A all B all C (-v3_struct_0(A) & v3_rlvect_1(A) & l1_rlvect_1(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(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]. 57.88/56.85 6934 (all A (l2_struct_0(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (B != k1_rlvect_1(A) <-> v8_rlvect_1(B,A)))))) # label(d13_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6935 (all A (v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) & v4_rlvect_1(A) & l1_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),B)))))) # label(t61_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6936 (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]. 57.88/56.85 6937 (exists A l1_rlvect_1(A)) # label(existence_l1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6938 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(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)) -> 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]. 57.88/56.85 6939 (all A (l2_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(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]. 57.88/56.85 6940 (all A (-v3_struct_0(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)) -> k2_rlvect_1(A,B,k2_rlvect_1(A,C,D)) = k2_rlvect_1(A,k2_rlvect_1(A,B,C),D)))))))))) # label(d6_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6941 $T # label(t9_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6942 (all A (v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(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,B,k5_rlvect_1(A,C))) = k6_rlvect_1(A,B,C))))))) # label(t77_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.85 6943 (all A all B all C (l2_rlvect_1(A) & m1_subset_1(C,k1_numbers) & m1_subset_1(B,u1_struct_0(A)) & -v3_struct_0(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]. 57.88/56.86 6944 (all A (l1_rlvect_1(A) -> v1_funct_1(u1_rlvect_1(A)) & v1_funct_2(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & m2_relset_1(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]. 57.88/56.86 6945 (all A all B all C (v3_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & -v3_struct_0(A) & l1_rlvect_1(A) -> k4_rlvect_1(A,B,C) = k4_rlvect_1(A,C,B))) # label(commutativity_k4_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.86 6946 (all A (v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(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]. 57.88/56.86 6947 (all A (l1_rlvect_1(A) & -v3_struct_0(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_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]. 57.88/56.86 6948 (all A (-v3_struct_0(A) & l2_rlvect_1(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]. 57.88/56.86 6949 $T # label(t8_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.86 6950 (all A (l1_struct_0(A) -> (all B (r2_hidden(B,u1_struct_0(A)) <-> r1_rlvect_1(A,B))))) # label(d1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.86 6951 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(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)) -> 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]. 57.88/56.86 6952 (all A (v6_rlvect_1(A) & -v3_struct_0(A) & v5_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]. 57.88/56.86 6953 (all A (m1_subset_1(A,k1_numbers) -> (all B (v5_rlvect_1(B) & v6_rlvect_1(B) & l2_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) & v4_rlvect_1(B) & v7_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k3_rlvect_1(B,k5_rlvect_1(B,C),k1_real_1(A)) = k3_rlvect_1(B,C,A))))))) # label(t40_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.86 6954 (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)) -> k9_rlvect_1(A,k7_rlvect_1(A,B,C)) = k2_rlvect_1(A,B,C))))))) # label(t62_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.86 6955 (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]. 57.88/56.86 6956 (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]. 57.88/56.86 6957 (all A (m1_subset_1(A,k1_numbers) -> (all B (v6_rlvect_1(B) & -v3_struct_0(B) & l2_rlvect_1(B) & v7_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> -(k1_rlvect_1(B) != C & A != np__0 & k1_rlvect_1(B) = k3_rlvect_1(B,C,A)))))))) # label(t24_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.86 6958 (all A (v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) & v4_rlvect_1(A) & l1_rlvect_1(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))) & k9_rlvect_1(A,k8_rlvect_1(A,k1_rlvect_1(A),B,k1_rlvect_1(A))) = B)))) # label(t91_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.86 6959 (all A (l1_rlvect_1(A) & v5_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)) -> k9_rlvect_1(A,k7_rlvect_1(A,k1_rlvect_1(A),B)) = B & B = k9_rlvect_1(A,k7_rlvect_1(A,B,k1_rlvect_1(A))))))) # label(t75_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.86 6960 (all A (m1_subset_1(A,k1_numbers) -> (all B (v5_rlvect_1(B) & v7_rlvect_1(B) & -v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l2_rlvect_1(B) -> (all C (m2_finseq_1(C,u1_struct_0(B)) -> (all D (m2_finseq_1(D,u1_struct_0(B)) -> (k3_finseq_1(D) = k3_finseq_1(C) & (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)) & k1_funct_1(D,E) = F -> k3_rlvect_1(B,F,A) = k1_funct_1(C,E)))))) -> k3_rlvect_1(B,k9_rlvect_1(B,D),A) = k9_rlvect_1(B,C)))))))))) # label(t56_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.86 6961 (exists A (l2_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A))) # label(rc6_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.86 6962 (exists A (v1_rlvect_1(A) & l1_rlvect_1(A))) # label(rc1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.86 6963 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & l1_rlvect_1(A) & v5_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)) -> (r2_hidden(D,k4_finseq_1(B)) & E = k1_funct_1(C,D) -> k1_funct_1(B,D) = k5_rlvect_1(A,E)))))) & k3_finseq_1(B) = k3_finseq_1(C) -> k5_rlvect_1(A,k9_rlvect_1(A,C)) = k9_rlvect_1(A,B)))))))) # label(t57_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.86 6964 (all A all B (l1_rlvect_1(A) & m1_finseq_1(B,u1_struct_0(A)) & -v3_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]. 57.88/56.86 6965 $T # label(t13_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.86 6966 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (v5_rlvect_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k2_rlvect_1(A,B,k1_rlvect_1(A))))))) # label(d7_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.86 6967 (all A (v4_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(A) & v5_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]. 57.88/56.86 6968 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k3_rlvect_1(A,B,k1_real_1(np__2)) = k9_rlvect_1(A,k7_rlvect_1(A,k5_rlvect_1(A,B),k5_rlvect_1(A,B))))))) # label(t80_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.86 6969 (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]. 57.88/56.86 6970 (all A (m1_subset_1(A,k1_numbers) -> (all B (v7_rlvect_1(B) & l2_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k5_rlvect_1(B,k3_rlvect_1(B,C,A)) = k3_rlvect_1(B,k5_rlvect_1(B,C),A))))))) # label(t39_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.86 6971 (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)) -> 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]. 57.88/56.86 6972 (all A (v6_rlvect_1(A) & l1_rlvect_1(A) & v4_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)) -> 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]. 57.88/56.86 6973 (all A (m1_subset_1(A,k1_numbers) -> (all B (v7_rlvect_1(B) & -v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & l2_rlvect_1(B) & v6_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]. 57.88/56.86 6974 (all A all B (l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & -v3_struct_0(A) -> m1_subset_1(k5_rlvect_1(A,B),u1_struct_0(A)))) # label(dt_k5_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.86 6975 (all A all B all C all D (m1_subset_1(D,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & -v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_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]. 57.88/56.86 6976 (all A all B all C (v3_rlvect_1(A) & -v3_struct_0(A) & l1_rlvect_1(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_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]. 57.88/56.86 6977 (all A (l1_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) & v6_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,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]. 57.88/56.86 6978 (all A (l1_rlvect_1(A) & v4_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)) -> 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]. 57.88/56.86 6979 (all A (l1_rlvect_1(A) & -v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k5_rlvect_1(A,k5_rlvect_1(A,B)))))) # label(t30_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.86 6980 (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) -> (k3_finseq_1(B) = D & r2_hidden(C,k2_finseq_1(D)) -> m1_subset_1(k1_funct_1(B,C),u1_struct_0(A))))))))))) # label(t54_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 57.88/56.86 6981 (all A (l2_rlvect_1(A) -> (v2_rlvect_1(A) -> A = g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A))))) # label(abstractness_v2_rlvect_1) # labelAlarm clock 120.95/120.02 Prover9 interrupted 120.95/120.02 EOF