0.03/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s 0.13/0.33 % Computer : n018.cluster.edu 0.13/0.33 % Model : x86_64 x86_64 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.33 % Memory : 8042.1875MB 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.33 % CPULimit : 180 0.13/0.33 % DateTime : Thu Aug 29 17:44:37 EDT 2019 0.13/0.33 % CPUTime : 4.13/4.19 ============================== Prover9 =============================== 4.13/4.19 Prover9 (32) version 2009-11A, November 2009. 4.13/4.19 Process 29518 was started by sandbox on n018.cluster.edu, 4.13/4.19 Thu Aug 29 17:44:41 2019 4.13/4.19 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 180 -f /tmp/Prover9_29365_n018.cluster.edu". 4.13/4.19 ============================== end of head =========================== 4.13/4.19 4.13/4.19 ============================== INPUT ================================= 4.13/4.19 4.13/4.19 % Reading from file /tmp/Prover9_29365_n018.cluster.edu 4.13/4.19 4.13/4.19 set(prolog_style_variables). 4.13/4.19 set(auto2). 4.13/4.19 % set(auto2) -> set(auto). 4.13/4.19 % set(auto) -> set(auto_inference). 4.13/4.19 % set(auto) -> set(auto_setup). 4.13/4.19 % set(auto_setup) -> set(predicate_elim). 4.13/4.19 % set(auto_setup) -> assign(eq_defs, unfold). 4.13/4.19 % set(auto) -> set(auto_limits). 4.13/4.19 % set(auto_limits) -> assign(max_weight, "100.000"). 4.13/4.19 % set(auto_limits) -> assign(sos_limit, 20000). 4.13/4.19 % set(auto) -> set(auto_denials). 4.13/4.19 % set(auto) -> set(auto_process). 4.13/4.19 % set(auto2) -> assign(new_constants, 1). 4.13/4.19 % set(auto2) -> assign(fold_denial_max, 3). 4.13/4.19 % set(auto2) -> assign(max_weight, "200.000"). 4.13/4.19 % set(auto2) -> assign(max_hours, 1). 4.13/4.19 % assign(max_hours, 1) -> assign(max_seconds, 3600). 4.13/4.19 % set(auto2) -> assign(max_seconds, 0). 4.13/4.19 % set(auto2) -> assign(max_minutes, 5). 4.13/4.19 % assign(max_minutes, 5) -> assign(max_seconds, 300). 4.13/4.19 % set(auto2) -> set(sort_initial_sos). 4.13/4.19 % set(auto2) -> assign(sos_limit, -1). 4.13/4.19 % set(auto2) -> assign(lrs_ticks, 3000). 4.13/4.19 % set(auto2) -> assign(max_megs, 400). 4.13/4.19 % set(auto2) -> assign(stats, some). 4.13/4.19 % set(auto2) -> clear(echo_input). 4.13/4.19 % set(auto2) -> set(quiet). 4.13/4.19 % set(auto2) -> clear(print_initial_clauses). 4.13/4.19 % set(auto2) -> clear(print_given). 4.13/4.19 assign(lrs_ticks,-1). 4.13/4.19 assign(sos_limit,10000). 4.13/4.19 assign(order,kbo). 4.13/4.19 set(lex_order_vars). 4.13/4.19 clear(print_given). 4.13/4.19 4.13/4.19 % formulas(sos). % not echoed (4103 formulas) 4.13/4.19 4.13/4.19 ============================== end of input ========================== 4.13/4.19 4.13/4.19 % From the command line: assign(max_seconds, 180). 4.13/4.19 4.13/4.19 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 4.13/4.19 4.13/4.19 % Formulas that are not ordinary clauses: 4.13/4.19 1 (all A all B (r2_hidden(A,B) -> -r2_hidden(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 2 $T # label(t8_tarski) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 3 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 4 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 5 (all A all B r1_tarski(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 6 (all A all B k2_tarski(A,B) = k2_tarski(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 7 $T # label(dt_k3_tarski) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 8 (all A all B ((all C ((exists D (r2_hidden(D,A) & r2_hidden(C,D))) <-> r2_hidden(C,B))) <-> B = k3_tarski(A))) # label(d4_tarski) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 9 (all A all B ((all C (r2_hidden(C,B) <-> r2_hidden(C,A))) -> B = A)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 10 (all A all B -((all C -((all D -(r2_hidden(D,B) & r2_hidden(D,C))) & r2_hidden(C,B))) & r2_hidden(A,B))) # label(t7_tarski) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 11 (all A all B all C (k2_tarski(A,B) = C <-> (all D (r2_hidden(D,C) <-> A = D | D = B)))) # label(d2_tarski) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 12 $T # label(t3_tarski) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 13 (all A all B ((exists C ((all D -((all E -(r2_hidden(k4_tarski(E,D),C) & r2_hidden(E,A))) & r2_hidden(D,B))) & (all D all E all F all G (r2_hidden(k4_tarski(D,E),C) & r2_hidden(k4_tarski(F,G),C) -> (D = F <-> E = G))) & (all D -(r2_hidden(D,A) & (all E -(r2_hidden(E,B) & r2_hidden(k4_tarski(D,E),C))))))) <-> r2_tarski(A,B))) # label(d6_tarski) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 14 $T # label(t1_tarski) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 15 (all A all B ((all C (A = C <-> r2_hidden(C,B))) <-> k1_tarski(A) = B)) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 16 $T # label(t6_tarski) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 17 (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]. 4.13/4.19 18 (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 -(r1_tarski(C,B) & -r2_tarski(C,B) & -r2_hidden(C,B))) & (all C all D (r2_hidden(C,B) & r1_tarski(D,C) -> r2_hidden(D,B))))) # label(t9_tarski) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 19 (all A all B all C (p1_s1_tarski(A,B) & p1_s1_tarski(A,C) -> C = B)) -> (exists A all B ((exists C (p1_s1_tarski(C,B) & r2_hidden(C,f1_s1_tarski))) <-> r2_hidden(B,A))) # label(s1_tarski) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 20 $T # label(t4_tarski) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 21 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 22 $T # label(t5_tarski) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 23 (all A all B k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A))) # label(d5_tarski) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 24 (all A all B (-v1_xboole_0(A) -> -v1_xboole_0(k2_xboole_0(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 25 (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]. 4.13/4.19 26 (all A all B (r1_tarski(B,A) | r1_tarski(A,B) <-> r3_xboole_0(A,B))) # label(d9_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 27 (all A all B k3_xboole_0(A,B) = k3_xboole_0(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 28 (all A ((all B -r2_hidden(B,A)) <-> A = k1_xboole_0)) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 29 (all A all B r3_xboole_0(A,A)) # label(reflexivity_r3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 30 (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]. 4.13/4.19 31 (exists A v1_xboole_0(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 32 (all A all B (r2_xboole_0(A,B) -> -r2_xboole_0(B,A))) # label(antisymmetry_r2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 33 (all A all B (r1_tarski(A,B) & A != B <-> r2_xboole_0(A,B))) # label(d8_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 34 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 35 (all A all B all C -(r1_xboole_0(A,B) & r2_hidden(C,k2_xboole_0(A,B)) & -(r2_hidden(C,A) & -r2_hidden(C,B)) & -(r2_hidden(C,B) & -r2_hidden(C,A)))) # label(t5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 36 (all A all B A = k2_xboole_0(A,A)) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 37 (all A all B (-(r1_xboole_0(A,B) & (exists C (r2_hidden(C,A) & r2_hidden(C,B)))) & -(-r1_xboole_0(A,B) & (all C -(r2_hidden(C,A) & r2_hidden(C,B)))))) # label(t3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 38 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 39 (all A all B A = k3_xboole_0(A,A)) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 40 (all A all B all C ((all D ((r2_hidden(D,C) <-> r2_hidden(D,B)) <-> -r2_hidden(D,A))) -> A = k5_xboole_0(B,C))) # label(t2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 41 (all A all B all C (C = k3_xboole_0(A,B) <-> (all D (r2_hidden(D,C) <-> r2_hidden(D,B) & r2_hidden(D,A))))) # label(d3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 42 $T # label(dt_k5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 43 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.13/4.19 44 (exists A all B (r2_hidden(B,f1_s1_xboole_0) & p1_s1_xboole_0(B) <-> r2_hidden(B,A))) # label(s1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 45 (all A all B all C (C = k2_xboole_0(A,B) <-> (all D (r2_hidden(D,A) | r2_hidden(D,B) <-> r2_hidden(D,C))))) # label(d2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 46 (all A all B (-v1_xboole_0(A) -> -v1_xboole_0(k2_xboole_0(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 47 (all A all B (r3_xboole_0(A,B) -> r3_xboole_0(B,A))) # label(symmetry_r3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 48 (all A (k1_xboole_0 = A <-> v1_xboole_0(A))) # label(d5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 49 (all A all B (k3_xboole_0(A,B) = k1_xboole_0 <-> r1_xboole_0(A,B))) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 50 (all A all B (r1_xboole_0(A,B) -> r1_xboole_0(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 51 (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]. 4.13/4.20 52 (all A all B k2_xboole_0(A,B) = k2_xboole_0(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 53 (all A all B (B = A <-> r1_tarski(A,B) & r1_tarski(B,A))) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 54 (all A all B k5_xboole_0(B,A) = k5_xboole_0(A,B)) # label(commutativity_k5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 55 (all A all B ((all C (p1_s3_xboole_0(C) <-> r2_hidden(C,A))) & (all C (p1_s3_xboole_0(C) <-> r2_hidden(C,B))) -> A = B)) # label(s3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 56 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 57 (all A (p1_s2_xboole_0(A) <-> r2_hidden(A,f2_s2_xboole_0))) & (all A (r2_hidden(A,f1_s2_xboole_0) <-> p1_s2_xboole_0(A))) -> f1_s2_xboole_0 = f2_s2_xboole_0 # label(s2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 58 (all A all B all C (k4_xboole_0(A,B) = C <-> (all D (r2_hidden(D,A) & -r2_hidden(D,B) <-> r2_hidden(D,C))))) # label(d4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 59 (exists A -v1_xboole_0(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 60 (all A all B -r2_xboole_0(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 61 (all A (v1_xboole_0(A) -> k1_xboole_0 = A)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 62 (all A A = k2_xboole_0(A,k1_xboole_0)) # label(t1_boole) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 63 (all A all B -(r2_hidden(A,B) & v1_xboole_0(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 64 (all A k3_xboole_0(A,k1_xboole_0) = k1_xboole_0) # label(t2_boole) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 65 (all A A = k5_xboole_0(A,k1_xboole_0)) # label(t5_boole) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 66 (all A k1_xboole_0 = k4_xboole_0(k1_xboole_0,A)) # label(t4_boole) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 67 (all A k4_xboole_0(A,k1_xboole_0) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 68 (all A all B -(v1_xboole_0(A) & A != B & v1_xboole_0(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 69 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k4_xboole_0(A,C),B))) # label(t109_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 70 (all A all B k2_xboole_0(A,B) = k5_xboole_0(k5_xboole_0(A,B),k3_xboole_0(A,B))) # label(t94_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 71 (all A all B all C (r1_tarski(A,k3_xboole_0(B,C)) -> r1_tarski(A,B))) # label(t18_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 72 (all A all B all C all D (r1_xboole_0(C,A) & r1_xboole_0(D,B) & k2_xboole_0(C,D) = k2_xboole_0(A,B) -> B = C)) # label(t72_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 73 (all A r1_tarski(k1_xboole_0,A)) # label(t2_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 74 (all A (-(A != k1_xboole_0 & r1_xboole_0(A,A)) & -(-r1_xboole_0(A,A) & A = k1_xboole_0))) # label(t66_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 75 (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]. 4.13/4.20 76 (all A all B r1_xboole_0(k3_xboole_0(A,B),k5_xboole_0(A,B))) # label(t103_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 77 (all A all B all C (r1_xboole_0(A,B) -> r1_xboole_0(A,k4_xboole_0(B,C)))) # label(t80_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 78 (all A all B k4_xboole_0(A,k4_xboole_0(A,B)) = k3_xboole_0(A,B)) # label(t48_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 79 (all A all B r1_tarski(k4_xboole_0(A,B),A)) # label(t36_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 80 (all A all B all C (r1_tarski(A,B) & r2_xboole_0(B,C) -> r2_xboole_0(A,C))) # label(t59_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 81 (all A all B all C (r1_tarski(A,k5_xboole_0(B,C)) <-> r1_xboole_0(A,k3_xboole_0(B,C)) & r1_tarski(A,k2_xboole_0(B,C)))) # label(t107_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 82 (all A all B r1_xboole_0(k3_xboole_0(A,B),k4_xboole_0(A,B))) # label(t89_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 83 (all A all B (r1_tarski(A,B) -> B = k2_xboole_0(A,k4_xboole_0(B,A)))) # label(t45_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 84 (all A all B (k4_xboole_0(B,A) = k4_xboole_0(A,B) -> B = A)) # label(t32_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 85 (all A all B all C (r2_xboole_0(A,B) & r1_tarski(B,C) -> r2_xboole_0(A,C))) # label(t58_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 86 (all A all B k3_xboole_0(A,B) = k5_xboole_0(k5_xboole_0(A,B),k2_xboole_0(A,B))) # label(t95_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 87 (all A all B r1_tarski(k3_xboole_0(A,B),A)) # label(t17_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 88 (all A all B k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(B,A)) = k4_xboole_0(k2_xboole_0(A,B),k3_xboole_0(A,B))) # label(t55_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 89 (all A all B k5_xboole_0(A,k4_xboole_0(B,A)) = k2_xboole_0(A,B)) # label(t98_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 90 (all A all B all C (r1_tarski(A,k2_xboole_0(B,C)) -> r1_tarski(k4_xboole_0(A,B),C))) # label(t43_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 91 (all A all B (r1_tarski(A,B) -> A = k3_xboole_0(A,B))) # label(t28_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 92 (all A all B all C k4_xboole_0(A,k3_xboole_0(B,C)) = k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(A,C))) # label(t54_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 93 (all A all B all C all D (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k4_xboole_0(A,D),k4_xboole_0(B,C)))) # label(t35_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 94 (all A all B r1_tarski(A,k2_xboole_0(A,B))) # label(t7_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 95 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k3_xboole_0(A,C),B))) # label(t108_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 96 (all A all B all C k2_xboole_0(k4_xboole_0(A,k2_xboole_0(B,C)),k3_xboole_0(k3_xboole_0(A,B),C)) = k4_xboole_0(A,k5_xboole_0(B,C))) # label(t102_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 97 (all A all B k3_xboole_0(A,k2_xboole_0(A,B)) = A) # label(t21_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 98 (all A (r1_tarski(A,k1_xboole_0) -> A = k1_xboole_0)) # label(t3_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 99 (all A all B all C k2_xboole_0(k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(B,C)),k3_xboole_0(C,A)) = k3_xboole_0(k3_xboole_0(k2_xboole_0(A,B),k2_xboole_0(B,C)),k2_xboole_0(C,A))) # label(t25_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 100 (all A all B all C (r1_tarski(A,B) -> r1_tarski(A,k2_xboole_0(C,B)))) # label(t10_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 101 (all A all B all C (r1_tarski(k2_xboole_0(A,B),C) -> r1_tarski(A,C))) # label(t11_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 102 (all A all B all C (r1_xboole_0(A,k4_xboole_0(B,C)) -> r1_xboole_0(B,k4_xboole_0(A,C)))) # label(t81_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 103 (all A all B all C k5_xboole_0(k5_xboole_0(A,B),C) = k5_xboole_0(A,k5_xboole_0(B,C))) # label(t91_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 104 (all A all B -(r2_xboole_0(B,A) & r2_xboole_0(A,B))) # label(t57_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 105 (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]. 4.13/4.20 106 (all A all B all C k2_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(A,k2_xboole_0(B,C))) # label(t4_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 107 (all A all B all C (r1_tarski(A,B) -> r1_xboole_0(A,k4_xboole_0(C,B)))) # label(t85_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 108 (all A all B all C (r1_tarski(A,B) & (all D (r1_tarski(D,B) & r1_tarski(D,C) -> r1_tarski(D,A))) & r1_tarski(A,C) -> k3_xboole_0(B,C) = A)) # label(t20_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 109 (all A all B r1_xboole_0(k4_xboole_0(A,B),B)) # label(t79_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 110 (all A all B all C k4_xboole_0(k3_xboole_0(A,B),C) = k3_xboole_0(A,k4_xboole_0(B,C))) # label(t49_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 111 (all A all B all C (r1_tarski(A,B) -> k3_xboole_0(k2_xboole_0(A,C),B) = k2_xboole_0(A,k3_xboole_0(C,B)))) # label(t30_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 112 (all A all B r1_xboole_0(k4_xboole_0(A,B),k4_xboole_0(B,A))) # label(t82_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 113 (all A all B all C ((all D (r1_tarski(A,D) & r1_tarski(C,D) -> r1_tarski(B,D))) & r1_tarski(C,B) & r1_tarski(A,B) -> k2_xboole_0(A,C) = B)) # label(t14_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 114 (all A (A != k1_xboole_0 -> r2_xboole_0(k1_xboole_0,A))) # label(t61_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 115 (all A all B (r1_tarski(A,k4_xboole_0(B,A)) -> k1_xboole_0 = A)) # label(t38_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 116 (all A all B all C (r1_tarski(k4_xboole_0(B,A),C) & r1_tarski(k4_xboole_0(A,B),C) -> r1_tarski(k5_xboole_0(A,B),C))) # label(t97_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 117 (all A all B all C (r1_tarski(B,C) & r1_tarski(A,B) -> r1_tarski(A,C))) # label(t1_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 118 (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]. 4.13/4.20 119 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k4_xboole_0(A,C),k4_xboole_0(B,C)))) # label(t33_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 120 (all A all B all C k4_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(k4_xboole_0(A,C),k4_xboole_0(B,C))) # label(t42_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 121 (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]. 4.13/4.20 122 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k4_xboole_0(C,B),k4_xboole_0(C,A)))) # label(t34_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 123 (all A all B all C -(r1_xboole_0(A,B) & -r1_xboole_0(A,k3_xboole_0(B,C)))) # label(t74_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 124 (all A all B all C (r1_tarski(A,B) & r1_tarski(A,C) -> r1_tarski(A,k3_xboole_0(B,C)))) # label(t19_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 125 (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]. 4.13/4.20 126 (all A all B all C (k2_xboole_0(C,B) = k2_xboole_0(A,B) & r1_xboole_0(C,B) & r1_xboole_0(A,B) -> A = C)) # label(t71_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 127 (all A all B k2_xboole_0(k5_xboole_0(A,B),k3_xboole_0(A,B)) = k2_xboole_0(A,B)) # label(t93_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 128 (all A all B all C (r2_xboole_0(A,B) & r2_xboole_0(B,C) -> r2_xboole_0(A,C))) # label(t56_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 129 (all A -r2_xboole_0(A,k1_xboole_0)) # label(t62_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 130 (all A all B -(-r1_xboole_0(A,B) & r1_xboole_0(k3_xboole_0(A,B),B))) # label(t75_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 131 (all A k1_xboole_0 = k5_xboole_0(A,A)) # label(t92_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 132 (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]. 4.13/4.20 133 (all A all B all C k4_xboole_0(k4_xboole_0(A,B),C) = k4_xboole_0(A,k2_xboole_0(B,C))) # label(t41_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 134 (all A all B (k1_xboole_0 = k2_xboole_0(A,B) -> k1_xboole_0 = A)) # label(t15_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 135 (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]. 4.13/4.20 136 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k3_xboole_0(A,C),k3_xboole_0(B,C)))) # label(t26_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 137 (all A all B all C k2_xboole_0(k2_xboole_0(A,C),k2_xboole_0(B,C)) = k2_xboole_0(k2_xboole_0(A,B),C)) # label(t5_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 138 (all A all B all C all D (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,D)))) # label(t13_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 139 (all A all B all C (-v1_xboole_0(C) -> -(r1_tarski(C,A) & r1_xboole_0(A,B) & r1_tarski(C,B)))) # label(t68_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 140 (all A all B all C all D k2_xboole_0(k2_xboole_0(k2_xboole_0(A,B),C),D) = k2_xboole_0(A,k2_xboole_0(k2_xboole_0(B,C),D))) # label(t113_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 141 (all A all B all C (r1_xboole_0(A,B) -> k3_xboole_0(A,C) = k3_xboole_0(A,k2_xboole_0(B,C)))) # label(t78_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 142 (all A all B k4_xboole_0(A,k3_xboole_0(A,B)) = k4_xboole_0(A,B)) # label(t47_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 143 (all A all B (r1_tarski(A,B) -> k2_xboole_0(A,B) = B)) # label(t12_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 144 (all A all B all C k4_xboole_0(k3_xboole_0(A,B),k3_xboole_0(C,B)) = k3_xboole_0(k4_xboole_0(A,C),B)) # label(t111_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 145 (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]. 4.13/4.20 146 (all A all B -(r1_tarski(A,B) & r2_xboole_0(B,A))) # label(t60_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 147 (all A all B all C (r1_tarski(k4_xboole_0(A,B),C) -> r1_tarski(A,k2_xboole_0(B,C)))) # label(t44_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 148 (all A all B all C k3_xboole_0(A,k2_xboole_0(B,C)) = k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C))) # label(t23_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 149 (all A all B r1_tarski(k4_xboole_0(A,B),k5_xboole_0(A,B))) # label(t96_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 150 (all A all B (k4_xboole_0(A,B) = A <-> r1_xboole_0(A,B))) # label(t83_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 151 (all A all B all C r1_tarski(k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C)),k2_xboole_0(B,C))) # label(t31_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 152 (all A all B k1_xboole_0 = k4_xboole_0(A,k2_xboole_0(A,B))) # label(t46_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 153 (all A all B all C -(-r1_xboole_0(A,B) & r1_xboole_0(A,k4_xboole_0(B,C)) & r1_xboole_0(A,C))) # label(t84_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 154 (all A all B all C (r1_tarski(A,C) & r1_xboole_0(B,C) & r1_tarski(A,B) -> A = k1_xboole_0)) # label(t67_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 155 (all A r1_xboole_0(A,k1_xboole_0)) # label(t65_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 156 (all A all B all C all D (r1_tarski(A,B) & r1_tarski(C,D) & r1_xboole_0(B,D) -> r1_xboole_0(A,C))) # label(t64_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 157 (all A all B all C r1_tarski(k3_xboole_0(A,B),k2_xboole_0(A,C))) # label(t29_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 158 (all A all B (-(-r2_xboole_0(B,A) & B != A & -r2_xboole_0(A,B)) <-> r3_xboole_0(A,B))) # label(t104_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 159 (all A all B all C k3_xboole_0(A,k4_xboole_0(B,C)) = k4_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C))) # label(t50_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 160 (all A all B r1_xboole_0(k4_xboole_0(A,k3_xboole_0(A,B)),B)) # label(t90_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 161 (all A all B all C k4_xboole_0(A,k4_xboole_0(B,C)) = k2_xboole_0(k4_xboole_0(A,B),k3_xboole_0(A,C))) # label(t52_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 162 (all A all B k4_xboole_0(A,B) = k5_xboole_0(A,k3_xboole_0(A,B))) # label(t100_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 163 (all A all B all C (r1_xboole_0(A,C) & r1_tarski(A,k2_xboole_0(B,C)) -> r1_tarski(A,B))) # label(t73_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 164 (all A all B all C (r1_xboole_0(A,B) -> r1_xboole_0(k3_xboole_0(C,A),k3_xboole_0(C,B)))) # label(t76_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 165 (all A all B all C (r1_xboole_0(A,B) -> k4_xboole_0(k2_xboole_0(C,B),A) = k2_xboole_0(k4_xboole_0(C,A),B))) # label(t87_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 166 (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]. 4.13/4.20 167 (all A all B A = k2_xboole_0(A,k3_xboole_0(A,B))) # label(t22_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 168 (all A all B all C k3_xboole_0(k5_xboole_0(A,C),B) = k5_xboole_0(k3_xboole_0(A,B),k3_xboole_0(C,B))) # label(t112_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 169 (all A all B A = k2_xboole_0(k3_xboole_0(A,B),k4_xboole_0(A,B))) # label(t51_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 170 (all A all B all C (r1_xboole_0(B,C) & r1_tarski(A,B) -> r1_xboole_0(A,C))) # label(t63_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 171 (all A all B all C all D (r1_xboole_0(B,D) & r1_xboole_0(C,D) & r1_xboole_0(A,D) -> r1_xboole_0(k2_xboole_0(k2_xboole_0(A,B),C),D))) # label(t114_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 172 (all A all B k4_xboole_0(A,B) = k4_xboole_0(k2_xboole_0(A,B),B)) # label(t40_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 173 (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,C) & r1_xboole_0(A,B) & -r1_xboole_0(A,k2_xboole_0(B,C))))) # label(t70_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 174 (all A all B (-v1_xboole_0(B) -> -(r1_xboole_0(B,A) & r1_tarski(B,A)))) # label(t69_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 175 (all A all B all C k2_xboole_0(k4_xboole_0(A,k2_xboole_0(B,C)),k4_xboole_0(B,k2_xboole_0(A,C))) = k4_xboole_0(k5_xboole_0(A,B),C)) # label(t99_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 176 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,C)))) # label(t9_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 177 (all A all B k2_xboole_0(A,B) = k2_xboole_0(A,k2_xboole_0(A,B))) # label(t6_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 178 (all A all B all C (r1_tarski(A,B) & r1_tarski(C,B) -> r1_tarski(k2_xboole_0(A,C),B))) # label(t8_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 179 (all A all B k2_xboole_0(A,B) = k2_xboole_0(A,k4_xboole_0(B,A))) # label(t39_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 180 (all A all B all C (r1_tarski(A,k4_xboole_0(B,C)) -> r1_xboole_0(A,C) & r1_tarski(A,B))) # label(t106_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 181 (all A all B (r1_tarski(A,B) <-> k4_xboole_0(A,B) = k1_xboole_0)) # label(t37_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 182 (all A all B (r1_xboole_0(A,B) -> A = k4_xboole_0(k2_xboole_0(A,B),B))) # label(t88_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 183 $T # label(t33_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 184 (all A all B all C all D all E all F k2_xboole_0(k1_tarski(A),k3_enumset1(B,C,D,E,F)) = k4_enumset1(A,B,C,D,E,F)) # label(t51_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 185 (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_enumset1(A,B,C),k2_enumset1(D,E,F,G))) # label(t58_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 186 (all A k4_enumset1(A,A,A,A,A,A) = k1_tarski(A)) # label(t91_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 187 (all A all B all C all D (k1_enumset1(A,B,C) = D <-> (all E (-(E != A & C != E & B != E) <-> r2_hidden(E,D))))) # label(d1_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 188 $T # label(t14_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 189 (all A all B k2_tarski(A,B) = k2_enumset1(A,A,A,B)) # label(t77_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 190 $T # label(t29_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 191 $T # label(t121_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 192 (all A all B all C all D k4_enumset1(A,A,A,B,C,D) = k2_enumset1(A,B,C,D)) # label(t79_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 193 $T # label(dt_k6_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 194 (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]. 4.13/4.20 195 (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]. 4.13/4.20 196 $T # label(t7_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 197 (all A all B k2_tarski(A,B) = k6_enumset1(A,A,A,A,A,A,A,B)) # label(t95_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 198 $T # label(t12_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 199 (all A all B all C all D all E all F all G all H all I ((all J (r2_hidden(J,I) <-> -(A != J & J != B & J != C & E != J & J != G & J != H & F != J & J != D))) <-> k6_enumset1(A,B,C,D,E,F,G,H) = I)) # label(d6_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 200 (all A all B all C all D all E all F all G k2_xboole_0(k1_tarski(A),k4_enumset1(B,C,D,E,F,G)) = k5_enumset1(A,B,C,D,E,F,G)) # label(t56_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 201 $T # label(t23_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 202 (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(k2_enumset1(A,B,C,D),k2_enumset1(E,F,G,H))) # label(t65_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 203 $T # label(t122_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 204 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(A,C,B,D)) # label(t104_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 205 $T # label(t6_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 206 (all A all B all C all D all E all F k4_enumset1(A,B,C,D,E,F) = k2_xboole_0(k2_enumset1(A,B,C,D),k2_tarski(E,F))) # label(t54_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 207 $T # label(t24_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 208 $T # label(t18_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 209 (all A all B all C all D all E all F k2_xboole_0(k1_enumset1(A,B,C),k1_enumset1(D,E,F)) = k4_enumset1(A,B,C,D,E,F)) # label(t53_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 210 (all A k6_enumset1(A,A,A,A,A,A,A,A) = k1_tarski(A)) # label(t96_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 211 $T # label(t1_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 212 (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]. 4.13/4.20 213 (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]. 4.13/4.20 214 (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]. 4.13/4.20 215 (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]. 4.13/4.20 216 $T # label(t5_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 217 (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]. 4.13/4.20 218 (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]. 4.13/4.20 219 $T # label(t38_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 220 (all A all B all C k1_enumset1(A,B,C) = k1_enumset1(B,A,C)) # label(t99_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 221 $T # label(t15_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 222 $T # label(t114_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 223 (all A all B all C all D k2_enumset1(B,D,A,C) = k2_enumset1(A,B,C,D)) # label(t112_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 224 (all A k1_tarski(A) = k3_enumset1(A,A,A,A,A)) # label(t87_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 225 (all A all B all C all D k2_enumset1(D,C,B,A) = k2_enumset1(A,B,C,D)) # label(t125_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 226 (all A k1_tarski(A) = k5_enumset1(A,A,A,A,A,A,A)) # label(t94_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 227 $T # label(t115_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 228 $T # label(t106_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 229 (all A k1_enumset1(A,A,A) = k1_tarski(A)) # label(t76_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 230 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(B,C,D,A)) # label(t111_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 231 $T # label(t17_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 232 $T # label(t39_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 233 $T # label(t4_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 234 (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]. 4.13/4.20 235 (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]. 4.13/4.20 236 (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]. 4.13/4.20 237 (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]. 4.13/4.20 238 (all A all B all C all D k2_enumset1(A,B,D,C) = k2_enumset1(A,B,C,D)) # label(t103_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 239 $T # label(dt_k5_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 240 $T # label(t22_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 241 (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]. 4.13/4.20 242 $T # label(t30_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 243 (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(k5_enumset1(A,B,C,D,E,F,G),k1_tarski(H))) # label(t68_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 244 $T # label(dt_k3_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 245 (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]. 4.13/4.20 246 $T # label(t11_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 247 (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]. 4.13/4.20 248 $T # label(t13_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 249 (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]. 4.13/4.20 250 (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]. 4.13/4.20 251 (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]. 4.13/4.20 252 $T # label(dt_k1_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 253 (all A all B all C all D k2_enumset1(C,D,B,A) = k2_enumset1(A,B,C,D)) # label(t119_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 254 (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]. 4.13/4.20 255 (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]. 4.13/4.20 256 (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(k2_tarski(A,B),k4_enumset1(C,D,E,F,G,H))) # label(t63_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 257 (all A all B all C all D all E all F k2_xboole_0(k2_tarski(A,B),k2_enumset1(C,D,E,F)) = k4_enumset1(A,B,C,D,E,F)) # label(t52_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 258 (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]. 4.13/4.20 259 $T # label(t8_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 260 (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]. 4.13/4.20 261 (all A all B all C k1_enumset1(A,B,C) = k6_enumset1(A,A,A,A,A,A,B,C)) # label(t93_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 262 $T # label(t35_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 263 (all A all B k2_tarski(A,B) = k2_xboole_0(k1_tarski(A),k1_tarski(B))) # label(t41_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 264 (all A all B all C all D all E (k2_enumset1(A,B,C,D) = E <-> (all F (r2_hidden(F,E) <-> -(F != B & C != F & F != D & A != F))))) # label(d2_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 265 (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]. 4.13/4.20 266 (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(k4_enumset1(A,B,C,D,E,F),k1_tarski(G))) # label(t61_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 267 (all A all B all C all D all E all F all G (k4_enumset1(A,B,C,D,E,F) = G <-> (all H (r2_hidden(H,G) <-> -(A != H & B != H & H != C & D != H & F != H & E != H))))) # label(d4_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 268 $T # label(dt_k4_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 269 (all A k1_tarski(A) = k2_enumset1(A,A,A,A)) # label(t82_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 270 (all A all B all C k1_enumset1(B,C,A) = k1_enumset1(A,B,C)) # label(t100_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 271 (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]. 4.13/4.20 272 (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]. 4.13/4.20 273 (all A all B all C all D all E all F all G all H k2_xboole_0(k4_enumset1(A,B,C,D,E,F),k2_tarski(G,H)) = k6_enumset1(A,B,C,D,E,F,G,H)) # label(t67_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 274 $T # label(t120_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 275 (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]. 4.13/4.20 276 (all A all B k2_tarski(A,B) = k3_enumset1(A,A,A,A,B)) # label(t83_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 277 (all A all B all C all D k2_xboole_0(k1_enumset1(A,B,C),k1_tarski(D)) = k2_enumset1(A,B,C,D)) # label(t46_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 278 (all A k2_tarski(A,A) = k1_tarski(A)) # label(t69_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 279 (all A all B all C all D all E all F all G all H k2_xboole_0(k1_tarski(A),k5_enumset1(B,C,D,E,F,G,H)) = k6_enumset1(A,B,C,D,E,F,G,H)) # label(t62_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 280 $T # label(dt_k2_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 281 $T # label(t32_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 282 (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]. 4.13/4.20 283 (all A all B all C all D k2_enumset1(A,D,C,B) = k2_enumset1(A,B,C,D)) # label(t107_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 284 $T # label(t34_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 285 $T # label(t40_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 286 $T # label(t10_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 287 (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]. 4.13/4.20 288 (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]. 4.13/4.20 289 (all A all B all C all D k2_xboole_0(k1_tarski(A),k1_enumset1(B,C,D)) = k2_enumset1(A,B,C,D)) # label(t44_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 290 $T # label(t28_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 291 (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]. 4.13/4.20 292 (all A all B all C all D k2_enumset1(D,B,C,A) = k2_enumset1(A,B,C,D)) # label(t123_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 293 (all A all B k1_enumset1(A,A,B) = k2_tarski(A,B)) # label(t70_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 294 (all A all B all C all D k2_enumset1(C,B,D,A) = k2_enumset1(A,B,C,D)) # label(t117_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 295 $T # label(t101_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 296 (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]. 4.13/4.20 297 $T # label(t19_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 298 $T # label(t124_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 299 $T # label(t36_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 300 $T # label(t31_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 301 (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]. 4.13/4.20 302 (all A all B all C all D all E all F all G all H ((all I (r2_hidden(I,H) <-> -(I != B & I != E & I != F & I != G & I != D & C != I & I != A))) <-> H = k5_enumset1(A,B,C,D,E,F,G))) # label(d5_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 303 $T # label(t37_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 304 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(B,D,C,A)) # label(t113_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 305 $T # label(t27_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 306 $T # label(t16_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 307 (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]. 4.13/4.20 308 $T # label(t25_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 309 $T # label(t97_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 310 $T # label(t21_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 311 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(B,A,D,C)) # label(t109_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 312 (all A all B all C all D all E all F ((all G (-(A != G & G != C & D != G & G != E & B != G) <-> r2_hidden(G,F))) <-> k3_enumset1(A,B,C,D,E) = F)) # label(d3_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 313 $T # label(t3_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 314 (all A all B all C all D all E all F k4_enumset1(A,B,C,D,E,F) = k2_xboole_0(k3_enumset1(A,B,C,D,E),k1_tarski(F))) # label(t55_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 315 $T # label(t9_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 316 $T # label(t26_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 317 (all A all B all C all D all E all F k4_enumset1(A,B,C,D,E,F) = k6_enumset1(A,A,A,B,C,D,E,F)) # label(t81_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 318 $T # label(t20_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 319 $T # label(t2_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 320 (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]. 4.13/4.20 321 (all A all B all C all D -(r1_tarski(k2_tarski(A,B),k2_tarski(C,D)) & A != C & D != A)) # label(t28_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 322 (all A all B all C (k2_zfmisc_1(C,k2_tarski(A,B)) = k2_xboole_0(k2_zfmisc_1(C,k1_tarski(A)),k2_zfmisc_1(C,k1_tarski(B))) & k2_zfmisc_1(k2_tarski(A,B),C) = k2_xboole_0(k2_zfmisc_1(k1_tarski(A),C),k2_zfmisc_1(k1_tarski(B),C)))) # label(t132_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 323 (all A all B -(A != k1_tarski(B) & (all C -(r2_hidden(C,A) & B != C)) & A != k1_xboole_0)) # label(t41_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 324 $T # label(t89_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 325 (all A all B (k4_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_tarski(A) <-> B != A)) # label(t20_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 326 (all A all B all C all D k4_xboole_0(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) = k2_xboole_0(k2_zfmisc_1(k4_xboole_0(A,C),B),k2_zfmisc_1(A,k4_xboole_0(B,D)))) # label(t126_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 327 (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]. 4.13/4.20 328 (all A k2_tarski(k1_xboole_0,k1_tarski(A)) = k1_zfmisc_1(k1_tarski(A))) # label(t30_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 329 (all A all B (k1_tarski(A) = k3_xboole_0(k1_tarski(A),k1_tarski(B)) -> A = B)) # label(t18_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 330 (all A all B (r2_hidden(A,B) -> B = k2_xboole_0(k4_xboole_0(B,k1_tarski(A)),k1_tarski(A)))) # label(t140_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 331 (all A exists B ((all C all D (r1_tarski(D,C) & r2_hidden(C,B) -> r2_hidden(D,B))) & (all C (r2_hidden(C,B) -> r2_hidden(k1_zfmisc_1(C),B))) & (all C -(r1_tarski(C,B) & -r2_hidden(C,B) & -r2_tarski(C,B))) & r2_hidden(A,B))) # label(t136_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 332 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 333 (all A all B (B != A -> k1_tarski(A) = k4_xboole_0(k2_tarski(A,B),k1_tarski(B)))) # label(t23_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 334 (all A all B (-r2_hidden(A,B) -> k4_xboole_0(k2_xboole_0(B,k1_tarski(A)),k1_tarski(A)) = B)) # label(t141_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 335 (all A all B k2_tarski(A,B) = k2_xboole_0(k1_tarski(A),k2_tarski(A,B))) # label(t14_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 336 (all A all B all C -(r2_hidden(B,C) & B != A & k1_tarski(A) = k3_xboole_0(k2_tarski(A,B),C))) # label(t59_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 337 (all A all B all C all D (B != A -> r1_xboole_0(k2_zfmisc_1(C,k1_tarski(A)),k2_zfmisc_1(D,k1_tarski(B))) & r1_xboole_0(k2_zfmisc_1(k1_tarski(A),C),k2_zfmisc_1(k1_tarski(B),D)))) # label(t131_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 338 (all A k3_tarski(k1_zfmisc_1(A)) = A) # label(t99_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 339 (all A all B k1_xboole_0 = k4_xboole_0(k1_tarski(A),k2_tarski(A,B))) # label(t22_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 340 (all A all B all C all D (r2_hidden(A,C) & r2_hidden(B,D) <-> r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D)))) # label(t106_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 341 (all A all B all C (k4_xboole_0(A,k2_tarski(B,C)) = k1_xboole_0 <-> -(k1_xboole_0 != A & k1_tarski(B) != A & k1_tarski(C) != A & A != k2_tarski(B,C)))) # label(t75_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 342 (all A all B all C (k4_xboole_0(k2_tarski(A,B),C) = k2_tarski(A,B) <-> -r2_hidden(B,C) & -r2_hidden(A,C))) # label(t72_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 343 (all A all B all C -(k1_tarski(A) = k2_xboole_0(B,C) & B != C & k1_xboole_0 != C & k1_xboole_0 != B)) # label(t44_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 344 (all A all B all C all D k2_xboole_0(k2_xboole_0(k2_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(A,D)),k2_zfmisc_1(B,C)),k2_zfmisc_1(B,D)) = k2_zfmisc_1(k2_xboole_0(A,B),k2_xboole_0(C,D))) # label(t121_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 345 (all A all B (r1_tarski(k1_tarski(A),k1_tarski(B)) -> B = A)) # label(t24_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 346 (all A all B (-r2_hidden(A,B) <-> k1_tarski(A) = k4_xboole_0(k1_tarski(A),B))) # label(t67_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 347 (all A all B r1_tarski(k2_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B)),k1_zfmisc_1(k2_xboole_0(A,B)))) # label(t81_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 348 (all A all B ((all C -((all D all E k4_tarski(D,E) != C) & r2_hidden(C,A))) & (all C -((all D all E C != k4_tarski(D,E)) & r2_hidden(C,B))) & (all C all D (r2_hidden(k4_tarski(C,D),A) <-> r2_hidden(k4_tarski(C,D),B))) -> B = A)) # label(t112_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 349 (all A all B (r1_tarski(A,B) -> r1_tarski(k1_zfmisc_1(A),k1_zfmisc_1(B)))) # label(t79_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 350 (all A all B all C (k4_xboole_0(k2_tarski(A,B),C) = k1_tarski(A) <-> -r2_hidden(A,C) & (r2_hidden(B,C) | B = A))) # label(t70_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 351 $T # label(t7_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 352 (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]. 4.13/4.20 353 (all A all B (r2_hidden(A,B) -> k1_tarski(A) = k3_xboole_0(B,k1_tarski(A)))) # label(t52_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 354 (all A all B all C (r1_tarski(A,k2_tarski(B,C)) <-> -(A != k2_tarski(B,C) & A != k1_tarski(C) & A != k1_tarski(B) & A != k1_xboole_0))) # label(t42_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 355 (all A all B r1_tarski(k2_zfmisc_1(A,B),k1_zfmisc_1(k1_zfmisc_1(k2_xboole_0(A,B))))) # label(t105_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 356 (all A all B all C all D (r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D)) -> r2_hidden(k4_tarski(B,A),k2_zfmisc_1(D,C)))) # label(t107_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 357 (all A all B all C k2_zfmisc_1(k2_zfmisc_1(A,B),C) = k3_zfmisc_1(A,B,C)) # label(d3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 358 (all A all B all C -(k1_tarski(A) = k2_xboole_0(B,C) & -(k1_tarski(A) = C & k1_xboole_0 = B) & -(k1_xboole_0 = C & k1_tarski(A) = B) & -(k1_tarski(A) = B & C = k1_tarski(A)))) # label(t43_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 359 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)) & r1_tarski(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)))) # label(t118_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 360 (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]. 4.13/4.20 361 $T # label(t4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 362 (all A all B all C all D (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)))) # label(t119_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 363 (all A all B all C ((all D ((exists E exists F (r2_hidden(E,A) & D = k4_tarski(E,F) & r2_hidden(F,B))) <-> r2_hidden(D,C))) <-> k2_zfmisc_1(A,B) = C)) # label(d2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 364 $T # label(t62_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 365 (all A all B ((all C (r2_hidden(C,A) -> r1_tarski(C,B))) -> r1_tarski(k3_tarski(A),B))) # label(t94_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 366 (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]. 4.13/4.20 367 (all A all B all C (r2_hidden(C,B) & r2_hidden(A,B) -> B = k2_xboole_0(k2_tarski(A,C),B))) # label(t48_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 368 $T # label(dt_k4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 369 $T # label(t77_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 370 (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_tarski(k4_tarski(A,C),k4_tarski(B,C)) = k2_zfmisc_1(k2_tarski(A,B),k1_tarski(C)))) # label(t36_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 371 (all A all B all C all D (k2_zfmisc_1(C,D) = k2_zfmisc_1(A,B) -> D = B & A = C | B = k1_xboole_0 | A = k1_xboole_0)) # label(t134_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 372 (all A all B (-r2_hidden(A,B) -> r1_xboole_0(k1_tarski(A),B))) # label(t56_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.20 373 (all A all B all C (k2_zfmisc_1(C,k4_xboole_0(A,B)) = k4_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) & k4_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)) = k2_zfmisc_1(k4_xboole_0(A,B),C))) # label(t125_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 374 $T # label(t3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 375 (all A all B (k1_tarski(A) = k4_xboole_0(k1_tarski(A),B) | k1_xboole_0 = k4_xboole_0(k1_tarski(A),B))) # label(t69_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 376 (all A all B -v1_xboole_0(k4_tarski(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 377 (all A all B -(A != k1_tarski(B) & A != k1_xboole_0 & k1_xboole_0 = k4_xboole_0(A,k1_tarski(B)))) # label(t66_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 378 (all A all B (r1_tarski(A,B) -> r1_tarski(k3_tarski(A),k3_tarski(B)))) # label(t95_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 379 (all A all B all C all D (r2_hidden(B,D) & A = C <-> r2_hidden(k4_tarski(A,B),k2_zfmisc_1(k1_tarski(C),D)))) # label(t128_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 380 $T # label(t76_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 381 (all A all B all C (r2_hidden(A,k4_xboole_0(B,k1_tarski(C))) <-> C != A & r2_hidden(A,B))) # label(t64_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 382 (all A all B all C all D -(k2_tarski(A,B) = k2_tarski(C,D) & A != C & D != A)) # label(t10_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 383 (all A all B k1_tarski(k4_tarski(A,B)) = k2_zfmisc_1(k1_tarski(A),k1_tarski(B))) # label(t35_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 384 (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]. 4.13/4.21 385 $T # label(t87_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 386 (all A all B r1_tarski(k1_tarski(A),k2_tarski(A,B))) # label(t12_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 387 $T # label(t85_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 388 (all A all B (A != B -> k2_tarski(A,B) = k5_xboole_0(k1_tarski(A),k1_tarski(B)))) # label(t29_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 389 (all A all B (A = k1_xboole_0 | k1_xboole_0 = B <-> k2_zfmisc_1(A,B) = k1_xboole_0)) # label(t113_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 390 (all A all B all C all D (r1_xboole_0(C,D) | r1_xboole_0(A,B) -> r1_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)))) # label(t127_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 391 (all A all B all C all D all E all F ((all G all H (r2_hidden(k4_tarski(G,H),A) <-> r2_hidden(k4_tarski(G,H),D))) & r1_tarski(D,k2_zfmisc_1(E,F)) & r1_tarski(A,k2_zfmisc_1(B,C)) -> D = A)) # label(t110_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 392 (all A all B all C all D -(r2_hidden(D,A) & (all E all F -(k4_tarski(E,F) = D & r2_hidden(F,C) & r2_hidden(E,B))) & r1_tarski(A,k2_zfmisc_1(B,C)))) # label(t103_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 393 $T # label(t5_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 394 (all A all B k3_xboole_0(k1_tarski(A),k2_tarski(A,B)) = k1_tarski(A)) # label(t19_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 395 (all A all B r1_tarski(k1_zfmisc_1(k4_xboole_0(A,B)),k2_xboole_0(k1_tarski(k1_xboole_0),k4_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B))))) # label(t84_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 396 (all A all B all C (r2_hidden(C,B) & r2_hidden(A,B) -> k2_tarski(A,C) = k3_xboole_0(k2_tarski(A,C),B))) # label(t53_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 397 (all A all B r1_tarski(k2_xboole_0(k1_zfmisc_1(k4_xboole_0(A,B)),k1_zfmisc_1(k4_xboole_0(B,A))),k1_zfmisc_1(k5_xboole_0(A,B)))) # label(t86_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 398 (all A all B (r2_hidden(A,B) -> k2_xboole_0(k1_tarski(A),B) = B)) # label(t46_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 399 (all A all B (r1_tarski(k1_tarski(A),k1_tarski(B)) -> B = A)) # label(t6_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 400 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 401 (all A all B -(B = A & r1_xboole_0(k1_tarski(A),k1_tarski(B)))) # label(t16_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 402 (all A all B all C (r1_tarski(k2_xboole_0(k2_tarski(A,B),C),C) -> r2_hidden(A,C))) # label(t47_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 403 (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]. 4.13/4.21 404 (all A all B all C -(A != B & A != C & r1_tarski(k1_tarski(A),k2_tarski(B,C)))) # label(t25_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 405 $T # label(t133_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 406 (all A all B all C all D (r1_tarski(C,D) & r1_tarski(A,B) -> k3_xboole_0(k2_zfmisc_1(A,D),k2_zfmisc_1(B,C)) = k2_zfmisc_1(A,C))) # label(t124_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 407 (all A all B (k2_zfmisc_1(B,A) = k2_zfmisc_1(A,B) -> A = B | B = k1_xboole_0 | A = k1_xboole_0)) # label(t114_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 408 (all A all B all C (r1_tarski(k2_tarski(A,B),C) <-> r2_hidden(A,C) & r2_hidden(B,C))) # label(t38_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 409 (all A all B all C (r1_tarski(k2_tarski(A,B),k1_tarski(C)) -> A = C)) # label(t26_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 410 (all A all B all C -(r2_hidden(A,k2_zfmisc_1(B,C)) & (all D all E A != k4_tarski(D,E)))) # label(t102_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 411 (all A all B (r1_xboole_0(k1_tarski(A),B) | k1_tarski(A) = k3_xboole_0(k1_tarski(A),B))) # label(t58_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 412 (all A all B ((all C all D (r2_hidden(D,k2_xboole_0(A,B)) & r2_hidden(C,k2_xboole_0(A,B)) -> D = C | r1_xboole_0(C,D))) -> k3_xboole_0(k3_tarski(A),k3_tarski(B)) = k3_tarski(k3_xboole_0(A,B)))) # label(t101_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 413 (all A all B (r1_tarski(k1_tarski(A),B) <-> r2_hidden(A,B))) # label(t37_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 414 (all A all B (r1_tarski(k2_xboole_0(k1_tarski(A),B),B) -> r2_hidden(A,B))) # label(t45_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 415 (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))) & -r1_tarski(B,C) & k1_xboole_0 != A)) # label(t117_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 416 (all A all B all C (k2_tarski(B,C) = k1_tarski(A) -> B = C)) # label(t9_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 417 (all A (r1_tarski(A,k2_zfmisc_1(A,A)) -> k1_xboole_0 = A)) # label(t116_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 418 (all A all B all C (r1_tarski(k2_tarski(A,B),k1_tarski(C)) -> k1_tarski(C) = k2_tarski(A,B))) # label(t27_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 419 (all A all B all C all D ((all E all F (r2_hidden(k4_tarski(E,F),k2_zfmisc_1(C,D)) <-> r2_hidden(k4_tarski(E,F),k2_zfmisc_1(A,B)))) -> k2_zfmisc_1(C,D) = k2_zfmisc_1(A,B))) # label(t108_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 420 (all A all B (-r2_hidden(B,A) <-> k4_xboole_0(A,k1_tarski(B)) = A)) # label(t65_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 421 (all A all B (k1_zfmisc_1(k2_xboole_0(A,B)) = k2_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B)) -> r3_xboole_0(A,B))) # label(t82_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 422 (all A all B r1_tarski(k3_tarski(k3_xboole_0(A,B)),k3_xboole_0(k3_tarski(A),k3_tarski(B)))) # label(t97_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 423 $T # label(t61_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 424 $T # label(t88_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 425 (all A all B all C -(r2_hidden(A,C) & r1_xboole_0(k2_tarski(A,B),C))) # label(t55_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 426 (all A all B all C (k2_zfmisc_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) & k2_zfmisc_1(k2_xboole_0(A,B),C) = k2_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)))) # label(t120_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 427 (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]. 4.13/4.21 428 (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]. 4.13/4.21 429 $T # label(t90_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 430 $T # label(t78_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 431 (all A all B (k2_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_tarski(A) -> B = A)) # label(t13_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 432 (all A all B (r1_tarski(A,k2_zfmisc_1(A,B)) | r1_tarski(A,k2_zfmisc_1(B,A)) -> A = k1_xboole_0)) # label(t135_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 433 (all A all B all C -(-r2_hidden(C,B) & -r1_xboole_0(k2_tarski(A,C),B) & -r2_hidden(A,B))) # label(t57_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 434 (all A k3_tarski(k1_tarski(A)) = A) # label(t31_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 435 $T # label(t11_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 436 (all A r1_tarski(k1_tarski(A),k1_zfmisc_1(A))) # label(t80_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 437 (all A all B all C all D (r1_tarski(A,k2_zfmisc_1(B,C)) & (all E all F (r2_hidden(k4_tarski(E,F),A) -> r2_hidden(k4_tarski(E,F),D))) -> r1_tarski(A,D))) # label(t109_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 438 $T # label(dt_k3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 439 (all A all B ((all C (r2_hidden(C,A) -> r1_xboole_0(C,B))) -> r1_xboole_0(k3_tarski(A),B))) # label(t98_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 440 $T # label(t15_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 441 (all A all B ((all C -((all D all E k4_tarski(D,E) != C) & r2_hidden(C,A))) & (all C all D (r2_hidden(k4_tarski(C,D),A) -> r2_hidden(k4_tarski(C,D),B))) -> r1_tarski(A,B))) # label(t111_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 442 (all A all B k3_tarski(k2_xboole_0(A,B)) = k2_xboole_0(k3_tarski(A),k3_tarski(B))) # label(t96_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 443 (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]. 4.13/4.21 444 (all A all B all C (k2_zfmisc_1(k3_xboole_0(A,B),C) = k3_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)) & k3_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) = k2_zfmisc_1(C,k3_xboole_0(A,B)))) # label(t122_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 445 $T # label(t71_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 446 (all A all B all C k1_xboole_0 != k2_xboole_0(k2_tarski(A,B),C)) # label(t50_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 447 (all A all B k2_xboole_0(A,B) = k3_tarski(k2_tarski(A,B))) # label(t93_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 448 (all A all B (A = k1_xboole_0 | k1_tarski(B) = A <-> r1_tarski(A,k1_tarski(B)))) # label(t39_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 449 (all A all B all C (r2_hidden(A,B) -> k1_tarski(A) = k3_xboole_0(k2_tarski(A,C),B) | C != A & r2_hidden(C,B))) # label(t60_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 450 $T # label(t91_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 451 (all A all B all C all D (k4_tarski(A,B) = k4_tarski(C,D) -> A = C & B = D)) # label(t33_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 452 (all A r1_tarski(A,k1_zfmisc_1(k3_tarski(A)))) # label(t100_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 453 (all A all B all C (r1_tarski(A,B) -> r2_hidden(C,A) | r1_tarski(A,k4_xboole_0(B,k1_tarski(C))))) # label(t40_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 454 (all A all B all C all D all E (r2_hidden(A,k2_zfmisc_1(B,C)) & r2_hidden(A,k2_zfmisc_1(D,E)) -> r2_hidden(A,k2_zfmisc_1(k3_xboole_0(B,D),k3_xboole_0(C,E))))) # label(t137_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 455 (all A all B (r2_hidden(A,B) -> r1_tarski(A,k3_tarski(B)))) # label(t92_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 456 (all A all B all C all D k3_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) = k2_zfmisc_1(k3_xboole_0(A,B),k3_xboole_0(C,D))) # label(t123_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 457 (all A all B -(r2_hidden(A,B) & r1_xboole_0(k1_tarski(A),B))) # label(t54_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 458 (all A all B all C (k4_xboole_0(k2_tarski(A,B),C) = k1_xboole_0 <-> r2_hidden(A,C) & r2_hidden(B,C))) # label(t73_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 459 (all A all B all C (k2_tarski(A,B) = k3_xboole_0(k2_tarski(A,B),C) -> r2_hidden(A,C))) # label(t63_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 460 (all A all B (A != k1_xboole_0 -> k1_xboole_0 != k2_zfmisc_1(A,k1_tarski(B)) & k2_zfmisc_1(k1_tarski(B),A) != k1_xboole_0)) # label(t130_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 461 (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]. 4.13/4.21 462 (all A all B all C -(k4_xboole_0(k2_tarski(A,B),C) != k1_xboole_0 & k4_xboole_0(k2_tarski(A,B),C) != k1_tarski(A) & k4_xboole_0(k2_tarski(A,B),C) != k2_tarski(A,B) & k1_tarski(B) != k4_xboole_0(k2_tarski(A,B),C))) # label(t74_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 463 (all A all B all C all D (r2_hidden(k4_tarski(A,B),k2_zfmisc_1(k1_tarski(C),k1_tarski(D))) <-> C = A & B = D)) # label(t34_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 464 (all A all B k2_xboole_0(k1_tarski(A),B) != k1_xboole_0) # label(t49_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 465 (all A all B (B != A -> r1_xboole_0(k1_tarski(A),k1_tarski(B)))) # label(t17_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 466 (all A all B all C all D (r2_hidden(A,C) & D = B <-> r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,k1_tarski(D))))) # label(t129_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 467 (all A all B all C all D k4_zfmisc_1(A,B,C,D) = k2_zfmisc_1(k3_zfmisc_1(A,B,C),D)) # label(d4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 468 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (B = k2_subset_1(A) <-> r1_tarski(k3_subset_1(A,B),B)))) # label(t39_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 469 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k5_subset_1(A,k3_subset_1(A,B),k3_subset_1(A,C)) = k3_subset_1(A,k4_subset_1(A,B,C)))))) # label(t29_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 470 (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,B) -> r2_hidden(D,C))) -> r1_tarski(B,C)))))) # label(t48_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 471 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> m1_subset_1(k3_subset_1(A,B),k1_zfmisc_1(A)))) # label(dt_k3_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 472 $T # label(t23_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 473 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> -((all C (m1_subset_1(C,A) -> -r2_hidden(C,B))) & k1_xboole_0 != B))) # label(t10_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 474 $T # label(t11_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 475 (all A all B (m1_subset_1(B,A) -> (k1_xboole_0 != A -> m1_subset_1(k1_tarski(B),k1_zfmisc_1(A))))) # label(t55_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 476 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> r1_tarski(k3_subset_1(A,k4_subset_1(A,B,C)),k3_subset_1(A,B)))))) # label(t41_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 477 (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,C,B) = k5_subset_1(A,B,C))) # label(commutativity_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 478 (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 = k5_subset_1(A,C,D)))))))) # label(t16_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 479 $T # label(t3_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 480 $T # label(t19_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 481 (all A -v1_xboole_0(k1_tarski(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 482 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k4_subset_1(A,B,B) = B)) # label(idempotence_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 483 (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)))) -> k4_subset_1(A,C,D) = B))))))) # label(t15_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 484 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> -r1_subset_1(A,A))) # label(irreflexivity_r1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 485 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k7_subset_1(A,B,C) = k7_subset_1(A,C,B))) # label(commutativity_k7_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 486 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> m1_subset_1(k4_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 487 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) & -v1_xboole_0(A) -> (all C (m2_subset_1(C,A,B) -> m1_subset_1(C,A))))) # label(dt_m2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 488 (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]. 4.13/4.21 489 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> ((all C (m1_subset_1(C,A) -> r2_hidden(C,B))) -> A = B))) # label(t49_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 490 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> -v1_xboole_0(k2_zfmisc_1(A,B)))) # label(fc4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 491 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_xboole_0(B,C) <-> r1_tarski(B,k3_subset_1(A,C))))))) # label(t43_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 492 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(k3_subset_1(A,C),k3_subset_1(A,B)) <-> r1_tarski(B,C)))))) # label(t31_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 493 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (A != k1_xboole_0 -> m1_subset_1(k3_enumset1(B,C,D,E,F),k1_zfmisc_1(A))))))))))))) # label(t59_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 494 (all A all B (r2_hidden(A,B) -> m1_subset_1(k1_tarski(A),k1_zfmisc_1(B)))) # label(t63_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 495 $T # label(t5_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 496 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> (r1_subset_1(A,B) <-> r1_xboole_0(A,B)))) # label(redefinition_r1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 497 (all A m1_subset_1(k8_subset_1(A),A)) # label(dt_k8_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 498 $T # label(d1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 499 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(B,k3_subset_1(A,C)) -> r1_tarski(C,k3_subset_1(A,B))))))) # label(t35_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 500 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> r1_xboole_0(B,k3_subset_1(A,B)))) # label(t26_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 501 $T # label(t13_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 502 (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]. 4.13/4.21 503 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> (r2_hidden(D,B) -> r2_hidden(D,C)))) -> r1_tarski(B,C)))))) # label(t7_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 504 (all A all B ((-v1_xboole_0(A) -> (r2_hidden(B,A) <-> m1_subset_1(B,A))) & (v1_xboole_0(A) -> (v1_xboole_0(B) <-> m1_subset_1(B,A))))) # label(d2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 505 (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]. 4.13/4.21 506 (all A k2_subset_1(A) = A) # label(d4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 507 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> m1_subset_1(k5_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 508 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (A != k1_xboole_0 -> m1_subset_1(k1_enumset1(B,C,D),k1_zfmisc_1(A))))))))) # label(t57_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 509 (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]. 4.13/4.21 510 (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) -> (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]. 4.13/4.21 511 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> B = k5_subset_1(A,B,B))) # label(idempotence_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 512 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (A != k1_xboole_0 -> m1_subset_1(k2_tarski(B,C),k1_zfmisc_1(A))))))) # label(t56_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 513 (all A (m1_subset_1(A,f1_s4_subset_1) -> (r2_hidden(A,f2_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,f3_s4_subset_1)))) -> f3_s4_subset_1 = f2_s4_subset_1 # label(s4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 514 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> m1_subset_1(k6_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k6_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 515 (all A all B -v1_xboole_0(k2_tarski(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 516 $T # label(t20_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 517 $T # label(t24_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 518 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(B,C) <-> r1_xboole_0(B,k3_subset_1(A,C))))))) # label(t44_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 519 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k4_subset_1(A,k5_subset_1(A,B,C),k5_subset_1(A,k3_subset_1(A,B),k3_subset_1(A,C))) = k3_subset_1(A,k7_subset_1(A,B,C)))))) # label(t34_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 520 (all A k2_subset_1(A) = k3_subset_1(A,k1_subset_1(A))) # label(t22_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 521 (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]. 4.13/4.21 522 (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]. 4.13/4.21 523 (all A -v1_xboole_0(k1_zfmisc_1(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 524 (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]. 4.13/4.21 525 (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]. 4.13/4.21 526 (all A m1_subset_1(k2_subset_1(A),k1_zfmisc_1(A))) # label(dt_k2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 527 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,A) -> (all I (m1_subset_1(I,A) -> (k1_xboole_0 != A -> m1_subset_1(k6_enumset1(B,C,D,E,F,G,H,I),k1_zfmisc_1(A))))))))))))))))))) # label(t62_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 528 (all A (m1_subset_1(k1_subset_1(A),k1_zfmisc_1(A)) & v1_xboole_0(k1_subset_1(A)))) # label(dt_k1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 529 $T # label(t2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 530 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) -> -(r2_hidden(B,k3_subset_1(A,C)) & r2_hidden(B,C)))) # label(t54_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 531 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(B,C) & r1_tarski(B,k3_subset_1(A,C)) -> B = k1_xboole_0))) # label(t40_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 532 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> (r2_hidden(D,B) <-> -r2_hidden(D,C)))) -> B = k3_subset_1(A,C)))))) # label(t51_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 533 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> (r1_subset_1(A,B) -> r1_subset_1(B,A)))) # label(symmetry_r1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 534 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 535 (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]. 4.13/4.21 536 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> -(r2_hidden(D,C) <-> r2_hidden(D,B)))) -> B = k3_subset_1(A,C)))))) # label(t53_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 537 $T # label(t37_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 538 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & -v1_xboole_0(C) & -v1_xboole_0(D) -> -v1_xboole_0(k4_zfmisc_1(A,B,C,D)))) # label(fc6_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 539 (all A (m1_subset_1(A,k1_zfmisc_1(f1_s2_subset_1)) -> (all B (m1_subset_1(B,k1_zfmisc_1(f1_s2_subset_1)) -> ((all C (m1_subset_1(C,f1_s2_subset_1) -> (p1_s2_subset_1(C) <-> r2_hidden(C,B)))) & (all C (m1_subset_1(C,f1_s2_subset_1) -> (p1_s2_subset_1(C) <-> r2_hidden(C,A)))) -> B = A))))) # label(s2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 540 (exists A (m1_subset_1(A,k1_zfmisc_1(f1_s1_subset_1)) & (all B (r2_hidden(B,A) <-> p1_s1_subset_1(B) & r2_hidden(B,f1_s1_subset_1))))) # label(s1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 541 (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]. 4.13/4.21 542 $T # label(t27_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 543 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> (r1_xboole_0(A,B) <-> r2_subset_1(A,B)))) # label(redefinition_r2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 544 (all A (-v1_xboole_0(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 545 (all A m1_subset_1(k1_xboole_0,k1_zfmisc_1(A))) # label(t4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 546 (all A (-$T -> (all B (m1_subset_1(B,A) -> k8_subset_1(A) = B)))) # label(d6_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 547 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> k4_subset_1(A,B,C) = k4_subset_1(A,C,B))) # label(commutativity_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 548 $T # label(t14_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 549 $T # label(t1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 550 (all A exists B m1_subset_1(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 551 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k4_subset_1(A,k3_subset_1(A,B),k3_subset_1(A,C)) = k3_subset_1(A,k5_subset_1(A,B,C)))))) # label(t30_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 552 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) & -v1_xboole_0(A) -> (exists C m2_subset_1(C,A,B)))) # label(existence_m2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 553 (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]. 4.13/4.21 554 (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]. 4.13/4.21 555 $T # label(t45_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 556 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(k3_subset_1(A,B),C) -> r1_tarski(k3_subset_1(A,C),B)))))) # label(t36_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 557 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k5_xboole_0(B,C) = k7_subset_1(A,B,C))) # label(redefinition_k7_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 558 $T # label(t12_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 559 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> B = k3_subset_1(A,k3_subset_1(A,B)))) # label(involutiveness_k3_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 560 (all A all B all C (-v1_xboole_0(B) & -v1_xboole_0(C) & -v1_xboole_0(A) -> -v1_xboole_0(k3_zfmisc_1(A,B,C)))) # label(fc5_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 561 $T # label(t6_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 562 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> r1_tarski(k3_subset_1(A,B),k3_subset_1(A,k5_subset_1(A,B,C))))))) # label(t42_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 563 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> (r2_subset_1(A,B) -> r2_subset_1(B,A)))) # label(symmetry_r2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 564 $T # label(t9_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 565 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k2_subset_1(A) = k4_subset_1(A,B,k2_subset_1(A)))) # label(t28_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 566 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k4_subset_1(A,B,C) = k2_xboole_0(B,C))) # label(redefinition_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 567 (all A k1_subset_1(A) = k1_xboole_0) # label(d3_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 568 (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]. 4.13/4.21 569 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,B) <-> -(r2_hidden(E,D) <-> r2_hidden(E,C))))) -> B = k7_subset_1(A,C,D)))))))) # label(t18_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 570 (exists A (m1_subset_1(A,k1_zfmisc_1(f1_s3_subset_1)) & (all B (m1_subset_1(B,f1_s3_subset_1) -> (p1_s3_subset_1(B) <-> r2_hidden(B,A)))))) # label(s3_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 571 (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_xboole_0(D,C) & r1_tarski(B,C) -> r1_tarski(B,k3_subset_1(A,D))))))))) # label(t47_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 572 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> (r2_hidden(D,C) <-> r2_hidden(D,B)))) -> B = C))))) # label(t8_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 573 (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 = k6_subset_1(A,C,D)))))))) # label(t17_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 574 (all A k3_subset_1(A,k2_subset_1(A)) = k1_subset_1(A)) # label(t21_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 575 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> -r2_subset_1(A,A))) # label(irreflexivity_r2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 576 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k4_subset_1(A,B,k3_subset_1(A,B)) = k2_subset_1(A))) # label(t25_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 577 (all A all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(A) -> (all C (m1_subset_1(C,B) <-> m2_subset_1(C,A,B))))) # label(redefinition_m2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 578 (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]. 4.13/4.21 579 (all A all B (r1_tarski(A,B) <-> m1_subset_1(A,k1_zfmisc_1(B)))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 580 (all A all B (r2_hidden(A,B) -> m1_subset_1(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 581 (all A all B all C -(r2_hidden(A,B) & v1_xboole_0(C) & m1_subset_1(B,k1_zfmisc_1(C)))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 582 (all A all B (m1_subset_1(A,B) -> r2_hidden(A,B) | v1_xboole_0(B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 583 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k4_xboole_0(k1_relat_1(A),k1_relat_1(B)),k1_relat_1(k4_xboole_0(A,B))))))) # label(t15_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 584 $T # label(t83_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 585 $T # label(t142_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 586 (all A all B (v1_relat_1(B) -> -((all C -r2_hidden(C,k1_relat_1(B))) & r2_hidden(A,k2_relat_1(B))))) # label(t19_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 587 (all A all B all C (v1_relat_1(C) -> k8_relat_1(k2_xboole_0(A,B),C) = k2_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)))) # label(t134_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 588 (all A (v1_relat_1(A) -> (all B (r1_xboole_0(B,k1_relat_1(A)) -> k7_relat_1(A,B) = k1_xboole_0)))) # label(t187_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 589 (exists A (-v1_xboole_0(A) & v1_relat_1(A))) # label(rc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 590 $T # label(t61_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 591 (exists A ((all B all C (r2_hidden(k4_tarski(B,C),A) <-> r2_hidden(C,f2_s1_relat_1) & p1_s1_relat_1(B,C) & r2_hidden(B,f1_s1_relat_1))) & v1_relat_1(A))) # label(s1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 592 $T # label(t35_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 593 (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]. 4.13/4.21 594 (exists A (v3_relat_1(A) & v1_relat_1(A))) # label(rc3_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 595 (all A (v1_relat_1(A) -> k10_relat_1(A,k1_xboole_0) = k1_xboole_0)) # label(t171_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 596 $T # label(t36_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 597 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(C)) & r2_hidden(A,B) <-> r2_hidden(A,k1_relat_1(k7_relat_1(C,B)))))) # label(t86_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 598 (all A k1_xboole_0 = k10_relat_1(k1_xboole_0,A)) # label(t172_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 599 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k2_relat_1(k5_relat_1(A,B)),k2_relat_1(B)))))) # label(t45_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 600 (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]. 4.13/4.21 601 (all A all B all C (v1_relat_1(C) -> r1_tarski(k4_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)),k9_relat_1(C,k4_xboole_0(A,B))))) # label(t155_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 602 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k10_relat_1(C,A),k10_relat_1(C,B))))) # label(t178_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 603 (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]. 4.13/4.21 604 $T # label(t59_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 605 (all A all B (v1_relat_1(B) -> v1_relat_1(k3_xboole_0(A,B)))) # label(t9_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 606 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k2_relat_1(k3_xboole_0(A,B)),k3_xboole_0(k2_relat_1(A),k2_relat_1(B))))))) # label(t27_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 607 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k1_relat_1(k3_xboole_0(A,B)),k3_xboole_0(k1_relat_1(A),k1_relat_1(B))))))) # label(t14_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 608 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k7_relat_1(k7_relat_1(C,A),B) = k7_relat_1(C,A)))) # label(t102_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 609 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(B,C) -> r1_tarski(k7_relat_1(B,A),k7_relat_1(C,A))))))) # label(t105_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 610 $T # label(dt_k3_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 611 $T # label(t84_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 612 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(k1_relat_1(A),k2_relat_1(B)) -> k2_relat_1(k5_relat_1(B,A)) = k2_relat_1(A)))))) # label(t47_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 613 (all A all B (v1_relat_1(B) -> r1_tarski(k2_relat_1(k7_relat_1(B,A)),k2_relat_1(B)))) # label(t99_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 614 (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(k4_tarski(A,B),D) & r2_hidden(A,C)))) # label(t74_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 615 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k9_relat_1(C,A),k9_relat_1(C,B))))) # label(t156_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 616 (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]. 4.13/4.21 617 (all A all B (v1_relat_1(B) -> k10_relat_1(B,k3_xboole_0(k2_relat_1(B),A)) = k10_relat_1(B,A))) # label(t168_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 618 (all A all B v1_relat_1(k2_zfmisc_1(A,B))) # label(t6_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 619 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k2_xboole_0(k2_relat_1(A),k2_relat_1(B)) = k2_relat_1(k2_xboole_0(A,B)))))) # label(t26_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 620 (all A (v1_relat_1(A) -> A = k5_relat_1(A,k6_relat_1(k2_relat_1(A))))) # label(t80_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 621 (all A (v1_relat_1(A) -> r1_tarski(k2_relat_1(A),k3_relat_1(A)) & r1_tarski(k1_relat_1(A),k3_relat_1(A)))) # label(t29_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 622 (all A all B (v1_relat_1(B) & v1_relat_1(A) -> v1_relat_1(k3_xboole_0(A,B)))) # label(fc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 623 $T # label(t2_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 624 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k9_relat_1(C,B)) <-> (exists D (r2_hidden(D,k1_relat_1(C)) & r2_hidden(k4_tarski(D,A),C) & r2_hidden(D,B)))))) # label(t143_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 625 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k8_relat_1(A,C),k8_relat_1(B,D))))))) # label(t133_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 626 (all A all B (v1_relat_1(B) -> -(r1_tarski(A,k2_relat_1(B)) & k1_xboole_0 = k10_relat_1(B,A) & A != k1_xboole_0))) # label(t174_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 627 (all A all B (v1_relat_1(A) -> v1_relat_1(k7_relat_1(A,B)))) # label(dt_k7_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 628 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k7_relat_1(A,k1_relat_1(B)) = k7_relat_1(A,k1_relat_1(k7_relat_1(B,k1_relat_1(A)))))))) # label(t189_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 629 $T # label(t113_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 630 (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))) <-> k10_relat_1(A,B) = C)))) # label(d14_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 631 (all A all B (v1_relat_1(B) -> k7_relat_1(k7_relat_1(B,A),A) = k7_relat_1(B,A))) # label(t101_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 632 (all A (v1_relat_1(A) -> k5_relat_1(A,k1_xboole_0) = k1_xboole_0 & k1_xboole_0 = k5_relat_1(k1_xboole_0,A))) # label(t62_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 633 (all A (v1_relat_1(A) -> (v2_relat_1(A) <-> -r2_hidden(k1_xboole_0,k2_relat_1(A))))) # label(d9_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 634 (all A (v1_relat_1(A) -> k8_relat_1(k2_relat_1(A),A) = A)) # label(t126_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 635 $T # label(dt_k9_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 636 (all A v1_relat_1(k6_relat_1(A))) # label(dt_k6_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 637 (all A all B all C all D (v1_relat_1(D) -> (r2_hidden(k4_tarski(A,B),k5_relat_1(D,k6_relat_1(C))) <-> r2_hidden(k4_tarski(A,B),D) & r2_hidden(B,C)))) # label(t75_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 638 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k4_xboole_0(k2_relat_1(A),k2_relat_1(B)),k2_relat_1(k4_xboole_0(A,B))))))) # label(t28_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 639 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(A),k1_relat_1(B)) -> k1_relat_1(A) = k1_relat_1(k5_relat_1(A,B))))))) # label(t46_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 640 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> r1_tarski(k5_relat_1(k7_relat_1(B,A),C),k5_relat_1(B,C)))))) # label(t92_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 641 (all A all B (v1_relat_1(B) -> k2_relat_1(k8_relat_1(A,B)) = k3_xboole_0(k2_relat_1(B),A))) # label(t119_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 642 (all A k1_xboole_0 = k7_relat_1(k1_xboole_0,A)) # label(t111_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 643 $T # label(t68_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 644 (all A all B all C all D all E (v1_relat_1(E) -> (k2_tarski(k4_tarski(A,B),k4_tarski(C,D)) = E -> k2_relat_1(E) = k2_tarski(B,D) & k1_relat_1(E) = k2_tarski(A,C)))) # label(t24_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 645 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k7_relat_1(C,A),k7_relat_1(C,B))))) # label(t104_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 646 (all A all B all C (v1_relat_1(C) -> (k1_tarski(k4_tarski(A,B)) = C -> k1_relat_1(C) = k1_tarski(A) & k2_relat_1(C) = k1_tarski(B)))) # label(t23_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 647 $T # label(t43_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 648 (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]. 4.13/4.21 649 (all A (v1_xboole_0(A) -> v1_relat_1(k1_relat_1(A)) & v1_xboole_0(k1_relat_1(A)))) # label(fc7_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 650 (all A all B (v1_relat_1(B) -> -(v3_relat_1(B) & -v3_relat_1(k7_relat_1(B,A))))) # label(t190_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 651 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k9_relat_1(B,k2_relat_1(A)) = k2_relat_1(k5_relat_1(A,B)))))) # label(t160_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 652 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (B = k4_relat_1(A) <-> (all C all D (r2_hidden(k4_tarski(D,C),A) <-> r2_hidden(k4_tarski(C,D),B)))))))) # label(d7_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 653 (all A all B all C (v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),C) -> r2_hidden(B,k3_relat_1(C)) & r2_hidden(A,k3_relat_1(C))))) # label(t30_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 654 (all A all B (v1_relat_1(B) -> (r1_tarski(A,k1_relat_1(B)) -> k1_relat_1(k7_relat_1(B,A)) = A))) # label(t91_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 655 (all A all B all C (v1_relat_1(C) -> (C = k1_tarski(k4_tarski(A,B)) -> k3_relat_1(C) = k2_tarski(A,B)))) # label(t32_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 656 (all A all B (v1_relat_1(B) -> -(A != k1_xboole_0 & r1_tarski(A,k1_relat_1(B)) & k1_xboole_0 = k9_relat_1(B,A)))) # label(t152_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 657 (all A all B all C (v1_relat_1(C) -> k2_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)) = k7_relat_1(C,k2_xboole_0(A,B)))) # label(t107_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 658 (all A (v1_relat_1(A) -> (v3_relat_1(A) <-> r1_tarski(k2_relat_1(A),k1_tarski(k1_xboole_0))))) # label(d15_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 659 (all A all B (v1_relat_1(B) -> r1_tarski(k10_relat_1(B,A),k1_relat_1(B)))) # label(t167_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.21 660 (all A all B (v1_relat_1(B) -> (r1_tarski(k1_relat_1(B),A) -> k7_relat_1(B,A) = B))) # label(t97_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 661 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k4_relat_1(k5_relat_1(A,B)) = k5_relat_1(k4_relat_1(B),k4_relat_1(A)))))) # label(t54_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 662 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k10_relat_1(C,B)) <-> (exists D (r2_hidden(D,k2_relat_1(C)) & r2_hidden(k4_tarski(A,D),C) & r2_hidden(D,B)))))) # label(t166_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 663 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(A,B) -> r1_tarski(k3_relat_1(A),k3_relat_1(B))))))) # label(t31_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 664 (all A (v1_relat_1(A) -> (v3_relat_1(A) <-> (all B (r2_hidden(B,k2_relat_1(A)) -> B = k1_xboole_0))))) # label(t184_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 665 (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]. 4.13/4.22 666 (all A (v1_relat_1(A) -> (all B all C (v1_relat_1(C) -> (k7_relat_1(A,B) = C <-> (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]. 4.13/4.22 667 (all A ((all B -(r2_hidden(B,A) & (all C all D B != k4_tarski(C,D)))) <-> v1_relat_1(A))) # label(d1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 668 (all A all B all C (v1_relat_1(C) -> k10_relat_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)))) # label(t175_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 669 (all A all B (v1_relat_1(B) -> k3_xboole_0(k1_relat_1(B),A) = k1_relat_1(k7_relat_1(B,A)))) # label(t90_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 670 (all A all B all C (v1_relat_1(C) -> k4_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)) = k7_relat_1(C,k4_xboole_0(A,B)))) # label(t109_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 671 $T # label(t8_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 672 (all A all B (v1_relat_1(B) & v1_xboole_0(A) -> v1_xboole_0(k5_relat_1(A,B)) & v1_relat_1(k5_relat_1(A,B)))) # label(fc9_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 673 $T # label(t85_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 674 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_xboole_0(k2_relat_1(A),k1_relat_1(B)) -> k1_xboole_0 = k5_relat_1(A,B)))))) # label(t67_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 675 (all A all B (v1_relat_1(B) -> k2_relat_1(k7_relat_1(B,A)) = k9_relat_1(B,A))) # label(t148_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 676 (all A (v1_relat_1(A) -> r1_tarski(A,k2_zfmisc_1(k1_relat_1(A),k2_relat_1(A))))) # label(t21_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 677 (all A (v1_xboole_0(A) -> v1_relat_1(k4_relat_1(A)) & v1_xboole_0(k4_relat_1(A)))) # label(fc11_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 678 (all A all B (v1_relat_1(B) -> v1_relat_1(k4_xboole_0(B,A)))) # label(t10_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 679 (all A (v1_relat_1(A) -> k2_relat_1(k4_relat_1(A)) = k1_relat_1(A) & k2_relat_1(A) = k1_relat_1(k4_relat_1(A)))) # label(t37_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 680 (all A all B (v1_relat_1(B) -> -((all C -r2_hidden(C,k2_relat_1(B))) & r2_hidden(A,k1_relat_1(B))))) # label(t18_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 681 (all A (v1_relat_1(A) -> k8_relat_1(k1_xboole_0,A) = k1_xboole_0)) # label(t137_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 682 (all A all B (v1_relat_1(B) -> (k7_relat_1(B,A) = k1_xboole_0 <-> r1_xboole_0(k1_relat_1(B),A)))) # label(t95_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 683 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k3_relat_1(k3_xboole_0(A,B)),k3_xboole_0(k3_relat_1(A),k3_relat_1(B))))))) # label(t34_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 684 (exists A (v1_relat_1(A) & v1_xboole_0(A))) # label(rc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 685 $T # label(t58_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 686 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k8_relat_1(A,k5_relat_1(B,C)) = k5_relat_1(B,k8_relat_1(A,C)))))) # label(t139_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 687 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k2_relat_1(k8_relat_1(B,C))) <-> r2_hidden(A,k2_relat_1(C)) & r2_hidden(A,B)))) # label(t115_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 688 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 689 (all A (-v1_xboole_0(A) & v1_relat_1(A) -> -v1_xboole_0(k2_relat_1(A)))) # label(fc6_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 690 (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))) <-> C = k5_relat_1(A,B)))))))) # label(d8_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 691 (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(C,A),k5_relat_1(C,B))))))))) # label(t48_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 692 $T # label(t63_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 693 $T # label(t42_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 694 (all A (v1_relat_1(A) -> k1_xboole_0 = k7_relat_1(A,k1_xboole_0))) # label(t110_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 695 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k2_xboole_0(k4_relat_1(A),k4_relat_1(B)) = k4_relat_1(k2_xboole_0(A,B)))))) # label(t40_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 696 (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]. 4.13/4.22 697 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (A = k1_relat_1(B) & r1_tarski(k2_relat_1(C),A) & k5_relat_1(C,B) = k6_relat_1(k1_relat_1(D)) & k6_relat_1(A) = k5_relat_1(B,D) -> C = D))))))) # label(t82_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 698 (all A all B (v1_relat_1(B) -> v1_relat_1(k8_relat_1(A,B)))) # label(dt_k8_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 699 (all A all B (v1_relat_1(B) & v1_relat_1(A) -> v1_relat_1(k5_relat_1(A,B)))) # label(dt_k5_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 700 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k4_relat_1(k4_xboole_0(A,B)) = k4_xboole_0(k4_relat_1(A),k4_relat_1(B)))))) # label(t41_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 701 (all A (v1_relat_1(A) -> (all B (B = k1_relat_1(A) <-> (all C (r2_hidden(C,B) <-> (exists D r2_hidden(k4_tarski(C,D),A)))))))) # label(d4_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 702 $T # label(t114_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 703 (all A all B all C (v1_relat_1(C) -> r1_tarski(k9_relat_1(k7_relat_1(C,A),B),k9_relat_1(C,B)))) # label(t161_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 704 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(B,C) -> r1_tarski(k9_relat_1(B,A),k9_relat_1(C,A))))))) # label(t157_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 705 (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]. 4.13/4.22 706 (all A all B (v1_relat_1(B) -> r1_tarski(k3_xboole_0(k2_relat_1(B),A),k10_relat_1(k4_relat_1(B),k10_relat_1(B,A))))) # label(t183_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 707 (all A all B all C (v1_relat_1(C) -> r1_tarski(k4_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)),k10_relat_1(C,k4_xboole_0(A,B))))) # label(t177_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 708 (all A all B (v1_relat_1(B) -> (r1_tarski(A,B) -> v1_relat_1(A)))) # label(t3_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 709 (all A all B (v1_relat_1(B) -> r1_tarski(k2_relat_1(k8_relat_1(A,B)),A))) # label(t116_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 710 (all A all B all C (v1_relat_1(C) -> k8_relat_1(A,k7_relat_1(C,B)) = k7_relat_1(k8_relat_1(A,C),B))) # label(t140_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 711 (all A (v1_relat_1(A) -> A = k3_xboole_0(A,k2_zfmisc_1(k1_relat_1(A),k2_relat_1(A))))) # label(t22_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 712 (all A all B (v1_relat_1(B) & v1_relat_1(A) -> v1_relat_1(k4_xboole_0(A,B)))) # label(fc3_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 713 (all A (v1_relat_1(A) -> k9_relat_1(A,k1_xboole_0) = k1_xboole_0)) # label(t149_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 714 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k1_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k1_relat_1(A),k1_relat_1(B)))))) # label(t13_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 715 (all A (v1_relat_1(A) -> k3_relat_1(A) = k2_xboole_0(k1_relat_1(A),k2_relat_1(A)))) # label(d6_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 716 (all A (v1_relat_1(A) -> v1_relat_1(k4_relat_1(A)))) # label(dt_k4_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 717 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(B,C) -> r1_tarski(k8_relat_1(A,B),k8_relat_1(A,C))))))) # label(t132_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 718 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(B,C) -> r1_tarski(k10_relat_1(B,A),k10_relat_1(C,A))))))) # label(t179_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 719 (all A all B (v1_relat_1(A) & v3_relat_1(A) -> v1_relat_1(k7_relat_1(A,B)) & v3_relat_1(k7_relat_1(A,B)))) # label(fc13_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 720 $T # label(t69_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 721 (all A k1_xboole_0 = k8_relat_1(A,k1_xboole_0)) # label(t138_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 722 (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]. 4.13/4.22 723 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> ((all C all D (r2_hidden(k4_tarski(C,D),A) <-> r2_hidden(k4_tarski(C,D),B))) <-> A = B))))) # label(d2_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 724 (all A all B (v1_relat_1(B) -> ((all C (r2_hidden(C,A) -> r2_hidden(k4_tarski(C,C),B))) -> r1_tarski(k6_relat_1(A),B)))) # label(t73_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 725 (all A all B all C (v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),C) -> r2_hidden(A,k1_relat_1(C)) & r2_hidden(B,k2_relat_1(C))))) # label(t20_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 726 (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]. 4.13/4.22 727 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k7_relat_1(C,A) = k7_relat_1(k7_relat_1(C,B),A)))) # label(t103_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 728 (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]. 4.13/4.22 729 (all A all B (v1_relat_1(B) -> r1_tarski(k9_relat_1(B,A),k9_relat_1(B,k1_relat_1(B))))) # label(t147_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 730 (all A all B (v1_relat_1(B) -> k7_relat_1(B,A) = k3_xboole_0(B,k2_zfmisc_1(A,k2_relat_1(B))))) # label(t96_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 731 (all A all B v1_relat_1(k1_tarski(k4_tarski(A,B)))) # label(t4_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 732 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k8_relat_1(A,C) = k8_relat_1(A,k8_relat_1(B,C))))) # label(t130_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 733 (all A (v1_relat_1(A) -> (all B ((all C (r2_hidden(C,B) <-> (exists D r2_hidden(k4_tarski(D,C),A)))) <-> B = k2_relat_1(A))))) # label(d5_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 734 (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]. 4.13/4.22 735 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k5_relat_1(A,k2_xboole_0(B,C)) = k2_xboole_0(k5_relat_1(A,B),k5_relat_1(A,C)))))))) # label(t51_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 736 (all A all B (v1_relat_1(B) -> k9_relat_1(B,k3_xboole_0(k1_relat_1(B),A)) = k9_relat_1(B,A))) # label(t145_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 737 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k2_xboole_0(k3_relat_1(A),k3_relat_1(B)) = k3_relat_1(k2_xboole_0(A,B)))))) # label(t33_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 738 (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]. 4.13/4.22 739 (all A (k1_relat_1(k6_relat_1(A)) = A & k2_relat_1(k6_relat_1(A)) = A)) # label(t71_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 740 (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(k7_relat_1(C,A),k7_relat_1(D,B))))))) # label(t106_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 741 (all A (v1_relat_1(A) & -v1_xboole_0(A) -> -v1_xboole_0(k1_relat_1(A)))) # label(fc5_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 742 (all A all B (v1_relat_1(B) -> r1_tarski(k10_relat_1(B,A),k10_relat_1(B,k2_relat_1(B))))) # label(t170_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 743 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k10_relat_1(C,A),k10_relat_1(D,B))))))) # label(t180_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 744 (all A all B (v1_relat_1(B) -> r1_tarski(k9_relat_1(B,A),k2_relat_1(B)))) # label(t144_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 745 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> r1_tarski(k4_xboole_0(k5_relat_1(A,B),k5_relat_1(A,C)),k5_relat_1(A,k4_xboole_0(B,C))))))))) # label(t53_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 746 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(A,B) -> r1_tarski(k2_relat_1(A),k2_relat_1(B)) & r1_tarski(k1_relat_1(A),k1_relat_1(B))))))) # label(t25_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 747 $T # label(t164_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 748 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k5_relat_1(k7_relat_1(B,A),C) = k7_relat_1(k5_relat_1(B,C),A))))) # label(t112_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 749 $T # label(dt_k10_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 750 (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]. 4.13/4.22 751 (all A all B all C (v1_relat_1(C) -> k7_relat_1(k7_relat_1(C,A),B) = k7_relat_1(C,k3_xboole_0(A,B)))) # label(t100_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 752 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k5_relat_1(A,C),k5_relat_1(B,D))))))))))) # label(t50_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 753 (all A all B (v1_relat_1(B) -> r1_tarski(k1_relat_1(k7_relat_1(B,A)),A))) # label(t87_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 754 (all A all B (v1_relat_1(B) -> r1_tarski(k3_xboole_0(k1_relat_1(B),A),k9_relat_1(k4_relat_1(B),k9_relat_1(B,A))))) # label(t163_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 755 $T # label(t1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 756 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k8_relat_1(A,C) = k8_relat_1(B,k8_relat_1(A,C))))) # label(t129_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 757 (all A all B (v1_relat_1(B) -> (r1_xboole_0(k2_relat_1(B),A) <-> k1_xboole_0 = k10_relat_1(B,A)))) # label(t173_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 758 (all A all B (v1_relat_1(B) -> ((all C all D (r2_hidden(k4_tarski(C,D),B) <-> r2_hidden(C,A) & D = C)) <-> k6_relat_1(A) = B))) # label(d10_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 759 (all A all B (v1_relat_1(B) -> (r1_tarski(k1_relat_1(B),A) -> B = k5_relat_1(k6_relat_1(A),B)))) # label(t77_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 760 $T # label(t70_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 761 (all A all B all C all D v1_relat_1(k2_tarski(k4_tarski(A,B),k4_tarski(C,D)))) # label(t5_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 762 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> r1_tarski(k5_relat_1(A,k3_xboole_0(B,C)),k3_xboole_0(k5_relat_1(A,B),k5_relat_1(A,C))))))))) # label(t52_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 763 $T # label(t162_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 764 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C all D (k7_relat_1(A,D) = k7_relat_1(B,D) & k7_relat_1(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]. 4.13/4.22 765 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(k1_relat_1(C),A) & r1_tarski(C,B) -> r1_tarski(C,k7_relat_1(B,A))))))) # label(t186_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 766 (all A all B (v1_relat_1(B) & v1_xboole_0(A) -> v1_relat_1(k5_relat_1(B,A)) & v1_xboole_0(k5_relat_1(B,A)))) # label(fc10_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 767 $T # label(t141_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 768 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 769 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> ((all D all E (r2_hidden(k4_tarski(D,E),C) <-> r2_hidden(k4_tarski(D,E),B) & r2_hidden(E,A))) <-> C = k8_relat_1(A,B)))))) # label(d12_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 770 (all A all B (v1_relat_1(B) -> r1_tarski(k7_relat_1(B,A),B))) # label(t88_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 771 (all A k1_xboole_0 = k9_relat_1(k1_xboole_0,A)) # label(t150_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 772 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> r1_tarski(k5_relat_1(B,k7_relat_1(C,A)),k5_relat_1(B,C)))))) # label(t93_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 773 (all A all B all C (v1_relat_1(C) -> r1_tarski(k10_relat_1(C,k3_xboole_0(A,B)),k3_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B))))) # label(t176_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 774 (all A (v1_relat_1(A) -> (k2_relat_1(A) = k1_xboole_0 | k1_xboole_0 = k1_relat_1(A) -> k1_xboole_0 = A))) # label(t64_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 775 (all A all B all C (v1_relat_1(C) -> k8_relat_1(k3_xboole_0(A,B),C) = k8_relat_1(A,k8_relat_1(B,C)))) # label(t127_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 776 $T # label(t16_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 777 (all A all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> k8_relat_1(A,B) = B))) # label(t125_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 778 $T # label(t57_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 779 (all A all B (v1_relat_1(B) -> k8_relat_1(A,B) = k3_xboole_0(B,k2_zfmisc_1(k1_relat_1(B),A)))) # label(t124_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 780 (all A all B (v1_relat_1(B) -> r1_tarski(k1_relat_1(k7_relat_1(B,A)),k1_relat_1(B)))) # label(t89_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 781 (all A (v1_relat_1(A) -> (k1_xboole_0 = k1_relat_1(A) <-> k1_xboole_0 = k2_relat_1(A)))) # label(t65_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 782 (all A (v1_relat_1(A) -> k3_relat_1(A) = k3_relat_1(k4_relat_1(A)))) # label(t38_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 783 (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]. 4.13/4.22 784 (all A all B all C (v1_relat_1(C) -> k7_relat_1(C,k3_xboole_0(A,B)) = k3_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)))) # label(t108_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 785 $T # label(t7_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 786 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k10_relat_1(A,k1_relat_1(B)) = k1_relat_1(k5_relat_1(A,B)))))) # label(t182_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 787 (all A all B all C (v1_relat_1(C) -> r1_tarski(k9_relat_1(C,k3_xboole_0(A,B)),k3_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B))))) # label(t154_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 788 (all A all B (v1_relat_1(B) -> r1_tarski(k5_relat_1(k6_relat_1(A),B),B) & r1_tarski(k5_relat_1(B,k6_relat_1(A)),B))) # label(t76_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 789 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k5_relat_1(A,C),k5_relat_1(B,C))))))))) # label(t49_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 790 (all A all B (v1_relat_1(B) -> k5_relat_1(k6_relat_1(A),B) = k7_relat_1(B,A))) # label(t94_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 791 (all A (v1_relat_1(A) -> A = k7_relat_1(A,k1_relat_1(A)))) # label(t98_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 792 $T # label(t17_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 793 (all A (v1_relat_1(A) -> k5_relat_1(k6_relat_1(k1_relat_1(A)),A) = A)) # label(t78_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 794 (all A (v1_relat_1(A) -> (all B all C (k9_relat_1(A,B) = C <-> (all D (r2_hidden(D,C) <-> (exists E (r2_hidden(k4_tarski(E,D),A) & r2_hidden(E,B))))))))) # label(d13_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 795 (all A (v1_xboole_0(A) -> v1_relat_1(A))) # label(cc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 796 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> r1_tarski(k5_relat_1(k8_relat_1(A,B),C),k5_relat_1(B,C)))))) # label(t121_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 797 (all A all B all C (v1_relat_1(C) -> k8_relat_1(k3_xboole_0(A,B),C) = k3_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)))) # label(t135_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 798 (all A (v1_xboole_0(A) -> v1_relat_1(k2_relat_1(A)) & v1_xboole_0(k2_relat_1(A)))) # label(fc8_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 799 (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]. 4.13/4.22 800 $T # label(t12_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 801 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k8_relat_1(A,C),k8_relat_1(B,C))))) # label(t131_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 802 $T # label(t11_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 803 (all A all B (v1_relat_1(B) -> r1_tarski(k8_relat_1(A,B),B))) # label(t117_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 804 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> r1_tarski(k5_relat_1(B,k8_relat_1(A,C)),k5_relat_1(B,C)))))) # label(t122_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 805 (all A all B (v1_relat_1(B) -> r1_tarski(k2_relat_1(k8_relat_1(A,B)),k2_relat_1(B)))) # label(t118_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 806 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k10_relat_1(B,k10_relat_1(C,A)) = k10_relat_1(k5_relat_1(B,C),A))))) # label(t181_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 807 $T # label(t165_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 808 (all A k4_relat_1(k6_relat_1(A)) = k6_relat_1(A)) # label(t72_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 809 (all A (v1_relat_1(A) -> k9_relat_1(A,k1_relat_1(A)) = k2_relat_1(A))) # label(t146_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 810 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(A,B) <-> (all C all D (r2_hidden(k4_tarski(C,D),A) -> r2_hidden(k4_tarski(C,D),B)))))))) # label(d3_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 811 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k1_relat_1(k5_relat_1(A,B)),k1_relat_1(A)))))) # label(t44_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 812 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k2_relat_1(k5_relat_1(C,B))) -> r2_hidden(A,k2_relat_1(B))))))) # label(t25_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 813 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (v2_funct_1(C) -> k4_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)) = k9_relat_1(C,k4_xboole_0(A,B))))) # label(t123_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 814 $T # label(t135_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 815 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_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) -> k2_funct_1(A) = B))))) # label(t63_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 816 (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(k5_relat_1(k6_relat_1(A),C),B) = k1_funct_1(C,B)))) # label(t38_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 817 $T # label(t107_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 818 $T # label(t91_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 819 $T # label(t132_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 820 $T # label(t95_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 821 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> k9_relat_1(k8_relat_1(A,C),B) = k3_xboole_0(A,k9_relat_1(C,B)))) # label(t126_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 822 $T # label(t5_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 823 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> v2_funct_1(k2_funct_1(A))))) # label(t62_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 824 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,A) -> k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B)))) # label(t72_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 825 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) & v2_funct_1(A) -> v2_funct_1(k5_relat_1(A,B))))))) # label(t46_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 826 (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))) & k1_relat_1(A) = k2_relat_1(k5_relat_1(A,k2_funct_1(A)))))) # label(t58_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 827 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k2_funct_1(k2_funct_1(A)) = A))) # label(t65_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 828 $T # label(t114_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 829 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) <-> (all B all C (r2_hidden(B,k1_relat_1(A)) & k1_funct_1(A,B) = k1_funct_1(A,C) & r2_hidden(C,k1_relat_1(A)) -> C = B))))) # label(d8_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 830 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(B) = A & (all C (r2_hidden(C,A) -> k1_funct_1(B,C) = C)) <-> B = k6_relat_1(A)))) # label(t34_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 831 $T # label(t74_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 832 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k1_relat_1(k8_relat_1(A,C))) -> k1_funct_1(k8_relat_1(A,C),B) = k1_funct_1(C,B)))) # label(t87_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 833 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> r2_hidden(k1_funct_1(B,A),k2_relat_1(B))))) # label(t12_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 834 $T # label(t130_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 835 (all A all B all C (p1_s2_funct_1(A,C) & p1_s2_funct_1(A,B) & r2_hidden(A,f1_s2_funct_1) -> B = C)) & (all A -(r2_hidden(A,f1_s2_funct_1) & (all B -p1_s2_funct_1(A,B)))) -> (exists A (v1_relat_1(A) & f1_s2_funct_1 = k1_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]. 4.13/4.22 836 (all A (k1_xboole_0 != A -> (all B exists C (v1_funct_1(C) & k1_tarski(B) = k2_relat_1(C) & A = k1_relat_1(C) & v1_relat_1(C))))) # label(t15_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 837 $T # label(d6_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 838 $T # label(t129_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 839 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> ((all D (r2_hidden(D,k1_relat_1(B)) <-> r2_hidden(D,k1_relat_1(C)) & r2_hidden(k1_funct_1(C,D),A))) & (all D (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(B,D) = k1_funct_1(C,D))) <-> B = k8_relat_1(A,C)))))) # label(t85_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 840 (all A all B (v1_funct_1(B) & v1_relat_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]. 4.13/4.22 841 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> k3_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)) = k10_relat_1(C,k3_xboole_0(A,B)))) # label(t137_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 842 $T # label(t93_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 843 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k2_relat_1(A) = k1_relat_1(B) & A = k5_relat_1(A,B) -> k6_relat_1(k1_relat_1(B)) = B))))) # label(t44_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 844 $T # label(t101_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 845 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) -> v2_funct_1(k7_relat_1(B,A))))) # label(t84_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 846 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(A) & v2_funct_1(B) -> k5_relat_1(k2_funct_1(B),k2_funct_1(A)) = k2_funct_1(k5_relat_1(A,B))))))) # label(t66_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 847 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> k1_relat_1(k5_relat_1(k6_relat_1(A),B)) = k3_xboole_0(k1_relat_1(B),A))) # label(t37_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 848 $T # label(t11_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 849 (all A all B k5_relat_1(k6_relat_1(B),k6_relat_1(A)) = k6_relat_1(k3_xboole_0(A,B))) # label(t43_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 850 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (A = k1_relat_1(C) & r1_tarski(k2_relat_1(C),A) & k5_relat_1(C,B) = B & v2_funct_1(B) & k1_relat_1(B) = A -> C = k6_relat_1(A)))))) # label(t50_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 851 (all A all B (v1_relat_1(B) -> (r1_tarski(A,k1_relat_1(B)) -> r1_tarski(A,k10_relat_1(B,k9_relat_1(B,A)))))) # label(t146_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 852 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) & r2_hidden(A,k2_relat_1(B)) -> k1_funct_1(k5_relat_1(k2_funct_1(B),B),A) = A & A = k1_funct_1(B,k1_funct_1(k2_funct_1(B),A))))) # label(t57_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 853 (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]. 4.13/4.22 854 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k9_relat_1(C,A),k9_relat_1(C,B)) & v2_funct_1(C) & r1_tarski(A,k1_relat_1(C)) -> r1_tarski(A,B)))) # label(t157_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 855 $T # label(t109_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 856 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) <-> (all B exists C r1_tarski(k10_relat_1(A,k1_tarski(B)),k1_tarski(C)))))) # label(t159_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 857 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k1_relat_1(k2_funct_1(A)) = k2_relat_1(A) & k2_relat_1(k2_funct_1(A)) = k1_relat_1(A)))) # label(t55_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 858 $T # label(t141_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 859 (exists A (v1_relat_1(A) & v1_funct_1(A) & v1_xboole_0(A))) # label(rc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 860 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(k2_relat_1(B),k1_relat_1(C)) -> r1_tarski(k10_relat_1(B,A),k10_relat_1(k5_relat_1(B,C),k9_relat_1(C,A)))))))) # label(t160_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 861 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B r1_tarski(k10_relat_1(A,k9_relat_1(A,B)),B)) -> v2_funct_1(A)))) # label(t153_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 862 $T # label(t24_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 863 (all A (v1_xboole_0(A) -> v1_funct_1(A))) # label(cc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 864 $T # label(t102_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 865 (all A (v1_funct_1(A) & v1_relat_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]. 4.13/4.22 866 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k6_relat_1(k1_relat_1(A)) = k5_relat_1(A,k2_funct_1(A)) & k5_relat_1(k2_funct_1(A),A) = k6_relat_1(k2_relat_1(A))))) # label(t61_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 867 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> k10_relat_1(C,k4_xboole_0(A,B)) = k4_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)))) # label(t138_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 868 (all A k2_funct_1(k6_relat_1(A)) = k6_relat_1(A)) # label(t67_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 869 $T # label(t6_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 870 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k2_relat_1(B),A) & (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) & k5_relat_1(B,D) = k5_relat_1(B,C) & k1_relat_1(C) = A -> C = D))))) -> A = k2_relat_1(B)))) # label(t33_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 871 (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)) -> k2_tarski(k1_funct_1(C,A),k1_funct_1(C,B)) = k9_relat_1(C,k2_tarski(A,B))))) # label(t118_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 872 (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]. 4.13/4.22 873 $T # label(t133_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 874 $T # label(t39_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 875 $T # label(t41_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 876 (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) -> (A = k2_relat_1(B) & A = k1_relat_1(C) & k5_relat_1(B,C) = k5_relat_1(B,D) & k1_relat_1(D) = A -> D = C))))))) # label(t156_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 877 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k2_relat_1(A) = k1_relat_1(k5_relat_1(k2_funct_1(A),A)) & k2_relat_1(k5_relat_1(k2_funct_1(A),A)) = k2_relat_1(A)))) # label(t59_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 878 $T # label(d2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 879 (all A v2_funct_1(k6_relat_1(A))) # label(t52_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 880 $T # label(t113_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 881 $T # label(t94_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 882 $T # label(t10_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 883 $T # label(t30_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 884 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (C = k10_relat_1(A,B) <-> (all D (r2_hidden(k1_funct_1(A,D),B) & r2_hidden(D,k1_relat_1(A)) <-> r2_hidden(D,C))))))) # label(d13_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 885 (all A (v1_relat_1(A) & v1_funct_1(A) -> A = k5_relat_1(k6_relat_1(k1_relat_1(A)),A) & A = k5_relat_1(A,k6_relat_1(k2_relat_1(A))))) # label(t42_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 886 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) -> v1_funct_1(k5_relat_1(A,B)) & v1_relat_1(k5_relat_1(A,B)))) # label(fc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 887 (exists A (v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A))) # label(rc3_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 888 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k1_relat_1(C)) & r2_hidden(k1_funct_1(C,B),A) <-> r2_hidden(B,k1_relat_1(k5_relat_1(C,k6_relat_1(A))))))) # label(t40_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 889 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k2_relat_1(B) = k1_relat_1(A) & k5_relat_1(B,A) = k6_relat_1(k2_relat_1(A)) & v2_funct_1(A) -> k2_funct_1(A) = B))))) # label(t64_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 890 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(k4_tarski(A,B),C) <-> r2_hidden(A,k1_relat_1(C)) & k1_funct_1(C,A) = B))) # label(t8_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 891 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> r1_tarski(k9_relat_1(k8_relat_1(A,C),B),k9_relat_1(C,B)))) # label(t120_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 892 (exists A (v3_relat_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc4_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 893 $T # label(dt_k1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 894 $T # label(t77_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 895 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> r1_tarski(k9_relat_1(C,k3_xboole_0(A,k10_relat_1(C,B))),k3_xboole_0(k9_relat_1(C,A),B)))) # label(t149_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 896 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,k2_relat_1(C)) & r1_tarski(k10_relat_1(C,A),k10_relat_1(C,B)) -> r1_tarski(A,B)))) # label(t158_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 897 $T # label(t26_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 898 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> k3_xboole_0(A,k9_relat_1(B,k1_relat_1(B))) = k9_relat_1(B,k10_relat_1(B,A)))) # label(t148_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 899 $T # label(t83_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 900 (all A (v1_funct_1(A) <-> (all B all C all D (r2_hidden(k4_tarski(B,D),A) & r2_hidden(k4_tarski(B,C),A) -> C = D)))) # label(d1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 901 $T # label(t90_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 902 $T # label(t88_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 903 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,B) -> k7_relat_1(k7_relat_1(C,A),B) = k7_relat_1(C,A) & k7_relat_1(C,A) = k7_relat_1(k7_relat_1(C,B),A)))) # label(t82_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 904 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) -> v2_funct_1(k8_relat_1(A,B))))) # label(t99_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 905 (all A all B all C (v1_relat_1(C) -> k3_xboole_0(A,k10_relat_1(C,B)) = k10_relat_1(k7_relat_1(C,A),B))) # label(t139_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 906 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B all C k4_xboole_0(k9_relat_1(A,B),k9_relat_1(A,C)) = k9_relat_1(A,k4_xboole_0(B,C))) -> v2_funct_1(A)))) # label(t124_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 907 $T # label(t3_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 908 $T # label(t105_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 909 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(k5_relat_1(C,B))) <-> r2_hidden(A,k1_relat_1(C)) & r2_hidden(k1_funct_1(C,A),k1_relat_1(B))))))) # label(t21_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 910 $T # label(t79_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 911 (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]. 4.13/4.22 912 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k3_xboole_0(k1_relat_1(C),A)) -> k1_funct_1(C,B) = k1_funct_1(k7_relat_1(C,A),B)))) # label(t71_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 913 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(k7_relat_1(B,A)),k2_relat_1(B)) & r1_tarski(k1_relat_1(k7_relat_1(B,A)),k1_relat_1(B)))) # label(t76_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 914 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (B = k2_relat_1(A) <-> (all C (r2_hidden(C,B) <-> (exists D (C = k1_funct_1(A,D) & r2_hidden(D,k1_relat_1(A)))))))))) # label(d5_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 915 $T # label(t119_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 916 $T # label(t7_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 917 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(k1_funct_1(C,B),A) & r2_hidden(B,k1_relat_1(C)) <-> r2_hidden(B,k1_relat_1(k8_relat_1(A,C)))))) # label(t86_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 918 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C -(r2_hidden(C,A) & (all D -(C = k1_funct_1(B,D) & r2_hidden(D,k1_relat_1(B)))))) -> r1_tarski(A,k2_relat_1(B))))) # label(t19_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 919 (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(A,C) = k1_funct_1(B,C))) & k1_relat_1(A) = k1_relat_1(B) -> A = B))))) # label(t9_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 920 $T # label(d3_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 921 $T # label(t29_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 922 $T # label(d10_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 923 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) <-> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_relat_1(B),k1_relat_1(A)) & r1_tarski(k2_relat_1(C),k1_relat_1(A)) & k5_relat_1(B,A) = k5_relat_1(C,A) & k1_relat_1(B) = k1_relat_1(C) -> C = B)))))))) # label(t49_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 924 $T # label(t80_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.22 925 $T # label(t31_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.23 926 (exists A (v1_relat_1(A) & f1_s4_funct_1 = k1_relat_1(A) & (all B (m1_subset_1(B,f1_s4_funct_1) -> f2_s4_funct_1(B) = k1_funct_1(A,B))) & v1_funct_1(A))) # label(s4_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.23 927 (all A all B all C (p1_s1_funct_1(A,B) & p1_s1_funct_1(A,C) -> C = B)) -> (exists 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))) & v1_funct_1(A) & v1_relat_1(A))) # label(s1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.23 928 $T # label(t1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.23 929 $T # label(t110_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.23 930 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k1_relat_1(C)) & r2_hidden(B,A) -> r2_hidden(k1_funct_1(C,B),k2_relat_1(k7_relat_1(C,A)))))) # label(t73_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.23 931 $T # label(t134_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.23 932 $T # label(t112_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.23 933 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C ((r2_hidden(B,k1_relat_1(A)) -> (r2_hidden(k4_tarski(B,C),A) <-> k1_funct_1(A,B) = C)) & (-r2_hidden(B,k1_relat_1(A)) -> (k1_xboole_0 = C <-> C = k1_funct_1(A,B))))))) # label(d4_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.23 934 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C all D ((k1_funct_1(A,D) = C & r2_hidden(D,k1_relat_1(A)) -> k1_funct_1(B,C) = D & r2_hidden(C,k2_relat_1(A))) & (r2_hidden(C,k2_relat_1(A)) & k1_funct_1(B,C) = D -> r2_hidden(D,k1_relat_1(A)) & k1_funct_1(A,D) = C))) & k2_relat_1(A) = k1_relat_1(B) <-> k2_funct_1(A) = B)))))) # label(t54_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.23 935 $T # label(t104_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.23 936 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(B) = k1_relat_1(C) & k1_tarski(A) = k2_relat_1(B) & k2_relat_1(C) = k1_tarski(A) -> C = B))))) # label(t17_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.23 937 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k3_xboole_0(k1_relat_1(C),A) = k1_relat_1(B) & (all D (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(C,D) = k1_funct_1(B,D))) <-> k7_relat_1(C,A) = B))))) # label(t68_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.23 938 $T # label(t92_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.23 939 (all A all B -(-(k1_xboole_0 != B & k1_xboole_0 = A) & (all C (v1_relat_1(C) & v1_funct_1(C) -> -(B = k1_relat_1(C) & r1_tarski(k2_relat_1(C),A)))))) # label(t18_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.23 940 (all A all B all C (v1_relat_1(C) -> r1_tarski(k3_xboole_0(A,k10_relat_1(C,B)),k10_relat_1(C,k3_xboole_0(k9_relat_1(C,A),B))))) # label(t151_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.23 941 $T # label(t4_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.23 942 $T # label(t45_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.23 943 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(k5_relat_1(B,A)) & r1_tarski(k2_relat_1(B),k1_relat_1(A)) -> v2_funct_1(B)))))) # label(t47_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.23 944 $T # label(t75_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.23 945 $T # label(t115_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.23 946 (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]. 4.13/4.23 947 $T # label(t28_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.13/4.23 948 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(B) = k1_relat_1(k5_relat_1(B,A)) -> r1_tarski(k2_relat_1(B),k1_relat_1(A))))))) # label(t27_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 949 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) & r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(k5_relat_1(B,k2_funct_1(B)),A) = A & k1_funct_1(k2_funct_1(B),k1_funct_1(B,A)) = A))) # label(t56_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 950 $T # label(t111_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 951 $T # label(t69_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 952 (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]. 4.18/4.23 953 $T # label(t32_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 954 $T # label(t13_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 955 $T # label(t103_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 956 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k9_relat_1(B,k10_relat_1(B,A)),A))) # label(t145_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 957 (all A (v1_funct_1(A) & v2_relat_1(A) & v1_relat_1(A) -> v1_setfam_1(k2_relat_1(A)))) # label(fc6_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 958 $T # label(t36_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 959 (all A (v1_funct_1(A) & v1_xboole_0(A) & v1_relat_1(A) -> v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A))) # label(cc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 960 $T # label(t108_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 961 (all A (v1_funct_1(k6_relat_1(A)) & v1_relat_1(k6_relat_1(A)))) # label(fc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 962 (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]. 4.18/4.23 963 $T # label(d7_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 964 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_tarski(A) = k1_relat_1(B) -> k1_tarski(k1_funct_1(B,A)) = k2_relat_1(B)))) # label(t14_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 965 $T # label(t98_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 966 $T # label(t78_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 967 $T # label(t96_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 968 (all A (v1_relat_1(A) & v1_funct_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]. 4.18/4.23 969 $T # label(t127_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 970 $T # label(t136_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 971 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (v2_funct_1(C) -> k9_relat_1(C,k3_xboole_0(A,B)) = k3_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B))))) # label(t121_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 972 (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(D,k1_relat_1(C)) -> k1_funct_1(C,D) = k1_funct_1(B,k1_funct_1(A,D)))) & (all D (r2_hidden(D,k1_relat_1(C)) <-> r2_hidden(k1_funct_1(A,D),k1_relat_1(B)) & r2_hidden(D,k1_relat_1(A)))) -> C = k5_relat_1(A,B)))))))) # label(t20_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 973 (all A all B (v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)))) # label(fc4_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 974 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> B = k9_relat_1(k6_relat_1(A),B))) # label(t162_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 975 (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) & (all C all D (r2_hidden(D,k1_relat_1(B)) & r2_hidden(C,k1_relat_1(A)) -> (k1_funct_1(A,C) = D <-> k1_funct_1(B,D) = C))) & v2_funct_1(A) -> k2_funct_1(A) = B))))) # label(t60_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 976 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,k2_relat_1(B)) -> k9_relat_1(B,k10_relat_1(B,A)) = A))) # label(t147_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 977 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(k5_relat_1(C,B))) -> k1_funct_1(k5_relat_1(C,B),A) = k1_funct_1(B,k1_funct_1(C,A))))))) # label(t22_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 978 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_relat_1(A) <-> (all B -(v1_xboole_0(k1_funct_1(A,B)) & r2_hidden(B,k1_relat_1(A))))))) # label(d15_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 979 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> v1_relat_1(k8_relat_1(A,B)) & v1_funct_1(k8_relat_1(A,B)))) # label(fc5_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 980 $T # label(t140_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 981 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k2_relat_1(k8_relat_1(A,B)),k2_relat_1(B)) & r1_tarski(k1_relat_1(k8_relat_1(A,B)),k1_relat_1(B)))) # label(t89_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 982 $T # label(t100_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 983 $T # label(t106_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 984 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) & r1_xboole_0(A,B) -> r1_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B))))) # label(t125_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 985 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v3_relat_1(A) <-> (all B (r2_hidden(B,k1_relat_1(A)) -> v1_xboole_0(k1_funct_1(A,B))))))) # label(d14_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 986 (all A ((all B all C all D (r2_hidden(k4_tarski(B,C),A) & r2_hidden(k4_tarski(B,D),A) -> C = D)) & (all B -(r2_hidden(B,A) & (all C all D k4_tarski(C,D) != B))) -> v1_relat_1(A) & v1_funct_1(A))) # label(t2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 987 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(k5_relat_1(B,C),A) = k1_funct_1(C,k1_funct_1(B,A))))))) # label(t23_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 988 (all A (v1_relat_1(A) & v2_funct_1(A) & v1_funct_1(A) -> v1_funct_1(k4_relat_1(A)) & v1_relat_1(k4_relat_1(A)))) # label(fc3_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 989 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) -> k9_relat_1(B,A) = k10_relat_1(k2_funct_1(B),A)))) # label(t154_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 990 $T # label(t131_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 991 (exists A (v1_funct_1(A) & v2_relat_1(A) & v1_relat_1(A))) # label(rc5_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 992 (exists A (v1_funct_1(A) & v1_relat_1(A))) # label(rc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 993 (exists A (f1_s3_funct_1 = k1_relat_1(A) & (all B (r2_hidden(B,f1_s3_funct_1) -> k1_funct_1(A,B) = f2_s3_funct_1(B))) & v1_funct_1(A) & v1_relat_1(A))) # label(s3_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 994 $T # label(t128_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 995 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,B) -> k8_relat_1(A,C) = k8_relat_1(B,k8_relat_1(A,C)) & k8_relat_1(A,C) = k8_relat_1(A,k8_relat_1(B,C))))) # label(t97_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 996 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(k5_relat_1(B,A)) & k1_relat_1(A) = k2_relat_1(B) -> v2_funct_1(B) & v2_funct_1(A)))))) # label(t48_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 997 $T # label(d11_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 998 $T # label(t81_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 999 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((exists B (v1_funct_1(B) & k6_relat_1(k1_relat_1(A)) = k5_relat_1(A,B) & v1_relat_1(B))) -> v2_funct_1(A)))) # label(t53_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1000 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(B,k2_relat_1(C)) & r1_tarski(A,k2_relat_1(C)) & k10_relat_1(C,A) = k10_relat_1(C,B) -> B = A))) # label(t161_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1001 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C ((all D ((exists E (r2_hidden(E,B) & D = k1_funct_1(A,E) & r2_hidden(E,k1_relat_1(A)))) <-> r2_hidden(D,C))) <-> k9_relat_1(A,B) = C)))) # label(d12_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1002 (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]. 4.18/4.23 1003 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) -> k9_relat_1(k2_funct_1(B),A) = k10_relat_1(B,A)))) # label(t155_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1004 (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]. 4.18/4.23 1005 $T # label(t116_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1006 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> k9_relat_1(C,k3_xboole_0(A,k10_relat_1(C,B))) = k3_xboole_0(k9_relat_1(C,A),B))) # label(t150_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1007 (all A ((all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(B) = A & A = k1_relat_1(C) -> C = B))))) -> k1_xboole_0 = A)) # label(t16_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1008 (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]. 4.18/4.23 1009 (all A (v3_ordinal1(A) -> v3_ordinal1(k3_tarski(A)) & v2_ordinal1(k3_tarski(A)) & v1_ordinal1(k3_tarski(A)))) # label(fc4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1010 $T # label(t17_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1011 (all A m1_ordinal1(k1_xboole_0,A)) # label(t45_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1012 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(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]. 4.18/4.23 1013 (all A r2_hidden(A,k1_ordinal1(A))) # label(t10_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1014 (all A all B (k1_ordinal1(B) = k1_ordinal1(A) -> B = A)) # label(t12_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1015 (all A (v1_xboole_0(A) -> v3_ordinal1(A) & v2_ordinal1(A) & v1_ordinal1(A))) # label(cc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1016 (all A all B (v3_ordinal1(B) -> (r2_hidden(A,B) -> v3_ordinal1(A)))) # label(t23_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1017 (exists A (v3_ordinal1(A) & p1_s1_ordinal1(A))) -> (exists A (v3_ordinal1(A) & (all B (v3_ordinal1(B) -> (p1_s1_ordinal1(B) -> r1_ordinal1(A,B)))) & p1_s1_ordinal1(A))) # label(s1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1018 (all A ((all B (r2_hidden(B,A) -> v3_ordinal1(B))) -> v3_ordinal1(k3_tarski(A)))) # label(t35_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1019 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> r1_ordinal1(A,B) | r1_ordinal1(B,A))) # label(connectedness_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1020 $T # label(t20_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1021 (all A all B (r2_hidden(A,k1_ordinal1(B)) <-> r2_hidden(A,B) | A = B)) # label(t13_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1022 (all A -(all B (r2_hidden(B,A) <-> v3_ordinal1(B)))) # label(t37_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1023 $T # label(d5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1024 (all A ((all B (r2_hidden(B,A) -> r1_tarski(B,A))) <-> v1_ordinal1(A))) # label(d2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1025 (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)))) & A != k1_xboole_0))) # label(t32_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1026 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> r3_xboole_0(A,B))))) # label(t25_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1027 (all A ((all B (r2_hidden(B,A) -> r1_tarski(B,A) & v3_ordinal1(B))) -> v3_ordinal1(A))) # label(t31_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1028 (all A (v1_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_xboole_0(A,B) -> r2_hidden(A,B)))))) # label(t21_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1029 $T # label(t1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1030 (all A (v3_ordinal1(A) <-> v1_ordinal1(A) & v2_ordinal1(A))) # label(d4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1031 $T # label(t18_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1032 (all A all B (r1_tarski(A,B) -> (all C (m1_ordinal1(C,A) -> m1_ordinal1(C,B))))) # label(t47_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1033 k1_relat_1(f3_s3_ordinal1) = f1_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(f4_s3_ordinal1,A) = B -> f2_s3_ordinal1(B) = k1_funct_1(f4_s3_ordinal1,A)))))) & (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) -> (B = k2_ordinal1(f3_s3_ordinal1,A) & r2_hidden(A,f1_s3_ordinal1) -> k1_funct_1(f3_s3_ordinal1,A) = f2_s3_ordinal1(B)))))) -> f3_s3_ordinal1 = f4_s3_ordinal1 # label(s3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1034 (all A (v6_ordinal1(A) & (all B (r2_hidden(B,A) -> v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B))) -> v1_relat_1(k3_tarski(A)) & v5_ordinal1(k3_tarski(A)) & v1_funct_1(k3_tarski(A)))) # label(t49_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1035 $T # label(t9_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1036 $T # label(t8_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1037 (all A (v3_ordinal1(A) -> v3_ordinal1(k3_tarski(A)))) # label(t30_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1038 (all A (v3_ordinal1(A) -> v1_ordinal1(A) & v2_ordinal1(A))) # label(cc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1039 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r1_ordinal1(k1_ordinal1(A),B) <-> r2_hidden(A,B)))))) # label(t33_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1040 (all A (v6_ordinal1(A) <-> (all B all C (r2_hidden(C,A) & r2_hidden(B,A) -> r3_xboole_0(B,C))))) # label(d9_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1041 (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s5_ordinal1)) -> k1_funct_1(f1_s5_ordinal1,A) = f2_s5_ordinal1(A)))) & (all A (v3_ordinal1(A) -> (all B (f2_s5_ordinal1(A) = B <-> (exists C (v1_relat_1(C) & f3_s5_ordinal1(C) = B & (all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k1_funct_1(C,D) = f3_s5_ordinal1(k2_ordinal1(C,D))))) & A = k1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C))))))) -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s5_ordinal1)) -> k1_funct_1(f1_s5_ordinal1,A) = f3_s5_ordinal1(k2_ordinal1(f1_s5_ordinal1,A))))) # label(s5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1042 (all A (v3_ordinal1(A) -> v3_ordinal1(k1_ordinal1(A)))) # label(t29_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1043 $T # label(t11_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1044 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -(-r2_hidden(A,B) & B != A & -r2_hidden(B,A)))))) # label(t24_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1045 $T # label(t28_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1046 $T # label(t16_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1047 (all A all B -(r2_hidden(A,B) & r1_tarski(B,A))) # label(t7_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1048 (exists A (v2_funct_1(A) & v1_xboole_0(A) & v1_ordinal1(A) & v3_ordinal1(A) & v2_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1049 (all A all B all C all D -(r2_hidden(C,D) & r2_hidden(D,A) & r2_hidden(B,C) & r2_hidden(A,B))) # label(t4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1050 (all A all B (v1_relat_1(A) & v5_ordinal1(A) & v3_ordinal1(B) & v1_funct_1(A) -> k7_relat_1(A,B) = k2_ordinal1(A,B))) # label(redefinition_k2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1051 (exists A (v1_relat_1(A) & v1_funct_1(A) & k1_relat_1(A) = f1_s4_ordinal1 & (all B (v3_ordinal1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) -> (C = k2_ordinal1(A,B) & r2_hidden(B,f1_s4_ordinal1) -> f2_s4_ordinal1(C) = k1_funct_1(A,B)))))) & v5_ordinal1(A))) # label(s4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1052 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v5_ordinal1(A) <-> v3_ordinal1(k1_relat_1(A))))) # label(d7_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1053 $T # label(dt_k1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1054 (all A all B all C -(r2_hidden(B,C) & r2_hidden(C,A) & r2_hidden(A,B))) # label(t3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1055 (all A -v1_xboole_0(k1_ordinal1(A))) # label(fc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1056 (all A -(all B (v3_ordinal1(B) -> r2_hidden(B,A)))) # label(t38_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1057 (all A (v2_ordinal1(A) <-> (all B all C -(r2_hidden(B,A) & r2_hidden(C,A) & -r2_hidden(B,C) & B != C & -r2_hidden(C,B))))) # label(d3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1058 (all A (v4_ordinal1(A) <-> k3_tarski(A) = A)) # label(d6_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1059 (all A all B all C all D all E all F -(r2_hidden(F,A) & r2_hidden(E,F) & r2_hidden(D,E) & r2_hidden(C,D) & r2_hidden(B,C) & r2_hidden(A,B))) # label(t6_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1060 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v1_ordinal1(C) -> (r2_hidden(C,A) & r2_hidden(A,B) -> r2_hidden(C,B)))))))) # label(t19_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1061 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> r1_ordinal1(A,A))) # label(reflexivity_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1062 (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]. 4.18/4.23 1063 $T # label(t2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1064 (all A exists B (v3_ordinal1(B) & -r2_hidden(B,A) & (all C (v3_ordinal1(C) -> (-r2_hidden(C,A) -> r1_ordinal1(B,C)))))) # label(t39_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1065 (exists A (v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & -v1_xboole_0(A))) # label(rc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1066 (all A k1_ordinal1(A) != A) # label(t14_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1067 (all A exists B m1_ordinal1(B,A)) # label(existence_m1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1068 (all A all B (v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) <-> m1_ordinal1(B,A)))) # label(d8_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1069 (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]. 4.18/4.23 1070 (all A all B all C all D all E -(r2_hidden(A,B) & r2_hidden(B,C) & r2_hidden(E,A) & r2_hidden(D,E) & r2_hidden(C,D))) # label(t5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1071 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -(-r2_xboole_0(A,B) & -r2_xboole_0(B,A) & A != B))))) # label(t50_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1072 $T # label(t15_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1073 (all A k2_xboole_0(A,k1_tarski(A)) = k1_ordinal1(A)) # label(d1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1074 (all A (v3_ordinal1(A) -> ((all B (v3_ordinal1(B) -> (r2_hidden(B,A) -> p1_s2_ordinal1(B)))) -> p1_s2_ordinal1(A)))) -> (all A (v3_ordinal1(A) -> p1_s2_ordinal1(A))) # label(s2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1075 (all A all B (m1_ordinal1(B,A) -> (all C (v3_ordinal1(C) -> m1_ordinal1(k2_ordinal1(B,C),A))))) # label(t48_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1076 $T # label(t40_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1077 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(A,k1_ordinal1(B)) <-> r1_ordinal1(A,B)))))) # label(t34_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1078 (all A all B (m1_ordinal1(B,A) -> v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B))) # label(dt_m1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1079 (all A all B (v1_relat_1(A) & v5_ordinal1(A) & v3_ordinal1(B) & v1_funct_1(A) -> m1_ordinal1(k2_ordinal1(A,B),k2_relat_1(A)))) # label(dt_k2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1080 (all A (v3_ordinal1(A) -> -(v4_ordinal1(A) & (exists B (A = k1_ordinal1(B) & v3_ordinal1(B)))) & -((all B (v3_ordinal1(B) -> A != k1_ordinal1(B))) & -v4_ordinal1(A)))) # label(t42_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1081 $T # label(t43_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1082 (exists A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A))) # label(rc4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1083 (all A -((all B (v3_ordinal1(B) -> -r1_tarski(A,B))) & (all B (r2_hidden(B,A) -> v3_ordinal1(B))))) # label(t36_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1084 $T # label(t44_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1085 (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]. 4.18/4.23 1086 (exists A (v3_ordinal1(A) & v2_ordinal1(A) & v1_ordinal1(A))) # label(rc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1087 (all A (v2_ordinal1(A) & v1_ordinal1(A) -> v3_ordinal1(A))) # label(cc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1088 (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]. 4.18/4.23 1089 (all A (v3_ordinal1(A) -> v1_ordinal1(k1_ordinal1(A)) & v2_ordinal1(k1_ordinal1(A)) & v3_ordinal1(k1_ordinal1(A)) & -v1_xboole_0(k1_ordinal1(A)))) # label(fc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1090 (all A all B exists C m2_relset_1(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1091 (all A all B exists C m1_relset_1(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1092 (all A all B all C all D (m1_relset_1(C,A,B) -> m1_subset_1(k11_relset_1(A,B,C,D),k1_zfmisc_1(A)))) # label(dt_k11_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1093 (all A all B all C all D (m2_relset_1(D,B,C) -> (r1_tarski(A,D) -> m2_relset_1(A,B,C)))) # label(t4_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1094 (all A all B all C all D (m2_relset_1(D,A,C) -> m2_relset_1(k8_relset_1(A,C,D,B),B,C))) # label(t33_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1095 $T # label(t1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1096 (all A m2_relset_1(k6_relat_1(A),A,A)) # label(t29_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1097 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,B,A) -> (all D (m1_subset_1(D,A) -> ((exists E (m1_subset_1(E,B) & r2_hidden(k4_tarski(E,D),C))) <-> r2_hidden(D,k5_relset_1(B,A,C))))))))))) # label(t48_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1098 (all A all B all C (m2_relset_1(C,B,A) -> (m2_relset_1(C,B,k1_xboole_0) -> k1_xboole_0 = C))) # label(t27_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1099 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> m2_relset_1(k2_relset_1(A,B,C,D),A,B))) # label(dt_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1100 (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 (m1_subset_1(E,B) & r2_hidden(k4_tarski(D,E),C))) <-> r2_hidden(D,k4_relset_1(A,B,C))))))))))) # label(t47_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1101 $T # label(t41_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1102 (all A all B all C (m2_relset_1(C,B,A) -> k10_relset_1(B,A,C,k11_relset_1(B,A,C,A)) = k5_relset_1(B,A,C) & k11_relset_1(B,A,C,k10_relset_1(B,A,C,B)) = k4_relset_1(B,A,C))) # label(t39_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1103 (all A all B all C (m2_relset_1(C,A,B) -> (k5_relset_1(A,B,C) = B <-> (all D -(r2_hidden(D,B) & (all E -r2_hidden(k4_tarski(E,D),C))))))) # label(t23_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1104 (all A all B all C (m1_relset_1(C,A,B) -> k2_relat_1(C) = k5_relset_1(A,B,C))) # label(redefinition_k5_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1105 (all A all B all C all D (m1_relset_1(C,A,B) -> m1_subset_1(k10_relset_1(A,B,C,D),k1_zfmisc_1(B)))) # label(dt_k10_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1106 (all A all B all C (m2_relset_1(C,A,B) -> (m2_relset_1(C,k1_xboole_0,B) -> C = k1_xboole_0))) # label(t26_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1107 (all A all B all C (m1_relset_1(C,A,B) -> k4_relat_1(C) = k6_relset_1(A,B,C))) # label(redefinition_k6_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1108 (all A all B all C all D (m2_relset_1(D,C,A) -> m2_relset_1(k9_relset_1(C,A,B,D),C,B))) # label(t35_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1109 (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(C,f2_s1_relset_1) & r2_hidden(B,f1_s1_relset_1) <-> r2_hidden(k4_tarski(B,C),A))))) # label(s1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1110 (all A all B all C all D (m2_relset_1(D,A,C) -> (r1_tarski(A,B) -> m2_relset_1(D,B,C)))) # label(t15_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1111 (all A all B all C all D (m1_relset_1(C,A,B) -> k10_relat_1(C,D) = k11_relset_1(A,B,C,D))) # label(redefinition_k11_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1112 (all A all B all C (m1_relset_1(C,A,B) -> m2_relset_1(k6_relset_1(A,B,C),B,A))) # label(dt_k6_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1113 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) -> (all D (m1_subset_1(D,A) -> -(r2_hidden(D,k4_relset_1(A,B,C)) & (all E (m1_subset_1(E,B) -> -r2_hidden(E,k5_relset_1(A,B,C))))))))))))) # label(t49_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1114 (all A all B all C all D (m2_relset_1(D,A,B) -> (r1_tarski(k6_relat_1(C),D) -> r1_tarski(C,k5_relset_1(A,B,D)) & r1_tarski(C,k4_relset_1(A,B,D))))) # label(t30_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1115 (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) -> (r2_hidden(k4_tarski(F,G),k7_relset_1(A,B,B,C,D,E)) <-> (exists H (r2_hidden(k4_tarski(H,G),E) & r2_hidden(k4_tarski(F,H),D) & m1_subset_1(H,B)))))))))))))))))) # label(t51_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1116 (all A all B all C (m1_relset_1(C,A,B) -> k6_relset_1(A,B,k6_relset_1(A,B,C)) = C)) # label(involutiveness_k6_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1117 $T # label(t3_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1118 (all A all B all C (m2_relset_1(C,A,B) -> k10_relset_1(A,B,C,A) = k5_relset_1(A,B,C) & k4_relset_1(A,B,C) = k11_relset_1(A,B,C,B))) # label(t38_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1119 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,B,A) -> (all D (m1_subset_1(D,A) -> -(r2_hidden(D,k5_relset_1(B,A,C)) & (all E (m1_subset_1(E,B) -> -r2_hidden(E,k4_relset_1(B,A,C))))))))))))) # label(t50_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1120 $T # label(t37_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1121 $T # label(t2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1122 $T # label(t21_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1123 (all A all B all C all D (m2_relset_1(D,C,A) -> (r1_tarski(k2_relat_1(D),B) -> m2_relset_1(D,C,B)))) # label(t14_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1124 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> m2_relset_1(k3_relset_1(A,B,C,D),A,B))) # label(dt_k3_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1125 $T # label(t18_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1126 (all A all B all C all D all E all F (m1_relset_1(E,A,B) & m1_relset_1(F,C,D) -> k7_relset_1(A,B,C,D,E,F) = k5_relat_1(E,F))) # label(redefinition_k7_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1127 (all A all B all C (m2_relset_1(C,B,A) -> (r1_tarski(k6_relat_1(B),C) -> r1_tarski(B,k5_relset_1(B,A,C)) & k4_relset_1(B,A,C) = B))) # label(t31_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1128 (all A all B all C all D (m1_relset_1(D,A,B) -> k9_relset_1(A,B,C,D) = k8_relat_1(C,D))) # label(redefinition_k9_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1129 (all A all B m2_relset_1(k1_xboole_0,A,B)) # label(t25_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1130 (all A all B all C (v1_relat_1(C) -> (r1_tarski(k1_relat_1(C),A) & r1_tarski(k2_relat_1(C),B) -> m2_relset_1(C,A,B)))) # label(t11_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1131 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> k2_relset_1(A,B,C,D) = k2_relset_1(A,B,D,C))) # label(commutativity_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1132 (all A all B all C (m2_relset_1(C,A,B) -> m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))))) # label(dt_m2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1133 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,C) -> (all E (m1_subset_1(E,A) -> (r2_hidden(E,k11_relset_1(A,C,D,B)) <-> (exists F (r2_hidden(F,B) & r2_hidden(k4_tarski(E,F),D) & m1_subset_1(F,C)))))))))))))) # label(t53_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1134 (all A all B all C (m2_relset_1(C,B,A) -> (k4_relset_1(B,A,C) = B <-> (all D -(r2_hidden(D,B) & (all E -r2_hidden(k4_tarski(D,E),C))))))) # label(t22_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1135 (all A all B all C all D (m1_relset_1(D,A,B) -> m2_relset_1(k9_relset_1(A,B,C,D),A,B))) # label(dt_k9_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1136 (all A r1_tarski(k6_relat_1(A),k2_zfmisc_1(A,A))) # label(t28_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1137 $T # label(t7_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1138 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> m2_relset_1(k1_relset_1(A,B,C,D),A,B))) # label(dt_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1139 (all A all B all C all D all E (m2_relset_1(E,A,C) -> (r1_tarski(C,D) & r1_tarski(A,B) -> m2_relset_1(E,B,D)))) # label(t17_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1140 (all A (-v1_xboole_0(A) -> k6_relat_1(A) != k1_xboole_0)) # label(t46_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1141 $T # label(t40_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1142 (all A all B all C all D (m2_relset_1(D,C,A) -> (r1_tarski(A,B) -> m2_relset_1(D,C,B)))) # label(t16_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1143 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) -> v1_relat_1(C))) # label(cc1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1144 $T # label(t20_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1145 (exists A ((all B (m1_subset_1(B,f1_s2_relset_1) -> (all C (m1_subset_1(C,f2_s2_relset_1) -> (r2_hidden(k4_tarski(B,C),A) <-> p1_s2_relset_1(B,C)))))) & m2_relset_1(A,f1_s2_relset_1,f2_s2_relset_1))) # label(s2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1146 (all A all B all C (m2_relset_1(C,A,B) -> k4_relset_1(B,A,k6_relset_1(A,B,C)) = k5_relset_1(A,B,C) & k4_relset_1(A,B,C) = k5_relset_1(B,A,k6_relset_1(A,B,C)))) # label(t24_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1147 (all A all B all C (m1_relset_1(C,A,B) -> m1_subset_1(k5_relset_1(A,B,C),k1_zfmisc_1(B)))) # label(dt_k5_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1148 $T # label(t5_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1149 $T # label(t44_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1150 (all A all B (v1_relat_1(B) -> (r1_tarski(k1_relat_1(B),A) -> m2_relset_1(B,A,k2_relat_1(B))))) # label(t9_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1151 (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) -> (r2_hidden(E,k10_relset_1(C,A,D,B)) <-> (exists F (r2_hidden(F,B) & r2_hidden(k4_tarski(F,E),D) & m1_subset_1(F,C)))))))))))))) # label(t52_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1152 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1153 (all A all B all C (m2_relset_1(C,A,B) -> (r1_tarski(k6_relat_1(B),C) -> B = k5_relset_1(A,B,C) & r1_tarski(B,k4_relset_1(A,B,C))))) # label(t32_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1154 (all A all B all C all D (m1_relset_1(C,A,B) -> m2_relset_1(k8_relset_1(A,B,C,D),A,B))) # label(dt_k8_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1155 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> k1_relset_1(A,B,C,C) = C)) # label(idempotence_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1156 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> k2_relset_1(A,B,C,C) = C)) # label(idempotence_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1157 $T # label(t42_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1158 (all A all B all C all D (m2_relset_1(D,A,C) -> (r1_tarski(k1_relat_1(D),B) -> m2_relset_1(D,B,C)))) # label(t13_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1159 (all A all B all C all D (m1_relset_1(C,A,B) -> k10_relset_1(A,B,C,D) = k9_relat_1(C,D))) # label(redefinition_k10_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1160 (all A all B all C all D (m2_relset_1(D,B,A) -> (r1_tarski(B,C) -> k8_relset_1(B,A,D,C) = D))) # label(t34_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1161 (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]. 4.18/4.23 1162 (all A all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> m2_relset_1(B,k1_relat_1(B),A)))) # label(t10_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.23 1163 (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]. 4.18/4.23 1164 (all A all B all C (m2_relset_1(C,A,B) -> r1_tarski(k2_relat_1(C),B) & r1_tarski(k1_relat_1(C),A))) # label(t12_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1165 (all A all B all C all D (m2_relset_1(D,A,B) -> (r1_tarski(B,C) -> k9_relset_1(A,B,C,D) = D))) # label(t36_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1166 (all A all B (m2_relset_1(B,A,A) -> B = k5_relat_1(k6_relat_1(A),B) & k5_relat_1(B,k6_relat_1(A)) = B)) # label(t45_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1167 $T # label(t43_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1168 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> k3_relset_1(A,B,C,D) = k4_xboole_0(C,D))) # label(redefinition_k3_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1169 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> k1_relset_1(A,B,C,D) = k1_relset_1(A,B,D,C))) # label(commutativity_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1170 (all A all B all C all D (m1_relset_1(C,A,B) -> k8_relset_1(A,B,C,D) = k7_relat_1(C,D))) # label(redefinition_k8_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1171 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> k1_relset_1(A,B,C,D) = k2_xboole_0(C,D))) # label(redefinition_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1172 (all A all B all C all D (m2_relset_1(D,A,B) -> -(r2_hidden(C,D) & (all E all F -(r2_hidden(F,B) & r2_hidden(E,A) & C = k4_tarski(E,F)))))) # label(t6_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1173 (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]. 4.18/4.24 1174 (all A all B all C (m1_relset_1(C,A,B) -> k1_relat_1(C) = k4_relset_1(A,B,C))) # label(redefinition_k4_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1175 (all A all B all C all D (r2_hidden(D,B) & r2_hidden(C,A) -> m2_relset_1(k1_tarski(k4_tarski(C,D)),A,B))) # label(t8_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1176 (all A all B all C (m1_relset_1(C,A,B) -> m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k4_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1177 (all A all B all C (m2_relset_1(C,A,B) -> r1_tarski(k3_relat_1(C),k2_xboole_0(A,B)))) # label(t19_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1178 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> k3_xboole_0(C,D) = k2_relset_1(A,B,C,D))) # label(redefinition_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1179 (all A all B all C all D k3_zfmisc_1(k2_tarski(A,B),k1_tarski(C),k1_tarski(D)) = k2_tarski(k3_mcart_1(A,C,D),k3_mcart_1(B,C,D))) # label(t40_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1180 (all A all B all C all D (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(D,k1_zfmisc_1(B)) -> m1_subset_1(k12_mcart_1(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(A,B))))) # label(dt_k12_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1181 (all A all B all C all D k3_zfmisc_1(k1_tarski(A),k1_tarski(B),k2_tarski(C,D)) = k2_tarski(k3_mcart_1(A,B,C),k3_mcart_1(A,B,D))) # label(t42_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1182 (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) -> G = E))))))))) -> k1_xboole_0 = B | k1_xboole_0 = C | k8_mcart_1(A,B,C,D,F) = E | D = k1_xboole_0 | A = k1_xboole_0))) # label(t79_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1183 (all A all B all C all D k4_mcart_1(A,B,C,D) = k3_mcart_1(k4_tarski(A,B),C,D)) # label(t32_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1184 (all A all B (B = k2_mcart_1(k4_tarski(A,B)) & A = k1_mcart_1(k4_tarski(A,B)))) # label(t7_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1185 (all A all B all C all D -(k1_xboole_0 != B & k1_xboole_0 != D & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,B) -> ((all G all H all I all J (k4_mcart_1(G,H,I,J) = E -> H = F)) <-> F = k9_mcart_1(A,B,C,D,E)))))) & C != k1_xboole_0 & k1_xboole_0 != A)) # label(d9_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1186 (all A all B all C all D all E k3_zfmisc_1(k1_tarski(A),k2_tarski(B,C),k2_tarski(D,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))) # label(t45_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1187 (all A all B all C all D all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> m1_subset_1(k11_mcart_1(A,B,C,D,E),D))) # label(dt_k11_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1188 (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(G,k1_zfmisc_1(C)) & m1_subset_1(F,k1_zfmisc_1(B)) & m1_subset_1(E,k1_zfmisc_1(A)) -> m1_subset_1(k14_mcart_1(A,B,C,D,E,F,G,H),k1_zfmisc_1(k4_zfmisc_1(A,B,C,D))))) # label(dt_k14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1189 (all A all B all C all D all E all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,D) -> (k4_mcart_1(G,H,I,J) = F -> I = E))))))))) -> A = k1_xboole_0 | k1_xboole_0 = C | k10_mcart_1(A,B,C,D,F) = E | k1_xboole_0 = D | B = k1_xboole_0))) # label(t81_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1190 (all A -((all B -(r2_hidden(B,A) & (all C all D (r2_hidden(C,D) & r2_hidden(D,B) -> r1_xboole_0(C,A))))) & A != k1_xboole_0)) # label(t3_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1191 (all A -(k1_xboole_0 != A & (all B -((all C all D all E all F (r2_hidden(C,D) & r2_hidden(E,F) & r2_hidden(F,B) & r2_hidden(D,E) -> r1_xboole_0(C,A))) & r2_hidden(B,A))))) # label(t5_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1192 (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 (D = k3_mcart_1(F,G,H) -> E = H))))))) & k1_xboole_0 != C & B != k1_xboole_0 & k1_xboole_0 != A)) # label(d7_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1193 (all A ((exists B exists C A = k4_tarski(B,C)) -> A != k2_mcart_1(A) & k1_mcart_1(A) != A)) # label(t20_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1194 (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]. 4.18/4.24 1195 $T # label(t27_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1196 (all A all B -(A != k1_xboole_0 & -(all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> k4_tarski(k1_mcart_1(C),k2_mcart_1(C)) = C)) & k1_xboole_0 != B)) # label(t24_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1197 (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]. 4.18/4.24 1198 $T # label(dt_k18_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1199 (all A all B all C all D -(k1_xboole_0 != A & D != k1_xboole_0 & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> k4_mcart_1(k8_mcart_1(A,B,C,D,E),k9_mcart_1(A,B,C,D,E),k10_mcart_1(A,B,C,D,E),k11_mcart_1(A,B,C,D,E)) = E)) & k1_xboole_0 != C & k1_xboole_0 != B)) # label(t60_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1200 (all A k17_mcart_1(A) = k1_mcart_1(k1_mcart_1(A))) # label(d14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1201 (all A all B all C all D all E all F (k3_zfmisc_1(A,B,C) = k3_zfmisc_1(D,E,F) -> k1_xboole_0 = A | F = C & B = E & A = D | k1_xboole_0 = C | k1_xboole_0 = B)) # label(t36_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1202 (all A all B all C all D all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> m1_subset_1(k10_mcart_1(A,B,C,D,E),C))) # label(dt_k10_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1203 (all A all B all C all D all E all F all G all H (r2_hidden(k4_mcart_1(A,B,C,D),k4_zfmisc_1(E,F,G,H)) <-> r2_hidden(A,E) & r2_hidden(C,G) & r2_hidden(D,H) & r2_hidden(B,F))) # label(t84_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1204 (all A -(A != k1_xboole_0 & (all B -(r2_hidden(B,A) & (all C all D all E all F -((r2_hidden(C,A) | r2_hidden(D,A)) & B = k4_mcart_1(C,D,E,F))))))) # label(t34_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1205 (all A all B all C k4_tarski(k4_tarski(A,B),C) = k3_mcart_1(A,B,C)) # label(d3_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1206 $T # label(dt_k4_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1207 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(B,k2_tarski(C,D))) -> (D = k2_mcart_1(A) | C = k2_mcart_1(A)) & r2_hidden(k1_mcart_1(A),B))) # label(t16_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1208 (all A all B all C all D all E all F (r1_tarski(E,F) & r1_tarski(C,D) & 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]. 4.18/4.24 1209 (all A all B all C all D -(A != k1_xboole_0 & k1_xboole_0 != C & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,C) -> ((all G all H all I all J (E = k4_mcart_1(G,H,I,J) -> I = F)) <-> F = k10_mcart_1(A,B,C,D,E)))))) & D != k1_xboole_0 & k1_xboole_0 != B)) # label(d10_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1210 (all A all B all C all D -(A != k1_xboole_0 & B != k1_xboole_0 & C != k1_xboole_0 & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> E != k8_mcart_1(A,B,C,D,E) & E != k9_mcart_1(A,B,C,D,E) & k10_mcart_1(A,B,C,D,E) != E & k11_mcart_1(A,B,C,D,E) != E)) & D != k1_xboole_0)) # label(t62_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1211 (all A all B -(A != k1_xboole_0 & k1_xboole_0 != B & -(all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> k1_mcart_1(C) != C & k2_mcart_1(C) != C)))) # label(t26_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1212 (all A all B all C all D -(A != k1_xboole_0 & B != k1_xboole_0 & (exists E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) & (exists F exists G exists H exists I (-(k8_mcart_1(A,B,C,D,E) = F & H = k10_mcart_1(A,B,C,D,E) & 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 & C != k1_xboole_0)) # label(t59_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1213 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k15_mcart_1(A)) & v1_funct_1(k15_mcart_1(A)))) # label(dt_k15_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1214 (all A all B all C all D all E all F (m1_subset_1(D,k1_zfmisc_1(A)) & m1_subset_1(E,k1_zfmisc_1(B)) & m1_subset_1(F,k1_zfmisc_1(C)) -> k13_mcart_1(A,B,C,D,E,F) = k3_zfmisc_1(D,E,F))) # label(redefinition_k13_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1215 (all A all B all C -(A != k1_xboole_0 & C != k1_xboole_0 & -(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) & k6_mcart_1(A,B,C,D) = k2_mcart_1(k1_mcart_1(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]. 4.18/4.24 1216 (all A all B all C all D all E all F all G all H (k4_zfmisc_1(A,B,C,D) = k4_zfmisc_1(E,F,G,H) -> B = k1_xboole_0 | C = k1_xboole_0 | k1_xboole_0 = D | A = E & F = B & C = G & D = H | A = k1_xboole_0)) # label(t56_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1217 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(B) = k1_relat_1(A) & (all C (r2_hidden(C,k1_relat_1(A)) -> k1_mcart_1(k1_funct_1(A,C)) = k1_funct_1(B,C))) <-> k15_mcart_1(A) = B))))) # label(d12_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1218 (all A all B all C all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> -(k1_xboole_0 != C & (exists E exists F exists G (-(k7_mcart_1(A,B,C,D) = G & F = k6_mcart_1(A,B,C,D) & k5_mcart_1(A,B,C,D) = E) & D = k3_mcart_1(E,F,G))) & B != k1_xboole_0 & k1_xboole_0 != A))) # label(t68_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1219 (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]. 4.18/4.24 1220 $T # label(t22_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1221 (all A all B all C all D (C != k1_xboole_0 & k1_xboole_0 != D & k1_xboole_0 != B & k1_xboole_0 != A <-> k1_xboole_0 != k4_zfmisc_1(A,B,C,D))) # label(t55_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1222 (all A ((exists B exists C k4_tarski(B,C) = A) -> k4_tarski(k1_mcart_1(A),k2_mcart_1(A)) = A)) # label(t8_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1223 (all A all B all C all D k4_tarski(k3_mcart_1(A,B,C),D) = k4_mcart_1(A,B,C,D)) # label(d4_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1224 $T # label(dt_k17_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1225 (all A all B all C (r2_hidden(A,k2_zfmisc_1(B,k1_tarski(C))) -> C = k2_mcart_1(A) & r2_hidden(k1_mcart_1(A),B))) # label(t13_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1226 (all A all B all C all D -(k1_xboole_0 != A & k1_xboole_0 != B & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,D) -> (F = k11_mcart_1(A,B,C,D,E) <-> (all G all H all I all J (k4_mcart_1(G,H,I,J) = E -> J = F))))))) & k1_xboole_0 != D & k1_xboole_0 != C)) # label(d11_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1227 (all A all B all C all D all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> m1_subset_1(k9_mcart_1(A,B,C,D,E),B))) # label(dt_k9_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1228 (all A all B all C all D all E k3_zfmisc_1(k2_tarski(A,B),k2_tarski(C,D),k1_tarski(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))) # label(t43_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1229 $T # label(dt_k1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1230 (all A all B all C all D all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> -(k1_xboole_0 != B & k1_xboole_0 != D & (exists F exists G exists H exists I (-(k8_mcart_1(A,B,C,D,E) = F & G = k9_mcart_1(A,B,C,D,E) & k10_mcart_1(A,B,C,D,E) = H & k11_mcart_1(A,B,C,D,E) = I) & k4_mcart_1(F,G,H,I) = E)) & C != k1_xboole_0 & A != k1_xboole_0))) # label(t78_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1231 (all A all B all C all D (-(-r1_tarski(A,k4_zfmisc_1(B,C,D,A)) & -r1_tarski(A,k4_zfmisc_1(C,D,A,B)) & -r1_tarski(A,k4_zfmisc_1(D,A,B,C)) & -r1_tarski(A,k4_zfmisc_1(A,B,C,D))) -> k1_xboole_0 = A)) # label(t63_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1232 (all A all B all C (r2_hidden(A,k2_zfmisc_1(B,C)) -> A = k4_tarski(k1_mcart_1(A),k2_mcart_1(A)))) # label(t23_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1233 (all A all B all C all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> m1_subset_1(k7_mcart_1(A,B,C,D),C))) # label(dt_k7_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1234 (all A all B all C k1_tarski(k3_mcart_1(A,B,C)) = k3_zfmisc_1(k1_tarski(A),k1_tarski(B),k1_tarski(C))) # label(t39_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1235 (all A all B all C all D all E all F all G all H (k4_zfmisc_1(E,F,G,H) = k4_zfmisc_1(A,B,C,D) -> k4_zfmisc_1(A,B,C,D) = k1_xboole_0 | A = E & F = B & C = G & H = D)) # label(t57_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1236 (all A all B all C all D all E -(r2_hidden(A,k4_zfmisc_1(B,C,D,E)) & (all F all G all H all I -(r2_hidden(F,B) & r2_hidden(I,E) & k4_mcart_1(F,G,H,I) = A & r2_hidden(H,D) & r2_hidden(G,C))))) # label(t83_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1237 (all A all B all C (r2_hidden(A,k2_zfmisc_1(k1_tarski(B),k1_tarski(C))) -> C = k2_mcart_1(A) & B = k1_mcart_1(A))) # label(t14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1238 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_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]. 4.18/4.24 1239 (all A k1_mcart_1(k2_mcart_1(A)) = k19_mcart_1(A)) # label(d16_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1240 $T # label(t21_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1241 (all A all B all C (r2_hidden(k2_mcart_1(A),C) & r2_hidden(k1_mcart_1(A),B) -> r2_hidden(A,k2_zfmisc_1(B,C)) | (all D all E A != k4_tarski(D,E)))) # label(t11_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1242 (all A all B all C (k1_xboole_0 != k3_zfmisc_1(A,B,C) <-> k1_xboole_0 != B & k1_xboole_0 != C & A != k1_xboole_0)) # label(t35_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1243 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(k2_tarski(B,C),D)) -> (B = k1_mcart_1(A) | k1_mcart_1(A) = C) & r2_hidden(k2_mcart_1(A),D))) # label(t15_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1244 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k16_mcart_1(A)) & v1_relat_1(k16_mcart_1(A)))) # label(dt_k16_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1245 (all A all B (k4_zfmisc_1(A,A,A,A) = k4_zfmisc_1(B,B,B,B) -> B = A)) # label(t58_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1246 (all A all B all C all D all E (r2_hidden(A,k2_zfmisc_1(k2_tarski(B,C),k2_tarski(D,E))) -> (k2_mcart_1(A) = D | E = k2_mcart_1(A)) & (B = k1_mcart_1(A) | k1_mcart_1(A) = C))) # label(t19_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1247 $T # label(dt_k19_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1248 (all A k20_mcart_1(A) = k2_mcart_1(k2_mcart_1(A))) # label(d17_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1249 (all A all B all C all D all E all F (-r1_xboole_0(k3_zfmisc_1(A,B,C),k3_zfmisc_1(D,E,F)) -> -r1_xboole_0(A,D) & -r1_xboole_0(B,E) & -r1_xboole_0(C,F))) # label(t52_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1250 (all A all B all C -(A != k1_xboole_0 & B != k1_xboole_0 & C != k1_xboole_0 & (exists D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) & (exists E exists F exists G (-(k5_mcart_1(A,B,C,D) = E & F = k6_mcart_1(A,B,C,D) & k7_mcart_1(A,B,C,D) = G) & k3_mcart_1(E,F,G) = D)))))) # label(t47_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1251 (all A all B all C all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> m1_subset_1(k6_mcart_1(A,B,C,D),B))) # label(dt_k6_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1252 (all A all B all C all D all E all F k3_zfmisc_1(k2_tarski(A,B),k2_tarski(C,D),k2_tarski(E,F)) = k6_enumset1(k3_mcart_1(A,C,E),k3_mcart_1(A,D,E),k3_mcart_1(A,C,F),k3_mcart_1(A,D,F),k3_mcart_1(B,C,E),k3_mcart_1(B,D,E),k3_mcart_1(B,C,F),k3_mcart_1(B,D,F))) # label(t46_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1253 (all A -(A != k1_xboole_0 & (all B -((all C all D all E all F all G (r2_hidden(G,B) & r2_hidden(F,G) & r2_hidden(E,F) & 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]. 4.18/4.24 1254 (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))))))))) -> k1_xboole_0 = B | k1_xboole_0 = D | E = k11_mcart_1(A,B,C,D,F) | k1_xboole_0 = C | k1_xboole_0 = A))) # label(t82_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1255 (all A all B all C all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> m1_subset_1(k5_mcart_1(A,B,C,D),A))) # label(dt_k5_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1256 (all A all B all C all D k4_mcart_1(A,B,C,D) = k4_tarski(k4_tarski(k4_tarski(A,B),C),D)) # label(t31_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1257 (all A all B all C all D all E all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,D) -> (F = k4_mcart_1(G,H,I,J) -> H = E))))))))) -> k1_xboole_0 = D | E = k9_mcart_1(A,B,C,D,F) | k1_xboole_0 = C | B = k1_xboole_0 | k1_xboole_0 = A))) # label(t80_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1258 (all A all B all C -(k1_xboole_0 != A & C != k1_xboole_0 & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> (all E (m1_subset_1(E,A) -> (E = k5_mcart_1(A,B,C,D) <-> (all F all G all H (D = k3_mcart_1(F,G,H) -> E = F))))))) & B != k1_xboole_0)) # label(d5_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1259 (all A all B all C all D k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,B),C),D) = k4_zfmisc_1(A,B,C,D)) # label(t53_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1260 (all A all B all C -(k1_xboole_0 != B & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> (all E (m1_subset_1(E,B) -> ((all F all G all H (k3_mcart_1(F,G,H) = D -> G = E)) <-> k6_mcart_1(A,B,C,D) = E))))) & k1_xboole_0 != C & A != k1_xboole_0)) # label(d6_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1261 (all A all B all C -(A != k1_xboole_0 & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> k3_mcart_1(k5_mcart_1(A,B,C,D),k6_mcart_1(A,B,C,D),k7_mcart_1(A,B,C,D)) = D)) & k1_xboole_0 != C & k1_xboole_0 != B)) # label(t48_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1262 (all A all B (k1_xboole_0 != k2_zfmisc_1(A,B) -> (all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> C != k2_mcart_1(C) & k1_mcart_1(C) != C)))) # label(t66_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1263 (all A all B all C all D all E all F (k3_zfmisc_1(A,B,C) = k3_zfmisc_1(D,E,F) -> A = D & C = F & E = B | k3_zfmisc_1(A,B,C) = k1_xboole_0)) # label(t37_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1264 (all A all B all C all D all E (m1_subset_1(E,k3_zfmisc_1(A,B,C)) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (k3_mcart_1(F,G,H) = E -> D = H))))))) -> k1_xboole_0 = B | k1_xboole_0 = C | k7_mcart_1(A,B,C,E) = D | k1_xboole_0 = A))) # label(t71_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1265 (all A -((all B -(r1_xboole_0(B,A) & r2_hidden(B,A))) & A != k1_xboole_0)) # label(t1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1266 (all A all B all C all D -(A != k1_xboole_0 & k1_xboole_0 != B & C != k1_xboole_0 & D != k1_xboole_0 & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> k1_mcart_1(k1_mcart_1(k1_mcart_1(E))) = k8_mcart_1(A,B,C,D,E) & k9_mcart_1(A,B,C,D,E) = k2_mcart_1(k1_mcart_1(k1_mcart_1(E))) & k10_mcart_1(A,B,C,D,E) = k2_mcart_1(k1_mcart_1(E)) & k11_mcart_1(A,B,C,D,E) = k2_mcart_1(E))))) # label(t61_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1267 (all A all B all C all D all E all F all G all H (m1_subset_1(F,k1_zfmisc_1(B)) & m1_subset_1(H,k1_zfmisc_1(D)) & m1_subset_1(G,k1_zfmisc_1(C)) & m1_subset_1(E,k1_zfmisc_1(A)) -> k4_zfmisc_1(E,F,G,H) = k14_mcart_1(A,B,C,D,E,F,G,H))) # label(redefinition_k14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1268 (all A all B (k3_zfmisc_1(A,A,A) = k3_zfmisc_1(B,B,B) -> A = B)) # label(t38_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1269 (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(D,H) & -r1_xboole_0(C,G) & -r1_xboole_0(B,F) & -r1_xboole_0(A,E))) # label(t64_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1270 (all A all B all C all D all E all F (k3_mcart_1(D,E,F) = k3_mcart_1(A,B,C) -> E = B & F = C & D = A)) # label(t28_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1271 (all A all B all C all D all E all F all G all H (k4_mcart_1(E,F,G,H) = k4_mcart_1(A,B,C,D) -> E = A & G = C & D = H & B = F)) # label(t33_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1272 (all A all B all C all D all E all F -(k1_xboole_0 != A & C != k1_xboole_0 & (exists G ((exists H (m1_subset_1(H,k3_zfmisc_1(D,E,F)) & -(k6_mcart_1(A,B,C,G) = k6_mcart_1(D,E,F,H) & k7_mcart_1(A,B,C,G) = k7_mcart_1(D,E,F,H) & k5_mcart_1(D,E,F,H) = k5_mcart_1(A,B,C,G)) & G = H)) & m1_subset_1(G,k3_zfmisc_1(A,B,C)))) & k1_xboole_0 != F & E != k1_xboole_0 & k1_xboole_0 != D & B != k1_xboole_0)) # label(t75_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1273 (all A all B all C all D k2_zfmisc_1(k2_tarski(A,B),k2_tarski(C,D)) = k2_enumset1(k4_tarski(A,C),k4_tarski(A,D),k4_tarski(B,C),k4_tarski(B,D))) # label(t25_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1274 $T # label(dt_k3_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1275 (all A all B all C all D all E ((all F (r2_hidden(F,A) <-> (exists G exists H exists I exists J (r2_hidden(G,B) & r2_hidden(I,D) & r2_hidden(J,E) & F = k4_mcart_1(G,H,I,J) & r2_hidden(H,C))))) -> A = k4_zfmisc_1(B,C,D,E))) # label(t85_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1276 (all A all B all C all D all E (m1_subset_1(E,k3_zfmisc_1(A,B,C)) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (E = k3_mcart_1(F,G,H) -> D = G))))))) -> D = k6_mcart_1(A,B,C,E) | k1_xboole_0 = C | k1_xboole_0 = B | A = k1_xboole_0))) # label(t70_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1277 (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]. 4.18/4.24 1278 (all A all B all C (r2_hidden(A,k2_zfmisc_1(B,C)) -> k1_mcart_1(A) != A & A != k2_mcart_1(A))) # label(t67_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1279 (all A -(k1_xboole_0 != A & (all B -(r2_hidden(B,A) & (all C all D -(B = k4_tarski(C,D) & (r2_hidden(C,A) | r2_hidden(D,A)))))))) # label(t9_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1280 (all A k18_mcart_1(A) = k2_mcart_1(k1_mcart_1(A))) # label(d15_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1281 (all A -((all B -(r2_hidden(B,A) & (all C all D all E (r2_hidden(D,E) & r2_hidden(E,B) & r2_hidden(C,D) -> r1_xboole_0(C,A))))) & A != k1_xboole_0)) # label(t4_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1282 $T # label(dt_k2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1283 (all A ((exists B exists C A = k4_tarski(B,C)) -> (all B ((all C all D (A = k4_tarski(C,D) -> B = D)) <-> k2_mcart_1(A) = B)))) # label(d2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1284 (all A all B all C all D -(A != k1_xboole_0 & B != k1_xboole_0 & D != k1_xboole_0 & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,A) -> ((all G all H all I all J (E = k4_mcart_1(G,H,I,J) -> G = F)) <-> F = k8_mcart_1(A,B,C,D,E)))))) & k1_xboole_0 != C)) # label(d8_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1285 (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)) -> D != k5_mcart_1(A,B,C,D) & k7_mcart_1(A,B,C,D) != D & D != k6_mcart_1(A,B,C,D))) & C != k1_xboole_0)) # label(t51_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1286 (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(k11_mcart_1(A,B,C,D,I),H) & r2_hidden(k8_mcart_1(A,B,C,D,I),E)))))))))))) # label(t87_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1287 (all A all B all C all D all E all F all G all H -(k1_xboole_0 != B & D != k1_xboole_0 & G != k1_xboole_0 & (exists I ((exists J (m1_subset_1(J,k4_zfmisc_1(E,F,G,H)) & -(k8_mcart_1(A,B,C,D,I) = k8_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) & k11_mcart_1(E,F,G,H,J) = k11_mcart_1(A,B,C,D,I)) & I = J)) & m1_subset_1(I,k4_zfmisc_1(A,B,C,D)))) & H != k1_xboole_0 & F != k1_xboole_0 & E != k1_xboole_0 & C != k1_xboole_0 & k1_xboole_0 != A)) # label(t86_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1288 (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) -> F = D))))))) -> A = k1_xboole_0 | k1_xboole_0 = C | D = k5_mcart_1(A,B,C,E) | B = k1_xboole_0))) # label(t69_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1289 $T # label(dt_k20_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1290 (all A -(A != k1_xboole_0 & (all B -(r2_hidden(B,A) & (all C (r2_hidden(C,B) -> r1_xboole_0(C,A))))))) # label(t2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1291 (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 & (D = k2_mcart_1(A) | C = k2_mcart_1(A)))) # label(t18_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1292 (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]. 4.18/4.24 1293 (all A ((exists B exists C k4_tarski(B,C) = A) -> (all B ((all C all D (k4_tarski(C,D) = A -> C = B)) <-> B = k1_mcart_1(A))))) # label(d1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1294 (all A all B all C all D all E all F (A = k17_mcart_1(k4_tarski(k4_tarski(A,B),C)) & k18_mcart_1(k4_tarski(k4_tarski(A,B),C)) = B & D = k19_mcart_1(k4_tarski(F,k4_tarski(D,E))) & k20_mcart_1(k4_tarski(F,k4_tarski(D,E))) = E)) # label(t89_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1295 $T # label(t30_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1296 (all A all B all C all D all E all F all G all H (r1_tarski(A,B) & r1_tarski(C,D) & r1_tarski(G,H) & r1_tarski(E,F) -> r1_tarski(k4_zfmisc_1(A,C,E,G),k4_zfmisc_1(B,D,F,H)))) # label(t88_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1297 (all A all B all C (r2_hidden(A,k2_zfmisc_1(B,C)) -> r2_hidden(k2_mcart_1(A),C) & r2_hidden(k1_mcart_1(A),B))) # label(t10_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1298 (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]. 4.18/4.24 1299 (all A all B all C (r2_hidden(A,k2_zfmisc_1(k1_tarski(B),C)) -> r2_hidden(k2_mcart_1(A),C) & k1_mcart_1(A) = B)) # label(t12_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1300 (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]. 4.18/4.24 1301 (all A all B all C all D all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> m1_subset_1(k8_mcart_1(A,B,C,D,E),A))) # label(dt_k8_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1302 (all A -(A != k1_xboole_0 & (all B -((all C all D all E -(k3_mcart_1(C,D,E) = B & (r2_hidden(D,A) | r2_hidden(C,A)))) & r2_hidden(B,A))))) # label(t29_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1303 (all A all B all C all D k4_zfmisc_1(k1_tarski(A),k1_tarski(B),k1_tarski(C),k1_tarski(D)) = k1_tarski(k4_mcart_1(A,B,C,D))) # label(t65_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1304 (all A all B all C all D -((all E all F all G -(r2_hidden(E,B) & r2_hidden(F,C) & r2_hidden(G,D) & A = k3_mcart_1(E,F,G))) & r2_hidden(A,k3_zfmisc_1(B,C,D)))) # label(t72_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1305 (all A all B all C all D ((all E (r2_hidden(E,A) <-> (exists F exists G exists H (r2_hidden(G,C) & r2_hidden(H,D) & E = k3_mcart_1(F,G,H) & r2_hidden(F,B))))) -> k3_zfmisc_1(B,C,D) = A)) # label(t74_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1306 (all A all B all C all D all E all F (r2_hidden(k3_mcart_1(A,B,C),k3_zfmisc_1(D,E,F)) <-> r2_hidden(A,D) & r2_hidden(B,E) & r2_hidden(C,F))) # label(t73_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1307 (all A all B all C all D all E all F (m1_subset_1(D,k1_zfmisc_1(A)) & m1_subset_1(E,k1_zfmisc_1(B)) & m1_subset_1(F,k1_zfmisc_1(C)) -> m1_subset_1(k13_mcart_1(A,B,C,D,E,F),k1_zfmisc_1(k3_zfmisc_1(A,B,C))))) # label(dt_k13_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1308 (all A all B all 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 (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(D,k4_tarski(F,G)) = k1_funct_1(E,k4_tarski(F,G)))))) -> E = D))))) # label(t120_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1309 (all A all B (v1_funct_1(B) & v3_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,A) & v3_funct_2(C,A,A) & v1_funct_2(C,A,A) -> (k6_partfun1(A) = k5_funct_2(A,B,C) -> C = k6_funct_2(A,B)))))) # label(t87_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1310 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> (all C (v1_funct_2(C,A,A) & m2_relset_1(C,A,A) & v1_funct_1(C) -> (v2_funct_1(B) & B = k4_funct_2(A,C,B) -> k6_partfun1(A) = C))))) # label(t76_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1311 (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) -> ((all D (r2_hidden(D,k4_relset_1(A,A,B)) -> k1_funct_1(C,D) = k1_funct_1(B,D))) <-> r1_partfun1(B,C)))))) # label(t146_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1312 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> -((k1_xboole_0 = B -> A = k1_xboole_0) & (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (exists E (k1_funct_1(C,E) != k1_funct_1(D,E) & r2_hidden(E,k4_relset_1(A,B,C))))))))) # label(t136_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1313 (all A all B all C all D (m1_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> k9_relat_1(C,D) = k2_funct_2(A,B,C,D))) # label(redefinition_k2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1314 (all A all B all C (m2_relset_1(C,A,k1_tarski(B)) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,k1_tarski(B)) & v1_funct_2(D,A,k1_tarski(B)) & v1_funct_1(D) -> k1_tarski(D) = k5_partfun1(A,k1_tarski(B),C))))) # label(t164_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1315 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> r1_tarski(k10_relat_1(D,C),A))) # label(t47_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1316 (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 (v1_funct_1(A) & m2_relset_1(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_2(A,f1_s14_funct_2,f2_s14_funct_2))) # label(s14_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1317 (all A all B all C (m2_relset_1(C,A,B) -> C = k7_relset_1(A,A,A,B,k6_partfun1(A),C) & C = k7_relset_1(A,B,B,B,C,k6_partfun1(B)))) # label(t23_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1318 $T # label(t140_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1319 $T # label(t52_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1320 $T # label(t33_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1321 (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(k1_funct_1(E,C),D) & r2_hidden(C,A) -> k1_funct_1(E,C) = k1_funct_1(k9_relset_1(A,B,D,E),C) | k1_xboole_0 = B))) # label(t41_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1322 (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) & v1_funct_2(D,B,A) & m2_relset_1(D,B,A) -> (v2_funct_1(C) & k6_partfun1(A) = k1_partfun1(A,B,B,A,C,D) & k2_relat_1(C) = B -> k1_xboole_0 = A | k2_funct_1(C) = D | k1_xboole_0 = B))))) # label(t36_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1323 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,k1_tarski(A),B) & v1_funct_2(D,k1_tarski(A),B) -> (B != k1_xboole_0 -> r1_tarski(k2_funct_2(k1_tarski(A),B,D,C),k1_tarski(k1_funct_1(D,A)))))) # label(t64_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1324 (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) -> (k5_funct_2(A,B,C) = C -> B = k6_partfun1(A)))))) # label(t86_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1325 $T # label(t91_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1326 $T # label(t124_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1327 (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]. 4.18/4.24 1328 (all A all B all C all D (m1_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> m1_subset_1(k2_funct_2(A,B,C,D),k1_zfmisc_1(B)))) # label(dt_k2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1329 (all A all B all C all D (m1_relset_1(C,A,B) & v1_funct_1(C) -> m1_subset_1(k3_funct_2(A,B,C,D),k1_zfmisc_1(A)))) # label(dt_k3_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1330 $T # label(t96_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1331 $T # label(t84_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1332 (all A all B all C all D (v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,A) & v1_funct_1(C) & -v1_xboole_0(A) -> k8_funct_2(A,B,C,D) = k1_funct_1(C,D))) # label(redefinition_k8_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1333 $T # label(t98_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1334 (all A -((all B -(p1_s1_funct_2(A,B) & r2_hidden(B,f2_s1_funct_2))) & r2_hidden(A,f1_s1_funct_2))) -> (exists A (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) & (all B (r2_hidden(B,f1_s1_funct_2) -> p1_s1_funct_2(B,k1_funct_1(A,B)))))) # label(s1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1335 (all A all B all C (m2_relset_1(C,k1_tarski(A),B) & v1_funct_2(C,k1_tarski(A),B) & v1_funct_1(C) -> (k1_xboole_0 != B -> r2_hidden(k1_funct_1(C,A),B)))) # label(t61_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1336 $T # label(t78_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1337 (all A all B all C all D (v1_funct_2(D,A,k1_tarski(B)) & m2_relset_1(D,A,k1_tarski(B)) & v1_funct_1(D) -> (r2_hidden(C,A) -> B = k1_funct_1(D,C)))) # label(t65_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1338 (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) -> ((all D all E (r2_hidden(D,A) & r2_hidden(E,A) & k1_funct_1(C,D) = k1_funct_1(C,E) -> D = E)) <-> v2_funct_1(C))))) # label(t25_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1339 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> ((all D -(r2_hidden(D,B) & (all E -(r2_hidden(E,A) & D = k1_funct_1(C,E))))) -> k2_relat_1(C) = B | B = k1_xboole_0))) # label(t16_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1340 $T # label(t112_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1341 (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) -> (k2_relat_1(C) = A & k2_relat_1(B) = A -> A = k2_relat_1(k4_funct_2(A,B,C))))))) # label(t73_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.24 1342 (all A (m1_subset_1(A,f1_s13_funct_2) -> m1_subset_1(f3_s13_funct_2(A),f2_s13_funct_2))) -> (exists A (v1_funct_1(A) & (all B (m1_subset_1(B,f1_s13_funct_2) -> f3_s13_funct_2(B) = k8_funct_2(f1_s13_funct_2,f2_s13_funct_2,A,B))) & m2_relset_1(A,f1_s13_funct_2,f2_s13_funct_2) & v1_funct_2(A,f1_s13_funct_2,f2_s13_funct_2))) # label(s13_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1343 (all A all B all C (m1_relset_1(C,A,B) -> (v1_partfun1(C,A,B) & v1_funct_1(C) -> v1_funct_1(C) & v1_funct_2(C,A,B)))) # label(cc1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1344 $T # label(t153_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1345 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_2(E,B,C) & m2_relset_1(E,B,C) & v1_funct_1(E) -> (-(B = k1_xboole_0 & A != k1_xboole_0 & k1_xboole_0 != C) -> v1_funct_1(k1_partfun1(A,B,B,C,D,E)) & 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)))))) # label(t19_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1346 $T # label(t2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1347 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (r2_hidden(C,A) -> r2_hidden(k1_funct_1(D,C),B) | B = k1_xboole_0))) # label(t7_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1348 (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]. 4.18/4.25 1349 (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) & v1_funct_2(F,B,C) & m2_relset_1(F,B,C) -> -((C = k1_xboole_0 -> k1_xboole_0 = B) & (k1_xboole_0 = B -> A = k1_xboole_0) & -r1_tarski(k3_funct_2(A,B,E,D),k3_funct_2(A,C,k1_partfun1(A,B,B,C,E,F),k2_funct_2(B,C,F,D)))))))) # label(t53_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1350 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (r1_tarski(B,C) -> m2_relset_1(D,A,C) & v1_funct_2(D,A,C) & v1_funct_1(D) | A != k1_xboole_0 & B = k1_xboole_0))) # label(t9_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1351 (all A all B all C (m1_relset_1(C,A,B) -> (v1_funct_1(C) & v2_funct_1(C) & v2_funct_2(C,A,B) & v1_funct_2(C,A,B) -> v1_funct_1(C) & v3_funct_2(C,A,B) & v1_funct_2(C,A,B)))) # label(cc3_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1352 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> -(r1_partfun1(C,D) & (all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> -(r1_partfun1(D,E) & r1_partfun1(C,E)))) & (B = k1_xboole_0 -> A = k1_xboole_0)))))) # label(t154_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1353 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (v2_funct_1(C) & v2_funct_2(C,A,B) <-> v3_funct_2(C,A,B)))) # label(d4_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1354 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(C,A,A) -> (A = k2_relat_1(B) & B = k4_funct_2(A,B,C) -> k6_partfun1(A) = C))))) # label(t75_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1355 $T # label(t114_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1356 $T # label(t110_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1357 (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,A,A) & m2_relset_1(C,A,A) & v1_funct_1(C) -> (r1_partfun1(B,C) -> C = B))))) # label(t143_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1358 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> ((k1_xboole_0 = B -> A = k1_xboole_0) -> k5_partfun1(A,B,k3_partfun1(C,A,B)) = k1_tarski(C)))) # label(t161_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1359 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (v2_funct_1(D) & r2_hidden(C,A) -> C = k1_funct_1(k2_funct_1(D),k1_funct_1(D,C)) | k1_xboole_0 = B))) # label(t32_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1360 (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) -> ((B = k1_xboole_0 -> k1_xboole_0 = A) -> ((all E (r2_hidden(E,k4_relset_1(A,B,C)) -> k1_funct_1(C,E) = k1_funct_1(D,E))) <-> r1_partfun1(C,D))))))) # label(t145_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1361 (all A all B (m2_relset_1(B,A,A) -> B = k7_relset_1(A,A,A,A,k6_partfun1(A),B) & B = k7_relset_1(A,A,A,A,B,k6_partfun1(A)))) # label(t74_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1362 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_xboole_0 = k1_relat_1(B) -> v1_funct_1(B) & m2_relset_1(B,k1_xboole_0,A) & v1_funct_2(B,k1_xboole_0,A)))) # label(t55_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1363 (all A all B (r2_hidden(A,f1_s6_funct_2) & r2_hidden(B,f2_s6_funct_2) -> r2_hidden(f4_s6_funct_2(A,B),f3_s6_funct_2))) -> (exists A (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(C,f2_s6_funct_2) & r2_hidden(B,f1_s6_funct_2) -> k1_funct_1(A,k4_tarski(B,C)) = f4_s6_funct_2(B,C))) & 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]. 4.18/4.25 1364 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (k4_relset_1(A,B,C) = A -> v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B)))) # label(t130_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1365 (all A (r2_hidden(A,f1_s2_funct_2) -> r2_hidden(f3_s2_funct_2(A),f2_s2_funct_2))) -> (exists A (m2_relset_1(A,f1_s2_funct_2,f2_s2_funct_2) & (all B (r2_hidden(B,f1_s2_funct_2) -> f3_s2_funct_2(B) = k1_funct_1(A,B))) & v1_funct_2(A,f1_s2_funct_2,f2_s2_funct_2) & v1_funct_1(A))) # label(s2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1366 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> ((k1_xboole_0 = B -> k1_xboole_0 = A) -> v1_partfun1(k3_partfun1(C,A,B),A,B)))) # label(t133_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1367 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(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) -> (k1_partfun1(A,B,B,A,C,D) = k6_partfun1(A) -> v2_funct_1(C) & k2_relat_1(D) = A | B = k1_xboole_0))))) # label(t29_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1368 $T # label(t54_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1369 $T # label(t105_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1370 (all A all B all C (v1_funct_1(C) & m1_relset_1(C,A,A) & v1_funct_2(C,A,A) & m1_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> k5_relat_1(B,C) = k4_funct_2(A,B,C))) # label(redefinition_k4_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1371 $T # label(t122_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1372 $T # label(t102_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1373 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> r1_tarski(k2_relat_1(B),A) & A = k4_relset_1(A,A,B))) # label(t67_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1374 (all A all B all C all D (-v1_xboole_0(A) & v1_funct_2(C,A,B) & m1_subset_1(D,A) & m1_relset_1(C,A,B) & v1_funct_1(C) -> m1_subset_1(k8_funct_2(A,B,C,D),B))) # label(dt_k8_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1375 $T # label(t109_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1376 $T # label(t56_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1377 $T # label(t94_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1378 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (r2_hidden(C,A) -> k1_xboole_0 = B | r2_hidden(k1_funct_1(D,C),k2_relat_1(D))))) # label(t6_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1379 $T # label(t147_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1380 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> (all C (m1_relset_1(C,A,B) -> (v1_funct_2(C,A,B) & v1_funct_1(C) -> v1_funct_1(C) & -v1_xboole_0(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B)))))) # label(cc6_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1381 $T # label(t1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1382 $T # label(t89_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1383 $T # label(t100_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1384 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> v1_partfun1(C,A,B) | A != k1_xboole_0 & B = k1_xboole_0))) # label(t132_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1385 $T # label(t123_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1386 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,A,B) -> k3_funct_2(A,B,C,D) = k10_relat_1(C,D))) # label(redefinition_k3_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1387 $T # label(t90_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1388 (all A all B all C (m1_relset_1(C,A,B) -> (v1_funct_1(C) & v1_funct_2(C,A,B) & v3_funct_2(C,A,B) -> v1_funct_1(C) & v2_funct_1(C) & v1_funct_2(C,A,B) & v2_funct_2(C,A,B)))) # label(cc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1389 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_2(D,A,B) & v1_funct_2(E,B,C) & m1_relset_1(E,B,C) & v1_funct_1(E) & m1_relset_1(D,A,B) & v1_funct_1(D) -> m2_relset_1(k7_funct_2(A,B,C,D,E),A,C) & v1_funct_2(k7_funct_2(A,B,C,D,E),A,C) & v1_funct_1(k7_funct_2(A,B,C,D,E)))) # label(dt_k7_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1390 (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]. 4.18/4.25 1391 (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 -((all F (m1_subset_1(F,A) -> -(r2_hidden(F,C) & E = k1_funct_1(D,F)))) & r2_hidden(E,k2_funct_2(A,B,D,C)))))) # label(t116_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1392 $T # label(t69_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1393 $T # label(t157_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1394 $T # label(t139_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1395 $T # label(t68_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1396 (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) -> (B = k2_relat_1(D) & v2_funct_1(k1_partfun1(A,B,B,C,D,E)) -> k1_xboole_0 = C & k1_xboole_0 != B | v2_funct_1(D) & v2_funct_1(E)))))) # label(t30_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1397 (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 (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (r1_partfun1(D,E) & r1_partfun1(C,E) -> r1_partfun1(C,D) | k1_xboole_0 = B & k1_xboole_0 != A))))))) # label(t151_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1398 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> k1_tarski(B) = k5_partfun1(A,A,k3_partfun1(B,A,A)))) # label(t162_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1399 $T # label(t93_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.18/4.25 1400 (all A (r2_hidden(A,f1_s9_funct_2) -> (p1_s9_funct_2(A) -> r2_hidden(f3_s9_funct_2(A),f2_s9_funct_2)) & (-p1_s9_funct_2(A) -> r2_hidden(f4_s9_funct_2(A),f2_s9_funct_2)))) -> (exists A (v1_funct_1(A) & (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)))) & m2_relset_1(A,f1_s9_funct_2,f2_s9_funct_2) & v1_funct_2(A,f1_s9_funct_2,f2_s9_funct_2))) # label(s9_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1401 (all A all 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) -> (r1_tarski(B,A) -> k3_funct_2(A,A,C,k2_funct_2(A,A,C,B)) = B & B = k2_funct_2(A,A,C,k3_funct_2(A,A,C,B))))) # label(t92_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1402 (all A all B -((all C -(r2_hidden(C,f3_s5_funct_2) & p1_s5_funct_2(A,B,C))) & r2_hidden(B,f2_s5_funct_2) & r2_hidden(A,f1_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))))) & m2_relset_1(A,k2_zfmisc_1(f1_s5_funct_2,f2_s5_funct_2),f3_s5_funct_2) & v1_funct_2(A,k2_zfmisc_1(f1_s5_funct_2,f2_s5_funct_2),f3_s5_funct_2))) # label(s5_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1403 $T # label(t10_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1404 (all A all B all C (v1_funct_2(C,A,A) & m2_relset_1(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]. 4.20/4.25 1405 (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))) | k1_xboole_0 = B & k1_xboole_0 != A))) # label(t50_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1406 $T # label(t42_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1407 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (k2_relat_1(C) = B <-> v2_funct_2(C,A,B)))) # label(d3_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1408 $T # label(t127_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1409 (all A all B (v1_funct_1(B) & m1_relset_1(B,A,A) & v3_funct_2(B,A,A) & v1_funct_2(B,A,A) -> k6_funct_2(A,B) = k2_funct_1(B))) # label(redefinition_k6_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1410 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> -((k1_xboole_0 = B -> A = k1_xboole_0) & (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> -r1_partfun1(C,D)))))) # label(t148_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1411 $T # label(t129_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1412 (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]. 4.20/4.25 1413 $T # label(t135_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1414 (exists A ((all B (m1_subset_1(B,f1_s8_funct_2) -> (all C (m1_subset_1(C,f2_s8_funct_2) -> k1_funct_1(A,k4_tarski(B,C)) = f4_s8_funct_2(B,C))))) & m2_relset_1(A,k2_zfmisc_1(f1_s8_funct_2,f2_s8_funct_2),f3_s8_funct_2) & v1_funct_2(A,k2_zfmisc_1(f1_s8_funct_2,f2_s8_funct_2),f3_s8_funct_2) & v1_funct_1(A))) # label(s8_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1415 (all A all B all C (v1_funct_1(B) & v1_funct_2(B,A,A) & v3_funct_2(B,A,A) & m1_relset_1(B,A,A) & v1_funct_2(C,A,A) & m1_relset_1(C,A,A) & v3_funct_2(C,A,A) & v1_funct_1(C) -> v1_funct_2(k5_funct_2(A,B,C),A,A) & v3_funct_2(k5_funct_2(A,B,C),A,A) & m2_relset_1(k5_funct_2(A,B,C),A,A) & v1_funct_1(k5_funct_2(A,B,C)))) # label(dt_k5_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1416 $T # label(t104_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1417 $T # label(dt_k1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1418 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (v1_partfun1(C,A,B) -> m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C)))) # label(t131_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1419 $T # label(t39_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1420 (all A all B r1_tarski(k1_funct_2(A,B),k4_partfun1(A,B))) # label(t141_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1421 (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_tarski(D,C) -> r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D))))))) # label(t165_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1422 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,C) & m2_relset_1(E,B,C) -> (B = k2_relat_1(D) & k2_relat_1(E) = C -> C = k2_relat_1(k1_partfun1(A,B,B,C,D,E)) | k1_xboole_0 = C | B = k1_xboole_0))))) # label(t20_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1423 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (r2_hidden(D,k5_partfun1(A,B,C)) -> v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D))))) # label(t158_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1424 f4_s11_funct_2 != f3_s11_funct_2 -> (exists A (v1_funct_1(A) & v1_funct_2(A,f1_s11_funct_2,f2_s11_funct_2) & f5_s11_funct_2 = k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,f3_s11_funct_2) & (all B (m1_subset_1(B,f1_s11_funct_2) -> -(f4_s11_funct_2 != B & k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,B) != f7_s11_funct_2(B) & B != f3_s11_funct_2))) & k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,f4_s11_funct_2) = f6_s11_funct_2 & m2_relset_1(A,f1_s11_funct_2,f2_s11_funct_2))) # label(s11_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1425 $T # label(t128_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1426 (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(k9_relat_1(D,C),B))) # label(t44_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1427 (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) -> (r1_partfun1(B,C) -> r2_hidden(C,k5_partfun1(A,A,B))))))) # label(t156_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1428 (all A all B (m2_relset_1(B,A,A) & v1_funct_1(B) -> (exists C (v1_funct_2(C,A,A) & r1_partfun1(B,C) & m2_relset_1(C,A,A) & v1_funct_1(C))))) # label(t149_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1429 (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) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (r1_partfun1(C,D) -> B = k1_xboole_0 & k1_xboole_0 != A | C = D))))) # label(t142_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1430 $T # label(t15_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1431 $T # label(t63_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1432 (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 -> A = k1_xboole_0) -> k3_funct_2(A,B,C,B) = A))) # label(t48_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1433 (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) -> k1_xboole_0 = k3_funct_2(k1_xboole_0,A,C,B))) # label(t60_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1434 $T # label(t101_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1435 $T # label(t97_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1436 $T # label(t125_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1437 (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) <-> (all D -(r2_hidden(D,B) & k3_funct_2(A,B,C,k1_tarski(D)) = k1_xboole_0))))) # label(t49_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1438 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(A,C) -> k2_partfun1(A,B,D,C) = D))) # label(t40_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1439 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(D,A,B) & v1_funct_2(E,B,C) & m1_relset_1(E,B,C) & v1_funct_1(E) & m1_relset_1(D,A,B) -> k5_relat_1(D,E) = k7_funct_2(A,B,C,D,E))) # label(redefinition_k7_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1440 $T # label(t13_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1441 (all A all B all C (C = k1_funct_2(A,B) <-> (all D ((exists E (v1_funct_1(E) & r1_tarski(k2_relat_1(E),B) & A = k1_relat_1(E) & E = D & v1_relat_1(E))) <-> r2_hidden(D,C))))) # label(d2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1442 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> ((all E (m1_subset_1(E,A) -> k1_funct_1(C,E) = k1_funct_1(D,E))) -> C = D))))) # label(t113_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1443 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (k2_relat_1(C) = B & 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]. 4.20/4.25 1444 $T # label(t144_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1445 $T # label(t81_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1446 (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 (v1_funct_2(E,B,D) & m2_relset_1(E,B,D) & v1_funct_1(E) -> (all F (v1_funct_2(F,B,D) & m2_relset_1(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]. 4.20/4.25 1447 (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 (v1_funct_1(A) & v1_funct_2(A,f1_s3_funct_2,f2_s3_funct_2) & m2_relset_1(A,f1_s3_funct_2,f2_s3_funct_2) & (all B (m1_subset_1(B,f1_s3_funct_2) -> p1_s3_funct_2(B,k8_funct_2(f1_s3_funct_2,f2_s3_funct_2,A,B)))))) # label(s3_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1448 (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 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]. 4.20/4.25 1449 $T # label(t103_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1450 (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 (r2_hidden(E,A) & r2_hidden(k1_funct_1(D,E),C) <-> r2_hidden(E,k10_relat_1(D,C))))))) # label(t46_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1451 $T # label(t117_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1452 (all A all B all C (m2_relset_1(C,A,B) -> (k1_xboole_0 = B -> k1_xboole_0 = A | (C = k1_xboole_0 <-> v1_funct_2(C,A,B))) & ((k1_xboole_0 = B -> A = k1_xboole_0) -> (v1_funct_2(C,A,B) <-> A = k4_relset_1(A,B,C))))) # label(d1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1453 $T # label(t126_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1454 $T # label(t71_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1455 (all A all B (m1_relset_1(B,A,A) -> (v1_funct_2(B,A,A) & v1_relat_2(B) & v1_partfun1(B,A,A) & v1_funct_1(B) -> v1_funct_1(B) & v2_funct_1(B) & v1_funct_2(B,A,A) & v3_funct_2(B,A,A) & v2_funct_2(B,A,A)))) # label(cc4_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1456 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(C,k1_funct_2(A,B)) -> k1_relat_1(C) = A & r1_tarski(k2_relat_1(C),B)))) # label(t169_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1457 (all A all B all C all D (v1_funct_2(D,k2_zfmisc_1(A,B),C) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (all E (v1_funct_2(E,k2_zfmisc_1(A,B),C) & m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_1(E) -> ((all F all G (r2_hidden(G,B) & r2_hidden(F,A) -> k1_funct_1(D,k4_tarski(F,G)) = k1_funct_1(E,k4_tarski(F,G)))) -> E = D))))) # label(t118_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1458 $T # label(t57_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1459 (all A (v1_funct_1(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)))) # label(t3_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1460 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (r1_partfun1(C,D) -> A != k1_xboole_0 & B = k1_xboole_0 | r2_hidden(D,k5_partfun1(A,B,C))))))) # label(t155_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1461 (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(k2_relat_1(D),C) -> v1_funct_1(D) & m2_relset_1(D,A,C) & v1_funct_2(D,A,C) | B = k1_xboole_0 & A != k1_xboole_0))) # label(t8_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1462 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (r1_tarski(C,A) -> v1_funct_2(k2_partfun1(A,B,D,C),C,B) & m2_relset_1(k2_partfun1(A,B,D,C),C,B) & v1_funct_1(k2_partfun1(A,B,D,C)) | B = k1_xboole_0 & A != k1_xboole_0))) # label(t38_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1463 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> ((all D (r2_hidden(D,A) -> r2_hidden(k1_funct_1(C,D),B))) & A = k1_relat_1(C) -> v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B)))) # label(t5_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1464 (all A all B (v3_funct_2(B,A,A) & m1_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> v1_funct_2(k6_funct_2(A,B),A,A) & v3_funct_2(k6_funct_2(A,B),A,A) & m2_relset_1(k6_funct_2(A,B),A,A) & v1_funct_1(k6_funct_2(A,B)))) # label(dt_k6_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1465 (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 -(k1_funct_1(D,E) = C & r2_hidden(E,A))) & k2_relat_1(D) = B & r2_hidden(C,B)))) # label(t17_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1466 $T # label(t138_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1467 $T # label(t163_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1468 (all A all B all C (m2_relset_1(C,k1_xboole_0,A) & v1_funct_2(C,k1_xboole_0,A) & v1_funct_1(C) -> k1_xboole_0 = k2_funct_2(k1_xboole_0,A,C,B))) # label(t59_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1469 $T # label(t95_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1470 $T # label(t58_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1471 (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) & v1_funct_2(D,B,A) & m2_relset_1(D,B,A) -> (k6_partfun1(B) = k1_partfun1(B,A,A,B,D,C) -> B = k2_relat_1(C)))))) # label(t24_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1472 (all A all B all C all D all E all F (v1_funct_1(F) & v1_funct_2(F,k2_zfmisc_1(A,B),C) & m2_relset_1(F,k2_zfmisc_1(A,B),C) -> (r2_hidden(E,B) & r2_hidden(D,A) -> r2_hidden(k1_funct_1(F,k4_tarski(D,E)),C) | C = k1_xboole_0))) # label(t119_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1473 (all A (m1_subset_1(A,f1_s12_funct_2) -> r2_hidden(f3_s12_funct_2(A),f2_s12_funct_2))) -> (exists A (v1_funct_1(A) & v1_funct_2(A,f1_s12_funct_2,f2_s12_funct_2) & (all B (m1_subset_1(B,f1_s12_funct_2) -> k8_funct_2(f1_s12_funct_2,f2_s12_funct_2,A,B) = f3_s12_funct_2(B))) & m2_relset_1(A,f1_s12_funct_2,f2_s12_funct_2))) # label(s12_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1474 $T # label(t150_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1475 $T # label(t111_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1476 (all A all B k5_partfun1(A,B,k3_partfun1(k1_xboole_0,A,B)) = k1_funct_2(A,B)) # label(t160_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1477 (all A (k1_xboole_0 != A -> k1_funct_2(A,k1_xboole_0) = k1_xboole_0)) # label(t14_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1478 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,C) & m2_relset_1(E,B,C) -> (k2_relat_1(k1_partfun1(A,B,B,C,D,E)) = C & v2_funct_1(E) -> k2_relat_1(D) = B | C = k1_xboole_0))))) # label(t28_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1479 (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 & -v2_funct_1(C) & (exists D (v1_funct_1(D) & k6_partfun1(A) = k1_partfun1(A,B,B,A,C,D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A)))))) # label(t37_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1480 $T # label(t106_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1481 (all A exists B (m1_relset_1(B,A,A) & v1_funct_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_relat_1(B))) # label(rc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1482 $T # label(t72_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1483 (all A all B all C (v1_funct_1(B) & v3_funct_2(B,A,A) & m1_relset_1(B,A,A) & v1_funct_2(C,A,A) & v3_funct_2(C,A,A) & m1_relset_1(C,A,A) & v1_funct_1(C) & v1_funct_2(B,A,A) -> k5_funct_2(A,B,C) = k5_relat_1(B,C))) # label(redefinition_k5_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1484 (all A all B exists C (v1_funct_1(C) & v1_funct_2(C,A,B) & v1_relat_1(C) & m1_relset_1(C,A,B))) # label(rc1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1485 (all A all B all C all D (v1_funct_2(D,k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & m2_relset_1(D,k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & v1_funct_1(D) -> k9_funct_2(A,B,C) = D)) # label(d5_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1486 (exists A (m2_relset_1(A,f1_s4_funct_2,f2_s4_funct_2) & (all B (m1_subset_1(B,f1_s4_funct_2) -> k8_funct_2(f1_s4_funct_2,f2_s4_funct_2,A,B) = f3_s4_funct_2(B))) & v1_funct_2(A,f1_s4_funct_2,f2_s4_funct_2) & v1_funct_1(A))) # label(s4_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1487 (exists A (m2_relset_1(A,f1_s10_funct_2,f2_s10_funct_2) & k8_funct_2(f1_s10_funct_2,f2_s10_funct_2,A,f3_s10_funct_2) = f4_s10_funct_2 & (all B (m1_subset_1(B,f1_s10_funct_2) -> (B != f3_s10_funct_2 -> k8_funct_2(f1_s10_funct_2,f2_s10_funct_2,A,B) = f5_s10_funct_2(B)))) & v1_funct_2(A,f1_s10_funct_2,f2_s10_funct_2) & v1_funct_1(A))) # label(s10_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1488 (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 -((all F -(r2_hidden(F,C) & k1_funct_1(D,F) = E & r2_hidden(F,A))) & r2_hidden(E,k2_funct_2(A,B,D,C)))))) # label(t115_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1489 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> (v2_funct_1(B) & A = k2_relat_1(B) -> v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v3_funct_2(B,A,A)))) # label(t83_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1490 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,k1_tarski(A),B) & v1_funct_2(C,k1_tarski(A),B) -> (B != k1_xboole_0 -> k1_tarski(k1_funct_1(C,A)) = k2_relat_1(C)))) # label(t62_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1491 $T # label(t107_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1492 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> (v2_funct_1(B) -> (all C all D (r2_hidden(C,A) & k1_funct_1(B,D) = k1_funct_1(B,C) & r2_hidden(D,A) -> D = C))))) # label(t85_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1493 $T # label(t137_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1494 (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 -> k1_xboole_0 = A) -> k2_funct_2(A,B,C,A) = k2_relat_1(C)))) # label(t45_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1495 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_relat_1(E) & v1_funct_1(E) -> (r2_hidden(C,A) -> k1_funct_1(E,k1_funct_1(D,C)) = k1_funct_1(k5_relat_1(D,E),C) | k1_xboole_0 = B))))) # label(t21_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1496 (all A all B all C (v1_funct_1(B) & v1_funct_2(C,A,A) & m1_relset_1(C,A,A) & v1_funct_1(C) & m1_relset_1(B,A,A) & v1_funct_2(B,A,A) -> v1_funct_2(k4_funct_2(A,B,C),A,A) & m2_relset_1(k4_funct_2(A,B,C),A,A) & v1_funct_1(k4_funct_2(A,B,C)))) # label(dt_k4_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1497 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> (v2_funct_1(B) <-> (all C all D (r2_hidden(D,A) & k1_funct_1(B,D) = k1_funct_1(B,C) & r2_hidden(C,A) -> C = D))))) # label(t77_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1498 (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) -> k5_funct_2(A,k6_funct_2(A,B),B) = k6_partfun1(A) & k6_partfun1(A) = k5_funct_2(A,B,k6_funct_2(A,B)))) # label(t88_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1499 (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]. 4.20/4.25 1500 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> r2_hidden(B,k1_funct_2(A,A)))) # label(t12_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1501 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (k2_relat_1(C) = B & (all E all F ((r2_hidden(F,A) & E = k1_funct_1(C,F) -> r2_hidden(E,B) & k1_funct_1(D,E) = F) & (F = k1_funct_1(D,E) & r2_hidden(E,B) -> r2_hidden(F,A) & k1_funct_1(C,F) = E))) & v2_funct_1(C) -> A = k1_xboole_0 | D = k2_funct_1(C) | k1_xboole_0 = B))))) # label(t34_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1502 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (k2_relat_1(C) = B & v2_funct_1(C) -> k1_xboole_0 = B | k6_partfun1(B) = k5_relat_1(k2_funct_1(C),C) & k6_partfun1(A) = k5_relat_1(C,k2_funct_1(C))))) # label(t35_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1503 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,C) & m2_relset_1(E,B,C) -> (v2_funct_1(k1_partfun1(A,B,B,C,D,E)) -> v2_funct_1(D) | k1_xboole_0 != A & B = k1_xboole_0 | C = k1_xboole_0 & k1_xboole_0 != B))))) # label(t26_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1504 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> k2_relat_1(B) = k2_funct_2(A,A,B,A))) # label(t79_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1505 (all A -v1_xboole_0(k1_funct_2(A,A))) # label(fc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1506 $T # label(t108_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1507 (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 (m2_relset_1(A,k2_zfmisc_1(f1_s7_funct_2,f2_s7_funct_2),f3_s7_funct_2) & (all B (m1_subset_1(B,f1_s7_funct_2) -> (all C (m1_subset_1(C,f2_s7_funct_2) -> p1_s7_funct_2(B,C,k1_funct_1(A,k4_tarski(B,C))))))) & v1_funct_2(A,k2_zfmisc_1(f1_s7_funct_2,f2_s7_funct_2),f3_s7_funct_2) & v1_funct_1(A))) # label(s7_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1508 (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) -> (k5_partfun1(A,B,C) = k5_partfun1(A,B,D) & (all E k1_tarski(E) != B) -> D = C))))) # label(t168_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1509 $T # label(t80_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1510 (all A all B all C (r2_hidden(C,k1_funct_2(A,B)) -> v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C))) # label(t121_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1511 (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 -> k1_xboole_0 = A) -> A = k3_funct_2(A,B,C,k2_funct_2(A,B,C,A))))) # label(t51_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1512 (all A all B (-v1_xboole_0(B) -> -v1_xboole_0(k1_funct_2(A,B)))) # label(fc1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1513 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> k3_funct_2(A,A,B,k2_funct_2(A,A,B,A)) = A)) # label(t82_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1514 (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 != A & -(v2_funct_1(C) <-> (all D all E (v1_funct_1(E) & v1_funct_2(E,D,A) & m2_relset_1(E,D,A) -> (all F (m2_relset_1(F,D,A) & v1_funct_2(F,D,A) & v1_funct_1(F) -> (k1_partfun1(D,A,A,B,F,C) = k1_partfun1(D,A,A,B,E,C) -> F = E)))))) & B != k1_xboole_0))) # label(t27_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1515 (all A all B all C (v1_funct_1(k9_funct_2(A,B,C)) & v1_funct_2(k9_funct_2(A,B,C),k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & m2_relset_1(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]. 4.20/4.25 1516 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> ((k1_xboole_0 = B -> k1_xboole_0 = A) -> r2_hidden(C,k1_funct_2(A,B))))) # label(t11_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1517 (all A all B (m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,A) -> (all D (m2_relset_1(D,A,A) & v1_funct_2(D,A,A) & v1_funct_1(D) -> (r1_partfun1(C,D) & r1_partfun1(B,D) -> r1_partfun1(B,C)))))))) # label(t152_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1518 $T # label(t99_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1519 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> v1_funct_2(B,k1_relat_1(B),A) & m2_relset_1(B,k1_relat_1(B),A) & v1_funct_1(B)))) # label(t4_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1520 (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_1(D) & m2_relset_1(D,A,k1_tarski(B)) & v1_funct_2(D,A,k1_tarski(B)) -> C = D)))) # label(t66_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1521 (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 ((exists F (r2_hidden(F,C) & E = k1_funct_1(D,F) & r2_hidden(F,A))) -> r2_hidden(E,k9_relat_1(D,C))))))) # label(t43_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1522 (all A (v1_funct_1(A) & v1_relat_1(A) -> r1_tarski(k2_relat_1(k3_funct_3(A)),k1_zfmisc_1(k1_relat_1(A))))) # label(t25_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1523 (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]. 4.20/4.25 1524 (all A (v1_funct_1(A) & v1_relat_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]. 4.20/4.25 1525 $T # label(t67_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1526 (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_zfmisc_1(k1_relat_1(A),k1_relat_1(B)) = k1_relat_1(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)))) <-> C = k15_funct_3(A,B)))))))) # label(d9_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.25 1527 (all A all B (v1_relat_1(A) & v1_funct_1(B) & v1_relat_1(B) & v1_funct_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]. 4.20/4.25 1528 (all A all B all C (v1_relat_1(C) & v1_funct_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]. 4.20/4.25 1529 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & 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]. 4.20/4.26 1530 $T # label(t23_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1531 (all A all B all C (v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & v1_funct_1(C) & -v1_xboole_0(B) -> k2_funct_3(A,B,C) = k1_funct_3(C))) # label(redefinition_k2_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1532 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,k2_relat_1(k5_relat_1(B,C))) & v2_funct_1(C) -> r1_tarski(k10_relat_1(C,A),k2_relat_1(B))))))) # label(t4_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1533 (all A all B -(r2_hidden(B,f2_s1_funct_3) & (all C -p1_s1_funct_3(A,B,C)) & r2_hidden(A,f1_s1_funct_3))) & (all A all B all C all D (r2_hidden(A,f1_s1_funct_3) & r2_hidden(B,f2_s1_funct_3) & p1_s1_funct_3(A,B,C) & p1_s1_funct_3(A,B,D) -> D = C)) -> (exists 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))))) & v1_funct_1(A) & v1_relat_1(A))) # label(s1_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1534 (all A k12_funct_3(A) = k11_funct_3(A)) # label(redefinition_k12_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1535 $T # label(t55_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1536 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> k2_relat_1(k15_funct_3(A,B)) = k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B)))))) # label(t88_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1537 $T # label(t51_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1538 (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]. 4.20/4.26 1539 (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_2(E,A,C) & v1_funct_1(E) -> (all F (m2_relset_1(F,B,D) & v1_funct_2(F,B,D) & v1_funct_1(F) -> k16_funct_3(A,B,C,D,E,F) = k13_funct_3(k5_relat_1(k9_funct_3(A,B),E),k5_relat_1(k10_funct_3(A,B),F)))))))))) # label(t98_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1540 $T # label(t54_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1541 (all A all B (v1_relat_1(B) & v1_funct_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]. 4.20/4.26 1542 $T # label(t52_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1543 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k2_relat_1(k13_funct_3(A,B)),k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B))))))) # label(t71_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1544 (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(k10_relat_1(k1_funct_3(D),B),k1_zfmisc_1(A)))))) # label(t14_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1545 (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]. 4.20/4.26 1546 (all A all B (v1_funct_1(k9_funct_3(A,B)) & m2_relset_1(k9_funct_3(A,B),k2_zfmisc_1(A,B),A) & v1_funct_2(k9_funct_3(A,B),k2_zfmisc_1(A,B),A))) # label(dt_k9_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1547 (all A (v1_funct_1(k11_funct_3(A)) & v1_relat_1(k11_funct_3(A)))) # label(dt_k11_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1548 $T # label(t7_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1549 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> m2_relset_1(k6_funct_3(A,B),B,A) & v1_funct_2(k6_funct_3(A,B),B,A) & v1_funct_1(k6_funct_3(A,B)))) # label(dt_k6_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1550 (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(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]. 4.20/4.26 1551 (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]. 4.20/4.26 1552 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (A = k1_relat_1(B) & k1_relat_1(C) = A -> k1_relat_1(k13_funct_3(B,C)) = A))))) # label(t70_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1553 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> k15_funct_3(A,B) = k13_funct_3(k5_relat_1(k9_funct_3(k1_relat_1(A),k1_relat_1(B)),A),k5_relat_1(k10_funct_3(k1_relat_1(A),k1_relat_1(B)),B)))))) # label(t87_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1554 (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]. 4.20/4.26 1555 $T # label(t26_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1556 (all A all B all C (v1_funct_1(C) & v1_relat_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]. 4.20/4.26 1557 $T # label(t65_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1558 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(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]. 4.20/4.26 1559 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(k3_funct_3(B))) -> k1_funct_1(k3_funct_3(B),A) = k10_relat_1(B,A)))) # label(t24_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1560 $T # label(t63_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1561 (all A all B (v1_funct_1(k5_funct_3(A,B)) & v1_funct_2(k5_funct_3(A,B),B,k2_tarski(np__0,np__1)) & m2_relset_1(k5_funct_3(A,B),B,k2_tarski(np__0,np__1)))) # label(dt_k5_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1562 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (C = k7_funct_3(A,B) <-> (all D all E (r2_hidden(E,B) & r2_hidden(D,A) -> D = k1_funct_1(C,k4_tarski(D,E)))) & k2_zfmisc_1(A,B) = k1_relat_1(C)))) # label(d5_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1563 (all A all B k9_funct_3(A,B) = k7_funct_3(A,B)) # label(redefinition_k9_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1564 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (B = k1_relat_1(D) & r2_hidden(A,B) & B = k1_relat_1(C) -> 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]. 4.20/4.26 1565 (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]. 4.20/4.26 1566 (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]. 4.20/4.26 1567 (all A all B (v1_relat_1(k4_funct_3(A,B)) & v1_funct_1(k4_funct_3(A,B)))) # label(dt_k4_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1568 (all A all B k5_funct_3(A,B) = k4_funct_3(A,B)) # label(redefinition_k5_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1569 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,C) & m2_relset_1(E,A,C) -> -(-(D = k5_relat_1(k13_funct_3(D,E),k9_funct_3(B,C)) & k5_relat_1(k13_funct_3(D,E),k10_funct_3(B,C)) = E) & (k1_xboole_0 = C -> k1_xboole_0 = A) & (k1_xboole_0 = B -> A = k1_xboole_0)))))) # label(t81_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1570 (all A (v1_relat_1(A) & v1_funct_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]. 4.20/4.26 1571 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C (r1_tarski(C,k2_relat_1(A)) -> k1_funct_1(B,C) = k10_relat_1(A,C))) & k1_zfmisc_1(k2_relat_1(A)) = k1_relat_1(B) <-> k3_funct_3(A) = B))))) # label(d2_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1572 $T # label(t11_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1573 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (B = k1_funct_3(A) <-> k1_zfmisc_1(k1_relat_1(A)) = k1_relat_1(B) & (all C (r1_tarski(C,k1_relat_1(A)) -> k1_funct_1(B,C) = k9_relat_1(A,C)))))))) # label(d1_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1574 (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,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]. 4.20/4.26 1575 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k3_funct_3(A)) & v1_funct_1(k3_funct_3(A)))) # label(dt_k3_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1576 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (all F (m2_relset_1(F,A,C) & v1_funct_2(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) -> (k14_funct_3(A,B,C,D,F) = k14_funct_3(A,B,C,E,G) -> F = G & D = E))))))))))))) # label(t84_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1577 (all A all B (A != k1_xboole_0 -> k2_relat_1(k8_funct_3(A,B)) = B)) # label(t62_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1578 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k1_relat_1(D) = k2_zfmisc_1(A,B) & (all E all F (r2_hidden(E,A) & r2_hidden(F,B) -> k1_funct_1(D,k4_tarski(E,F)) = k1_funct_1(C,k4_tarski(E,F)))) & k1_relat_1(C) = k2_zfmisc_1(A,B) -> C = D))))) # label(t6_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1579 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (C = k4_funct_3(A,B) <-> B = k1_relat_1(C) & (all D (r2_hidden(D,B) -> (-r2_hidden(D,A) -> np__0 = k1_funct_1(C,D)) & (r2_hidden(D,A) -> k1_funct_1(C,D) = np__1)))))) # label(d3_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1580 (all A (v1_relat_1(A) & v1_funct_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]. 4.20/4.26 1581 (all A all B all C all D all E all F (m1_relset_1(F,B,D) & v1_funct_2(F,B,D) & v1_funct_1(F) & m1_relset_1(E,A,C) & v1_funct_2(E,A,C) & v1_funct_1(E) -> k16_funct_3(A,B,C,D,E,F) = k15_funct_3(E,F))) # label(redefinition_k16_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1582 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k3_tarski(k10_relat_1(k1_funct_3(B),A)),k10_relat_1(B,k3_tarski(A))))) # label(t18_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1583 (all A all B k10_funct_3(A,B) = k8_funct_3(A,B)) # label(redefinition_k10_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1584 $T # label(d4_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1585 (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]. 4.20/4.26 1586 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k10_relat_1(C,A),k2_relat_1(B)) & r1_tarski(A,k2_relat_1(C)) -> r1_tarski(A,k2_relat_1(k5_relat_1(B,C)))))))) # label(t5_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1587 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,k1_relat_1(k5_relat_1(B,C))) -> r1_tarski(k9_relat_1(B,A),k1_relat_1(C))))))) # label(t2_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1588 $T # label(t40_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1589 (all A (v1_funct_1(A) & v1_relat_1(A) -> k1_funct_1(k1_funct_3(A),k1_xboole_0) = k1_xboole_0)) # label(t9_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1590 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k1_relat_1(D) = k1_relat_1(C) & k13_funct_3(A,B) = k13_funct_3(D,C) & k1_relat_1(B) = k1_relat_1(A) -> D = A & B = C))))))))) # label(t74_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1591 $T # label(t64_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1592 (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]. 4.20/4.26 1593 (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]. 4.20/4.26 1594 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(B) = A & (all C (r2_hidden(C,A) -> k4_tarski(C,C) = k1_funct_1(B,C))) <-> B = k11_funct_3(A)))) # label(d7_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1595 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(D,A,B) & v1_funct_1(E) & m1_relset_1(E,A,C) & v1_funct_2(E,A,C) & m1_relset_1(D,A,B) & -v1_xboole_0(C) -> k13_funct_3(D,E) = k14_funct_3(A,B,C,D,E))) # label(redefinition_k14_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1596 (all A all B all C (k1_funct_1(k4_funct_3(B,C),A) = np__1 -> r2_hidden(A,B))) # label(t42_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1597 (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]. 4.20/4.26 1598 (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_xboole_0(k1_relat_1(A),k1_relat_1(B)) = k1_relat_1(C) & (all D (r2_hidden(D,k1_relat_1(C)) -> k4_tarski(k1_funct_1(A,D),k1_funct_1(B,D)) = k1_funct_1(C,D))) <-> k13_funct_3(A,B) = C))))))) # label(d8_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1599 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,k1_zfmisc_1(k1_relat_1(B))) -> k9_relat_1(B,k3_tarski(A)) = k3_tarski(k9_relat_1(k1_funct_3(B),A))))) # label(t16_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1600 (all A (v1_funct_1(A) & v1_relat_1(A) -> k1_relat_1(A) = k2_funct_2(k2_zfmisc_1(k1_relat_1(A),k2_relat_1(A)),k1_relat_1(A),k9_funct_3(k1_relat_1(A),k2_relat_1(A)),A))) # label(t100_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1601 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,C) & m2_relset_1(E,A,C) -> 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]. 4.20/4.26 1602 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k1_funct_3(A)) & m2_relset_1(k1_funct_3(A),k1_zfmisc_1(k1_relat_1(A)),k1_zfmisc_1(k2_relat_1(A))) & v1_funct_2(k1_funct_3(A),k1_zfmisc_1(k1_relat_1(A)),k1_zfmisc_1(k2_relat_1(A))))) # label(t21_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1603 (all A (v1_relat_1(A) & v1_funct_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]. 4.20/4.26 1604 (all A all B all C all D all E all F (v1_funct_1(E) & v1_funct_2(E,A,C) & m1_relset_1(F,B,D) & v1_funct_2(F,B,D) & v1_funct_1(F) & m1_relset_1(E,A,C) -> v1_funct_1(k16_funct_3(A,B,C,D,E,F)) & m2_relset_1(k16_funct_3(A,B,C,D,E,F),k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) & v1_funct_2(k16_funct_3(A,B,C,D,E,F),k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)))) # label(dt_k16_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1605 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k1_funct_3(A)) & v1_relat_1(k1_funct_3(A)))) # label(dt_k1_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1606 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_2(E,A,C) & m2_relset_1(E,A,C) & v1_funct_1(E) -> -((k1_xboole_0 = B -> k1_xboole_0 = A) & -(m2_relset_1(k13_funct_3(D,E),A,k2_zfmisc_1(B,C)) & v1_funct_2(k13_funct_3(D,E),A,k2_zfmisc_1(B,C)) & v1_funct_1(k13_funct_3(D,E))) & (C = k1_xboole_0 -> A = k1_xboole_0)))))) # label(t78_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1607 (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]. 4.20/4.26 1608 (all A all B (m2_relset_1(k10_funct_3(A,B),k2_zfmisc_1(A,B),B) & v1_funct_2(k10_funct_3(A,B),k2_zfmisc_1(A,B),B) & v1_funct_1(k10_funct_3(A,B)))) # label(dt_k10_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1609 (all A all B all C (r1_tarski(A,B) & r1_tarski(C,B) & k4_funct_3(C,B) = k4_funct_3(A,B) -> C = A)) # label(t47_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1610 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k10_relat_1(k1_funct_3(B),A),k1_zfmisc_1(k1_relat_1(B))))) # label(t13_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1611 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> (all F (v1_funct_2(F,A,C) & m2_relset_1(F,A,C) & v1_funct_1(F) -> (all G (v1_funct_2(G,A,C) & m2_relset_1(G,A,C) & v1_funct_1(G) -> (k13_funct_3(D,F) = k13_funct_3(E,G) -> B = k1_xboole_0 & k1_xboole_0 != A | A != k1_xboole_0 & C = k1_xboole_0 | F = G & E = D))))))))) # label(t83_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1612 $T # label(t44_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1613 (all A all B all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,C) & m2_relset_1(D,A,C) -> (r1_tarski(B,k1_zfmisc_1(A)) -> k3_tarski(k9_relat_1(k1_funct_3(D),B)) = k2_funct_2(A,C,D,k3_tarski(B))))))) # label(t17_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1614 (all A all B (v1_funct_1(B) & v1_relat_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]. 4.20/4.26 1615 $T # label(t50_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1616 (exists A (v1_relat_1(A) & v1_funct_1(A) & k1_relat_1(A) = k2_zfmisc_1(f1_s2_funct_3,f2_s2_funct_3) & (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))))) # label(s2_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1617 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(D,A,B) & v1_funct_1(E) & m1_relset_1(E,A,C) & v1_funct_2(E,A,C) & m1_relset_1(D,A,B) & -v1_xboole_0(C) -> v1_funct_2(k14_funct_3(A,B,C,D,E),A,k2_zfmisc_1(B,C)) & m2_relset_1(k14_funct_3(A,B,C,D,E),A,k2_zfmisc_1(B,C)) & v1_funct_1(k14_funct_3(A,B,C,D,E)))) # label(dt_k14_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1618 (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]. 4.20/4.26 1619 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k8_funct_3(A,B) = C <-> k2_zfmisc_1(A,B) = k1_relat_1(C) & (all D all E (r2_hidden(D,A) & r2_hidden(E,B) -> k1_funct_1(C,k4_tarski(D,E)) = E))))) # label(d6_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1620 (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]. 4.20/4.26 1621 (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) -> (all F (m2_relset_1(F,C,D) & v1_funct_2(F,C,D) & v1_funct_1(F) -> m2_relset_1(k15_funct_3(E,F),k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) & v1_funct_2(k15_funct_3(E,F),k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) & v1_funct_1(k15_funct_3(E,F)))))) # label(t95_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1622 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C all D (r2_hidden(k4_tarski(C,D),k2_zfmisc_1(k1_relat_1(A),k1_relat_1(B))) -> k4_tarski(k1_funct_1(A,C),k1_funct_1(B,D)) = k1_funct_1(k15_funct_3(A,B),k4_tarski(C,D)))))))) # label(t86_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1623 $T # label(t41_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1624 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(B) -> v1_funct_1(k13_funct_3(A,B)) & v1_relat_1(k13_funct_3(A,B)))) # label(dt_k13_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1625 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k1_relat_1(D) = k1_relat_1(C) & r1_tarski(k2_relat_1(C),A) & r1_tarski(k2_relat_1(D),B) -> k5_relat_1(k13_funct_3(C,D),k10_funct_3(A,B)) = D & k5_relat_1(k13_funct_3(C,D),k9_funct_3(A,B)) = C))))) # label(t72_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1626 (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]. 4.20/4.26 1627 (all A all B all C all D all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (all F (m2_relset_1(F,C,D) & v1_funct_2(F,C,D) & v1_funct_1(F) -> -((D = k1_xboole_0 -> k1_xboole_0 = C) & k13_funct_3(k5_relat_1(k9_funct_3(A,C),E),k5_relat_1(k10_funct_3(A,C),F)) != k16_funct_3(A,C,B,D,E,F) & (B = k1_xboole_0 -> A = k1_xboole_0)))))) # label(t97_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1628 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> k5_relat_1(C,k13_funct_3(A,B)) = k13_funct_3(k5_relat_1(C,A),k5_relat_1(C,B)))))))) # label(t75_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1629 (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]. 4.20/4.26 1630 (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]. 4.20/4.26 1631 $T # label(t85_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1632 (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]. 4.20/4.26 1633 (all A all B k15_funct_3(k6_relat_1(A),k6_relat_1(B)) = k6_relat_1(k2_zfmisc_1(A,B))) # label(t90_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1634 (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 -> A = k1_xboole_0) -> 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]. 4.20/4.26 1635 (all A all B all C (v1_funct_1(C) & m1_relset_1(C,A,B) & v1_funct_2(C,A,B) & -v1_xboole_0(B) -> 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]. 4.20/4.26 1636 (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]. 4.20/4.26 1637 (all A all B (v1_funct_2(B,A,k2_tarski(np__0,np__1)) & m2_relset_1(B,A,k2_tarski(np__0,np__1)) & v1_funct_1(B) -> B = k4_funct_3(k3_funct_2(A,k2_tarski(np__0,np__1),B,k1_tarski(np__1)),A))) # label(t49_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1638 (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]. 4.20/4.26 1639 (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]. 4.20/4.26 1640 (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]. 4.20/4.26 1641 (all A all B (v1_funct_1(B) & v1_relat_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]. 4.20/4.26 1642 (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]. 4.20/4.26 1643 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,C) & v1_funct_2(E,A,C) -> r1_tarski(k2_relat_1(k13_funct_3(D,E)),k2_zfmisc_1(B,C)))))) # label(t80_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1644 (all A all B (v1_funct_1(B) & v1_relat_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]. 4.20/4.26 1645 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) & r1_tarski(A,k1_zfmisc_1(k1_relat_1(B))) -> k9_relat_1(B,k3_tarski(A)) = k3_tarski(k10_relat_1(k3_funct_3(B),A))))) # label(t32_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1646 (all A all B (r1_tarski(A,B) -> k7_relat_1(k6_relat_1(B),A) = k6_relat_1(A))) # label(t1_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1647 $T # label(t57_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1648 (all A all B (v1_funct_1(B) & v1_relat_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]. 4.20/4.26 1649 $T # label(t46_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1650 (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]. 4.20/4.26 1651 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k9_relat_1(k3_funct_3(B),A),k1_zfmisc_1(k1_relat_1(B))))) # label(t27_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1652 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> k5_relat_1(k13_funct_3(B,D),k15_funct_3(A,C)) = k13_funct_3(k5_relat_1(B,A),k5_relat_1(D,C)))))))))) # label(t91_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1653 $T # label(t58_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1654 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> (all F (m2_relset_1(F,C,D) & v1_funct_2(F,C,D) & v1_funct_1(F) -> (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]. 4.20/4.26 1655 $T # label(t45_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1656 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k9_relat_1(B,A),k1_relat_1(C)) & r1_tarski(A,k1_relat_1(B)) -> r1_tarski(A,k1_relat_1(k5_relat_1(B,C)))))))) # label(t3_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1657 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k7_subset_1(A,B,C) = a_3_7_domain_1(A,B,C))))))) # label(t64_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1658 (all A all B (-v1_xboole_0(B) -> ((exists C (C = A & -$T & m1_subset_1(C,B))) <-> r2_hidden(A,a_1_1_domain_1(B))))) # label(fraenkel_a_1_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1659 (all A all B all C all D all E (-v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(E,k1_zfmisc_1(C)) & m1_subset_1(D,k1_zfmisc_1(B)) -> ((exists F exists G (m1_subset_1(F,B) & A = k1_domain_1(B,C,F,G) & r2_hidden(G,E) & r2_hidden(F,D) & 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]. 4.20/4.26 1660 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> m1_subset_1(a_4_2_domain_1(A,B,C,D),k1_zfmisc_1(k4_zfmisc_1(A,B,C,D))))))))))) # label(s4_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1661 $T # label(t6_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1662 (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)) -> k6_subset_1(A,B,C) = a_3_3_domain_1(A,B,C))))))) # label(t60_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1663 (all A all B all C all D all E all F all G (-v1_xboole_0(B) & m1_subset_1(E,k1_zfmisc_1(B)) & m1_subset_1(F,k1_zfmisc_1(C)) & m1_subset_1(G,k1_zfmisc_1(D)) & -v1_xboole_0(D) & -v1_xboole_0(C) -> ((exists H exists I exists J (m1_subset_1(J,D) & A = k4_domain_1(B,C,D,H,I,J) & r2_hidden(H,E) & r2_hidden(I,F) & r2_hidden(J,G) & m1_subset_1(I,C) & m1_subset_1(H,B))) <-> 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]. 4.20/4.26 1664 (all A (-v1_xboole_0(A) -> a_1_0_domain_1(A) = A)) # label(t48_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1665 (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)) -> (k7_mcart_1(A,B,C,E) = k7_mcart_1(A,B,C,D) & k6_mcart_1(A,B,C,E) = k6_mcart_1(A,B,C,D) & k5_mcart_1(A,B,C,D) = k5_mcart_1(A,B,C,E) -> E = D))))))))))) # label(t28_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1666 (all A all B all C all D (m1_subset_1(D,k2_zfmisc_1(A,k2_zfmisc_1(B,C))) & -v1_xboole_0(C) & -v1_xboole_0(B) & -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]. 4.20/4.26 1667 (all A all B all C all D all E (m1_subset_1(C,A) & m1_subset_1(E,A) & m1_subset_1(D,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]. 4.20/4.26 1668 (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_7_domain_1(B,C,D)) <-> (exists E (A = E & -(r2_hidden(E,C) <-> r2_hidden(E,D)) & m1_subset_1(E,B)))))) # label(fraenkel_a_3_7_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1669 (all A all B all C all D all E all F (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(E,A) & m1_subset_1(F,A) & m1_subset_1(D,A) & m1_subset_1(C,A) -> m1_subset_1(k10_domain_1(A,B,C,D,E,F),k1_zfmisc_1(A)))) # label(dt_k10_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1670 (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_3_domain_1(B,C,D)) <-> (exists E (m1_subset_1(E,B) & A = E & -r2_hidden(E,D) & r2_hidden(E,C)))))) # label(fraenkel_a_3_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1671 (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 (m1_subset_1(H,C) & (exists I (m1_subset_1(I,D) & (exists J (k4_mcart_1(G,H,I,J) = F & m1_subset_1(J,E))))))))) <-> r2_hidden(F,A))) <-> k4_zfmisc_1(B,C,D,E) = A))))))))))) # label(t33_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1672 (all A all B all C all D all E all F all G all H (-v1_xboole_0(D) & m1_subset_1(E,A) & m1_subset_1(G,C) & m1_subset_1(H,D) & m1_subset_1(F,B) & -v1_xboole_0(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k4_mcart_1(E,F,G,H) = k5_domain_1(A,B,C,D,E,F,G,H))) # label(redefinition_k5_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1673 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> a_3_1_domain_1(A,B,C) = k5_subset_1(A,B,C))))))) # label(t58_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1674 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(C,A) & m1_subset_1(D,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]. 4.20/4.26 1675 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k7_subset_1(A,B,C) = a_3_4_domain_1(A,B,C))))))) # label(t61_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1676 (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]. 4.20/4.26 1677 $T # label(t1_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1678 (all A (r2_hidden(A,a_0_2_domain_1) <-> (exists B exists C (f4_s9_domain_1(B,C) = A & p1_s9_domain_1(B,C) & m1_subset_1(C,f2_s9_domain_1) & m1_subset_1(B,f1_s9_domain_1))))) # label(fraenkel_a_0_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1679 $T # label(t21_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1680 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (r2_hidden(A,k4_zfmisc_1(B,C,D,E)) <-> (exists F (m1_subset_1(F,B) & (exists G ((exists H ((exists I (k4_mcart_1(F,G,H,I) = A & m1_subset_1(I,E))) & m1_subset_1(H,D))) & m1_subset_1(G,C)))))))))))))) # label(t31_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1681 (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)) -> ((exists E (m1_subset_1(E,B) & A = E & (r2_hidden(E,D) <-> -r2_hidden(E,C)))) <-> r2_hidden(A,a_3_5_domain_1(B,C,D))))) # label(fraenkel_a_3_5_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1682 (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(k17_domain_1(A,B,C,D),C))) # label(dt_k17_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1683 $T # label(t34_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1684 $T # label(t3_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1685 $T # label(t8_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1686 $T # label(t36_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1687 (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 ((exists I (m1_subset_1(I,D) & (exists J (k4_mcart_1(G,H,I,J) = F & m1_subset_1(J,E))))) & m1_subset_1(H,C))))))) -> k4_zfmisc_1(B,C,D,E) = A))))))))))) # label(t32_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1688 (all A (-v1_xboole_0(A) -> m1_subset_1(a_1_2_domain_1(A),k1_zfmisc_1(A)))) # label(s1_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1689 (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) -> k1_enumset1(B,C,D) = k8_domain_1(A,B,C,D))) # label(redefinition_k8_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1690 (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]. 4.20/4.26 1691 $T # label(t18_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1692 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> ((exists E ((exists F ((exists G (A = k3_mcart_1(E,F,G) & m1_subset_1(G,D))) & m1_subset_1(F,C))) & m1_subset_1(E,B))) <-> r2_hidden(A,k3_zfmisc_1(B,C,D))))))))) # label(t15_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1693 $T # label(t5_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1694 (all A all B all C (-v1_xboole_0(B) & m1_subset_1(C,k2_zfmisc_1(A,B)) & -v1_xboole_0(A) -> k2_mcart_1(C) = k3_domain_1(A,B,C))) # label(redefinition_k3_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1695 (all A (r2_hidden(A,a_0_1_domain_1) <-> (exists B (m1_subset_1(B,f1_s8_domain_1) & p1_s8_domain_1(B) & f3_s8_domain_1(B) = A)))) # label(fraenkel_a_0_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1696 $T # label(t13_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1697 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(D,k2_zfmisc_1(A,k2_zfmisc_1(B,C))) & -v1_xboole_0(C) & -v1_xboole_0(A) -> k16_domain_1(A,B,C,D) = k19_mcart_1(D))) # label(redefinition_k16_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1698 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (k3_zfmisc_1(B,C,D) = A <-> (all E ((exists F ((exists G ((exists H (m1_subset_1(H,D) & E = k3_mcart_1(F,G,H))) & m1_subset_1(G,C))) & m1_subset_1(F,B))) <-> r2_hidden(E,A)))))))))))) # label(t17_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1699 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_5_domain_1(B)) <-> (exists C (p1_s6_domain_1(C) & A = C & m1_subset_1(C,B)))))) # label(fraenkel_a_1_5_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1700 $T # label(t22_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1701 $T # label(t2_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1702 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) -> k1_tarski(B) = k6_domain_1(A,B))) # label(redefinition_k6_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1703 $T # label(t44_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1704 (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]. 4.20/4.26 1705 (all A all B all C all D all E all F all G (m1_subset_1(B,A) & m1_subset_1(D,A) & m1_subset_1(E,A) & m1_subset_1(G,A) & m1_subset_1(F,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k11_domain_1(A,B,C,D,E,F,G) = k4_enumset1(B,C,D,E,F,G))) # label(redefinition_k11_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1706 (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 (A = k1_domain_1(B,C,D,E) & p1_s2_domain_1(D,E) & m1_subset_1(E,C) & m1_subset_1(D,B)))))) # label(fraenkel_a_2_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.26 1707 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_2_domain_1(B)) <-> (exists C (p1_s1_domain_1(C) & A = C & m1_subset_1(C,B)))))) # label(fraenkel_a_1_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1708 (all A (r2_hidden(A,a_0_3_domain_1) <-> (exists B (m1_subset_1(B,f1_s10_domain_1) & p1_s10_domain_1(B) & p2_s10_domain_1(B) & A = B)))) # label(fraenkel_a_0_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1709 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(C,k1_zfmisc_1(B)) & -v1_xboole_0(B) -> ((exists E (E = A & r2_hidden(E,C) & r2_hidden(E,D) & m1_subset_1(E,B))) <-> r2_hidden(A,a_3_1_domain_1(B,C,D))))) # label(fraenkel_a_3_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1710 (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(I,A) & m1_subset_1(H,A) & m1_subset_1(G,A) & m1_subset_1(F,A) & m1_subset_1(D,A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> 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]. 4.20/4.27 1711 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> m1_subset_1(k7_domain_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k7_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1712 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(B)) & -v1_xboole_0(B) -> ((exists D (-r2_hidden(D,C) & D = A & m1_subset_1(D,B))) <-> r2_hidden(A,a_2_2_domain_1(B,C))))) # label(fraenkel_a_2_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1713 (all A all B all C all D all E all F (-v1_xboole_0(B) & m1_subset_1(D,A) & m1_subset_1(F,C) & m1_subset_1(E,B) & -v1_xboole_0(C) & -v1_xboole_0(A) -> k3_mcart_1(D,E,F) = k4_domain_1(A,B,C,D,E,F))) # label(redefinition_k4_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1714 (all A (-v1_xboole_0(A) -> a_1_1_domain_1(A) = k1_subset_1(A))) # label(t56_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1715 (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 -> A = F))))))) <-> A = k5_mcart_1(B,C,D,E)))))))))) # label(t24_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1716 (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) -> (F = k5_domain_1(B,C,D,E,G,H,I,J) -> H = A))))))))) <-> k9_mcart_1(B,C,D,E,F) = A))))))))))) # label(t41_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1717 $T # label(t14_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1718 (all A all B all C all D (m1_subset_1(B,A) & m1_subset_1(C,A) & m1_subset_1(D,A) & -v1_xboole_0(A) -> m1_subset_1(k8_domain_1(A,B,C,D),k1_zfmisc_1(A)))) # label(dt_k8_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1719 (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) -> k17_domain_1(A,B,C,D) = k20_mcart_1(D))) # label(redefinition_k17_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1720 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (m1_subset_1(F,k4_zfmisc_1(B,C,D,E)) -> (k11_mcart_1(B,C,D,E,F) = A <-> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (all I (m1_subset_1(I,D) -> (all J (m1_subset_1(J,E) -> (F = k5_domain_1(B,C,D,E,G,H,I,J) -> A = J)))))))))))))))))))) # label(t43_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1721 $T # label(t11_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1722 (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 ((exists H (E = k3_mcart_1(F,G,H) & m1_subset_1(H,D))) & m1_subset_1(G,C))))) <-> r2_hidden(E,A))) -> A = k3_zfmisc_1(B,C,D)))))))))) # label(t16_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1723 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(B)) & -v1_xboole_0(B) -> (r2_hidden(A,a_2_1_domain_1(B,C)) <-> (exists D (m1_subset_1(D,B) & r2_hidden(D,C) & A = D))))) # label(fraenkel_a_2_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1724 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,k2_zfmisc_1(A,B)) & -v1_xboole_0(B) -> m1_subset_1(k3_domain_1(A,B,C),B))) # label(dt_k3_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1725 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> -((all D (m1_subset_1(D,B) -> (all E (m1_subset_1(E,C) -> k4_tarski(D,E) != A)))) & r2_hidden(A,k2_zfmisc_1(B,C))))))) # label(t9_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1726 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) & -v1_xboole_0(A) -> m1_subset_1(k14_domain_1(A,B,C,D),A))) # label(dt_k14_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1727 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> (all D (m1_subset_1(D,k2_zfmisc_1(A,B)) -> (k1_mcart_1(C) = k1_mcart_1(D) & k2_mcart_1(D) = k2_mcart_1(C) -> D = C))))))))) # label(t12_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1728 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> m1_subset_1(a_2_3_domain_1(A,B),k1_zfmisc_1(k2_zfmisc_1(A,B))))))) # label(s2_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1729 (all A all B all C all D all E all F all G all H (-v1_xboole_0(A) & m1_subset_1(G,A) & m1_subset_1(H,A) & m1_subset_1(F,A) & m1_subset_1(E,A) & m1_subset_1(D,A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> k12_domain_1(A,B,C,D,E,F,G,H) = k5_enumset1(B,C,D,E,F,G,H))) # label(redefinition_k12_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1730 (all A all B all C (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(C,k2_zfmisc_1(A,B)) -> k1_mcart_1(C) = k2_domain_1(A,B,C))) # label(redefinition_k2_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1731 (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_2_domain_1(B,C,D)) <-> (exists E ((r2_hidden(E,D) | r2_hidden(E,C)) & A = E & m1_subset_1(E,B)))))) # label(fraenkel_a_3_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1732 $T # label(t37_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1733 $T # label(t39_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1734 $T # label(t23_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1735 (all A all B all C (-v1_xboole_0(C) & -v1_xboole_0(B) -> ((exists D exists E (m1_subset_1(D,B) & m1_subset_1(E,C) & A = k1_domain_1(B,C,D,E))) <-> r2_hidden(A,a_2_0_domain_1(B,C))))) # label(fraenkel_a_2_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1736 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> a_3_0_domain_1(A,B,C) = k3_zfmisc_1(A,B,C))))))) # label(t50_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1737 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_3_domain_1(B)) <-> (exists C (C = A & p1_s5_domain_1(C) & m1_subset_1(C,B)))))) # label(fraenkel_a_1_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1738 (all A all B all C all D all E all F all G all H all I (-v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(F,k1_zfmisc_1(B)) & m1_subset_1(I,k1_zfmisc_1(E)) & m1_subset_1(H,k1_zfmisc_1(D)) & m1_subset_1(G,k1_zfmisc_1(C)) & -v1_xboole_0(E) & -v1_xboole_0(D) -> (r2_hidden(A,a_8_0_domain_1(B,C,D,E,F,G,H,I)) <-> (exists J exists K exists L exists M (m1_subset_1(J,B) & k5_domain_1(B,C,D,E,J,K,L,M) = A & r2_hidden(M,I) & r2_hidden(L,H) & r2_hidden(K,G) & r2_hidden(J,F) & m1_subset_1(M,E) & m1_subset_1(L,D) & m1_subset_1(K,C)))))) # label(fraenkel_a_8_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1739 (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]. 4.20/4.27 1740 (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,C) <-> -r2_hidden(E,D)) & A = E))))) # label(fraenkel_a_3_6_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1741 $T # label(t7_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1742 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> k2_zfmisc_1(A,B) = a_2_0_domain_1(A,B))))) # label(t49_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1743 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> a_3_5_domain_1(A,B,C) = k7_subset_1(A,B,C))))))) # label(t62_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1744 (all A all B all C (m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k7_domain_1(A,B,C) = k2_tarski(B,C))) # label(redefinition_k7_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1745 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) -> k15_domain_1(A,B,C,D) = k18_mcart_1(D))) # label(redefinition_k15_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1746 (all A all B all C all D (m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) & -v1_xboole_0(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> m1_subset_1(k15_domain_1(A,B,C,D),B))) # label(dt_k15_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1747 (all A all B all C all D all E all F (m1_subset_1(B,A) & m1_subset_1(D,A) & m1_subset_1(F,A) & m1_subset_1(E,A) & m1_subset_1(C,A) & -v1_xboole_0(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]. 4.20/4.27 1748 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,k3_zfmisc_1(B,C,D)) -> ((all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,C) -> (all H (m1_subset_1(H,D) -> (E = k4_domain_1(B,C,D,F,G,H) -> A = H))))))) <-> k7_mcart_1(B,C,D,E) = A))))))))) # label(t26_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1749 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (p1_s5_domain_1(B) -> p2_s5_domain_1(B)))) -> r1_tarski(a_1_3_domain_1(A),a_1_4_domain_1(A))))) # label(s5_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1750 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(D,B) & m1_subset_1(C,A) -> k1_domain_1(A,B,C,D) = k4_tarski(C,D))) # label(redefinition_k1_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1751 (all A all B all C all D all E (-v1_xboole_0(B) & -v1_xboole_0(C) & -v1_xboole_0(E) & -v1_xboole_0(D) -> ((exists F exists G exists H exists I (m1_subset_1(G,C) & m1_subset_1(H,D) & A = k5_domain_1(B,C,D,E,F,G,H,I) & p1_s4_domain_1(F,G,H,I) & m1_subset_1(I,E) & m1_subset_1(F,B))) <-> r2_hidden(A,a_4_2_domain_1(B,C,D,E))))) # label(fraenkel_a_4_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1752 (all A all B all C all D all E all F all G all H (-v1_xboole_0(A) & -v1_xboole_0(C) & m1_subset_1(H,D) & m1_subset_1(G,C) & m1_subset_1(F,B) & m1_subset_1(E,A) & -v1_xboole_0(D) & -v1_xboole_0(B) -> m1_subset_1(k5_domain_1(A,B,C,D,E,F,G,H),k4_zfmisc_1(A,B,C,D)))) # label(dt_k5_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1753 (all A all B (-v1_xboole_0(B) -> ((exists C (m1_subset_1(C,B) & p2_s5_domain_1(C) & C = A)) <-> r2_hidden(A,a_1_4_domain_1(B))))) # label(fraenkel_a_1_4_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1754 (all A (r2_hidden(A,a_0_4_domain_1) <-> (exists B (m1_subset_1(B,f1_s10_domain_1) & A = B & p1_s10_domain_1(B))))) # label(fraenkel_a_0_4_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1755 $T # label(t29_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1756 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> (k8_mcart_1(A,B,C,D,E) = k8_mcart_1(A,B,C,D,F) & k10_mcart_1(A,B,C,D,F) = k10_mcart_1(A,B,C,D,E) & k11_mcart_1(A,B,C,D,E) = k11_mcart_1(A,B,C,D,F) & k9_mcart_1(A,B,C,D,E) = k9_mcart_1(A,B,C,D,F) -> F = E))))))))))))) # label(t45_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1757 (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]. 4.20/4.27 1758 $T # label(t4_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1759 $T # label(t20_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1760 (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(H,A) & m1_subset_1(F,A) & m1_subset_1(D,A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> m1_subset_1(k12_domain_1(A,B,C,D,E,F,G,H),k1_zfmisc_1(A)))) # label(dt_k12_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1761 (all A (r2_hidden(A,a_0_5_domain_1) <-> (exists B (m1_subset_1(B,f1_s10_domain_1) & p2_s10_domain_1(B) & B = A)))) # label(fraenkel_a_0_5_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1762 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> k4_zfmisc_1(A,B,C,D) = a_4_0_domain_1(A,B,C,D))))))))) # label(t51_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1763 (all A all B all C all D all E (m1_subset_1(B,A) & m1_subset_1(D,A) & m1_subset_1(E,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> m1_subset_1(k9_domain_1(A,B,C,D,E),k1_zfmisc_1(A)))) # label(dt_k9_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1764 $T # label(t46_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1765 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k7_domain_1(A,B,C) = k7_domain_1(A,C,B))) # label(commutativity_k7_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1766 (all A all B all C all D all E (-v1_xboole_0(C) & -v1_xboole_0(E) & -v1_xboole_0(D) & -v1_xboole_0(B) -> (r2_hidden(A,a_4_0_domain_1(B,C,D,E)) <-> (exists F exists G exists H exists I (m1_subset_1(F,B) & m1_subset_1(G,C) & m1_subset_1(I,E) & k5_domain_1(B,C,D,E,F,G,H,I) = A & m1_subset_1(H,D)))))) # label(fraenkel_a_4_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1767 $T # label(t38_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1768 (all A all B (-v1_xboole_0(B) -> ((exists C (m1_subset_1(C,B) & C = A)) <-> r2_hidden(A,a_1_0_domain_1(B))))) # label(fraenkel_a_1_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1769 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (p2_s6_domain_1(B) <-> p1_s6_domain_1(B)))) -> a_1_6_domain_1(A) = a_1_5_domain_1(A)))) # label(s6_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1770 $T # label(t35_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1771 $T # label(t19_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1772 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (m1_subset_1(F,k4_zfmisc_1(B,C,D,E)) -> (k8_mcart_1(B,C,D,E,F) = A <-> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (all I (m1_subset_1(I,D) -> (all J (m1_subset_1(J,E) -> (F = k5_domain_1(B,C,D,E,G,H,I,J) -> G = A)))))))))))))))))))) # label(t40_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1773 (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) -> G = A)))))))))))))))) # label(t25_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1774 $T # label(t30_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1775 (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 -> I = A))))))))) <-> k10_mcart_1(B,C,D,E,F) = A))))))))))) # label(t42_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1776 (all A all B all C all D all E all F all G all H all I (-v1_xboole_0(A) & m1_subset_1(E,A) & m1_subset_1(G,A) & m1_subset_1(I,A) & m1_subset_1(H,A) & m1_subset_1(F,A) & m1_subset_1(D,A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> m1_subset_1(k13_domain_1(A,B,C,D,E,F,G,H,I),k1_zfmisc_1(A)))) # label(dt_k13_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1777 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (all E (m1_subset_1(E,k1_zfmisc_1(B)) -> (all F (m1_subset_1(F,k1_zfmisc_1(C)) -> a_6_0_domain_1(A,B,C,D,E,F) = k13_mcart_1(A,B,C,D,E,F))))))))))))) # label(t54_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1778 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(C) & -v1_xboole_0(D) -> ((exists E exists F exists G (m1_subset_1(F,C) & m1_subset_1(G,D) & p1_s3_domain_1(E,F,G) & A = k4_domain_1(B,C,D,E,F,G) & m1_subset_1(E,B))) <-> r2_hidden(A,a_3_8_domain_1(B,C,D))))) # label(fraenkel_a_3_8_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1779 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> a_3_6_domain_1(A,B,C) = k7_subset_1(A,B,C))))))) # label(t63_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1780 $T # label(t10_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1781 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> m1_subset_1(a_3_8_domain_1(A,B,C),k1_zfmisc_1(k3_zfmisc_1(A,B,C))))))))) # label(s3_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1782 (all A all B all C all D (-v1_xboole_0(D) & -v1_xboole_0(C) & -v1_xboole_0(B) -> (r2_hidden(A,a_3_0_domain_1(B,C,D)) <-> (exists E exists F exists G (m1_subset_1(E,B) & m1_subset_1(F,C) & m1_subset_1(G,D) & k4_domain_1(B,C,D,E,F,G) = A))))) # label(fraenkel_a_3_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1783 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (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)) -> a_8_0_domain_1(A,B,C,D,E,F,G,H) = k14_mcart_1(A,B,C,D,E,F,G,H))))))))))))))))) # label(t55_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1784 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> B = a_2_1_domain_1(A,B))))) # label(t52_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1785 (all A all B all C all D all E all F (-v1_xboole_0(C) & m1_subset_1(D,A) & m1_subset_1(E,B) & m1_subset_1(F,C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> m1_subset_1(k4_domain_1(A,B,C,D,E,F),k3_zfmisc_1(A,B,C)))) # label(dt_k4_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1786 $T # label(t27_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1787 (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_4_domain_1(B,C,D)) <-> (exists E (m1_subset_1(E,B) & A = E & (r2_hidden(E,D) & -r2_hidden(E,C) | -r2_hidden(E,D) & r2_hidden(E,C))))))) # label(fraenkel_a_3_4_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1788 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) -> k17_mcart_1(D) = k14_domain_1(A,B,C,D))) # label(redefinition_k14_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1789 $T # label(t47_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1790 (all A all B all C all D all E all F all G (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & m1_subset_1(E,A) & m1_subset_1(G,A) & m1_subset_1(F,A) & m1_subset_1(D,A) -> m1_subset_1(k11_domain_1(A,B,C,D,E,F,G),k1_zfmisc_1(A)))) # label(dt_k11_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1791 (all A all B (-v1_xboole_0(B) -> ((exists C (C = A & p2_s6_domain_1(C) & m1_subset_1(C,B))) <-> r2_hidden(A,a_1_6_domain_1(B))))) # label(fraenkel_a_1_6_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1792 (all A (r2_hidden(A,a_0_0_domain_1) <-> (exists B (p1_s7_domain_1(B) & B = A & m1_subset_1(B,f1_s7_domain_1))))) # label(fraenkel_a_0_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1793 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k1_funcop_1(A)) & v1_relat_1(k1_funcop_1(A)))) # label(dt_k1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1794 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v1_funcop_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))))))) # label(d6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1795 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C -(k1_xboole_0 = k1_relat_1(k5_relat_1(k2_funcop_1(B,C),A)) & r2_hidden(C,k1_relat_1(A)) & B != k1_xboole_0)))) # label(t24_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1796 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) -> v1_relat_1(k1_funct_1(A,B)) & v1_funct_1(k1_funct_1(A,B)))) # label(fc7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1797 $T # label(dt_k3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1798 (all A all B all C (r2_hidden(B,C) -> A = k10_relat_1(k2_funcop_1(A,B),C))) # label(t20_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1799 (all A all B all C (v1_funct_1(A) & v1_relat_1(C) & v1_funct_1(C) & v1_relat_1(A) -> v1_relat_1(k5_funcop_1(A,B,C)) & v1_funct_1(k5_funcop_1(A,B,C)))) # label(fc6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1800 (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) -> k7_funcop_1(B,A,C,k7_funcop_1(B,A,C,D,E),F) = k7_funcop_1(B,A,C,D,k2_binop_1(B,B,B,C,E,F))))))))))))))) # label(t78_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1801 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D k5_relat_1(k6_partfun1(B),k5_funcop_1(C,D,A)) = k5_funcop_1(C,D,k7_relat_1(A,B))))))) # label(t46_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1802 (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) & v1_funct_2(D,B,A) & m2_relset_1(D,B,A) -> (all E (v1_funct_1(E) & m2_relset_1(E,B,A) & v1_funct_2(E,B,A) -> (all F (m1_subset_1(F,A) -> ((all G (m1_subset_1(G,B) -> k2_binop_1(A,A,A,C,k8_funct_2(B,A,E,G),F) = k8_funct_2(B,A,D,G))) -> D = k7_funcop_1(A,B,C,E,F)))))))))))))) # label(t61_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1803 (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 all E (v1_funct_1(E) & v1_relat_1(E) -> (k7_relat_1(B,D) = k7_relat_1(A,D) -> k7_relat_1(k3_funcop_1(E,A,C),D) = k7_relat_1(k3_funcop_1(E,B,C),D)))))))))) # label(t29_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1804 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_1(C) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(E,B,A) & m1_relset_1(E,B,A) & v1_funct_1(E) & m1_subset_1(D,A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & -v1_xboole_0(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]. 4.20/4.27 1805 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (v2_binop_1(C,B) -> k8_funcop_1(B,A,C,E,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]. 4.20/4.27 1806 (all A all B (v1_xboole_0(B) -> v1_xboole_0(k2_funcop_1(B,A)) & v2_funct_1(k2_funcop_1(B,A)) & v1_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]. 4.20/4.27 1807 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_1(D) & v1_funct_2(D,B,A) & m2_relset_1(D,B,A) -> (all E (m1_subset_1(E,B) -> (v3_binop_1(C,A) -> k8_funct_2(B,A,k7_funcop_1(A,B,C,D,k8_funct_2(B,A,D,E)),E) = k8_funct_2(B,A,D,E)))))))))))) # label(t83_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1808 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(B) = k1_xboole_0 & k1_xboole_0 = k1_relat_1(A) -> B = A))))) # label(t4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1809 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C k2_funcop_1(k10_relat_1(A,B),C) = k5_relat_1(A,k2_funcop_1(B,C))))) # label(t25_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1810 $T # label(t50_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1811 (all A all B all C all D (-v1_xboole_0(B) & v1_funct_1(D) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & -v1_xboole_0(C) & -v1_xboole_0(A) -> v1_funct_2(k10_funcop_1(A,B,C,D),A,k2_zfmisc_1(C,B)) & m2_relset_1(k10_funcop_1(A,B,C,D),A,k2_zfmisc_1(C,B)) & v1_funct_1(k10_funcop_1(A,B,C,D)))) # label(dt_k10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1812 (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) -> k3_funcop_1(k5_relat_1(D,A),B,C) = k5_relat_1(k3_funcop_1(D,B,C),A))))))))) # label(t32_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1813 (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 k5_relat_1(k4_funcop_1(C,B,D),A) = k4_funcop_1(k5_relat_1(C,A),B,D)))))))) # label(t38_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1814 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B ((all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(A,C) = B)) -> A = k2_funcop_1(k1_relat_1(A),B))))) # label(t17_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1815 (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 (m1_subset_1(E,B) -> k7_funct_2(A,B,B,D,k7_funcop_1(B,B,C,k6_partfun1(B),E)) = k7_funcop_1(B,A,C,D,E))))))))))) # label(t63_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1816 (all A all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,B) -> v1_funct_1(k2_funcop_1(A,C)) & m2_relset_1(k2_funcop_1(A,C),A,B) & v1_funct_2(k2_funcop_1(A,C),A,B))))) # label(t58_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1817 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (v1_funct_1(C) & v1_relat_1(C) -> k5_relat_1(k13_funct_3(k2_funcop_1(k1_relat_1(C),B),C),A) = k5_funcop_1(A,B,C))))) # label(d5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1818 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C k13_funct_3(A,k7_relat_1(B,C)) = k7_relat_1(k13_funct_3(A,B),C)))))) # label(t11_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1819 (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_subset_1(E,A) & m1_relset_1(D,B,A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k4_funcop_1(C,D,E) = k7_funcop_1(A,B,C,D,E))) # label(redefinition_k7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1820 (all A (v1_relat_1(A) -> (all B all C (k2_zfmisc_1(B,C) = A -> k1_xboole_0 = B | B = k1_relat_1(A) & C = k2_relat_1(A) | k1_xboole_0 = C)))) # label(t1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1821 (all A all B all C k1_funcop_1(k2_funcop_1(A,k4_tarski(B,C))) = k2_funcop_1(A,k4_tarski(C,B))) # label(t26_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1822 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> k8_funct_2(A,A,k7_funcop_1(A,A,B,k6_partfun1(A),C),C) = k2_binop_1(A,A,A,B,C,C))))))) # label(t64_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1823 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D all E (v1_relat_1(E) & v1_funct_1(E) -> (k7_relat_1(A,D) = k7_relat_1(B,D) -> k7_relat_1(k3_funcop_1(E,C,A),D) = k7_relat_1(k3_funcop_1(E,C,B),D)))))))))) # label(t30_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1824 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & -v1_xboole_0(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k10_funcop_1(A,B,C,D) = k1_funcop_1(D))) # label(redefinition_k10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1825 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D k5_relat_1(k6_partfun1(B),k4_funcop_1(C,A,D)) = k4_funcop_1(C,k7_relat_1(A,B),D)))))) # label(t39_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1826 (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 (m1_subset_1(E,B) -> (v1_binop_1(C,B) -> k7_funcop_1(B,A,C,D,E) = k8_funcop_1(B,A,C,E,D)))))))))))) # label(t79_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1827 (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) -> (all E (m1_subset_1(E,B) -> (v3_binop_1(C,A) -> k8_funct_2(B,A,D,E) = k8_funct_2(B,A,k8_funcop_1(A,B,C,k8_funct_2(B,A,D,E),D),E)))))))))))) # label(t82_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1828 (exists A (v1_relat_1(A) & v1_funcop_1(A) & v1_funct_1(A))) # label(rc1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1829 (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_funct_1(D) & v1_relat_1(D) -> (k1_relat_1(D) = k1_relat_1(k3_funcop_1(C,A,B)) & (all E (r2_hidden(E,k1_relat_1(k3_funcop_1(C,A,B))) -> k1_binop_1(C,k1_funct_1(A,E),k1_funct_1(B,E)) = k1_funct_1(D,E))) -> D = k3_funcop_1(C,A,B)))))))))) # label(t27_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1830 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_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]. 4.20/4.27 1831 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (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]. 4.20/4.27 1832 (all A k1_funcop_1(k12_funct_3(A)) = k12_funct_3(A)) # label(t9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1833 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B k7_relat_1(k1_funcop_1(A),B) = k1_funcop_1(k7_relat_1(A,B))))) # label(t7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1834 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (k1_tarski(B) = k2_relat_1(A) -> k2_funcop_1(k1_relat_1(A),B) = A)))) # label(t15_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1835 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D k5_relat_1(B,k4_funcop_1(C,A,D)) = k4_funcop_1(C,k5_relat_1(B,A),D)))))))) # label(t37_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1836 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (all D (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]. 4.20/4.27 1837 $T # label(dt_k5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1838 (all A all B all C all D all E (-v1_xboole_0(A) & v1_funct_1(C) & 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(D,B,A) & v1_funct_2(D,B,A) & v1_funct_1(D) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & -v1_xboole_0(B) -> k3_funcop_1(C,D,E) = k6_funcop_1(A,B,C,D,E))) # label(redefinition_k6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1839 (all A all B all C (r2_hidden(B,A) -> k1_funct_1(k2_funcop_1(A,C),B) = C)) # label(t13_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1840 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (all F (v1_funct_2(F,A,B) & m2_relset_1(F,A,B) & v1_funct_1(F) -> (v2_binop_1(C,B) -> k6_funcop_1(B,A,C,k6_funcop_1(B,A,C,D,E),F) = k6_funcop_1(B,A,C,D,k6_funcop_1(B,A,C,E,F))))))))))))))) # label(t76_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1841 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_2(E,B,B) & m2_relset_1(E,B,B) & v1_funct_1(E) -> k6_funcop_1(B,A,C,k7_funct_2(A,B,B,D,E),D) = k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,E,k6_partfun1(B))))))))))))) # label(t52_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1842 (all A all B (v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)))) # label(fc1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1843 (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]. 4.20/4.27 1844 $T # label(t8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1845 (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_funct_1(D) & v1_relat_1(D) -> (all E (k7_relat_1(A,C) = k7_relat_1(B,C) -> k7_relat_1(k5_funcop_1(D,E,A),C) = k7_relat_1(k5_funcop_1(D,E,B),C))))))))) # label(t43_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1846 $T # label(t68_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1847 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & m2_relset_1(D,A,k2_zfmisc_1(B,C)) -> (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]. 4.20/4.27 1848 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C all D (r2_hidden(C,k1_relat_1(k4_funcop_1(B,A,D))) -> k1_binop_1(B,k1_funct_1(A,C),D) = k1_funct_1(k4_funcop_1(B,A,D),C))))))) # label(t35_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1849 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C k13_funct_3(k7_relat_1(A,C),B) = k7_relat_1(k13_funct_3(A,B),C)))))) # label(t10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1850 (all A all B all C all D (-v1_xboole_0(B) & v1_funct_1(D) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & -v1_xboole_0(C) & -v1_xboole_0(A) -> k9_funcop_1(A,B,C,D) = k2_relat_1(D))) # label(redefinition_k9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1851 $T # label(dt_k2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1852 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (v2_binop_1(C,B) -> k8_funcop_1(B,A,C,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]. 4.20/4.27 1853 (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_tarski(k2_zfmisc_1(k2_relat_1(B),k2_relat_1(C)),k1_relat_1(A)) -> k3_xboole_0(k1_relat_1(B),k1_relat_1(C)) = k1_relat_1(k3_funcop_1(A,B,C))))))))) # label(t84_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1854 (all A all B (v1_funcop_1(A) & v1_funct_1(B) & v1_relat_1(B) & v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k5_relat_1(B,A)) & v1_funcop_1(k5_relat_1(B,A)) & v1_funct_1(k5_relat_1(B,A)))) # label(fc8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1855 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C k4_funcop_1(A,B,C) = k5_relat_1(k13_funct_3(B,k2_funcop_1(k1_relat_1(B),C)),A)))))) # label(d4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1856 $T # label(dt_k4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1857 $T # label(t62_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1858 (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,k6_funcop_1(A,A,B,k6_partfun1(A),k6_partfun1(A)),C))))))) # label(t56_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1859 (all A (v2_funct_1(k2_funcop_1(k1_xboole_0,A)) & v1_funct_1(k2_funcop_1(k1_xboole_0,A)) & v1_relat_1(k2_funcop_1(k1_xboole_0,A)) & v1_xboole_0(k2_funcop_1(k1_xboole_0,A)))) # label(fc2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.27 1860 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (all E (m1_subset_1(E,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]. 4.20/4.28 1861 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (v3_binop_1(C,B) -> k6_funcop_1(B,A,C,D,D) = D))))))))) # label(t81_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1862 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(A) = k1_relat_1(B) -> k1_relat_1(k5_relat_1(C,A)) = k1_relat_1(k5_relat_1(C,B))))))))) # label(t3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1863 (all A all B (-v1_xboole_0(B) -> v1_relat_1(k2_funcop_1(A,B)) & v2_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)))) # label(fc9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1864 (all A all B all C all D all E (-v1_xboole_0(A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & v1_funct_2(D,B,A) & m1_relset_1(D,B,A) & v1_funct_2(E,B,A) & m1_relset_1(E,B,A) & v1_funct_1(E) & v1_funct_1(C) & -v1_xboole_0(B) -> 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]. 4.20/4.28 1865 (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,D,k7_funct_2(A,B,B,D,E)) = k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,k6_partfun1(B),E)))))))))))) # label(t51_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1866 (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 (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> (all F (v1_funct_1(F) & m2_relset_1(F,A,B) & 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]. 4.20/4.28 1867 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(C) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_1(D) & -v1_xboole_0(A) -> D = k10_funcop_1(A,B,C,k10_funcop_1(A,B,C,D)))) # label(involutiveness_k10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1868 $T # label(t5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1869 (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) -> k5_relat_1(C,k3_funcop_1(D,A,B)) = k3_funcop_1(D,k5_relat_1(C,A),k5_relat_1(C,B)))))))))) # label(t31_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1870 (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_2(D,A,A) & v1_funct_1(D) -> k8_funct_2(A,A,k6_funcop_1(A,A,B,D,k6_partfun1(A)),C) = k2_binop_1(A,A,A,B,k8_funct_2(A,A,D,C),C))))))))) # label(t55_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1871 (all A all B (r1_tarski(k2_relat_1(k2_funcop_1(A,B)),k1_tarski(B)) & k1_relat_1(k2_funcop_1(A,B)) = A)) # label(t19_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1872 (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(A,C) = k7_relat_1(B,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]. 4.20/4.28 1873 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> k6_funcop_1(B,A,C,D,D) = k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,k6_partfun1(B),k6_partfun1(B))))))))))) # label(t53_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1874 (all A (k2_relat_1(k2_funcop_1(k1_xboole_0,A)) = k1_xboole_0 & k1_relat_1(k2_funcop_1(k1_xboole_0,A)) = k1_xboole_0)) # label(t16_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1875 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D 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]. 4.20/4.28 1876 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (all F (m1_subset_1(F,B) -> (v2_binop_1(C,B) -> k6_funcop_1(B,A,C,D,k8_funcop_1(B,A,C,F,E)) = k6_funcop_1(B,A,C,k7_funcop_1(B,A,C,D,F),E)))))))))))))) # label(t75_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1877 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D k5_funcop_1(k5_relat_1(C,A),D,B) = k5_relat_1(k5_funcop_1(C,D,B),A)))))))) # label(t45_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1878 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,F),E) = k8_funct_2(B,A,k7_funcop_1(A,B,C,D,E),F))))))))))))) # label(t60_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1879 (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]. 4.20/4.28 1880 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (r2_hidden(D,k1_relat_1(k3_funcop_1(C,A,B))) -> k1_funct_1(k3_funcop_1(C,A,B),D) = k1_binop_1(C,k1_funct_1(A,D),k1_funct_1(B,D)))))))))) # label(t28_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1881 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> k8_funct_2(A,A,k8_funcop_1(A,A,B,C,k6_partfun1(A)),C) = k2_binop_1(A,A,A,B,C,C))))))) # label(t70_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1882 (all A all B all C (-r2_hidden(B,C) -> k10_relat_1(k2_funcop_1(A,B),C) = k1_xboole_0)) # label(t22_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1883 $T # label(t12_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1884 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (r2_hidden(C,k1_relat_1(A)) -> k5_relat_1(k2_funcop_1(B,C),A) = k2_funcop_1(B,k1_funct_1(A,C)))))) # label(t23_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1885 (all A all B all C all D all E (-v1_xboole_0(A) & v1_funct_1(D) & v1_funct_2(D,B,A) & m1_subset_1(E,A) & m1_relset_1(D,B,A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & -v1_xboole_0(B) -> v1_funct_2(k7_funcop_1(A,B,C,D,E),B,A) & m2_relset_1(k7_funcop_1(A,B,C,D,E),B,A) & v1_funct_1(k7_funcop_1(A,B,C,D,E)))) # label(dt_k7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1886 (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]. 4.20/4.28 1887 (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]. 4.20/4.28 1888 (all A all B all C (v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(B) & v1_relat_1(A) -> 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]. 4.20/4.28 1889 (all A all B all C (r2_hidden(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(t57_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1890 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_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]. 4.20/4.28 1891 (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_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(E) & m1_relset_1(E,B,A) & v1_funct_2(E,B,A) & m1_subset_1(D,A) & v1_funct_1(C) & -v1_xboole_0(A) -> m2_relset_1(k8_funcop_1(A,B,C,D,E),B,A) & v1_funct_2(k8_funcop_1(A,B,C,D,E),B,A) & v1_funct_1(k8_funcop_1(A,B,C,D,E)))) # label(dt_k8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1892 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> v1_funct_1(k3_funcop_1(C,D,E)) & v1_funct_2(k3_funcop_1(C,D,E),A,B) & m2_relset_1(k3_funcop_1(C,D,E),A,B))))))))))) # label(t47_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1893 (all A (v1_funct_1(A) & v1_relat_1(A) -> A = k1_funcop_1(k1_funcop_1(A)))) # label(involutiveness_k1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1894 (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) -> k3_funcop_1(A,B,C) = k5_relat_1(k13_funct_3(B,C),A))))))) # label(d3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1895 (all A all B k2_funcop_1(A,B) = k2_zfmisc_1(A,k1_tarski(B))) # label(d2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1896 $T # label(t40_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1897 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_1(D) & v1_funct_2(D,B,A) & m2_relset_1(D,B,A) -> (all E (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) -> k2_binop_1(A,A,A,C,F,k8_funct_2(B,A,E,G)) = k8_funct_2(B,A,D,G))) -> D = k8_funcop_1(A,B,C,F,E)))))))))))))) # label(t67_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1898 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (all E (v1_funct_2(E,B,A) & m2_relset_1(E,B,A) & v1_funct_1(E) -> (all F (m1_subset_1(F,B) -> k8_funct_2(B,A,k6_funcop_1(A,B,C,D,E),F) = k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,F),k8_funct_2(B,A,E,F)))))))))))))) # label(t48_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1899 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(C) & v1_funct_1(D) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & -v1_xboole_0(B) -> m2_relset_1(k9_funcop_1(A,B,C,D),B,C))) # label(dt_k9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1900 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> k8_funcop_1(B,A,C,E,D) = k7_funct_2(A,B,B,D,k8_funcop_1(B,B,C,E,k6_partfun1(B))))))))))))) # label(t69_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1901 $T # label(t33_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1902 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (m1_subset_1(E,B) -> v1_funct_2(k4_funcop_1(C,D,E),A,B) & m2_relset_1(k4_funcop_1(C,D,E),A,B) & v1_funct_1(k4_funcop_1(C,D,E)))))))))))) # label(t59_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1903 (all A all B all C k2_funcop_1(k3_xboole_0(A,C),B) = k7_relat_1(k2_funcop_1(A,B),C)) # label(t18_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1904 (all A all B (k1_xboole_0 != A -> k1_tarski(B) = k2_relat_1(k2_funcop_1(A,B)))) # label(t14_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1905 (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_2(D,A,A) & v1_funct_1(D) -> 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]. 4.20/4.28 1906 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_2(D,A,k2_zfmisc_1(B,C)) & m2_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_1(D) -> k4_relat_1(k9_funcop_1(A,B,C,D)) = k9_funcop_1(A,C,B,k10_funcop_1(A,B,C,D)))))))))) # label(t73_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1907 (all A all B all C (v1_relat_1(B) & v1_funct_1(C) & v1_relat_1(C) & v1_funct_1(B) & v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k3_funcop_1(A,B,C)) & v1_relat_1(k3_funcop_1(A,B,C)))) # label(fc4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1908 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> k1_funcop_1(k13_funct_3(B,A)) = k13_funct_3(A,B))))) # label(t6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1909 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(A) = k1_relat_1(B) & (all C (r2_hidden(C,k1_relat_1(A)) -> (all D all E (k4_tarski(D,E) = k1_funct_1(A,C) -> k1_funct_1(B,C) = k4_tarski(E,D))) & -((all D all E k4_tarski(D,E) != k1_funct_1(A,C)) & k1_funct_1(A,C) != k1_funct_1(B,C)))) <-> k1_funcop_1(A) = B))))) # label(d1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1910 (all A (v1_relat_1(A) & v1_funct_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]. 4.20/4.28 1911 (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(C,k1_relat_1(B)) -> k7_relat_1(k1_funct_4(A,B),C) = k7_relat_1(A,C))))))) # label(t76_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1912 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> k7_relat_1(k1_funct_4(A,B),k1_relat_1(B)) = B)))) # label(t24_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1913 (all A all B all C all D (v1_relat_1(k4_funct_4(A,B,C,D)) & v1_funct_1(k4_funct_4(A,B,C,D)))) # label(fc1_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1914 (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(C,k4_tarski(B,A)) = k1_funct_1(k2_funct_4(C),k4_tarski(A,B))))) # label(t44_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1915 (all A all B all C all D (r1_tarski(k2_funcop_1(A,B),k2_funcop_1(C,D)) -> r1_tarski(A,C))) # label(t6_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1916 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_partfun1(A,B) <-> k1_funct_4(A,B) = k1_funct_4(B,A)))))) # label(t35_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1917 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B k1_funct_4(A,k7_relat_1(A,B)) = A))) # label(t80_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1918 $T # label(dt_k4_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1919 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (-r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(C,A) = k1_funct_1(k1_funct_4(C,B),A)))))) # label(t12_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1920 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k2_zfmisc_1(A,B) = k1_relat_1(C) -> k2_zfmisc_1(B,A) = k1_relat_1(k2_funct_4(C))))) # label(t47_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1921 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k1_relat_1(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]. 4.20/4.28 1922 (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) = k1_relat_1(B) -> k1_funct_4(k1_funct_4(A,B),C) = k1_funct_4(A,C)))))))) # label(t78_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1923 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C all D (r1_tarski(k1_relat_1(B),D) & r1_xboole_0(C,D) & r1_tarski(k1_relat_1(A),C) -> k7_relat_1(k1_funct_4(A,B),D) = B & A = k7_relat_1(k1_funct_4(A,B),C))))))) # label(t81_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1924 (all A all B (r1_tarski(k6_partfun1(A),k6_partfun1(B)) <-> r1_tarski(A,B))) # label(t4_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1925 (all A all B all C all D all E (v1_funct_1(E) & v1_relat_1(E) -> (all F (v1_funct_1(F) & v1_relat_1(F) -> (r2_hidden(k4_tarski(k4_tarski(A,B),k4_tarski(C,D)),k1_relat_1(k3_funct_4(E,F))) -> k4_tarski(k1_funct_1(E,k4_tarski(A,C)),k1_funct_1(F,k4_tarski(B,D))) = k1_funct_1(k3_funct_4(E,F),k4_tarski(k4_tarski(A,B),k4_tarski(C,D)))))))) # label(t58_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1926 (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]. 4.20/4.28 1927 (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)) -> k7_relat_1(k1_funct_4(A,B),k1_relat_1(A)) = A))))) # label(t34_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1928 (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]. 4.20/4.28 1929 (all A all B all C all D (k1_relat_1(k4_funct_4(A,B,C,D)) = k2_tarski(A,B) & r1_tarski(k2_relat_1(k4_funct_4(A,B,C,D)),k2_tarski(C,D)))) # label(t65_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1930 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k2_relat_1(k1_funct_4(A,B)),k2_xboole_0(k2_relat_1(A),k2_relat_1(B))))))) # label(t18_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1931 (all A -((all B -(r2_hidden(B,A) & (all C all D B != k4_tarski(C,D)))) & (all B all C -r1_tarski(A,k2_zfmisc_1(B,C))))) # label(t1_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1932 (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)) -> B = k1_funct_4(A,B)))))) # label(t20_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1933 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> r1_tarski(k2_funcop_1(k1_tarski(A),k1_funct_1(B,A)),B)))) # label(t8_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1934 (all A all B all C all D all E (-v1_xboole_0(A) & m1_subset_1(D,A) & m1_subset_1(E,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]. 4.20/4.28 1935 (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(k2_funct_4(C)),k2_zfmisc_1(B,A))))) # label(t46_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1936 (all A all B all C all D (C != A -> 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]. 4.20/4.28 1937 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> k2_funct_4(k2_funct_4(C)) = C))) # label(t53_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1938 (all A (v1_relat_1(A) & v1_funct_1(A) -> r1_tarski(k2_relat_1(k2_funct_4(A)),k2_relat_1(A)))) # label(t42_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1939 (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) -> (r1_partfun1(A,k1_funct_4(B,C)) -> r1_partfun1(A,C)))))))) # label(t28_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1940 (all A all B all C all D (A != B -> k2_tarski(C,D) = k2_relat_1(k4_funct_4(A,B,C,D)))) # label(t67_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1941 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(A,k1_funct_4(B,A)))))) # label(t26_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1942 (all A all B all C all D all E all F (k4_funct_4(A,B,E,F) = k4_funct_4(A,B,C,D) -> F = D & E = C | B = A)) # label(t72_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1943 (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) -> 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]. 4.20/4.28 1944 (all A all B all C all D all E (-v1_xboole_0(E) -> (all F (-v1_xboole_0(F) -> (all G (m2_relset_1(G,k2_zfmisc_1(A,B),E) & v1_funct_2(G,k2_zfmisc_1(A,B),E) & v1_funct_1(G) -> (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) -> 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)) & v1_funct_1(k3_funct_4(G,H)))))))))) # label(t64_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1945 (all A all B all C all D all E all F all G (v1_funct_1(G) & m2_relset_1(G,k2_zfmisc_1(A,B),C) & v1_funct_2(G,k2_zfmisc_1(A,B),C) -> (all H (v1_funct_1(H) & m2_relset_1(H,k2_zfmisc_1(D,E),F) & v1_funct_2(H,k2_zfmisc_1(D,E),F) -> -(F != k1_xboole_0 & -(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_2(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))) & k1_xboole_0 != C))))) # label(t63_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1946 (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)) -> k1_funct_4(A,B) = k1_funct_4(B,A)))))) # label(t36_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1947 (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) -> (C = k1_funct_4(A,B) <-> 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(C,D) = k1_funct_1(B,D)) & (-r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(A,D) = k1_funct_1(C,D))))))))))) # label(d1_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1948 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C all D (r2_hidden(k4_tarski(C,D),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 (r2_hidden(k4_tarski(D,E),k1_relat_1(A)) & C = k4_tarski(E,D))))) <-> B = k2_funct_4(A)))))) # label(d2_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1949 (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_xboole_0(k1_relat_1(B),k1_relat_1(C)) -> k1_funct_1(k1_funct_4(B,C),A) = k1_funct_1(B,A)))))) # label(t17_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1950 (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]. 4.20/4.28 1951 (all A all B all C all D all E (v1_funct_1(E) & v1_relat_1(E) -> (all F (v1_funct_1(F) & v1_relat_1(F) -> (r1_tarski(k1_relat_1(E),k2_zfmisc_1(A,B)) & r1_tarski(k1_relat_1(F),k2_zfmisc_1(C,D)) -> r1_tarski(k1_relat_1(k3_funct_4(E,F)),k2_zfmisc_1(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)))))))) # label(t60_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1952 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_partfun1(A,k1_funct_4(B,C)) -> r1_partfun1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),k1_relat_1(C))),B)))))))) # label(t27_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1953 (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_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> ((B = k1_xboole_0 -> A = k1_xboole_0) -> k1_funct_4(C,D) = D))))) # label(t38_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1954 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C k1_funct_4(k7_relat_1(A,C),k7_relat_1(B,C)) = k7_relat_1(k1_funct_4(A,B),C)))))) # label(t75_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1955 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C k1_funct_4(k7_relat_1(A,B),k7_relat_1(A,C)) = k7_relat_1(A,k2_xboole_0(B,C))))) # label(t83_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1956 (all A all B (v1_relat_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_funct_1(A) -> A = k1_funct_4(A,A))) # label(idempotence_k1_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1957 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k2_relat_1(k3_funct_4(A,B)),k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B))))))) # label(t59_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1958 (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 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)) -> k4_tarski(k1_funct_1(A,k4_tarski(D,E)),k1_funct_1(B,k4_tarski(F,G))) = k1_funct_1(C,k4_tarski(k4_tarski(D,F),k4_tarski(E,G))))) & (all D ((exists E exists F exists G exists H (r2_hidden(k4_tarski(G,H),k1_relat_1(B)) & r2_hidden(k4_tarski(E,F),k1_relat_1(A)) & D = k4_tarski(k4_tarski(E,G),k4_tarski(F,H)))) <-> r2_hidden(D,k1_relat_1(C)))) <-> k3_funct_4(A,B) = C))))))) # label(d3_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1959 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(k1_funct_4(C,B),A) = k1_funct_1(B,A)))))) # label(t14_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1960 (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) -> (r1_tarski(k2_relat_1(C),k1_relat_1(A)) & r1_partfun1(A,B) & r1_tarski(k2_relat_1(D),k1_relat_1(B)) -> k1_funct_4(k5_relat_1(C,A),k5_relat_1(D,B)) = k5_relat_1(k1_funct_4(C,D),k1_funct_4(A,B))))))))))) # label(t73_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1961 (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(k4_tarski(B,A),k1_relat_1(k2_funct_4(C)))))) # label(t43_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1962 (all A all B k1_tarski(k4_tarski(A,B)) = k2_funcop_1(k1_tarski(A),B)) # label(t70_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1963 (all A all B all C all D all E (v1_funct_1(E) & v1_relat_1(E) -> (k1_funct_1(E,A) = C & D = k1_funct_1(E,B) & k2_tarski(A,B) = k1_relat_1(E) -> k4_funct_4(A,B,C,D) = E))) # label(t69_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1964 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k7_relat_1(k1_funct_4(A,B),k4_xboole_0(k1_relat_1(A),k1_relat_1(B))),A))))) # label(t25_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1965 (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]. 4.20/4.28 1966 (all A all B all C all D (m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> k2_funct_4(k2_funct_4(D)) = D)) # label(t54_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1967 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,B),C) -> v1_funct_1(k2_funct_4(D)) & m2_relset_1(k2_funct_4(D),k2_zfmisc_1(B,A),C))) # label(t49_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1968 (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) -> (k1_relat_1(F) = k2_zfmisc_1(C,D) & k1_relat_1(E) = k2_zfmisc_1(A,B) -> 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]. 4.20/4.28 1969 (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 (m2_relset_1(H,k2_zfmisc_1(D,E),F) & v1_funct_1(H) -> m2_relset_1(k3_funct_4(G,H),k2_zfmisc_1(k2_zfmisc_1(A,D),k2_zfmisc_1(B,E)),k2_zfmisc_1(C,F)) & v1_funct_1(k3_funct_4(G,H)))))) # label(t62_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1970 (all A all B (v1_funct_1(B) & v1_relat_1(B) & v1_funct_1(A) & v1_relat_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]. 4.20/4.28 1971 (all A (v1_funct_1(A) & v1_relat_1(A) -> A = k1_funct_4(k1_xboole_0,A))) # label(t21_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1972 (all A (v1_relat_1(A) & v1_funct_1(A) -> k1_funct_4(A,k1_xboole_0) = A)) # label(t22_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1973 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,B) -> B = k1_funct_4(A,B) & k1_funct_4(B,A) = B))))) # label(t79_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1974 (all A all B all 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) -> (C != k1_xboole_0 -> v1_funct_2(k2_funct_4(D),k2_zfmisc_1(B,A),C) & m2_relset_1(k2_funct_4(D),k2_zfmisc_1(B,A),C) & v1_funct_1(k2_funct_4(D))))) # label(t50_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1975 (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)) -> k1_funct_4(A,B) = k2_xboole_0(A,B)))))) # label(t32_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1976 (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]. 4.20/4.28 1977 (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(k7_relat_1(k8_relat_1(A,C),B),k7_relat_1(k8_relat_1(A,D),B))))))) # label(t10_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1978 $T # label(t3_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1979 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(B) -> v1_relat_1(k3_funct_4(A,B)) & v1_funct_1(k3_funct_4(A,B)))) # label(dt_k3_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1980 (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]. 4.20/4.28 1981 (all A all B all C all D all E (-v1_xboole_0(A) & m1_subset_1(E,A) & m1_subset_1(D,A) -> m2_relset_1(k5_funct_4(A,B,C,D,E),k2_tarski(B,C),A) & v1_funct_2(k5_funct_4(A,B,C,D,E),k2_tarski(B,C),A) & v1_funct_1(k5_funct_4(A,B,C,D,E)))) # label(dt_k5_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1982 (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]. 4.20/4.28 1983 (all A all B all C all D (A != B -> D = k1_funct_1(k4_funct_4(A,B,C,D),B) & k1_funct_1(k4_funct_4(A,B,C,D),A) = C)) # label(t66_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1984 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k2_xboole_0(A,B) = k1_funct_4(A,B) <-> r1_partfun1(A,B)))))) # label(t31_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1985 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k2_relat_1(A),k2_relat_1(k1_funct_4(B,A))))))) # label(t19_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1986 (all A all B all C all D k4_funct_4(A,B,C,D) = k1_funct_4(k2_funcop_1(k1_tarski(A),C),k2_funcop_1(k1_tarski(B),D))) # label(d4_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1987 (all A (v1_relat_1(A) & v1_funct_1(A) -> r1_tarski(k2_funct_4(k2_funct_4(A)),A))) # label(t52_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1988 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,k1_funct_4(A,B)) <-> r1_partfun1(A,B)))))) # label(t29_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1989 (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]. 4.20/4.28 1990 (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_tarski(A,k1_funct_4(A,B))))))) # label(t33_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1991 (all A all B all C (-v1_xboole_0(C) -> (all D (v1_funct_2(D,k2_zfmisc_1(A,B),C) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> v1_funct_2(k2_funct_4(D),k2_zfmisc_1(B,A),C) & m2_relset_1(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]. 4.20/4.28 1992 (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(C) = k2_relat_1(k2_funct_4(C))))) # label(t48_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1993 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (r1_xboole_0(k1_relat_1(A),C) -> k7_relat_1(B,C) = k7_relat_1(k1_funct_4(A,B),C))))))) # label(t77_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1994 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k2_funcop_1(A,C),k2_funcop_1(B,C)))) # label(t5_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1995 (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_partfun1(B,C) -> k1_funct_1(B,A) = k1_funct_1(k1_funct_4(B,C),A)))))) # label(t16_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1996 (all A all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> k1_funct_4(C,D) = D)))))) # label(t40_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1997 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> (all C (v1_funct_2(C,A,A) & m2_relset_1(C,A,A) & v1_funct_1(C) -> C = k1_funct_4(B,C))))) # label(t39_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1998 (all A all B k6_partfun1(k2_xboole_0(A,B)) = k1_funct_4(k6_partfun1(A),k6_partfun1(B))) # label(t23_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 1999 (all A all B all C all D (m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (C != k1_xboole_0 -> k2_funct_4(k2_funct_4(D)) = D))) # label(t55_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 2000 (all A all B all C all D all E (v1_funct_1(E) & v1_relat_1(E) -> (all F (v1_relat_1(F) & v1_funct_1(F) -> (r2_hidden(k4_tarski(B,D),k1_relat_1(F)) & r2_hidden(k4_tarski(A,C),k1_relat_1(E)) <-> r2_hidden(k4_tarski(k4_tarski(A,B),k4_tarski(C,D)),k1_relat_1(k3_funct_4(E,F)))))))) # label(t57_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.28 2001 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(B)) | r2_hidden(A,k1_relat_1(C)) <-> r2_hidden(A,k1_relat_1(k1_funct_4(B,C)))))))) # label(t13_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2002 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (r1_tarski(k1_relat_1(A),k2_xboole_0(B,C)) -> A = k1_funct_4(k7_relat_1(A,B),k7_relat_1(A,C)))))) # label(t74_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2003 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_tarski(k7_relat_1(k8_relat_1(A,C),B),C))) # label(t9_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2004 (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) -> k2_funct_4(k2_funct_4(D)) = D)))) # label(t56_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2005 $T # label(t43_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2006 (all A (v3_ordinal1(A) -> k1_ordinal1(A) = k14_ordinal2(A,k4_ordinal2))) # label(t48_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2007 (all A (v3_ordinal1(A) -> (all B -(r2_hidden(A,k7_ordinal2(B)) & (all C (v3_ordinal1(C) -> -(r1_ordinal1(A,C) & r2_hidden(C,B)))))))) # label(t29_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2008 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (B = f1_s14_ordinal2(A) <-> (exists C (v1_funct_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & k1_ordinal2(C) = B & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f3_s14_ordinal2(D,k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> f4_s14_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D) | D = k1_xboole_0))) & f2_s14_ordinal2 = k1_funct_1(C,k1_xboole_0) & k1_relat_1(C) = k1_ordinal1(A) & v1_relat_1(C)))))))) -> f2_s14_ordinal2 = f1_s14_ordinal2(k1_xboole_0) # label(s14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2009 (all A (v1_funct_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & v1_relat_1(A) -> (v3_ordinal2(A) <-> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (k1_funct_1(A,B) = C & v4_ordinal1(B) & r2_hidden(B,k1_relat_1(A)) -> r1_ordinal2(C,k2_ordinal1(A,B)) | k1_xboole_0 = B)))))))) # label(d17_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2010 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r1_ordinal1(A,B) <-> r1_ordinal1(k1_ordinal1(A),k1_ordinal1(B))))))) # label(t1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2011 (exists A (v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal1(A) & v1_ordinal1(A))) # label(rc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2012 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k1_ordinal1(k14_ordinal2(A,B)) = k14_ordinal2(A,k1_ordinal1(B)))))) # label(t45_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2013 (all A (v3_ordinal1(A) -> (r2_hidden(k1_xboole_0,A) & v4_ordinal1(A) -> r1_ordinal1(k5_ordinal2,A)))) # label(t19_ordinal2_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2014 $T # label(t36_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2015 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -((exists C (v1_funct_1(C) & v5_ordinal1(C) & k1_ordinal2(C) = A & k1_funct_1(C,k1_xboole_0) = f2_s13_ordinal2 & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(f1_s13_ordinal2)) -> D = k1_xboole_0 | f4_s13_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s13_ordinal2)) -> k1_funct_1(C,k1_ordinal1(D)) = f3_s13_ordinal2(D,k1_funct_1(C,D))))) & k1_ordinal1(f1_s13_ordinal2) = k1_relat_1(C) & v1_ordinal2(C) & v1_relat_1(C))) & (exists 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))))) & (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) | D = k1_xboole_0))) & k1_funct_1(C,k1_xboole_0) = f2_s13_ordinal2 & B = k1_ordinal2(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C))) & A != B))))) # label(s13_ordinal2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2016 (exists A (v3_ordinal1(A) & (exists B (v1_funct_1(B) & v5_ordinal1(B) & f2_s13_ordinal2 = k1_funct_1(B,k1_xboole_0) & (all C (v3_ordinal1(C) -> (v4_ordinal1(C) & r2_hidden(C,k1_ordinal1(f1_s13_ordinal2)) -> k1_xboole_0 = C | k1_funct_1(B,C) = f4_s13_ordinal2(C,k2_ordinal1(B,C))))) & (all C (v3_ordinal1(C) -> (r2_hidden(k1_ordinal1(C),k1_ordinal1(f1_s13_ordinal2)) -> f3_s13_ordinal2(C,k1_funct_1(B,C)) = k1_funct_1(B,k1_ordinal1(C))))) & k1_ordinal1(f1_s13_ordinal2) = k1_relat_1(B) & A = k1_ordinal2(B) & v1_ordinal2(B) & v1_relat_1(B))))) # label(s13_ordinal2_AndRHS) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2017 (all A all B (k3_ordinal2(A) = B <-> (all C (r2_hidden(C,B) <-> r2_hidden(C,A) & (exists D (v4_ordinal1(D) & D = C & v3_ordinal1(D))))))) # label(d3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2018 (all A all B (B = k2_ordinal2(A) <-> (all C (r2_hidden(C,B) <-> v3_ordinal1(C) & r2_hidden(C,A))))) # label(d2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2019 (all A k1_setfam_1(k2_ordinal2(A)) = k6_ordinal2(A)) # label(d6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2020 (all A all B (v1_funct_1(A) & v1_ordinal2(A) & v3_ordinal1(B) & v5_ordinal1(A) & v1_relat_1(A) -> v2_ordinal1(k1_funct_1(A,B)) & v3_ordinal1(k1_funct_1(A,B)) & v1_ordinal1(k1_funct_1(A,B)))) # label(fc3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2021 (all A (v3_ordinal1(A) -> (all B (B = f4_s9_ordinal2(A) <-> (exists 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)))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f2_s9_ordinal2(D,k1_funct_1(C,D))))) & k1_funct_1(C,k1_xboole_0) = f1_s9_ordinal2 & B = k1_ordinal2(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C))))))) -> (all A (v3_ordinal1(A) -> f2_s9_ordinal2(A,f4_s9_ordinal2(A)) = f4_s9_ordinal2(k1_ordinal1(A)))) # label(s9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2022 (all A (v3_ordinal1(A) -> (all B ((exists C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & f2_s8_ordinal2 = k1_funct_1(C,k1_xboole_0) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> f4_s8_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D) | k1_xboole_0 = D))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f3_s8_ordinal2(D,k1_funct_1(C,D))))) & k1_ordinal1(A) = k1_relat_1(C) & k1_ordinal2(C) = B)) <-> f1_s8_ordinal2(A) = B)))) -> f2_s8_ordinal2 = f1_s8_ordinal2(k1_xboole_0) # label(s8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2023 (all A all B (r1_tarski(A,B) -> r1_tarski(k2_ordinal2(A),k2_ordinal2(B)))) # label(t11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2024 $T # label(t40_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2025 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) -> k1_funct_1(A,k3_tarski(k1_relat_1(A))) = k1_ordinal2(A))) # label(d1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2026 (all A (v3_ordinal1(A) -> (all B (r2_hidden(A,B) -> r2_hidden(k6_ordinal2(B),B))))) # label(t25_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2027 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (k16_ordinal2(A,B) = C <-> (exists D (v1_relat_1(D) & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(B)) -> k15_ordinal2(A,k1_funct_1(D,E)) = k1_funct_1(D,k1_ordinal1(E))))) & (all E (v3_ordinal1(E) -> (r2_hidden(E,k1_ordinal1(B)) & v4_ordinal1(E) -> k12_ordinal2(k2_ordinal1(D,E)) = k1_funct_1(D,E) | E = k1_xboole_0))) & k1_funct_1(D,k1_xboole_0) = k4_ordinal2 & k1_relat_1(D) = k1_ordinal1(B) & C = k1_ordinal2(D) & v1_ordinal2(D) & v5_ordinal1(D) & v1_funct_1(D)))))))))) # label(d20_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2028 $T # label(t42_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2029 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal1(A,B) -> r1_ordinal1(k15_ordinal2(C,A),k15_ordinal2(C,B))))))))) # label(t59_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2030 (all A (v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> v3_ordinal1(k9_ordinal2(A)))) # label(dt_k9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2031 (all A (k5_ordinal2 = A <-> r2_hidden(k1_xboole_0,A) & v3_ordinal1(A) & (all B (v3_ordinal1(B) -> (v4_ordinal1(B) & r2_hidden(k1_xboole_0,B) -> r1_tarski(A,B)))) & v4_ordinal1(A))) # label(d5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2032 (all A (v3_ordinal1(A) -> (all B all C (r2_hidden(A,B) & r1_tarski(B,C) -> r1_ordinal1(k6_ordinal2(C),k6_ordinal2(B)))))) # label(t24_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2033 $T # label(dt_k1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2034 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_ordinal2(C) & v5_ordinal1(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)))) | A = k1_xboole_0))))) # label(t54_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2035 (exists A (v1_funct_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v1_relat_1(A))) # label(rc2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2036 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> k8_ordinal2(A) = k7_ordinal2(k2_relat_1(A)))) # label(d9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2037 (exists A (v1_relat_1(A) & v1_funct_1(A) & k1_relat_1(A) = f1_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))))) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s5_ordinal2) & v4_ordinal1(B) -> f4_s5_ordinal2(B,k2_ordinal1(A,B)) = k1_funct_1(A,B) | B = k1_xboole_0))) & (r2_hidden(k1_xboole_0,f1_s5_ordinal2) -> f2_s5_ordinal2 = k1_funct_1(A,k1_xboole_0)) & v5_ordinal1(A))) # label(s5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2038 (all A (v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> k7_ordinal2(k2_relat_1(A)) = k8_ordinal2(A) & k6_ordinal2(k2_relat_1(A)) = k9_ordinal2(A))) # label(t35_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2039 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(A)) -> k1_funct_1(C,D) = k6_ordinal2(k2_relat_1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),D))))))) & k1_relat_1(C) = k1_relat_1(A) & k8_ordinal2(C) = B)) <-> k11_ordinal2(A) = B))))) # label(d12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2040 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v1_relat_1(C) & k1_relat_1(C) = k1_relat_1(A) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(A)) -> k7_ordinal2(k2_relat_1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),D)))) = k1_funct_1(C,D)))) & k9_ordinal2(C) = B & v1_ordinal2(C) & v5_ordinal1(C) & v1_funct_1(C))) <-> B = k10_ordinal2(A)))))) # label(d11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2041 (all A (v3_ordinal1(A) -> (all B (v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> v3_ordinal1(k1_funct_1(B,A))))))) # label(t34_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2042 $T # label(t20_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2043 $T # label(t38_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.20/4.30 2044 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(A,B) -> r2_hidden(k14_ordinal2(C,A),k14_ordinal2(C,B))))))))) # label(t49_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.28/4.37 2045 $T # label(t64_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.28/4.37 2046 $T # label(t39_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.28/4.37 2047 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k15_ordinal2(A,k16_ordinal2(A,B)) = k16_ordinal2(A,k1_ordinal1(B)))))) # label(t61_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.28/4.37 2048 $T # label(t6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.28/4.37 2049 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v1_ordinal2(A) <-> (exists B (v3_ordinal1(B) & r1_tarski(k2_relat_1(A),B)))))) # label(d8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.28/4.37 2050 (all A (v3_ordinal1(A) -> k7_ordinal2(k1_tarski(A)) = k1_ordinal1(A))) # label(t31_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.28/4.37 2051 (all A (r2_hidden(A,k5_ordinal2) <-> v4_ordinal2(A))) # label(d21_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.28/4.37 2052 (all A all B (v3_ordinal1(B) -> v1_relat_1(k2_funcop_1(A,B)) & v1_ordinal2(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)))) # label(fc4_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.28/4.37 2053 (all A (v3_ordinal1(A) -> k2_ordinal2(A) = A)) # label(t10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.28/4.37 2054 (exists A (v1_relat_1(A) & v1_funct_1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s2_ordinal2) -> k1_funct_1(A,B) = f2_s2_ordinal2(B)))) & k1_relat_1(A) = f1_s2_ordinal2 & v5_ordinal1(A))) # label(s2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.28/4.37 2055 (all A r1_ordinal1(k6_ordinal2(A),k7_ordinal2(A))) # label(t32_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.28/4.37 2056 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k15_ordinal2(k1_ordinal1(A),B) = k14_ordinal2(k15_ordinal2(A,B),B))))) # label(t53_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.28/4.37 2057 $T # label(t12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.28/4.37 2058 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal1(A,B) -> r1_ordinal1(k14_ordinal2(A,C),k14_ordinal2(B,C))))))))) # label(t51_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.28/4.37 2059 f3_s12_ordinal2 = k1_relat_1(f1_s12_ordinal2) & (r2_hidden(k1_xboole_0,f3_s12_ordinal2) -> f4_s12_ordinal2 = k1_funct_1(f1_s12_ordinal2,k1_xboole_0)) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f3_s12_ordinal2) -> f5_s12_ordinal2(A,k1_funct_1(f1_s12_ordinal2,A)) = k1_funct_1(f1_s12_ordinal2,k1_ordinal1(A))))) & (all A (v3_ordinal1(A) -> (r2_hidden(A,f3_s12_ordinal2) & v4_ordinal1(A) -> A = k1_xboole_0 | k1_funct_1(f1_s12_ordinal2,A) = f6_s12_ordinal2(A,k2_ordinal1(f1_s12_ordinal2,A))))) & (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v1_ordinal2(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))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_xboole_0 = D | f6_s12_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & k1_ordinal1(A) = k1_relat_1(C) & B = k1_ordinal2(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C))) <-> f2_s12_ordinal2(A) = B))))) -> (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]. 4.28/4.37 2060 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) -> v3_ordinal1(k10_ordinal2(A)))) # label(dt_k10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.28/4.37 2061 (all A r1_tarski(k3_ordinal2(A),A)) # label(t13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.28/4.37 2062 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> (all C (v5_ordinal1(C) & v1_ordinal2(C) & v1_funct_1(C) & v1_relat_1(C) -> ((all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k1_funct_1(C,D) = k14_ordinal2(B,D)))) & k1_relat_1(C) = A -> k14_ordinal2(B,A) = k8_ordinal2(C)))) | k1_xboole_0 = A))))) # label(t46_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.40 2063 (all A (v3_ordinal1(A) -> (all B (r2_hidden(A,B) -> r1_ordinal1(k6_ordinal2(B),A))))) # label(t22_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.40 2064 (all A (v3_ordinal1(A) -> k1_xboole_0 = k15_ordinal2(k1_xboole_0,A))) # label(t52_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.40 2065 (all A (v3_ordinal1(A) -> (all B (m1_ordinal1(B,A) -> v1_ordinal2(B))))) # label(cc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.40 2066 (all A (v3_ordinal1(A) -> k3_tarski(k1_ordinal1(A)) = A)) # label(t2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.40 2067 (all A r1_tarski(k3_ordinal2(A),k2_ordinal2(A))) # label(t15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.40 2068 (all A ((all B (r2_hidden(B,A) -> v3_ordinal1(B))) -> v3_ordinal1(k1_setfam_1(A)))) # label(t17_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.40 2069 f2_s10_ordinal2 != k1_xboole_0 & (all A (v3_ordinal1(A) -> (r2_hidden(A,f2_s10_ordinal2) -> k1_funct_1(f1_s10_ordinal2,A) = f3_s10_ordinal2(A)))) & f2_s10_ordinal2 = k1_relat_1(f1_s10_ordinal2) & v4_ordinal1(f2_s10_ordinal2) & (all A (v3_ordinal1(A) -> (all B (B = f3_s10_ordinal2(A) <-> (exists C (v1_funct_1(C) & k1_ordinal2(C) = B & f4_s10_ordinal2 = k1_funct_1(C,k1_xboole_0) & (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)))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f5_s10_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & k1_ordinal1(A) = k1_relat_1(C) & v5_ordinal1(C) & v1_relat_1(C))))))) -> f6_s10_ordinal2(f2_s10_ordinal2,f1_s10_ordinal2) = f3_s10_ordinal2(f2_s10_ordinal2) # label(s10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.40 2070 k1_relat_1(f5_s4_ordinal2) = f1_s4_ordinal2 & (all A (v3_ordinal1(A) -> (r2_hidden(A,f1_s4_ordinal2) & v4_ordinal1(A) -> f4_s4_ordinal2(A,k2_ordinal1(f5_s4_ordinal2,A)) = k1_funct_1(f5_s4_ordinal2,A) | k1_xboole_0 = A))) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f1_s4_ordinal2) -> f3_s4_ordinal2(A,k1_funct_1(f6_s4_ordinal2,A)) = k1_funct_1(f6_s4_ordinal2,k1_ordinal1(A))))) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & r2_hidden(A,f1_s4_ordinal2) -> f4_s4_ordinal2(A,k2_ordinal1(f6_s4_ordinal2,A)) = k1_funct_1(f6_s4_ordinal2,A) | A = k1_xboole_0))) & (r2_hidden(k1_xboole_0,f1_s4_ordinal2) -> f2_s4_ordinal2 = k1_funct_1(f6_s4_ordinal2,k1_xboole_0)) & f1_s4_ordinal2 = k1_relat_1(f6_s4_ordinal2) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f1_s4_ordinal2) -> f3_s4_ordinal2(A,k1_funct_1(f5_s4_ordinal2,A)) = k1_funct_1(f5_s4_ordinal2,k1_ordinal1(A))))) & (r2_hidden(k1_xboole_0,f1_s4_ordinal2) -> k1_funct_1(f5_s4_ordinal2,k1_xboole_0) = f2_s4_ordinal2) -> f6_s4_ordinal2 = f5_s4_ordinal2 # label(s4_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.40 2071 (all A (v1_funct_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & v1_relat_1(A) -> (v2_ordinal2(A) <-> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(B,C) & r2_hidden(C,k1_relat_1(A)) -> r2_hidden(k1_funct_1(A,B),k1_funct_1(A,C)))))))))) # label(d16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.40 2072 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal1(A,B) -> r1_ordinal1(k14_ordinal2(C,A),k14_ordinal2(C,B))))))))) # label(t50_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.40 2073 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v5_ordinal1(B) & v1_ordinal2(B) & v1_funct_1(B) -> (k1_xboole_0 != A -> (r1_ordinal2(A,B) <-> (all C (v3_ordinal1(C) -> (all D (v3_ordinal1(D) -> -(r2_hidden(A,D) & (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))))))) & r2_hidden(C,A)))))))) & (A = k1_xboole_0 -> ((exists C (r2_hidden(C,k1_relat_1(B)) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(B)) & r1_ordinal1(C,D) -> k1_xboole_0 = k1_funct_1(B,D)))) & v3_ordinal1(C))) <-> r1_ordinal2(A,B))))))) # label(d13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.41 2074 (all A (v3_ordinal1(A) -> (all B (r2_hidden(A,B) -> r2_hidden(A,k7_ordinal2(B)))))) # label(t27_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.41 2075 $T # label(dt_k5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.41 2076 (all A (v3_ordinal1(A) -> (exists B ((exists C (v3_ordinal1(C) & v4_ordinal1(B) & A = k14_ordinal2(B,C) & v4_ordinal2(C))) & v3_ordinal1(B))))) # label(t65_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.41 2077 $T # label(t21_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.41 2078 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> ((exists D (v1_ordinal2(D) & C = k1_ordinal2(D) & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(B)) -> k1_ordinal1(k1_funct_1(D,E)) = k1_funct_1(D,k1_ordinal1(E))))) & (all E (v3_ordinal1(E) -> (r2_hidden(E,k1_ordinal1(B)) & v4_ordinal1(E) -> k1_xboole_0 = E | k8_ordinal2(k2_ordinal1(D,E)) = k1_funct_1(D,E)))) & A = k1_funct_1(D,k1_xboole_0) & k1_relat_1(D) = k1_ordinal1(B) & v5_ordinal1(D) & v1_funct_1(D) & v1_relat_1(D))) <-> k14_ordinal2(A,B) = C))))))) # label(d18_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.41 2079 (all A (v3_ordinal1(A) -> A = k14_ordinal2(k1_xboole_0,A))) # label(t47_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.41 2080 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> v3_ordinal1(k8_ordinal2(A)))) # label(dt_k8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.41 2081 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(B,C) -> k1_xboole_0 = A | r2_hidden(k15_ordinal2(B,A),k15_ordinal2(C,A))))))))) # label(t57_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.41 2082 $T # label(t18_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.41 2083 (all A (v3_ordinal1(A) -> (all B (v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B) -> (k1_ordinal1(A) = k1_relat_1(B) -> k1_funct_1(B,A) = k1_ordinal2(B)))))) # label(t7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.41 2084 (all A (v3_ordinal1(A) -> (all B ((all C (v3_ordinal1(C) -> (r2_hidden(C,B) -> r2_hidden(C,A)))) -> r1_ordinal1(k7_ordinal2(B),A))))) # label(t28_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.41 2085 (all A all B (r1_tarski(A,B) -> r1_ordinal1(k7_ordinal2(A),k7_ordinal2(B)))) # label(t30_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.41 2086 (exists A (v1_funct_1(A) & v5_ordinal1(A) & f1_s11_ordinal2 = k1_relat_1(A) & (r2_hidden(k1_xboole_0,f1_s11_ordinal2) -> k1_funct_1(A,k1_xboole_0) = f2_s11_ordinal2) & (all B (v3_ordinal1(B) -> (v4_ordinal1(B) & r2_hidden(B,f1_s11_ordinal2) -> B = k1_xboole_0 | f4_s11_ordinal2(B,k2_ordinal1(A,B)) = k1_funct_1(A,B)))) & (all B (v3_ordinal1(B) -> (r2_hidden(k1_ordinal1(B),f1_s11_ordinal2) -> k1_funct_1(A,k1_ordinal1(B)) = f3_s11_ordinal2(B,k1_funct_1(A,B))))) & v1_ordinal2(A) & v1_relat_1(A))) # label(s11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.41 2087 (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))) & p1_s1_ordinal2(k1_xboole_0) -> (all A (v3_ordinal1(A) -> p1_s1_ordinal2(A))) # label(s1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.41 2088 (exists A exists B (v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & k1_ordinal2(B) = A & (all C (v3_ordinal1(C) -> (r2_hidden(C,k1_ordinal1(f1_s7_ordinal2)) & v4_ordinal1(C) -> k1_funct_1(B,C) = f4_s7_ordinal2(C,k2_ordinal1(B,C)) | k1_xboole_0 = C))) & (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))))) & f2_s7_ordinal2 = k1_funct_1(B,k1_xboole_0) & k1_relat_1(B) = k1_ordinal1(f1_s7_ordinal2))) # label(s7_ordinal2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 4.45/4.52 2089 (all A all B -((exists C (v1_funct_1(C) & k1_ordinal1(f1_s7_ordinal2) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s7_ordinal2)) -> f3_s7_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(f1_s7_ordinal2)) -> D = k1_xboole_0 | k1_funct_1(C,D) = f4_s7_ordinal2(D,k2_ordinal1(C,D))))) & f2_s7_ordinal2 = k1_funct_1(C,k1_xboole_0) & k1_ordinal2(C) = A & v5_ordinal1(C) & v1_relat_1(C))) & B != A & (exists C (v5_ordinal1(C) & B = k1_ordinal2(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s7_ordinal2)) -> f3_s7_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(f1_s7_ordinal2)) -> k1_funct_1(C,D) = f4_s7_ordinal2(D,k2_ordinal1(C,D)) | D = k1_xboole_0))) & k1_funct_1(C,k1_xboole_0) = f2_s7_ordinal2 & k1_ordinal1(f1_s7_ordinal2) = k1_relat_1(C) & v1_funct_1(C) & v1_relat_1(C))))) # label(s7_ordinal2_AndRHS) # label(axiom) # label(non_clause). [assumption]. 4.45/4.52 2090 (all A all B (r1_tarski(A,B) -> r1_tarski(k3_ordinal2(A),k3_ordinal2(B)))) # label(t14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.45/4.52 2091 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) -> k12_ordinal2(k2_ordinal1(B,A)) = k13_ordinal2(A,B))))) # label(d15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.45/4.52 2092 (all A (v3_ordinal1(A) -> A = k14_ordinal2(A,k1_xboole_0))) # label(t44_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.45/4.52 2093 (all A (v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> ((exists B (v3_ordinal1(B) & r1_ordinal2(B,A))) -> (all B (v3_ordinal1(B) -> (k12_ordinal2(A) = B <-> r1_ordinal2(B,A))))))) # label(d14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.45/4.52 2094 (all A (v3_ordinal1(A) -> (all B (f2_s6_ordinal2(A) = B <-> (exists C (v1_funct_1(C) & k1_ordinal2(C) = B & k1_relat_1(C) = k1_ordinal1(A) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f5_s6_ordinal2(D,k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_xboole_0 = D | k1_funct_1(C,D) = f6_s6_ordinal2(D,k2_ordinal1(C,D))))) & k1_funct_1(C,k1_xboole_0) = f4_s6_ordinal2 & v5_ordinal1(C) & v1_relat_1(C))))))) & (r2_hidden(k1_xboole_0,f3_s6_ordinal2) -> f4_s6_ordinal2 = k1_funct_1(f1_s6_ordinal2,k1_xboole_0)) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & r2_hidden(A,f3_s6_ordinal2) -> A = k1_xboole_0 | f6_s6_ordinal2(A,k2_ordinal1(f1_s6_ordinal2,A)) = k1_funct_1(f1_s6_ordinal2,A)))) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f3_s6_ordinal2) -> f5_s6_ordinal2(A,k1_funct_1(f1_s6_ordinal2,A)) = k1_funct_1(f1_s6_ordinal2,k1_ordinal1(A))))) & k1_relat_1(f1_s6_ordinal2) = f3_s6_ordinal2 -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s6_ordinal2)) -> k1_funct_1(f1_s6_ordinal2,A) = f2_s6_ordinal2(A)))) # label(s6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.45/4.52 2095 (exists A (v1_relat_1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s3_ordinal2) -> k1_funct_1(A,B) = f2_s3_ordinal2(B)))) & k1_relat_1(A) = f1_s3_ordinal2 & v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_1(A))) # label(s3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.45/4.52 2096 (all A (v3_ordinal1(A) -> k4_ordinal2 = k16_ordinal2(A,k1_xboole_0))) # label(t60_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.45/4.52 2097 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal1(A,B) -> r1_ordinal1(k15_ordinal2(A,C),k15_ordinal2(B,C))))))))) # label(t58_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.45/4.52 2098 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & B = k1_ordinal2(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f2_s15_ordinal2(D,k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_funct_1(C,D) = f3_s15_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & k1_funct_1(C,k1_xboole_0) = f1_s15_ordinal2 & k1_ordinal1(A) = k1_relat_1(C) & v1_ordinal2(C))) <-> f4_s15_ordinal2(A) = B))))) -> (all A (v3_ordinal1(A) -> f4_s15_ordinal2(k1_ordinal1(A)) = f2_s15_ordinal2(A,f4_s15_ordinal2(A)))) # label(s15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.45/4.53 2099 (all A (v3_ordinal1(A) -> (all B ((all C (v3_ordinal1(C) -> (r2_hidden(C,B) -> r1_ordinal1(A,C)))) -> r1_ordinal1(A,k6_ordinal2(B)) | k1_xboole_0 = k2_ordinal2(B))))) # label(t23_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.45/4.53 2100 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> (all C (v1_relat_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & v1_funct_1(C) -> (k1_relat_1(C) = A & (all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k16_ordinal2(B,D) = k1_funct_1(C,D)))) -> k16_ordinal2(B,A) = k12_ordinal2(C)))) | A = k1_xboole_0))))) # label(t62_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.45/4.53 2101 (all A (v3_ordinal1(A) -> r1_tarski(k1_ordinal1(A),k1_zfmisc_1(A)))) # label(t3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.45/4.53 2102 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (k15_ordinal2(A,B) = C <-> (exists D (v1_relat_1(D) & v1_funct_1(D) & k1_funct_1(D,k1_xboole_0) = k1_xboole_0 & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(A)) -> k14_ordinal2(k1_funct_1(D,E),B) = k1_funct_1(D,k1_ordinal1(E))))) & (all E (v3_ordinal1(E) -> (v4_ordinal1(E) & r2_hidden(E,k1_ordinal1(A)) -> k1_xboole_0 = E | k1_funct_1(D,E) = k3_tarski(k8_ordinal2(k2_ordinal1(D,E)))))) & k1_relat_1(D) = k1_ordinal1(A) & k1_ordinal2(D) = C & v1_ordinal2(D) & v5_ordinal1(D)))))))))) # label(d19_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.45/4.53 2103 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_ordinal2(A) -> v3_ordinal1(k12_ordinal2(A)))) # label(dt_k12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.45/4.53 2104 (all A (v3_ordinal1(A) -> k1_xboole_0 = k15_ordinal2(A,k1_xboole_0))) # label(t55_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.45/4.53 2105 (all A v3_ordinal1(k6_ordinal2(A))) # label(dt_k6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.45/4.53 2106 (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]. 4.45/4.53 2107 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_ordinal2(B) & v5_ordinal1(B) & v3_ordinal1(A) -> v3_ordinal1(k13_ordinal2(A,B)))) # label(dt_k13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.45/4.53 2108 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> v3_ordinal1(k15_ordinal2(A,B)))) # label(dt_k15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.45/4.53 2109 $T # label(dt_k3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.45/4.53 2110 $T # label(t8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.45/4.53 2111 $T # label(t41_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.45/4.53 2112 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> v3_ordinal1(k14_ordinal2(A,B)))) # label(dt_k14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.45/4.53 2113 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) -> v3_ordinal1(k11_ordinal2(A)))) # label(dt_k11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.45/4.53 2114 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> k6_ordinal2(k2_relat_1(A)) = k9_ordinal2(A))) # label(d10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.45/4.53 2115 (all A (v3_ordinal1(A) -> k15_ordinal2(k4_ordinal2,A) = A & k15_ordinal2(A,k4_ordinal2) = A)) # label(t56_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.45/4.53 2116 $T # label(t33_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.45/4.53 2117 $T # label(t37_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2118 (all A (v3_ordinal1(A) -> (exists B (r2_hidden(A,B) & v4_ordinal1(B) & v3_ordinal1(B))))) # label(t16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2119 (all A r1_tarski(k2_ordinal2(A),A)) # label(t9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2120 (all A (v3_ordinal1(A) -> A = k7_ordinal2(A))) # label(t26_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2121 (all A (v3_ordinal1(A) -> r1_ordinal1(k3_tarski(A),A))) # label(t5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2122 (all A v3_ordinal1(k7_ordinal2(A))) # label(dt_k7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2123 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v1_relat_1(C) & v5_ordinal1(C) & k1_funct_1(C,k1_xboole_0) = f4_s16_ordinal2 & (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))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f5_s16_ordinal2(D,k1_funct_1(C,D))))) & k1_relat_1(C) = k1_ordinal1(A) & k1_ordinal2(C) = B & v1_ordinal2(C) & v1_funct_1(C))) <-> B = f3_s16_ordinal2(A)))))) & f2_s16_ordinal2 != k1_xboole_0 & v4_ordinal1(f2_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_relat_1(f1_s16_ordinal2) -> f6_s16_ordinal2(f2_s16_ordinal2,f1_s16_ordinal2) = f3_s16_ordinal2(f2_s16_ordinal2) # label(s16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2124 (all A all B (v1_relat_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v3_ordinal1(B) & v1_funct_1(A) -> v1_ordinal2(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)) & v1_relat_1(k7_relat_1(A,B)))) # label(fc2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2125 (all A (v3_ordinal1(A) -> k16_ordinal2(k4_ordinal2,A) = k4_ordinal2 & A = k16_ordinal2(A,k4_ordinal2))) # label(t63_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2126 (all A all B (v3_ordinal1(B) -> (r1_tarski(k2_ordinal2(A),B) & (all C (v3_ordinal1(C) -> (r1_tarski(k2_ordinal2(A),C) -> r1_ordinal1(B,C)))) <-> B = k7_ordinal2(A)))) # label(d7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2127 $T # label(dt_k2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2128 $T # label(t8_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2129 (all A all B (v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k2_zfmisc_1(A,B)))) # label(t19_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2130 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v1_finset_1(k1_relat_1(A)) -> v1_finset_1(k2_relat_1(A))))) # label(t26_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2131 (all A all B (v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k2_xboole_0(A,B)))) # label(t14_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2132 (all A all B (v1_finset_1(B) & r1_tarski(A,B) -> v1_finset_1(A))) # label(t13_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2133 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,k2_relat_1(B)) & v1_finset_1(k10_relat_1(B,A)) -> v1_finset_1(A)))) # label(t27_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2134 $T # label(t4_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2135 (all A all B (v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k5_xboole_0(A,B)))) # label(fc17_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2136 (all A all B (v1_finset_1(B) -> v1_finset_1(k3_xboole_0(A,B)))) # label(fc10_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2137 $T # label(t6_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2138 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v1_finset_1(k1_relat_1(A)) <-> v1_finset_1(A)))) # label(t29_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2139 (all A all B (v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k5_xboole_0(A,B)))) # label(t28_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2140 (all A all B all C (v1_finset_1(B) & v1_finset_1(C) & v1_finset_1(A) -> v1_finset_1(k3_zfmisc_1(A,B,C)))) # label(fc15_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2141 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v1_finset_1(A) -> v1_finset_1(k9_relat_1(B,A))))) # label(t17_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2142 $T # label(t12_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2143 (all A all B (v1_finset_1(A) -> v1_finset_1(k4_xboole_0(A,B)))) # label(fc12_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2144 (all A -((all B -(r2_hidden(B,A) & (all C (r2_hidden(C,A) -> r1_tarski(B,C))))) & v6_ordinal1(A) & A != k1_xboole_0 & v1_finset_1(A))) # label(t30_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2145 (exists A (v1_finset_1(A) & -v1_xboole_0(A))) # label(rc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2146 $T # label(t9_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2147 (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]. 4.49/4.53 2148 (all A (-v1_xboole_0(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(A)) & v1_finset_1(B) & -v1_xboole_0(B))))) # label(rc4_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2149 $T # label(t3_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2150 (all A all B all C all D all E v1_finset_1(k3_enumset1(A,B,C,D,E))) # label(fc5_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2151 (exists A (v1_funct_1(A) & f1_s1_finset_1 = k1_relat_1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s1_finset_1) -> (p1_s1_finset_1(B) -> k1_funct_1(A,B) = f2_s1_finset_1(B)) & (-p1_s1_finset_1(B) -> f3_s1_finset_1(B) = k1_funct_1(A,B))))) & v1_relat_1(A))) # label(s1_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2152 $T # label(t2_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2153 (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]. 4.49/4.53 2154 $T # label(t7_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2155 (all A all B all C all D all E all F all G v1_finset_1(k5_enumset1(A,B,C,D,E,F,G))) # label(fc7_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2156 $T # label(t10_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2157 (all A (v1_finset_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v1_finset_1(B))))) # label(cc2_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2158 (all A all B all C all D v1_finset_1(k2_enumset1(A,B,C,D))) # label(fc4_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2159 (all A all B (v1_finset_1(k2_zfmisc_1(B,A)) -> v1_finset_1(B) | k1_xboole_0 = A)) # label(t22_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2160 (all A (v1_finset_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> -((all C -((all D (r2_hidden(D,B) & r1_tarski(C,D) -> D = C)) & r2_hidden(C,B))) & B != k1_xboole_0))))) # label(t18_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2161 (all A (v1_finset_1(A) <-> (exists B (v1_relat_1(B) & v1_funct_1(B) & k2_relat_1(B) = A & r2_hidden(k1_relat_1(B),k5_ordinal2))))) # label(d1_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2162 (all A all B (v1_finset_1(A) -> v1_finset_1(k3_xboole_0(A,B)))) # label(t15_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2163 v1_finset_1(f1_s2_finset_1) & p1_s2_finset_1(k1_xboole_0) & (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(f1_s2_finset_1) # label(s2_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2164 (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]. 4.49/4.53 2165 $T # label(t1_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2166 (all A all B (v1_finset_1(A) -> v1_finset_1(k3_xboole_0(A,B)))) # label(fc11_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2167 (all A all B all C v1_finset_1(k1_enumset1(A,B,C))) # label(fc3_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2168 (all A -(v6_ordinal1(A) & (all B -((all C (r2_hidden(C,A) -> r1_tarski(C,B))) & r2_hidden(B,A))) & k1_xboole_0 != A & v1_finset_1(A))) # label(t31_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2169 $T # label(t11_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2170 (all A all B all C (v1_finset_1(B) & v1_finset_1(C) & v1_finset_1(A) -> v1_finset_1(k3_zfmisc_1(A,B,C)))) # label(t20_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2171 (all A all B all C all D (v1_finset_1(B) & v1_finset_1(C) & v1_finset_1(D) & v1_finset_1(A) -> v1_finset_1(k4_zfmisc_1(A,B,C,D)))) # label(t21_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2172 (all A (-v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)))) # label(fc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2173 $T # label(t5_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2174 (all A (v1_finset_1(k1_zfmisc_1(A)) <-> v1_finset_1(A))) # label(t24_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2175 (all A all B (v1_finset_1(k2_zfmisc_1(A,B)) -> k1_xboole_0 = A | v1_finset_1(B))) # label(t23_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2176 (all A (v1_xboole_0(A) -> v1_finset_1(A))) # label(cc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2177 (all A all B (v1_relat_1(A) & v1_finset_1(B) & v1_funct_1(A) -> v1_finset_1(k9_relat_1(A,B)))) # label(fc13_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2178 (all A all B all C all D all E all F v1_finset_1(k4_enumset1(A,B,C,D,E,F))) # label(fc6_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2179 (all A all B all C all D all E all F all G all H v1_finset_1(k6_enumset1(A,B,C,D,E,F,G,H))) # label(fc8_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2180 (all A all B (v1_finset_1(A) -> v1_finset_1(k4_xboole_0(A,B)))) # label(t16_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2181 (all A exists B (m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) & v1_relat_1(B) & v2_funct_1(B) & v2_ordinal1(B) & v4_ordinal2(B) & v1_finset_1(B) & v3_ordinal1(B) & v1_ordinal1(B) & v1_funct_1(B))) # label(rc2_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2182 (all A all B (v1_finset_1(A) & v1_finset_1(B) -> v1_finset_1(k2_zfmisc_1(A,B)))) # label(fc14_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2183 (all A (-v1_xboole_0(A) -> (exists B (-v1_xboole_0(B) & v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)))))) # label(rc3_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2184 (all A all B (v1_finset_1(k2_tarski(A,B)) & -v1_xboole_0(k2_tarski(A,B)))) # label(fc2_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2185 (all A ((exists B (A = k8_funct_2(f1_s9_fraenkel,f2_s9_fraenkel,f4_s9_fraenkel,B) & p1_s9_fraenkel(B) & r2_hidden(B,f3_s9_fraenkel) & m1_subset_1(B,f1_s9_fraenkel))) <-> r2_hidden(A,a_0_16_fraenkel))) # label(fraenkel_a_0_16_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2186 (all A (r2_hidden(A,a_0_2_fraenkel) <-> (exists B exists C (m1_subset_1(C,f2_s2_fraenkel) & A = f3_s2_fraenkel(B,C) & p1_s2_fraenkel(B,C) & m1_subset_1(B,f1_s2_fraenkel))))) # label(fraenkel_a_0_2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2187 v1_finset_1(f3_s22_fraenkel) & v1_finset_1(f4_s22_fraenkel) -> v1_finset_1(a_0_39_fraenkel) # label(s22_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2188 (all A ((exists B (m1_subset_1(B,f1_s15_fraenkel) & p2_s15_fraenkel(B) & A = B)) <-> r2_hidden(A,a_0_28_fraenkel))) # label(fraenkel_a_0_28_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2189 (all A ((exists B exists C (m1_subset_1(B,f1_s4_fraenkel) & f3_s4_fraenkel(B,C) = A & p2_s4_fraenkel(B,C) & m1_subset_1(C,f2_s4_fraenkel))) <-> r2_hidden(A,a_0_7_fraenkel))) # label(fraenkel_a_0_7_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2190 (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) & f3_s19_fraenkel(B,f4_s19_fraenkel) = A)))) # label(fraenkel_a_0_35_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2191 (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))))) & (all A (m1_subset_1(A,f1_s8_fraenkel) -> (all B (m1_subset_1(B,f2_s8_fraenkel) -> (p2_s8_fraenkel(A,B) <-> p1_s8_fraenkel(A,B)))))) -> a_0_15_fraenkel = a_0_14_fraenkel # label(s8_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2192 (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]. 4.49/4.53 2193 (exists A (v1_fraenkel(A) & -v1_xboole_0(A))) # label(rc1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2194 (all A ((all B (r2_hidden(B,A) -> v1_relat_1(B) & v1_funct_1(B))) <-> v1_fraenkel(A))) # label(d1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2195 $T # label(t1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2196 (all A (m1_subset_1(A,f1_s26_fraenkel) -> -(r2_hidden(A,f3_s26_fraenkel) & (all B (m1_subset_1(B,f2_s26_fraenkel) -> -p1_s26_fraenkel(A,B)))))) -> (exists A (v1_funct_1(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))) # label(s26_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2197 (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]. 4.49/4.53 2198 $T # label(t7_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2199 (all A ((exists B (m1_subset_1(B,f1_s9_fraenkel) & p2_s9_fraenkel(B) & r2_hidden(B,f3_s9_fraenkel) & k8_funct_2(f1_s9_fraenkel,f2_s9_fraenkel,f5_s9_fraenkel,B) = A)) <-> r2_hidden(A,a_0_17_fraenkel))) # label(fraenkel_a_0_17_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2200 (all A (-v1_xboole_0(A) -> (all B all C all D (r1_tarski(C,B) & r1_tarski(D,A) -> (all E (m1_subset_1(E,k1_funct_2(C,D)) -> (exists F (m2_fraenkel(F,B,A,k1_fraenkel(B,A)) & E = k7_relat_1(F,C))))) | k1_funct_2(C,D) = k1_xboole_0)))) # label(t14_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2201 (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(f5_s9_fraenkel,f3_s9_fraenkel) = k7_relat_1(f4_s9_fraenkel,f3_s9_fraenkel) -> a_0_16_fraenkel = a_0_17_fraenkel # label(s9_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2202 (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]. 4.49/4.53 2203 (all A (r2_hidden(A,a_0_23_fraenkel) <-> (exists B exists C (A = f4_s13_fraenkel(B,C) & p1_s13_fraenkel(B,C) & p2_s13_fraenkel(f4_s13_fraenkel(B,C)) & m1_subset_1(C,f2_s13_fraenkel) & m1_subset_1(B,f1_s13_fraenkel))))) # label(fraenkel_a_0_23_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2204 (all A (r2_hidden(A,a_0_15_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s8_fraenkel) & A = f3_s8_fraenkel(C,B) & p2_s8_fraenkel(B,C) & m1_subset_1(C,f2_s8_fraenkel))))) # label(fraenkel_a_0_15_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2205 (all A (v1_fraenkel(A) -> (all B (r1_tarski(B,A) -> v1_fraenkel(B))))) # label(t17_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2206 (all A (m1_subset_1(A,f1_s19_fraenkel) -> (all B (m1_subset_1(B,f2_s19_fraenkel) -> (p2_s19_fraenkel(A,B) <-> B = f4_s19_fraenkel & p1_s19_fraenkel(A,B)))))) -> a_0_34_fraenkel = a_0_35_fraenkel # label(s19_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2207 (all A (r2_hidden(A,a_0_24_fraenkel) <-> (exists B (f2_s14_fraenkel(B) = A & p1_s14_fraenkel(B) & r2_hidden(B,a_0_25_fraenkel) & m1_subset_1(B,f1_s14_fraenkel))))) # label(fraenkel_a_0_24_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2208 (all A ((exists B exists C (m1_subset_1(B,f1_s16_fraenkel) & f3_s16_fraenkel(B,C) = A & p1_s16_fraenkel(B,C) & m1_subset_1(C,f2_s16_fraenkel))) <-> r2_hidden(A,a_0_30_fraenkel))) # label(fraenkel_a_0_30_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2209 (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]. 4.49/4.53 2210 (all A ((exists B exists C (p1_s20_fraenkel(B,C) & f4_s20_fraenkel = C & f3_s20_fraenkel(B,C) = A & m1_subset_1(C,f2_s20_fraenkel) & m1_subset_1(B,f1_s20_fraenkel))) <-> r2_hidden(A,a_0_36_fraenkel))) # label(fraenkel_a_0_36_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2211 (all A all B (-v1_xboole_0(B) -> k1_funct_2(A,B) = k1_fraenkel(A,B))) # label(redefinition_k1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2212 (all A ((exists B (m1_subset_1(B,f1_s6_fraenkel) & f2_s6_fraenkel(B) = A & p1_s6_fraenkel(B))) <-> r2_hidden(A,a_0_10_fraenkel))) # label(fraenkel_a_0_10_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2213 (all A (r2_hidden(A,a_0_19_fraenkel) <-> (exists B exists C (m1_subset_1(C,f2_s11_fraenkel) & f3_s11_fraenkel(B,C) = A & p1_s11_fraenkel(B,C) & m1_subset_1(B,f1_s11_fraenkel))))) # label(fraenkel_a_0_19_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2214 (all A ((exists B (m1_subset_1(B,f1_s1_fraenkel) & f2_s1_fraenkel(B) = A & p2_s1_fraenkel(B))) <-> r2_hidden(A,a_0_1_fraenkel))) # label(fraenkel_a_0_1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2215 (all A all B all C (-v1_xboole_0(C) & v1_fraenkel(C) -> ((all D (m1_subset_1(D,C) -> m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D))) <-> m1_fraenkel(C,A,B)))) # label(d2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2216 (all A ((exists B (m1_subset_1(B,f1_s17_fraenkel) & f3_s17_fraenkel(B) = A & p1_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]. 4.49/4.53 2217 (all A (r2_hidden(A,a_0_29_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s15_fraenkel) & f3_s15_fraenkel(B,C) = A & p1_s15_fraenkel(B,C) & p2_s15_fraenkel(B) & m1_subset_1(C,f2_s15_fraenkel))))) # label(fraenkel_a_0_29_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2218 (all A ((exists B exists C (m1_subset_1(B,f1_s16_fraenkel) & m1_subset_1(C,f2_s16_fraenkel) & p2_s16_fraenkel(B,C) & A = f3_s16_fraenkel(B,C))) <-> r2_hidden(A,a_0_31_fraenkel))) # label(fraenkel_a_0_31_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2219 (all A ((exists B (m1_subset_1(B,f3_s13_fraenkel) & p2_s13_fraenkel(B) & r2_hidden(B,a_0_22_fraenkel) & B = A)) <-> r2_hidden(A,a_0_21_fraenkel))) # label(fraenkel_a_0_21_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2220 (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]. 4.49/4.53 2221 (all A ((exists B (m1_subset_1(B,f1_s18_fraenkel) & f3_s18_fraenkel(B) = A & -r2_hidden(f3_s18_fraenkel(B),f2_s18_fraenkel) & p1_s18_fraenkel(B))) <-> r2_hidden(A,a_0_33_fraenkel))) # label(fraenkel_a_0_33_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2222 v1_finset_1(f3_s25_fraenkel) & v1_finset_1(f4_s25_fraenkel) & (all A (m2_fraenkel(A,f1_s25_fraenkel,f2_s25_fraenkel,k1_fraenkel(f1_s25_fraenkel,f2_s25_fraenkel)) -> (all B (m2_fraenkel(B,f1_s25_fraenkel,f2_s25_fraenkel,k1_fraenkel(f1_s25_fraenkel,f2_s25_fraenkel)) -> (k7_relat_1(A,f3_s25_fraenkel) = k7_relat_1(B,f3_s25_fraenkel) -> f5_s25_fraenkel(B) = f5_s25_fraenkel(A)))))) -> v1_finset_1(a_0_40_fraenkel) # label(s25_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2223 (all A (-v1_xboole_0(A) -> (all B all C all D (r1_tarski(C,B) & r1_tarski(D,A) -> (all E (m1_subset_1(E,k1_funct_2(C,D)) -> v1_funct_1(E) & m2_relset_1(E,B,A))) | k1_xboole_0 = k1_funct_2(C,D))))) # label(t6_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2224 (all A all B all C (m1_fraenkel(C,A,B) & -v1_xboole_0(B) -> (all D (m2_fraenkel(D,A,B,C) -> m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D))))) # label(dt_m2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2225 (all A (m1_subset_1(A,f1_s16_fraenkel) -> (all B (m1_subset_1(B,f2_s16_fraenkel) -> -(p1_s16_fraenkel(A,B) & (all C (m1_subset_1(C,f1_s16_fraenkel) -> -(f3_s16_fraenkel(A,B) = f3_s16_fraenkel(C,B) & p2_s16_fraenkel(C,B))))))))) -> r1_tarski(a_0_30_fraenkel,a_0_31_fraenkel) # label(s16_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2226 (all A (r2_hidden(A,a_0_3_fraenkel) <-> (exists B exists C (m1_subset_1(C,f2_s2_fraenkel) & A = f3_s2_fraenkel(B,C) & p2_s2_fraenkel(B,C) & m1_subset_1(B,f1_s2_fraenkel))))) # label(fraenkel_a_0_3_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2227 (all A ((exists B (m2_fraenkel(B,f1_s25_fraenkel,f2_s25_fraenkel,k1_fraenkel(f1_s25_fraenkel,f2_s25_fraenkel)) & f5_s25_fraenkel(B) = A & r1_tarski(k2_funct_2(f1_s25_fraenkel,f2_s25_fraenkel,B,f3_s25_fraenkel),f4_s25_fraenkel))) <-> r2_hidden(A,a_0_40_fraenkel))) # label(fraenkel_a_0_40_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2228 (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]. 4.49/4.53 2229 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> m1_fraenkel(k2_setwiseo(k1_zfmisc_1(k2_zfmisc_1(A,B)),C),A,B))) # label(t10_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2230 (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_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (k7_relat_1(C,E) = k7_relat_1(D,E) -> (all F (m1_subset_1(F,A) -> (r2_hidden(F,E) -> k8_funct_2(A,B,D,F) = k8_funct_2(A,B,C,F)))))))))))))) # label(t3_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2231 v1_finset_1(f2_s21_fraenkel) -> v1_finset_1(a_0_38_fraenkel) # label(s21_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2232 (all A ((exists B (A = B & p2_s14_fraenkel(B) & m1_subset_1(B,f1_s14_fraenkel))) <-> r2_hidden(A,a_0_25_fraenkel))) # label(fraenkel_a_0_25_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2233 $T # label(t2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2234 (all A ((exists B exists C (m1_subset_1(B,f1_s22_fraenkel) & m1_subset_1(C,f2_s22_fraenkel) & r2_hidden(B,f3_s22_fraenkel) & r2_hidden(C,f4_s22_fraenkel) & f5_s22_fraenkel(B,C) = A)) <-> r2_hidden(A,a_0_39_fraenkel))) # label(fraenkel_a_0_39_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2235 (exists A ((all B (m1_subset_1(B,f1_s24_fraenkel) -> ((exists C (r2_hidden(C,f3_s24_fraenkel) & p1_s24_fraenkel(B,C) & f4_s24_fraenkel(C) = B & m1_subset_1(C,f2_s24_fraenkel))) <-> r2_hidden(B,A)))) & m1_subset_1(A,k5_finsub_1(f1_s24_fraenkel)))) # label(s24_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2236 (all A (m1_subset_1(A,f1_s5_fraenkel) -> f2_s5_fraenkel(A) = f3_s5_fraenkel(A))) -> a_0_8_fraenkel = a_0_9_fraenkel # label(s5_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2237 (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]. 4.49/4.53 2238 (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,k3_xboole_0(B,C)) = k7_relat_1(D,C))))) # label(t15_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2239 (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]. 4.49/4.53 2240 (all A (m1_subset_1(A,f1_s27_fraenkel) -> -(r2_hidden(A,f3_s27_fraenkel) & (all B (m1_subset_1(B,f2_s27_fraenkel) -> -p1_s27_fraenkel(A,B)))))) -> (exists A ((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))))) & m2_fraenkel(A,f1_s27_fraenkel,f2_s27_fraenkel,k1_fraenkel(f1_s27_fraenkel,f2_s27_fraenkel)))) # label(s27_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2241 (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]. 4.49/4.53 2242 (all A ((exists B (A = f2_s14_fraenkel(B) & p2_s14_fraenkel(B) & p1_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]. 4.49/4.53 2243 (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]. 4.49/4.53 2244 (all A ((exists B exists C (m1_subset_1(C,f2_s13_fraenkel) & p1_s13_fraenkel(B,C) & f4_s13_fraenkel(B,C) = A & m1_subset_1(B,f1_s13_fraenkel))) <-> r2_hidden(A,a_0_22_fraenkel))) # label(fraenkel_a_0_22_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2245 (all A (r2_hidden(A,a_0_0_fraenkel) <-> (exists B (p1_s1_fraenkel(B) & A = f2_s1_fraenkel(B) & m1_subset_1(B,f1_s1_fraenkel))))) # label(fraenkel_a_0_0_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2246 (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]. 4.49/4.53 2247 (all A (r2_hidden(A,a_0_14_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s8_fraenkel) & m1_subset_1(C,f2_s8_fraenkel) & A = f3_s8_fraenkel(B,C) & p1_s8_fraenkel(B,C))))) # label(fraenkel_a_0_14_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2248 (all A all B v1_fraenkel(k1_funct_2(A,B))) # label(fc1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2249 (all A (r2_hidden(A,a_0_18_fraenkel) <-> (exists B (A = B & p1_s10_fraenkel(B) & m1_subset_1(B,f1_s10_fraenkel))))) # label(fraenkel_a_0_18_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2250 (all A (r2_hidden(A,a_0_5_fraenkel) <-> (exists B (m1_subset_1(B,f1_s3_fraenkel) & A = f2_s3_fraenkel(B) & p2_s3_fraenkel(B))))) # label(fraenkel_a_0_5_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2251 (all A (m1_subset_1(A,f1_s6_fraenkel) -> (p1_s6_fraenkel(A) -> f2_s6_fraenkel(A) = f3_s6_fraenkel(A)))) -> a_0_10_fraenkel = a_0_11_fraenkel # label(s6_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2252 (all A ((exists B exists C (m1_subset_1(B,f1_s7_fraenkel) & p1_s7_fraenkel(B,C) & f3_s7_fraenkel(B,C) = A & m1_subset_1(C,f2_s7_fraenkel))) <-> r2_hidden(A,a_0_12_fraenkel))) # label(fraenkel_a_0_12_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2253 (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]. 4.49/4.53 2254 (all A ((exists B (m1_subset_1(B,f1_s6_fraenkel) & f3_s6_fraenkel(B) = A & p1_s6_fraenkel(B))) <-> r2_hidden(A,a_0_11_fraenkel))) # label(fraenkel_a_0_11_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2255 (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_13_fraenkel = a_0_12_fraenkel # label(s7_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2256 (all A (m1_subset_1(A,f1_s23_fraenkel) -> p1_s23_fraenkel(A,A))) & (all A (m1_subset_1(A,f1_s23_fraenkel) -> (all B (m1_subset_1(B,f1_s23_fraenkel) -> (all C (m1_subset_1(C,f1_s23_fraenkel) -> (p1_s23_fraenkel(B,C) & p1_s23_fraenkel(A,B) -> p1_s23_fraenkel(A,C)))))))) -> (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]. 4.49/4.53 2257 (all A all B (v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k1_funct_2(A,B)))) # label(t16_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2258 (all A all B exists C m1_fraenkel(C,A,B)) # label(existence_m1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2259 (all A ((exists B (A = f3_s21_fraenkel(B) & r2_hidden(B,f2_s21_fraenkel) & m1_subset_1(B,f1_s21_fraenkel))) <-> r2_hidden(A,a_0_38_fraenkel))) # label(fraenkel_a_0_38_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2260 (all A ((exists B exists C (m1_subset_1(C,f2_s15_fraenkel) & f3_s15_fraenkel(B,C) = A & p1_s15_fraenkel(B,C) & r2_hidden(B,a_0_28_fraenkel) & 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]. 4.49/4.53 2261 (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]. 4.49/4.53 2262 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_fraenkel(k1_tarski(A)))) # label(t8_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2263 (all A (r2_hidden(A,a_0_37_fraenkel) <-> (exists B (m1_subset_1(B,f1_s20_fraenkel) & A = f3_s20_fraenkel(B,f4_s20_fraenkel) & p1_s20_fraenkel(B,f4_s20_fraenkel))))) # label(fraenkel_a_0_37_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2264 $T # label(t9_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2265 (all A (r2_hidden(A,a_0_6_fraenkel) <-> (exists B exists C (p1_s4_fraenkel(B,C) & A = f3_s4_fraenkel(B,C) & m1_subset_1(C,f2_s4_fraenkel) & m1_subset_1(B,f1_s4_fraenkel))))) # label(fraenkel_a_0_6_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2266 (all A (m1_subset_1(A,f1_s3_fraenkel) -> (p1_s3_fraenkel(A) <-> p2_s3_fraenkel(A)))) -> a_0_5_fraenkel = a_0_4_fraenkel # label(s3_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2267 (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]. 4.49/4.53 2268 $T # label(t13_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2269 $T # label(t12_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2270 $T # label(t4_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2271 (all A (r2_hidden(A,a_0_9_fraenkel) <-> (exists B (p1_s5_fraenkel(B) & A = f3_s5_fraenkel(B) & m1_subset_1(B,f1_s5_fraenkel))))) # label(fraenkel_a_0_9_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2272 (all A (r2_hidden(A,a_0_20_fraenkel) <-> (exists B exists C (A = f3_s12_fraenkel(B,C) & p1_s12_fraenkel(B,C) & m1_subset_1(C,f2_s12_fraenkel) & m1_subset_1(B,f1_s12_fraenkel))))) # label(fraenkel_a_0_20_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2273 (all A (r2_hidden(A,a_0_4_fraenkel) <-> (exists B (f2_s3_fraenkel(B) = A & p1_s3_fraenkel(B) & m1_subset_1(B,f1_s3_fraenkel))))) # label(fraenkel_a_0_4_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2274 (all A (r2_hidden(A,a_0_13_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s7_fraenkel) & m1_subset_1(C,f2_s7_fraenkel) & p1_s7_fraenkel(B,C) & f4_s7_fraenkel(B,C) = A)))) # label(fraenkel_a_0_13_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.53 2275 (all A (r2_hidden(A,a_0_34_fraenkel) <-> (exists B exists C (A = f3_s19_fraenkel(B,C) & p2_s19_fraenkel(B,C) & m1_subset_1(C,f2_s19_fraenkel) & m1_subset_1(B,f1_s19_fraenkel))))) # label(fraenkel_a_0_34_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2276 $T # label(dt_k4_numbers) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2277 $T # label(dt_k1_numbers) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2278 (all A ((exists B (np__0 = k1_funct_1(B,k13_arytm_3) & B = A & m1_subset_1(B,k1_funct_2(k2_tarski(np__0,k13_arytm_3),k1_numbers)))) <-> r2_hidden(A,a_0_0_numbers))) # label(fraenkel_a_0_0_numbers) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2279 $T # label(dt_k2_numbers) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2280 $T # label(dt_k3_numbers) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2281 (all A k1_card_1(k1_tarski(A)) = k4_ordinal2) # label(t50_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2282 (all A all B (v1_funct_1(B) & v1_relat_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]. 4.49/4.54 2283 $T # label(t15_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2284 $T # label(t77_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2285 (all A all B (r2_wellord2(A,B) -> k2_card_1(B) = k2_card_1(A))) # label(t35_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2286 (all A (r2_hidden(A,k5_ordinal2) -> v1_card_1(A))) # label(t65_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2287 (all A (v1_finset_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k1_card_1(B) = k1_card_1(A) <-> k4_card_1(A) = B))))) # label(d11_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2288 $T # label(t62_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2289 (all A (v1_card_1(A) & v1_finset_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]. 4.49/4.54 2290 $T # label(d2_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2291 (all A all B ((exists C (v1_relat_1(C) & v1_funct_1(C) & r1_tarski(A,k2_relat_1(C)) & k1_relat_1(C) = B)) <-> r1_tarski(k1_card_1(A),k1_card_1(B)))) # label(t28_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2292 (all A all B (r2_wellord2(A,B) <-> k1_card_1(A) = k1_card_1(B))) # label(t21_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2293 (all A (v3_ordinal1(A) -> k2_card_1(k3_card_1(A)) = k3_card_1(k1_ordinal1(A)))) # label(t39_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2294 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (k3_card_1(A) = k3_card_1(B) -> B = A))))) # label(t42_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2295 $T # label(t53_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2296 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r1_ordinal1(A,B) <-> r1_xreal_0(A,B)))))) # label(t56_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2297 $T # label(t9_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2298 $T # label(t10_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2299 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (B != A & r1_tarski(A,B) <-> r2_hidden(A,B)))))) # label(t13_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2300 (all A (v1_card_1(A) -> r2_hidden(A,k2_card_1(A)))) # label(t32_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2301 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r1_tarski(k3_card_1(A),k3_card_1(B)) <-> r1_ordinal1(A,B)))))) # label(t43_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2302 (all A (v3_ordinal1(A) -> (all B (k3_card_1(A) = B <-> (exists C (v1_relat_1(C) & v5_ordinal1(C) & k1_relat_1(C) = k1_ordinal1(A) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_funct_1(C,D) = k1_card_1(k8_ordinal2(k2_ordinal1(C,D))) | D = k1_xboole_0))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k2_card_1(k3_tarski(k1_tarski(k1_funct_1(C,D)))) = k1_funct_1(C,k1_ordinal1(D))))) & k1_card_1(k5_numbers) = k1_funct_1(C,k1_xboole_0) & B = k1_ordinal2(C) & v1_funct_1(C))))))) # label(d8_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2303 (all A (m1_subset_1(A,k5_numbers) -> v1_ordinal1(A) & -v3_xreal_0(A) & v1_card_1(A) & v1_xreal_0(A) & v1_finset_1(A) & v1_xcmplx_0(A) & v4_ordinal2(A) & v3_ordinal1(A) & v2_ordinal1(A))) # label(cc3_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2304 (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]. 4.49/4.54 2305 $T # label(t70_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2306 $T # label(t31_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2307 $T # label(t37_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2308 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> r2_wellord2(k3_relat_1(A),k2_wellord2(A))))) # label(t22_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2309 (all A all B all C (r1_tarski(A,B) & r2_wellord2(A,C) & r1_tarski(B,C) -> r2_wellord2(B,C) & r2_wellord2(A,B))) # label(t44_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2310 (all A r2_hidden(k1_card_1(k1_xboole_0),k2_card_1(A))) # label(t33_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2311 (all A all B (v1_finset_1(A) & r2_wellord2(A,B) -> v1_finset_1(B))) # label(t68_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2312 $T # label(t63_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2313 $T # label(t18_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2314 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(k1_card_1(A),k1_card_1(B)) <-> -r1_xreal_0(B,A)))))) # label(t73_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2315 (all A ((exists B (v3_ordinal1(B) & (all C (v3_ordinal1(C) -> (r2_wellord2(C,B) -> r1_ordinal1(B,C)))) & A = B)) <-> v1_card_1(A))) # label(d1_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2316 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (-r1_tarski(B,A) <-> r2_hidden(A,B)))))) # label(t14_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2317 $T # label(t20_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2318 $T # label(t1_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2319 (all A (v3_ordinal1(A) -> (v4_ordinal1(A) -> A = k1_xboole_0 | (all B (v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) -> ((all C (v3_ordinal1(C) -> (r2_hidden(C,A) -> k3_card_1(C) = k1_funct_1(B,C)))) & A = k1_relat_1(B) -> k1_card_1(k8_ordinal2(B)) = k3_card_1(A))))))) # label(t40_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2320 (all A all B ((exists C (v1_relat_1(C) & v1_funct_1(C) & A = k1_relat_1(C) & r1_tarski(k2_relat_1(C),B) & v2_funct_1(C))) <-> r1_tarski(k1_card_1(A),k1_card_1(B)))) # label(t26_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2321 (all A (v3_ordinal1(A) -> r1_ordinal1(k1_card_1(A),A))) # label(t24_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2322 (exists A v1_card_1(A)) # label(rc1_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2323 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k1_card_1(k1_nat_1(A,np__1)) = k2_card_1(k1_card_1(A)))) # label(t76_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2324 $T # label(t67_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2325 $T # label(t5_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2326 (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]. 4.49/4.54 2327 $T # label(t75_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2328 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> v1_finset_1(k1_card_1(A)) & v1_finset_1(A))) # label(t69_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2329 $T # label(t12_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2330 $T # label(d10_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2331 p1_s1_card_1(k1_xboole_0) & (all A (v1_card_1(A) -> (p1_s1_card_1(A) -> p1_s1_card_1(k2_card_1(A))))) & (all A (v1_card_1(A) -> (v2_card_1(A) & (all B (v1_card_1(B) -> (r2_hidden(B,A) -> p1_s1_card_1(B)))) -> p1_s1_card_1(A) | A = k1_xboole_0))) -> (all A (v1_card_1(A) -> p1_s1_card_1(A))) # label(s1_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2332 (all A (v1_card_1(A) -> v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A))) # label(cc1_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2333 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k1_card_1(A) = A)) # label(t66_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2334 (all A (v1_card_1(A) -> (v2_card_1(A) <-> (all B (v1_card_1(B) -> A != k2_card_1(B)))))) # label(d7_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2335 $T # label(t54_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2336 (all A (v1_finset_1(A) -> k4_card_1(A) = k1_card_1(A))) # label(redefinition_k4_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2337 (all A v1_card_1(k1_card_1(A))) # label(dt_k1_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2338 $T # label(t6_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2339 (all A all B all C (r2_hidden(C,B) & r2_hidden(A,B) -> r2_wellord2(k4_xboole_0(B,k1_tarski(A)),k4_xboole_0(B,k1_tarski(C))))) # label(t59_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2340 $T # label(d4_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2341 (all A r2_hidden(k1_card_1(A),k1_card_1(k1_zfmisc_1(A)))) # label(t30_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2342 (all A (v3_ordinal1(A) -> v3_ordinal1(k3_card_1(A)) & v1_card_1(k3_card_1(A)) & v2_ordinal1(k3_card_1(A)) & v1_ordinal1(k3_card_1(A)))) # label(fc1_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2343 (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]. 4.49/4.54 2344 (all A all B (k1_card_1(B) = k1_card_1(A) -> k2_card_1(B) = k2_card_1(A))) # label(t34_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2345 (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]. 4.49/4.54 2346 $T # label(t19_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2347 (all A all B (v1_card_1(B) -> (B = k1_card_1(A) <-> r2_wellord2(A,B)))) # label(d5_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2348 (all A all B (v1_card_1(B) -> (r2_hidden(k1_card_1(A),B) & (all C (v1_card_1(C) -> (r2_hidden(k1_card_1(A),C) -> r1_tarski(B,C)))) <-> k2_card_1(A) = B))) # label(d6_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2349 (all A (v1_finset_1(A) -> v1_ordinal1(k1_card_1(A)) & v2_ordinal1(k1_card_1(A)) & v1_finset_1(k1_card_1(A)) & v1_card_1(k1_card_1(A)) & v3_ordinal1(k1_card_1(A)))) # label(fc2_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2350 $T # label(t17_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2351 (all A (m1_subset_1(A,k5_numbers) -> v4_ordinal2(A) & -v3_xreal_0(A) & v1_card_1(A) & v1_xreal_0(A) & v1_xcmplx_0(A) & v3_ordinal1(A) & v2_ordinal1(A) & v1_ordinal1(A))) # label(cc2_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2352 $T # label(dt_k3_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2353 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (B = A <-> r2_wellord2(A,B)))))) # label(t8_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2354 (all A np__1 = k4_card_1(k1_tarski(A))) # label(t79_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2355 (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]. 4.49/4.54 2356 (all A (k1_xboole_0 = A <-> r2_wellord2(A,k1_xboole_0))) # label(t46_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2357 (all A all B (v1_card_1(B) -> (r2_hidden(A,B) -> r2_hidden(k1_card_1(A),B)))) # label(t25_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2358 $T # label(t57_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2359 (all A all B (r1_tarski(A,B) -> r1_tarski(k1_card_1(A),k1_card_1(B)))) # label(t27_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2360 $T # label(d9_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2361 $T # label(t3_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2362 (all A (v1_finset_1(A) -> v1_finset_1(k2_card_1(A)))) # label(t82_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2363 $T # label(t2_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2364 (all A (v1_finset_1(A) -> (all B (v1_finset_1(B) -> (r1_tarski(A,B) -> r1_xreal_0(k4_card_1(A),k4_card_1(B))))))) # label(t80_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2365 (all A -((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> -r2_wellord2(A,B))) & v1_finset_1(A))) # label(t74_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2366 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k1_card_1(B) = k1_card_1(A) -> A = B))))) # label(t71_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2367 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(A,B) <-> r2_hidden(k3_card_1(A),k3_card_1(B))))))) # label(t41_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2368 (all A (v1_finset_1(A) -> m2_subset_1(k4_card_1(A),k1_numbers,k5_numbers))) # label(dt_k4_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2369 $T # label(t11_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2370 (all A v1_card_1(k2_card_1(A))) # label(dt_k2_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2371 (exists A (v1_card_1(A) & v1_finset_1(A) & v3_ordinal1(A) & v2_ordinal1(A) & v1_ordinal1(A))) # label(rc2_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2372 (all A (v1_finset_1(A) -> (all B (v1_finset_1(B) -> (r2_wellord2(A,B) -> k4_card_1(A) = k4_card_1(B)))))) # label(t81_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2373 (all A exists B (r2_wellord2(A,B) & v3_ordinal1(B))) # label(t4_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2374 (all A -r2_wellord2(A,k1_zfmisc_1(A))) # label(t29_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2375 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_wellord2(A,B) -> B = A))))) # label(t64_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2376 (all A (v1_card_1(A) -> ((all B (v1_card_1(B) -> (r2_hidden(B,A) -> p1_s2_card_1(B)))) -> p1_s2_card_1(A)))) -> (all A (v1_card_1(A) -> p1_s2_card_1(A))) # label(s2_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2377 $T # label(t55_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2378 (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]. 4.49/4.54 2379 $T # label(t16_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2380 $T # label(d3_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2381 (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]. 4.49/4.54 2382 (all A (v3_ordinal1(A) -> r2_hidden(A,k2_card_1(A)))) # label(t36_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2383 $T # label(t7_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2384 (all A all B (v1_card_1(B) -> (r1_tarski(A,B) -> r1_tarski(k1_card_1(A),B)))) # label(t23_card_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2385 $T # label(t28_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2386 $T # label(t54_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2387 (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) -> (v2_funct_1(B) & v2_funct_1(A) & k2_relat_1(A) = k2_relat_1(B) -> k3_finseq_1(A) = k3_finseq_1(B)))))) # label(t65_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2388 (all A all 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)) & v1_relat_1(k10_finseq_1(A,B)))) # label(fc7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2389 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_xreal_0(A,B) & r1_xreal_0(np__1,A) <-> r2_hidden(A,k2_finseq_1(B))))))) # label(t3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2390 $T # label(t2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2391 (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]. 4.49/4.54 2392 (all A (v4_ordinal2(A) -> v1_finset_1(k1_finseq_1(A)))) # label(fc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2393 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> -((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(r2_hidden(C,k4_finseq_1(B)) & k4_tarski(C,k1_funct_1(B,C)) = A))) & r2_hidden(A,B)))) # label(t16_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2394 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(C,k3_finseq_1(B)) & r1_xreal_0(np__1,C) -> k1_funct_1(B,C) = k1_funct_1(k7_finseq_1(A,B),k1_nat_1(k3_finseq_1(A),C))))))))) # label(t86_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2395 (exists A (v1_relat_1(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)))))) # label(s2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2396 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (A = k1_xboole_0 <-> k1_xboole_0 = k4_finseq_1(A)))) # label(t26_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2397 (all A k1_tarski(k4_tarski(np__1,A)) = k5_finseq_1(A)) # label(d5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2398 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_xreal_0(A,B) -> k2_finseq_1(A) = k5_subset_1(k5_numbers,k2_finseq_1(B),k2_finseq_1(A))))))) # label(t9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2399 (all A (v4_ordinal2(A) -> m1_subset_1(k2_finseq_1(A),k1_zfmisc_1(k5_numbers)))) # label(dt_k2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2400 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (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]. 4.49/4.54 2401 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(A) & v2_finseq_1(A) & v1_funct_1(A))) # label(t68_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2402 (all A all B (v1_relat_1(A) & v1_finset_1(A) & v1_funct_1(A) -> v1_finset_1(k10_relat_1(A,B)))) # label(fc18_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2403 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (r2_hidden(A,k4_finseq_1(B)) -> r2_hidden(k1_nat_1(k3_finseq_1(C),A),k4_finseq_1(k7_finseq_1(C,B)))))))))) # label(t41_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2404 (all A m2_finseq_1(k14_finseq_1(A),k5_numbers)) # label(dt_k14_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2405 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(r2_hidden(C,k4_finseq_1(k7_finseq_1(A,B))) & -r2_hidden(C,k4_finseq_1(A)) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> -(r2_hidden(D,k4_finseq_1(B)) & C = k1_nat_1(k3_finseq_1(A),D))))))))))) # label(t38_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2406 (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 (m2_finseq_1(k7_finseq_1(A,B),C) -> m2_finseq_1(A,C) & m2_finseq_1(B,C))))))) # label(t50_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2407 (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]. 4.49/4.54 2408 (all A (v4_ordinal2(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (k7_relat_1(B,k2_finseq_1(A)) = C & r1_xreal_0(A,k3_finseq_1(B)) -> A = k3_finseq_1(C) & k2_finseq_1(A) = k4_finseq_1(C)))))))) # label(t21_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2409 (all A all B (v4_ordinal2(B) -> ((exists C (m2_subset_1(C,k1_numbers,k5_numbers) & A = C & r1_xreal_0(C,B) & r1_xreal_0(np__1,C))) <-> r2_hidden(A,a_1_0_finseq_1(B))))) # label(fraenkel_a_1_0_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2410 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> A = k7_finseq_1(k1_xboole_0,A) & k7_finseq_1(A,k1_xboole_0) = A)) # label(t47_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2411 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(C,k3_finseq_1(A)) & r1_xreal_0(np__1,C) -> k1_funct_1(A,C) = k1_funct_1(k7_finseq_1(A,B),C)))))))) # label(t85_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2412 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r2_hidden(B,k2_finseq_1(A)) -> r2_hidden(k2_xcmplx_0(B,C),k2_finseq_1(k2_xcmplx_0(A,C)))))))))) # label(t81_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2413 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> k1_relat_1(A) = k4_finseq_1(A))) # label(redefinition_k4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2414 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> A = k4_card_1(k1_card_1(A)) & A = k4_card_1(A))) # label(t78_finseq_1_AndLHS) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2415 (all A (v4_ordinal2(A) -> A = k4_card_1(k2_finseq_1(A)))) # label(t78_finseq_1_AndRHS) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2416 (all A (v1_relat_1(A) & v2_finseq_1(A) & v1_funct_1(A) -> v1_relat_1(k15_finseq_1(A)) & v1_funct_1(k15_finseq_1(A)))) # label(dt_k15_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2417 (all A (v4_ordinal2(A) -> r2_hidden(k2_xcmplx_0(A,np__1),k2_finseq_1(k2_xcmplx_0(A,np__1))))) # label(t6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2418 (all A (v1_relat_1(A) & v2_finseq_1(A) & v1_funct_1(A) -> k5_relat_1(k14_finseq_1(k1_relat_1(A)),A) = k15_finseq_1(A))) # label(d14_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2419 (all A (v4_ordinal2(A) -> (all B all C (m2_finseq_1(C,B) -> m2_finseq_1(k7_relat_1(C,k2_finseq_1(A)),B))))) # label(t23_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2420 (all A all B ((all C (r2_hidden(C,B) <-> m2_finseq_1(C,A))) <-> k13_finseq_1(A) = B)) # label(d11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2421 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (k2_finseq_1(A) = k2_finseq_1(B) -> B = A))))) # label(t8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2422 $T # label(dt_k13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2423 (all A all B (m1_subset_1(B,A) & -v1_xboole_0(A) -> k12_finseq_1(A,B) = k5_finseq_1(B))) # label(redefinition_k12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2424 (exists A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A))) # label(rc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2425 (all A exists B m1_finseq_1(B,A)) # label(existence_m1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2426 $T # label(t22_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2427 $T # label(dt_k5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2428 $T # label(t1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2429 (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_tarski(k2_relat_1(A),k2_relat_1(k7_finseq_1(A,B))))))) # label(t42_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2430 (all A all B (m1_finseq_1(B,A) -> v1_funct_1(k16_finseq_1(A,B,np__0)) & v2_funct_1(k16_finseq_1(A,B,np__0)) & v1_finseq_1(k16_finseq_1(A,B,np__0)) & v1_finset_1(k16_finseq_1(A,B,np__0)) & v1_relat_1(k16_finseq_1(A,B,np__0)) & v1_xboole_0(k16_finseq_1(A,B,np__0)))) # label(fc15_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2431 (all A (v2_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> k2_relat_1(k14_finseq_1(k1_relat_1(A))) = k1_relat_1(A))) # label(t71_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2432 (all A all B all C (m1_finseq_1(C,A) & m1_finseq_1(B,A) -> k7_finseq_1(B,C) = k8_finseq_1(A,B,C))) # label(redefinition_k8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2433 $T # label(t67_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2434 (all A (v1_relat_1(A) & v1_funct_1(A) -> -((all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> -r1_tarski(A,B))) & (exists B (m2_subset_1(B,k1_numbers,k5_numbers) & r1_tarski(k1_relat_1(A),k2_finseq_1(B))))))) # label(t15_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2435 (all A all B (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_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)))) # label(dt_k7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2436 (all A all B (v1_finseq_1(A) & v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) & -v1_xboole_0(B) & v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k7_finseq_1(B,A)) & v1_funct_1(k7_finseq_1(B,A)) & v1_finset_1(k7_finseq_1(B,A)) & v1_finseq_1(k7_finseq_1(B,A)) & -v1_xboole_0(k7_finseq_1(B,A)))) # label(fc14_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2437 (all A all B all C (m1_finseq_1(C,A) & m1_finseq_1(B,A) -> m2_finseq_1(k8_finseq_1(A,B,C),A))) # label(dt_k8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2438 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> v1_funct_1(A) & v1_finset_1(A) & v1_relat_1(A))) # label(cc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2439 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> -(r2_hidden(A,k2_finseq_1(f2_s5_finseq_1)) & (all B (m1_subset_1(B,f1_s5_finseq_1) -> -p1_s5_finseq_1(A,B)))))) -> (exists A (m2_finseq_1(A,f1_s5_finseq_1) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(B,k2_finseq_1(f2_s5_finseq_1)) -> p1_s5_finseq_1(B,k1_funct_1(A,B))))) & k2_finseq_1(f2_s5_finseq_1) = k4_finseq_1(A))) # label(s5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2440 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v4_ordinal2(C) -> (r1_xreal_0(k1_nat_1(k3_finseq_1(A),np__1),C) & r1_xreal_0(C,k1_nat_1(k3_finseq_1(A),k3_finseq_1(B))) -> k1_funct_1(k7_finseq_1(A,B),C) = k1_funct_1(B,k6_xcmplx_0(C,k3_finseq_1(A)))))))))) # label(t36_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2441 (all A all B (m2_finseq_1(B,A) -> (all C (v4_ordinal2(C) -> (r1_xreal_0(k3_finseq_1(B),C) -> k16_finseq_1(A,B,C) = B))))) # label(t79_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2442 $T # label(t53_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2443 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_wellord2(k2_finseq_1(A),k2_finseq_1(B)) -> A = B))))) # label(t74_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2444 (all A (v1_fraenkel(k13_finseq_1(A)) & -v1_xboole_0(k13_finseq_1(A)))) # label(fc16_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2445 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (k7_finseq_1(B,A) = k7_finseq_1(B,C) | k7_finseq_1(A,B) = k7_finseq_1(C,B) -> C = A))))))) # label(t46_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2446 (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) -> k7_relat_1(k7_finseq_1(A,B),k4_finseq_1(A)) = A)))) # label(t33_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2447 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v4_ordinal2(C) -> (r1_xreal_0(C,k3_finseq_1(k7_finseq_1(A,B))) -> k1_funct_1(B,k6_xcmplx_0(C,k3_finseq_1(A))) = k1_funct_1(k7_finseq_1(A,B),C) | r1_xreal_0(C,k3_finseq_1(A))))))))) # label(t37_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2448 (all A all B all C (k7_finseq_1(k9_finseq_1(A),k10_finseq_1(B,C)) = k11_finseq_1(A,B,C) & k11_finseq_1(A,B,C) = k7_finseq_1(k10_finseq_1(A,B),k9_finseq_1(C)))) # label(t60_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2449 $T # label(t30_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2450 (all A (v4_ordinal2(A) -> k1_finseq_1(A) = a_1_0_finseq_1(A))) # label(d1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2451 (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]. 4.49/4.54 2452 (all A (v1_relat_1(A) -> v1_relat_1(k17_finseq_1(A)))) # label(dt_k17_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2453 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers))) # label(dt_k3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2454 (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) -> (k3_finseq_1(B) = k3_finseq_1(A) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,C) & r1_xreal_0(C,k3_finseq_1(A)) -> k1_funct_1(B,C) = k1_funct_1(A,C)))) -> B = A))))) # label(t18_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2455 (all A ((exists B (r1_tarski(A,k2_finseq_1(B)) & m2_subset_1(B,k1_numbers,k5_numbers))) -> (k1_xboole_0 = k14_finseq_1(A) <-> A = k1_xboole_0))) # label(t72_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2456 $T # label(t34_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2457 (all A all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> k1_funct_1(k7_finseq_1(k9_finseq_1(A),B),np__1) = A)) # label(t58_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2458 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (B = k1_funct_1(C,np__2) & A = k1_funct_1(C,np__1) & np__2 = k3_finseq_1(C) <-> k10_finseq_1(A,B) = C))) # label(t61_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2459 (all A (v4_ordinal2(A) -> k2_finseq_1(k2_xcmplx_0(A,np__1)) = k2_xboole_0(k2_finseq_1(A),k1_tarski(k2_xcmplx_0(A,np__1))))) # label(t11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2460 (exists A (v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_funct_1(A) & v1_relat_1(A) & v1_xboole_0(A))) # label(rc3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2461 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),k1_relat_1(A)) -> v1_finseq_1(k5_relat_1(B,A)) & v1_funct_1(k5_relat_1(B,A)) & v1_relat_1(k5_relat_1(B,A))))))) # label(t20_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2462 (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]. 4.49/4.54 2463 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (B = k17_finseq_1(A) <-> (all C all D (r2_hidden(C,k3_relat_1(A)) & (exists E (r1_xreal_0(np__1,k3_finseq_1(E)) & C = k1_funct_1(E,np__1) & D = k1_funct_1(E,k3_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_finseq_1(E) & v1_funct_1(E) & v1_relat_1(E))) & r2_hidden(D,k3_relat_1(A)) <-> r2_hidden(k4_tarski(C,D),B)))))))) # label(d16_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2464 (all A exists B (v1_relat_1(B) & v1_finseq_1(B) & v1_finset_1(B) & v1_funct_1(B) & m1_relset_1(B,k5_numbers,A))) # label(rc2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2465 (all A all B all C all D (v1_finseq_1(D) & v1_funct_1(D) & v1_relat_1(D) -> (D = k11_finseq_1(A,B,C) <-> C = k1_funct_1(D,np__3) & B = k1_funct_1(D,np__2) & k1_funct_1(D,np__1) = A & np__3 = k3_finseq_1(D)))) # label(t62_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2466 (all A -v1_xboole_0(k13_finseq_1(A))) # label(fc9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2467 (all A all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (k1_tarski(A) = k2_relat_1(B) & k3_finseq_1(B) = np__1 <-> k9_finseq_1(A) = B))) # label(t56_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2468 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> v2_finseq_1(k7_relat_1(B,A)) & v2_finseq_1(k8_relat_1(A,B)) & v1_funct_1(k8_relat_1(A,B)) & v1_relat_1(k8_relat_1(A,B)) & v1_funct_1(k7_relat_1(B,A)) & v1_relat_1(k7_relat_1(B,A)))) # label(t69_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2469 (all A (v1_funct_1(A) & v1_finset_1(A) & v1_relat_1(A) -> v1_finset_1(k1_relat_1(A)))) # label(fc17_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2470 (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]. 4.49/4.54 2471 (exists A (v1_relat_1(A) & v1_funct_1(A) & v2_finseq_1(A))) # label(rc5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2472 (all A ((exists B (v4_ordinal2(B) & r1_tarski(A,k2_finseq_1(B)))) -> (all B (m2_finseq_1(B,k5_numbers) -> (B = k14_finseq_1(A) <-> 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) & k1_funct_1(B,D) = F & r1_xreal_0(F,E) & E = k1_funct_1(B,C) & r1_xreal_0(D,k3_finseq_1(B)) & -r1_xreal_0(D,C))))))))))))))) # label(d13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2473 (all A (v4_ordinal2(A) -> k1_finseq_1(A) = k2_finseq_1(A))) # label(redefinition_k2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2474 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k1_card_1(A) = k1_card_1(k2_finseq_1(A)))) # label(t76_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2475 (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) -> 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]. 4.49/4.54 2476 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_tarski(k2_finseq_1(A),k2_finseq_1(B)) <-> r1_xreal_0(A,B)))))) # label(t7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2477 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (np__0 = k3_finseq_1(A) <-> A = k1_xboole_0))) # label(t25_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.54 2478 $T # label(t51_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2479 (all A (v4_ordinal2(A) -> r2_hidden(A,k2_finseq_1(A)) | A = np__0)) # label(t5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2480 (all A all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (k9_finseq_1(A) = B <-> k1_funct_1(B,np__1) = A & k3_finseq_1(B) = np__1))) # label(t57_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2481 $T # label(dt_k10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2482 (all A all B (m1_finseq_1(B,A) -> v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B))) # label(dt_m1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2483 (all A all B (v1_relat_1(k10_finseq_1(A,B)) & v1_funct_1(k10_finseq_1(A,B)))) # label(fc5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2484 (all A (v4_ordinal2(A) -> k4_xboole_0(k2_finseq_1(k2_xcmplx_0(A,np__1)),k1_tarski(k2_xcmplx_0(A,np__1))) = k2_finseq_1(A))) # label(t12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2485 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> m1_subset_1(k4_finseq_1(A),k1_zfmisc_1(k5_numbers)))) # label(dt_k4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2486 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k2_finseq_1(B) = k1_relat_1(A) <-> k3_finseq_1(A) = B))))) # label(d3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2487 (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_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> ((all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(B)) -> k1_funct_1(C,k1_nat_1(k3_finseq_1(A),D)) = k1_funct_1(B,D)))) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(A)) -> k1_funct_1(C,D) = k1_funct_1(A,D)))) & 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]. 4.49/4.55 2488 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (k6_finseq_1(B) = A <-> k3_finseq_1(A) = np__0)))) # label(t32_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2489 (all A exists B m2_finseq_1(B,A)) # label(existence_m2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2490 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> r2_wellord2(k2_finseq_1(A),A))) # label(t75_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2491 (all A all B all C (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_funct_1(k11_finseq_1(A,B,C)))) # label(fc8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2492 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (B = k9_finseq_1(A) <-> k2_finseq_1(np__1) = k1_relat_1(B) & k1_funct_1(B,np__1) = A))) # label(d8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2493 (exists A (v1_xboole_0(A) & v1_relat_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_funct_1(A))) # label(rc6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2494 (all A all B (m2_finseq_1(B,A) -> v1_finseq_1(B) & m2_relset_1(B,k5_numbers,A) & v1_funct_1(B))) # label(dt_m2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2495 $T # label(t31_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2496 (all A all B (v1_funct_1(B) & v1_finseq_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]. 4.49/4.55 2497 (all A r2_hidden(k1_xboole_0,k13_finseq_1(A))) # label(t66_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2498 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B all C (p1_s1_finseq_1(A,C) & p1_s1_finseq_1(A,B) & r2_hidden(A,k2_finseq_1(f1_s1_finseq_1)) -> C = B)))) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> -(r2_hidden(A,k2_finseq_1(f1_s1_finseq_1)) & (all B -p1_s1_finseq_1(A,B))))) -> (exists A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & k4_finseq_1(A) = k2_finseq_1(f1_s1_finseq_1) & (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]. 4.49/4.55 2499 $T # label(t49_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2500 $T # label(t13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2501 (all A k1_tarski(k4_tarski(np__1,A)) = k9_finseq_1(A)) # label(t52_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2502 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (k2_finseq_1(A) = k5_subset_1(k5_numbers,k2_finseq_1(A),k2_finseq_1(B)) -> r1_xreal_0(A,B)))))) # label(t10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2503 (all A (v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)))) # label(fc3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2504 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(A),k2_relat_1(k7_finseq_1(B,A))))))) # label(t43_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2505 (all A all B all C k11_finseq_1(A,B,C) = k7_finseq_1(k7_finseq_1(k9_finseq_1(A),k9_finseq_1(B)),k9_finseq_1(C))) # label(d10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2506 (all A all B (v1_funct_1(A) & -v1_xboole_0(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) & v1_finseq_1(A) & v1_relat_1(A) -> v1_relat_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & -v1_xboole_0(k7_finseq_1(A,B)))) # label(fc13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2507 (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]. 4.49/4.55 2508 (exists A (-v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A))) # label(rc7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2509 (all A all B (m1_subset_1(B,A) & -v1_xboole_0(A) -> m2_finseq_1(k12_finseq_1(A,B),A))) # label(dt_k12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2510 (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) -> k1_nat_1(k3_finseq_1(A),k3_finseq_1(B)) = k3_finseq_1(k7_finseq_1(A,B)))))) # label(t35_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2511 (all A m2_finseq_1(k1_xboole_0,A)) # label(t29_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2512 p1_s3_finseq_1(k1_xboole_0) & (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (p1_s3_finseq_1(A) -> p1_s3_finseq_1(k7_finseq_1(A,k9_finseq_1(B))))))) -> (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> p1_s3_finseq_1(A))) # label(s3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2513 (all A (v1_relat_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)))) # label(fc4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2514 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> -((all D (m2_subset_1(D,k1_numbers,k5_numbers) -> -(D = A & r2_hidden(k1_nat_1(k3_finseq_1(C),D),k4_finseq_1(k7_finseq_1(C,B)))))) & r2_hidden(A,k4_finseq_1(B))))))) # label(t40_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2515 (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) & k4_finseq_1(B) = k2_finseq_1(np__1)))) # label(t55_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2516 (all A all B (m2_finseq_1(B,A) -> (all C (v4_ordinal2(C) -> k7_relat_1(B,k2_finseq_1(C)) = k16_finseq_1(A,B,C))))) # label(d15_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2517 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (k7_finseq_1(A,B) = k1_xboole_0 -> k1_xboole_0 = A & k1_xboole_0 = B))))) # label(t48_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2518 $T # label(t70_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2519 (all A (v1_finseq_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_relat_1(k5_finseq_1(A)) & -v1_xboole_0(k5_finseq_1(A)))) # label(fc12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2520 (all A k1_xboole_0 = k6_finseq_1(A)) # label(d6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2521 (all A all B (v1_relat_1(B) & v1_funct_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]. 4.49/4.55 2522 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_finseq_1(A) <-> (exists B (r1_tarski(k1_relat_1(A),k2_finseq_1(B)) & m2_subset_1(B,k1_numbers,k5_numbers)))))) # label(d12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2523 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (r1_tarski(A,B) -> r1_xreal_0(k3_finseq_1(A),k3_finseq_1(B))))))) # label(t84_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2524 $T # label(dt_k11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2525 (all A (v4_ordinal2(A) -> (all B (-v1_xboole_0(B) -> (exists C (A = k3_finseq_1(C) & m2_finseq_1(C,B))))))) # label(t24_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2526 (all A all B k7_finseq_1(k9_finseq_1(A),k9_finseq_1(B)) = k10_finseq_1(A,B)) # label(d9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2527 $T # label(dt_k1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2528 (exists A (-v1_xboole_0(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2529 (all A k5_finseq_1(A) = k9_finseq_1(A)) # label(redefinition_k9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2530 (all A exists B (m1_finseq_1(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_funct_1(B) & v1_xboole_0(B))) # label(rc4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2531 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> k3_finseq_1(A) = k1_card_1(A))) # label(redefinition_k3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2532 (all A all B (m2_finseq_1(B,A) <-> m1_finseq_1(B,A))) # label(redefinition_m2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2533 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (A = k1_xboole_0 <-> k1_xboole_0 = k2_relat_1(A)))) # label(t27_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2534 (all A (v1_funct_1(k9_finseq_1(A)) & v1_relat_1(k9_finseq_1(A)))) # label(dt_k9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2535 (all A (v4_ordinal2(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> v1_funct_1(k7_relat_1(B,k2_finseq_1(A))) & v1_finseq_1(k7_relat_1(B,k2_finseq_1(A))) & v1_relat_1(k7_relat_1(B,k2_finseq_1(A))))))) # label(t19_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2536 (exists A all B (r2_hidden(B,A) <-> (exists C (r2_hidden(C,k13_finseq_1(f1_s4_finseq_1)) & p1_s4_finseq_1(C) & B = C & v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C))))) # label(s4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2537 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(C,k4_finseq_1(A)) -> k1_funct_1(B,C) = k1_funct_1(A,C)))) & k4_finseq_1(B) = k4_finseq_1(A) -> A = B))))) # label(t17_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2538 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_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]. 4.49/4.55 2539 (all A all B all C (m1_finseq_1(B,A) & v4_ordinal2(C) -> m2_finseq_1(k16_finseq_1(A,B,C),A))) # label(dt_k16_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2540 (all A all B (r1_tarski(A,B) -> r1_tarski(k13_finseq_1(A),k13_finseq_1(B)))) # label(t83_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2541 (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) -> (all D (v1_finseq_1(D) & v1_funct_1(D) & v1_relat_1(D) -> -(k7_finseq_1(A,B) = k7_finseq_1(C,D) & (all E (v1_relat_1(E) & v1_finseq_1(E) & v1_funct_1(E) -> C != k7_finseq_1(A,E))) & r1_xreal_0(k3_finseq_1(A),k3_finseq_1(C))))))))))) # label(t64_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2542 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> r1_tarski(k4_finseq_1(A),k4_finseq_1(k7_finseq_1(A,B))))))) # label(t39_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2543 (all A (v1_funct_1(A) & v2_finseq_1(A) & v1_relat_1(A) -> v1_relat_1(k15_finseq_1(A)) & v1_funct_1(k15_finseq_1(A)) & v1_finseq_1(k15_finseq_1(A)) & v1_finset_1(k15_finseq_1(A)))) # label(fc10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2544 (all A (v1_finset_1(A) <-> (exists B (v1_relat_1(B) & v1_funct_1(B) & A = k2_relat_1(B) & v1_finseq_1(B))))) # label(t73_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2545 (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]. 4.49/4.55 2546 (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(B)) <-> (exists D exists E (v1_relat_1(E) & v1_funct_1(E) & (exists F (r2_hidden(F,k1_relat_1(E)) & k1_funct_1(A,D) = E & r2_hidden(D,k1_relat_1(A)) & C = k4_tarski(D,F))))))) & (all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(C,k1_relat_1(B)) & k1_funct_1(A,k1_mcart_1(C)) = D -> k1_funct_1(D,k2_mcart_1(C)) = k1_funct_1(B,C)))) <-> B = k4_funct_5(A)))))) # label(d4_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2547 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k3_funct_5(C) = k3_funct_5(D) & r1_tarski(k1_relat_1(D),k2_zfmisc_1(A,B)) & r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> D = C))))) # label(t59_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2548 (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)))) -> k4_funct_5(A) = k1_xboole_0 & k1_xboole_0 = k6_funct_5(A)))) # label(t35_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2549 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(k5_funct_5(B))) -> v1_funct_1(k1_funct_1(k5_funct_5(B),A)) & v1_relat_1(k1_funct_1(k5_funct_5(B),A))))) # label(t40_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2550 (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)) -> C = k6_funct_5(k5_funct_5(C)) & C = k4_funct_5(k3_funct_5(C))))) # label(t57_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2551 $T # label(t25_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2552 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k1_relat_1(D) = k2_zfmisc_1(A,B) & k5_funct_5(D) = k5_funct_5(C) & k2_zfmisc_1(A,B) = k1_relat_1(C) -> C = D))))) # label(t52_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2553 (all A all B (r1_tarski(A,B) -> r1_tarski(k2_funct_5(A),k2_funct_5(B)) & r1_tarski(k1_funct_5(A),k1_funct_5(B)))) # label(t5_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2554 (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]. 4.49/4.55 2555 (all A all B (r1_tarski(k2_funct_5(k3_xboole_0(A,B)),k3_xboole_0(k2_funct_5(A),k2_funct_5(B))) & r1_tarski(k1_funct_5(k3_xboole_0(A,B)),k3_xboole_0(k1_funct_5(A),k1_funct_5(B))))) # label(t7_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2556 (all A all B all C (r1_xboole_0(A,B) -> 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)) & r2_wellord2(k1_funct_2(k2_xboole_0(A,B),C),k2_zfmisc_1(k1_funct_2(A,C),k1_funct_2(B,C))))) # label(t69_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2557 (all A all B all C all D (k2_funct_5(k2_tarski(k4_tarski(A,B),k4_tarski(C,D))) = k2_tarski(B,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]. 4.49/4.55 2558 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k4_funct_5(C) = k4_funct_5(D) & r1_tarski(k2_relat_1(D),k1_funct_2(A,B)) & r1_tarski(k2_relat_1(C),k1_funct_2(A,B)) -> C = D | A = k1_xboole_0))))) # label(t53_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2559 (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]. 4.49/4.55 2560 (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(A,B) = k1_xboole_0 | k1_relat_1(k3_funct_5(C)) = A & B = k1_relat_1(k5_funct_5(C))))) # label(t31_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2561 (all A all B (r1_tarski(k5_xboole_0(k1_funct_5(A),k1_funct_5(B)),k1_funct_5(k5_xboole_0(A,B))) & r1_tarski(k5_xboole_0(k2_funct_5(A),k2_funct_5(B)),k2_funct_5(k5_xboole_0(A,B))))) # label(t9_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2562 (all A k1_tarski(k1_xboole_0) = k1_funct_2(k1_xboole_0,A)) # label(t64_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2563 $T # label(t14_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2564 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_relat_1(C),k4_partfun1(A,B)) -> r2_hidden(k1_xboole_0,k2_relat_1(C)) | k5_funct_5(k6_funct_5(C)) = C & k3_funct_5(k4_funct_5(C)) = C))) # label(t58_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2565 (all A (v1_funct_1(A) & v1_relat_1(A) -> k2_funct_5(k1_relat_1(A)) = k1_relat_1(k5_funct_5(A)))) # label(t30_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2566 (all A ((all B all C -r2_hidden(k4_tarski(B,C),A)) -> k1_funct_5(A) = k1_xboole_0 & k2_funct_5(A) = k1_xboole_0)) # label(t17_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2567 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(k4_tarski(A,B),k1_relat_1(C)) -> v1_funct_1(k1_funct_1(k5_funct_5(C),B)) & v1_relat_1(k1_funct_1(k5_funct_5(C),B)) & r2_hidden(B,k1_relat_1(k5_funct_5(C)))))) # label(t28_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2568 (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]. 4.49/4.55 2569 (all A all B all 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))) & k1_card_1(k2_zfmisc_1(k1_funct_2(A,B),k1_funct_2(A,C))) = k1_card_1(k1_funct_2(A,k2_zfmisc_1(B,C))))) # label(t71_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2570 (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(k3_funct_5(B),A) = C & r2_hidden(A,k1_relat_1(k3_funct_5(B))) -> k1_relat_1(C) = k2_funct_5(k3_xboole_0(k1_relat_1(B),k2_zfmisc_1(k1_tarski(A),k2_funct_5(k1_relat_1(B))))) & r1_tarski(k2_relat_1(C),k2_relat_1(B)) & (all D (r2_hidden(D,k1_relat_1(C)) -> r2_hidden(k4_tarski(A,D),k1_relat_1(B)) & k1_funct_1(B,k4_tarski(A,D)) = k1_funct_1(C,D))) & r1_tarski(k1_relat_1(C),k2_funct_5(k1_relat_1(B)))))))) # label(t38_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2571 (all A (v1_relat_1(A) -> k1_funct_5(A) = k1_relat_1(A) & k2_relat_1(A) = k2_funct_5(A))) # label(t21_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2572 (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(D) & k2_zfmisc_1(A,B) = k1_relat_1(C) -> C = D))))) # label(t51_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2573 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k2_zfmisc_1(A,B) = k1_relat_1(C) -> r1_tarski(k2_relat_1(k5_funct_5(C)),k1_funct_2(A,k2_relat_1(C))) & r1_tarski(k2_relat_1(k3_funct_5(C)),k1_funct_2(B,k2_relat_1(C)))))) # label(t42_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2574 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_relat_1(C),k4_partfun1(A,B)) -> r1_tarski(k2_relat_1(k4_funct_5(C)),B) & r1_tarski(k2_relat_1(k6_funct_5(C)),B)))) # label(t47_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2575 (all A all B (r1_tarski(k2_funct_5(k2_zfmisc_1(A,B)),B) & r1_tarski(k1_funct_5(k2_zfmisc_1(A,B)),A))) # label(t12_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2576 $T # label(t2_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2577 (all A all B (r2_wellord2(A,k1_funct_2(k1_tarski(B),A)) & k1_card_1(k1_funct_2(k1_tarski(B),A)) = k1_card_1(A))) # label(t65_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2578 (all A all B all C all D (k1_card_1(A) = k1_card_1(B) & k1_card_1(D) = k1_card_1(C) -> k1_card_1(k1_funct_2(A,C)) = k1_card_1(k1_funct_2(B,D)))) # label(t68_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2579 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> -(r2_hidden(C,B) & (all E (v1_relat_1(E) & v1_funct_1(E) -> -(r1_tarski(k2_relat_1(E),k2_relat_1(D)) & (all F (r2_hidden(F,A) -> k1_funct_1(E,F) = k1_funct_1(D,k4_tarski(F,C)))) & A = k1_relat_1(E) & k1_funct_1(k5_funct_5(D),C) = E))) & k2_zfmisc_1(A,B) = k1_relat_1(D) & k2_zfmisc_1(A,B) != k1_xboole_0))) # label(t39_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2580 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(A,k1_relat_1(C)) & D = k1_funct_1(C,A) & 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]. 4.49/4.55 2581 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> r1_tarski(k1_relat_1(k3_funct_5(C)),A) & r1_tarski(k1_relat_1(k5_funct_5(C)),B)))) # label(t32_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2582 (all A all B all C (r1_tarski(A,k2_zfmisc_1(B,C)) -> r1_tarski(k2_funct_5(A),C) & r1_tarski(k1_funct_5(A),B))) # label(t13_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2583 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_relat_1(C),k4_partfun1(A,B)) -> r1_tarski(k1_relat_1(k4_funct_5(C)),k2_zfmisc_1(k1_relat_1(C),A)) & r1_tarski(k1_relat_1(k6_funct_5(C)),k2_zfmisc_1(A,k1_relat_1(C)))))) # label(t44_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2584 (all A all B (-(k1_xboole_0 = k2_zfmisc_1(A,B) & k2_zfmisc_1(B,A) = k1_xboole_0 & A = k1_xboole_0) -> k1_funct_5(k2_zfmisc_1(B,A)) = B & B = k2_funct_5(k2_zfmisc_1(A,B)))) # label(t11_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2585 (all A all B all C (A != B -> k1_card_1(k1_zfmisc_1(C)) = k1_card_1(k1_funct_2(C,k2_tarski(A,B))) & r2_wellord2(k1_funct_2(C,k2_tarski(A,B)),k1_zfmisc_1(C)))) # label(t72_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2586 (all A all B (k2_xboole_0(k1_funct_5(A),k1_funct_5(B)) = k1_funct_5(k2_xboole_0(A,B)) & k2_xboole_0(k2_funct_5(A),k2_funct_5(B)) = k2_funct_5(k2_xboole_0(A,B)))) # label(t6_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2587 (all A all B all C all D (r2_wellord2(C,D) & r2_wellord2(A,B) -> k1_card_1(k1_funct_2(B,D)) = k1_card_1(k1_funct_2(A,C)) & r2_wellord2(k1_funct_2(A,C),k1_funct_2(B,D)))) # label(t67_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2588 $T # label(t22_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2589 (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]. 4.49/4.55 2590 (all A all B all C (r2_hidden(k4_tarski(A,B),C) -> r2_hidden(A,k1_funct_5(C)) & r2_hidden(B,k2_funct_5(C)))) # label(t4_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2591 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r1_tarski(k1_relat_1(D),k2_zfmisc_1(A,B)) & k5_funct_5(C) = k5_funct_5(D) & r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> C = D))))) # label(t60_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2592 (all A all B (k1_tarski(A) = k1_funct_5(k1_tarski(k4_tarski(A,B))) & k2_funct_5(k1_tarski(k4_tarski(A,B))) = k1_tarski(B))) # label(t15_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2593 (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_funct_5(B))) & C = k1_funct_1(k5_funct_5(B),A) -> k1_funct_5(k3_xboole_0(k1_relat_1(B),k2_zfmisc_1(k1_funct_5(k1_relat_1(B)),k1_tarski(A)))) = k1_relat_1(C) & (all D (r2_hidden(D,k1_relat_1(C)) -> r2_hidden(k4_tarski(D,A),k1_relat_1(B)) & k1_funct_1(B,k4_tarski(D,A)) = k1_funct_1(C,D))) & r1_tarski(k2_relat_1(C),k2_relat_1(B)) & r1_tarski(k1_relat_1(C),k1_funct_5(k1_relat_1(B)))))))) # label(t41_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2594 (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)) -> k2_zfmisc_1(k1_relat_1(C),A) = k1_relat_1(k4_funct_5(C)) & 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]. 4.49/4.55 2595 (all A (v1_relat_1(A) & v1_funct_1(A) -> k3_funct_5(k2_funct_4(A)) = k5_funct_5(A))) # label(d5_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2596 (all A all B k1_tarski(k2_funcop_1(A,B)) = k1_funct_2(A,k1_tarski(B))) # label(t66_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2597 (exists A (v1_relat_1(A) & v1_funct_1(A) & (all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(B,f1_s1_funct_5) -> f2_s1_funct_5(B) = k1_funct_1(A,B)))) & f1_s1_funct_5 = k1_relat_1(A))) # label(s1_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2598 (all A all B all C (B != A -> r2_wellord2(k1_funct_2(k2_tarski(A,B),C),k2_zfmisc_1(C,C)) & k1_card_1(k1_funct_2(k2_tarski(A,B),C)) = k1_card_1(k2_zfmisc_1(C,C)))) # label(t73_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2599 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_relat_1(C),k1_funct_2(A,B)) -> r1_tarski(k2_relat_1(k6_funct_5(C)),B) & r1_tarski(k2_relat_1(k4_funct_5(C)),B)))) # label(t48_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2600 (all A all B (k2_funct_5(A) = B <-> (all C ((exists D r2_hidden(k4_tarski(D,C),A)) <-> r2_hidden(C,B))))) # label(d2_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2601 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r1_tarski(k2_relat_1(C),k1_funct_2(A,B)) & r1_tarski(k2_relat_1(D),k1_funct_2(A,B)) & k6_funct_5(D) = k6_funct_5(C) -> A = k1_xboole_0 | D = C))))) # label(t54_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2602 (all A all B (v1_funct_1(B) & v1_relat_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]. 4.49/4.55 2603 (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 = k5_funct_5(A) & k1_xboole_0 = k3_funct_5(A)))) # label(t34_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2604 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k3_funct_5(A) = B <-> k1_funct_5(k1_relat_1(A)) = k1_relat_1(B) & (all C -(r2_hidden(C,k1_funct_5(k1_relat_1(A))) & (all D (v1_funct_1(D) & v1_relat_1(D) -> -(k1_relat_1(D) = k2_funct_5(k3_xboole_0(k1_relat_1(A),k2_zfmisc_1(k1_tarski(C),k2_funct_5(k1_relat_1(A))))) & (all E (r2_hidden(E,k1_relat_1(D)) -> k1_funct_1(D,E) = k1_funct_1(A,k4_tarski(C,E)))) & k1_funct_1(B,C) = D)))))))))) # label(d3_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2605 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(A,k1_relat_1(C)) & D = k1_funct_1(C,A) & r2_hidden(B,k1_relat_1(D)) -> r2_hidden(k4_tarski(B,A),k1_relat_1(k6_funct_5(C))) & k1_funct_1(D,B) = k1_funct_1(k6_funct_5(C),k4_tarski(B,A)) & r2_hidden(k1_funct_1(D,B),k2_relat_1(k6_funct_5(C)))))))) # label(t46_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2606 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k5_funct_5(A)) & v1_relat_1(k5_funct_5(A)))) # label(dt_k5_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2607 (all A all B all C (v1_relat_1(C) & v1_funct_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]. 4.49/4.55 2608 $T # label(t3_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2609 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k3_funct_5(A)) & v1_funct_1(k3_funct_5(A)))) # label(dt_k3_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2610 (all A all B (B = k1_funct_5(A) <-> (all C (r2_hidden(C,B) <-> (exists D r2_hidden(k4_tarski(C,D),A)))))) # label(d1_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2611 (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(k2_relat_1(D),k4_partfun1(A,B)) & k6_funct_5(C) = k6_funct_5(D) & r1_tarski(k2_relat_1(C),k4_partfun1(A,B)) -> D = C | r2_hidden(k1_xboole_0,k2_relat_1(D)) | r2_hidden(k1_xboole_0,k2_relat_1(C))))))) # label(t62_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2612 (all A (v1_funct_1(A) & v1_relat_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]. 4.49/4.55 2613 (all A (k2_funct_5(A) = k1_xboole_0 <-> k1_funct_5(A) = k1_xboole_0)) # label(t19_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2614 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> -(k1_relat_1(D) = k2_zfmisc_1(A,B) & r2_hidden(C,A) & (all E (v1_relat_1(E) & v1_funct_1(E) -> -(B = k1_relat_1(E) & (all F (r2_hidden(F,B) -> k1_funct_1(E,F) = k1_funct_1(D,k4_tarski(C,F)))) & r1_tarski(k2_relat_1(E),k2_relat_1(D)) & E = k1_funct_1(k3_funct_5(D),C)))) & k1_xboole_0 != k2_zfmisc_1(A,B)))) # label(t36_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2615 (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)) -> k1_xboole_0 = A | k3_funct_5(k4_funct_5(C)) = C & k5_funct_5(k6_funct_5(C)) = C))) # label(t55_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2616 (all A (v1_relat_1(A) & v1_funct_1(A) -> k6_funct_5(A) = k2_funct_4(k4_funct_5(A)))) # label(d6_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2617 (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 & k6_funct_5(k5_funct_5(C)) = C))) # label(t56_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2618 $T # label(dt_k2_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2619 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(k4_tarski(A,B),k1_relat_1(C)) & D = k1_funct_1(k3_funct_5(C),A) -> k1_funct_1(C,k4_tarski(A,B)) = k1_funct_1(D,B) & r2_hidden(B,k1_relat_1(D))))))) # label(t27_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2620 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k4_funct_5(C) = k4_funct_5(D) & r1_tarski(k2_relat_1(D),k4_partfun1(A,B)) & r1_tarski(k2_relat_1(C),k4_partfun1(A,B)) -> r2_hidden(k1_xboole_0,k2_relat_1(C)) | D = C | r2_hidden(k1_xboole_0,k2_relat_1(D))))))) # label(t61_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2621 (all A all B (r1_tarski(k4_xboole_0(k2_funct_5(A),k2_funct_5(B)),k2_funct_5(k4_xboole_0(A,B))) & r1_tarski(k4_xboole_0(k1_funct_5(A),k1_funct_5(B)),k1_funct_5(k4_xboole_0(A,B))))) # label(t8_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2622 $T # label(dt_k1_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2623 $T # label(t23_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2624 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k4_funct_5(A)) & v1_funct_1(k4_funct_5(A)))) # label(dt_k4_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2625 (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(k4_tarski(A,B),k1_relat_1(C)) & D = k1_funct_1(k5_funct_5(C),B) -> r2_hidden(A,k1_relat_1(D)) & k1_funct_1(C,k4_tarski(A,B)) = k1_funct_1(D,A)))))) # label(t29_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2626 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k1_funct_2(C,A),k1_funct_2(C,B)))) # label(t63_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2627 $T # label(t24_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2628 (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 (m2_finseq_1(E,A) -> (all F (m2_finseq_1(F,B) -> k3_funcop_1(D,k6_finseq_1(A),F) = k6_finseq_1(C) & k6_finseq_1(C) = k3_funcop_1(D,E,k6_finseq_1(B)))))))))))))) # label(t87_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2629 (all A (v4_ordinal2(A) -> k2_finseq_1(A) = k4_finseq_1(k1_finseq_2(A)))) # label(t54_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2630 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) -> (all C (m2_finseq_1(C,B) -> m2_finseq_1(C,A))))))) # label(t27_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2631 (all A (v4_ordinal2(A) -> v1_relat_1(k1_finseq_2(A)) & v1_finseq_1(k1_finseq_2(A)) & v1_funct_1(k1_finseq_2(A)))) # label(dt_k1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2632 (all A k13_finseq_1(A) = k3_finseq_2(A)) # label(redefinition_k3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2633 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (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]. 4.49/4.55 2634 (all A all B (-v1_xboole_0(B) & m1_finseq_2(B,A) -> r1_tarski(B,k3_finseq_2(A)))) # label(t105_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2635 (all A all B (v4_ordinal2(A) -> 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(dt_k2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2636 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_finseq_2(D,B,k4_finseq_2(A,B)) -> (all E (v1_funct_1(E) & m2_relset_1(E,B,C) & v1_funct_2(E,B,C) -> m2_finseq_2(k1_partfun1(k5_numbers,B,B,C,D,E),C,k4_finseq_2(A,C)))))))))))) # label(t133_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2637 (all A (-v1_xboole_0(A) -> a_1_2_finseq_2(A) = k4_finseq_2(np__3,A))) # label(t122_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2638 (all A exists B (m1_finseq_2(B,A) & -v1_xboole_0(B))) # label(rc1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2639 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C all D (r2_hidden(B,k1_relat_1(A)) & r2_hidden(D,k1_relat_1(A)) & r2_hidden(C,k1_relat_1(A)) -> k11_finseq_1(k1_funct_1(A,B),k1_funct_1(A,C),k1_funct_1(A,D)) = k5_relat_1(k11_finseq_1(B,C,D),A))))) # label(t146_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2640 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> -(np__0 != k3_finseq_1(B) & (all C (m2_finseq_1(C,A) -> (all D (m1_subset_1(D,A) -> k8_finseq_1(A,C,k12_finseq_1(A,D)) != B))))))))) # label(t22_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2641 (all A k2_finseq_2(np__2,A) = k10_finseq_1(A,A)) # label(t75_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2642 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (r2_hidden(B,k1_relat_1(A)) & r2_hidden(C,k1_relat_1(A)) -> k5_relat_1(k10_finseq_1(B,C),A) = k10_finseq_1(k1_funct_1(A,B),k1_funct_1(A,C)))))) # label(t145_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2643 (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) -> (I = k11_finseq_1(E,F,G) -> k5_funcop_1(H,D,I) = k11_finseq_1(k2_binop_1(A,B,C,H,D,E),k2_binop_1(A,B,C,H,D,F),k2_binop_1(A,B,C,H,D,G))))))))))))))))))))) # label(t96_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2644 (all A m1_subset_1(k6_finseq_1(A),k4_finseq_2(np__0,A))) # label(t114_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2645 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (all D (m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(B)) & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(B)) & v1_funct_1(D) -> (r1_xreal_0(B,k3_finseq_1(C)) -> A != np__0 & np__0 = B | 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]. 4.49/4.55 2646 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,B) -> m2_finseq_2(k2_finseq_2(A,C),B,k4_finseq_2(A,B)))))))) # label(t132_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2647 (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_finseq_1(A) = k2_relat_1(D) -> m2_finseq_2(k1_partfun1(k2_finseq_1(A),k2_finseq_1(A),k5_numbers,B,D,C),B,k4_finseq_2(A,B))))))))))) # label(t134_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2648 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> m2_finseq_1(k10_finseq_1(B,C),A))))))) # label(t15_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2649 (all A (v4_ordinal2(A) -> (all B k2_funcop_1(k2_finseq_1(A),B) = k2_finseq_2(A,B)))) # label(d2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2650 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B k2_finseq_2(k1_nat_1(A,np__1),B) = k7_finseq_1(k2_finseq_2(A,B),k9_finseq_1(B))))) # label(t74_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2651 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k4_finseq_1(A),k4_finseq_1(A)) & v3_funct_2(C,k4_finseq_1(A),k4_finseq_1(A)) & v1_funct_2(C,k4_finseq_1(A),k4_finseq_1(A)) -> (k5_relat_1(C,A) = B -> k3_finseq_1(A) = k3_finseq_1(B)))))))) # label(t48_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.55 2652 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k5_numbers,B) & v1_funct_2(C,k5_numbers,B) & v1_funct_1(C) -> m2_finseq_1(k2_partfun1(k5_numbers,B,C,k2_finseq_1(A)),B))))))) # label(t31_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2653 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(A,B)) -> (all D (m2_finseq_2(D,B,k4_finseq_2(A,B)) -> ((all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (r2_hidden(E,k2_finseq_1(A)) -> k1_funct_1(C,E) = k1_funct_1(D,E)))) -> D = C))))))))) # label(t139_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2654 (all A all B (-v1_xboole_0(B) & m1_finseq_2(B,A) -> (all C (m2_finseq_2(C,A,B) <-> m1_subset_1(C,B))))) # label(redefinition_m2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2655 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C k7_finseq_1(k2_finseq_2(A,C),k2_finseq_2(B,C)) = k2_finseq_2(k1_nat_1(A,B),C)))))) # label(t143_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2656 (all A (-v1_xboole_0(A) -> a_1_1_finseq_2(A) = k4_finseq_2(np__2,A))) # label(t119_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2657 (all A all B (m2_finseq_1(B,A) -> m1_subset_1(B,k4_finseq_2(k3_finseq_1(B),A)))) # label(t110_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2658 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_finseq_1(A),B) & v1_funct_2(C,k2_finseq_1(A),B) -> m2_finseq_1(C,B))))))) # label(t28_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2659 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> k4_finseq_2(A,B) = k1_funct_2(k2_finseq_1(A),B))))) # label(t111_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2660 (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]. 4.49/4.56 2661 (all A all B all C (v4_ordinal2(B) -> ((exists D (m2_finseq_2(D,C,k3_finseq_2(C)) & k3_finseq_1(D) = B & D = A)) <-> r2_hidden(A,a_2_0_finseq_2(B,C))))) # label(fraenkel_a_2_0_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2662 (all A (v4_ordinal2(A) -> (all B A = k3_finseq_1(k2_finseq_2(A,B))))) # label(t69_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2663 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(np__0,B)) -> (all D (m2_finseq_2(D,B,k4_finseq_2(A,B)) -> k8_finseq_1(B,D,C) = D & k8_finseq_1(B,C,D) = D)))))))) # label(t115_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2664 $T # label(t29_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2665 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B all C (m2_finseq_1(C,B) -> (r2_hidden(A,k4_finseq_1(C)) -> r2_hidden(k1_funct_1(C,A),B)))))) # label(t13_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2666 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B)),k1_relat_1(C)) -> v1_finseq_1(k3_funcop_1(C,A,B)) & v1_funct_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]. 4.49/4.56 2667 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> m2_finseq_2(k1_finseq_2(A),k5_numbers,k4_finseq_2(A,k5_numbers)))) # label(t131_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2668 $T # label(t12_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2669 (all A (-v1_xboole_0(A) -> k3_finseq_2(A) = k3_tarski(a_1_3_finseq_2(A)))) # label(t128_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2670 (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]. 4.49/4.56 2671 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> -(r2_hidden(A,k2_relat_1(B)) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(A = k1_funct_1(B,C) & r2_hidden(C,k4_finseq_1(B)))))))) # label(t11_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2672 (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_finseq_1(E) & v1_relat_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) -> (k5_funcop_1(F,D,G) = E -> k3_finseq_1(G) = k3_finseq_1(E)))))))))))))))) # label(t92_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2673 (all A all B (m1_finseq_2(B,A) <-> (all C (r2_hidden(C,B) -> m2_finseq_1(C,A))))) # label(d3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2674 (all A all B (-v1_xboole_0(B) -> ((exists C (A = k4_finseq_2(C,B) & m2_subset_1(C,k1_numbers,k5_numbers))) <-> r2_hidden(A,a_1_3_finseq_2(B))))) # label(fraenkel_a_1_3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2675 (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_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) -> (k2_relat_1(D) = k2_finseq_1(A) & C = k5_relat_1(D,B) & r1_xreal_0(A,k3_finseq_1(B)) -> A = k3_finseq_1(C)))))))))) # label(t45_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2676 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(A,B),C) & m2_relset_1(E,k2_zfmisc_1(A,B),C) -> (all F (m2_finseq_1(F,A) -> m2_finseq_1(k4_funcop_1(E,F,D),C))))))))))))) # label(t97_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2677 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,B) -> (all F (m2_relset_1(F,k2_zfmisc_1(A,B),C) & v1_funct_2(F,k2_zfmisc_1(A,B),C) & v1_funct_1(F) -> (all G (m2_finseq_1(G,A) -> (G = k12_finseq_1(A,D) -> k12_finseq_1(C,k2_binop_1(A,B,C,F,D,E)) = k4_funcop_1(F,G,E)))))))))))))))) # label(t100_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2678 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_finseq_1(D) & v1_funct_1(D) & v1_relat_1(D) -> (all E (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) -> (k3_funcop_1(E,F,G) = D -> k3_finseq_1(D) = k3_square_1(k3_finseq_1(F),k3_finseq_1(G))))))))))))))))) # label(t85_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2679 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> m2_finseq_2(k12_finseq_1(A,B),A,k4_finseq_2(np__1,A)))))) # label(t118_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2680 (all A (v4_ordinal2(A) -> k1_finseq_2(A) = k6_partfun1(k2_finseq_1(A)))) # label(d1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2681 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_relat_1(D) & v1_finseq_1(D) & v1_funct_1(D) -> (all E (v1_funct_2(E,k2_zfmisc_1(A,B),C) & m2_relset_1(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) -> (k3_funcop_1(E,F,G) = D & k3_finseq_1(G) = k3_finseq_1(F) -> k3_finseq_1(F) = k3_finseq_1(D) & k3_finseq_1(G) = k3_finseq_1(D)))))))))))))))) # label(t86_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2682 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_2(C,k2_finseq_1(A),k2_finseq_1(A)) & m2_relset_1(C,k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_1(C) -> (r1_xreal_0(A,k3_finseq_1(B)) -> v1_relat_1(k5_relat_1(C,B)) & v1_finseq_1(k5_relat_1(C,B)) & v1_funct_1(k5_relat_1(C,B))))))))) # label(t43_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2683 (exists A (m2_finseq_1(A,f2_s1_finseq_2) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(B,k2_finseq_1(f1_s1_finseq_2)) -> k1_funct_1(A,B) = f3_s1_finseq_2(B)))) & f1_s1_finseq_2 = k3_finseq_1(A))) # label(s1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2684 $T # label(t108_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2685 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (k3_square_1(B,C) = A -> k5_subset_1(k5_numbers,k2_finseq_1(B),k2_finseq_1(C)) = k2_finseq_1(A)))))))) # label(t2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2686 (all A all B all C (m2_finseq_1(C,A) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & 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]. 4.49/4.56 2687 (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 (m2_relset_1(F,C,D) & v1_funct_2(F,C,D) & v1_funct_1(F) -> (E = k10_finseq_1(A,B) -> 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]. 4.49/4.56 2688 (all A (v4_ordinal2(A) -> A = k3_finseq_1(k1_finseq_2(A)))) # label(t55_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2689 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (-v1_xboole_0(C) -> (all D (m2_finseq_2(D,C,k4_finseq_2(A,C)) -> (all E (m2_finseq_2(E,C,k4_finseq_2(B,C)) -> m2_finseq_2(k8_finseq_1(C,D,E),C,k4_finseq_2(k1_nat_1(A,B),C)))))))))))) # label(t127_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2690 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(B)) -> (all D (m2_finseq_2(D,C,k4_finseq_2(A,C)) -> m2_finseq_2(D,B,k4_finseq_2(A,B)))))))))) # label(t129_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2691 (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(k1_nat_1(A,B),C) = a_3_0_finseq_2(A,B,C))))))) # label(t125_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2692 $T # label(t103_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2693 (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]. 4.49/4.56 2694 (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_finseq_1(C) & v1_funct_1(C) -> (k3_finseq_1(B) = k3_finseq_1(A) & r1_tarski(B,C) & r1_tarski(A,C) -> A = B))))))) # label(t149_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2695 (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) -> -(k3_finseq_1(C) = k1_nat_1(A,B) & (all D (v1_finseq_1(D) & v1_funct_1(D) & v1_relat_1(D) -> (all E (v1_finseq_1(E) & v1_funct_1(E) & v1_relat_1(E) -> -(k3_finseq_1(E) = B & C = k7_finseq_1(D,E) & A = k3_finseq_1(D))))))))))))) # label(t25_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2696 (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]. 4.49/4.56 2697 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (B = k7_relat_1(C,k2_finseq_1(A)) -> k3_finseq_1(B) = k3_square_1(A,k3_finseq_1(C))))))))) # label(t24_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2698 (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(A,C) = k4_finseq_2(B,C) -> A = B))))))) # label(t130_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2699 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> m2_finseq_2(k10_finseq_1(B,C),A,k4_finseq_2(np__2,A)))))))) # label(t121_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2700 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(B,C),D) & m2_relset_1(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]. 4.49/4.56 2701 (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]. 4.49/4.56 2702 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> m2_finseq_1(k11_finseq_1(B,C,D),A))))))))) # label(t16_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2703 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (r2_hidden(A,k4_finseq_1(B)) -> r2_hidden(A,k4_finseq_1(k7_finseq_1(B,C)))))))))) # label(t18_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2704 $T # label(dt_m1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2705 $T # label(t106_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2706 (all A exists B m1_finseq_2(B,A)) # label(existence_m1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2707 (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_funct_2(E,k2_zfmisc_1(A,B),C) & m2_relset_1(E,k2_zfmisc_1(A,B),C) -> (all F (m2_finseq_1(F,B) -> m2_finseq_1(k5_funcop_1(E,D,F),C))))))))))))) # label(t91_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2708 (all A (m1_finseq_2(k13_finseq_1(A),A) & -v1_xboole_0(k13_finseq_1(A)))) # label(t104_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2709 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(C,k4_finseq_1(A)) -> r2_hidden(k1_funct_1(A,C),B)))) -> m2_finseq_1(A,B))))) # label(t14_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2710 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(A,k2_finseq_1(B)) -> A = k1_funct_1(k1_finseq_2(B),A)))))) # label(t56_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2711 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k5_relat_1(A,C) = B & r1_tarski(k2_relat_1(A),k1_relat_1(C)) -> k3_finseq_1(B) = k3_finseq_1(A)))))))) # label(t33_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2712 (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]. 4.49/4.56 2713 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> m2_finseq_2(k11_finseq_1(B,C,D),A,k4_finseq_2(np__3,A)))))))))) # label(t124_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2714 (all A all B (v4_ordinal2(A) & -v1_xboole_0(B) -> -v1_xboole_0(k4_finseq_2(A,B)))) # label(fc1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2715 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (all D (v1_funct_1(D) & 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)) & C = k5_relat_1(D,B) -> k3_finseq_1(C) = A))))))))) # label(t47_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2716 (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]. 4.49/4.56 2717 $T # label(t7_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2718 (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) -> (k12_finseq_1(A,D) = G & H = k12_finseq_1(B,E) -> k12_finseq_1(C,k2_binop_1(A,B,C,F,D,E)) = k3_funcop_1(F,G,H)))))))))))))))))) # label(t88_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2719 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_0_finseq_2(B)) <-> (exists C (k12_finseq_1(B,C) = A & m1_subset_1(C,B)))))) # label(fraenkel_a_1_0_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2720 (all A all B all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (all D (v1_finseq_1(D) & v1_funct_1(D) & v1_relat_1(D) -> (k7_finseq_1(C,k9_finseq_1(A)) = k7_finseq_1(D,k9_finseq_1(B)) -> A = B & D = C))))) # label(t20_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2721 (all A (v4_ordinal2(A) -> (all B a_2_0_finseq_2(A,B) = k4_finseq_2(A,B)))) # label(d4_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2722 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (C = k3_funcop_1(D,A,B) & 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]. 4.49/4.56 2723 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_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]. 4.49/4.56 2724 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,B) -> (all H (v1_funct_1(H) & m2_relset_1(H,k2_zfmisc_1(A,B),C) & v1_funct_2(H,k2_zfmisc_1(A,B),C) -> (all I (m2_finseq_1(I,A) -> (all J (m2_finseq_1(J,B) -> (I = k10_finseq_1(D,E) & J = k10_finseq_1(F,G) -> k3_funcop_1(H,I,J) = k10_finseq_1(k2_binop_1(A,B,C,H,D,F),k2_binop_1(A,B,C,H,E,G))))))))))))))))))))))) # label(t89_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2725 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (r1_xreal_0(k3_finseq_1(C),A) & B = k7_relat_1(C,k2_finseq_1(A)) -> C = B))))))) # label(t23_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2726 (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]. 4.49/4.56 2727 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> (all G (v1_funct_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,A) -> (k10_finseq_1(D,E) = H -> k4_funcop_1(G,H,F) = k10_finseq_1(k2_binop_1(A,B,C,G,D,F),k2_binop_1(A,B,C,G,E,F))))))))))))))))))) # label(t101_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2728 (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 (k11_finseq_1(C,D,E) = B & m1_subset_1(E,A))) & m1_subset_1(D,A))) & m1_subset_1(C,A))))))) # label(t123_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2729 (all A all B k2_tarski(A,B) = k2_relat_1(k10_finseq_1(A,B))) # label(t147_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2730 $T # label(t17_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2731 (all 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 (v1_funct_1(D) & v1_relat_1(D) -> (r1_tarski(k2_zfmisc_1(k1_tarski(A),k2_relat_1(B)),k1_relat_1(D)) & C = k5_funcop_1(D,A,B) -> k3_finseq_1(C) = k3_finseq_1(B)))))))) # label(t81_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2732 (all A all B (-v1_xboole_0(B) -> (all C (v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C) -> (all D (m2_finseq_1(D,A) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(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]. 4.49/4.56 2733 (all A all B (-v1_xboole_0(B) -> ((exists C exists D (m1_subset_1(C,B) & m1_subset_1(D,B) & A = k10_finseq_1(C,D))) <-> r2_hidden(A,a_1_1_finseq_2(B))))) # label(fraenkel_a_1_1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2734 (all A (v4_ordinal2(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,B) -> m2_finseq_1(k2_finseq_2(A,C),B))))))) # label(t77_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2735 (all A (v4_ordinal2(A) -> (all B all C (r2_hidden(B,k2_finseq_1(A)) -> C = k1_funct_1(k2_finseq_2(A,C),B))))) # label(t70_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2736 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k3_square_1(np__0,A) = np__0 & k3_square_1(A,np__0) = np__0 & k4_square_1(A,np__0) = A & A = k4_square_1(np__0,A))) # label(t6_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2737 (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_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C) -> (all D B != k7_finseq_1(C,k9_finseq_1(D))))) & k1_nat_1(A,np__1) = k3_finseq_1(B)))))) # label(t21_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2738 (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) -> (G = k12_finseq_1(B,E) -> k12_finseq_1(C,k2_binop_1(A,B,C,F,D,E)) = k5_funcop_1(F,D,G)))))))))))))))) # label(t94_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2739 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> k3_finseq_1(k7_finseq_1(B,k9_finseq_1(A))) = k1_nat_1(k3_finseq_1(B),np__1))) # label(t19_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2740 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,B) -> (all E (v1_funct_1(E) & v1_finseq_1(E) & v1_relat_1(E) -> (all F (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) -> (k4_funcop_1(F,G,D) = E -> k3_finseq_1(E) = k3_finseq_1(G)))))))))))))))) # label(t98_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2741 $T # label(t53_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2742 (all A all B (m1_subset_1(B,k4_finseq_2(np__0,A)) -> k6_finseq_1(A) = B)) # label(t113_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2743 (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)))))))) & p1_s2_finseq_2(k6_finseq_1(f1_s2_finseq_2)) -> (all A (m2_finseq_1(A,f1_s2_finseq_2) -> p1_s2_finseq_2(A))) # label(s2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2744 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (C = k4_funcop_1(D,B,A) & r1_tarski(k2_zfmisc_1(k2_relat_1(B),k1_tarski(A)),k1_relat_1(D)) -> k3_finseq_1(B) = k3_finseq_1(C)))))))) # label(t83_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2745 (all A (v4_ordinal2(A) -> (all B (v1_relat_1(k2_funcop_1(k2_finseq_1(A),B)) & v1_funct_1(k2_funcop_1(k2_finseq_1(A),B)) & v1_finseq_1(k2_funcop_1(k2_finseq_1(A),B)))))) # label(t66_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2746 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_2(B,A,k4_finseq_2(np__1,A)) -> (exists C (B = k12_finseq_1(A,C) & m1_subset_1(C,A))))))) # label(t117_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2747 $T # label(t67_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2748 (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 -> k10_finseq_1(k2_binop_1(A,B,C,G,D,E),k2_binop_1(A,B,C,G,D,F)) = k5_funcop_1(G,D,H)))))))))))))))))) # label(t95_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2749 (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) & m2_relset_1(G,D,E) & v1_funct_2(G,D,E) -> (k11_finseq_1(A,B,C) = F -> k11_finseq_1(k1_funct_1(G,A),k1_funct_1(G,B),k1_funct_1(G,C)) = k1_partfun1(k5_numbers,D,D,E,F,G)))))))))) # label(t41_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2750 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> (all H (v1_funct_1(H) & m2_relset_1(H,k2_zfmisc_1(A,B),C) & v1_funct_2(H,k2_zfmisc_1(A,B),C) -> (all I (m2_finseq_1(I,A) -> (k11_finseq_1(D,E,F) = I -> k11_finseq_1(k2_binop_1(A,B,C,H,D,G),k2_binop_1(A,B,C,H,E,G),k2_binop_1(A,B,C,H,F,G)) = k4_funcop_1(H,I,G)))))))))))))))))))) # label(t102_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2751 (all A all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> k1_partfun1(k5_numbers,A,A,B,k6_finseq_1(A),C) = k6_finseq_1(B))))) # label(t38_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2752 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (all D (v1_funct_2(D,k5_numbers,B) & m2_relset_1(D,k5_numbers,B) & v1_funct_1(D) -> (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]. 4.49/4.56 2753 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(A,B),C) & m2_relset_1(E,k2_zfmisc_1(A,B),C) -> k6_finseq_1(C) = k4_funcop_1(E,k6_finseq_1(A),D))))))))))) # label(t99_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2754 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r1_xreal_0(A,B) -> k2_square_1(np__0,k6_xcmplx_0(A,B)) = np__0))))) # label(t3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2755 (all A all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_zfmisc_1(k2_relat_1(B),k1_tarski(A)),k1_relat_1(C)) -> v1_relat_1(k4_funcop_1(C,B,A)) & v1_funct_1(k4_funcop_1(C,B,A)) & v1_finseq_1(k4_funcop_1(C,B,A))))))) # label(t82_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2756 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_2_finseq_2(B)) <-> (exists C exists D exists E (m1_subset_1(C,B) & m1_subset_1(D,B) & A = k11_finseq_1(C,D,E) & m1_subset_1(E,B)))))) # label(fraenkel_a_1_2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2757 (all A all B all C k2_relat_1(k11_finseq_1(A,B,C)) = k1_enumset1(A,B,C)) # label(t148_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2758 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(A,k2_finseq_1(B)) -> r2_hidden(A,k2_finseq_1(k1_nat_1(B,C)))))))))) # label(t9_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2759 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (B = k2_finseq_1(A) -> (all C (v1_finseq_1(C) & v1_funct_1(C) & v1_relat_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]. 4.49/4.56 2760 (all A k4_finseq_2(np__0,A) = k6_domain_1(k1_zfmisc_1(k2_zfmisc_1(k5_numbers,A)),k6_finseq_1(A))) # label(t112_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2761 (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 (m2_finseq_2(E,C,k4_finseq_2(A,C)) & (exists F (m2_finseq_2(F,C,k4_finseq_2(B,C)) & k8_finseq_1(C,E,F) = D)))))))))))) # label(t126_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2762 (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]. 4.49/4.56 2763 (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]. 4.49/4.56 2764 (all A (-v1_xboole_0(A) -> k4_finseq_2(np__1,A) = a_1_0_finseq_2(A))) # label(t116_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2765 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> m2_subset_1(k2_square_1(np__0,k6_xcmplx_0(A,B)),k1_numbers,k5_numbers))))) # label(t5_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2766 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (A = k3_finseq_1(B) & A = k3_finseq_1(C) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k2_finseq_1(A)) -> k1_funct_1(C,D) = k1_funct_1(B,D)))) -> B = C))))))) # label(t10_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2767 (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]. 4.49/4.56 2768 (all A k11_finseq_1(A,A,A) = k2_finseq_2(np__3,A)) # label(t76_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2769 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,C) -> (all F (m2_relset_1(F,k2_zfmisc_1(B,C),D) & v1_funct_2(F,k2_zfmisc_1(B,C),D) & v1_funct_1(F) -> (all G (m2_finseq_2(G,B,k4_finseq_2(A,B)) -> m2_finseq_2(k4_funcop_1(F,G,E),D,k4_finseq_2(A,D)))))))))))))))) # label(t142_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2770 (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]. 4.49/4.56 2771 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(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)) -> (k2_relat_1(C) = k4_finseq_1(A) & k5_relat_1(C,A) = B -> k3_finseq_1(B) = k3_finseq_1(A)))))))) # label(t46_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2772 (all A (v4_ordinal2(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (r1_xreal_0(k3_finseq_1(B),A) -> k5_relat_1(k1_finseq_2(A),B) = B))))) # label(t64_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2773 (all A (v4_ordinal2(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> k5_relat_1(k1_finseq_2(A),B) = k7_relat_1(B,k2_finseq_1(A)))))) # label(t63_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2774 (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(G,H,I) = L & K = k11_finseq_1(D,E,F) -> k3_funcop_1(J,K,L) = k11_finseq_1(k2_binop_1(A,B,C,J,D,G),k2_binop_1(A,B,C,J,E,H),k2_binop_1(A,B,C,J,F,I))))))))))))))))))))))))))) # label(t90_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2775 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_finseq_1(D,B) -> (all E (m2_relset_1(E,B,C) & v1_funct_2(E,B,C) & v1_funct_1(E) -> (k9_finseq_1(A) = D -> 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]. 4.49/4.56 2776 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(A,B)) -> k3_finseq_1(C) = A)))))) # label(t109_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2777 (all A (v4_ordinal2(A) -> m2_finseq_1(k6_partfun1(k2_finseq_1(A)),k5_numbers))) # label(t52_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2778 (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]. 4.49/4.56 2779 (all A all B all C all D (m2_subset_1(B,k1_numbers,k5_numbers) & -v1_xboole_0(D) & m2_subset_1(C,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)) & k8_finseq_1(D,E,F) = A & m2_finseq_2(E,D,k4_finseq_2(B,D))))))) # label(fraenkel_a_3_0_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2780 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(A,B)) -> k5_relat_1(k1_finseq_2(A),C) = C)))))) # label(t138_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2781 (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(k1_nat_1(B,np__1))) & k1_nat_1(B,np__1) != A & -r2_hidden(A,k2_finseq_1(B))))))) # label(t8_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2782 (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) & A = k3_finseq_1(E)))))) & k3_finseq_1(D) = k1_nat_1(A,B)))))))))) # label(t26_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2783 (all A all B (v4_ordinal2(A) -> m1_finseq_2(k4_finseq_2(A,B),B))) # label(dt_k4_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2784 (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 (m2_relset_1(F,k2_zfmisc_1(B,C),D) & v1_funct_2(F,k2_zfmisc_1(B,C),D) & v1_funct_1(F) -> (all G (m2_finseq_2(G,C,k4_finseq_2(A,C)) -> m2_finseq_2(k5_funcop_1(F,E,G),D,k4_finseq_2(A,D)))))))))))))))) # label(t141_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2785 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k4_finseq_1(A),k4_finseq_1(A)) & m2_relset_1(B,k4_finseq_1(A),k4_finseq_1(A)) -> v1_relat_1(k5_relat_1(B,A)) & v1_finseq_1(k5_relat_1(B,A)) & v1_funct_1(k5_relat_1(B,A)))))) # label(t44_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2786 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_finseq_2(C,B) & -v1_xboole_0(C) -> m1_finseq_2(C,A) & -v1_xboole_0(C))))))) # label(t107_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2787 (all A k2_finseq_2(np__1,A) = k9_finseq_1(A)) # label(t73_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2788 (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]. 4.49/4.56 2789 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_1(C,B) -> (all D (m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_1(D) -> (r1_xreal_0(A,k3_finseq_1(C)) -> m2_finseq_1(k1_partfun1(k2_finseq_1(A),k2_finseq_1(A),k5_numbers,B,D,C),B)))))))))) # label(t50_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2790 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(A,B)) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) & v3_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) -> m2_finseq_2(k1_partfun1(k2_finseq_1(A),k2_finseq_1(A),k5_numbers,B,D,C),B,k4_finseq_2(A,B)))))))))) # label(t135_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2791 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> (all C (v1_funct_2(C,k4_finseq_1(B),k4_finseq_1(B)) & m2_relset_1(C,k4_finseq_1(B),k4_finseq_1(B)) & v1_funct_1(C) -> m2_finseq_1(k1_partfun1(k4_finseq_1(B),k4_finseq_1(B),k5_numbers,A,C,B),A))))))) # label(t51_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2792 (all A (v4_ordinal2(A) -> v1_funct_2(k1_finseq_2(A),k2_finseq_1(A),k2_finseq_1(A)) & m2_relset_1(k1_finseq_2(A),k2_finseq_1(A),k2_finseq_1(A)) & 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]. 4.49/4.56 2793 (all A all B (m1_finseq_2(B,A) & -v1_xboole_0(B) -> (all C (m2_finseq_2(C,A,B) -> m2_finseq_1(C,A))))) # label(dt_m2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2794 (all A k2_finseq_2(np__0,A) = k1_xboole_0) # label(t72_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2795 (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_1(E) & m2_relset_1(E,k2_finseq_1(A),k2_finseq_1(B)) & v1_funct_2(E,k2_finseq_1(A),k2_finseq_1(B)) -> (r1_xreal_0(B,k3_finseq_1(D)) -> m2_finseq_1(k1_partfun1(k2_finseq_1(A),k2_finseq_1(B),k5_numbers,C,E,D),C) | np__0 != A & B = np__0))))))))))) # label(t49_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2796 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> m2_subset_1(k3_square_1(A,B),k1_numbers,k5_numbers) & m2_subset_1(k4_square_1(A,B),k1_numbers,k5_numbers))))) # label(t1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2797 (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]. 4.49/4.56 2798 $T # label(t7_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2799 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) <-> (exists B (m1_subset_1(B,k8_qc_lang1) & (exists C (k13_qc_lang1(B,C) = A & m1_subset_1(C,k8_qc_lang1)))))))) # label(d19_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2800 (all A (m1_subset_1(A,k8_qc_lang1) -> A = k10_qc_lang1(A))) # label(d12_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.56 2801 (all A (m1_subset_1(A,k8_qc_lang1) -> (k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) = np__3 -> v5_qc_lang1(A)) & ((exists B (m2_subset_1(B,k1_numbers,k5_numbers) & m2_subset_1(k1_funct_1(k10_qc_lang1(A),np__1),k5_qc_lang1,k7_qc_lang1(B)))) -> v2_qc_lang1(A)) & (np__2 = k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) -> v4_qc_lang1(A)) & (np__1 = k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) -> v3_qc_lang1(A)) & (np__0 = k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) -> A = k11_qc_lang1))) # label(t36_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2802 $T # label(t6_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2803 (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]. 4.49/4.57 2804 $T # label(t26_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2805 $T # label(t39_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2806 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang1(A) <-> (exists B ((exists C (m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(B)) & (exists D (m1_qc_lang1(D,B) & k9_qc_lang1(C,D) = A)))) & m2_subset_1(B,k1_numbers,k5_numbers)))))) # label(d17_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2807 $T # label(t43_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2808 (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]. 4.49/4.57 2809 $T # label(t19_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2810 $T # label(t42_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2811 (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]. 4.49/4.57 2812 $T # label(t8_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2813 $T # label(t18_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2814 (all A (m1_subset_1(A,k8_qc_lang1) -> (v3_qc_lang1(A) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (k17_qc_lang1(A) = B <-> k12_qc_lang1(B) = A)))))) # label(d23_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2815 $T # label(t14_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2816 $T # label(t44_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2817 (all A all B (m2_subset_1(B,k1_numbers,k5_numbers) -> ((exists C (C = A & B = k6_qc_lang1(C) & m1_subset_1(C,k5_qc_lang1))) <-> r2_hidden(A,a_1_0_qc_lang1(B))))) # label(fraenkel_a_1_0_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2818 (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]. 4.49/4.57 2819 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) -> (all B (m1_subset_1(B,k8_qc_lang1) -> ((exists C (k13_qc_lang1(B,C) = A & m1_subset_1(C,k8_qc_lang1))) <-> k18_qc_lang1(A) = B)))))) # label(d24_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2820 $T # label(t28_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2821 (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]. 4.49/4.57 2822 (all A (m2_finseq_1(A,k1_qc_lang1) -> a_1_1_qc_lang1(A) = k22_qc_lang1(A))) # label(d28_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2823 (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]. 4.49/4.57 2824 (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]. 4.49/4.57 2825 (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]. 4.49/4.57 2826 $T # label(t15_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2827 (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]. 4.49/4.57 2828 $T # label(t20_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2829 (all A ((exists B exists C (m2_subset_1(B,k1_numbers,k5_numbers) & m2_subset_1(C,k1_numbers,k5_numbers) & r1_xreal_0(np__7,B) & A = k4_tarski(B,C))) <-> r2_hidden(A,a_0_0_qc_lang1))) # label(fraenkel_a_0_0_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2830 $T # label(t32_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2831 $T # label(t11_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2832 $T # label(t12_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2833 (all A (m1_subset_1(A,k8_qc_lang1) -> (v5_qc_lang1(A) -> (all B (m1_subset_1(B,k8_qc_lang1) -> ((exists C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) & k14_qc_lang1(C,B) = A)) <-> k21_qc_lang1(A) = B)))))) # label(d27_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2834 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang1(A) -> (all B (m1_subset_1(B,k5_qc_lang1) -> ((exists C (m2_subset_1(C,k1_numbers,k5_numbers) & (exists D ((exists E (B = E & k9_qc_lang1(E,D) = A & m2_subset_1(E,k5_qc_lang1,k7_qc_lang1(C)))) & m1_qc_lang1(D,C))))) <-> B = k15_qc_lang1(A))))))) # label(d21_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2835 (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]. 4.49/4.57 2836 (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]. 4.49/4.57 2837 $T # label(t25_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2838 $T # label(t9_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2839 (exists A (v1_funct_1(A) & v1_funct_2(A,k8_qc_lang1,f1_s3_qc_lang1) & k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,k11_qc_lang1) = f2_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)) & (v5_qc_lang1(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,B)) & (v4_qc_lang1(B) -> f5_s3_qc_lang1(k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,k18_qc_lang1(B)),k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,k19_qc_lang1(B))) = k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,B)) & (v3_qc_lang1(B) -> k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,B) = f4_s3_qc_lang1(k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,k17_qc_lang1(B)))))) & m2_relset_1(A,k8_qc_lang1,f1_s3_qc_lang1))) # label(s3_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2840 $T # label(t3_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2841 (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]. 4.49/4.57 2842 $T # label(t41_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2843 $T # label(dt_k1_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2844 (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]. 4.49/4.57 2845 (all A (-v1_xboole_0(A) -> ((all B (-v1_xboole_0(B) -> (v1_qc_lang1(B) -> r1_tarski(A,B)))) & v1_qc_lang1(A) <-> A = k8_qc_lang1))) # label(d10_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2846 $T # label(t29_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2847 (all A all B (m2_finseq_1(B,k1_qc_lang1) -> ((exists C (m2_subset_1(C,k1_numbers,k5_numbers) & r1_xreal_0(C,k3_finseq_1(B)) & r2_hidden(k1_funct_1(B,C),k2_qc_lang1) & r1_xreal_0(np__1,C) & k1_funct_1(B,C) = A)) <-> r2_hidden(A,a_1_1_qc_lang1(B))))) # label(fraenkel_a_1_1_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2848 (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)))))))) & p1_s1_qc_lang1(k11_qc_lang1) & (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (p1_s1_qc_lang1(B) & p1_s1_qc_lang1(A) -> p1_s1_qc_lang1(k13_qc_lang1(A,B))))))) & (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (p1_s1_qc_lang1(B) -> p1_s1_qc_lang1(k14_qc_lang1(A,B))))))) & (all A (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]. 4.49/4.57 2849 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A)) -> k1_mcart_1(B) != np__2 & np__3 != k1_mcart_1(B) & k1_mcart_1(B) != np__1 & k1_mcart_1(B) != np__0)))) # label(t48_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2850 $T # label(t17_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2851 (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]. 4.49/4.57 2852 $T # label(t38_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2853 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) -> (all B (m1_subset_1(B,k8_qc_lang1) -> ((exists C (m1_subset_1(C,k8_qc_lang1) & A = k13_qc_lang1(C,B))) <-> k19_qc_lang1(A) = B)))))) # label(d25_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2854 (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]. 4.49/4.57 2855 (all A (m1_subset_1(A,k8_qc_lang1) -> -(-v2_qc_lang1(A) & -v3_qc_lang1(A) & -v4_qc_lang1(A) & -v5_qc_lang1(A) & A != k11_qc_lang1))) # label(t33_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2856 (all A (m1_subset_1(A,k8_qc_lang1) -> -((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)) & (v4_qc_lang1(A) -> k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) = np__2) & (v5_qc_lang1(A) -> np__3 = k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1))) & (v3_qc_lang1(A) -> k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) = np__1) & np__0 = k1_mcart_1(k1_funct_1(k10_qc_lang1(k11_qc_lang1),np__1)))) # label(t49_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2857 (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 (m2_subset_1(D,k5_qc_lang1,k7_qc_lang1(C)) & (exists E (A = k9_qc_lang1(D,E) & B = E & m1_qc_lang1(E,C))))) & m2_subset_1(C,k1_numbers,k5_numbers))) <-> B = k16_qc_lang1(A))))))) # label(d22_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2858 $T # label(t16_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2859 (all A (m1_subset_1(A,k8_qc_lang1) -> ((exists B (k12_qc_lang1(B) = A & m1_subset_1(B,k8_qc_lang1))) <-> v3_qc_lang1(A)))) # label(d18_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2860 $T # label(t27_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2861 (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]. 4.49/4.57 2862 (all A all B (m1_subset_1(B,k8_qc_lang1) -> (r2_hidden(A,a_1_2_qc_lang1(B)) <-> (exists C (m2_subset_1(C,k1_numbers,k5_numbers) & r1_xreal_0(C,k3_finseq_1(k16_qc_lang1(B))) & r2_hidden(k1_funct_1(k16_qc_lang1(B),C),k2_qc_lang1) & r1_xreal_0(np__1,C) & A = k1_funct_1(k16_qc_lang1(B),C)))))) # label(fraenkel_a_1_2_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2863 (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]. 4.49/4.57 2864 (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]. 4.49/4.57 2865 (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_funct_1(C) & v1_relat_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]. 4.49/4.57 2866 $T # label(t13_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2867 (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]. 4.49/4.57 2868 (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]. 4.49/4.57 2869 (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]. 4.49/4.57 2870 (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]. 4.49/4.57 2871 (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]. 4.49/4.57 2872 (all A (m1_subset_1(A,k8_qc_lang1) -> -(v5_qc_lang1(A) & v4_qc_lang1(A)) & -(v3_qc_lang1(A) & v5_qc_lang1(A)) & -(v4_qc_lang1(A) & v3_qc_lang1(A)) & -(v5_qc_lang1(A) & v2_qc_lang1(A)) & -(v4_qc_lang1(A) & v2_qc_lang1(A)) & -(v2_qc_lang1(A) & v3_qc_lang1(A)))) # label(t51_qc_lang1_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2873 $T # label(t24_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2874 $T # label(t22_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2875 (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]. 4.49/4.57 2876 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang1(A) -> np__1 != 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__3 & np__2 != 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__0))) # label(t50_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2877 (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(k21_qc_lang1(A)))) & v5_qc_lang1(A)))) # label(t47_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.57 2878 (all A (m1_subset_1(A,k8_qc_lang1) -> p1_s2_qc_lang1(k11_qc_lang1) & (v3_qc_lang1(A) & p1_s2_qc_lang1(k17_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(k21_qc_lang1(A)) & v5_qc_lang1(A) -> p1_s2_qc_lang1(A)) & (v2_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]. 4.49/4.57 2879 (all A all B (m1_subset_1(B,k8_qc_lang1) & m1_subset_1(A,k2_qc_lang1) -> m1_subset_1(k14_qc_lang1(A,B),k8_qc_lang1))) # label(dt_k14_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2880 (all A (m1_subset_1(A,k8_qc_lang1) -> (v5_qc_lang1(A) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> ((exists C (k14_qc_lang1(B,C) = A & m1_subset_1(C,k8_qc_lang1))) <-> k20_qc_lang1(A) = B)))))) # label(d26_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2881 $T # label(t31_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2882 (all A (m1_subset_1(A,k1_zfmisc_1(k13_finseq_1(k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)))) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(B)) -> (all D (m1_qc_lang1(D,B) -> r2_hidden(k7_finseq_1(k12_finseq_1(k7_qc_lang1(B),C),D),A))))))) & (all B (m2_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)))) & (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_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)))))) & r2_hidden(k9_finseq_1(k4_tarski(np__0,np__0)),A) <-> v1_qc_lang1(A))) # label(d9_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2883 $T # label(t30_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2884 (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]. 4.49/4.58 2885 $T # label(t5_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2886 (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]. 4.49/4.58 2887 (all A (m1_subset_1(A,k5_qc_lang1) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k1_nat_1(np__7,B) = k1_mcart_1(A) <-> B = k6_qc_lang1(A)))))) # label(d6_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2888 $T # label(dt_k5_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2889 $T # label(t40_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2890 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_finseq_1(B,k1_qc_lang1) -> (k3_finseq_1(B) = A <-> m1_qc_lang1(B,A)))))) # label(d8_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2891 (all A (m1_subset_1(A,k8_qc_lang1) -> ((exists B ((exists C (m1_subset_1(C,k8_qc_lang1) & k14_qc_lang1(B,C) = A)) & m2_subset_1(B,k1_qc_lang1,k2_qc_lang1))) <-> v5_qc_lang1(A)))) # label(d20_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2892 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k1_zfmisc_1(k2_qc_lang1)) -> ((exists C (k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,A) = B & (all D (m1_subset_1(D,k8_qc_lang1) -> (v2_qc_lang1(D) -> a_1_2_qc_lang1(D) = k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,D)) & (v3_qc_lang1(D) -> k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,k17_qc_lang1(D)) = k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,D)) & (v5_qc_lang1(D) -> k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,D) = k6_subset_1(k2_qc_lang1,k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,k21_qc_lang1(D)),k23_qc_lang1(k20_qc_lang1(D)))) & (v4_qc_lang1(D) -> k4_subset_1(k2_qc_lang1,k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,k18_qc_lang1(D)),k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,k19_qc_lang1(D))) = k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,D)) & k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,k11_qc_lang1) = k1_xboole_0)) & m2_relset_1(C,k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1)) & v1_funct_2(C,k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1)) & v1_funct_1(C))) <-> B = k24_qc_lang1(A)))))) # label(d29_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2893 (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]. 4.49/4.58 2894 (all A all B (m1_finseq_1(B,k1_qc_lang1) & m1_subset_1(A,k5_qc_lang1) -> m1_subset_1(k9_qc_lang1(A,B),k8_qc_lang1))) # label(dt_k9_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2895 (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]. 4.49/4.58 2896 (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(k19_qc_lang1(A)))) & -r1_xreal_0(k3_finseq_1(k10_qc_lang1(A)),k3_finseq_1(k10_qc_lang1(k18_qc_lang1(A))))))) # label(t46_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2897 (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]. 4.49/4.58 2898 (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]. 4.49/4.58 2899 (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]. 4.49/4.58 2900 (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]. 4.49/4.58 2901 (all A all B all C (m1_subset_1(C,k8_qc_lang1) & m1_subset_1(B,k2_qc_lang1) & m1_subset_1(A,k2_qc_lang1) -> m1_subset_1(k6_qc_lang2(A,B,C),k8_qc_lang1))) # label(dt_k6_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2902 (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]. 4.49/4.58 2903 (all A (m1_subset_1(A,k8_qc_lang1) -> (v1_qc_lang2(A) <-> (exists B (m1_subset_1(B,k8_qc_lang1) & (exists C (m1_subset_1(C,k8_qc_lang1) & A = k3_qc_lang2(B,C)))))))) # label(d10_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2904 (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(B,k3_qc_lang2(A,B)) & r3_qc_lang2(k12_qc_lang1(B),k3_qc_lang2(A,B)) & r3_qc_lang2(k12_qc_lang1(A),k3_qc_lang2(A,B)) & r3_qc_lang2(k13_qc_lang1(k12_qc_lang1(A),k12_qc_lang1(B)),k3_qc_lang2(A,B)))))) # label(t94_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2905 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k15_qc_lang2(k4_qc_lang2(A,B)) = k2_xboole_0(k2_xboole_0(k15_qc_lang2(A),k15_qc_lang2(B)),k5_enumset1(k12_qc_lang1(B),k13_qc_lang1(A,k12_qc_lang1(B)),k2_qc_lang2(A,B),k12_qc_lang1(A),k13_qc_lang1(B,k12_qc_lang1(A)),k2_qc_lang2(B,A),k4_qc_lang2(A,B))))))) # label(t115_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2906 (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]. 4.49/4.58 2907 (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]. 4.49/4.58 2908 (all A (m1_subset_1(A,k8_qc_lang1) -> ((exists B (m1_subset_1(B,k8_qc_lang1) & (exists C (A = k2_qc_lang2(B,C) & m1_subset_1(C,k8_qc_lang1))))) <-> v2_qc_lang2(A)))) # label(d11_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2909 $T # label(t15_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2910 (all A (m1_subset_1(A,k8_qc_lang1) -> (k15_qc_lang2(A) = k1_tarski(A) <-> v2_qc_lang1(A) | A = k11_qc_lang1))) # label(t116_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2911 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> k14_qc_lang1(A,k14_qc_lang1(B,C)) = k6_qc_lang2(A,B,C))))))) # label(d6_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2912 (all A (m1_subset_1(A,k8_qc_lang1) -> k12_qc_lang2(k18_qc_lang1(A)) = k13_qc_lang2(A))) # label(d18_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2913 (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) -> k15_qc_lang2(k9_qc_lang1(B,C)) = k1_tarski(k9_qc_lang1(B,C)))))))) # label(t108_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2914 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (k4_qc_lang2(C,D) = k4_qc_lang2(A,B) -> B = D & C = A))))))))) # label(t18_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2915 (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) -> C = A & k14_qc_lang1(B,D) = E))))))))))) # label(t22_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2916 $T # label(t41_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2917 $T # label(t69_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2918 $T # label(t36_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2919 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> k14_qc_lang1(A,k6_qc_lang2(B,C,D)) = k8_qc_lang2(A,B,C,D))))))))) # label(d8_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2920 (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]. 4.49/4.58 2921 $T # label(t57_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2922 (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) -> E = k6_qc_lang2(B,C,D) & F = A))))))))))))) # label(t28_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2923 (all A (m1_subset_1(A,k8_qc_lang1) -> k14_qc_lang2(A) = k11_qc_lang2(k18_qc_lang1(A)))) # label(d19_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2924 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r2_qc_lang2(A,B) <-> (exists C (m2_subset_1(C,k1_numbers,k5_numbers) & (exists D (B = k1_funct_1(D,C) & (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> -(r1_xreal_0(np__1,E) & -r1_xreal_0(C,E) & (all F (m1_subset_1(F,k8_qc_lang1) -> (all G (m1_subset_1(G,k8_qc_lang1) -> -(k1_funct_1(D,E) = F & r1_qc_lang2(F,G) & G = k1_funct_1(D,k1_nat_1(E,np__1)))))))))) & A = k1_funct_1(D,np__1) & k3_finseq_1(D) = C & r1_xreal_0(np__1,C) & v1_finseq_1(D) & v1_funct_1(D) & v1_relat_1(D)))))))))) # label(d21_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2925 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> A = k12_qc_lang2(k2_qc_lang2(A,B)) & k13_qc_lang1(A,k12_qc_lang1(B)) = k17_qc_lang1(k2_qc_lang2(A,B)) & k11_qc_lang2(k2_qc_lang2(A,B)) = B)))) # label(t46_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2926 (all A (m1_subset_1(A,k8_qc_lang1) -> (v3_qc_lang2(A) -> v2_qc_lang2(k19_qc_lang1(A)) & v2_qc_lang2(k18_qc_lang1(A)) & v4_qc_lang1(A)))) # label(t51_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2927 (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]. 4.49/4.58 2928 (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)),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))) = k15_qc_lang2(k3_qc_lang2(A,B)))))) # label(t114_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2929 (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]. 4.49/4.58 2930 (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) -> A = F & E = k7_qc_lang2(B,C,D)))))))))))))) # label(t31_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2931 (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]. 4.49/4.58 2932 (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]. 4.49/4.58 2933 (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]. 4.49/4.58 2934 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v4_qc_lang1(A) -> (r1_qc_lang2(B,A) <-> B = k18_qc_lang1(A) | k19_qc_lang1(A) = B)))))) # label(t66_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2935 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (A = B | A = C <-> r1_qc_lang2(A,k13_qc_lang1(B,C))))))))) # label(t62_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2936 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang2(A) -> v4_qc_lang1(k17_qc_lang1(A)) & v3_qc_lang1(k19_qc_lang1(k17_qc_lang1(A))) & v3_qc_lang1(A)))) # label(t50_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2937 $T # label(t68_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2938 (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_tarski(k13_qc_lang1(A,B))) = k15_qc_lang2(k13_qc_lang1(A,B)))))) # label(t111_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2939 (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]. 4.49/4.58 2940 (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]. 4.49/4.58 2941 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> k7_qc_lang2(A,B,C) = k5_qc_lang2(A,k5_qc_lang2(B,C)))))))) # label(d7_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2942 $T # label(t37_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2943 (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]. 4.49/4.58 2944 (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)) & k19_qc_lang1(k13_qc_lang1(A,B)) = B)))) # label(t5_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2945 (all A (m1_subset_1(A,k8_qc_lang1) -> (r3_qc_lang2(A,k1_qc_lang2) <-> r2_qc_lang2(A,k11_qc_lang1)))) # label(t88_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2946 (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)) & k9_qc_lang2(A,B,C,D) = k5_qc_lang2(A,k7_qc_lang2(B,C,D)))))))))) # label(t26_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2947 (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) -> (k5_qc_lang2(C,E) = k7_qc_lang2(A,B,D) -> k5_qc_lang2(B,D) = E & C = A))))))))))) # label(t24_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2948 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (r2_qc_lang2(k13_qc_lang1(A,B),C) -> r3_qc_lang2(A,C) & r3_qc_lang2(B,C)))))))) # label(t90_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2949 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m2_subset_1(D,k1_qc_lang1,k2_qc_lang1) -> (all E (m2_subset_1(E,k1_qc_lang1,k2_qc_lang1) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_qc_lang1,k2_qc_lang1) -> (all H (m2_subset_1(H,k1_qc_lang1,k2_qc_lang1) -> (k9_qc_lang2(D,F,H,B) = k9_qc_lang2(C,E,G,A) -> C = D & A = B & H = G & E = F))))))))))))))))) # label(t30_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2950 (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]. 4.49/4.58 2951 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (k13_qc_lang1(A,B) = k13_qc_lang1(C,D) -> A = C & B = D))))))))) # label(t3_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2952 (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,C) | r2_qc_lang2(A,B)))))))) # label(t89_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2953 (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(C,E,A) = k6_qc_lang2(D,F,B) -> D = C & A = B & E = F))))))))))))) # label(t21_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2954 (all A (m1_subset_1(A,k8_qc_lang1) -> (v3_qc_lang1(A) -> k2_xboole_0(k15_qc_lang2(k17_qc_lang1(A)),k1_tarski(A)) = k15_qc_lang2(A)))) # label(t117_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2955 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v3_qc_lang1(A) -> (B = k17_qc_lang1(A) <-> r1_qc_lang2(B,A))))))) # label(t65_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2956 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (-(-(r3_qc_lang2(B,C) & r2_qc_lang2(A,B)) & -(r2_qc_lang2(A,B) & r1_qc_lang2(B,C)) & -(r1_qc_lang2(A,B) & r2_qc_lang2(B,C)) & -(r3_qc_lang2(B,C) & r1_qc_lang2(A,B)) & -(r1_qc_lang2(B,C) & r3_qc_lang2(A,B)) & -(r3_qc_lang2(A,B) & r2_qc_lang2(B,C))) -> r3_qc_lang2(A,C)))))))) # label(t83_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2957 $T # label(t40_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2958 $T # label(t35_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2959 (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]. 4.49/4.58 2960 (all A (m1_subset_1(A,k8_qc_lang1) -> k15_qc_lang2(k12_qc_lang1(A)) = k2_xboole_0(k15_qc_lang2(A),k1_tarski(k12_qc_lang1(A))))) # label(t110_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2961 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B ((all C ((exists D (m1_subset_1(D,k8_qc_lang1) & C = D & r2_qc_lang2(D,A))) <-> r2_hidden(C,B))) <-> B = k15_qc_lang2(A))))) # label(d23_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2962 (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]. 4.49/4.58 2963 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang2(A) -> A = k2_qc_lang2(k12_qc_lang2(A),k11_qc_lang2(A))))) # label(t54_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2964 (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]. 4.49/4.58 2965 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (r2_hidden(B,k15_qc_lang2(C)) -> r2_hidden(A,k15_qc_lang2(C)) | -r3_qc_lang2(A,B) & -r2_qc_lang2(A,B) & -r1_qc_lang2(A,B)))))))) # label(t120_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2966 $T # label(d17_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2967 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> B = k14_qc_lang2(k4_qc_lang2(A,B)) & k2_qc_lang2(B,A) = k19_qc_lang1(k4_qc_lang2(A,B)) & k2_qc_lang2(A,B) = k18_qc_lang1(k4_qc_lang2(A,B)) & k13_qc_lang2(k4_qc_lang2(A,B)) = A)))) # label(t47_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2968 (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]. 4.49/4.58 2969 (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]. 4.49/4.58 2970 (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(A,B) = k3_qc_lang2(C,D) -> C = A & B = D))))))))) # label(t16_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2971 (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]. 4.49/4.58 2972 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k10_qc_lang2(k3_qc_lang2(A,B)) = A & k17_qc_lang1(k3_qc_lang2(A,B)) = k13_qc_lang1(k12_qc_lang1(A),k12_qc_lang1(B)) & B = k11_qc_lang2(k3_qc_lang2(A,B)))))) # label(t45_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2973 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r1_qc_lang2(A,B) & r1_xreal_0(k3_finseq_1(k10_qc_lang1(B)),k3_finseq_1(k10_qc_lang1(A)))))))) # label(t71_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2974 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (r2_qc_lang2(A,B) <-> r3_qc_lang2(A,k14_qc_lang1(C,B))))))))) # label(t91_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.58 2975 (all A (m1_subset_1(A,k8_qc_lang1) -> ((exists B ((exists C (k4_qc_lang2(B,C) = A & m1_subset_1(C,k8_qc_lang1))) & m1_subset_1(B,k8_qc_lang1))) <-> v3_qc_lang2(A)))) # label(d12_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 2976 (all A (m1_subset_1(A,k8_qc_lang1) -> (v5_qc_lang1(A) -> k14_qc_lang1(k20_qc_lang1(A),k21_qc_lang1(A)) = A))) # label(t7_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 2977 (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]. 4.49/4.59 2978 $T # label(t10_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 2979 (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]. 4.49/4.59 2980 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m2_subset_1(D,k1_qc_lang1,k2_qc_lang1) -> (all E (m2_subset_1(E,k1_qc_lang1,k2_qc_lang1) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_qc_lang1,k2_qc_lang1) -> (all H (m2_subset_1(H,k1_qc_lang1,k2_qc_lang1) -> (k8_qc_lang2(C,E,G,A) = k8_qc_lang2(D,F,H,B) -> G = H & B = A & E = F & C = D))))))))))))))))) # label(t27_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 2981 $T # label(t12_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 2982 (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]. 4.49/4.59 2983 (all A (m1_subset_1(A,k8_qc_lang1) -> (k11_qc_lang1 = A | k1_qc_lang2 = A <-> r2_qc_lang2(A,k1_qc_lang2)))) # label(t101_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 2984 $T # label(dt_k15_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 2985 (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]. 4.49/4.59 2986 (all A all B (m1_subset_1(A,k8_qc_lang1) & m1_subset_1(B,k8_qc_lang1) -> r2_qc_lang2(A,A))) # label(reflexivity_r2_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 2987 (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) -> A = B & E = F & D = C))))))))))))) # label(t23_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 2988 $T # label(t44_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 2989 (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]. 4.49/4.59 2990 (all A (m1_subset_1(A,k8_qc_lang1) -> k12_qc_lang2(A) = k18_qc_lang1(k17_qc_lang1(A)))) # label(d16_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 2991 (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) -> E = k14_qc_lang1(C,D) & B = G & A = F))))))))))))))) # label(t29_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 2992 (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]. 4.49/4.59 2993 (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(A,B) = k2_qc_lang2(C,D) -> A = C & D = B))))))))) # label(t17_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 2994 (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]. 4.49/4.59 2995 (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]. 4.49/4.59 2996 (all A (m1_subset_1(A,k8_qc_lang1) -> k17_qc_lang1(k19_qc_lang1(k17_qc_lang1(A))) = k11_qc_lang2(A))) # label(d15_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 2997 (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]. 4.49/4.59 2998 (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]. 4.49/4.59 2999 (all A all B (m1_subset_1(B,k8_qc_lang1) & m1_subset_1(A,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]. 4.49/4.59 3000 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k12_qc_lang1(k13_qc_lang1(A,k12_qc_lang1(B))) = k2_qc_lang2(A,B))))) # label(d2_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3001 $T # label(t11_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3002 (all A all B all C (m1_subset_1(C,k8_qc_lang1) & m1_subset_1(B,k2_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]. 4.49/4.59 3003 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (A != B & r2_qc_lang2(A,B) <-> r3_qc_lang2(A,B)))))) # label(d22_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3004 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (all E (m1_subset_1(E,k8_qc_lang1) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_qc_lang1,k2_qc_lang1) -> (k9_qc_lang2(A,B,C,D) = k7_qc_lang2(F,G,E) -> F = A & E = k5_qc_lang2(C,D) & B = G))))))))))))))) # label(t32_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3005 (all A all B all C all D (m1_subset_1(B,k2_qc_lang1) & m1_subset_1(D,k8_qc_lang1) & m1_subset_1(C,k2_qc_lang1) & m1_subset_1(A,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]. 4.49/4.59 3006 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r2_qc_lang2(B,A) & r3_qc_lang2(A,B)))))) # label(t79_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3007 $T # label(t43_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3008 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(v2_qc_lang1(A) & r1_qc_lang2(B,A)))))) # label(t64_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3009 (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]. 4.49/4.59 3010 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r2_qc_lang2(A,B) & r1_qc_lang2(B,A)))))) # label(t81_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3011 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v5_qc_lang1(A) -> (k21_qc_lang1(A) = B <-> r1_qc_lang2(B,A))))))) # label(t67_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3012 (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]. 4.49/4.59 3013 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang2(A) -> v3_qc_lang1(k21_qc_lang1(k17_qc_lang1(A))) & v5_qc_lang1(k17_qc_lang1(A)) & v3_qc_lang1(A)))) # label(t52_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3014 (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) -> (B = A <-> r1_qc_lang2(A,k14_qc_lang1(C,B))))))))) # label(t63_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3015 $T # label(t34_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3016 (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]. 4.49/4.59 3017 (all A (m1_subset_1(A,k8_qc_lang1) -> (r1_qc_lang2(A,k1_qc_lang2) <-> A = k11_qc_lang1))) # label(t61_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3018 (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]. 4.49/4.59 3019 $T # label(t70_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3020 (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]. 4.49/4.59 3021 (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]. 4.49/4.59 3022 (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) & k14_qc_lang1(A,k14_qc_lang1(B,C)) = k6_qc_lang2(A,B,C))))))) # label(t20_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3023 (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]. 4.49/4.59 3024 (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]. 4.49/4.59 3025 (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]. 4.49/4.59 3026 $T # label(t9_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3027 (all A (m1_subset_1(A,k8_qc_lang1) -> (A = k11_qc_lang1 <-> r2_qc_lang2(A,k11_qc_lang1)))) # label(t99_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3028 $T # label(t106_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3029 (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)) & A = k20_qc_lang1(k8_qc_lang2(A,B,C,D)) & v5_qc_lang1(k8_qc_lang2(A,B,C,D)))))))))) # label(t33_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3030 $T # label(t102_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3031 (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]. 4.49/4.59 3032 (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) -> (k9_qc_lang1(C,D) = A <-> r2_qc_lang2(A,k9_qc_lang1(C,D))))))))))) # label(t100_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3033 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> k9_qc_lang2(A,B,C,D) = k5_qc_lang2(A,k7_qc_lang2(B,C,D)))))))))) # label(d9_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3034 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k12_qc_lang1(k13_qc_lang1(k12_qc_lang1(A),k12_qc_lang1(B))) = k3_qc_lang2(A,B))))) # label(d3_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3035 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (k14_qc_lang1(B,D) = k14_qc_lang1(A,C) -> B = A & D = C))))))))) # label(t6_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3036 (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]. 4.49/4.59 3037 (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]. 4.49/4.59 3038 (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]. 4.49/4.59 3039 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r1_qc_lang2(A,B) <-> -(k12_qc_lang1(A) != B & (all C (m1_subset_1(C,k8_qc_lang1) -> B != k13_qc_lang1(A,C) & k13_qc_lang1(C,A) != B)) & (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> k14_qc_lang1(C,A) != B)))))))) # label(d20_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3040 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) -> A = k13_qc_lang1(k18_qc_lang1(A),k19_qc_lang1(A))))) # label(t4_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3041 (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]. 4.49/4.59 3042 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> k14_qc_lang1(B,C) = k21_qc_lang1(k6_qc_lang2(A,B,C)) & k20_qc_lang1(k6_qc_lang2(A,B,C)) = A & v5_qc_lang1(k6_qc_lang2(A,B,C)))))))) # label(t25_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3043 (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]. 4.49/4.59 3044 (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(A,C) = k5_qc_lang2(B,D) -> A = B & C = D))))))))) # label(t19_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3045 (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]. 4.49/4.59 3046 (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) -> B = A))))) # label(t1_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3047 $T # label(t42_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3048 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k3_qc_lang2(A,B) = k2_qc_lang2(k12_qc_lang1(A),B))))) # label(t14_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3049 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r3_qc_lang2(B,A) & r3_qc_lang2(A,B)))))) # label(t80_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3050 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> A = k20_qc_lang1(k14_qc_lang1(A,B)) & k21_qc_lang1(k14_qc_lang1(A,B)) = B)))) # label(t8_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3051 (all A (m1_subset_1(A,k8_qc_lang1) -> (v1_qc_lang2(A) -> v2_qc_lang2(A) & v4_qc_lang1(k17_qc_lang1(A)) & v3_qc_lang1(k18_qc_lang1(k17_qc_lang1(A))) & v3_qc_lang1(k19_qc_lang1(k17_qc_lang1(A))) & v3_qc_lang1(A)))) # label(t49_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3052 $T # label(t39_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3053 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang2(A) <-> (exists B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) & (exists C (m1_subset_1(C,k8_qc_lang1) & k5_qc_lang2(B,C) = A))))))) # label(d13_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3054 (all A all B (m1_subset_1(B,k2_qc_lang1) & m1_subset_1(A,k4_qc_lang1) -> k3_cqc_lang(A,B) = k6_cqc_lang(A,B))) # label(redefinition_k6_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3055 (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 (v1_funct_2(D,k8_qc_lang1,k8_qc_lang1) & m2_relset_1(D,k8_qc_lang1,k8_qc_lang1) & C = k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,A) & (all E (m1_subset_1(E,k8_qc_lang1) -> k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,k9_cqc_lang) = k9_cqc_lang & (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)) & (v4_qc_lang1(E) -> k13_qc_lang1(k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,k18_qc_lang1(E)),k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,k19_qc_lang1(E))) = k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,E)) & (v5_qc_lang1(E) -> k2_cqc_lang(k8_qc_lang1,k20_qc_lang1(E),B,E,k14_qc_lang1(k20_qc_lang1(E),k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,k21_qc_lang1(E)))) = k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,E)) & (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)))))) & v1_funct_1(D))) <-> k17_cqc_lang(A,B) = C))))))) # label(d6_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3056 $T # label(t4_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3057 (all A all B (m1_subset_1(A,k7_cqc_lang) & m1_subset_1(B,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]. 4.49/4.59 3058 (all A all B all C (m1_qc_lang1(C,A) & v1_cqc_lang(C,A) & m1_subset_1(B,k7_qc_lang1(A)) & m1_subset_1(A,k5_numbers) -> 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]. 4.49/4.59 3059 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k4_qc_lang1) -> m2_relset_1(k3_cqc_lang(B,A),k4_qc_lang1,k1_qc_lang1) & v1_funct_1(k3_cqc_lang(B,A)))))) # label(t10_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3060 (all A all B all C k3_cqc_lang(k4_tarski(A,B),C) = k9_funct_2(A,B,C)) # label(t42_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3061 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(A)) -> (all D (m1_qc_lang1(D,A) -> k9_qc_lang1(C,k5_cqc_lang(A,D,k6_cqc_lang(k3_qc_lang3(np__0),B))) = k17_cqc_lang(k9_qc_lang1(C,D),B))))))))) # label(t30_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3062 (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]. 4.49/4.59 3063 $T # label(t12_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3064 $T # label(dt_k3_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3065 (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]. 4.49/4.59 3066 (all A all B (m1_subset_1(B,k7_cqc_lang) & m1_subset_1(A,k7_cqc_lang) -> k2_qc_lang2(A,B) = k12_cqc_lang(A,B))) # label(redefinition_k12_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3067 $T # label(t8_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3068 (all A all B all C (m1_qc_lang1(C,B) & m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(A,a_2_1_cqc_lang(B,C)) <-> (exists D (r1_xreal_0(np__1,D) & r2_hidden(k1_funct_1(C,D),k3_qc_lang1) & r1_xreal_0(D,k3_finseq_1(C)) & k1_funct_1(C,D) = A & m2_subset_1(D,k1_numbers,k5_numbers)))))) # label(fraenkel_a_2_1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3069 (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]. 4.49/4.59 3070 (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]. 4.49/4.59 3071 (all A all B B = k1_funct_1(k3_cqc_lang(A,B),A)) # label(t6_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3072 (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) -> (m2_subset_1(k9_qc_lang1(B,C),k8_qc_lang1,k7_cqc_lang) <-> a_2_1_cqc_lang(A,C) = k1_xboole_0 & k1_xboole_0 = a_2_0_cqc_lang(A,C)))))))) # label(t17_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3073 (all A all B all C (m2_subset_1(B,k1_numbers,k5_numbers) & m1_qc_lang1(C,B) -> (r2_hidden(A,a_2_0_cqc_lang(B,C)) <-> (exists D (m2_subset_1(D,k1_numbers,k5_numbers) & k1_funct_1(C,D) = A & r2_hidden(k1_funct_1(C,D),k4_qc_lang1) & r1_xreal_0(D,k3_finseq_1(C)) & r1_xreal_0(np__1,D)))))) # label(fraenkel_a_2_0_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3074 (exists A (m1_subset_1(A,f1_s4_cqc_lang) & (exists B (v1_funct_1(B) & (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)) -> f4_s4_cqc_lang(F,H,G) = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,k8_cqc_lang(F,H,G)) & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,k15_cqc_lang(E,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,k11_cqc_lang(C,D)) = 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)) & 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)))))))))))))) & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,k9_cqc_lang) = f3_s4_cqc_lang & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,f2_s4_cqc_lang) = A & m2_relset_1(B,k7_cqc_lang,f1_s4_cqc_lang) & v1_funct_2(B,k7_cqc_lang,f1_s4_cqc_lang))))) # label(s4_cqc_lang_AndLHS) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3075 (all A (m1_subset_1(A,f1_s4_cqc_lang) -> (all B (m1_subset_1(B,f1_s4_cqc_lang) -> -(B != A & (exists C (v1_funct_1(C) & v1_funct_2(C,k7_cqc_lang,f1_s4_cqc_lang) & f3_s4_cqc_lang = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k9_cqc_lang) & (all D (m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) -> (all E (m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (all H (v1_cqc_lang(H,G) & m1_qc_lang1(H,G) -> (all I (m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G)) -> k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s4_cqc_lang(G,I,H) & 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)) & 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)))))))))))))) & B = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,f2_s4_cqc_lang) & m2_relset_1(C,k7_cqc_lang,f1_s4_cqc_lang))) & (exists C (m2_relset_1(C,k7_cqc_lang,f1_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)) -> k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s4_cqc_lang(G,I,H) & 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,k11_cqc_lang(D,E)) = 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,k15_cqc_lang(F,D)) = f7_s4_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D)))))))))))))) & f3_s4_cqc_lang = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k9_cqc_lang) & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,f2_s4_cqc_lang) = A & v1_funct_2(C,k7_cqc_lang,f1_s4_cqc_lang) & v1_funct_1(C)))))))) # label(s4_cqc_lang_AndRHS) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3076 (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) | k20_qc_lang1(B) = A))))) # label(t36_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3077 (all A all B all C all D ((A = B -> k1_cqc_lang(A,B,C,D) = C) & (A != B -> D = k1_cqc_lang(A,B,C,D)))) # label(d1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3078 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m1_subset_1(B,f1_s5_cqc_lang) -> ((exists C (v1_funct_1(C) & m2_relset_1(C,k7_cqc_lang,f1_s5_cqc_lang) & k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,A) = B & (all D (m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) -> (all E (m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (all H (m1_qc_lang1(H,G) & v1_cqc_lang(H,G) -> (all I (m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G)) -> k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s5_cqc_lang(G,I,H) & k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k10_cqc_lang(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,k15_cqc_lang(F,D)) = f7_s5_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,D)) & k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k11_cqc_lang(D,E)) = f6_s5_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,E)))))))))))))) & f3_s5_cqc_lang = k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k9_cqc_lang) & v1_funct_2(C,k7_cqc_lang,f1_s5_cqc_lang))) <-> f2_s5_cqc_lang(A) = B))))) -> f3_s5_cqc_lang = f2_s5_cqc_lang(k9_cqc_lang) # label(s5_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3079 (all A all B (m1_subset_1(B,k7_cqc_lang) & m1_subset_1(A,k7_cqc_lang) -> k13_qc_lang1(A,B) = k11_cqc_lang(A,B))) # label(redefinition_k11_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3080 (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) -> k13_qc_lang1(k17_cqc_lang(k18_qc_lang1(B),A),k17_cqc_lang(k19_qc_lang1(B),A)) = k17_cqc_lang(B,A)))))) # label(t33_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3081 (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]. 4.49/4.59 3082 $T # label(dt_k1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3083 (all A all B (k1_tarski(A) = k1_relat_1(k3_cqc_lang(A,B)) & k2_relat_1(k3_cqc_lang(A,B)) = k1_tarski(B))) # label(t5_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3084 (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]. 4.49/4.59 3085 (all A all B (m1_subset_1(A,k2_qc_lang1) & m1_subset_1(B,k7_cqc_lang) -> k15_cqc_lang(A,B) = k14_qc_lang1(A,B))) # label(redefinition_k15_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3086 (all A all B all C C = k1_binop_1(k9_funct_2(A,B,C),A,B)) # label(t43_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3087 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m1_subset_1(B,f1_s6_cqc_lang) -> (B = f3_s6_cqc_lang(A) <-> (exists C (B = k8_funct_2(k7_cqc_lang,f1_s6_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 (m1_qc_lang1(H,G) & v1_cqc_lang(H,G) -> (all I (m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G)) -> f4_s6_cqc_lang(G,I,H) = k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k8_cqc_lang(G,I,H)) & f9_s6_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,E)) = k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k11_cqc_lang(D,E)) & 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)) & f8_s6_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,D)) = k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k10_cqc_lang(D)))))))))))))) & f2_s6_cqc_lang = k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k9_cqc_lang) & m2_relset_1(C,k7_cqc_lang,f1_s6_cqc_lang) & 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]. 4.49/4.59 3088 $T # label(t14_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3089 (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]. 4.49/4.59 3090 $T # label(t27_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3091 (all A (m1_subset_1(A,k7_cqc_lang) -> k10_cqc_lang(A) = k12_qc_lang1(A))) # label(redefinition_k10_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3092 (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) & k1_xboole_0 = a_2_0_cqc_lang(A,B) <-> m1_qc_lang1(B,A) & v1_cqc_lang(B,A)))))) # label(t15_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3093 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> B = k17_cqc_lang(B,A))))) # label(t40_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3094 (all A all B all C (m1_subset_1(B,k7_qc_lang1(A)) & v1_cqc_lang(C,A) & m1_qc_lang1(C,A) & m1_subset_1(A,k5_numbers) -> k8_cqc_lang(A,B,C) = k9_qc_lang1(B,C))) # label(redefinition_k8_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3095 (all A (m1_subset_1(A,k5_numbers) -> (exists B (m1_qc_lang1(B,A) & v1_cqc_lang(B,A) & v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B))))) # label(rc1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3096 (all A all B (m1_subset_1(B,k2_qc_lang1) & m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k17_cqc_lang(A,B),k8_qc_lang1))) # label(dt_k17_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3097 (all A all B (m1_subset_1(B,k7_cqc_lang) & m1_subset_1(A,k7_cqc_lang) -> k14_cqc_lang(A,B) = k4_qc_lang2(A,B))) # label(redefinition_k14_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3098 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (k1_xboole_0 = k5_qc_lang3(B) -> k17_cqc_lang(B,A) = B))))) # label(t39_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3099 (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]. 4.49/4.59 3100 (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]. 4.49/4.59 3101 (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]. 4.49/4.59 3102 $T # label(t26_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3103 $T # label(t2_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3104 (all A all B (m1_subset_1(A,k2_qc_lang1) & m1_subset_1(B,k7_cqc_lang) -> m2_subset_1(k15_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang))) # label(dt_k15_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3105 $T # label(t3_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3106 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (v1_cqc_lang(E,D) & m1_qc_lang1(E,D) -> (all F (m2_subset_1(F,k5_qc_lang1,k7_qc_lang1(D)) -> p1_s1_cqc_lang(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(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(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]. 4.49/4.59 3107 (all A all B (m1_subset_1(B,k2_qc_lang1) & m1_subset_1(A,k4_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]. 4.49/4.59 3108 (all A all B (m1_subset_1(A,k7_cqc_lang) & m1_subset_1(B,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]. 4.49/4.59 3109 (exists A (v1_funct_2(A,k7_cqc_lang,f1_s2_cqc_lang) & m2_relset_1(A,k7_cqc_lang,f1_s2_cqc_lang) & (all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> (all C (m2_subset_1(C,k8_qc_lang1,k7_cqc_lang) -> (all D (m2_subset_1(D,k1_qc_lang1,k2_qc_lang1) -> (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (all F (v1_cqc_lang(F,E) & m1_qc_lang1(F,E) -> (all G (m2_subset_1(G,k5_qc_lang1,k7_qc_lang1(E)) -> k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k8_cqc_lang(E,G,F)) = f3_s2_cqc_lang(E,G,F) & f6_s2_cqc_lang(D,k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,B)) = k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k15_cqc_lang(D,B)) & 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)) & k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k10_cqc_lang(B)) = f4_s2_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,B)))))))))))))) & f2_s2_cqc_lang = k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k9_cqc_lang) & v1_funct_1(A))) # label(s2_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.59 3110 (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]. 4.49/4.59 3111 (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]. 4.49/4.59 3112 (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]. 4.49/4.60 3113 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> k17_cqc_lang(k9_cqc_lang,A) = k9_cqc_lang)) # label(t28_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3114 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m1_subset_1(B,f1_s7_cqc_lang) -> (f2_s7_cqc_lang(A) = B <-> (exists C (v1_funct_1(C) & v1_funct_2(C,k7_cqc_lang,f1_s7_cqc_lang) & (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,k8_cqc_lang(G,I,H)) = f4_s7_cqc_lang(G,I,H) & k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k10_cqc_lang(D)) = 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,k15_cqc_lang(F,D)) = f8_s7_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,D)) & f7_s7_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,E)) = k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k11_cqc_lang(D,E)))))))))))))) & f3_s7_cqc_lang = k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k9_cqc_lang) & B = k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,A) & m2_relset_1(C,k7_cqc_lang,f1_s7_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]. 4.49/4.60 3115 (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) -> (k6_cqc_lang(C,B) = F & k4_cqc_lang(E,F) = D & r1_xreal_0(np__1,A) & r1_xreal_0(A,k3_finseq_1(E)) -> (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]. 4.49/4.60 3116 (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]. 4.49/4.60 3117 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> k13_qc_lang1(k17_cqc_lang(B,A),k17_cqc_lang(C,A)) = k17_cqc_lang(k13_qc_lang1(B,C),A))))))) # label(t34_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3118 (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]. 4.49/4.60 3119 (all A all B (m1_subset_1(B,k7_cqc_lang) & m1_subset_1(A,k7_cqc_lang) -> k3_qc_lang2(A,B) = k13_cqc_lang(A,B))) # label(redefinition_k13_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3120 (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]. 4.49/4.60 3121 (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) -> k5_cqc_lang(A,B,C) = k4_cqc_lang(B,C))) # label(redefinition_k5_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3122 (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]. 4.49/4.60 3123 (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]. 4.49/4.60 3124 (all A all B all C all D all E (m1_subset_1(D,A) & m1_subset_1(E,A) & -v1_xboole_0(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]. 4.49/4.60 3125 (all A (m2_finseq_1(A,k1_qc_lang1) -> (all B (m2_relset_1(B,k4_qc_lang1,k1_qc_lang1) & v1_funct_1(B) -> (all C (m2_finseq_1(C,k1_qc_lang1) -> (k3_finseq_1(C) = k3_finseq_1(A) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,D) & r1_xreal_0(D,k3_finseq_1(A)) -> (-r2_hidden(k1_funct_1(A,D),k1_relat_1(B)) -> k1_funct_1(A,D) = k1_funct_1(C,D)) & (r2_hidden(k1_funct_1(A,D),k1_relat_1(B)) -> k1_funct_1(C,D) = k1_funct_1(B,k1_funct_1(A,D)))))) <-> k4_cqc_lang(A,B) = C))))))) # label(d3_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3126 (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]. 4.49/4.60 3127 (all A (m1_subset_1(A,k8_qc_lang1) -> (k5_qc_lang3(A) = k1_xboole_0 & k6_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]. 4.49/4.60 3128 $T # label(t1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3129 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (v1_cqc_lang(E,D) & m1_qc_lang1(E,D) -> (all F (m2_subset_1(F,k5_qc_lang1,k7_qc_lang1(D)) -> k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,k8_cqc_lang(D,F,E)) = f5_s3_cqc_lang(D,F,E) & k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,k10_cqc_lang(A)) = f6_s3_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,A)) & f7_s3_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,A),k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,B)) = k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,k11_cqc_lang(A,B)) & 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)))))))))))))) & (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)) -> f5_s3_cqc_lang(D,F,E) = k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,k8_cqc_lang(D,F,E)) & 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,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)) & 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,k9_cqc_lang) = f4_s3_cqc_lang & f4_s3_cqc_lang = k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,k9_cqc_lang) -> f3_s3_cqc_lang = f2_s3_cqc_lang # label(s3_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3130 (all A (r2_hidden(A,k1_qc_lang1) <-> -(-r2_hidden(A,k3_qc_lang1) & -r2_hidden(A,k4_qc_lang1) & -r2_hidden(A,k2_qc_lang1)))) # label(t7_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3131 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m1_subset_1(B,f1_s8_cqc_lang) -> ((exists C (m2_relset_1(C,k7_cqc_lang,f1_s8_cqc_lang) & k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,A) = B & k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k9_cqc_lang) = f3_s8_cqc_lang & (all D (m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) -> (all E (m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (all H (v1_cqc_lang(H,G) & m1_qc_lang1(H,G) -> (all I (m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G)) -> f4_s8_cqc_lang(G,I,H) = k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k8_cqc_lang(G,I,H)) & 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)) & 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)) & 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)))))))))))))) & v1_funct_2(C,k7_cqc_lang,f1_s8_cqc_lang) & v1_funct_1(C))) <-> B = f2_s8_cqc_lang(A)))))) -> f6_s8_cqc_lang(f2_s8_cqc_lang(f7_s8_cqc_lang),f2_s8_cqc_lang(f8_s8_cqc_lang)) = f2_s8_cqc_lang(k11_cqc_lang(f7_s8_cqc_lang,f8_s8_cqc_lang)) # label(s8_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3132 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) <-> m2_subset_1(k14_qc_lang1(A,B),k8_qc_lang1,k7_cqc_lang)))))) # label(t23_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3133 $T # label(t9_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3134 (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]. 4.49/4.60 3135 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (A = k20_qc_lang1(B) & v5_qc_lang1(B) -> k17_cqc_lang(B,A) = B))))) # label(t35_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3136 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m1_subset_1(B,f1_s9_cqc_lang) -> ((exists C (v1_funct_1(C) & f3_s9_cqc_lang = k8_funct_2(k7_cqc_lang,f1_s9_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)) -> k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s9_cqc_lang(G,I,H) & 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)) & f6_s9_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,E)) = k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k11_cqc_lang(D,E)) & k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k15_cqc_lang(F,D)) = f7_s9_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,D)))))))))))))) & B = k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,A) & m2_relset_1(C,k7_cqc_lang,f1_s9_cqc_lang) & v1_funct_2(C,k7_cqc_lang,f1_s9_cqc_lang))) <-> f2_s9_cqc_lang(A) = B))))) -> f2_s9_cqc_lang(k15_cqc_lang(f8_s9_cqc_lang,f9_s9_cqc_lang)) = f7_s9_cqc_lang(f8_s9_cqc_lang,f2_s9_cqc_lang(f9_s9_cqc_lang)) # label(s9_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3137 (all A all B (m1_subset_1(B,k7_cqc_lang) & m1_subset_1(A,k7_cqc_lang) -> m2_subset_1(k13_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang))) # label(dt_k13_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3138 (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) -> m1_qc_lang1(k5_cqc_lang(A,B,C),A))) # label(dt_k5_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3139 (all A ((exists B (k1_xboole_0 = k5_qc_lang3(B) & k6_qc_lang3(B) = k1_xboole_0 & A = B & m1_subset_1(B,k8_qc_lang1))) <-> r2_hidden(A,a_0_0_cqc_lang))) # label(fraenkel_a_0_0_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3140 $T # label(t25_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3141 (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]. 4.49/4.60 3142 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k4_pboole(A,k4_pboole(A,B,C),C),k4_pboole(A,B,C)))))) # label(t84_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3143 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,k4_pboole(A,B,C),D) -> r2_pboole(A,B,k2_pboole(A,C,D))))))))) # label(t88_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3144 (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]. 4.49/4.60 3145 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k5_pboole(A,k5_pboole(A,B,C),D),k5_pboole(A,B,k5_pboole(A,C,D))))))))) # label(t98_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3146 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,k2_pboole(A,C,D)) -> r2_pboole(A,k4_pboole(A,B,C),D) & r2_pboole(A,k4_pboole(A,B,D),C)))))))) # label(t82_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3147 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r5_pboole(A,k4_pboole(A,B,C),k4_pboole(A,C,B)))))) # label(t129_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3148 (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) -> 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)) & v1_funct_1(k1_funct_1(D,E)))) <-> m3_pboole(D,A,B,C)))))))) # label(d18_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3149 $T # label(t93_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3150 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k4_pboole(A,k4_pboole(A,B,C),D),k4_pboole(A,B,k2_pboole(A,C,D))))))))) # label(t79_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3151 (exists A ((all B (r2_hidden(B,f1_s4_pboole) -> k1_funct_1(A,B) = f2_s4_pboole(B))) & m1_pboole(A,f1_s4_pboole))) # label(s4_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3152 (exists A (m1_pboole(A,f1_s5_pboole) & (all B (m1_subset_1(B,f1_s5_pboole) -> f2_s5_pboole(B) = k1_funct_1(A,B))))) # label(s5_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3153 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r6_pboole(A,k4_pboole(A,B,C),B) <-> r6_pboole(A,k3_pboole(A,B,C),k1_pboole(A))))))) # label(t77_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3154 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) -> r7_pboole(A,B,C)))))) # label(t130_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3155 (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]. 4.49/4.60 3156 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r2_pboole(A,D,E) & r2_pboole(A,B,C) -> r2_pboole(A,k3_pboole(A,B,D),k3_pboole(A,C,E))))))))))) # label(t23_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3157 (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]. 4.49/4.60 3158 (all A all B (v1_funct_1(k10_pboole(A,B)) & m2_relset_1(k10_pboole(A,B),A,k1_tarski(B)) & v1_funct_2(k10_pboole(A,B),A,k1_tarski(B)))) # label(dt_k10_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3159 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k4_pboole(A,k2_pboole(A,B,C),k3_pboole(A,B,C)),k2_pboole(A,k4_pboole(A,B,C),k4_pboole(A,C,B))))))) # label(t83_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3160 (all A (m1_pboole(A,k1_xboole_0) -> A = k1_xboole_0)) # label(t134_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3161 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,k4_pboole(A,C,B),D) & r2_pboole(A,k4_pboole(A,B,C),D) -> r2_pboole(A,k5_pboole(A,B,C),D)))))))) # label(t99_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3162 (all A k1_pboole(A) = k2_funcop_1(A,k1_xboole_0)) # label(d6_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3163 $T # label(t107_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3164 (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,B,k1_pboole(A)) & r6_pboole(A,C,k1_pboole(A))))))) # label(t54_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3165 (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]. 4.49/4.60 3166 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) -> r2_pboole(A,k4_pboole(A,B,D),k4_pboole(A,C,D))))))))) # label(t59_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3167 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) & r6_pboole(A,k3_pboole(A,C,D),k1_pboole(A)) & r2_pboole(A,B,D) -> r6_pboole(A,B,k1_pboole(A))))))))) # label(t51_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3168 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r4_pboole(A,B,C) & r2_pboole(A,B,D) -> r4_pboole(A,D,C)))))))) # label(t109_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3169 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) -> r2_pboole(A,k2_pboole(A,D,B),k2_pboole(A,D,C)) & r2_pboole(A,k2_pboole(A,B,D),k2_pboole(A,C,D))))))))) # label(t20_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3170 (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]. 4.49/4.60 3171 (all A all B (m1_pboole(B,A) -> (r6_pboole(A,B,k1_pboole(A)) <-> v3_relat_1(B)))) # label(t141_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3172 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k3_pboole(A,B,k2_pboole(A,B,C)),B) & r6_pboole(A,k3_pboole(A,k2_pboole(A,C,B),B),B) & r6_pboole(A,k3_pboole(A,B,k2_pboole(A,C,B)),B) & r6_pboole(A,k3_pboole(A,k2_pboole(A,B,C),B),B))))) # label(t36_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3173 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v3_relat_1(A) <-> k2_relat_1(A) = k1_tarski(k1_xboole_0) | k1_xboole_0 = A))) # label(t2_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3174 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r4_pboole(A,B,k4_pboole(A,C,D)) -> r4_pboole(A,C,k4_pboole(A,B,D))))))))) # label(t115_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3175 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) -> r6_pboole(A,k3_pboole(A,B,C),B) & r6_pboole(A,k3_pboole(A,C,B),B)))))) # label(t25_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3176 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r5_pboole(A,k3_pboole(A,B,C),k5_pboole(A,B,C)))))) # label(t120_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3177 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> ((all D (r2_hidden(D,A) -> k1_funct_1(B,D) = k1_funct_1(C,D))) -> C = B))))) # label(t3_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3178 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r5_pboole(A,B,C) -> r6_pboole(A,k4_pboole(A,k2_pboole(A,B,C),C),B)))))) # label(t127_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3179 (all A exists B (v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B) & m1_pboole(B,A))) # label(rc3_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3180 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k3_pboole(A,k3_pboole(A,B,C),D),k3_pboole(A,k3_pboole(A,B,D),k3_pboole(A,C,D))) & r6_pboole(A,k3_pboole(A,B,k3_pboole(A,C,D)),k3_pboole(A,k3_pboole(A,B,C),k3_pboole(A,B,D))))))))) # label(t46_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3181 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k4_pboole(A,B,C),k5_pboole(A,B,k3_pboole(A,B,C))))))) # label(t102_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3182 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k4_pboole(A,B,C),k5_pboole(A,C,k2_pboole(A,C,B))))))) # label(t103_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3183 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r4_pboole(A,B,C) & r2_pboole(A,B,D) -> r4_pboole(A,B,k3_pboole(A,C,D))))))))) # label(t112_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3184 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k4_pboole(A,B,k3_pboole(A,C,B)),k4_pboole(A,B,C)) & r6_pboole(A,k4_pboole(A,B,k3_pboole(A,B,C)),k4_pboole(A,B,C)))))) # label(t76_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3185 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r5_pboole(A,B,C) -> r6_pboole(A,k3_pboole(A,B,C),k1_pboole(A))))))) # label(t121_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3186 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r7_pboole(A,B,C) <-> (all D (m1_pboole(D,A) -> (r1_pboole(A,D,B) -> r1_pboole(A,D,C))))))))) # label(d14_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3187 (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]. 4.49/4.60 3188 (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)))) & r4_pboole(A,B,C)))))) # label(t11_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3189 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r7_pboole(A,B,C) & v2_relat_1(B) -> r2_pboole(A,B,C)))))) # label(t144_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3190 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r6_pboole(A,k3_pboole(A,B,D),k1_pboole(A)) & r2_pboole(A,B,k2_pboole(A,C,D)) -> r2_pboole(A,B,C)))))))) # label(t56_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3191 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k2_pboole(A,k2_pboole(A,B,C),D),k2_pboole(A,B,k2_pboole(A,C,D))))))))) # label(t34_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3192 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r2_pboole(A,B,C) & r2_pboole(A,D,E) -> r2_pboole(A,k4_pboole(A,B,E),k4_pboole(A,C,D))))))))))) # label(t61_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3193 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k2_pboole(A,B,C),k5_pboole(A,k5_pboole(A,B,C),k3_pboole(A,B,C))))))) # label(t104_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3194 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r2_pboole(A,B,C) & r4_pboole(A,B,D) & r2_pboole(A,D,E) -> r4_pboole(A,C,E)))))))))) # label(t110_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3195 (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]. 4.49/4.60 3196 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k4_pboole(A,B,k4_pboole(A,C,D)),k2_pboole(A,k4_pboole(A,B,C),k3_pboole(A,B,D))))))))) # label(t70_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3197 (all A all B (m1_pboole(B,A) -> v1_relat_1(B) & v1_funct_1(B))) # label(dt_m1_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3198 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> m1_pboole(k2_pboole(A,B,C),A))) # label(dt_k2_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3199 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> -(-r5_pboole(A,B,C) & r2_pboole(A,C,D) & r5_pboole(A,B,D)))))))) # label(t116_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3200 $T # label(t31_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3201 (all A all B (m1_pboole(B,A) -> (v1_pboole(B,A) <-> v3_relat_1(B)))) # label(redefinition_v1_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3202 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,C,D) & r2_pboole(A,B,C) -> r2_pboole(A,B,D)))))))) # label(t15_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3203 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r6_pboole(A,k4_pboole(A,B,C),B) -> r5_pboole(A,B,C)))))) # label(t128_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3204 (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]. 4.49/4.60 3205 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r1_pboole(A,B,D) & r1_pboole(A,B,C) -> r4_pboole(A,C,D)))))))) # label(t10_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3206 (all A all B (v2_relat_1(B) & m1_pboole(B,A) -> (exists C (m1_pboole(C,A) & r1_pboole(A,C,B))))) # label(t146_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3207 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,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]. 4.49/4.60 3208 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k4_pboole(A,B,k4_pboole(A,B,C)),k3_pboole(A,B,C)))))) # label(t74_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3209 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> k5_pboole(A,B,C) = k5_pboole(A,C,B))) # label(commutativity_k5_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3210 (all A all B (m1_pboole(B,A) -> (all C (m2_pboole(C,A,B) -> m1_pboole(C,A))))) # label(dt_m2_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3211 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k4_pboole(A,B,k5_pboole(A,C,D)),k2_pboole(A,k4_pboole(A,B,k2_pboole(A,C,D)),k3_pboole(A,k3_pboole(A,B,C),D))))))))) # label(t97_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3212 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> B = k3_pboole(A,B,B))) # label(idempotence_k3_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3213 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r2_pboole(A,k3_pboole(A,B,C),C) & r2_pboole(A,k3_pboole(A,B,C),B))))) # label(t17_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3214 (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]. 4.49/4.60 3215 (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)) -> k4_card_3(k5_relat_1(D,B)) = k1_funct_1(C,D))) <-> k6_pboole(A,B) = C))))) # label(d19_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3216 (all A all B (m1_pboole(B,A) -> r6_pboole(A,k4_pboole(A,B,B),k1_pboole(A)))) # label(t64_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3217 (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]. 4.49/4.60 3218 (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]. 4.49/4.60 3219 (all A all B (m1_pboole(B,A) -> r6_pboole(A,k5_pboole(A,k1_pboole(A),B),B) & r6_pboole(A,k5_pboole(A,B,k1_pboole(A)),B))) # label(t91_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3220 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> (r4_pboole(A,B,C) -> r4_pboole(A,C,B)))) # label(symmetry_r4_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3221 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> B = k2_pboole(A,B,B))) # label(idempotence_k2_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3222 $T # label(t125_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3223 (all A m1_pboole(k1_pboole(A),A)) # label(dt_k1_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3224 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k3_pboole(A,B,k4_pboole(A,C,D)),k4_pboole(A,k3_pboole(A,B,C),D)))))))) # label(t68_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3225 (all A all B all C (-v1_xboole_0(A) & m1_pboole(B,A) & m1_subset_1(C,A) & v2_relat_1(B) -> -v1_xboole_0(k1_funct_1(B,C)))) # label(fc2_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3226 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) -> r2_pboole(A,k4_pboole(A,D,C),k4_pboole(A,D,B))))))))) # label(t60_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3227 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> -(r4_pboole(A,B,C) & r6_pboole(A,k3_pboole(A,B,C),k1_pboole(A))))))))) # label(t139_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3228 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r2_pboole(A,D,E) & r2_pboole(A,B,C) -> r2_pboole(A,k2_pboole(A,B,D),k2_pboole(A,C,E))))))))))) # label(t22_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3229 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k4_pboole(A,B,k3_pboole(A,C,D)),k2_pboole(A,k4_pboole(A,B,C),k4_pboole(A,B,D))))))))) # label(t75_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3230 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r6_pboole(A,k3_pboole(A,k2_pboole(A,B,C),k2_pboole(A,B,D)),B) -> r2_pboole(A,k3_pboole(A,C,D),B)))))))) # label(t41_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3231 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> r2_pboole(A,B,B))) # label(reflexivity_r2_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3232 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r1_pboole(A,B,C) | r1_pboole(A,B,D) -> r1_pboole(A,B,k2_pboole(A,C,D))))))))) # label(t7_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3233 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k2_pboole(A,k2_pboole(A,B,C),C),k2_pboole(A,B,C)) & r6_pboole(A,k2_pboole(A,B,k2_pboole(A,B,C)),k2_pboole(A,B,C)))))) # label(t47_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3234 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) -> r6_pboole(A,k2_pboole(A,B,k3_pboole(A,D,C)),k3_pboole(A,k2_pboole(A,B,D),C))))))))) # label(t27_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3235 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k3_pboole(A,B,C),k5_pboole(A,k5_pboole(A,B,C),k2_pboole(A,B,C))))))) # label(t105_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3236 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r7_pboole(A,B,C) & r7_pboole(A,C,D) -> r7_pboole(A,B,D)))))))) # label(t132_pboole) # label(axiom) # label(non_clause). [assumption]. 4.49/4.60 3237 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r2_pboole(A,k4_pboole(A,B,C),k5_pboole(A,B,C)))))) # label(t89_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3238 (all A all B k1_funct_1(k1_pboole(B),A) = k1_xboole_0) # label(t5_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3239 (all A all B (m1_pboole(B,A) -> (v2_relat_1(B) <-> v2_pboole(B,A)))) # label(redefinition_v2_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3240 (exists A (v1_relat_1(A) & v1_funct_1(A) & v3_relat_1(A))) # label(rc1_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3241 (all A (v1_funcop_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_funcop_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funcop_1(C) & v1_funct_1(C) -> (C = k13_pboole(A,B) <-> k3_xboole_0(k1_relat_1(A),k1_relat_1(B)) = k1_relat_1(C) & (all D (r2_hidden(D,k1_relat_1(C)) -> k5_relat_1(k1_funct_1(A,D),k1_funct_1(B,D)) = k1_funct_1(C,D)))))))))) # label(d24_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3242 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k2_pboole(A,B,C),k2_pboole(A,k5_pboole(A,B,C),k3_pboole(A,B,C))))))) # label(t94_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3243 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k4_pboole(A,k2_pboole(A,B,C),C),k4_pboole(A,B,C)))))) # label(t81_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3244 (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]. 4.57/4.60 3245 (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) -> (r6_pboole(A,k2_pboole(A,B,C),k2_pboole(A,D,E)) & r5_pboole(A,E,C) & r5_pboole(A,D,B) -> r6_pboole(A,E,B) & r6_pboole(A,D,C)))))))))) # label(t124_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3246 (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) & k1_pboole(A) = k3_pboole(A,C,D) & r3_pboole(A,B,C)))))))))) # label(t137_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3247 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> ((all E (r2_hidden(E,A) -> k3_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E)) = k1_funct_1(D,E))) <-> k3_pboole(A,B,C) = D))))))) # label(d8_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3248 $T # label(t117_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3249 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) <-> (all D (r2_hidden(D,A) -> r1_tarski(k1_funct_1(B,D),k1_funct_1(C,D))))))))) # label(d5_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3250 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k4_pboole(A,k3_pboole(A,B,C),D),k3_pboole(A,k4_pboole(A,B,D),k4_pboole(A,C,D))))))))) # label(t80_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3251 (all A all B (m1_pboole(B,A) -> (exists C m4_pboole(C,A,B)))) # label(existence_m4_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3252 (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]. 4.57/4.60 3253 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> m1_pboole(k11_pboole(A,B,C),A))) # label(dt_k11_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3254 (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]. 4.57/4.60 3255 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r2_pboole(A,k3_pboole(A,B,C),k2_pboole(A,B,D)))))))) # label(t26_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3256 $T # label(t13_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3257 (all A exists B (v1_relat_1(B) & v1_funct_1(B) & v1_funcop_1(B) & m1_pboole(B,A))) # label(rc4_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3258 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r6_pboole(A,B,k2_pboole(A,C,D)) <-> r2_pboole(A,C,B) & r2_pboole(A,D,B) & (all E (m1_pboole(E,A) -> (r2_pboole(A,C,E) & r2_pboole(A,D,E) -> r2_pboole(A,B,E))))))))))) # label(t28_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3259 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (D = k2_pboole(A,B,C) <-> (all E (r2_hidden(E,A) -> k1_funct_1(D,E) = k2_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E))))))))))) # label(d7_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3260 (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]. 4.57/4.60 3261 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k3_pboole(A,B,k4_pboole(A,C,D)),k4_pboole(A,k3_pboole(A,B,C),k3_pboole(A,B,D))))))))) # label(t87_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3262 (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]. 4.57/4.60 3263 $T # label(d1_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3264 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k2_pboole(A,k2_pboole(A,k3_pboole(A,B,C),k3_pboole(A,C,D)),k3_pboole(A,D,B)),k3_pboole(A,k3_pboole(A,k2_pboole(A,B,C),k2_pboole(A,C,D)),k2_pboole(A,D,B))))))))) # label(t42_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3265 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k2_pboole(A,k4_pboole(A,B,C),k3_pboole(A,B,C)),B) & r6_pboole(A,k2_pboole(A,k3_pboole(A,B,C),k4_pboole(A,B,C)),B))))) # label(t71_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3266 (all A all B all C all D (-v1_xboole_0(B) & m1_relset_1(C,A,B) & m1_pboole(D,B) & v2_relat_1(D) & v1_funct_2(C,A,B) & v1_funct_1(C) -> k8_pboole(A,B,C,D) = k5_relat_1(C,D))) # label(redefinition_k8_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3267 $T # label(t90_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3268 $T # label(t131_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3269 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k5_pboole(A,B,C),k4_pboole(A,k2_pboole(A,B,C),k3_pboole(A,B,C))))))) # label(t95_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3270 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) & r6_pboole(A,k3_pboole(A,C,B),k1_pboole(A)) -> r6_pboole(A,B,k1_pboole(A))))))) # label(t57_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3271 (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) <-> r1_pboole(A,D,B)))) -> r6_pboole(A,C,B)))))) # label(t147_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3272 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) -> r6_pboole(A,C,k2_pboole(A,k4_pboole(A,C,B),B)) & r6_pboole(A,C,k2_pboole(A,B,k4_pboole(A,C,B)))))))) # label(t72_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3273 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,C,B) <-> m4_pboole(C,A,B)))))) # label(d23_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3274 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_funct_1(B) & v1_funcop_1(B) & v1_relat_1(B) & v1_funcop_1(A) -> v1_relat_1(k13_pboole(A,B)) & v1_funct_1(k13_pboole(A,B)) & v1_funcop_1(k13_pboole(A,B)))) # label(dt_k13_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3275 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r2_pboole(A,C,k2_pboole(A,B,C)) & r2_pboole(A,B,k2_pboole(A,B,C)))))) # label(t16_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3276 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> m1_pboole(k5_pboole(A,B,C),A))) # label(dt_k5_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3277 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k3_pboole(A,B,C),k5_pboole(A,B,k4_pboole(A,B,C))))))) # label(t101_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3278 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) & v2_relat_1(D) -> ((all E (m1_pboole(E,A) -> (r1_pboole(A,E,C) & r1_pboole(A,E,B) <-> r1_pboole(A,E,D)))) -> r6_pboole(A,D,k3_pboole(A,B,C))))))))) # label(t148_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3279 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) & r2_pboole(A,D,C) -> r2_pboole(A,k2_pboole(A,B,D),C)))))))) # label(t18_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3280 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> (v3_relat_1(B) -> -v2_relat_1(B)))))) # label(cc2_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3281 (all A all B (m1_pboole(B,A) -> r6_pboole(A,k4_pboole(A,B,k1_pboole(A)),B))) # label(t65_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3282 (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) & r1_pboole(A,B,C) -> r1_pboole(A,B,D)))))))) # label(t9_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3283 (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]. 4.57/4.60 3284 $T # label(t33_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3285 (all A exists B m1_pboole(B,A)) # label(existence_m1_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3286 (all A all B (m1_pboole(B,A) & v2_relat_1(B) -> v1_relat_1(k6_pboole(A,B)) & -v3_relat_1(k6_pboole(A,B)) & v1_funct_1(k6_pboole(A,B)) & v2_relat_1(k6_pboole(A,B)))) # label(fc1_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3287 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r5_pboole(A,k3_pboole(A,B,C),k4_pboole(A,B,C)))))) # label(t119_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3288 (all A -(k1_xboole_0 = f2_s1_pboole(A) & r2_hidden(A,f1_s1_pboole))) -> (exists A (m1_pboole(A,f1_s1_pboole) & (all B (r2_hidden(B,f1_s1_pboole) -> r2_hidden(k1_funct_1(A,B),f2_s1_pboole(B)))))) # label(s1_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3289 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> ((all D (r2_hidden(D,A) -> m1_subset_1(k1_funct_1(C,D),k1_funct_1(B,D)))) <-> m2_pboole(C,A,B)))))) # label(d17_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3290 $T # label(t14_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3291 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r6_pboole(A,k4_pboole(A,B,C),k4_pboole(A,C,B)) -> r6_pboole(A,B,C)))))) # label(t86_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3292 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,k3_pboole(A,C,D)) -> r2_pboole(A,B,D) & r2_pboole(A,B,C)))))))) # label(t44_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3293 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r1_pboole(A,B,C) <-> (all D (r2_hidden(D,A) -> r2_hidden(k1_funct_1(B,D),k1_funct_1(C,D))))))))) # label(d4_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3294 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> r6_pboole(A,B,B))) # label(reflexivity_r6_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3295 $T # label(d2_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3296 (all A all B (m1_pboole(B,A) -> r6_pboole(A,k4_pboole(A,k1_pboole(A),B),k1_pboole(A)))) # label(t66_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.60 3297 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k3_pboole(A,C,k4_pboole(A,B,C)),k1_pboole(A)) & r6_pboole(A,k3_pboole(A,k4_pboole(A,B,C),C),k1_pboole(A)))))) # label(t69_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3298 (all A all B (m1_pboole(B,A) -> m1_pboole(k6_pboole(A,B),k3_finseq_2(A)))) # label(dt_k6_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3299 $T # label(t32_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3300 (all A all B (m1_pboole(B,A) -> (all C (r2_hidden(C,A) -> m1_subset_1(k1_funct_1(B,C),k2_relat_1(B)))))) # label(t151_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3301 (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]. 4.57/4.61 3302 (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]. 4.57/4.61 3303 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r4_pboole(A,B,D) | r4_pboole(A,B,C) -> r4_pboole(A,B,k2_pboole(A,C,D))))))))) # label(t106_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3304 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> ((all D (r2_hidden(D,A) -> r1_xboole_0(k1_funct_1(B,D),k1_funct_1(C,D)))) <-> r5_pboole(A,B,C)))))) # label(d11_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3305 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k3_pboole(A,k3_pboole(A,B,C),C),k3_pboole(A,B,C)) & r6_pboole(A,k3_pboole(A,B,k3_pboole(A,B,C)),k3_pboole(A,B,C)))))) # label(t48_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3306 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r2_pboole(A,k4_pboole(A,B,C),B))))) # label(t62_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3307 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> m1_pboole(k4_pboole(A,B,C),A))) # label(dt_k4_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3308 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) & r6_pboole(A,k3_pboole(A,C,D),k1_pboole(A)) -> r6_pboole(A,k3_pboole(A,B,D),k1_pboole(A))))))))) # label(t52_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3309 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,k4_pboole(A,C,B)) -> r6_pboole(A,B,k1_pboole(A))))))) # label(t63_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3310 (all A (v1_funct_1(k1_pboole(A)) & v3_relat_1(k1_pboole(A)) & v1_relat_1(k1_pboole(A)))) # label(fc3_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3311 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> -r3_pboole(A,B,k1_pboole(A)))))) # label(t136_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3312 (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]. 4.57/4.61 3313 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k2_pboole(A,B,k2_pboole(A,C,D)),k2_pboole(A,k2_pboole(A,B,C),k2_pboole(A,B,D))) & r6_pboole(A,k2_pboole(A,k2_pboole(A,B,C),D),k2_pboole(A,k2_pboole(A,B,D),k2_pboole(A,C,D))))))))) # label(t45_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3314 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) & -v1_xboole_0(A) -> (r3_pboole(A,B,C) <-> r1_pboole(A,B,C)))) # label(redefinition_r3_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3315 (all A all B (m1_pboole(B,A) -> (r2_pboole(A,B,k1_pboole(A)) -> r6_pboole(A,B,k1_pboole(A))))) # label(t50_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3316 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k2_pboole(A,B,C),k5_pboole(A,B,k4_pboole(A,C,B))))))) # label(t100_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3317 (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]. 4.57/4.61 3318 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> (r6_pboole(A,B,C) <-> C = B))) # label(redefinition_r6_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3319 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r4_pboole(A,B,k4_pboole(A,C,D)) -> r4_pboole(A,B,C)))))))) # label(t113_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3320 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k3_pboole(A,k3_pboole(A,B,C),D),k3_pboole(A,B,k3_pboole(A,C,D))))))))) # label(t35_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3321 (all A all B (m1_pboole(B,A) -> (exists C m2_pboole(C,A,B)))) # label(existence_m2_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3322 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r5_pboole(A,B,k4_pboole(A,C,B)))))) # label(t118_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3323 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r6_pboole(A,k2_pboole(A,k3_pboole(A,B,C),k3_pboole(A,B,D)),B) -> r2_pboole(A,B,k2_pboole(A,C,D))))))))) # label(t40_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3324 (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]. 4.57/4.61 3325 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,B) -> m1_pboole(C,A))))) # label(dt_m4_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3326 (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]. 4.57/4.61 3327 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k4_pboole(A,k2_pboole(A,B,C),D),k2_pboole(A,k4_pboole(A,B,D),k4_pboole(A,C,D))))))))) # label(t78_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3328 (all A all B (m1_pboole(B,A) -> r6_pboole(A,k2_pboole(A,k1_pboole(A),B),B) & r6_pboole(A,k2_pboole(A,B,k1_pboole(A)),B))) # label(t53_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3329 (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]. 4.57/4.61 3330 (all A all B (v2_relat_1(B) & m1_pboole(B,A) -> -r2_hidden(k1_xboole_0,k2_relat_1(B)))) # label(t149_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3331 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> (all D (m3_pboole(D,A,B,C) -> v1_funcop_1(D))))) # label(cc3_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3332 (all A all B (m1_pboole(B,A) -> r2_pboole(A,k1_pboole(A),B))) # label(t49_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3333 (all A all B all C all D (v1_funct_1(C) & v1_funct_2(C,A,B) & v2_relat_1(D) & m1_pboole(D,B) & m1_relset_1(C,A,B) & -v1_xboole_0(B) -> m1_pboole(k8_pboole(A,B,C,D),A) & v2_relat_1(k8_pboole(A,B,C,D)))) # label(dt_k8_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3334 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,C,D) & r4_pboole(A,B,C) -> r4_pboole(A,B,D)))))))) # label(t108_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3335 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k2_pboole(A,B,k3_pboole(A,B,C)),B) & r6_pboole(A,k2_pboole(A,k3_pboole(A,B,C),B),B) & r6_pboole(A,k2_pboole(A,k3_pboole(A,C,B),B),B) & r6_pboole(A,k2_pboole(A,B,k3_pboole(A,C,B)),B))))) # label(t37_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3336 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (k4_pboole(A,B,C) = D <-> (all E (r2_hidden(E,A) -> k4_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E)) = k1_funct_1(D,E)))))))))) # label(d9_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3337 (all A all B (m1_pboole(B,A) -> -(k1_pboole(A) != B & r5_pboole(A,B,B)))) # label(t122_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3338 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r1_pboole(A,B,k4_pboole(A,C,D)) -> r1_pboole(A,B,C)))))))) # label(t12_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3339 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> -(-r4_pboole(A,B,C) & r4_pboole(A,k3_pboole(A,D,B),k3_pboole(A,D,C))))))))) # label(t114_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3340 (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]. 4.57/4.61 3341 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) <-> r6_pboole(A,k4_pboole(A,B,C),k1_pboole(A))))))) # label(t58_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3342 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r1_pboole(A,B,D) & r1_pboole(A,B,C) <-> r1_pboole(A,B,k3_pboole(A,C,D))))))))) # label(t8_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3343 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> (v2_relat_1(B) -> -v3_relat_1(B)))))) # label(cc1_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3344 (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)) -> (D = k2_funcop_1(k1_tarski(C),A) -> k1_funct_2(k2_finseq_1(B),A) = k1_funct_1(k7_pboole(k5_numbers,k3_finseq_2(k1_tarski(C)),k9_pboole(C),k6_pboole(k1_tarski(C),D)),B)))))))) # label(t153_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3345 (all A all B k2_funcop_1(A,B) = k10_pboole(A,B)) # label(redefinition_k10_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3346 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r5_pboole(A,B,C) -> r6_pboole(A,k4_pboole(A,B,C),B)))))) # label(t126_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3347 (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,E,D) & r2_pboole(A,E,C) -> r2_pboole(A,E,B)))) & r2_pboole(A,B,D) & r2_pboole(A,B,C) <-> r6_pboole(A,B,k3_pboole(A,C,D))))))))) # label(t29_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3348 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (A = k1_relat_1(B) <-> m1_pboole(B,A)))) # label(d3_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3349 (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]. 4.57/4.61 3350 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> -(r4_pboole(A,B,C) & r5_pboole(A,B,C)))))))) # label(t135_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3351 (all A all B all C all D (-v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_pboole(D,B) & m1_relset_1(C,A,B) -> m1_pboole(k7_pboole(A,B,C,D),A))) # label(dt_k7_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3352 (all A all B (v2_relat_1(B) & m1_pboole(B,A) -> (exists C (m4_pboole(C,A,B) & v1_relat_1(C) & v1_funct_1(C) & v2_relat_1(C))))) # label(rc5_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3353 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k4_pboole(A,k5_pboole(A,B,C),D),k2_pboole(A,k4_pboole(A,B,k2_pboole(A,C,D)),k4_pboole(A,C,k2_pboole(A,B,D)))))))))) # label(t96_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3354 (all A exists B (v1_relat_1(B) & v3_relat_1(B) & v1_funct_1(B) & m1_pboole(B,A))) # label(rc2_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3355 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r4_pboole(A,B,k3_pboole(A,C,D)) -> r4_pboole(A,B,C) & r4_pboole(A,B,D)))))))) # label(t111_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3356 (all A all B (m1_pboole(B,A) -> ((all C (r2_hidden(C,A) -> k1_xboole_0 = k1_funct_1(B,C))) -> B = k1_pboole(A)))) # label(t6_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3357 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,A,B) & m1_pboole(D,B) & v1_funct_2(C,A,B) & -v1_xboole_0(B) -> k7_pboole(A,B,C,D) = k5_relat_1(C,D))) # label(redefinition_k7_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3358 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) -> r2_pboole(A,k3_pboole(A,D,B),k3_pboole(A,D,C)) & r2_pboole(A,k3_pboole(A,B,D),k3_pboole(A,C,D))))))))) # label(t21_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3359 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (k12_pboole(A,B,C) = D <-> (all E (r2_hidden(E,A) -> k1_funct_2(k1_funct_1(B,E),k1_funct_1(C,E)) = k1_funct_1(D,E)))))))))) # label(d22_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3360 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) & v2_relat_1(B) -> v2_relat_1(C)))))) # label(t143_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3361 (exists A (m1_pboole(A,f1_s2_pboole) & (all B (r2_hidden(B,f1_s2_pboole) -> (all C (p1_s2_pboole(B,C) & r2_hidden(C,k1_funct_1(f2_s2_pboole,B)) <-> r2_hidden(C,k1_funct_1(A,B)))))))) # label(s2_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3362 (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]. 4.57/4.61 3363 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (r2_hidden(D,A) -> k5_xboole_0(k1_funct_1(B,D),k1_funct_1(C,D)) = k1_funct_1(k5_pboole(A,B,C),D))))))) # label(t4_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3364 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> k3_pboole(A,C,B) = k3_pboole(A,B,C))) # label(commutativity_k3_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3365 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (D = k11_pboole(A,B,C) <-> (all E (r2_hidden(E,A) -> k1_funct_1(D,E) = k2_zfmisc_1(k1_funct_1(B,E),k1_funct_1(C,E))))))))))) # label(d21_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3366 (all A all B (m1_pboole(B,A) -> (v3_relat_1(B) <-> (all C (r2_hidden(C,A) -> v1_xboole_0(k1_funct_1(B,C))))))) # label(d15_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3367 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r4_pboole(A,B,C) <-> (all D -(r2_hidden(D,A) & r1_xboole_0(k1_funct_1(B,D),k1_funct_1(C,D))))))))) # label(d10_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3368 (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))) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k8_funct_2(k5_numbers,k3_finseq_2(k1_tarski(A)),B,C) = k2_finseq_2(C,A))) <-> B = k9_pboole(A)))) # label(d20_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3369 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k4_pboole(A,B,k2_pboole(A,C,D)),k3_pboole(A,k4_pboole(A,B,C),k4_pboole(A,B,D))))))))) # label(t85_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3370 $T # label(t30_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3371 (all A all B (m1_pboole(B,A) -> r6_pboole(A,k5_pboole(A,B,B),k1_pboole(A)))) # label(t92_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3372 (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]. 4.57/4.61 3373 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k3_pboole(A,B,k2_pboole(A,C,D)),k2_pboole(A,k3_pboole(A,B,C),k3_pboole(A,B,D))))))))) # label(t38_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3374 (all A all B (m1_pboole(B,A) -> r6_pboole(A,k3_pboole(A,k1_pboole(A),B),k1_pboole(A)) & r6_pboole(A,k3_pboole(A,B,k1_pboole(A)),k1_pboole(A)))) # label(t55_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3375 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> (exists D m3_pboole(D,A,B,C)))) # label(existence_m3_pboole) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3376 (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)) -> (k2_cat_1(A,B) = k3_cat_1(A,D) & 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,D) = k2_cat_1(A,C) -> D = C))))) <-> v3_cat_1(B,A)))))) # label(d10_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3377 $T # label(t28_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3378 (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,k4_cat_1(A,B,C)) = k3_cat_1(A,C) & k2_cat_1(A,B) = k2_cat_1(A,k4_cat_1(A,B,C))))))))) # label(t42_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3379 (all A (l1_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)) & v1_funct_2(u3_cat_1(A),u2_cat_1(A),u1_cat_1(A)))) # label(dt_u3_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3380 (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]. 4.57/4.61 3381 $T # label(t106_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3382 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> (k10_cat_1(B,E) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) -> 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]. 4.57/4.61 3383 $T # label(t5_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3384 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,B,C) -> (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]. 4.57/4.61 3385 (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)) -> (k6_cat_1(A,D,E) != k1_xboole_0 -> (all F (m1_cat_1(F,A,D,E) -> m1_cat_1(k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,F),B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E))))))))))))))) # label(t125_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3386 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),B) = k3_cat_1(A,B))))) # label(d3_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3387 (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)) -> (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]. 4.57/4.61 3388 (all A all B all C all D (v2_cat_1(A) & l1_cat_1(A) & l1_cat_1(B) & m1_subset_1(D,u1_cat_1(A)) & m2_cat_1(C,A,B) & v2_cat_1(B) -> 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]. 4.57/4.61 3389 (all A (l1_cat_1(A) & v2_cat_1(A) -> v8_cat_1(k15_cat_1(A),A,A))) # label(t122_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3390 (all A all B (v2_cat_1(A) & l1_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) -> k5_cat_1(A,B) = k10_cat_1(A,B))) # label(redefinition_k10_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3391 (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) -> (m2_cat_1(C,A,B) <-> (all D (m1_subset_1(D,u2_cat_1(A)) -> (all E (m1_subset_1(E,u2_cat_1(A)) -> (r2_hidden(k4_tarski(E,D),k1_relat_1(u5_cat_1(A))) -> k1_funct_1(u5_cat_1(B),k4_tarski(k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) = k1_funct_1(C,k1_funct_1(u5_cat_1(A),k4_tarski(E,D)))))))) & (all D (m1_subset_1(D,u2_cat_1(A)) -> k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),D))) = k8_funct_2(u1_cat_1(B),u2_cat_1(B),u6_cat_1(B),k8_funct_2(u2_cat_1(B),u1_cat_1(B),u4_cat_1(B),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) & k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),D))) = k8_funct_2(u1_cat_1(B),u2_cat_1(B),u6_cat_1(B),k8_funct_2(u2_cat_1(B),u1_cat_1(B),u3_cat_1(B),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))))) & (all D (m1_subset_1(D,u1_cat_1(A)) -> (exists E (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)) & m1_subset_1(E,u1_cat_1(B))))))))))))) # label(d18_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3392 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (k6_cat_1(A,B,C) != k1_xboole_0 -> ((all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_cat_1(F,A,E,B) -> (all G (m1_cat_1(G,A,E,B) -> (k9_cat_1(A,E,B,C,F,D) = k9_cat_1(A,E,B,C,G,D) -> F = G | k1_xboole_0 = k6_cat_1(A,E,B)))))))) <-> v3_cat_1(D,A))))))))))) # label(t60_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3393 (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)) -> (k3_cat_1(A,B) = k2_cat_1(A,C) & k3_cat_1(A,B) = k2_cat_1(A,D) & k3_cat_1(A,D) = k3_cat_1(A,C) & k4_cat_1(A,B,D) = k4_cat_1(A,B,C) -> D = C)))))))))) # label(d11_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3394 (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) <-> r2_hidden(k4_tarski(B,C),k1_relat_1(u5_cat_1(A)))))))))) # label(t40_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3395 (all A all B all C all D all E (v2_cat_1(A) & l1_cat_1(A) & l1_cat_1(B) & l1_cat_1(C) & m2_cat_1(D,A,B) & m2_cat_1(E,B,C) & v2_cat_1(C) & v2_cat_1(B) -> k5_relat_1(D,E) = k14_cat_1(A,B,C,D,E))) # label(redefinition_k14_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3396 (all A all B all C (m1_subset_1(B,u1_cat_1(A)) & m1_subset_1(C,u1_cat_1(A)) & l1_cat_1(A) -> m1_subset_1(k6_cat_1(A,B,C),k1_zfmisc_1(u2_cat_1(A))))) # label(dt_k6_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3397 (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,B) = k5_cat_1(A,C) -> B = C))))))) # label(t45_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3398 $T # label(t119_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3399 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,B,C) -> 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]. 4.57/4.61 3400 (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]. 4.57/4.61 3401 (all A (l1_cat_1(A) & v2_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)) -> k1_xboole_0 != k6_cat_1(A,C,B) & (exists D (m1_cat_1(D,A,C,B) & (all E (m1_cat_1(E,A,C,B) -> E = D))))))))))) # label(d15_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3402 (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) -> -((exists E (m1_cat_1(E,A,C,B) & (exists F (k9_cat_1(A,C,B,C,E,D) = k10_cat_1(A,C) & k9_cat_1(A,B,C,B,D,F) = k10_cat_1(A,B) & E != F & m1_cat_1(F,A,C,B))))) & k6_cat_1(A,C,B) != k1_xboole_0 & k6_cat_1(A,B,C) != k1_xboole_0))))))))) # label(t71_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3403 (all A all B all C (k1_relat_1(k1_cat_1(A,B,C)) = k2_zfmisc_1(k1_tarski(A),k1_tarski(B)) & k1_relat_1(k1_cat_1(A,B,C)) = k1_tarski(k4_tarski(A,B)))) # label(t7_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3404 (exists A (v2_cat_1(A) & v1_cat_1(A) & l1_cat_1(A))) # label(rc3_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3405 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,u1_cat_1(A),u1_cat_1(B)) & m2_relset_1(D,u1_cat_1(A),u1_cat_1(B)) -> ((all E (m1_subset_1(E,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)))) & (all E (m1_subset_1(E,u2_cat_1(A)) -> (all F (m1_subset_1(F,u2_cat_1(A)) -> (k3_cat_1(A,E) = k2_cat_1(A,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)) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k4_cat_1(A,E,F))))))) & (all E (m1_subset_1(E,u2_cat_1(A)) -> k8_funct_2(u1_cat_1(A),u1_cat_1(B),D,k2_cat_1(A,E)) = 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,k3_cat_1(A,E)) = k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)))) -> m2_cat_1(C,A,B)))))))))) # label(t100_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3406 (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) -> ((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) -> k6_cat_1(A,C,E) = k1_xboole_0 | F = G))))))) <-> v4_cat_1(D,A))))))))))) # label(t65_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3407 (all A (l1_cat_1(A) -> -v1_xboole_0(u2_cat_1(A)))) # label(dt_u2_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3408 (all A all B all C all D (-v1_xboole_0(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,D) & v1_funct_2(E,A,D) -> (r1_tarski(k2_funct_2(A,D,E,B),C) & r1_tarski(B,A) -> v1_funct_2(k2_partfun1(A,D,E,B),B,C) & m2_relset_1(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]. 4.57/4.61 3409 (all A all B (m1_subset_1(B,u2_cat_1(A)) & l1_cat_1(A) -> m1_subset_1(k3_cat_1(A,B),u1_cat_1(A)))) # label(dt_k3_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3410 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (k6_cat_1(A,B,C) = k1_tarski(D) -> (all E (m1_cat_1(E,A,B,C) -> E = D))))))))))) # label(t25_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3411 (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]. 4.57/4.61 3412 $T # label(t3_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3413 (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)) -> (k2_cat_1(A,C) = k3_cat_1(A,B) & k2_cat_1(A,D) = k3_cat_1(A,C) -> k4_cat_1(A,k4_cat_1(A,B,C),D) = k4_cat_1(A,B,k4_cat_1(A,C,D))))))))))) # label(t43_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3414 (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) -> (v2_funct_1(C) & u2_cat_1(B) = k2_relat_1(C) & u1_cat_1(B) = k2_relat_1(k12_cat_1(A,B,C)) <-> v8_cat_1(C,A,B)))))))) # label(d22_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3415 (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)) -> (k10_cat_1(B,E) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) -> k13_cat_1(A,B,C,D) = E))))))))))) # label(t107_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3416 (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)) -> 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]. 4.57/4.61 3417 (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(E,A) & v4_cat_1(F,A) -> v4_cat_1(k9_cat_1(A,B,C,D,E,F),A) | k1_xboole_0 = k6_cat_1(A,C,D) | k1_xboole_0 = k6_cat_1(A,B,C)))))))))))))) # label(t66_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3418 (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]. 4.57/4.61 3419 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,B,C) -> (v10_cat_1(D,A,B) & v10_cat_1(E,B,C) -> v10_cat_1(k14_cat_1(A,B,C,D,E),A,C)))))))))))) # label(t128_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3420 $T # label(t2_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3421 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,B,C) -> (all F (m1_cat_1(F,A,C,D) -> (v3_cat_1(F,A) & v3_cat_1(E,A) -> k1_xboole_0 = k6_cat_1(A,C,D) | v3_cat_1(k9_cat_1(A,B,C,D,E,F),A) | k6_cat_1(A,B,C) = k1_xboole_0))))))))))))) # label(t61_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3422 (all A all B (v2_cat_1(A) & l1_cat_1(A) & l1_cat_1(B) & v2_cat_1(B) -> (exists C m2_cat_1(C,A,B)))) # label(existence_m2_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3423 (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]. 4.57/4.61 3424 (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)) -> (k2_cat_1(A,D) = B & C = k3_cat_1(A,D) <-> r2_hidden(D,k6_cat_1(A,B,C))))))))))) # label(t18_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3425 (all A (l1_cat_1(A) -> -v1_xboole_0(u1_cat_1(A)))) # label(dt_u1_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3426 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> ((all C (m1_subset_1(C,u1_cat_1(A)) -> (exists D (m1_cat_1(D,A,B,C) & k6_cat_1(A,B,C) = k1_tarski(D))))) <-> v7_cat_1(B,A)))))) # label(t82_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3427 (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) -> v4_cat_1(D,A) & v3_cat_1(D,A) | k6_cat_1(A,B,C) = k1_xboole_0))))))))) # label(t73_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3428 $T # label(t49_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3429 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_1(C) -> ((all D (m1_subset_1(D,u1_cat_1(A)) -> (exists E (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)) & 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) -> (D = k12_cat_1(A,B,C) <-> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_subset_1(F,u1_cat_1(B)) -> (k8_funct_2(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(B),u2_cat_1(B),u6_cat_1(B),F) -> k8_funct_2(u1_cat_1(A),u1_cat_1(B),D,E) = F))))))))))))))) # label(d19_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3430 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> k8_funct_2(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)) & k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_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(t105_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3431 $T # label(t10_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3432 (all A all B all C (m2_relset_1(k1_cat_1(A,B,C),k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & v1_funct_1(k1_cat_1(A,B,C)))) # label(dt_k1_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3433 (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]. 4.57/4.61 3434 (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) -> -(k6_cat_1(A,B,C) != k1_xboole_0 & k6_cat_1(A,C,D) != k1_xboole_0 & -r2_hidden(k4_cat_1(A,E,F),k6_cat_1(A,B,D))))))))))))))) # label(t51_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3435 (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]. 4.57/4.61 3436 (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_subset_1(C,u1_cat_1(A)) & m1_subset_1(D,u1_cat_1(A)) & m1_cat_1(E,A,B,C) & m1_cat_1(F,A,C,D) -> 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]. 4.57/4.61 3437 (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))) -> k6_cat_1(k8_cat_1(A,B),C,D) != k1_xboole_0)))) # label(t38_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3438 (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) -> k1_xboole_0 = k6_cat_1(A,B,C) | k1_xboole_0 = k6_cat_1(A,C,D) | v3_cat_1(E,A)))))))))))))) # label(t62_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3439 (exists A (v2_cat_1(A) & l1_cat_1(A))) # label(rc2_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3440 (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]. 4.57/4.61 3441 $T # label(t30_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3442 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,B,C) -> (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]. 4.57/4.61 3443 (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)) -> 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]. 4.57/4.61 3444 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_1(C) -> ((all D (m1_subset_1(D,u1_cat_1(A)) -> (exists E (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,k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k3_cat_1(A,D))) & k10_cat_1(B,k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k2_cat_1(A,D))))) & (all D (m1_subset_1(D,u2_cat_1(A)) -> (all E (m1_subset_1(E,u2_cat_1(A)) -> (k2_cat_1(A,E) = k3_cat_1(A,D) -> 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]. 4.57/4.61 3445 $T # label(t114_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3446 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (k6_cat_1(A,B,C) != k1_xboole_0 & (exists D ((exists E (k9_cat_1(A,C,B,C,E,D) = k10_cat_1(A,C) & k9_cat_1(A,B,C,B,D,E) = k10_cat_1(A,B) & m1_cat_1(E,A,C,B))) & m1_cat_1(D,A,B,C))) & k6_cat_1(A,C,B) != k1_xboole_0 <-> r1_cat_1(A,B,C)))))))) # label(t81_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3447 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,B,C) -> (v9_cat_1(D,A,B) & v9_cat_1(E,B,C) -> v9_cat_1(k14_cat_1(A,B,C,D,E),A,C)))))))))))) # label(t127_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3448 (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) -> (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)) -> k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)) = k2_relat_1(k16_cat_1(A,B,C,D,E))))))))))))) # label(t132_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3449 (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) -> (F = G -> k1_xboole_0 = k6_cat_1(A,B,C) | B = D & C = E | k1_xboole_0 = k6_cat_1(A,D,E)))))))))))))))) # label(t24_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3450 (all A all B all C all D (l1_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) & m1_cat_1(D,A,B,C) & m1_subset_1(C,u1_cat_1(A)) & v2_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]. 4.57/4.61 3451 (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]. 4.57/4.61 3452 $T # label(t11_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3453 $T # label(t15_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 3454 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (all E (m1_cat_1(E,A,C,B) -> (k10_cat_1(A,C) = k9_cat_1(A,C,B,C,E,D) -> k1_xboole_0 = k6_cat_1(A,C,B) | v4_cat_1(D,A) | k1_xboole_0 = k6_cat_1(A,B,C)))))))))))) # label(t68_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 3455 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> B = k3_cat_1(A,k5_cat_1(A,B)) & k2_cat_1(A,k5_cat_1(A,B)) = B)))) # label(t44_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 3456 (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(C,A) & v6_cat_1(B,A) -> r1_cat_1(A,B,C)))))))) # label(t88_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 3457 (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]. 4.57/4.62 3458 (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]. 4.57/4.62 3459 (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]. 4.57/4.62 3460 (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,C,D) & r1_cat_1(A,B,C) -> r1_cat_1(A,B,D)))))))))) # label(t93_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 3461 $T # label(t94_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 3462 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (k1_xboole_0 != k6_cat_1(A,B,C) -> D = k9_cat_1(A,B,C,C,D,k10_cat_1(A,C))))))))))) # label(t57_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 3463 (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]. 4.57/4.62 3464 (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]. 4.57/4.62 3465 $T # label(t121_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 3466 (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]. 4.57/4.62 3467 (all A all B (v2_cat_1(A) & l1_cat_1(B) & v2_cat_1(B) & l1_cat_1(A) -> (all C (m2_cat_1(C,A,B) -> 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))))) # label(dt_m2_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 3468 (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_xboole_0 -> B = k2_cat_1(A,D) & C = k3_cat_1(A,D)))))))))) # label(t23_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 3469 $T # label(dt_l1_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 3470 (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)) -> -(k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)) = k1_xboole_0 & k1_xboole_0 != k6_cat_1(A,D,E)))))))))))) # label(t126_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 3471 (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) -> G = H)))))))))))) # label(t39_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 3472 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> k2_cat_1(A,B) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),B))))) # label(d2_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 3473 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> k6_cat_1(A,B,B) != k1_xboole_0)))) # label(t56_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 3474 (all A all 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)) = k8_cat_1(A,B)) # label(d9_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 3475 $T # label(t78_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 3476 (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]. 4.57/4.62 3477 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,k13_cat_1(A,B,C,D)))))))))) # label(t108_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 3478 (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]. 4.57/4.62 3479 $T # label(t101_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 3480 $T # label(t130_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 3481 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> r2_hidden(k5_cat_1(A,B),k6_cat_1(A,B,B)))))) # label(t55_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 3482 (all A all B all C all D all E (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(C) & m2_cat_1(E,B,C) & m2_cat_1(D,A,B) & v2_cat_1(C) & l1_cat_1(B) -> m2_cat_1(k14_cat_1(A,B,C,D,E),A,C))) # label(dt_k14_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 3483 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (all E (m1_cat_1(E,A,C,B) -> (k9_cat_1(A,C,B,C,E,D) = k10_cat_1(A,C) -> v3_cat_1(E,A) | k1_xboole_0 = k6_cat_1(A,C,B) | k1_xboole_0 = k6_cat_1(A,B,C)))))))))))) # label(t63_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 3484 $T # label(t20_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 3485 (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(F,A) & v5_cat_1(E,A) -> k6_cat_1(A,C,D) = k1_xboole_0 | v5_cat_1(k9_cat_1(A,B,C,D,E,F),A) | k6_cat_1(A,B,C) = k1_xboole_0))))))))))))) # label(t75_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 3486 $T # label(t48_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 3487 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (v6_cat_1(B,A) -> (all C (m1_cat_1(C,A,B,B) -> C = k10_cat_1(A,B)))))))) # label(t87_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 3488 (all A (l1_cat_1(A) -> (v1_cat_1(A) -> g1_cat_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A)) = A))) # label(abstractness_v1_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 3489 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,B,C) -> (all F (m1_cat_1(F,A,C,D) -> -(k1_xboole_0 != k6_cat_1(A,B,C) & k9_cat_1(A,B,C,D,E,F) != k4_cat_1(A,E,F) & k1_xboole_0 != k6_cat_1(A,C,D)))))))))))))) # label(d13_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 3490 (all A all B all C (m1_subset_1(C,u2_cat_1(k8_cat_1(A,B))) -> C = B)) # label(t35_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 3491 (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)) -> (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]. 4.57/4.62 3492 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> ((all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)) != k1_xboole_0 -> (all F (m1_cat_1(F,B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)) -> k1_xboole_0 != k6_cat_1(A,D,E) & (exists G (m1_cat_1(G,A,D,E) & F = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,G)))))))))) <-> v9_cat_1(C,A,B)))))))) # label(d23_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 3493 (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]. 4.57/4.62 3494 (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)) -> 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]. 4.57/4.62 3495 $T # label(t79_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 3496 (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]. 4.57/4.62 3497 (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)) -> 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]. 4.57/4.62 3498 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (v5_cat_1(D,A) -> (all E (m1_cat_1(E,A,C,B) -> (k9_cat_1(A,C,B,C,E,D) = k10_cat_1(A,C) & k10_cat_1(A,B) = k9_cat_1(A,B,C,B,D,E) <-> k11_cat_1(A,B,C,D) = E))) | k6_cat_1(A,B,C) = k1_xboole_0))))))))) # label(d14_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 3499 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (v5_cat_1(B,A) <-> (exists C (m1_subset_1(C,u2_cat_1(A)) & k4_cat_1(A,B,C) = k5_cat_1(A,k2_cat_1(A,B)) & k4_cat_1(A,C,B) = k5_cat_1(A,k3_cat_1(A,B)) & k3_cat_1(A,C) = k2_cat_1(A,B) & k3_cat_1(A,B) = k2_cat_1(A,C)))))))) # label(d12_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 3500 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> k8_funct_2(u2_cat_1(A),u2_cat_1(A),k15_cat_1(A),B) = B)))) # label(t115_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 3501 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (k1_xboole_0 != k6_cat_1(A,B,C) -> k9_cat_1(A,B,B,C,k10_cat_1(A,B),D) = D))))))))) # label(t58_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 3502 (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(B,A) & v7_cat_1(C,A) -> r1_cat_1(A,B,C)))))))) # label(t84_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 3503 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) -> ((all D (m1_subset_1(D,u1_cat_1(A)) -> (exists E (m1_subset_1(E,u1_cat_1(B)) & k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,E))))) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> (k10_cat_1(B,E) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) -> E = k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D))))))))))))) # label(t102_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.80/4.84 3504 (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) -> 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)) & 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))))))))))))) # label(t99_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.80/4.84 3505 $T # label(t72_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.80/4.84 3506 (all A all B (v1_funct_1(k7_cat_1(A,B)) & v1_funct_2(k7_cat_1(A,B),k1_tarski(A),k1_tarski(B)) & m2_relset_1(k7_cat_1(A,B),k1_tarski(A),k1_tarski(B)))) # label(dt_k7_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.80/4.84 3507 (all A (l1_cat_1(A) -> v1_funct_1(u6_cat_1(A)) & m2_relset_1(u6_cat_1(A),u1_cat_1(A),u2_cat_1(A)) & v1_funct_2(u6_cat_1(A),u1_cat_1(A),u2_cat_1(A)))) # label(dt_u6_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.80/4.84 3508 (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) -> (v6_cat_1(B,A) -> k6_cat_1(A,B,C) = k1_xboole_0 | v3_cat_1(D,A)))))))))) # label(t90_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.80/4.84 3509 $T # label(t53_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.80/4.84 3510 (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)) -> (k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),B) -> k1_funct_1(u4_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(u3_cat_1(A),k1_funct_1(u5_cat_1(A),k4_tarski(C,B))) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),B)))))) & (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),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),u4_cat_1(A),C) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),D) -> 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,u1_cat_1(A)) -> 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 & (all C (m1_subset_1(C,u2_cat_1(A)) -> (k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C) = B -> k1_funct_1(u5_cat_1(A),k4_tarski(k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B),C)) = C))) & (all C (m1_subset_1(C,u2_cat_1(A)) -> (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))) & 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),u4_cat_1(A),B) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C) <-> r2_hidden(k4_tarski(C,B),k1_relat_1(u5_cat_1(A))))))))))) # label(d8_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.80/4.84 3511 $T # label(t6_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.80/4.84 3512 (all A all B all C (l1_cat_1(A) & m1_subset_1(C,u2_cat_1(A)) & m1_subset_1(B,u2_cat_1(A)) -> m1_subset_1(k4_cat_1(A,B,C),u2_cat_1(A)))) # label(dt_k4_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.80/4.84 3513 (all A all B all C all D (m1_subset_1(C,u1_cat_1(B)) & m1_subset_1(D,u1_cat_1(B)) & l1_cat_1(B) -> (r2_hidden(A,a_3_0_cat_1(B,C,D)) <-> (exists E (A = E & C = k2_cat_1(B,E) & k3_cat_1(B,E) = D & m1_subset_1(E,u2_cat_1(B))))))) # label(fraenkel_a_3_0_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.80/4.84 3514 (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)) -> (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))))))))))) # label(t97_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3515 (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)) -> (v7_cat_1(B,A) & r1_cat_1(A,B,C) -> v7_cat_1(C,A)))))))) # label(t85_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3516 (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]. 4.88/4.92 3517 $T # label(t95_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3518 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> r1_cat_1(A,B,B))))) # label(t91_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3519 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (v10_cat_1(C,A,B) <-> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (k6_cat_1(A,D,E) != k1_xboole_0 -> (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) -> G = F))))))))))))))))) # label(d24_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3520 (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]. 4.88/4.92 3521 (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]. 4.88/4.92 3522 (all A all B all C all D all E all F (-v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(D,B,A) & m1_relset_1(E,k2_zfmisc_1(B,B),B) & v1_funct_1(F) & v1_funct_2(F,A,B) & m1_relset_1(F,A,B) & v1_funct_1(E) & m1_relset_1(D,B,A) & m1_relset_1(C,B,A) & v1_funct_2(C,B,A) & v1_funct_1(C) & -v1_xboole_0(A) -> l1_cat_1(g1_cat_1(A,B,C,D,E,F)) & v1_cat_1(g1_cat_1(A,B,C,D,E,F)))) # label(dt_g1_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3523 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> B = k13_cat_1(A,A,k15_cat_1(A),B))))) # label(t118_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3524 (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]. 4.88/4.92 3525 $T # label(t1_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3526 $T # label(t80_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3527 (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)) -> (k2_cat_1(A,C) = k3_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)) -> (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))))))) & (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (k2_cat_1(A,C) = k3_cat_1(A,B) & k2_cat_1(A,D) = k3_cat_1(A,C) -> k4_cat_1(A,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 = k3_cat_1(A,C) -> k4_cat_1(A,C,k5_cat_1(A,B)) = C))) & (all C (m1_subset_1(C,u2_cat_1(A)) -> (k2_cat_1(A,C) = B -> C = k4_cat_1(A,k5_cat_1(A,B),C)))) & B = k3_cat_1(A,k5_cat_1(A,B)))) -> v2_cat_1(A)))) # label(t29_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3528 $T # label(t13_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3529 (all A all B all C (m1_subset_1(C,u1_cat_1(k8_cat_1(A,B))) -> C = A)) # label(t34_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3530 (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)) -> (k3_cat_1(A,C) = B -> k4_cat_1(A,C,k5_cat_1(A,B)) = C))))))) # label(t46_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3531 (exists A l1_cat_1(A)) # label(existence_l1_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3532 (all A all B all C all D (m1_subset_1(D,k1_tarski(A)) -> (all E (m1_subset_1(E,k1_tarski(B)) -> C = k1_funct_1(k1_cat_1(A,B,C),k4_tarski(D,E)))))) # label(t9_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3533 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (k2_cat_1(A,B) = k3_cat_1(A,C) -> k1_funct_1(u5_cat_1(A),k4_tarski(B,C)) = k4_cat_1(A,C,B)))))))) # label(t41_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3534 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> k6_cat_1(A,B,C) = a_3_0_cat_1(A,B,C))))))) # label(d6_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3535 (all A (l1_cat_1(A) & v2_cat_1(A) -> k15_cat_1(A) = k6_partfun1(u2_cat_1(A)))) # label(d21_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3536 (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,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]. 4.88/4.92 3537 (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,k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k3_cat_1(A,D))) & k10_cat_1(B,k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k2_cat_1(A,D))))))))))) # label(t98_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3538 (all A all B (v1_cat_1(k8_cat_1(A,B)) & l1_cat_1(k8_cat_1(A,B)) & v2_cat_1(k8_cat_1(A,B)))) # label(dt_k8_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3539 (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)) -> (k1_xboole_0 != k6_cat_1(A,B,C) -> (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]. 4.88/4.92 3540 (all A (l1_cat_1(A) & v2_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]. 4.88/4.92 3541 (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]. 4.88/4.92 3542 (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]. 4.88/4.92 3543 (all A all B (l1_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) -> m1_subset_1(k5_cat_1(A,B),u2_cat_1(A)))) # label(dt_k5_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3544 $T # label(t120_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3545 (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) & k10_cat_1(A,B) = k9_cat_1(A,B,C,B,D,E) & k10_cat_1(A,C) = k9_cat_1(A,C,B,C,E,D))) & k6_cat_1(A,C,B) != k1_xboole_0 <-> v5_cat_1(D,A))))))))))) # label(t70_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3546 (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]. 4.88/4.92 3547 (all A all B all C (m1_subset_1(C,u1_cat_1(A)) & m1_subset_1(B,u1_cat_1(A)) & l1_cat_1(A) -> (all D (m1_cat_1(D,A,B,C) -> m1_subset_1(D,u2_cat_1(A)))))) # label(dt_m1_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3548 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (k1_xboole_0 != k6_cat_1(A,D,E) -> (all F (m1_cat_1(F,A,D,E) -> k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,F) = k1_funct_1(k16_cat_1(A,B,C,D,E),F)))))))))))))) # label(t131_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3549 (all A all B all C (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & v1_funct_1(C) & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & m1_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & l1_cat_1(B) -> m2_relset_1(k12_cat_1(A,B,C),u1_cat_1(A),u1_cat_1(B)) & v1_funct_2(k12_cat_1(A,B,C),u1_cat_1(A),u1_cat_1(B)) & v1_funct_1(k12_cat_1(A,B,C)))) # label(dt_k12_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3550 (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)) -> v2_funct_1(k16_cat_1(A,B,C,D,E)))))) <-> v10_cat_1(C,A,B)))))))) # label(t133_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3551 $T # label(t12_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3552 (exists A (v1_cat_1(A) & l1_cat_1(A))) # label(rc1_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3553 $T # label(t17_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3554 (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) <-> (exists D (m1_cat_1(D,A,B,C) & v5_cat_1(D,A))) & k1_xboole_0 != k6_cat_1(A,B,C)))))))) # label(d17_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3555 (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) -> -(k1_xboole_0 != k6_cat_1(A,B,C) & k1_xboole_0 != k6_cat_1(A,C,D) & k6_cat_1(A,D,E) != k1_xboole_0 & k9_cat_1(A,B,D,E,k9_cat_1(A,B,C,D,F,G),H) != k9_cat_1(A,B,C,E,F,k9_cat_1(A,C,D,E,G,H))))))))))))))))))) # label(t54_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3556 (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_xboole_0 = k6_cat_1(A,B,C) | k1_tarski(D) = k6_cat_1(A,B,C)))))))))) # label(t26_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3557 (all A all B all C k3_cqc_lang(k4_tarski(A,B),C) = k1_cat_1(A,B,C)) # label(d1_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3558 $T # label(t31_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3559 (all A all B all C all D all E (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & m2_cat_1(C,A,B) & m1_subset_1(E,u1_cat_1(A)) & m1_subset_1(D,u1_cat_1(A)) & l1_cat_1(B) -> v1_funct_1(k16_cat_1(A,B,C,D,E)) & v1_funct_2(k16_cat_1(A,B,C,D,E),k6_cat_1(A,D,E),k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E))) & 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))))) # label(dt_k16_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3560 $T # label(t16_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3561 $T # label(t50_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3562 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,B,C) -> (all F (m1_cat_1(F,A,C,D) -> (v4_cat_1(k9_cat_1(A,B,C,D,E,F),A) -> k1_xboole_0 = k6_cat_1(A,B,C) | k1_xboole_0 = k6_cat_1(A,C,D) | v4_cat_1(F,A)))))))))))))) # label(t67_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3563 (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) -> k9_cat_1(A,D,C,B,k11_cat_1(A,C,D,F),k11_cat_1(A,B,C,E)) = k11_cat_1(A,B,D,k9_cat_1(A,B,C,D,E,F)) | k1_xboole_0 = k6_cat_1(A,C,D) | k6_cat_1(A,B,C) = k1_xboole_0))))))))))))) # label(t77_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3564 (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]. 4.88/4.92 3565 (all A all B all C all D all E all F (-v1_xboole_0(B) & v1_funct_2(C,B,A) & m1_relset_1(D,B,A) & v1_funct_1(F) & v1_funct_2(F,A,B) & m1_relset_1(F,A,B) & m1_relset_1(E,k2_zfmisc_1(B,B),B) & v1_funct_1(E) & v1_funct_2(D,B,A) & v1_funct_1(D) & m1_relset_1(C,B,A) & v1_funct_1(C) & -v1_xboole_0(A) -> (all G all H all I all J all K all L (g1_cat_1(A,B,C,D,E,F) = g1_cat_1(G,H,I,J,K,L) -> B = H & D = J & L = F & K = E & C = I & G = A)))) # label(free_g1_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3566 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (k2_cat_1(A,C) = B -> k4_cat_1(A,k5_cat_1(A,B),C) = C))))))) # label(t47_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3567 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (v5_cat_1(D,A) -> v5_cat_1(k11_cat_1(A,B,C,D),A) | k6_cat_1(A,B,C) = k1_xboole_0))))))))) # label(t76_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3568 $T # label(t14_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3569 (all A (l1_cat_1(A) -> v1_funct_1(u4_cat_1(A)) & m2_relset_1(u4_cat_1(A),u2_cat_1(A),u1_cat_1(A)) & v1_funct_2(u4_cat_1(A),u2_cat_1(A),u1_cat_1(A)))) # label(dt_u4_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3570 (all A all B k3_cqc_lang(A,B) = k7_cat_1(A,B)) # label(redefinition_k7_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3571 (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,u2_cat_1(A)) -> k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)) = k13_cat_1(A,B,C,k2_cat_1(A,D)) & k3_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)))))))))) # label(t109_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3572 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,B) -> (all F (v1_funct_1(F) & v1_funct_2(F,k2_zfmisc_1(A,B),C) & m2_relset_1(F,k2_zfmisc_1(A,B),C) -> k8_funct_2(k2_zfmisc_1(A,B),C,F,k1_domain_1(A,B,D,E)) = k8_funct_2(A,C,k1_cat_2(B,A,C,k1_fraenkel(A,C),k3_cat_2(A,B,C,F),E),D))))))))))))) # label(t4_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3573 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> (r1_cat_2(B,A) <-> v9_cat_1(k8_cat_2(A,B),B,A)))))) # label(t27_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3574 (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 (v1_funct_1(D) & v1_funct_2(D,u1_cat_1(A),k7_cat_2(B,C)) & m2_relset_1(D,u1_cat_1(A),k7_cat_2(B,C)) -> (all E (v1_funct_1(E) & m2_relset_1(E,u1_cat_1(B),k7_cat_2(A,C)) & v1_funct_2(E,u1_cat_1(B),k7_cat_2(A,C)) -> ((exists F ((all G (m1_subset_1(G,u1_cat_1(A)) -> (all H (m1_subset_1(H,u1_cat_1(B)) -> k6_cat_2(u1_cat_1(B),A,C,k7_cat_2(A,C),E,H) = k14_cat_2(B,A,C,F,H) & k6_cat_2(u1_cat_1(A),B,C,k7_cat_2(B,C),D,G) = k15_cat_2(B,A,C,F,G))))) & m2_cat_1(F,k11_cat_2(B,A),C))) -> (all F (m1_subset_1(F,u2_cat_1(B)) -> (all G (m1_subset_1(G,u2_cat_1(A)) -> k4_cat_1(C,k8_funct_2(u2_cat_1(A),u2_cat_1(C),k6_cat_2(u1_cat_1(B),A,C,k7_cat_2(A,C),E,k2_cat_1(B,F)),G),k8_funct_2(u2_cat_1(B),u2_cat_1(C),k6_cat_2(u1_cat_1(A),B,C,k7_cat_2(B,C),D,k3_cat_1(A,G)),F)) = k4_cat_1(C,k8_funct_2(u2_cat_1(B),u2_cat_1(C),k6_cat_2(u1_cat_1(A),B,C,k7_cat_2(B,C),D,k2_cat_1(A,G)),F),k8_funct_2(u2_cat_1(A),u2_cat_1(C),k6_cat_2(u1_cat_1(B),A,C,k7_cat_2(A,C),E,k3_cat_1(B,F)),G))))))))))))))))) # label(t53_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3575 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m3_cat_2(B,A) -> v10_cat_1(k8_cat_2(A,B),B,A))))) # label(t24_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3576 $T # label(t9_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3577 $T # label(t56_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3578 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (-v1_xboole_0(C) -> (m1_cat_2(C,A,B) <-> (all D (m1_subset_1(D,C) -> m2_cat_1(D,A,B)))))))))) # label(d3_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3579 $T # label(t49_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3580 (all A all B all C all D all E all F (-v1_xboole_0(B) & -v1_xboole_0(C) & -v1_xboole_0(D) & v1_funct_1(E) & m1_relset_1(E,A,C) & m1_relset_1(F,B,D) & v1_funct_2(F,B,D) & v1_funct_1(F) & v1_funct_2(E,A,C) & -v1_xboole_0(A) -> k15_funct_3(E,F) = k9_cat_2(A,B,C,D,E,F))) # label(redefinition_k9_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3581 $T # label(t26_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3582 (all A all B all C all D (v2_cat_1(A) & l1_cat_1(B) & m1_subset_1(C,u2_cat_1(A)) & m1_subset_1(D,u2_cat_1(B)) & v2_cat_1(B) & l1_cat_1(A) -> m1_subset_1(k13_cat_2(A,B,C,D),u2_cat_1(k11_cat_2(A,B))))) # label(dt_k13_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3583 (all A all B all C all D all E (v2_cat_1(A) & v2_cat_1(C) & l1_cat_1(C) & m2_cat_1(E,A,C) & m2_cat_1(D,A,B) & l1_cat_1(B) & v2_cat_1(B) & l1_cat_1(A) -> k13_funct_3(D,E) = k18_cat_2(A,B,C,D,E))) # label(redefinition_k18_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3584 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_subset_1(F,u2_cat_1(B)) -> k8_funct_2(u2_cat_1(B),u2_cat_1(C),k14_cat_2(A,B,C,D,E),F) = k8_funct_2(u2_cat_1(k11_cat_2(A,B)),u2_cat_1(C),D,k13_cat_2(A,B,k10_cat_1(A,E),F)))))))))))))) # label(t47_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3585 (all A all B all C all D all E (v2_cat_1(A) & l1_cat_1(A) & l1_cat_1(B) & v2_cat_1(C) & l1_cat_1(C) & m1_subset_1(E,u1_cat_1(B)) & m2_cat_1(D,k11_cat_2(A,B),C) & v2_cat_1(B) -> m2_cat_1(k15_cat_2(A,B,C,D,E),A,C))) # label(dt_k15_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3586 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) -> m1_subset_1(k3_tarski(a_2_0_cat_2(A,B)),k1_zfmisc_1(u2_cat_1(A))) & -v1_xboole_0(k3_tarski(a_2_0_cat_2(A,B))))))) # label(t28_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3587 (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,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> k1_funct_1(k5_funct_5(D),k10_cat_1(B,E)) = k15_cat_2(A,B,C,D,E))))))))))) # label(d9_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3588 (all A all B all C all D all E all F (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(D) & m2_cat_1(E,A,C) & m2_cat_1(F,B,D) & v2_cat_1(D) & l1_cat_1(C) & v2_cat_1(C) & l1_cat_1(B) -> m2_cat_1(k19_cat_2(A,B,C,D,E,F),k11_cat_2(A,B),k11_cat_2(C,D)))) # label(dt_k19_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3589 $T # label(t46_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3590 $T # label(t8_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.92 3591 (all A all B all C all D all E all F (-v1_xboole_0(B) & v1_funct_1(E) & v1_funct_2(E,A,C) & v1_funct_1(F) & v1_funct_2(F,B,D) & m1_relset_1(F,B,D) & m1_relset_1(E,A,C) & -v1_xboole_0(D) & -v1_xboole_0(C) & -v1_xboole_0(A) -> m2_relset_1(k9_cat_2(A,B,C,D,E,F),k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) & v1_funct_2(k9_cat_2(A,B,C,D,E,F),k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) & v1_funct_1(k9_cat_2(A,B,C,D,E,F)))) # label(dt_k9_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3592 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_subset_1(F,u1_cat_1(B)) -> k8_funct_2(u1_cat_1(k11_cat_2(A,B)),u1_cat_1(C),k12_cat_1(k11_cat_2(A,B),C,D),k12_cat_2(A,B,E,F)) = k8_funct_2(u1_cat_1(A),u1_cat_1(C),k12_cat_1(A,C,k15_cat_2(A,B,C,D,F)),E))))))))))))) # label(t51_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3593 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(k11_cat_2(A,B))) -> (exists D ((exists E (m1_subset_1(E,u1_cat_1(B)) & k12_cat_2(A,B,D,E) = C)) & m1_subset_1(D,u1_cat_1(A)))))))))) # label(t35_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3594 $T # label(t10_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3595 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> D = k8_funct_2(u1_cat_1(k11_cat_2(A,B)),u1_cat_1(B),k12_cat_1(k11_cat_2(A,B),B,k17_cat_2(A,B)),k12_cat_2(A,B,C,D)))))))))) # label(t61_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3596 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(B)) -> m1_subset_1(k1_domain_1(u2_cat_1(A),u2_cat_1(B),C,D),u2_cat_1(k11_cat_2(A,B))))))))))) # label(t36_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3597 $T # label(dt_k5_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3598 $T # label(t32_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3599 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> m2_cat_1(k1_funct_1(k5_funct_5(D),k10_cat_1(B,E)),A,C))))))))))) # label(t45_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3600 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> m2_cat_1(k10_funct_3(u2_cat_1(A),u2_cat_1(B)),k11_cat_2(A,B),B))))) # label(t55_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3601 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> m1_subset_1(k1_domain_1(u1_cat_1(A),u1_cat_1(B),C,D),u1_cat_1(k11_cat_2(A,B))))))))))) # label(t34_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3602 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(B)) -> D = k8_funct_2(u2_cat_1(k11_cat_2(A,B)),u2_cat_1(B),k17_cat_2(A,B),k13_cat_2(A,B,C,D)))))))))) # label(t60_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3603 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (l1_cat_1(D) & v2_cat_1(D) -> (all E (m2_cat_1(E,A,B) -> (all F (m2_cat_1(F,C,D) -> m2_cat_1(k9_cat_2(u2_cat_1(A),u2_cat_1(C),u2_cat_1(B),u2_cat_1(D),E,F),k11_cat_2(A,C),k11_cat_2(B,D)))))))))))))) # label(t65_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3604 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (m3_cat_2(B,A) <-> (all C (m1_subset_1(C,u1_cat_1(B)) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_subset_1(F,u1_cat_1(A)) -> (C = E & D = F -> r1_tarski(k6_cat_1(B,C,D),k6_cat_1(A,E,F))))))))))) & r1_tarski(u5_cat_1(B),u5_cat_1(A)) & (all C (m1_subset_1(C,u1_cat_1(B)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (C = D -> k10_cat_1(B,C) = k10_cat_1(A,D)))))) & r1_tarski(u1_cat_1(B),u1_cat_1(A))))))) # label(d4_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3605 (all A all B all C (l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m1_cat_2(C,A,B) & v2_cat_1(A) -> (all D (m1_subset_1(D,C) <-> m2_cat_2(D,A,B,C))))) # label(redefinition_m2_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3606 $T # label(t57_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3607 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (k5_cat_2(A,B) = C <-> (all D (m2_cat_1(D,A,B) <-> r2_hidden(D,C))))))))) # label(d2_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3608 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> m2_cat_1(k15_cat_1(B),B,A))))) # label(t19_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3609 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m3_cat_2(B,A) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> C = k8_funct_2(u1_cat_1(B),u1_cat_1(A),k12_cat_1(B,A,k8_cat_2(A,B)),C))))))) # label(t22_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3610 (all A all B (v2_cat_1(A) & l1_cat_1(A) & l1_cat_1(B) & v2_cat_1(B) -> m2_cat_1(k16_cat_2(A,B),k11_cat_2(A,B),A))) # label(dt_k16_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3611 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> m1_subset_1(C,u1_cat_1(A)))))))) # label(t12_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3612 (all A all B all C all D all E all F (v1_funct_2(E,A,D) & m1_relset_1(E,A,D) & m1_subset_1(F,A) & v1_funct_1(E) & m1_fraenkel(D,B,C) & -v1_xboole_0(C) & -v1_xboole_0(A) -> k1_cat_2(A,B,C,D,E,F) = k1_funct_1(E,F))) # label(redefinition_k1_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3613 (all A all B all C (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & m1_cat_2(C,A,B) & l1_cat_1(B) -> (exists D m2_cat_2(D,A,B,C)))) # label(existence_m2_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3614 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m3_cat_2(B,A) -> (all C (m1_subset_1(C,u2_cat_1(B)) -> (all D (m1_subset_1(D,u2_cat_1(B)) -> (all E (m1_subset_1(E,u2_cat_1(A)) -> (all F (m1_subset_1(F,u2_cat_1(A)) -> (D = F & k3_cat_1(B,C) = k2_cat_1(B,D) & C = E -> k4_cat_1(B,C,D) = k4_cat_1(A,E,F)))))))))))))) # label(t17_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3615 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,C,B) & m2_relset_1(D,C,B) -> (all E (v1_funct_1(E) & m2_relset_1(E,C,B) & v1_funct_2(E,C,B) -> (all F (m2_relset_1(F,k2_zfmisc_1(C,C),C) & v1_funct_1(F) -> (all G (v1_funct_2(G,B,C) & m2_relset_1(G,B,C) & v1_funct_1(G) -> (r1_cat_2(g1_cat_1(B,C,D,E,F,G),A) -> E = k2_partfun1(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C) & k1_realset1(u5_cat_1(A),C) = F & G = k2_partfun1(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B) & D = k2_partfun1(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C) & C = k3_tarski(a_2_0_cat_2(A,B))))))))))))))))) # label(t31_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3616 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (all E (m1_subset_1(E,u2_cat_1(B)) -> (all F (m1_subset_1(F,u2_cat_1(B)) -> (k3_cat_1(B,E) = k2_cat_1(B,F) & k2_cat_1(A,D) = k3_cat_1(A,C) -> k13_cat_2(A,B,k4_cat_1(A,C,D),k4_cat_1(B,E,F)) = k4_cat_1(k11_cat_2(A,B),k13_cat_2(A,B,C,E),k13_cat_2(A,B,D,F))))))))))))))) # label(t39_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3617 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(C) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) & -v1_xboole_0(B) -> m2_relset_1(k2_cat_2(A,B,C,D),A,k1_fraenkel(B,C)) & v1_funct_2(k2_cat_2(A,B,C,D),A,k1_fraenkel(B,C)) & v1_funct_1(k2_cat_2(A,B,C,D)))) # label(dt_k2_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3618 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> k2_zfmisc_1(u1_cat_1(A),u1_cat_1(B)) = u1_cat_1(k11_cat_2(A,B)) & k9_cat_2(u2_cat_1(A),u2_cat_1(B),u1_cat_1(A),u1_cat_1(B),u4_cat_1(A),u4_cat_1(B)) = u4_cat_1(k11_cat_2(A,B)) & u6_cat_1(k11_cat_2(A,B)) = k9_cat_2(u1_cat_1(A),u1_cat_1(B),u2_cat_1(A),u2_cat_1(B),u6_cat_1(A),u6_cat_1(B)) & u5_cat_1(k11_cat_2(A,B)) = k10_cat_2(u2_cat_1(A),u2_cat_1(B),u5_cat_1(A),u5_cat_1(B)) & k9_cat_2(u2_cat_1(A),u2_cat_1(B),u1_cat_1(A),u1_cat_1(B),u3_cat_1(A),u3_cat_1(B)) = u3_cat_1(k11_cat_2(A,B)) & k2_zfmisc_1(u2_cat_1(A),u2_cat_1(B)) = u2_cat_1(k11_cat_2(A,B)))))) # label(t33_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3619 (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,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> k14_cat_2(A,B,C,D,E) = k1_funct_1(k3_funct_5(D),k10_cat_1(A,E)))))))))))) # label(d8_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3620 (all A (l1_cat_1(A) & v2_cat_1(A) -> (exists B (v2_cat_1(B) & v1_cat_1(B) & m3_cat_2(B,A))))) # label(rc1_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3621 (all A (v2_cat_1(A) & l1_cat_1(A) -> m3_cat_2(A,A))) # label(t18_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3622 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> (all C (m1_subset_1(C,u2_cat_1(B)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (C = D -> k2_cat_1(A,D) = k2_cat_1(B,C) & k3_cat_1(A,D) = k3_cat_1(B,C)))))))))) # label(t15_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3623 (all A all B all C all D all E all F (m1_cat_2(D,B,C) & v1_funct_2(E,A,D) & m1_relset_1(E,A,D) & m1_subset_1(F,A) & v1_funct_1(E) & l1_cat_1(C) & v2_cat_1(C) & l1_cat_1(B) & v2_cat_1(B) & -v1_xboole_0(A) -> m2_cat_2(k6_cat_2(A,B,C,D,E,F),B,C,D))) # label(dt_k6_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3624 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(B)) -> k3_cat_1(k11_cat_2(A,B),k13_cat_2(A,B,C,D)) = k12_cat_2(A,B,k3_cat_1(A,C),k3_cat_1(B,D)) & k2_cat_1(k11_cat_2(A,B),k13_cat_2(A,B,C,D)) = k12_cat_2(A,B,k2_cat_1(A,C),k2_cat_1(B,D)))))))))) # label(t38_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3625 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> (v9_cat_1(k8_cat_2(A,B),B,A) <-> (all C (m1_subset_1(C,u1_cat_1(B)) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_subset_1(F,u1_cat_1(A)) -> (D = F & C = E -> k6_cat_1(B,C,D) = k6_cat_1(A,E,F))))))))))))))) # label(t25_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3626 (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) -> k8_funct_2(k2_zfmisc_1(A,B),C,F,k1_domain_1(A,B,D,E)) = k8_funct_2(B,C,k1_cat_2(A,B,C,k1_fraenkel(B,C),k2_cat_2(A,B,C,F),D),E))))))))))))) # label(t3_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3627 (all A all B (l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(A) -> (exists C m1_cat_2(C,A,B)))) # label(existence_m1_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3628 (all A (l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (m3_cat_2(A,B) & (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> (all F (m1_subset_1(F,u1_cat_1(B)) -> (D = F & E = C -> k6_cat_1(A,C,D) = k6_cat_1(B,E,F)))))))))) <-> r1_cat_2(A,B)))))) # label(d6_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3629 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> r1_tarski(u2_cat_1(B),u2_cat_1(A)))))) # label(t13_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3630 (all A all B all C all D (v2_cat_1(A) & v2_cat_1(B) & m1_subset_1(C,u2_cat_1(A)) & m1_subset_1(D,u2_cat_1(B)) & l1_cat_1(B) & l1_cat_1(A) -> k4_tarski(C,D) = k13_cat_2(A,B,C,D))) # label(redefinition_k13_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3631 (all A all B (v2_cat_1(A) & l1_cat_1(A) & l1_cat_1(B) & v2_cat_1(B) -> m2_cat_1(k17_cat_2(A,B),k11_cat_2(A,B),B))) # label(dt_k17_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3632 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & -v1_xboole_0(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k3_cat_2(A,B,C,D) = k5_funct_5(D))) # label(redefinition_k3_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3633 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> m2_cat_1(k1_funct_1(k3_funct_5(D),k10_cat_1(A,E)),B,C))))))))))) # label(t44_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3634 (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(B,A),C) & v1_funct_2(D,k2_zfmisc_1(B,A),C) -> v1_funct_1(k5_funct_5(D)) & v1_funct_2(k5_funct_5(D),A,k1_fraenkel(B,C)) & m2_relset_1(k5_funct_5(D),A,k1_fraenkel(B,C)))))))))) # label(t2_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3635 $T # label(t20_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3636 (all A all B (v2_cat_1(B) & l1_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> v2_cat_1(k11_cat_2(A,B)) & v1_cat_1(k11_cat_2(A,B)))) # label(fc2_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3637 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) & -v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,C,B) & v1_funct_2(D,C,B) & v1_funct_1(D) -> (all E (m2_relset_1(E,C,B) & v1_funct_2(E,C,B) & v1_funct_1(E) -> (all F (v1_funct_1(F) & m2_relset_1(F,k2_zfmisc_1(C,C),C) -> (all G (v1_funct_2(G,B,C) & m2_relset_1(G,B,C) & v1_funct_1(G) -> (D = k2_partfun1(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C) & G = k2_partfun1(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B) & F = k1_realset1(u5_cat_1(A),C) & E = k2_partfun1(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C) & C = k3_tarski(a_2_0_cat_2(A,B)) -> r1_cat_2(g1_cat_1(B,C,D,E,F,G),A)))))))))))))))) # label(t30_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3638 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_subset_1(F,u1_cat_1(A)) -> (all G (m1_cat_1(G,B,C,D) -> (F = D & E = C -> m1_cat_1(G,A,E,F) | k1_xboole_0 = k6_cat_1(B,C,D)))))))))))))))) # label(t16_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3639 (all A all B (l1_cat_1(B) & v2_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> m1_cat_2(k7_cat_2(A,B),A,B))) # label(dt_k7_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3640 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> k8_funct_2(u1_cat_1(k11_cat_2(A,B)),u1_cat_1(A),k12_cat_1(k11_cat_2(A,B),A,k16_cat_2(A,B)),k12_cat_2(A,B,C,D)) = C)))))))) # label(t59_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3641 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> l1_cat_1(B) & v2_cat_1(B))))) # label(dt_m3_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3642 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (v2_cat_1(D) & l1_cat_1(D) -> (all E (m2_cat_1(E,A,B) -> (all F (m2_cat_1(F,C,D) -> k18_cat_2(k11_cat_2(A,C),B,D,k14_cat_1(k11_cat_2(A,C),A,B,k16_cat_2(A,C),E),k14_cat_1(k11_cat_2(A,C),C,D,k17_cat_2(A,C),F)) = k9_cat_2(u2_cat_1(A),u2_cat_1(C),u2_cat_1(B),u2_cat_1(D),E,F))))))))))))) # label(t64_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3643 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> (all F (m1_subset_1(F,u1_cat_1(B)) -> k2_zfmisc_1(k6_cat_1(A,C,D),k6_cat_1(B,E,F)) = k6_cat_1(k11_cat_2(A,B),k12_cat_2(A,B,C,E),k12_cat_2(A,B,D,F)))))))))))))) # label(t42_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3644 (all A all B (l1_cat_1(A) & l1_cat_1(B) & v2_cat_1(B) & v2_cat_1(A) -> (all C (m1_cat_2(C,A,B) -> -v1_xboole_0(C))))) # label(dt_m1_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3645 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m2_relset_1(D,k2_zfmisc_1(A,B),C) -> v1_funct_2(k3_funct_5(D),A,k1_fraenkel(B,C)) & m2_relset_1(k3_funct_5(D),A,k1_fraenkel(B,C)) & v1_funct_1(k3_funct_5(D)))))))))) # label(t1_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3646 $T # label(t11_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3647 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(B)) -> k8_funct_2(u2_cat_1(k11_cat_2(A,B)),u2_cat_1(A),k16_cat_2(A,B),k13_cat_2(A,B,C,D)) = C)))))))) # label(t58_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3648 (all A all B all C all D (v2_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m1_subset_1(C,u1_cat_1(A)) & m1_subset_1(D,u1_cat_1(B)) & l1_cat_1(A) -> k4_tarski(C,D) = k12_cat_2(A,B,C,D))) # label(redefinition_k12_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3649 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (all E (m1_subset_1(E,u2_cat_1(B)) -> (all F (m1_subset_1(F,u2_cat_1(B)) -> (k3_cat_1(k11_cat_2(A,B),k13_cat_2(A,B,C,E)) = k2_cat_1(k11_cat_2(A,B),k13_cat_2(A,B,D,F)) -> k13_cat_2(A,B,k4_cat_1(A,C,D),k4_cat_1(B,E,F)) = k4_cat_1(k11_cat_2(A,B),k13_cat_2(A,B,C,E),k13_cat_2(A,B,D,F))))))))))))))) # label(t40_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3650 (all A all B all C all D all E (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & l1_cat_1(C) & m2_cat_1(E,A,C) & m2_cat_1(D,A,B) & v2_cat_1(C) -> m2_cat_1(k18_cat_2(A,B,C,D,E),A,k11_cat_2(B,C)))) # label(dt_k18_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3651 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,C) -> m2_cat_1(k14_funct_3(u2_cat_1(A),u2_cat_1(B),u2_cat_1(C),D,E),A,k11_cat_2(B,C)))))))))))) # label(t62_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3652 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> m2_cat_1(k9_funct_3(u2_cat_1(A),u2_cat_1(B)),k11_cat_2(A,B),A))))) # label(t54_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3653 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) & -v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (C = k3_tarski(a_2_0_cat_2(A,B)) -> v1_funct_1(k2_partfun1(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C)) & m2_relset_1(k2_partfun1(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C),C,B) & v1_funct_1(k2_partfun1(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C)) & v1_funct_2(k2_partfun1(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C),C,B) & m2_relset_1(k2_partfun1(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C),C,B) & v1_funct_1(k1_realset1(u5_cat_1(A),C)) & v1_funct_1(k2_partfun1(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B)) & m2_relset_1(k2_partfun1(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B),B,C) & v1_funct_2(k2_partfun1(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B),B,C) & m2_relset_1(k1_realset1(u5_cat_1(A),C),k2_zfmisc_1(C,C),C) & v1_funct_2(k2_partfun1(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C),C,B)))))))) # label(t29_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3654 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> k9_funct_3(u2_cat_1(A),u2_cat_1(B)) = k16_cat_2(A,B))))) # label(d10_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3655 (all A all B (m3_cat_2(B,A) & l1_cat_1(A) & v2_cat_1(A) -> m2_cat_1(k8_cat_2(A,B),B,A))) # label(dt_k8_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3656 $T # label(t5_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3657 (all A all B (v2_cat_1(B) & l1_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> k5_cat_2(A,B) = k7_cat_2(A,B))) # label(redefinition_k7_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3658 (all A all B all C all D (-v1_xboole_0(B) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) & -v1_xboole_0(C) & -v1_xboole_0(A) -> k3_funct_5(D) = k2_cat_2(A,B,C,D))) # label(redefinition_k2_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3659 (all A all B all C (v2_cat_1(B) & l1_cat_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_cat_1(B))) & -v1_xboole_0(C) -> ((exists D exists E (m1_subset_1(D,u1_cat_1(B)) & m1_subset_1(E,u1_cat_1(B)) & r2_hidden(D,C) & r2_hidden(E,C) & k6_cat_1(B,D,E) = A)) <-> r2_hidden(A,a_2_0_cat_2(B,C))))) # label(fraenkel_a_2_0_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3660 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m3_cat_2(B,A) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> C = k13_cat_1(B,A,k8_cat_2(A,B),C))))))) # label(t23_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3661 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,C) -> (all F (m1_subset_1(F,u1_cat_1(A)) -> k8_funct_2(u1_cat_1(A),u1_cat_1(k11_cat_2(B,C)),k12_cat_1(A,k11_cat_2(B,C),k18_cat_2(A,B,C,D,E)),F) = k12_cat_2(B,C,k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,D),F),k8_funct_2(u1_cat_1(A),u1_cat_1(C),k12_cat_1(A,C,E),F)))))))))))))) # label(t63_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3662 (all A all B all C all D all E all F (-v1_xboole_0(C) & m1_fraenkel(D,B,C) & v1_funct_2(E,A,D) & m1_subset_1(F,A) & m1_relset_1(E,A,D) & v1_funct_1(E) & -v1_xboole_0(A) -> m2_fraenkel(k1_cat_2(A,B,C,D,E,F),B,C,D))) # label(dt_k1_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3663 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (v2_cat_1(D) & l1_cat_1(D) -> (all E (m2_cat_1(E,A,B) -> (all F (m2_cat_1(F,C,D) -> (all G (m1_subset_1(G,u1_cat_1(A)) -> (all H (m1_subset_1(H,u1_cat_1(C)) -> k8_funct_2(u1_cat_1(k11_cat_2(A,C)),u1_cat_1(k11_cat_2(B,D)),k12_cat_1(k11_cat_2(A,C),k11_cat_2(B,D),k19_cat_2(A,C,B,D,E,F)),k12_cat_2(A,C,G,H)) = k12_cat_2(B,D,k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,E),G),k8_funct_2(u1_cat_1(C),u1_cat_1(D),k12_cat_1(C,D,F),H)))))))))))))))))) # label(t66_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3664 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,C,D) -> (all F (m1_subset_1(F,u1_cat_1(B)) -> (all G (m1_subset_1(G,u1_cat_1(B)) -> (all H (m1_cat_1(H,B,F,G) -> -(-m1_cat_1(k13_cat_2(A,B,E,H),k11_cat_2(A,B),k12_cat_2(A,B,C,F),k12_cat_2(A,B,D,G)) & k6_cat_1(B,F,G) != k1_xboole_0 & k1_xboole_0 != k6_cat_1(A,C,D)))))))))))))))))) # label(t43_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3665 (all A (v2_cat_1(A) & l1_cat_1(A) -> (exists B m3_cat_2(B,A)))) # label(existence_m3_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3666 (all A all B all C all D (v1_funct_1(D) & m1_relset_1(D,k2_zfmisc_1(B,B),B) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> v1_funct_1(k10_cat_2(A,B,C,D)) & m2_relset_1(k10_cat_2(A,B,C,D),k2_zfmisc_1(k2_zfmisc_1(A,B),k2_zfmisc_1(A,B)),k2_zfmisc_1(A,B)))) # label(dt_k10_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3667 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> k10_funct_3(u2_cat_1(A),u2_cat_1(B)) = k17_cat_2(A,B))))) # label(d11_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3668 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u2_cat_1(k11_cat_2(A,B))) -> (exists D (m1_subset_1(D,u2_cat_1(A)) & (exists E (k13_cat_2(A,B,D,E) = C & m1_subset_1(E,u2_cat_1(B)))))))))))) # label(t37_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3669 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> (all C (m1_subset_1(C,u2_cat_1(B)) -> C = k8_funct_2(u2_cat_1(B),u2_cat_1(A),k8_cat_2(A,B),C))))))) # label(t21_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3670 (all A all B all C all D (v1_funct_2(D,k2_zfmisc_1(A,B),C) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) & -v1_xboole_0(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> v1_funct_1(k3_cat_2(A,B,C,D)) & m2_relset_1(k3_cat_2(A,B,C,D),B,k1_fraenkel(A,C)) & v1_funct_2(k3_cat_2(A,B,C,D),B,k1_fraenkel(A,C)))) # label(dt_k3_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3671 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> g1_cat_1(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(B)),k2_zfmisc_1(u2_cat_1(A),u2_cat_1(B)),k9_cat_2(u2_cat_1(A),u2_cat_1(B),u1_cat_1(A),u1_cat_1(B),u3_cat_1(A),u3_cat_1(B)),k9_cat_2(u2_cat_1(A),u2_cat_1(B),u1_cat_1(A),u1_cat_1(B),u4_cat_1(A),u4_cat_1(B)),k10_cat_2(u2_cat_1(A),u2_cat_1(B),u5_cat_1(A),u5_cat_1(B)),k9_cat_2(u1_cat_1(A),u1_cat_1(B),u2_cat_1(A),u2_cat_1(B),u6_cat_1(A),u6_cat_1(B))) = k11_cat_2(A,B))))) # label(d7_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3672 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> (all F (m1_subset_1(F,u2_cat_1(A)) -> k8_funct_2(u2_cat_1(k11_cat_2(A,B)),u2_cat_1(C),D,k13_cat_2(A,B,F,k10_cat_1(B,E))) = k8_funct_2(u2_cat_1(A),u2_cat_1(C),k15_cat_2(A,B,C,D,E),F))))))))))))) # label(t50_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3673 (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 (v1_funct_2(D,u1_cat_1(A),k7_cat_2(B,C)) & m2_relset_1(D,u1_cat_1(A),k7_cat_2(B,C)) & v1_funct_1(D) -> (all E (m2_relset_1(E,u1_cat_1(B),k7_cat_2(A,C)) & v1_funct_2(E,u1_cat_1(B),k7_cat_2(A,C)) & v1_funct_1(E) -> -((all F (m1_subset_1(F,u1_cat_1(A)) -> (all G (m1_subset_1(G,u1_cat_1(B)) -> k8_funct_2(u2_cat_1(B),u2_cat_1(C),k6_cat_2(u1_cat_1(A),B,C,k7_cat_2(B,C),D,F),k10_cat_1(B,G)) = k8_funct_2(u2_cat_1(A),u2_cat_1(C),k6_cat_2(u1_cat_1(B),A,C,k7_cat_2(A,C),E,G),k10_cat_1(A,F)))))) & (all F (m1_subset_1(F,u2_cat_1(B)) -> (all G (m1_subset_1(G,u2_cat_1(A)) -> k4_cat_1(C,k8_funct_2(u2_cat_1(B),u2_cat_1(C),k6_cat_2(u1_cat_1(A),B,C,k7_cat_2(B,C),D,k2_cat_1(A,G)),F),k8_funct_2(u2_cat_1(A),u2_cat_1(C),k6_cat_2(u1_cat_1(B),A,C,k7_cat_2(A,C),E,k3_cat_1(B,F)),G)) = k4_cat_1(C,k8_funct_2(u2_cat_1(A),u2_cat_1(C),k6_cat_2(u1_cat_1(B),A,C,k7_cat_2(A,C),E,k2_cat_1(B,F)),G),k8_funct_2(u2_cat_1(B),u2_cat_1(C),k6_cat_2(u1_cat_1(A),B,C,k7_cat_2(B,C),D,k3_cat_1(A,G)),F)))))) & (all F (m2_cat_1(F,k11_cat_2(B,A),C) -> -(all G (m1_subset_1(G,u2_cat_1(B)) -> (all H (m1_subset_1(H,u2_cat_1(A)) -> k4_cat_1(C,k8_funct_2(u2_cat_1(A),u2_cat_1(C),k6_cat_2(u1_cat_1(B),A,C,k7_cat_2(A,C),E,k2_cat_1(B,G)),H),k8_funct_2(u2_cat_1(B),u2_cat_1(C),k6_cat_2(u1_cat_1(A),B,C,k7_cat_2(B,C),D,k3_cat_1(A,H)),G)) = k8_funct_2(u2_cat_1(k11_cat_2(B,A)),u2_cat_1(C),F,k13_cat_2(B,A,G,H))))))))))))))))))) # label(t52_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3674 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> k13_cat_2(A,B,k10_cat_1(A,C),k10_cat_1(B,D)) = k10_cat_1(k11_cat_2(A,B),k12_cat_2(A,B,C,D)))))))))) # label(t41_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3675 (all A all B all C all D all E (l1_cat_1(B) & v2_cat_1(C) & l1_cat_1(C) & m2_cat_1(D,k11_cat_2(A,B),C) & m1_subset_1(E,u1_cat_1(A)) & v2_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> m2_cat_1(k14_cat_2(A,B,C,D,E),B,C))) # label(dt_k14_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3676 (all A all B all C all D all E all F (-v1_xboole_0(A) & v2_cat_1(C) & l1_cat_1(C) & v1_funct_1(E) & m1_relset_1(E,A,D) & m1_subset_1(F,A) & v1_funct_2(E,A,D) & m1_cat_2(D,B,C) & l1_cat_1(B) & v2_cat_1(B) -> k1_funct_1(E,F) = k6_cat_2(A,B,C,D,E,F))) # label(redefinition_k6_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.93 3677 (all A all B (v2_cat_1(B) & l1_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> v2_cat_1(k11_cat_2(A,B)) & l1_cat_1(k11_cat_2(A,B)))) # label(dt_k11_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3678 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> k15_cat_1(B) = k8_cat_2(A,B))))) # label(d5_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3679 (all A all B all C all D (v2_cat_1(B) & m1_subset_1(D,u1_cat_1(B)) & m1_subset_1(C,u1_cat_1(A)) & l1_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> m1_subset_1(k12_cat_2(A,B,C,D),u1_cat_1(k11_cat_2(A,B))))) # label(dt_k12_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3680 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> k4_cat_2(A,B,C) = k10_pboole(u2_cat_1(A),k10_cat_1(B,C)))))))) # label(d1_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3681 (all A all B all C (v2_cat_1(B) & m1_subset_1(C,u1_cat_1(B)) & l1_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> m2_cat_1(k4_cat_2(A,B,C),A,B))) # label(dt_k4_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3682 (all A all B (v2_cat_1(A) & l1_cat_1(A) & l1_cat_1(B) & v2_cat_1(B) -> -v1_xboole_0(k5_cat_2(A,B)))) # label(fc1_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3683 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m3_cat_2(B,A) -> (all C (m1_subset_1(C,u2_cat_1(B)) -> m1_subset_1(C,u2_cat_1(A)))))))) # label(t14_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3684 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> C = k8_funct_2(u1_cat_1(B),u1_cat_1(A),k12_cat_1(B,A,k4_cat_2(B,A,C)),D))))))))) # label(t7_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3685 (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,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_subset_1(F,u1_cat_1(B)) -> k8_funct_2(u1_cat_1(B),u1_cat_1(C),k12_cat_1(B,C,k14_cat_2(A,B,C,D,E)),F) = k8_funct_2(u1_cat_1(k11_cat_2(A,B)),u1_cat_1(C),k12_cat_1(k11_cat_2(A,B),C,D),k12_cat_2(A,B,E,F)))))))))))))) # label(t48_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3686 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(B)) -> k8_funct_2(u2_cat_1(B),u2_cat_1(A),k4_cat_2(B,A,C),D) = k10_cat_1(A,C))))))))) # label(t6_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3687 (all A all B all C all D all E all F (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & v2_cat_1(C) & v2_cat_1(D) & m2_cat_1(F,B,D) & m2_cat_1(E,A,C) & l1_cat_1(D) & l1_cat_1(C) & l1_cat_1(B) -> k15_funct_3(E,F) = k19_cat_2(A,B,C,D,E,F))) # label(redefinition_k19_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3688 (all A all B all C all D (v1_funct_1(C) & v1_funct_1(D) & m1_relset_1(D,k2_zfmisc_1(B,B),B) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k10_cat_2(A,B,C,D) = k3_funct_4(C,D))) # label(redefinition_k10_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3689 (all A all B all C (v2_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m1_cat_2(C,A,B) & l1_cat_1(A) -> (all D (m2_cat_2(D,A,B,C) -> m2_cat_1(D,A,B))))) # label(dt_m2_cat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3690 (all A all B all C all D (m1_relset_1(C,A,B) & m1_subset_1(D,k1_zfmisc_1(A)) & v1_funct_2(C,A,B) & v1_funct_1(C) & -v1_xboole_0(B) -> k1_nattra_1(A,B,C,D) = k7_relat_1(C,D))) # label(redefinition_k1_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3691 (all A all B k8_cat_1(A,B) = k13_nattra_1(k8_cat_1(A,B))) # label(t54_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3692 (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,B,A) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> k10_cat_1(A,k13_cat_1(B,A,C,D)) = k5_nattra_1(B,A,C,C,k4_nattra_1(B,A,C),D))))))))) # label(t21_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3693 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v1_cat_1(C) & l1_cat_1(C) & v2_cat_1(C) -> (C = k12_nattra_1(A,B) <-> u1_cat_1(C) = k7_cat_2(A,B) & (all D (m1_subset_1(D,u2_cat_1(C)) -> (all E (m1_subset_1(E,u2_cat_1(C)) -> (k3_cat_1(C,D) = k2_cat_1(C,E) -> r2_hidden(k13_cat_2(C,C,E,D),k1_relat_1(u5_cat_1(C)))))))) & (all D (m1_subset_1(D,u1_cat_1(C)) -> (all E (m2_cat_1(E,A,B) -> (E = D -> k10_cat_1(C,D) = k4_tarski(k4_tarski(E,E),k7_nattra_1(A,B,E))))))) & (all D (m1_subset_1(D,u2_cat_1(C)) -> (all E (m1_subset_1(E,u2_cat_1(C)) -> -(r2_hidden(k13_cat_2(C,C,E,D),k1_relat_1(u5_cat_1(C))) & (all F (m2_cat_1(F,A,B) -> (all G (m2_cat_1(G,A,B) -> (all H (m2_cat_1(H,A,B) -> (all I (m2_nattra_1(I,A,B,F,G) -> (all J (m2_nattra_1(J,A,B,G,H) -> -(D = k4_tarski(k4_tarski(F,G),I) & k4_tarski(k4_tarski(G,H),J) = E & k4_tarski(k4_tarski(F,H),k8_nattra_1(A,B,F,G,H,I,J)) = k1_funct_1(u5_cat_1(C),k13_cat_2(C,C,E,D)))))))))))))))))) & (all D (m1_subset_1(D,u2_cat_1(C)) -> k1_mcart_1(k1_mcart_1(D)) = k2_cat_1(C,D) & k2_mcart_1(k1_mcart_1(D)) = k3_cat_1(C,D))) & u2_cat_1(C) = k11_nattra_1(A,B)))))))) # label(d18_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3694 $T # label(t29_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3695 (all A (l1_cat_1(A) & v2_cat_1(A) -> ((all B (m1_subset_1(B,u2_cat_1(A)) -> (exists C (k10_cat_1(A,C) = B & m1_subset_1(C,u1_cat_1(A)))))) <-> v2_nattra_1(A)))) # label(d19_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3696 (exists A (v2_nattra_1(A) & v2_cat_1(A) & l1_cat_1(A))) # label(rc1_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3697 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) & -v1_xboole_0(C) -> (all D (-v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(B)) -> (all E (m2_relset_1(E,k2_zfmisc_1(A,A),A) & v1_funct_1(E) -> (all F (v1_funct_1(F) & m2_relset_1(F,k2_zfmisc_1(B,B),B) -> (all G (v1_funct_1(G) & m2_relset_1(G,k12_mcart_1(A,A,C,C),C) -> (G = k1_realset1(E,C) -> (all H (v1_funct_1(H) & m2_relset_1(H,k12_mcart_1(B,B,D,D),D) -> (k1_realset1(F,D) = H -> k1_realset1(k10_cat_2(A,B,E,F),k12_mcart_1(A,B,C,D)) = k2_nattra_1(A,B,C,D,G,H))))))))))))))))))) # label(t2_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3698 (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(B)) -> (k3_nattra_1(A,B,C,D,D,k10_cat_1(A,D)) = k10_cat_1(B,E) -> k13_cat_1(A,B,C,D) = E))))))))))) # label(t14_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3699 $T # label(t38_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3700 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (v2_nattra_1(A) & v2_nattra_1(B) -> v2_nattra_1(k11_cat_2(A,B))))))) # label(t48_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3701 (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 (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (all F (m2_cat_1(F,A,B) -> (all G (m2_nattra_1(G,A,B,E,F) -> (all H (m2_nattra_1(H,A,B,C,D) -> (all I (m1_subset_1(I,u2_cat_1(k12_nattra_1(A,B))) -> (all J (m1_subset_1(J,u2_cat_1(k12_nattra_1(A,B))) -> (J = k4_tarski(k4_tarski(C,D),H) & k4_tarski(k4_tarski(E,F),G) = I -> (r4_nattra_1(u2_cat_1(A),u2_cat_1(B),u2_cat_1(A),u2_cat_1(B),F,C) <-> r2_hidden(k13_cat_2(k12_nattra_1(A,B),k12_nattra_1(A,B),J,I),k1_relat_1(u5_cat_1(k12_nattra_1(A,B)))))))))))))))))))))))))) # label(t41_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3702 (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 (m2_cat_1(D,A,B) -> (all E (m2_nattra_1(E,A,B,C,D) -> (all F (m1_subset_1(F,u2_cat_1(k12_nattra_1(A,B))) -> (k4_tarski(k4_tarski(C,D),E) = F -> k2_cat_1(k12_nattra_1(A,B),F) = C & D = k3_cat_1(k12_nattra_1(A,B),F)))))))))))))) # label(t39_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3703 (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)) -> (-r1_xboole_0(k6_cat_1(A,B,C),k6_cat_1(A,D,E)) -> C = E & B = D))))))))))) # label(t17_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3704 (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 (m2_cat_1(D,A,B) -> (r1_nattra_1(A,B,C,D) -> (all E (m1_nattra_1(E,A,B,C,D) -> (all F (m1_subset_1(F,u1_cat_1(A)) -> k8_funct_2(u1_cat_1(A),u2_cat_1(B),E,F) = k5_nattra_1(A,B,C,D,E,F)))))))))))))) # label(d5_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3705 (all A all B all C all D all E (v2_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C,A,B) & m2_nattra_1(E,A,B,C,D) & m2_cat_1(D,A,B) & l1_cat_1(A) -> m2_nattra_1(k10_nattra_1(A,B,C,D,E),A,B,D,C))) # label(dt_k10_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3706 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v1_cat_1(B) & m3_cat_2(B,A) & v2_nattra_1(B) -> (k13_nattra_1(A) = B <-> u2_cat_1(B) = a_1_0_nattra_1(A) & u1_cat_1(A) = u1_cat_1(B)))))) # label(d20_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3707 (all A all B all C all D all E all F all G (l1_cat_1(A) & v2_cat_1(B) & m2_cat_1(E,A,B) & m1_nattra_1(G,A,B,D,E) & m1_nattra_1(F,A,B,C,D) & m2_cat_1(D,A,B) & m2_cat_1(C,A,B) & l1_cat_1(B) & v2_cat_1(A) -> m1_nattra_1(k6_nattra_1(A,B,C,D,E,F,G),A,B,C,E))) # label(dt_k6_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3708 (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 (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (all F (m2_nattra_1(F,A,B,C,D) -> (all G (m2_nattra_1(G,A,B,D,E) -> (all H (m1_subset_1(H,u2_cat_1(k12_nattra_1(A,B))) -> (all I (m1_subset_1(I,u2_cat_1(k12_nattra_1(A,B))) -> (k4_tarski(k4_tarski(D,E),G) = I & k4_tarski(k4_tarski(C,D),F) = H -> k4_tarski(k4_tarski(C,E),k8_nattra_1(A,B,C,D,E,F,G)) = k4_cat_1(k12_nattra_1(A,B),H,I)))))))))))))))))))) # label(t42_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3709 (all A all B all C (l1_cat_1(B) & m2_cat_1(C,A,B) & v2_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> m1_nattra_1(k4_nattra_1(A,B,C),A,B,C,C))) # label(dt_k4_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3710 (all A all B all C all D all E all F (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_relset_1(E,A,B) & v1_funct_1(F) & m1_relset_1(F,C,D) & v1_funct_2(F,C,D) & v1_funct_2(E,A,B) & v1_funct_1(E) & -v1_xboole_0(D) & -v1_xboole_0(C) -> (F = E <-> r4_nattra_1(A,B,C,D,E,F)))) # label(redefinition_r4_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3711 (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,C,A) & m2_relset_1(E,C,A) -> (all F (m2_relset_1(F,D,B) & v1_funct_2(F,D,B) & v1_funct_1(F) -> (all G (m1_subset_1(G,k1_zfmisc_1(C)) & -v1_xboole_0(G) -> (all H (-v1_xboole_0(H) & m1_subset_1(H,k1_zfmisc_1(D)) -> k1_nattra_1(k2_zfmisc_1(C,D),k2_zfmisc_1(A,B),k9_cat_2(C,D,A,B,E,F),k12_mcart_1(C,D,G,H)) = k9_cat_2(G,H,A,B,k1_nattra_1(C,A,E,G),k1_nattra_1(D,B,F,H)))))))))))))))))) # label(t1_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3712 (all A (v2_cat_1(A) & v2_nattra_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,B,A) -> (all D (m1_nattra_1(D,B,A,C,C) -> r4_nattra_1(u1_cat_1(B),u2_cat_1(A),u1_cat_1(B),u2_cat_1(A),D,k7_nattra_1(B,A,C)))))))))) # label(t50_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3713 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_cat_1(C,A,B,B) -> r2_hidden(C,k6_cat_1(A,B,B)))))))) # label(t3_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3714 (all A all B all C all D (m2_cat_1(C,A,B) & m2_cat_1(D,A,B) & l1_cat_1(B) & v2_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> r2_nattra_1(A,B,C,C))) # label(reflexivity_r2_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3715 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> m3_cat_2(k8_cat_1(B,k10_cat_1(A,B)),A))))) # label(t7_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3716 (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 (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (r3_nattra_1(A,B,D,E) & r3_nattra_1(A,B,C,D) -> r3_nattra_1(A,B,C,E)))))))))))) # label(t32_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3717 (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 (m2_cat_1(D,A,B) -> (r3_nattra_1(A,B,C,D) -> r3_nattra_1(A,B,D,C)))))))))) # label(t31_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3718 (all A all B all C (v2_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C,A,B) & l1_cat_1(A) -> k7_nattra_1(A,B,C) = k4_nattra_1(A,B,C))) # label(redefinition_k7_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3719 (all A (v2_cat_1(A) & l1_cat_1(A) -> (exists B (v1_cat_1(B) & v2_nattra_1(B) & v2_cat_1(B) & m3_cat_2(B,A))))) # label(rc2_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3720 (all A all B all C all D all E all F (-v1_xboole_0(C) & v1_funct_1(E) & m1_relset_1(E,A,B) & v1_funct_1(F) & v1_funct_2(F,C,D) & m1_relset_1(F,C,D) & v1_funct_2(E,A,B) & -v1_xboole_0(D) & -v1_xboole_0(B) & -v1_xboole_0(A) -> (r4_nattra_1(A,B,C,D,E,F) -> r4_nattra_1(A,B,C,D,F,E)))) # label(symmetry_r4_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3721 (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,B,A) -> (all D (m2_cat_1(D,B,A) -> (r1_nattra_1(B,A,C,D) -> (all E (m1_nattra_1(E,B,A,C,D) -> (all F (m1_nattra_1(F,B,A,C,D) -> ((all G (m1_subset_1(G,u1_cat_1(B)) -> k5_nattra_1(B,A,C,D,E,G) = k5_nattra_1(B,A,C,D,F,G))) -> E = F)))))))))))))) # label(t20_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3722 (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 (m2_cat_1(D,A,B) -> (r2_nattra_1(A,B,C,D) -> (all E (m2_nattra_1(E,A,B,C,D) -> E = k8_nattra_1(A,B,C,D,D,E,k7_nattra_1(A,B,D)) & E = k8_nattra_1(A,B,C,C,D,k7_nattra_1(A,B,C),E)))))))))))) # label(t26_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3723 (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 (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (r1_nattra_1(A,B,D,E) & r1_nattra_1(A,B,C,D) -> r1_nattra_1(A,B,C,E)))))))))))) # label(t19_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3724 (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,B,A) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> k3_nattra_1(B,A,C,D,D,k10_cat_1(B,D)) = k10_cat_1(A,k13_cat_1(B,A,C,D)))))))))) # label(t15_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3725 (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) -> k3_nattra_1(A,B,C,D,E,F) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,F)))))))))))))) # label(d1_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3726 (all A all B all C all D all E all F (-v1_xboole_0(B) & m1_relset_1(E,A,B) & v1_funct_1(F) & v1_funct_2(F,C,D) & m1_relset_1(F,C,D) & v1_funct_2(E,A,B) & v1_funct_1(E) & -v1_xboole_0(D) & -v1_xboole_0(C) & -v1_xboole_0(A) -> r4_nattra_1(A,B,C,D,E,E))) # label(reflexivity_r4_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3727 (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 (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (all F (m2_cat_1(F,A,B) -> (all G (m2_nattra_1(G,A,B,C,D) -> (all H (m2_nattra_1(H,A,B,D,E) -> (r2_nattra_1(A,B,C,D) & r2_nattra_1(A,B,D,E) & r2_nattra_1(A,B,E,F) -> (all I (m2_nattra_1(I,A,B,E,F) -> k8_nattra_1(A,B,C,D,F,G,k8_nattra_1(A,B,D,E,F,H,I)) = k8_nattra_1(A,B,C,E,F,k8_nattra_1(A,B,C,D,E,G,H),I)))))))))))))))))))) # label(t28_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3728 (all A (l1_cat_1(A) & v2_nattra_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,B,A) -> (all D (m2_cat_1(D,B,A) -> (r1_nattra_1(B,A,C,D) -> r4_nattra_1(u2_cat_1(B),u2_cat_1(A),u2_cat_1(B),u2_cat_1(A),C,D)))))))))) # label(t49_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3729 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (-v1_xboole_0(C) -> (m4_nattra_1(C,A,B) <-> (all D -((all E (m2_cat_1(E,A,B) -> (all F (m2_cat_1(F,A,B) -> (all G (m2_nattra_1(G,A,B,E,F) -> -(k4_tarski(k4_tarski(E,F),G) = D & r2_nattra_1(A,B,E,F)))))))) & r2_hidden(D,C)))))))))) # label(d15_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3730 (all A all B all C all D all E all F (l1_cat_1(A) & v2_cat_1(B) & m1_subset_1(D,u1_cat_1(A)) & m1_cat_1(F,A,D,E) & m1_subset_1(E,u1_cat_1(A)) & m2_cat_1(C,A,B) & l1_cat_1(B) & v2_cat_1(A) -> m1_cat_1(k3_nattra_1(A,B,C,D,E,F),B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)))) # label(dt_k3_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3731 (all A all B all C all D (-v1_xboole_0(B) & v1_funct_1(C) & m1_subset_1(D,k1_zfmisc_1(A)) & m1_relset_1(C,A,B) & v1_funct_2(C,A,B) -> v1_funct_1(k1_nattra_1(A,B,C,D)) & v1_funct_2(k1_nattra_1(A,B,C,D),D,B) & m2_relset_1(k1_nattra_1(A,B,C,D),D,B))) # label(dt_k1_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3732 (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 (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (all F (m2_cat_1(F,A,B) -> (r1_nattra_1(A,B,C,D) & r1_nattra_1(A,B,E,F) & r1_nattra_1(A,B,D,E) -> (all G (m1_nattra_1(G,A,B,C,D) -> (all H (m1_nattra_1(H,A,B,D,E) -> (all I (m1_nattra_1(I,A,B,E,F) -> k6_nattra_1(A,B,C,E,F,k6_nattra_1(A,B,C,D,E,G,H),I) = k6_nattra_1(A,B,C,D,F,G,k6_nattra_1(A,B,D,E,F,H,I))))))))))))))))))))) # label(t23_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3733 (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 (m2_cat_1(D,A,B) -> (all E (m2_nattra_1(E,A,B,C,D) -> (r2_hidden(k4_tarski(k4_tarski(C,D),E),k11_nattra_1(A,B)) <-> r2_nattra_1(A,B,C,D)))))))))))) # label(t35_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3734 $T # label(t43_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3735 (all A all B all C all D all E all F (v2_cat_1(B) & m2_cat_1(D,A,B) & m1_subset_1(F,u1_cat_1(A)) & m1_nattra_1(E,A,B,C,D) & m2_cat_1(C,A,B) & l1_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> m1_cat_1(k5_nattra_1(A,B,C,D,E,F),B,k13_cat_1(A,B,C,F),k13_cat_1(A,B,D,F)))) # label(dt_k5_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3736 (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 (m2_cat_1(D,A,B) -> (r1_nattra_1(A,B,C,D) -> (all E (m1_nattra_1(E,A,B,C,D) -> E = k6_nattra_1(A,B,C,D,D,E,k4_nattra_1(A,B,D)) & E = k6_nattra_1(A,B,C,C,D,k4_nattra_1(A,B,C),E)))))))))))) # label(t22_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3737 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m3_cat_2(B,A) -> k7_relat_1(u3_cat_1(A),u2_cat_1(B)) = u3_cat_1(B) & k7_relat_1(u6_cat_1(A),u1_cat_1(B)) = u6_cat_1(B) & u5_cat_1(B) = k1_realset1(u5_cat_1(A),u2_cat_1(B)) & k7_relat_1(u4_cat_1(A),u2_cat_1(B)) = u4_cat_1(B))))) # label(t8_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3738 (all A all B all C all D (l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C,A,B) & m2_cat_1(D,A,B) & v2_cat_1(A) -> r3_nattra_1(A,B,C,C))) # label(reflexivity_r3_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3739 (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 (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (r2_nattra_1(A,B,D,E) & r2_nattra_1(A,B,C,D) -> (all F (m2_nattra_1(F,A,B,C,D) -> (all G (m2_nattra_1(G,A,B,D,E) -> k6_nattra_1(A,B,C,D,E,F,G) = k8_nattra_1(A,B,C,D,E,F,G)))))))))))))))) # label(d9_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3740 (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 (m2_cat_1(D,A,B) -> (all E (m1_nattra_1(E,A,B,C,D) -> (v1_nattra_1(E,A,B,C,D) <-> (all F (m1_subset_1(F,u1_cat_1(A)) -> v5_cat_1(k5_nattra_1(A,B,C,D,E,F),B)))))))))))))) # label(d10_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3741 (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 (m2_cat_1(D,A,B) -> (all E (m2_nattra_1(E,A,B,C,D) -> (r2_nattra_1(A,B,C,D) & v1_nattra_1(E,A,B,C,D) -> k10_nattra_1(A,B,C,D,E) = k9_nattra_1(A,B,C,D,E)))))))))))) # label(d13_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3742 (all A (v2_cat_1(A) & l1_cat_1(A) -> m3_cat_2(k13_nattra_1(A),A) & v2_nattra_1(k13_nattra_1(A)) & v1_cat_1(k13_nattra_1(A)))) # label(dt_k13_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3743 (all A all B all C all D (m2_cat_1(D,A,B) & m2_cat_1(C,A,B) & l1_cat_1(B) & v2_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> r1_nattra_1(A,B,C,C))) # label(reflexivity_r1_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3744 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (v2_nattra_1(A) -> v2_nattra_1(k12_nattra_1(B,A))))))) # label(t51_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3745 (all A all B (l1_cat_1(A) & l1_cat_1(B) & v2_cat_1(B) & v2_cat_1(A) -> m4_nattra_1(k11_nattra_1(A,B),A,B))) # label(dt_k11_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3746 (all A all B all C all D all E (l1_cat_1(A) & v2_cat_1(B) & m2_cat_1(C,A,B) & m2_cat_1(D,A,B) & m1_nattra_1(E,A,B,C,D) & l1_cat_1(B) & v2_cat_1(A) -> m1_nattra_1(k9_nattra_1(A,B,C,D,E),A,B,D,C))) # label(dt_k9_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3747 $T # label(t24_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3748 (all A all B all C (l1_cat_1(A) & v2_cat_1(B) & m2_cat_1(C,A,B) & l1_cat_1(B) & v2_cat_1(A) -> m2_nattra_1(k7_nattra_1(A,B,C),A,B,C,C))) # label(dt_k7_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3749 (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,B,A) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> (all F (m1_subset_1(F,u1_cat_1(B)) -> -(-(all G (m1_cat_1(G,B,D,E) -> (all H (m1_cat_1(H,B,E,F) -> k9_cat_1(A,k13_cat_1(B,A,C,D),k13_cat_1(B,A,C,E),k13_cat_1(B,A,C,F),k3_nattra_1(B,A,C,D,E,G),k3_nattra_1(B,A,C,E,F,H)) = k3_nattra_1(B,A,C,D,F,k9_cat_1(B,D,E,F,G,H)))))) & k1_xboole_0 != k6_cat_1(B,E,F) & k1_xboole_0 != k6_cat_1(B,D,E)))))))))))))) # label(t13_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3750 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m4_nattra_1(C,A,B) -> (k11_nattra_1(A,B) = C <-> (all D (r2_hidden(D,C) <-> (exists E ((exists F (m2_cat_1(F,A,B) & (exists G (m2_nattra_1(G,A,B,E,F) & r2_nattra_1(A,B,E,F) & k4_tarski(k4_tarski(E,F),G) = D)))) & m2_cat_1(E,A,B)))))))))))) # label(d16_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3751 (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 (m2_cat_1(D,A,B) -> (r1_nattra_1(A,B,C,D) -> (all E (m1_nattra_1(E,A,B,C,D) -> (v1_nattra_1(E,A,B,C,D) -> (all F (m1_nattra_1(F,A,B,D,C) -> ((all G (m1_subset_1(G,u1_cat_1(A)) -> k5_nattra_1(A,B,D,C,F,G) = k11_cat_1(B,k13_cat_1(A,B,C,G),k13_cat_1(A,B,D,G),k5_nattra_1(A,B,C,D,E,G)))) <-> F = k9_nattra_1(A,B,C,D,E)))))))))))))))) # label(d12_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3752 (all A (l1_cat_1(A) & v2_cat_1(A) & v1_cat_1(A) -> (v2_nattra_1(A) -> A = k13_nattra_1(A)))) # label(t52_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3753 (all A (v2_cat_1(A) & l1_cat_1(A) -> (v2_nattra_1(A) <-> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (C != B -> k6_cat_1(A,B,C) = k1_xboole_0))))) & (all B (m1_subset_1(B,u1_cat_1(A)) -> (exists C (np__1 = k4_card_1(C) & k6_cat_1(A,B,B) = C & v1_finset_1(C)))))))) # label(t45_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3754 (all A (m1_subset_1(A,f1_s1_nattra_1) -> -r1_xboole_0(f2_s1_nattra_1,f3_s1_nattra_1(A)))) -> (exists A (v1_funct_1(A) & v1_funct_2(A,f1_s1_nattra_1,f2_s1_nattra_1) & m2_relset_1(A,f1_s1_nattra_1,f2_s1_nattra_1) & (all B (m1_subset_1(B,f1_s1_nattra_1) -> r2_hidden(k8_funct_2(f1_s1_nattra_1,f2_s1_nattra_1,A,B),f3_s1_nattra_1(B)))))) # label(s1_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3755 (all A all B all C all D (l1_cat_1(B) & m2_cat_1(D,A,B) & m2_cat_1(C,A,B) & v2_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> (all E (m3_nattra_1(E,A,B,C,D) -> m2_nattra_1(E,A,B,C,D))))) # label(dt_m3_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3756 (all A (v2_nattra_1(A) & l1_cat_1(A) & v2_cat_1(A) -> (all B (m3_cat_2(B,A) -> v2_nattra_1(B))))) # label(t47_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3757 (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 (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (r2_nattra_1(A,B,D,E) & r2_nattra_1(A,B,C,D) -> r2_nattra_1(A,B,C,E)))))))))))) # label(t25_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3758 (all A all B all C all D (l1_cat_1(A) & m2_cat_1(C,A,B) & m2_cat_1(D,A,B) & l1_cat_1(B) & v2_cat_1(B) & v2_cat_1(A) -> (all E (m2_nattra_1(E,A,B,C,D) -> m1_nattra_1(E,A,B,C,D))))) # label(dt_m2_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3759 (all A all B all C all D all E all F (-v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(D,k1_zfmisc_1(B)) & v1_funct_1(E) & v1_funct_1(F) & m1_relset_1(F,k12_mcart_1(B,B,D,D),D) & m1_relset_1(E,k12_mcart_1(A,A,C,C),C) & -v1_xboole_0(D) & -v1_xboole_0(A) -> k2_nattra_1(A,B,C,D,E,F) = k3_funct_4(E,F))) # label(redefinition_k2_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3760 (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 (m2_cat_1(D,A,B) -> (all E (m2_nattra_1(E,A,B,C,D) -> (r2_nattra_1(A,B,C,D) & v1_nattra_1(E,A,B,C,D) -> (all F (m1_subset_1(F,u1_cat_1(A)) -> k5_nattra_1(A,B,D,C,k10_nattra_1(A,B,C,D,E),F) = k11_cat_1(B,k13_cat_1(A,B,C,F),k13_cat_1(A,B,D,F),k5_nattra_1(A,B,C,D,E,F))))))))))))))) # label(t30_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3761 (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 (m2_cat_1(D,A,B) -> (r1_nattra_1(A,B,C,D) -> (all E (v1_funct_1(E) & m2_relset_1(E,u1_cat_1(A),u2_cat_1(B)) & v1_funct_2(E,u1_cat_1(A),u2_cat_1(B)) -> ((all F (m1_subset_1(F,u1_cat_1(A)) -> m1_cat_1(k8_funct_2(u1_cat_1(A),u2_cat_1(B),E,F),B,k13_cat_1(A,B,C,F),k13_cat_1(A,B,D,F)))) <-> m1_nattra_1(E,A,B,C,D))))))))))))) # label(d3_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3762 (all A (v1_cat_1(A) & v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) & v1_cat_1(B) -> (u1_cat_1(B) = u1_cat_1(A) & u2_cat_1(A) = u2_cat_1(B) -> B = A))))) # label(t10_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3763 (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_nattra_1(D,A,B,C,C) -> (k4_nattra_1(A,B,C) = D <-> (all E (m1_subset_1(E,u1_cat_1(A)) -> k8_funct_2(u1_cat_1(A),u2_cat_1(B),D,E) = k10_cat_1(B,k13_cat_1(A,B,C,E))))))))))))) # label(d4_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3764 (all A all B all C all D (v2_cat_1(B) & m2_cat_1(C,A,B) & m2_cat_1(D,A,B) & l1_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> (exists E m3_nattra_1(E,A,B,C,D)))) # label(existence_m3_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3765 (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) -> m3_nattra_1(k7_nattra_1(A,B,C),A,B,C,C))))))) # label(t33_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.95 3766 (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 (m2_cat_1(D,A,B) -> (r2_nattra_1(A,B,C,D) -> (all E (m1_nattra_1(E,A,B,C,D) -> ((all F (m1_subset_1(F,u1_cat_1(A)) -> (all G (m1_subset_1(G,u1_cat_1(A)) -> (k6_cat_1(A,F,G) != k1_xboole_0 -> (all H (m1_cat_1(H,A,F,G) -> k9_cat_1(B,k13_cat_1(A,B,C,F),k13_cat_1(A,B,D,F),k13_cat_1(A,B,D,G),k5_nattra_1(A,B,C,D,E,F),k3_nattra_1(A,B,D,F,G,H)) = k9_cat_1(B,k13_cat_1(A,B,C,F),k13_cat_1(A,B,C,G),k13_cat_1(A,B,D,G),k3_nattra_1(A,B,C,F,G,H),k5_nattra_1(A,B,C,D,E,G))))))))) <-> m2_nattra_1(E,A,B,C,D))))))))))))) # label(d8_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3767 $T # label(t37_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3768 (all A all B (v2_cat_1(B) & l1_cat_1(B) -> (r2_hidden(A,a_1_0_nattra_1(B)) <-> (exists C (m1_subset_1(C,u1_cat_1(B)) & k10_cat_1(B,C) = A))))) # label(fraenkel_a_1_0_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3769 (all A all B (l1_cat_1(B) & v2_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> (exists C m4_nattra_1(C,A,B)))) # label(existence_m4_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3770 (all A all B all C (m1_subset_1(C,u2_cat_1(k8_cat_1(A,B))) -> (all D (m1_subset_1(D,u2_cat_1(k8_cat_1(A,B))) -> C = D)))) # label(t4_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3771 (all A all B v2_nattra_1(k8_cat_1(A,B))) # label(t46_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3772 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(k12_nattra_1(A,B))) -> (all D (m1_subset_1(D,u1_cat_1(k12_nattra_1(A,B))) -> (all E (m1_cat_1(E,k12_nattra_1(A,B),C,D) -> -(k1_xboole_0 != k6_cat_1(k12_nattra_1(A,B),C,D) & (all F (m2_cat_1(F,A,B) -> (all G (m2_cat_1(G,A,B) -> (all H (m2_nattra_1(H,A,B,F,G) -> -(E = k4_tarski(k4_tarski(F,G),H) & G = D & F = C)))))))))))))))))) # label(t40_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3773 (all A all B all C all D (v2_cat_1(A) & v2_cat_1(B) & m2_cat_1(C,A,B) & m2_cat_1(D,A,B) & l1_cat_1(B) & l1_cat_1(A) -> (exists E m2_nattra_1(E,A,B,C,D)))) # label(existence_m2_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3774 (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,B,A) -> (all D (m2_cat_1(D,B,A) -> (all E (m2_cat_1(E,B,A) -> (r2_nattra_1(B,A,C,D) & r2_nattra_1(B,A,D,E) -> (all F (m2_nattra_1(F,B,A,C,D) -> (all G (m2_nattra_1(G,B,A,D,E) -> (all H (m1_subset_1(H,u1_cat_1(B)) -> k9_cat_1(A,k13_cat_1(B,A,C,H),k13_cat_1(B,A,D,H),k13_cat_1(B,A,E,H),k5_nattra_1(B,A,C,D,F,H),k5_nattra_1(B,A,D,E,G,H)) = k5_nattra_1(B,A,C,E,k8_nattra_1(B,A,C,D,E,F,G),H)))))))))))))))))) # label(t27_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3775 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> k13_nattra_1(k11_cat_2(A,B)) = k11_cat_2(k13_nattra_1(A),k13_nattra_1(B)))))) # label(t55_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3776 (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 (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (r3_nattra_1(A,B,D,E) & r3_nattra_1(A,B,C,D) -> (all F (m3_nattra_1(F,A,B,C,D) -> (all G (m3_nattra_1(G,A,B,D,E) -> m3_nattra_1(k8_nattra_1(A,B,C,D,E,F,G),A,B,C,E)))))))))))))))) # label(t34_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3777 (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 (m2_relset_1(F,C,D) & v1_funct_2(F,C,D) & v1_funct_1(F) -> (r4_nattra_1(A,B,C,D,E,F) <-> A = C & (all G (m1_subset_1(G,A) -> k8_funct_2(A,B,E,G) = k1_funct_1(F,G)))))))))))))))) # label(d17_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3778 (all A all B all C all D (l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C,A,B) & m2_cat_1(D,A,B) & v2_cat_1(A) -> (exists E m1_nattra_1(E,A,B,C,D)))) # label(existence_m1_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3779 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> r2_hidden(k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,k10_cat_1(A,B),k10_cat_1(A,B)),k10_cat_1(A,B)),u5_cat_1(A)))))) # label(t5_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3780 (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 (m2_cat_1(D,A,B) -> (r1_nattra_1(A,B,C,D) & (exists E (m1_nattra_1(E,A,B,C,D) & (all F (m1_subset_1(F,u1_cat_1(A)) -> (all G (m1_subset_1(G,u1_cat_1(A)) -> (k1_xboole_0 != k6_cat_1(A,F,G) -> (all H (m1_cat_1(H,A,F,G) -> k9_cat_1(B,k13_cat_1(A,B,C,F),k13_cat_1(A,B,C,G),k13_cat_1(A,B,D,G),k3_nattra_1(A,B,C,F,G,H),k5_nattra_1(A,B,C,D,E,G)) = k9_cat_1(B,k13_cat_1(A,B,C,F),k13_cat_1(A,B,D,F),k13_cat_1(A,B,D,G),k5_nattra_1(A,B,C,D,E,F),k3_nattra_1(A,B,D,F,G,H))))))))))) <-> r2_nattra_1(A,B,C,D)))))))))) # label(d7_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3781 (all A all B all C all D (v2_cat_1(A) & l1_cat_1(A) & m2_cat_1(C,A,B) & m2_cat_1(D,A,B) & l1_cat_1(B) & v2_cat_1(B) -> (all E (m1_nattra_1(E,A,B,C,D) -> v1_funct_1(E) & m2_relset_1(E,u1_cat_1(A),u2_cat_1(B)) & v1_funct_2(E,u1_cat_1(A),u2_cat_1(B)))))) # label(dt_m1_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3782 (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 (m2_cat_1(D,A,B) -> (r3_nattra_1(A,B,C,D) <-> (exists E (m2_nattra_1(E,A,B,C,D) & v1_nattra_1(E,A,B,C,D))) & r2_nattra_1(A,B,C,D)))))))))) # label(d11_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3783 (all A all B u5_cat_1(k8_cat_1(A,B)) = k1_tarski(k4_tarski(k4_tarski(B,B),B))) # label(t6_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3784 (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 (m2_cat_1(D,A,B) -> (r3_nattra_1(A,B,C,D) -> (all E (m2_nattra_1(E,A,B,C,D) -> (v1_nattra_1(E,A,B,C,D) <-> m3_nattra_1(E,A,B,C,D))))))))))))) # label(d14_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3785 (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 (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (r1_nattra_1(A,B,D,E) & r1_nattra_1(A,B,C,D) -> (all F (m1_nattra_1(F,A,B,C,D) -> (all G (m1_nattra_1(G,A,B,D,E) -> (all H (m1_nattra_1(H,A,B,C,E) -> (H = k6_nattra_1(A,B,C,D,E,F,G) <-> (all I (m1_subset_1(I,u1_cat_1(A)) -> k9_cat_1(B,k13_cat_1(A,B,C,I),k13_cat_1(A,B,D,I),k13_cat_1(A,B,E,I),k5_nattra_1(A,B,C,D,F,I),k5_nattra_1(A,B,D,E,G,I)) = k5_nattra_1(A,B,C,E,H,I))))))))))))))))))))) # label(d6_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3786 (all A (l1_cat_1(A) & v2_cat_1(A) -> k13_nattra_1(k13_nattra_1(A)) = k13_nattra_1(A))) # label(t53_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3787 (all A all B (v2_cat_1(A) & l1_cat_1(B) & v2_cat_1(B) & l1_cat_1(A) -> (all C (m4_nattra_1(C,A,B) -> -v1_xboole_0(C))))) # label(dt_m4_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3788 (all A (v2_cat_1(A) & l1_cat_1(A) & v2_nattra_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> k6_cat_1(A,B,B) = k1_tarski(k10_cat_1(A,B)))))) # label(t44_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3789 (all A all B (l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(A) -> l1_cat_1(k12_nattra_1(A,B)) & v2_cat_1(k12_nattra_1(A,B)) & v1_cat_1(k12_nattra_1(A,B)))) # label(dt_k12_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3790 $T # label(t36_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3791 (all A all B all C all D all E all F (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(D,k1_zfmisc_1(B)) & m1_relset_1(E,k12_mcart_1(A,A,C,C),C) & v1_funct_1(F) & m1_relset_1(F,k12_mcart_1(B,B,D,D),D) & v1_funct_1(E) & -v1_xboole_0(D) & -v1_xboole_0(C) -> m2_relset_1(k2_nattra_1(A,B,C,D,E,F),k12_mcart_1(k2_zfmisc_1(A,B),k2_zfmisc_1(A,B),k12_mcart_1(A,B,C,D),k12_mcart_1(A,B,C,D)),k12_mcart_1(A,B,C,D)) & v1_funct_1(k2_nattra_1(A,B,C,D,E,F)))) # label(dt_k2_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3792 (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 (m2_cat_1(D,A,B) -> (r1_nattra_1(A,B,C,D) <-> (all E (m1_subset_1(E,u1_cat_1(A)) -> k1_xboole_0 != k6_cat_1(B,k13_cat_1(A,B,C,E),k13_cat_1(A,B,D,E))))))))))))) # label(d2_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3793 (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,C,A) -> (all E (m2_cat_1(E,A,B) -> (all F (m1_subset_1(F,u1_cat_1(C)) -> (all G (m1_subset_1(G,u1_cat_1(C)) -> (k1_xboole_0 != k6_cat_1(C,F,G) -> (all H (m1_cat_1(H,C,F,G) -> k3_nattra_1(A,B,E,k13_cat_1(C,A,D,F),k13_cat_1(C,A,D,G),k3_nattra_1(C,A,D,F,G,H)) = k3_nattra_1(C,B,k14_cat_1(C,A,B,D,E),F,G,H)))))))))))))))))) # label(t11_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3794 $T # label(t18_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3795 (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)) -> (k1_xboole_0 != k6_cat_1(A,B,C) -> (all D (m1_cat_1(D,A,B,C) -> D = k3_nattra_1(A,A,k15_cat_1(A),B,C,D)))))))))) # label(t16_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3796 (all A all B all C all D all E all F all G (l1_cat_1(A) & l1_cat_1(B) & m2_cat_1(C,A,B) & m2_cat_1(D,A,B) & m2_cat_1(E,A,B) & m2_nattra_1(F,A,B,C,D) & m2_nattra_1(G,A,B,D,E) & v2_cat_1(B) & v2_cat_1(A) -> m2_nattra_1(k8_nattra_1(A,B,C,D,E,F,G),A,B,C,E))) # label(dt_k8_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3797 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) & -v1_xboole_0(B) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u2_cat_1(A))) -> (all D (v1_funct_2(D,C,B) & m2_relset_1(D,C,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,C,B) & m2_relset_1(E,C,B) -> (k1_nattra_1(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C) = D & E = k1_nattra_1(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C) -> (all F (m2_relset_1(F,k2_zfmisc_1(C,C),C) & v1_funct_1(F) -> (k1_realset1(u5_cat_1(A),C) = F -> (all G (v1_funct_1(G) & m2_relset_1(G,B,C) & v1_funct_2(G,B,C) -> (G = k1_nattra_1(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B) -> m3_cat_2(g1_cat_1(B,C,D,E,F,G),A)))))))))))))))))) # label(t9_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3798 (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 (m2_cat_1(D,A,B) -> ((all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_subset_1(F,u1_cat_1(A)) -> (k6_cat_1(A,E,F) != k1_xboole_0 -> (all G (m1_cat_1(G,A,E,F) -> k3_nattra_1(A,B,C,E,F,G) = k3_nattra_1(A,B,D,E,F,G)))))))) -> C = D))))))))) # label(t12_nattra_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3799 (all A (v2_cat_1(A) & l1_cat_1(A) -> m2_cat_1(k1_isocat_1(A),A,A))) # label(dt_k1_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3800 (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,B,A) -> (v8_cat_1(C,B,A) -> r4_nattra_1(u2_cat_1(B),u2_cat_1(B),u2_cat_1(B),u2_cat_1(B),k2_isocat_1(B,A,B,C,k3_isocat_1(B,A,C)),k1_isocat_1(B)) & r4_nattra_1(u2_cat_1(A),u2_cat_1(A),u2_cat_1(A),u2_cat_1(A),k2_isocat_1(A,B,A,k3_isocat_1(B,A,C),C),k1_isocat_1(A))))))))) # label(t16_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3801 $T # label(t51_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3802 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (l1_cat_1(D) & v2_cat_1(D) -> (r1_isocat_1(C,D) & r1_isocat_1(A,B) -> r1_isocat_1(k11_cat_2(A,C),k11_cat_2(B,D))))))))))) # label(t24_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3803 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (all F (m2_cat_1(F,B,C) -> (all G (m2_cat_1(G,B,C) -> (r1_nattra_1(A,B,D,E) & r1_nattra_1(B,C,F,G) -> r1_nattra_1(A,C,k14_cat_1(A,B,C,D,F),k14_cat_1(A,B,C,E,G))))))))))))))))) # label(t8_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3804 (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 (l1_cat_1(D) & v2_cat_1(D) -> (all E (m2_cat_1(E,A,B) -> (all F (m2_cat_1(F,A,B) -> (all G (m2_cat_1(G,B,C) -> (all H (m2_cat_1(H,B,C) -> (all I (m2_cat_1(I,C,D) -> (all J (m2_cat_1(J,C,D) -> (all K (m2_nattra_1(K,A,B,E,F) -> (all L (m2_nattra_1(L,B,C,G,H) -> (all M (m2_nattra_1(M,C,D,I,J) -> (r2_nattra_1(C,D,I,J) & r2_nattra_1(B,C,G,H) & r2_nattra_1(A,B,E,F) -> r4_nattra_1(u1_cat_1(A),u2_cat_1(D),u1_cat_1(A),u2_cat_1(D),k8_isocat_1(A,C,D,k2_isocat_1(A,B,C,E,G),k2_isocat_1(A,B,C,F,H),I,J,k8_isocat_1(A,B,C,E,F,G,H,K,L),M),k8_isocat_1(A,B,D,E,F,k2_isocat_1(B,C,D,G,I),k2_isocat_1(B,C,D,H,J),K,k8_isocat_1(B,C,D,G,H,I,J,L,M)))))))))))))))))))))))))))))) # label(t44_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3805 (all A all B (v2_cat_1(A) & l1_cat_1(B) & v2_cat_1(B) & l1_cat_1(A) -> r2_isocat_1(A,A))) # label(reflexivity_r2_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3806 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (r1_nattra_1(A,B,D,E) -> (all F (m1_nattra_1(F,A,B,D,E) -> (all G (m2_cat_1(G,B,C) -> (all H (m1_subset_1(H,u1_cat_1(A)) -> k5_nattra_1(A,C,k2_isocat_1(A,B,C,D,G),k2_isocat_1(A,B,C,E,G),k4_isocat_1(A,B,C,D,E,F,G),H) = k3_nattra_1(B,C,G,k13_cat_1(A,B,D,H),k13_cat_1(A,B,E,H),k5_nattra_1(A,B,D,E,F,H))))))))))))))))))) # label(t26_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3807 (all A all B all C all D all E all F all G (v2_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & l1_cat_1(C) & m2_cat_1(F,A,B) & m1_nattra_1(G,B,C,D,E) & m2_cat_1(E,B,C) & m2_cat_1(D,B,C) & v2_cat_1(C) & l1_cat_1(A) -> m1_nattra_1(k5_isocat_1(A,B,C,D,E,F,G),A,C,k2_isocat_1(A,B,C,F,D),k2_isocat_1(A,B,C,F,E)))) # label(dt_k5_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3808 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,B,C) -> (all E (m2_cat_1(E,B,C) -> (all F (m2_cat_1(F,C,A) -> (all G (m2_nattra_1(G,B,C,D,E) -> (r2_nattra_1(B,C,D,E) -> r4_nattra_1(u1_cat_1(B),u2_cat_1(A),u1_cat_1(B),u2_cat_1(A),k6_isocat_1(B,C,A,D,E,G,F),k8_isocat_1(B,C,A,D,E,F,F,G,k7_nattra_1(C,A,F)))))))))))))))))) # label(t46_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3809 (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 (m2_cat_1(D,A,B) -> (all E (m2_nattra_1(E,A,B,C,D) -> (r2_nattra_1(A,B,C,D) -> r4_nattra_1(u1_cat_1(A),u2_cat_1(B),u1_cat_1(A),u2_cat_1(B),k8_isocat_1(A,B,B,C,D,k1_isocat_1(B),k1_isocat_1(B),E,k7_nattra_1(B,B,k1_isocat_1(B))),E)))))))))))) # label(t42_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3810 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,B,C) -> r4_nattra_1(u1_cat_1(A),u2_cat_1(C),u1_cat_1(A),u2_cat_1(C),k7_isocat_1(A,B,C,E,E,D,k7_nattra_1(B,C,E)),k7_nattra_1(A,C,k2_isocat_1(A,B,C,D,E))))))))))))) # label(t37_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3811 (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,B,A) -> (all D (m1_subset_1(D,u2_cat_1(B)) -> (v5_cat_1(D,B) -> v5_cat_1(k8_funct_2(u2_cat_1(B),u2_cat_1(A),C,D),A)))))))))) # label(t3_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3812 (all A all B (v2_cat_1(B) & l1_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> (all C (m1_isocat_1(C,A,B) -> m2_cat_1(C,A,B))))) # label(dt_m1_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3813 (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) -> (v8_cat_1(C,A,B) -> r4_nattra_1(u2_cat_1(A),u2_cat_1(B),u2_cat_1(A),u2_cat_1(B),k3_isocat_1(B,A,k3_isocat_1(A,B,C)),C)))))))) # label(t15_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3814 (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,A,B) -> (r1_nattra_1(A,B,D,E) -> (all F (m1_nattra_1(F,A,B,D,E) -> (all G (m2_cat_1(G,B,C) -> k7_funct_2(u1_cat_1(A),u2_cat_1(B),u2_cat_1(C),F,G) = k4_isocat_1(A,B,C,D,E,F,G)))))))))))))))) # label(d5_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3815 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (v2_cat_1(D) & l1_cat_1(D) -> (all E (m2_cat_1(E,A,C) -> (all F (m2_cat_1(F,C,D) -> (all G (m2_cat_1(G,C,D) -> (all H (m2_cat_1(H,D,B) -> (all I (m2_nattra_1(I,C,D,F,G) -> (r2_nattra_1(C,D,F,G) -> r4_nattra_1(u1_cat_1(A),u2_cat_1(B),u1_cat_1(A),u2_cat_1(B),k7_isocat_1(A,C,B,k2_isocat_1(C,D,B,F,H),k2_isocat_1(C,D,B,G,H),E,k6_isocat_1(C,D,B,F,G,I,H)),k6_isocat_1(A,D,B,k2_isocat_1(A,C,D,E,F),k2_isocat_1(A,C,D,E,G),k7_isocat_1(A,C,D,F,G,E,I),H))))))))))))))))))))) # label(t35_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3816 (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) -> (v8_cat_1(C,A,B) -> v8_cat_1(k3_isocat_1(A,B,C),B,A)))))))) # label(t13_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3817 (all A (v2_cat_1(A) & l1_cat_1(A) -> m1_isocat_1(k1_isocat_1(A),A,A))) # label(t54_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3818 (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,B,A) -> (all D (m2_cat_1(D,B,A) -> (r2_nattra_1(B,A,C,D) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> k1_xboole_0 != k6_cat_1(A,k13_cat_1(B,A,C,E),k13_cat_1(B,A,D,E))))))))))))) # label(t30_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3819 (all A (l1_cat_1(A) & v2_cat_1(A) -> k15_cat_1(A) = k1_isocat_1(A))) # label(redefinition_k1_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3820 (all A all B (v2_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & l1_cat_1(A) -> (r2_isocat_1(A,B) -> r2_isocat_1(B,A)))) # label(symmetry_r2_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3821 (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,B,A) -> (all D (m2_cat_1(D,B,A) -> (r2_nattra_1(B,A,C,D) -> (all E (m2_nattra_1(E,B,A,C,D) -> (all F (m2_nattra_1(F,B,A,C,D) -> ((all G (m1_subset_1(G,u1_cat_1(B)) -> k5_nattra_1(B,A,C,D,F,G) = k5_nattra_1(B,A,C,D,E,G))) -> r4_nattra_1(u1_cat_1(B),u2_cat_1(A),u1_cat_1(B),u2_cat_1(A),E,F))))))))))))))) # label(t31_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3822 (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) -> (r1_isocat_1(B,C) & r1_isocat_1(A,B) -> r1_isocat_1(A,C)))))))) # label(t20_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3823 $T # label(t5_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3824 (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) -> r1_isocat_1(k11_cat_2(k11_cat_2(A,B),C),k11_cat_2(A,k11_cat_2(B,C))))))))) # label(t23_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3825 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> ((exists C ((exists D (r3_nattra_1(B,B,k2_isocat_1(B,A,B,D,C),k1_isocat_1(B)) & r3_nattra_1(A,A,k2_isocat_1(A,B,A,C,D),k1_isocat_1(A)) & m2_cat_1(D,B,A))) & m2_cat_1(C,A,B))) <-> r2_isocat_1(A,B)))))) # label(d10_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3826 (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) -> (v8_cat_1(C,A,B) -> k2_funct_1(k12_cat_1(A,B,C)) = k12_cat_1(B,A,k3_isocat_1(A,B,C))))))))) # label(t14_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3827 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,B,C) -> (all E (m2_cat_1(E,B,C) -> (all F (m2_cat_1(F,B,C) -> (all G (m2_cat_1(G,C,A) -> (all H (m2_nattra_1(H,B,C,D,E) -> (all I (m2_nattra_1(I,B,C,E,F) -> (r2_nattra_1(B,C,E,F) & r2_nattra_1(B,C,D,E) -> r4_nattra_1(u1_cat_1(B),u2_cat_1(A),u1_cat_1(B),u2_cat_1(A),k6_isocat_1(B,C,A,D,F,k8_nattra_1(B,C,D,E,F,H,I),G),k8_nattra_1(B,A,k2_isocat_1(B,C,A,D,G),k2_isocat_1(B,C,A,E,G),k2_isocat_1(B,C,A,F,G),k6_isocat_1(B,C,A,D,E,H,G),k6_isocat_1(B,C,A,E,F,I,G)))))))))))))))))))))) # label(t32_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3828 (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 (l1_cat_1(D) & v2_cat_1(D) -> (all E (m2_cat_1(E,A,B) -> (all F (m2_cat_1(F,B,C) -> (all G (m2_cat_1(G,C,D) -> (all H (m2_cat_1(H,C,D) -> (all I (m2_nattra_1(I,C,D,G,H) -> (r2_nattra_1(C,D,G,H) -> r4_nattra_1(u1_cat_1(A),u2_cat_1(D),u1_cat_1(A),u2_cat_1(D),k7_isocat_1(A,B,D,k2_isocat_1(B,C,D,F,G),k2_isocat_1(B,C,D,F,H),E,k7_isocat_1(B,C,D,G,H,F,I)),k7_isocat_1(A,C,D,G,H,k2_isocat_1(A,B,C,E,F),I))))))))))))))))))))) # label(t34_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3829 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> r1_isocat_1(k11_cat_2(A,B),k11_cat_2(B,A)))))) # label(t22_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3830 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) & v2_funct_1(A) -> v2_funct_1(k15_funct_3(A,B))))))) # label(t1_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3831 (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 (m2_cat_1(D,B,A) -> r4_nattra_1(u2_cat_1(A),u2_cat_1(B),u2_cat_1(A),u2_cat_1(B),k14_cat_1(A,A,B,k15_cat_1(A),C),C) & r4_nattra_1(u2_cat_1(B),u2_cat_1(A),u2_cat_1(B),u2_cat_1(A),k14_cat_1(B,A,A,D,k15_cat_1(A)),D))))))))) # label(t4_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3832 (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 (m2_cat_1(D,A,B) -> (r1_nattra_1(A,B,C,D) -> (all E (m1_nattra_1(E,A,B,C,D) -> (all F (m1_subset_1(F,u1_cat_1(A)) -> r2_hidden(k5_nattra_1(A,B,C,D,E,F),k6_cat_1(B,k13_cat_1(A,B,C,F),k13_cat_1(A,B,D,F)))))))))))))))) # label(t7_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3833 (all A all B (v2_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & l1_cat_1(A) -> (exists C m1_isocat_1(C,A,B)))) # label(existence_m1_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3834 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (r1_nattra_1(A,B,D,E) -> (all F (m2_cat_1(F,C,A) -> (all G (m1_nattra_1(G,A,B,D,E) -> (all H (m1_subset_1(H,u1_cat_1(C)) -> k5_nattra_1(A,B,D,E,G,k13_cat_1(C,A,F,H)) = k5_nattra_1(C,B,k2_isocat_1(C,A,B,F,D),k2_isocat_1(C,A,B,F,E),k5_isocat_1(C,A,B,D,E,F,G),H)))))))))))))))))) # label(t25_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3835 (all A all B all C all D all E (l1_cat_1(A) & v2_cat_1(B) & v2_cat_1(C) & l1_cat_1(C) & m2_cat_1(E,B,C) & m2_cat_1(D,A,B) & l1_cat_1(B) & v2_cat_1(A) -> m2_cat_1(k2_isocat_1(A,B,C,D,E),A,C))) # label(dt_k2_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3836 (all A all B all C (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C,A,B) -> m2_cat_1(k3_isocat_1(A,B,C),B,A))) # label(dt_k3_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3837 (all A all B all C all D all E all F all G (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(C) & m2_cat_1(E,B,C) & m2_cat_1(F,A,B) & m2_nattra_1(G,B,C,D,E) & m2_cat_1(D,B,C) & l1_cat_1(C) & l1_cat_1(B) & v2_cat_1(B) -> m2_nattra_1(k7_isocat_1(A,B,C,D,E,F,G),A,C,k2_isocat_1(A,B,C,F,D),k2_isocat_1(A,B,C,F,E)))) # label(dt_k7_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3838 (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) -> (v8_cat_1(C,A,B) -> k3_isocat_1(A,B,C) = k2_funct_1(C)))))))) # label(d2_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3839 $T # label(t18_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3840 (all A all B all C all D all E all F all G all H all I (l1_cat_1(B) & m2_nattra_1(H,A,B,D,E) & m2_nattra_1(I,B,C,F,G) & m2_cat_1(G,B,C) & m2_cat_1(F,B,C) & m2_cat_1(E,A,B) & m2_cat_1(D,A,B) & l1_cat_1(C) & v2_cat_1(C) & v2_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> m2_nattra_1(k8_isocat_1(A,B,C,D,E,F,G,H,I),A,C,k2_isocat_1(A,B,C,D,F),k2_isocat_1(A,B,C,E,G)))) # label(dt_k8_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3841 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (v2_cat_1(D) & l1_cat_1(D) -> (all E (m2_cat_1(E,A,B) -> (all F (m2_cat_1(F,C,D) -> (all G (m2_cat_1(G,B,C) -> (all H (m2_cat_1(H,B,C) -> (r3_nattra_1(B,C,G,H) -> r3_nattra_1(A,C,k2_isocat_1(A,B,C,E,G),k2_isocat_1(A,B,C,E,H)) & r3_nattra_1(B,D,k2_isocat_1(B,C,D,G,F),k2_isocat_1(B,C,D,H,F))))))))))))))))))) # label(t48_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3842 (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,A,B) -> (all F (m2_cat_1(F,B,C) -> (all G (m2_cat_1(G,B,C) -> (all H (m2_nattra_1(H,A,B,D,E) -> (all I (m2_nattra_1(I,B,C,F,G) -> k8_isocat_1(A,B,C,D,E,F,G,H,I) = k8_nattra_1(A,C,k2_isocat_1(A,B,C,D,F),k2_isocat_1(A,B,C,E,F),k2_isocat_1(A,B,C,E,G),k6_isocat_1(A,B,C,D,E,H,F),k7_isocat_1(A,B,C,F,G,E,I)))))))))))))))))))) # label(d9_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3843 (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 (m2_cat_1(D,B,A) -> (all E (m2_cat_1(E,A,A) -> (r3_nattra_1(A,A,E,k1_isocat_1(A)) -> r3_nattra_1(A,B,k2_isocat_1(A,A,B,E,C),C) & r3_nattra_1(B,A,k2_isocat_1(B,A,A,D,E),D)))))))))))) # label(t49_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3844 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,B,C) -> (all E (m2_cat_1(E,B,C) -> (r2_nattra_1(B,C,D,E) -> (all F (m2_cat_1(F,A,B) -> (all G (m2_nattra_1(G,B,C,D,E) -> k5_isocat_1(A,B,C,D,E,F,G) = k7_isocat_1(A,B,C,D,E,F,G)))))))))))))))) # label(d8_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3845 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (r2_isocat_1(A,B) -> (all C (m2_cat_1(C,A,B) -> (m1_isocat_1(C,A,B) <-> (exists D (r3_nattra_1(A,A,k2_isocat_1(A,B,A,C,D),k1_isocat_1(A)) & r3_nattra_1(B,B,k2_isocat_1(B,A,B,D,C),k1_isocat_1(B)) & m2_cat_1(D,B,A))))))))))) # label(d11_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3846 (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) -> (v2_funct_1(C) -> v2_funct_1(k12_cat_1(A,B,C))))))))) # label(t12_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3847 (all A all B all C all D all E all F all G (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & m2_cat_1(G,B,C) & m1_nattra_1(F,A,B,D,E) & m2_cat_1(E,A,B) & m2_cat_1(D,A,B) & l1_cat_1(C) & v2_cat_1(C) & l1_cat_1(B) -> m1_nattra_1(k4_isocat_1(A,B,C,D,E,F,G),A,C,k2_isocat_1(A,B,C,D,G),k2_isocat_1(A,B,C,E,G)))) # label(dt_k4_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3848 (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,B,A) -> (all D (m2_cat_1(D,B,A) -> (all E (m2_nattra_1(E,B,A,C,D) -> (r2_nattra_1(B,A,C,D) -> r4_nattra_1(u1_cat_1(B),u2_cat_1(A),u1_cat_1(B),u2_cat_1(A),k7_isocat_1(B,B,A,C,D,k1_isocat_1(B),E),E)))))))))))) # label(t39_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3849 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (r2_nattra_1(A,B,D,E) -> (all F (m2_nattra_1(F,A,B,D,E) -> (all G (m2_cat_1(G,B,C) -> (all H (m1_subset_1(H,u1_cat_1(A)) -> k5_nattra_1(A,C,k2_isocat_1(A,B,C,D,G),k2_isocat_1(A,B,C,E,G),k6_isocat_1(A,B,C,D,E,F,G),H) = k3_nattra_1(B,C,G,k13_cat_1(A,B,D,H),k13_cat_1(A,B,E,H),k5_nattra_1(A,B,D,E,F,H))))))))))))))))))) # label(t28_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3850 (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,B,A) -> (v8_cat_1(C,B,A) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (exists E (D = k13_cat_1(B,A,C,E) & m1_subset_1(E,u1_cat_1(B))))))))))))) # label(t11_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3851 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (r1_isocat_1(A,B) -> r2_isocat_1(A,B)))))) # label(t50_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3852 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (all F (m2_cat_1(F,B,C) -> (all G (m2_cat_1(G,B,C) -> (r2_nattra_1(B,C,F,G) & r2_nattra_1(A,B,D,E) -> r2_nattra_1(A,C,k2_isocat_1(A,B,C,D,F),k2_isocat_1(A,B,C,E,G))))))))))))))))) # label(t27_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3853 $T # label(t19_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3854 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,B,C) -> (all E (m2_cat_1(E,B,C) -> (r1_nattra_1(B,C,D,E) -> (all F (m2_cat_1(F,A,B) -> (all G (m1_nattra_1(G,B,C,D,E) -> k7_funct_2(u1_cat_1(A),u1_cat_1(B),u2_cat_1(C),k12_cat_1(A,B,F),G) = k5_isocat_1(A,B,C,D,E,F,G)))))))))))))))) # label(d6_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3855 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (all F (m2_cat_1(F,A,B) -> (all G (m2_cat_1(G,B,C) -> (all H (m2_cat_1(H,B,C) -> (all I (m2_cat_1(I,B,C) -> (all J (m2_nattra_1(J,A,B,D,E) -> (all K (m2_nattra_1(K,A,B,E,F) -> (all L (m2_nattra_1(L,B,C,G,H) -> (all M (m2_nattra_1(M,B,C,H,I) -> (r2_nattra_1(A,B,D,E) & r2_nattra_1(B,C,H,I) & r2_nattra_1(B,C,G,H) & r2_nattra_1(A,B,E,F) -> r4_nattra_1(u1_cat_1(A),u2_cat_1(C),u1_cat_1(A),u2_cat_1(C),k8_isocat_1(A,B,C,D,F,G,I,k8_nattra_1(A,B,D,E,F,J,K),k8_nattra_1(B,C,G,H,I,L,M)),k8_nattra_1(A,C,k2_isocat_1(A,B,C,D,G),k2_isocat_1(A,B,C,E,H),k2_isocat_1(A,B,C,F,I),k8_isocat_1(A,B,C,D,E,G,H,J,L),k8_isocat_1(A,B,C,E,F,H,I,K,M)))))))))))))))))))))))))))))) # label(t47_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3856 (all A all B all C all D all E all F all G (v2_cat_1(B) & m2_cat_1(D,A,B) & m2_cat_1(G,B,C) & m2_nattra_1(F,A,B,D,E) & m2_cat_1(E,A,B) & l1_cat_1(C) & v2_cat_1(C) & l1_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> m2_nattra_1(k6_isocat_1(A,B,C,D,E,F,G),A,C,k2_isocat_1(A,B,C,D,G),k2_isocat_1(A,B,C,E,G)))) # label(dt_k6_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3857 (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) -> (all F (m2_cat_1(F,B,C) -> (all G (m2_nattra_1(G,B,C,E,F) -> (r2_nattra_1(B,C,E,F) -> r4_nattra_1(u1_cat_1(A),u2_cat_1(C),u1_cat_1(A),u2_cat_1(C),k7_isocat_1(A,B,C,E,F,D,G),k8_isocat_1(A,B,C,D,D,E,F,k7_nattra_1(A,B,D),G))))))))))))))))) # label(t45_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3858 (all A all B all C all D all E (v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(D,A,B) & m2_cat_1(E,B,C) & l1_cat_1(C) & v2_cat_1(C) & l1_cat_1(A) & v2_cat_1(A) -> k5_relat_1(D,E) = k2_isocat_1(A,B,C,D,E))) # label(redefinition_k2_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3859 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (v2_cat_1(D) & l1_cat_1(D) -> (all E (m2_cat_1(E,C,D) -> (all F (m2_cat_1(F,C,D) -> (all G (m2_cat_1(G,D,A) -> (all H (m2_cat_1(H,A,B) -> (all I (m2_nattra_1(I,C,D,E,F) -> (r2_nattra_1(C,D,E,F) -> r4_nattra_1(u1_cat_1(C),u2_cat_1(B),u1_cat_1(C),u2_cat_1(B),k6_isocat_1(C,D,B,E,F,I,k2_isocat_1(D,A,B,G,H)),k6_isocat_1(C,A,B,k2_isocat_1(C,D,A,E,G),k2_isocat_1(C,D,A,F,G),k6_isocat_1(C,D,A,E,F,I,G),H))))))))))))))))))))) # label(t36_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3860 (all A all B (l1_cat_1(A) & l1_cat_1(B) & v2_cat_1(B) & v2_cat_1(A) -> r1_isocat_1(A,A))) # label(reflexivity_r1_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3861 $T # label(t6_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3862 (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 (m2_cat_1(D,A,B) -> (all E (m2_nattra_1(E,A,B,C,D) -> (r2_nattra_1(A,B,C,D) -> r4_nattra_1(u1_cat_1(A),u2_cat_1(B),u1_cat_1(A),u2_cat_1(B),k6_isocat_1(A,B,B,C,D,E,k1_isocat_1(B)),E)))))))))))) # label(t40_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3863 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (r2_nattra_1(A,B,D,E) -> (all F (m2_cat_1(F,C,A) -> (all G (m2_nattra_1(G,A,B,D,E) -> (all H (m1_subset_1(H,u1_cat_1(C)) -> k5_nattra_1(A,B,D,E,G,k13_cat_1(C,A,F,H)) = k5_nattra_1(C,B,k2_isocat_1(C,A,B,F,D),k2_isocat_1(C,A,B,F,E),k7_isocat_1(C,A,B,D,E,F,G),H)))))))))))))))))) # label(t29_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3864 (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) -> (v8_cat_1(C,A,B) <-> k2_relat_1(C) = u2_cat_1(B) & v2_funct_1(C)))))))) # label(d3_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3865 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (r2_isocat_1(A,B) -> (all C (m1_isocat_1(C,A,B) -> (exists D (m1_isocat_1(D,B,A) & r3_nattra_1(B,B,k2_isocat_1(B,A,B,D,C),k1_isocat_1(B)) & r3_nattra_1(A,A,k2_isocat_1(A,B,A,C,D),k1_isocat_1(A))))))))))) # label(t56_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3866 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_1(C) -> (m2_cat_1(C,A,B) <-> (all D (m1_subset_1(D,u1_cat_1(A)) -> (exists E (k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,E) & m1_subset_1(E,u1_cat_1(B)))))) & (all D (m1_subset_1(D,u2_cat_1(A)) -> k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k2_cat_1(A,D))) = k10_cat_1(B,k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) & 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))))) & (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)))))))))))))) # label(d1_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3867 (all A all B (v2_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & l1_cat_1(A) -> (r1_isocat_1(A,B) -> r1_isocat_1(B,A)))) # label(symmetry_r1_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3868 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (all F (m2_cat_1(F,B,C) -> (all G (m2_cat_1(G,B,C) -> (all H (m2_nattra_1(H,A,B,D,E) -> (all I (m2_nattra_1(I,B,C,F,G) -> (r2_nattra_1(A,B,D,E) & r2_nattra_1(B,C,F,G) -> r4_nattra_1(u1_cat_1(A),u2_cat_1(C),u1_cat_1(A),u2_cat_1(C),k8_isocat_1(A,B,C,D,E,F,G,H,I),k8_nattra_1(A,C,k2_isocat_1(A,B,C,D,F),k2_isocat_1(A,B,C,D,G),k2_isocat_1(A,B,C,E,G),k7_isocat_1(A,B,C,F,G,D,I),k6_isocat_1(A,B,C,D,E,H,G)))))))))))))))))))))) # label(t41_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3869 $T # label(t52_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3870 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (r2_isocat_1(A,B) -> (all C (m1_isocat_1(C,A,B) -> v9_cat_1(C,A,B) & v10_cat_1(C,A,B) & (all D (m1_subset_1(D,u1_cat_1(B)) -> (exists E (r1_cat_1(B,D,k13_cat_1(A,B,C,E)) & m1_subset_1(E,u1_cat_1(A))))))))))))) # label(t58_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3871 (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,B,A) -> (v8_cat_1(C,B,A) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (exists E (m1_subset_1(E,u2_cat_1(B)) & k8_funct_2(u2_cat_1(B),u2_cat_1(A),C,E) = D))))))))))) # label(t10_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3872 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,B,C) -> r4_nattra_1(u1_cat_1(A),u2_cat_1(C),u1_cat_1(A),u2_cat_1(C),k6_isocat_1(A,B,C,D,D,k7_nattra_1(A,B,D),E),k7_nattra_1(A,C,k2_isocat_1(A,B,C,D,E))))))))))))) # label(t38_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3873 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B all C r1_isocat_1(k11_cat_2(k8_cat_1(B,C),A),A)))) # label(t21_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3874 (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,A,B) -> (r2_nattra_1(A,B,D,E) -> (all F (m2_nattra_1(F,A,B,D,E) -> (all G (m2_cat_1(G,B,C) -> k6_isocat_1(A,B,C,D,E,F,G) = k4_isocat_1(A,B,C,D,E,F,G)))))))))))))))) # label(d7_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3875 (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,B,A) -> (all D (m2_cat_1(D,B,A) -> (all E (m2_nattra_1(E,B,A,C,D) -> (r2_nattra_1(B,A,C,D) -> r4_nattra_1(u1_cat_1(B),u2_cat_1(A),u1_cat_1(B),u2_cat_1(A),k8_isocat_1(B,B,A,k1_isocat_1(B),k1_isocat_1(B),C,D,k7_nattra_1(B,B,k1_isocat_1(B)),E),E)))))))))))) # label(t43_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3876 (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) -> (r2_isocat_1(A,B) & r2_isocat_1(B,C) -> (all D (m1_isocat_1(D,A,B) -> (all E (m1_isocat_1(E,B,C) -> m1_isocat_1(k2_isocat_1(A,B,C,D,E),A,C)))))))))))) # label(t55_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3877 (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 (m2_cat_1(D,A,B) -> (r1_nattra_1(A,B,C,D) -> (all E (m1_nattra_1(E,A,B,C,D) -> (v1_nattra_1(E,A,B,C,D) -> (all F (m1_subset_1(F,u1_cat_1(A)) -> r1_cat_1(B,k13_cat_1(A,B,C,F),k13_cat_1(A,B,D,F)))))))))))))))) # label(t9_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3878 (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) -> (r2_isocat_1(B,C) & r2_isocat_1(A,B) -> r2_isocat_1(A,C)))))))) # label(t53_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3879 (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 (m2_cat_1(D,B,A) -> (r3_nattra_1(A,A,k2_isocat_1(A,B,A,C,D),k1_isocat_1(A)) -> v10_cat_1(C,A,B)))))))))) # label(t57_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3880 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,B,C) -> (v8_cat_1(E,B,C) & v8_cat_1(D,A,B) -> v8_cat_1(k2_isocat_1(A,B,C,D,E),A,C)))))))))))) # label(t17_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3881 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,B,C) -> (all F (m2_cat_1(F,B,C) -> (all G (m2_cat_1(G,B,C) -> (all H (m2_nattra_1(H,B,C,E,F) -> (all I (m2_nattra_1(I,B,C,F,G) -> (r2_nattra_1(B,C,F,G) & r2_nattra_1(B,C,E,F) -> r4_nattra_1(u1_cat_1(A),u2_cat_1(C),u1_cat_1(A),u2_cat_1(C),k7_isocat_1(A,B,C,E,G,D,k8_nattra_1(B,C,E,F,G,H,I)),k8_nattra_1(A,C,k2_isocat_1(A,B,C,D,E),k2_isocat_1(A,B,C,D,F),k2_isocat_1(A,B,C,D,G),k7_isocat_1(A,B,C,E,F,D,H),k7_isocat_1(A,B,C,F,G,D,I)))))))))))))))))))))) # label(t33_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3882 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> ((exists C (m2_cat_1(C,A,B) & v8_cat_1(C,A,B))) <-> r1_isocat_1(A,B)))))) # label(d4_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3883 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> k2_relat_1(k17_cat_2(B,A)) = u2_cat_1(A) & k2_relat_1(k16_cat_2(A,B)) = u2_cat_1(A))))) # label(t2_isocat_1) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3884 (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) <-> m1_subset_1(C,u1_cat_1(k12_nattra_1(A,B))))))))) # label(t8_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3885 (all A all B all C all D (v2_cat_1(A) & l1_cat_1(A) & l1_cat_1(B) & v2_cat_1(C) & m2_cat_1(D,A,k11_cat_2(B,C)) & l1_cat_1(C) & v2_cat_1(B) -> m2_cat_1(k11_isocat_2(A,B,C,D),A,B))) # label(dt_k11_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3886 (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,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u2_cat_1(A)) -> (all F (m1_subset_1(F,u1_cat_1(B)) -> k5_nattra_1(B,C,k14_cat_2(A,B,C,D,k2_cat_1(A,E)),k14_cat_2(A,B,C,D,k3_cat_1(A,E)),k4_isocat_2(A,B,C,D,E),F) = k8_funct_2(u2_cat_1(k11_cat_2(A,B)),u2_cat_1(C),D,k13_cat_2(A,B,E,k10_cat_1(B,F))))))))))))))) # label(t19_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3887 (all A all B (v2_cat_1(A) & l1_cat_1(A) & l1_cat_1(B) & v2_cat_1(B) -> k8_isocat_2(A,B) = k16_cat_2(A,B))) # label(redefinition_k8_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3888 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m2_cat_1(E,k11_cat_2(A,B),C) -> (r2_nattra_1(k11_cat_2(A,B),C,D,E) -> (all F (m2_nattra_1(F,k11_cat_2(A,B),C,D,E) -> (all G (m2_nattra_1(G,A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E)) -> ((all H (v1_funct_1(H) & v1_funct_2(H,k2_zfmisc_1(u1_cat_1(A),u1_cat_1(B)),u2_cat_1(C)) & m2_relset_1(H,k2_zfmisc_1(u1_cat_1(A),u1_cat_1(B)),u2_cat_1(C)) -> (r4_nattra_1(u1_cat_1(k11_cat_2(A,B)),u2_cat_1(C),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(B)),u2_cat_1(C),F,H) -> (all I (m1_subset_1(I,u1_cat_1(A)) -> k4_tarski(k12_cat_2(k12_nattra_1(B,C),k12_nattra_1(B,C),k13_cat_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),I),k13_cat_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,E),I)),k1_cat_2(u1_cat_1(A),u1_cat_1(B),u2_cat_1(C),k1_fraenkel(u1_cat_1(B),u2_cat_1(C)),k2_cat_2(u1_cat_1(A),u1_cat_1(B),u2_cat_1(C),H),I)) = k5_nattra_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E),G,I)))))) <-> G = k6_isocat_2(A,B,C,D,E,F))))))))))))))))) # label(d5_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3889 (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,k11_cat_2(A,B),C) -> r4_nattra_1(u1_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),u1_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),k7_nattra_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D)),k6_isocat_2(A,B,C,D,D,k7_nattra_1(k11_cat_2(A,B),C,D))))))))))) # label(t28_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3890 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,k11_cat_2(B,C)) -> (all E (m2_cat_1(E,A,k11_cat_2(B,C)) -> (all F (m2_nattra_1(F,A,k11_cat_2(B,C),D,E) -> k13_isocat_2(A,B,C,D,E,F) = k6_isocat_1(A,k11_cat_2(B,C),B,D,E,F,k8_isocat_2(B,C)))))))))))))) # label(d9_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.96 3891 (all A all B all C (v2_cat_1(A) & m1_subset_1(C,u1_cat_1(A)) & l1_cat_1(B) & v2_cat_1(B) & l1_cat_1(A) -> m2_cat_1(k2_isocat_2(A,B,C),k12_nattra_1(A,B),B))) # label(dt_k2_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3892 (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 (m2_cat_1(D,A,B) -> (r1_nattra_1(A,B,C,D) -> (all E (m1_nattra_1(E,A,B,C,D) -> (all F (m1_subset_1(F,u1_cat_1(A)) -> r2_hidden(k5_nattra_1(A,B,C,D,E,F),k6_cat_1(B,k13_cat_1(A,B,C,F),k13_cat_1(A,B,D,F)))))))))))))))) # label(l27_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3893 (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,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u2_cat_1(A)) -> k1_funct_1(k3_funct_5(D),E) = k3_isocat_2(A,B,C,D,E))))))))))) # label(d2_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3894 (all A all B (l1_cat_1(B) & v2_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> m2_cat_1(k9_isocat_2(A,B),k11_cat_2(A,B),B))) # label(dt_k9_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3895 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) -> (all E (v1_funct_2(E,A,k2_zfmisc_1(B,C)) & m2_relset_1(E,A,k2_zfmisc_1(B,C)) & v1_funct_1(E) -> (r4_nattra_1(A,C,A,C,k7_funct_2(A,k2_zfmisc_1(B,C),C,D,k10_funct_3(B,C)),k7_funct_2(A,k2_zfmisc_1(B,C),C,E,k10_funct_3(B,C))) & r4_nattra_1(A,B,A,B,k7_funct_2(A,k2_zfmisc_1(B,C),B,D,k9_funct_3(B,C)),k7_funct_2(A,k2_zfmisc_1(B,C),B,E,k9_funct_3(B,C))) -> r4_nattra_1(A,k2_zfmisc_1(B,C),A,k2_zfmisc_1(B,C),D,E)))))))))))) # label(t5_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3896 (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,k1_fraenkel(B,C)) & v1_funct_2(D,A,k1_fraenkel(B,C)) & v1_funct_1(D) -> r4_nattra_1(A,k1_fraenkel(B,C),A,k1_fraenkel(B,C),k2_cat_2(A,B,C,k1_isocat_2(A,B,C,D)),D))))))))) # label(t1_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3897 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,A) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> r2_hidden(k8_funct_2(A,B,D,C),k2_relat_1(D)))))))))) # label(t4_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3898 (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,k1_fraenkel(B,C)) & m2_relset_1(D,A,k1_fraenkel(B,C)) & v1_funct_1(D) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> k8_funct_2(B,C,k1_cat_2(A,B,C,k1_fraenkel(B,C),D,E),F) = k1_funct_1(k1_isocat_2(A,B,C,D),k4_tarski(E,F)))))))))))))) # label(t2_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3899 (all A all B all C all D all E all F all G all H all I (v2_cat_1(A) & l1_cat_1(A) & l1_cat_1(B) & v2_cat_1(C) & m2_cat_1(F,A,C) & m2_cat_1(G,A,C) & m2_nattra_1(H,A,B,D,E) & m2_nattra_1(I,A,C,F,G) & m2_cat_1(E,A,B) & m2_cat_1(D,A,B) & l1_cat_1(C) & v2_cat_1(B) -> m2_nattra_1(k16_isocat_2(A,B,C,D,E,F,G,H,I),A,k11_cat_2(B,C),k10_isocat_2(A,B,C,D,F),k10_isocat_2(A,B,C,E,G)))) # label(dt_k16_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3900 (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,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> m2_cat_1(k13_cat_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),E),B,C))))))))))) # label(t25_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3901 (all A all B (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) -> m2_cat_1(k8_isocat_2(A,B),k11_cat_2(A,B),A))) # label(dt_k8_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3902 (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,k11_cat_2(A,B),C) -> (all E (m2_cat_1(E,k11_cat_2(A,B),C) -> (r2_nattra_1(k11_cat_2(A,B),C,D,E) -> (all F (m2_nattra_1(F,k11_cat_2(A,B),C,D,E) -> (all G (m1_subset_1(G,u1_cat_1(A)) -> m2_nattra_1(k1_funct_1(k3_funct_5(F),G),B,C,k14_cat_2(A,B,C,D,G),k14_cat_2(A,B,C,E,G)) & r2_nattra_1(B,C,k14_cat_2(A,B,C,D,G),k14_cat_2(A,B,C,E,G))))))))))))))))) # label(t15_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3903 (all A all B all C all D all E all F (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(C) & m2_cat_1(E,A,k11_cat_2(B,C)) & m2_nattra_1(F,A,k11_cat_2(B,C),D,E) & m2_cat_1(D,A,k11_cat_2(B,C)) & v2_cat_1(C) & l1_cat_1(B) -> m2_nattra_1(k13_isocat_2(A,B,C,D,E,F),A,B,k11_isocat_2(A,B,C,D),k11_isocat_2(A,B,C,E)))) # label(dt_k13_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3904 (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) -> r1_isocat_1(k12_nattra_1(k11_cat_2(A,B),C),k12_nattra_1(A,k12_nattra_1(B,C))))))))) # label(t34_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3905 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m2_cat_1(E,k11_cat_2(A,B),C) -> (r2_nattra_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E)) -> (all F (m2_nattra_1(F,A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E)) -> r2_nattra_1(k11_cat_2(A,B),C,D,E) & (exists G (r4_nattra_1(u1_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),u1_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),F,k6_isocat_2(A,B,C,D,E,G)) & m2_nattra_1(G,k11_cat_2(A,B),C,D,E)))))))))))))))) # label(t32_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3906 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,k11_cat_2(B,C)) -> (all E (m2_cat_1(E,A,k11_cat_2(B,C)) -> (all F (m2_nattra_1(F,A,k11_cat_2(B,C),D,E) -> k14_isocat_2(A,B,C,D,E,F) = k6_isocat_1(A,k11_cat_2(B,C),C,D,E,F,k9_isocat_2(B,C)))))))))))))) # label(d10_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3907 (all A all B all C all D (v2_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(D,A,k11_cat_2(B,C)) & l1_cat_1(C) & v2_cat_1(C) & l1_cat_1(A) -> m2_cat_1(k12_isocat_2(A,B,C,D),A,C))) # label(dt_k12_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3908 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (all F (m2_cat_1(F,B,C) -> (r2_nattra_1(A,B,D,E) -> (all G (m2_nattra_1(G,A,B,D,E) -> k6_isocat_1(A,B,C,D,E,G,F) = k5_relat_1(G,F)))))))))))))))) # label(t35_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3909 (all A all B all C all D (-v1_xboole_0(C) & m1_relset_1(D,A,k1_fraenkel(B,C)) & v1_funct_2(D,A,k1_fraenkel(B,C)) & v1_funct_1(D) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k4_funct_5(D) = k1_isocat_2(A,B,C,D))) # label(redefinition_k1_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3910 (all A all B all C all D (-v1_xboole_0(C) & v1_funct_1(D) & v1_funct_2(D,A,k1_fraenkel(B,C)) & m1_relset_1(D,A,k1_fraenkel(B,C)) & -v1_xboole_0(B) & -v1_xboole_0(A) -> v1_funct_1(k1_isocat_2(A,B,C,D)) & v1_funct_2(k1_isocat_2(A,B,C,D),k2_zfmisc_1(A,B),C) & m2_relset_1(k1_isocat_2(A,B,C,D),k2_zfmisc_1(A,B),C))) # label(dt_k1_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3911 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> r4_nattra_1(u1_cat_1(B),u2_cat_1(C),u1_cat_1(B),u2_cat_1(C),k7_nattra_1(B,C,k14_cat_2(A,B,C,D,E)),k4_isocat_2(A,B,C,D,k10_cat_1(A,E))))))))))))) # label(t20_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3912 (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,k12_nattra_1(k11_cat_2(A,B),C),k12_nattra_1(A,k12_nattra_1(B,C))) -> (D = k7_isocat_2(A,B,C) <-> (all E (m2_cat_1(E,k11_cat_2(A,B),C) -> (all F (m2_cat_1(F,k11_cat_2(A,B),C) -> (r2_nattra_1(k11_cat_2(A,B),C,E,F) -> (all G (m2_nattra_1(G,k11_cat_2(A,B),C,E,F) -> k1_funct_1(D,k4_tarski(k4_tarski(E,F),G)) = k4_tarski(k4_tarski(k5_isocat_2(A,B,C,E),k5_isocat_2(A,B,C,F)),k6_isocat_2(A,B,C,E,F,G)))))))))))))))))) # label(d6_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3913 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,k12_nattra_1(B,C)) -> (exists E (r4_nattra_1(u2_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),u2_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),D,k5_isocat_2(A,B,C,E)) & m2_cat_1(E,k11_cat_2(A,B),C))))))))))) # label(t31_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3914 (all A all B all C all D all E (l1_cat_1(A) & v2_cat_1(C) & m1_subset_1(E,u2_cat_1(A)) & m2_cat_1(D,k11_cat_2(A,B),C) & l1_cat_1(C) & l1_cat_1(B) & v2_cat_1(B) & v2_cat_1(A) -> m2_nattra_1(k4_isocat_2(A,B,C,D,E),B,C,k14_cat_2(A,B,C,D,k2_cat_1(A,E)),k14_cat_2(A,B,C,D,k3_cat_1(A,E))))) # label(dt_k4_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3915 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u2_cat_1(k12_nattra_1(A,B))) -> (exists D ((exists E ((exists F (k2_cat_1(k12_nattra_1(A,B),C) = D & E = k3_cat_1(k12_nattra_1(A,B),C) & C = k4_tarski(k4_tarski(D,E),F) & r2_nattra_1(A,B,D,E) & m2_nattra_1(F,A,B,D,E))) & m2_cat_1(E,A,B))) & m2_cat_1(D,A,B))))))))) # label(t9_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3916 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> (all F (m1_subset_1(F,u1_cat_1(B)) -> (k6_cat_1(k11_cat_2(A,B),k12_cat_2(A,B,C,E),k12_cat_2(A,B,D,F)) != k1_xboole_0 -> (all G (m1_subset_1(G,u2_cat_1(A)) -> (all H (m1_subset_1(H,u2_cat_1(B)) -> (m1_cat_1(k13_cat_2(A,B,G,H),k11_cat_2(A,B),k12_cat_2(A,B,C,E),k12_cat_2(A,B,D,F)) <-> m1_cat_1(G,A,C,D) & m1_cat_1(H,B,E,F))))))))))))))))))) # label(t14_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3917 (all A all B all C all D all E (v2_cat_1(A) & l1_cat_1(B) & m2_cat_1(E,A,C) & m2_cat_1(D,A,B) & l1_cat_1(C) & v2_cat_1(C) & v2_cat_1(B) & l1_cat_1(A) -> m2_cat_1(k10_isocat_2(A,B,C,D,E),A,k11_cat_2(B,C)))) # label(dt_k10_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3918 (all A all B all C all D all E all F all G all H all I (l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(C) & l1_cat_1(C) & m2_cat_1(E,A,B) & m2_cat_1(G,A,C) & m1_nattra_1(I,A,C,F,G) & m1_nattra_1(H,A,B,D,E) & m2_cat_1(F,A,C) & m2_cat_1(D,A,B) & v2_cat_1(A) -> m1_nattra_1(k15_isocat_2(A,B,C,D,E,F,G,H,I),A,k11_cat_2(B,C),k10_isocat_2(A,B,C,D,F),k10_isocat_2(A,B,C,E,G)))) # label(dt_k15_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3919 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u2_cat_1(A)) -> r2_nattra_1(B,C,k14_cat_2(A,B,C,D,k2_cat_1(A,E)),k14_cat_2(A,B,C,D,k3_cat_1(A,E))))))))))))) # label(t18_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3920 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m2_cat_1(E,k11_cat_2(A,B),C) -> (r2_nattra_1(k11_cat_2(A,B),C,D,E) -> (all F (m2_nattra_1(F,k11_cat_2(A,B),C,D,E) -> (all G (m2_nattra_1(G,k11_cat_2(A,B),C,D,E) -> (r4_nattra_1(u1_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),u1_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),k6_isocat_2(A,B,C,D,E,F),k6_isocat_2(A,B,C,D,E,G)) -> r4_nattra_1(u1_cat_1(k11_cat_2(A,B)),u2_cat_1(C),u1_cat_1(k11_cat_2(A,B)),u2_cat_1(C),F,G))))))))))))))))) # label(t30_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3921 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m2_cat_1(E,k11_cat_2(A,B),C) -> (all F (m2_cat_1(F,k11_cat_2(A,B),C) -> (r2_nattra_1(k11_cat_2(A,B),C,E,F) & r2_nattra_1(k11_cat_2(A,B),C,D,E) -> (all G (m2_nattra_1(G,k11_cat_2(A,B),C,D,E) -> (all H (m2_nattra_1(H,k11_cat_2(A,B),C,E,F) -> r4_nattra_1(u1_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),u1_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),k6_isocat_2(A,B,C,D,F,k8_nattra_1(k11_cat_2(A,B),C,D,E,F,G,H)),k8_nattra_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E),k5_isocat_2(A,B,C,F),k6_isocat_2(A,B,C,D,E,G),k6_isocat_2(A,B,C,E,F,H)))))))))))))))))))) # label(t29_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3922 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B all C r1_isocat_1(k12_nattra_1(k8_cat_1(B,C),A),A)))) # label(t11_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3923 (all A all B all C (v2_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & l1_cat_1(C) & v2_cat_1(C) & l1_cat_1(A) -> m2_cat_1(k7_isocat_2(A,B,C),k12_nattra_1(k11_cat_2(A,B),C),k12_nattra_1(A,k12_nattra_1(B,C))))) # label(dt_k7_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3924 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> (all F (m1_subset_1(F,u1_cat_1(B)) -> (all G (m1_subset_1(G,u2_cat_1(A)) -> (all H (m1_subset_1(H,u2_cat_1(B)) -> (r2_hidden(G,k6_cat_1(A,C,D)) & r2_hidden(H,k6_cat_1(B,E,F)) -> r2_hidden(k13_cat_2(A,B,G,H),k6_cat_1(k11_cat_2(A,B),k12_cat_2(A,B,C,E),k12_cat_2(A,B,D,F)))))))))))))))))))) # label(t16_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3925 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,C) -> r4_nattra_1(u2_cat_1(A),u2_cat_1(C),u2_cat_1(A),u2_cat_1(C),k12_isocat_2(A,B,C,k10_isocat_2(A,B,C,D,E)),E) & r4_nattra_1(u2_cat_1(A),u2_cat_1(B),u2_cat_1(A),u2_cat_1(B),k11_isocat_2(A,B,C,k10_isocat_2(A,B,C,D,E)),D))))))))))) # label(t36_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3926 (all A all B all C all D (l1_cat_1(A) & l1_cat_1(C) & m2_cat_1(D,k11_cat_2(A,B),C) & v2_cat_1(C) & l1_cat_1(B) & v2_cat_1(B) & v2_cat_1(A) -> m2_cat_1(k5_isocat_2(A,B,C,D),A,k12_nattra_1(B,C)))) # label(dt_k5_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3927 (all A all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k1_tarski(A),B) & v1_funct_2(C,k1_tarski(A),B) & v1_funct_1(C) -> (all D (m2_relset_1(D,k1_tarski(A),B) & v1_funct_2(D,k1_tarski(A),B) & v1_funct_1(D) -> (k1_funct_1(C,A) = k1_funct_1(D,A) -> r4_nattra_1(k1_tarski(A),B,k1_tarski(A),B,C,D)))))))) # label(t3_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3928 (all A all B (k1_tarski(A) = u1_cat_1(k8_cat_1(A,B)) & u2_cat_1(k8_cat_1(A,B)) = k1_tarski(B))) # label(l11_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3929 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m2_cat_1(E,k11_cat_2(A,B),C) -> (r2_nattra_1(k11_cat_2(A,B),C,D,E) -> (all F (m2_nattra_1(F,k11_cat_2(A,B),C,D,E) -> (exists G (m2_nattra_1(G,A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E)) & (all H (m2_relset_1(H,k2_zfmisc_1(u1_cat_1(A),u1_cat_1(B)),u2_cat_1(C)) & v1_funct_2(H,k2_zfmisc_1(u1_cat_1(A),u1_cat_1(B)),u2_cat_1(C)) & v1_funct_1(H) -> (r4_nattra_1(u1_cat_1(k11_cat_2(A,B)),u2_cat_1(C),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(B)),u2_cat_1(C),F,H) -> (all I (m1_subset_1(I,u1_cat_1(A)) -> k4_tarski(k12_cat_2(k12_nattra_1(B,C),k12_nattra_1(B,C),k13_cat_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),I),k13_cat_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,E),I)),k1_cat_2(u1_cat_1(A),u1_cat_1(B),u2_cat_1(C),k1_fraenkel(u1_cat_1(B),u2_cat_1(C)),k2_cat_2(u1_cat_1(A),u1_cat_1(B),u2_cat_1(C),H),I)) = k5_nattra_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E),G,I)))))))) & r2_nattra_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E))))))))))))))) # label(t27_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3930 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_subset_1(F,u1_cat_1(B)) -> k13_cat_1(B,C,k14_cat_2(A,B,C,D,E),F) = k13_cat_1(k11_cat_2(A,B),C,D,k12_cat_2(A,B,E,F)))))))))))))) # label(t12_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3931 (all A all B (v2_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & l1_cat_1(A) -> k9_isocat_2(A,B) = k17_cat_2(A,B))) # label(redefinition_k9_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3932 (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,k11_cat_2(B,C)) -> k2_isocat_1(A,k11_cat_2(B,C),C,D,k9_isocat_2(B,C)) = k12_isocat_2(A,B,C,D))))))))) # label(d8_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3933 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_subset_1(F,u1_cat_1(A)) -> (k6_cat_1(A,E,F) != k1_xboole_0 -> (all G (m1_cat_1(G,A,E,F) -> m2_nattra_1(k7_funct_2(u1_cat_1(B),u2_cat_1(B),u2_cat_1(C),u6_cat_1(B),k3_isocat_2(A,B,C,D,G)),B,C,k14_cat_2(A,B,C,D,E),k14_cat_2(A,B,C,D,F)) & r2_nattra_1(B,C,k14_cat_2(A,B,C,D,E),k14_cat_2(A,B,C,D,F))))))))))))))))) # label(t17_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3934 (all A all B all C all D all E all F (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(C) & m2_cat_1(E,k11_cat_2(A,B),C) & m2_nattra_1(F,k11_cat_2(A,B),C,D,E) & m2_cat_1(D,k11_cat_2(A,B),C) & v2_cat_1(C) & l1_cat_1(B) -> m2_nattra_1(k6_isocat_2(A,B,C,D,E,F),A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E)))) # label(dt_k6_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3935 (all A all B all C all D all E (v2_cat_1(A) & v2_cat_1(B) & m2_cat_1(E,A,C) & m2_cat_1(D,A,B) & l1_cat_1(C) & v2_cat_1(C) & l1_cat_1(B) & l1_cat_1(A) -> k13_funct_3(D,E) = k10_isocat_2(A,B,C,D,E))) # label(redefinition_k10_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3936 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> k4_cat_1(A,k10_cat_1(A,k2_cat_1(A,B)),B) = B)))) # label(t7_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3937 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m2_cat_1(D,k12_nattra_1(A,B),B) -> (D = k2_isocat_2(A,B,C) <-> (all E (m2_cat_1(E,A,B) -> (all F (m2_cat_1(F,A,B) -> (all G (m2_nattra_1(G,A,B,E,F) -> (r2_nattra_1(A,B,E,F) -> k1_funct_1(D,k4_tarski(k4_tarski(E,F),G)) = k5_nattra_1(A,B,E,F,G,C))))))))))))))))) # label(d1_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3938 (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,k11_cat_2(B,C)) -> k11_isocat_2(A,B,C,D) = k2_isocat_1(A,k11_cat_2(B,C),B,D,k8_isocat_2(B,C)))))))))) # label(d7_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3939 (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,k11_cat_2(A,B),C) -> (all E (m2_cat_1(E,A,k12_nattra_1(B,C)) -> ((all F (m1_subset_1(F,u2_cat_1(A)) -> k4_tarski(k4_tarski(k14_cat_2(A,B,C,D,k2_cat_1(A,F)),k14_cat_2(A,B,C,D,k3_cat_1(A,F))),k4_isocat_2(A,B,C,D,F)) = k8_funct_2(u2_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),E,F))) <-> k5_isocat_2(A,B,C,D) = E))))))))))) # label(d4_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3940 (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,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u2_cat_1(A)) -> k4_isocat_2(A,B,C,D,E) = k7_funct_2(u1_cat_1(B),u2_cat_1(B),u2_cat_1(C),u6_cat_1(B),k3_isocat_2(A,B,C,D,E)))))))))))) # label(d3_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3941 $T # label(t10_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3942 (all A all B all C all D all E (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & v2_cat_1(C) & m2_cat_1(D,k11_cat_2(A,B),C) & m1_subset_1(E,u2_cat_1(A)) & l1_cat_1(C) & l1_cat_1(B) -> v1_funct_1(k3_isocat_2(A,B,C,D,E)) & m2_relset_1(k3_isocat_2(A,B,C,D,E),u2_cat_1(B),u2_cat_1(C)) & v1_funct_2(k3_isocat_2(A,B,C,D,E),u2_cat_1(B),u2_cat_1(C)))) # label(dt_k3_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3943 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> v8_cat_1(k7_isocat_2(A,B,C),k12_nattra_1(k11_cat_2(A,B),C),k12_nattra_1(A,k12_nattra_1(B,C))))))))) # label(t33_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3944 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> B = k4_cat_1(A,B,k10_cat_1(A,k3_cat_1(A,B))))))) # label(t6_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3945 $T # label(t23_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3946 (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,k11_cat_2(B,C)) -> (all E (m2_cat_1(E,A,k11_cat_2(B,C)) -> (r4_nattra_1(u2_cat_1(A),u2_cat_1(C),u2_cat_1(A),u2_cat_1(C),k12_isocat_2(A,B,C,D),k12_isocat_2(A,B,C,E)) & r4_nattra_1(u2_cat_1(A),u2_cat_1(B),u2_cat_1(A),u2_cat_1(B),k11_isocat_2(A,B,C,D),k11_isocat_2(A,B,C,E)) -> r4_nattra_1(u2_cat_1(A),u2_cat_1(k11_cat_2(B,C)),u2_cat_1(A),u2_cat_1(k11_cat_2(B,C)),D,E)))))))))))) # label(t37_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3947 (all A all B all C all D all E all F (m2_nattra_1(F,A,k11_cat_2(B,C),D,E) & m2_cat_1(E,A,k11_cat_2(B,C)) & m2_cat_1(D,A,k11_cat_2(B,C)) & l1_cat_1(C) & v2_cat_1(C) & l1_cat_1(B) & v2_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> m2_nattra_1(k14_isocat_2(A,B,C,D,E,F),A,C,k12_isocat_2(A,B,C,D),k12_isocat_2(A,B,C,E)))) # label(dt_k14_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3948 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> (all F (m1_subset_1(F,u1_cat_1(B)) -> (k1_xboole_0 != k6_cat_1(A,C,D) & k6_cat_1(B,E,F) != k1_xboole_0 <-> k1_xboole_0 != k6_cat_1(k11_cat_2(A,B),k12_cat_2(A,B,C,E),k12_cat_2(A,B,D,F))))))))))))))) # label(t13_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3949 $T # label(t22_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3950 (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,k11_cat_2(A,B),C) -> (all E (m2_cat_1(E,k11_cat_2(A,B),C) -> (r4_nattra_1(u2_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),u2_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E)) -> r4_nattra_1(u2_cat_1(k11_cat_2(A,B)),u2_cat_1(C),u2_cat_1(k11_cat_2(A,B)),u2_cat_1(C),D,E)))))))))))) # label(t26_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3951 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u2_cat_1(A)) -> (all F (m1_subset_1(F,u2_cat_1(A)) -> (k3_cat_1(A,F) = k2_cat_1(A,E) -> (all G (m2_nattra_1(G,B,C,k14_cat_2(A,B,C,D,k2_cat_1(A,F)),k14_cat_2(A,B,C,D,k2_cat_1(A,E))) -> (r4_nattra_1(u1_cat_1(B),u2_cat_1(C),u1_cat_1(B),u2_cat_1(C),G,k4_isocat_2(A,B,C,D,F)) -> r4_nattra_1(u1_cat_1(B),u2_cat_1(C),u1_cat_1(B),u2_cat_1(C),k4_isocat_2(A,B,C,D,k4_cat_1(A,F,E)),k8_nattra_1(B,C,k14_cat_2(A,B,C,D,k2_cat_1(A,F)),k14_cat_2(A,B,C,D,k2_cat_1(A,E)),k14_cat_2(A,B,C,D,k3_cat_1(A,E)),G,k4_isocat_2(A,B,C,D,E))))))))))))))))))) # label(t21_isocat_2) # label(axiom) # label(non_clause). [assumption]. 4.88/4.97 3952 (all A all B all C (v2_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(C) & l1_cat_1(C) & l1_cat_1(A) -> m2_cat_1(k17_isocat_2(A,B,C),k12_nattra_1(A,k11_cat_2(B,C)),k11_cat_2(k12_nattra_1(A,B),k12_nattra_1(A,C))))) # label(dt_k17_isocat_2) # label(axiom) # label(non_clause). [assumption]. 103.29/103.36 3953 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> k13_cat_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),E) = k14_cat_2(A,B,C,D,E))))))))))) # label(t24_isocat_2) # label(axiom) # label(non_clause). [assumption]. 103.29/103.36 3954 -(all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,k11_cat_2(B,C)) -> (all E (m2_cat_1(E,A,k11_cat_2(B,C)) -> (r2_nattra_1(A,k11_cat_2(B,C),D,E) -> r2_nattra_1(A,B,k11_isocat_2(A,B,C,D),k11_isocat_2(A,B,C,E)) & r2_nattra_1(A,C,k12_isocat_2(A,B,C,D),k12_isocat_2(A,B,C,E))))))))))))) # label(t38_isocat_2) # label(negated_conjecture) # label(non_clause). [assumption]. 103.29/103.36 103.29/103.36 ============================== end of process non-clausal formulas === 103.29/103.36 103.29/103.36 ============================== PROCESS INITIAL CLAUSES =============== 103.29/103.36 103.29/103.36 ============================== PREDICATE ELIMINATION ================= 103.29/103.36 3955 p1_s1_xboole_0(A) | -r2_hidden(A,c6) # label(s1_xboole_0) # label(axiom). [clausify(44)]. 103.29/103.36 3956 -r2_hidden(A,f1_s1_xboole_0) | -p1_s1_xboole_0(A) | r2_hidden(A,c6) # label(s1_xboole_0) # label(axiom). [clausify(44)]. 103.29/103.36 3957 r2_hidden(A,c12) | -p1_s1_subset_1(A) | -r2_hidden(A,f1_s1_subset_1) # label(s1_subset_1) # label(axiom). [clausify(540)]. 103.29/103.36 3958 -r2_hidden(A,c12) | p1_s1_subset_1(A) # label(s1_subset_1) # label(axiom). [clausify(540)]. 103.29/103.36 3959 -m1_subset_1(A,f1_s3_subset_1) | p1_s3_subset_1(A) | -r2_hidden(A,c13) # label(s3_subset_1) # label(axiom). [clausify(570)]. 103.29/103.36 3960 -m1_subset_1(A,f1_s3_subset_1) | -p1_s3_subset_1(A) | r2_hidden(A,c13) # label(s3_subset_1) # label(axiom). [clausify(570)]. 103.29/103.36 3961 r2_hidden(k4_tarski(A,B),c15) | -r2_hidden(B,f2_s1_relat_1) | -p1_s1_relat_1(A,B) | -r2_hidden(A,f1_s1_relat_1) # label(s1_relat_1) # label(axiom). [clausify(591)]. 103.29/103.36 3962 -r2_hidden(k4_tarski(A,B),c15) | p1_s1_relat_1(A,B) # label(s1_relat_1) # label(axiom). [clausify(591)]. 103.29/103.36 3963 v3_ordinal1(A) | -v1_ordinal1(A) | -v2_ordinal1(A) # label(d4_ordinal1) # label(axiom). [clausify(1030)]. 103.29/103.36 3964 -v3_ordinal1(A) | v2_ordinal1(k3_tarski(A)) # label(fc4_ordinal1) # label(axiom). [clausify(1009)]. 103.29/103.36 3965 -v1_relat_1(A) | -v1_funct_1(A) | -v5_ordinal1(A) | v2_ordinal1(k1_relat_1(A)) # label(fc5_ordinal1) # label(axiom). [clausify(1012)]. 103.29/103.36 3966 -v1_xboole_0(A) | v2_ordinal1(A) # label(cc3_ordinal1) # label(axiom). [clausify(1015)]. 103.29/103.36 3967 -v3_ordinal1(A) | v2_ordinal1(A) # label(d4_ordinal1) # label(axiom). [clausify(1030)]. 103.29/103.36 Derived: v3_ordinal1(A) | -v1_ordinal1(A) | -v1_xboole_0(A). [resolve(3963,c,3966,b)]. 103.29/103.36 3968 -v3_ordinal1(A) | v2_ordinal1(A) # label(cc1_ordinal1) # label(axiom). [clausify(1038)]. 103.29/103.36 3969 v2_ordinal1(c43) # label(rc2_ordinal1) # label(axiom). [clausify(1048)]. 103.29/103.36 Derived: v3_ordinal1(c43) | -v1_ordinal1(c43). [resolve(3969,a,3963,c)]. 103.29/103.36 3970 -v2_ordinal1(A) | -r2_hidden(B,A) | -r2_hidden(C,A) | r2_hidden(B,C) | C = B | r2_hidden(C,B) # label(d3_ordinal1) # label(axiom). [clausify(1057)]. 103.29/103.36 Derived: -r2_hidden(A,k3_tarski(B)) | -r2_hidden(C,k3_tarski(B)) | r2_hidden(A,C) | C = A | r2_hidden(C,A) | -v3_ordinal1(B). [resolve(3970,a,3964,b)]. 103.29/103.36 Derived: -r2_hidden(A,k1_relat_1(B)) | -r2_hidden(C,k1_relat_1(B)) | r2_hidden(A,C) | C = A | r2_hidden(C,A) | -v1_relat_1(B) | -v1_funct_1(B) | -v5_ordinal1(B). [resolve(3970,a,3965,d)]. 103.29/103.36 Derived: -r2_hidden(A,B) | -r2_hidden(C,B) | r2_hidden(A,C) | C = A | r2_hidden(C,A) | -v1_xboole_0(B). [resolve(3970,a,3966,b)]. 103.29/103.36 Derived: -r2_hidden(A,B) | -r2_hidden(C,B) | r2_hidden(A,C) | C = A | r2_hidden(C,A) | -v3_ordinal1(B). [resolve(3970,a,3967,b)]. 103.29/103.36 Derived: -r2_hidden(A,c43) | -r2_hidden(B,c43) | r2_hidden(A,B) | B = A | r2_hidden(B,A). [resolve(3970,a,3969,a)]. 103.29/103.36 3971 v2_ordinal1(A) | r2_hidden(f184(A),A) # label(d3_ordinal1) # label(axiom). [clausify(1057)]. 103.29/103.36 Derived: r2_hidden(f184(A),A) | v3_ordinal1(A) | -v1_ordinal1(A). [resolve(3971,a,3963,c)]. 103.29/103.36 Derived: r2_hidden(f184(A),A) | -r2_hidden(B,A) | -r2_hidden(C,A) | r2_hidden(B,C) | C = B | r2_hidden(C,B). [resolve(3971,a,3970,a)]. 108.37/108.40 3972 v2_ordinal1(A) | r2_hidden(f185(A),A) # label(d3_ordinal1) # label(axiom). [clausify(1057)]. 108.37/108.40 Derived: r2_hidden(f185(A),A) | v3_ordinal1(A) | -v1_ordinal1(A). [resolve(3972,a,3963,c)]. 108.37/108.40 Derived: r2_hidden(f185(A),A) | -r2_hidden(B,A) | -r2_hidden(C,A) | r2_hidden(B,C) | C = B | r2_hidden(C,B). [resolve(3972,a,3970,a)]. 108.37/108.40 3973 v2_ordinal1(A) | -r2_hidden(f184(A),f185(A)) # label(d3_ordinal1) # label(axiom). [clausify(1057)]. 108.37/108.40 Derived: -r2_hidden(f184(A),f185(A)) | v3_ordinal1(A) | -v1_ordinal1(A). [resolve(3973,a,3963,c)]. 108.37/108.40 Derived: -r2_hidden(f184(A),f185(A)) | -r2_hidden(B,A) | -r2_hidden(C,A) | r2_hidden(B,C) | C = B | r2_hidden(C,B). [resolve(3973,a,3970,a)]. 108.37/108.40 3974 v2_ordinal1(A) | f185(A) != f184(A) # label(d3_ordinal1) # label(axiom). [clausify(1057)]. 108.37/108.40 Derived: f185(A) != f184(A) | v3_ordinal1(A) | -v1_ordinal1(A). [resolve(3974,a,3963,c)]. 108.37/108.40 Derived: f185(A) != f184(A) | -r2_hidden(B,A) | -r2_hidden(C,A) | r2_hidden(B,C) | C = B | r2_hidden(C,B). [resolve(3974,a,3970,a)]. 108.37/108.40 3975 v2_ordinal1(A) | -r2_hidden(f185(A),f184(A)) # label(d3_ordinal1) # label(axiom). [clausify(1057)]. 108.37/108.40 Derived: -r2_hidden(f185(A),f184(A)) | v3_ordinal1(A) | -v1_ordinal1(A). [resolve(3975,a,3963,c)]. 108.37/108.40 Derived: -r2_hidden(f185(A),f184(A)) | -r2_hidden(B,A) | -r2_hidden(C,A) | r2_hidden(B,C) | C = B | r2_hidden(C,B). [resolve(3975,a,3970,a)]. 108.37/108.40 3976 v2_ordinal1(c45) # label(rc3_ordinal1) # label(axiom). [clausify(1065)]. 108.37/108.40 Derived: -r2_hidden(A,c45) | -r2_hidden(B,c45) | r2_hidden(A,B) | B = A | r2_hidden(B,A). [resolve(3976,a,3970,a)]. 108.37/108.40 3977 v2_ordinal1(k1_xboole_0) # label(fc2_ordinal1_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom). [assumption]. 108.37/108.40 Derived: -r2_hidden(A,k1_xboole_0) | -r2_hidden(B,k1_xboole_0) | r2_hidden(A,B) | B = A | r2_hidden(B,A). [resolve(3977,a,3970,a)]. 108.37/108.40 3978 v2_ordinal1(c48) # label(rc1_ordinal1) # label(axiom). [clausify(1086)]. 108.37/108.40 Derived: v3_ordinal1(c48) | -v1_ordinal1(c48). [resolve(3978,a,3963,c)]. 108.37/108.40 Derived: -r2_hidden(A,c48) | -r2_hidden(B,c48) | r2_hidden(A,B) | B = A | r2_hidden(B,A). [resolve(3978,a,3970,a)]. 108.37/108.40 3979 -v2_ordinal1(A) | -v1_ordinal1(A) | v3_ordinal1(A) # label(cc2_ordinal1) # label(axiom). [clausify(1087)]. 108.37/108.40 Derived: -v1_ordinal1(k3_tarski(A)) | v3_ordinal1(k3_tarski(A)) | -v3_ordinal1(A). [resolve(3979,a,3964,b)]. 108.37/108.40 Derived: -v1_ordinal1(k1_relat_1(A)) | v3_ordinal1(k1_relat_1(A)) | -v1_relat_1(A) | -v1_funct_1(A) | -v5_ordinal1(A). [resolve(3979,a,3965,d)]. 108.37/108.40 Derived: -v1_ordinal1(c45) | v3_ordinal1(c45). [resolve(3979,a,3976,a)]. 108.37/108.40 Derived: -v1_ordinal1(k1_xboole_0) | v3_ordinal1(k1_xboole_0). [resolve(3979,a,3977,a)]. 108.37/108.40 3980 -v3_ordinal1(A) | v2_ordinal1(k1_ordinal1(A)) # label(fc3_ordinal1) # label(axiom). [clausify(1089)]. 108.37/108.40 Derived: -v3_ordinal1(A) | -r2_hidden(B,k1_ordinal1(A)) | -r2_hidden(C,k1_ordinal1(A)) | r2_hidden(B,C) | C = B | r2_hidden(C,B). [resolve(3980,b,3970,a)]. 108.37/108.40 3981 v2_ordinal1(c90) # label(rc1_ordinal2) # label(axiom). [clausify(2011)]. 108.37/108.40 Derived: -r2_hidden(A,c90) | -r2_hidden(B,c90) | r2_hidden(A,B) | B = A | r2_hidden(B,A). [resolve(3981,a,3970,a)]. 108.37/108.40 3982 -v1_funct_1(A) | -v1_ordinal2(A) | -v3_ordinal1(B) | -v5_ordinal1(A) | -v1_relat_1(A) | v2_ordinal1(k1_funct_1(A,B)) # label(fc3_ordinal2) # label(axiom). [clausify(2020)]. 108.37/108.40 Derived: -v1_funct_1(A) | -v1_ordinal2(A) | -v3_ordinal1(B) | -v5_ordinal1(A) | -v1_relat_1(A) | -r2_hidden(C,k1_funct_1(A,B)) | -r2_hidden(D,k1_funct_1(A,B)) | r2_hidden(C,D) | D = C | r2_hidden(D,C). [resolve(3982,f,3970,a)]. 108.37/108.40 3983 v2_ordinal1(k5_ordinal2) # label(fc1_ordinal2_AndRHS_AndLHS) # label(axiom). [assumption]. 108.37/108.40 Derived: -r2_hidden(A,k5_ordinal2) | -r2_hidden(B,k5_ordinal2) | r2_hidden(A,B) | B = A | r2_hidden(B,A). [resolve(3983,a,3970,a)]. 108.37/108.40 3984 v2_ordinal1(f556(A)) # label(rc2_finset_1) # label(axiom). [clausify(2181)]. 108.37/108.40 Derived: -r2_hidden(A,f556(B)) | -r2_hidden(C,f556(B)) | r2_hidden(A,C) | C = A | r2_hidden(C,A). [resolve(3984,a,3970,a)]. 108.37/108.40 3985 -m1_subset_1(A,k5_numbers) | v2_ordinal1(A) # label(cc3_card_1) # label(axiom). [clausify(2303)]. 108.37/108.40 Derived: -m1_subset_1(A,k5_numbers) | -r2_hidden(B,A) | -r2_hidden(C,A) | r2_hidden(B,C) | C = B | r2_hidden(C,B). [resolve(3985,b,3970,a)]. 122.65/122.75 3986 -v1_card_1(A) | v2_ordinal1(A) # label(cc1_card_1) # label(axiom). [clausify(2332)]. 122.65/122.75 Derived: -v1_card_1(A) | -r2_hidden(B,A) | -r2_hidden(C,A) | r2_hidden(B,C) | C = B | r2_hidden(C,B). [resolve(3986,b,3970,a)]. 122.65/122.75 3987 -v3_ordinal1(A) | v2_ordinal1(k3_card_1(A)) # label(fc1_card_1) # label(axiom). [clausify(2342)]. 122.65/122.75 Derived: -v3_ordinal1(A) | v3_ordinal1(k3_card_1(A)) | -v1_ordinal1(k3_card_1(A)). [resolve(3987,b,3963,c)]. 122.65/122.75 Derived: -v3_ordinal1(A) | -r2_hidden(B,k3_card_1(A)) | -r2_hidden(C,k3_card_1(A)) | r2_hidden(B,C) | C = B | r2_hidden(C,B). [resolve(3987,b,3970,a)]. 122.65/122.75 3988 -v1_finset_1(A) | v2_ordinal1(k1_card_1(A)) # label(fc2_card_1) # label(axiom). [clausify(2349)]. 122.65/122.75 Derived: -v1_finset_1(A) | -r2_hidden(B,k1_card_1(A)) | -r2_hidden(C,k1_card_1(A)) | r2_hidden(B,C) | C = B | r2_hidden(C,B). [resolve(3988,b,3970,a)]. 122.65/122.75 3989 -m1_subset_1(A,k5_numbers) | v2_ordinal1(A) # label(cc2_card_1) # label(axiom). [clausify(2351)]. 122.65/122.75 Derived: -m1_subset_1(A,k5_numbers) | v3_ordinal1(A) | -v1_ordinal1(A). [resolve(3989,b,3963,c)]. 122.65/122.75 3990 v2_ordinal1(c174) # label(rc2_card_1) # label(axiom). [clausify(2371)]. 122.65/122.75 Derived: v3_ordinal1(c174) | -v1_ordinal1(c174). [resolve(3990,a,3963,c)]. 122.65/122.75 Derived: -r2_hidden(A,c174) | -r2_hidden(B,c174) | r2_hidden(A,B) | B = A | r2_hidden(B,A). [resolve(3990,a,3970,a)]. 122.65/122.75 3991 v6_ordinal1(A) | r2_hidden(f181(A),A) # label(d9_ordinal1) # label(axiom). [clausify(1040)]. 122.65/122.75 3992 -v6_ordinal1(A) | r2_hidden(f179(A),A) | v1_relat_1(k3_tarski(A)) # label(t49_ordinal1) # label(axiom). [clausify(1034)]. 122.65/122.75 3993 -v6_ordinal1(A) | r2_hidden(f179(A),A) | v5_ordinal1(k3_tarski(A)) # label(t49_ordinal1) # label(axiom). [clausify(1034)]. 122.65/122.75 3994 -v6_ordinal1(A) | r2_hidden(f179(A),A) | v1_funct_1(k3_tarski(A)) # label(t49_ordinal1) # label(axiom). [clausify(1034)]. 122.65/122.75 3995 -v6_ordinal1(A) | -v1_relat_1(f179(A)) | -v5_ordinal1(f179(A)) | -v1_funct_1(f179(A)) | v1_relat_1(k3_tarski(A)) # label(t49_ordinal1) # label(axiom). [clausify(1034)]. 122.65/122.75 3996 -v6_ordinal1(A) | -v1_relat_1(f179(A)) | -v5_ordinal1(f179(A)) | -v1_funct_1(f179(A)) | v5_ordinal1(k3_tarski(A)) # label(t49_ordinal1) # label(axiom). [clausify(1034)]. 122.65/122.75 3997 -v6_ordinal1(A) | -v1_relat_1(f179(A)) | -v5_ordinal1(f179(A)) | -v1_funct_1(f179(A)) | v1_funct_1(k3_tarski(A)) # label(t49_ordinal1) # label(axiom). [clausify(1034)]. 122.65/122.75 3998 -v6_ordinal1(A) | -r2_hidden(B,A) | -r2_hidden(C,A) | r3_xboole_0(C,B) # label(d9_ordinal1) # label(axiom). [clausify(1040)]. 122.65/122.75 Derived: r2_hidden(f181(A),A) | r2_hidden(f179(A),A) | v1_relat_1(k3_tarski(A)). [resolve(3991,a,3992,a)]. 122.65/122.75 Derived: r2_hidden(f181(A),A) | r2_hidden(f179(A),A) | v5_ordinal1(k3_tarski(A)). [resolve(3991,a,3993,a)]. 122.65/122.75 Derived: r2_hidden(f181(A),A) | r2_hidden(f179(A),A) | v1_funct_1(k3_tarski(A)). [resolve(3991,a,3994,a)]. 122.65/122.75 Derived: r2_hidden(f181(A),A) | -v1_relat_1(f179(A)) | -v5_ordinal1(f179(A)) | -v1_funct_1(f179(A)) | v1_relat_1(k3_tarski(A)). [resolve(3991,a,3995,a)]. 122.65/122.75 Derived: r2_hidden(f181(A),A) | -v1_relat_1(f179(A)) | -v5_ordinal1(f179(A)) | -v1_funct_1(f179(A)) | v5_ordinal1(k3_tarski(A)). [resolve(3991,a,3996,a)]. 122.65/122.75 Derived: r2_hidden(f181(A),A) | -v1_relat_1(f179(A)) | -v5_ordinal1(f179(A)) | -v1_funct_1(f179(A)) | v1_funct_1(k3_tarski(A)). [resolve(3991,a,3997,a)]. 122.65/122.75 Derived: r2_hidden(f181(A),A) | -r2_hidden(B,A) | -r2_hidden(C,A) | r3_xboole_0(C,B). [resolve(3991,a,3998,a)]. 122.65/122.75 3999 v6_ordinal1(A) | r2_hidden(f180(A),A) # label(d9_ordinal1) # label(axiom). [clausify(1040)]. 122.65/122.75 Derived: r2_hidden(f180(A),A) | r2_hidden(f179(A),A) | v1_relat_1(k3_tarski(A)). [resolve(3999,a,3992,a)]. 122.65/122.75 Derived: r2_hidden(f180(A),A) | r2_hidden(f179(A),A) | v5_ordinal1(k3_tarski(A)). [resolve(3999,a,3993,a)]. 122.65/122.75 Derived: r2_hidden(f180(A),A) | r2_hidden(f179(A),A) | v1_funct_1(k3_tarski(A)). [resolve(3999,a,3994,a)]. 122.65/122.75 Derived: r2_hidden(f180(A),A) | -v1_relat_1(f179(A)) | -v5_ordinal1(f179(A)) | -v1_funct_1(f179(A)) | v1_relat_1(k3_tarski(A)). [resolve(3999,a,3995,a)]. 122.65/122.75 Derived: r2_hidden(f180(A),A) | -v1_relat_1(f179(A)) | -v5_ordinal1(f179(A)) | -v1_funct_1(f179(A)) | v5_ordinal1(k3_tarski(A)). [resolve(3999,a,3996,a)]. 161.65/161.77 Derived: r2_hidden(f180(A),A) | -v1_relat_1(f179(A)) | -v5_ordinal1(f179(A)) | -v1_funct_1(f179(A)) | v1_funct_1(k3_tarski(A)). [resolve(3999,a,3997,a)]. 161.65/161.77 Derived: r2_hidden(f180(A),A) | -r2_hidden(B,A) | -r2_hidden(C,A) | r3_xboole_0(C,B). [resolve(3999,a,3998,a)]. 161.65/161.77 4000 v6_ordinal1(A) | -r3_xboole_0(f180(A),f181(A)) # label(d9_ordinal1) # label(axiom). [clausify(1040)]. 161.65/161.77 Derived: -r3_xboole_0(f180(A),f181(A)) | r2_hidden(f179(A),A) | v1_relat_1(k3_tarski(A)). [resolve(4000,a,3992,a)]. 161.65/161.77 Derived: -r3_xboole_0(f180(A),f181(A)) | r2_hidden(f179(A),A) | v5_ordinal1(k3_tarski(A)). [resolve(4000,a,3993,a)]. 161.65/161.77 Derived: -r3_xboole_0(f180(A),f181(A)) | r2_hidden(f179(A),A) | v1_funct_1(k3_tarski(A)). [resolve(4000,a,3994,a)]. 161.65/161.77 Derived: -r3_xboole_0(f180(A),f181(A)) | -v1_relat_1(f179(A)) | -v5_ordinal1(f179(A)) | -v1_funct_1(f179(A)) | v1_relat_1(k3_tarski(A)). [resolve(4000,a,3995,a)]. 161.65/161.77 Derived: -r3_xboole_0(f180(A),f181(A)) | -v1_relat_1(f179(A)) | -v5_ordinal1(f179(A)) | -v1_funct_1(f179(A)) | v5_ordinal1(k3_tarski(A)). [resolve(4000,a,3996,a)]. 161.65/161.77 Derived: -r3_xboole_0(f180(A),f181(A)) | -v1_relat_1(f179(A)) | -v5_ordinal1(f179(A)) | -v1_funct_1(f179(A)) | v1_funct_1(k3_tarski(A)). [resolve(4000,a,3997,a)]. 161.65/161.77 Derived: -r3_xboole_0(f180(A),f181(A)) | -r2_hidden(B,A) | -r2_hidden(C,A) | r3_xboole_0(C,B). [resolve(4000,a,3998,a)]. 161.65/161.77 4001 r2_hidden(f550(A),A) | -v6_ordinal1(A) | k1_xboole_0 = A | -v1_finset_1(A) # label(t30_finset_1) # label(axiom). [clausify(2144)]. 161.65/161.77 Derived: r2_hidden(f550(A),A) | k1_xboole_0 = A | -v1_finset_1(A) | r2_hidden(f181(A),A). [resolve(4001,b,3991,a)]. 161.65/161.77 Derived: r2_hidden(f550(A),A) | k1_xboole_0 = A | -v1_finset_1(A) | r2_hidden(f180(A),A). [resolve(4001,b,3999,a)]. 161.65/161.77 Derived: r2_hidden(f550(A),A) | k1_xboole_0 = A | -v1_finset_1(A) | -r3_xboole_0(f180(A),f181(A)). [resolve(4001,b,4000,a)]. 161.65/161.77 4002 -r2_hidden(A,B) | r1_tarski(f550(B),A) | -v6_ordinal1(B) | k1_xboole_0 = B | -v1_finset_1(B) # label(t30_finset_1) # label(axiom). [clausify(2144)]. 161.65/161.77 Derived: -r2_hidden(A,B) | r1_tarski(f550(B),A) | k1_xboole_0 = B | -v1_finset_1(B) | r2_hidden(f181(B),B). [resolve(4002,c,3991,a)]. 161.65/161.77 Derived: -r2_hidden(A,B) | r1_tarski(f550(B),A) | k1_xboole_0 = B | -v1_finset_1(B) | r2_hidden(f180(B),B). [resolve(4002,c,3999,a)]. 161.65/161.77 Derived: -r2_hidden(A,B) | r1_tarski(f550(B),A) | k1_xboole_0 = B | -v1_finset_1(B) | -r3_xboole_0(f180(B),f181(B)). [resolve(4002,c,4000,a)]. 161.65/161.77 4003 -v6_ordinal1(A) | -r2_hidden(B,A) | r1_tarski(B,f555(A)) | k1_xboole_0 = A | -v1_finset_1(A) # label(t31_finset_1) # label(axiom). [clausify(2168)]. 161.65/161.77 Derived: -r2_hidden(A,B) | r1_tarski(A,f555(B)) | k1_xboole_0 = B | -v1_finset_1(B) | r2_hidden(f181(B),B). [resolve(4003,a,3991,a)]. 161.65/161.77 Derived: -r2_hidden(A,B) | r1_tarski(A,f555(B)) | k1_xboole_0 = B | -v1_finset_1(B) | r2_hidden(f180(B),B). [resolve(4003,a,3999,a)]. 161.65/161.77 Derived: -r2_hidden(A,B) | r1_tarski(A,f555(B)) | k1_xboole_0 = B | -v1_finset_1(B) | -r3_xboole_0(f180(B),f181(B)). [resolve(4003,a,4000,a)]. 161.65/161.77 4004 -v6_ordinal1(A) | r2_hidden(f555(A),A) | k1_xboole_0 = A | -v1_finset_1(A) # label(t31_finset_1) # label(axiom). [clausify(2168)]. 161.65/161.77 Derived: r2_hidden(f555(A),A) | k1_xboole_0 = A | -v1_finset_1(A) | r2_hidden(f181(A),A). [resolve(4004,a,3991,a)]. 161.65/161.77 Derived: r2_hidden(f555(A),A) | k1_xboole_0 = A | -v1_finset_1(A) | r2_hidden(f180(A),A). [resolve(4004,a,3999,a)]. 161.65/161.77 Derived: r2_hidden(f555(A),A) | k1_xboole_0 = A | -v1_finset_1(A) | -r3_xboole_0(f180(A),f181(A)). [resolve(4004,a,4000,a)]. 161.65/161.77 4005 p1_s1_relset_1(A,B) | -r2_hidden(k4_tarski(A,B),c49) # label(s1_relset_1) # label(axiom). [clausify(1109)]. 161.65/161.77 4006 -p1_s1_relset_1(A,B) | -r2_hidden(B,f2_s1_relset_1) | -r2_hidden(A,f1_s1_relset_1) | r2_hidden(k4_tarski(A,B),c49) # label(s1_relset_1) # label(axiom). [clausify(1109)]. 161.65/161.77 4007 -m1_subset_1(A,f1_s2_relset_1) | -m1_subset_1(B,f2_s2_relset_1) | r2_hidden(k4_tarski(A,B),c50) | -p1_s2_relset_1(A,B) # label(s2_relset_1) # label(axiom). [clausify(1145)]. 161.65/161.77 4008 -m1_subset_1(A,f1_s2_relset_1) | -m1_subset_1(B,f2_s2_relset_1) | Cputime limit exceeded (core dumped) 180.04/180.09 EOF