0.11/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s 0.13/0.34 % Computer : n015.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 180 0.13/0.34 % DateTime : Thu Aug 29 16:28:23 EDT 2019 0.13/0.34 % CPUTime : 16.81/16.18 ============================== Prover9 =============================== 16.81/16.18 Prover9 (32) version 2009-11A, November 2009. 16.81/16.18 Process 2792 was started by sandbox on n015.cluster.edu, 16.81/16.18 Thu Aug 29 16:28:37 2019 16.81/16.18 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 180 -f /tmp/Prover9_2335_n015.cluster.edu". 16.81/16.18 ============================== end of head =========================== 16.81/16.18 16.81/16.18 ============================== INPUT ================================= 16.81/16.18 16.81/16.18 % Reading from file /tmp/Prover9_2335_n015.cluster.edu 16.81/16.18 16.81/16.18 set(prolog_style_variables). 16.81/16.18 set(auto2). 16.81/16.18 % set(auto2) -> set(auto). 16.81/16.18 % set(auto) -> set(auto_inference). 16.81/16.18 % set(auto) -> set(auto_setup). 16.81/16.18 % set(auto_setup) -> set(predicate_elim). 16.81/16.18 % set(auto_setup) -> assign(eq_defs, unfold). 16.81/16.18 % set(auto) -> set(auto_limits). 16.81/16.18 % set(auto_limits) -> assign(max_weight, "100.000"). 16.81/16.18 % set(auto_limits) -> assign(sos_limit, 20000). 16.81/16.18 % set(auto) -> set(auto_denials). 16.81/16.18 % set(auto) -> set(auto_process). 16.81/16.18 % set(auto2) -> assign(new_constants, 1). 16.81/16.18 % set(auto2) -> assign(fold_denial_max, 3). 16.81/16.18 % set(auto2) -> assign(max_weight, "200.000"). 16.81/16.18 % set(auto2) -> assign(max_hours, 1). 16.81/16.18 % assign(max_hours, 1) -> assign(max_seconds, 3600). 16.81/16.18 % set(auto2) -> assign(max_seconds, 0). 16.81/16.18 % set(auto2) -> assign(max_minutes, 5). 16.81/16.18 % assign(max_minutes, 5) -> assign(max_seconds, 300). 16.81/16.18 % set(auto2) -> set(sort_initial_sos). 16.81/16.18 % set(auto2) -> assign(sos_limit, -1). 16.81/16.18 % set(auto2) -> assign(lrs_ticks, 3000). 16.81/16.18 % set(auto2) -> assign(max_megs, 400). 16.81/16.18 % set(auto2) -> assign(stats, some). 16.81/16.18 % set(auto2) -> clear(echo_input). 16.81/16.18 % set(auto2) -> set(quiet). 16.81/16.18 % set(auto2) -> clear(print_initial_clauses). 16.81/16.18 % set(auto2) -> clear(print_given). 16.81/16.18 assign(lrs_ticks,-1). 16.81/16.18 assign(sos_limit,10000). 16.81/16.18 assign(order,kbo). 16.81/16.18 set(lex_order_vars). 16.81/16.18 clear(print_given). 16.81/16.18 16.81/16.18 % formulas(sos). % not echoed (14360 formulas) 16.81/16.18 16.81/16.18 ============================== end of input ========================== 16.81/16.18 16.81/16.18 % From the command line: assign(max_seconds, 180). 16.81/16.18 16.81/16.18 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 16.81/16.19 16.81/16.19 % Formulas that are not ordinary clauses: 16.81/16.19 1 (all A all B (r2_hidden(A,B) -> -r2_hidden(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 2 $T # label(t8_tarski) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 3 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 4 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 5 (all A all B r1_tarski(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 6 (all A all B k2_tarski(A,B) = k2_tarski(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 7 $T # label(dt_k3_tarski) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 12 $T # label(t3_tarski) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 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]. 16.81/16.19 14 $T # label(t1_tarski) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 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]. 16.81/16.19 16 $T # label(t6_tarski) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 20 $T # label(t4_tarski) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 21 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 22 $T # label(t5_tarski) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 28 (all A ((all B -r2_hidden(B,A)) <-> A = k1_xboole_0)) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 29 (all A all B r3_xboole_0(A,A)) # label(reflexivity_r3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 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]. 16.81/16.19 31 (exists A v1_xboole_0(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 34 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 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]. 16.81/16.19 36 (all A all B A = k2_xboole_0(A,A)) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 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]. 16.81/16.19 38 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 39 (all A all B A = k3_xboole_0(A,A)) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 42 $T # label(dt_k5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 43 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 48 (all A (k1_xboole_0 = A <-> v1_xboole_0(A))) # label(d5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 56 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 59 (exists A -v1_xboole_0(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 60 (all A all B -r2_xboole_0(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 61 (all A (v1_xboole_0(A) -> k1_xboole_0 = A)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 62 (all A A = k2_xboole_0(A,k1_xboole_0)) # label(t1_boole) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 63 (all A all B -(r2_hidden(A,B) & v1_xboole_0(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 64 (all A k3_xboole_0(A,k1_xboole_0) = k1_xboole_0) # label(t2_boole) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 65 (all A A = k5_xboole_0(A,k1_xboole_0)) # label(t5_boole) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 66 (all A k1_xboole_0 = k4_xboole_0(k1_xboole_0,A)) # label(t4_boole) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 67 (all A k4_xboole_0(A,k1_xboole_0) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 68 (all A all B -(v1_xboole_0(A) & A != B & v1_xboole_0(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 73 (all A r1_tarski(k1_xboole_0,A)) # label(t2_xboole_1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 79 (all A all B r1_tarski(k4_xboole_0(A,B),A)) # label(t36_xboole_1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 87 (all A all B r1_tarski(k3_xboole_0(A,B),A)) # label(t17_xboole_1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 94 (all A all B r1_tarski(A,k2_xboole_0(A,B))) # label(t7_xboole_1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 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]. 16.81/16.19 98 (all A (r1_tarski(A,k1_xboole_0) -> A = k1_xboole_0)) # label(t3_xboole_1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 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]. 16.81/16.19 100 (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]. 16.81/16.19 101 (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]. 16.81/16.19 102 (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]. 16.81/16.19 103 (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]. 16.81/16.19 104 (all A all B -(r2_xboole_0(B,A) & r2_xboole_0(A,B))) # label(t57_xboole_1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 105 (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]. 16.81/16.19 106 (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]. 16.81/16.19 107 (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]. 16.81/16.19 108 (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]. 16.81/16.19 109 (all A all B r1_xboole_0(k4_xboole_0(A,B),B)) # label(t79_xboole_1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 110 (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]. 16.81/16.19 111 (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]. 16.81/16.19 112 (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]. 16.81/16.19 113 (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]. 16.81/16.19 114 (all A (A != k1_xboole_0 -> r2_xboole_0(k1_xboole_0,A))) # label(t61_xboole_1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 115 (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]. 16.81/16.19 116 (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]. 16.81/16.19 117 (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]. 16.81/16.19 118 (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]. 16.81/16.19 119 (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]. 16.81/16.19 120 (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]. 16.81/16.19 121 (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]. 16.81/16.19 122 (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]. 16.81/16.19 123 (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]. 16.81/16.19 124 (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]. 16.81/16.19 125 (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]. 16.81/16.19 126 (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]. 16.81/16.19 127 (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]. 16.81/16.19 128 (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]. 16.81/16.19 129 (all A -r2_xboole_0(A,k1_xboole_0)) # label(t62_xboole_1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 130 (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]. 16.81/16.19 131 (all A k1_xboole_0 = k5_xboole_0(A,A)) # label(t92_xboole_1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 132 (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]. 16.81/16.19 133 (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]. 16.81/16.19 134 (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]. 16.81/16.19 135 (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]. 16.81/16.19 136 (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]. 16.81/16.19 137 (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]. 16.81/16.19 138 (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]. 16.81/16.19 139 (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]. 16.81/16.19 140 (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]. 16.81/16.19 141 (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]. 16.81/16.19 142 (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]. 16.81/16.19 143 (all A all B (r1_tarski(A,B) -> k2_xboole_0(A,B) = B)) # label(t12_xboole_1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 144 (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]. 16.81/16.19 145 (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]. 16.81/16.19 146 (all A all B -(r1_tarski(A,B) & r2_xboole_0(B,A))) # label(t60_xboole_1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 147 (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]. 16.81/16.19 148 (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]. 16.81/16.19 149 (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]. 16.81/16.19 150 (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]. 16.81/16.19 151 (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]. 16.81/16.19 152 (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]. 16.81/16.19 153 (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]. 16.81/16.19 154 (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]. 16.81/16.19 155 (all A r1_xboole_0(A,k1_xboole_0)) # label(t65_xboole_1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 156 (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]. 16.81/16.19 157 (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]. 16.81/16.19 158 (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]. 16.81/16.19 159 (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]. 16.81/16.19 160 (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]. 16.81/16.19 161 (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]. 16.81/16.19 162 (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]. 16.81/16.19 163 (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]. 16.81/16.19 164 (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]. 16.81/16.19 165 (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]. 16.81/16.19 166 (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]. 16.81/16.19 167 (all A all B A = k2_xboole_0(A,k3_xboole_0(A,B))) # label(t22_xboole_1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 168 (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]. 16.81/16.19 169 (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]. 16.81/16.19 170 (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]. 16.81/16.19 171 (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]. 16.81/16.19 172 (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]. 16.81/16.19 173 (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]. 16.81/16.19 174 (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]. 16.81/16.19 175 (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]. 16.81/16.19 176 (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]. 16.81/16.19 177 (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]. 16.81/16.19 178 (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]. 16.81/16.19 179 (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]. 16.81/16.19 180 (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]. 16.81/16.19 181 (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]. 16.81/16.19 182 (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]. 16.81/16.19 183 $T # label(t33_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 184 (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]. 16.81/16.19 185 (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]. 16.81/16.19 186 (all A k4_enumset1(A,A,A,A,A,A) = k1_tarski(A)) # label(t91_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 187 (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]. 16.81/16.19 188 $T # label(t14_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 189 (all A all B k2_tarski(A,B) = k2_enumset1(A,A,A,B)) # label(t77_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 190 $T # label(t29_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 191 $T # label(t121_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 192 (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]. 16.81/16.19 193 $T # label(dt_k6_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 194 (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]. 16.81/16.19 195 (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]. 16.81/16.19 196 $T # label(t7_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 197 (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]. 16.81/16.19 198 $T # label(t12_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 199 (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]. 16.81/16.19 200 (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]. 16.81/16.19 201 $T # label(t23_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 202 (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]. 16.81/16.19 203 $T # label(t122_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 204 (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]. 16.81/16.19 205 $T # label(t6_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 206 (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]. 16.81/16.19 207 $T # label(t24_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 208 $T # label(t18_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 209 (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]. 16.81/16.19 210 (all A k6_enumset1(A,A,A,A,A,A,A,A) = k1_tarski(A)) # label(t96_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 211 $T # label(t1_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 212 (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]. 16.81/16.19 213 (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]. 16.81/16.19 214 (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]. 16.81/16.19 215 (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]. 16.81/16.19 216 $T # label(t5_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 217 (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]. 16.81/16.19 218 (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]. 16.81/16.19 219 $T # label(t38_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 220 (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]. 16.81/16.19 221 $T # label(t15_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 222 $T # label(t114_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 223 (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]. 16.81/16.19 224 (all A k1_tarski(A) = k3_enumset1(A,A,A,A,A)) # label(t87_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 225 (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]. 16.81/16.19 226 (all A k1_tarski(A) = k5_enumset1(A,A,A,A,A,A,A)) # label(t94_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 227 $T # label(t115_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 228 $T # label(t106_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 229 (all A k1_enumset1(A,A,A) = k1_tarski(A)) # label(t76_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 230 (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]. 16.81/16.19 231 $T # label(t17_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 232 $T # label(t39_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 233 $T # label(t4_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 234 (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]. 16.81/16.19 235 (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]. 16.81/16.19 236 (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]. 16.81/16.19 237 (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]. 16.81/16.19 238 (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]. 16.81/16.19 239 $T # label(dt_k5_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 240 $T # label(t22_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 241 (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]. 16.81/16.19 242 $T # label(t30_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 243 (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]. 16.81/16.19 244 $T # label(dt_k3_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 245 (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]. 16.81/16.19 246 $T # label(t11_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 247 (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]. 16.81/16.19 248 $T # label(t13_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 249 (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]. 16.81/16.19 250 (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]. 16.81/16.19 251 (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]. 16.81/16.19 252 $T # label(dt_k1_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 253 (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]. 16.81/16.19 254 (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]. 16.81/16.19 255 (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]. 16.81/16.19 256 (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]. 16.81/16.19 257 (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]. 16.81/16.19 258 (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]. 16.81/16.19 259 $T # label(t8_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 260 (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]. 16.81/16.19 261 (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]. 16.81/16.19 262 $T # label(t35_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.81/16.19 263 (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]. 16.81/16.19 264 (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]. 16.81/16.19 265 (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]. 16.81/16.19 266 (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]. 16.82/16.19 267 (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]. 16.82/16.19 268 $T # label(dt_k4_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.19 269 (all A k1_tarski(A) = k2_enumset1(A,A,A,A)) # label(t82_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.19 270 (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]. 16.82/16.19 271 (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]. 16.82/16.19 272 (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]. 16.82/16.19 273 (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]. 16.82/16.19 274 $T # label(t120_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.19 275 (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]. 16.82/16.19 276 (all A all B k2_tarski(A,B) = k3_enumset1(A,A,A,A,B)) # label(t83_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.19 277 (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]. 16.82/16.19 278 (all A k2_tarski(A,A) = k1_tarski(A)) # label(t69_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.19 279 (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]. 16.82/16.19 280 $T # label(dt_k2_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.19 281 $T # label(t32_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.19 282 (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]. 16.82/16.19 283 (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]. 16.82/16.19 284 $T # label(t34_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.19 285 $T # label(t40_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.19 286 $T # label(t10_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.19 287 (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]. 16.82/16.19 288 (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]. 16.82/16.19 289 (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]. 16.82/16.19 290 $T # label(t28_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.19 291 (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]. 16.82/16.19 292 (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]. 16.82/16.19 293 (all A all B k1_enumset1(A,A,B) = k2_tarski(A,B)) # label(t70_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.19 294 (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]. 16.82/16.19 295 $T # label(t101_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.19 296 (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]. 16.82/16.19 297 $T # label(t19_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.19 298 $T # label(t124_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.19 299 $T # label(t36_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.19 300 $T # label(t31_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.19 301 (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]. 16.82/16.19 302 (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]. 16.82/16.19 303 $T # label(t37_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.19 304 (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]. 16.82/16.19 305 $T # label(t27_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.19 306 $T # label(t16_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.19 307 (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]. 16.82/16.19 308 $T # label(t25_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.19 309 $T # label(t97_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.19 310 $T # label(t21_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.19 311 (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]. 16.82/16.19 312 (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]. 16.82/16.19 313 $T # label(t3_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.19 314 (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]. 16.82/16.19 315 $T # label(t9_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.19 316 $T # label(t26_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.19 317 (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]. 16.82/16.19 318 $T # label(t20_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.19 319 $T # label(t2_enumset1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.19 320 (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]. 16.82/16.19 321 (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]. 16.82/16.19 322 (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]. 16.82/16.19 323 (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]. 16.82/16.19 324 $T # label(t89_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.19 325 (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]. 16.82/16.19 326 (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]. 16.82/16.19 327 (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]. 16.82/16.20 328 (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]. 16.82/16.20 329 (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]. 16.82/16.20 330 (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]. 16.82/16.20 331 (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]. 16.82/16.20 332 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 333 (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]. 16.82/16.20 334 (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]. 16.82/16.20 335 (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]. 16.82/16.20 336 (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]. 16.82/16.20 337 (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]. 16.82/16.20 338 (all A k3_tarski(k1_zfmisc_1(A)) = A) # label(t99_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 339 (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]. 16.82/16.20 340 (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]. 16.82/16.20 341 (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]. 16.82/16.20 342 (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]. 16.82/16.20 343 (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]. 16.82/16.20 344 (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]. 16.82/16.20 345 (all A all B (r1_tarski(k1_tarski(A),k1_tarski(B)) -> B = A)) # label(t24_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 346 (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]. 16.82/16.20 347 (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]. 16.82/16.20 348 (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]. 16.82/16.20 349 (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]. 16.82/16.20 350 (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]. 16.82/16.20 351 $T # label(t7_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 352 (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]. 16.82/16.20 353 (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]. 16.82/16.20 354 (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]. 16.82/16.20 355 (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]. 16.82/16.20 356 (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]. 16.82/16.20 357 (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]. 16.82/16.20 358 (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]. 16.82/16.20 359 (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]. 16.82/16.20 360 (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]. 16.82/16.20 361 $T # label(t4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 362 (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]. 16.82/16.20 363 (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]. 16.82/16.20 364 $T # label(t62_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 365 (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]. 16.82/16.20 366 (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]. 16.82/16.20 367 (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]. 16.82/16.20 368 $T # label(dt_k4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 369 $T # label(t77_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 370 (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]. 16.82/16.20 371 (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]. 16.82/16.20 372 (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]. 16.82/16.20 373 (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]. 16.82/16.20 374 $T # label(t3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 375 (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]. 16.82/16.20 376 (all A all B -v1_xboole_0(k4_tarski(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 377 (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]. 16.82/16.20 378 (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]. 16.82/16.20 379 (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]. 16.82/16.20 380 $T # label(t76_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 381 (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]. 16.82/16.20 382 (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]. 16.82/16.20 383 (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]. 16.82/16.20 384 (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]. 16.82/16.20 385 $T # label(t87_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 386 (all A all B r1_tarski(k1_tarski(A),k2_tarski(A,B))) # label(t12_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 387 $T # label(t85_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 388 (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]. 16.82/16.20 389 (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]. 16.82/16.20 390 (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]. 16.82/16.20 391 (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]. 16.82/16.20 392 (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]. 16.82/16.20 393 $T # label(t5_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 394 (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]. 16.82/16.20 395 (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]. 16.82/16.20 396 (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]. 16.82/16.20 397 (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]. 16.82/16.20 398 (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]. 16.82/16.20 399 (all A all B (r1_tarski(k1_tarski(A),k1_tarski(B)) -> B = A)) # label(t6_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 400 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 401 (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]. 16.82/16.20 402 (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]. 16.82/16.20 403 (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]. 16.82/16.20 404 (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]. 16.82/16.20 405 $T # label(t133_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 406 (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]. 16.82/16.20 407 (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]. 16.82/16.20 408 (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]. 16.82/16.20 409 (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]. 16.82/16.20 410 (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]. 16.82/16.20 411 (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]. 16.82/16.20 412 (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]. 16.82/16.20 413 (all A all B (r1_tarski(k1_tarski(A),B) <-> r2_hidden(A,B))) # label(t37_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 414 (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]. 16.82/16.20 415 (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]. 16.82/16.20 416 (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]. 16.82/16.20 417 (all A (r1_tarski(A,k2_zfmisc_1(A,A)) -> k1_xboole_0 = A)) # label(t116_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 418 (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]. 16.82/16.20 419 (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]. 16.82/16.20 420 (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]. 16.82/16.20 421 (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]. 16.82/16.20 422 (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]. 16.82/16.20 423 $T # label(t61_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 424 $T # label(t88_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 425 (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]. 16.82/16.20 426 (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]. 16.82/16.20 427 (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]. 16.82/16.20 428 (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]. 16.82/16.20 429 $T # label(t90_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 430 $T # label(t78_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 431 (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]. 16.82/16.20 432 (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]. 16.82/16.20 433 (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]. 16.82/16.20 434 (all A k3_tarski(k1_tarski(A)) = A) # label(t31_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 435 $T # label(t11_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 436 (all A r1_tarski(k1_tarski(A),k1_zfmisc_1(A))) # label(t80_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 437 (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]. 16.82/16.20 438 $T # label(dt_k3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 439 (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]. 16.82/16.20 440 $T # label(t15_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 441 (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]. 16.82/16.20 442 (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]. 16.82/16.20 443 (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]. 16.82/16.20 444 (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]. 16.82/16.20 445 $T # label(t71_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 446 (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]. 16.82/16.20 447 (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]. 16.82/16.20 448 (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]. 16.82/16.20 449 (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]. 16.82/16.20 450 $T # label(t91_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 451 (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]. 16.82/16.20 452 (all A r1_tarski(A,k1_zfmisc_1(k3_tarski(A)))) # label(t100_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 453 (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]. 16.82/16.20 454 (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]. 16.82/16.20 455 (all A all B (r2_hidden(A,B) -> r1_tarski(A,k3_tarski(B)))) # label(t92_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 456 (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]. 16.82/16.20 457 (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]. 16.82/16.20 458 (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]. 16.82/16.20 459 (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]. 16.82/16.20 460 (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]. 16.82/16.20 461 (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]. 16.82/16.20 462 (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]. 16.82/16.20 463 (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]. 16.82/16.20 464 (all A all B k2_xboole_0(k1_tarski(A),B) != k1_xboole_0) # label(t49_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 465 (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]. 16.82/16.20 466 (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]. 16.82/16.20 467 (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]. 16.82/16.20 468 (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]. 16.82/16.20 469 (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]. 16.82/16.20 470 (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]. 16.82/16.20 471 (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]. 16.82/16.20 472 $T # label(t23_subset_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 473 (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]. 16.82/16.20 474 $T # label(t11_subset_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 475 (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]. 16.82/16.20 476 (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]. 16.82/16.20 477 (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]. 16.82/16.20 478 (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]. 16.82/16.20 479 $T # label(t3_subset_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 480 $T # label(t19_subset_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 481 (all A -v1_xboole_0(k1_tarski(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 482 (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]. 16.82/16.20 483 (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]. 16.82/16.20 484 (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]. 16.82/16.20 485 (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]. 16.82/16.20 486 (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]. 16.82/16.20 487 (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]. 16.82/16.20 488 (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]. 16.82/16.20 489 (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]. 16.82/16.20 490 (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]. 16.82/16.20 491 (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]. 16.82/16.20 492 (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]. 16.82/16.20 493 (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]. 16.82/16.20 494 (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]. 16.82/16.20 495 $T # label(t5_subset_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 496 (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]. 16.82/16.20 497 (all A m1_subset_1(k8_subset_1(A),A)) # label(dt_k8_subset_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 498 $T # label(d1_subset_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 499 (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]. 16.82/16.20 500 (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]. 16.82/16.20 501 $T # label(t13_subset_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 502 (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]. 16.82/16.20 503 (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]. 16.82/16.20 504 (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]. 16.82/16.20 505 (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]. 16.82/16.20 506 (all A k2_subset_1(A) = A) # label(d4_subset_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 507 (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]. 16.82/16.20 508 (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]. 16.82/16.20 509 (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]. 16.82/16.20 510 (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]. 16.82/16.20 511 (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]. 16.82/16.20 512 (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]. 16.82/16.20 513 (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]. 16.82/16.20 514 (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]. 16.82/16.20 515 (all A all B -v1_xboole_0(k2_tarski(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 516 $T # label(t20_subset_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 517 $T # label(t24_subset_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 518 (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]. 16.82/16.20 519 (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]. 16.82/16.20 520 (all A k2_subset_1(A) = k3_subset_1(A,k1_subset_1(A))) # label(t22_subset_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 521 (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]. 16.82/16.20 522 (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]. 16.82/16.20 523 (all A -v1_xboole_0(k1_zfmisc_1(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 524 (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]. 16.82/16.20 525 (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]. 16.82/16.20 526 (all A m1_subset_1(k2_subset_1(A),k1_zfmisc_1(A))) # label(dt_k2_subset_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 527 (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]. 16.82/16.20 528 (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]. 16.82/16.20 529 $T # label(t2_subset_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 530 (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]. 16.82/16.20 531 (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]. 16.82/16.20 532 (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]. 16.82/16.20 533 (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]. 16.82/16.20 534 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 535 (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]. 16.82/16.20 536 (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]. 16.82/16.20 537 $T # label(t37_subset_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 538 (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]. 16.82/16.20 539 (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]. 16.82/16.20 540 (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]. 16.82/16.20 541 (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]. 16.82/16.20 542 $T # label(t27_subset_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 543 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> (r1_xboole_0(A,B) <-> r2_subset_1(A,B)))) # label(redefinition_r2_subset_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 544 (all A (-v1_xboole_0(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 545 (all A m1_subset_1(k1_xboole_0,k1_zfmisc_1(A))) # label(t4_subset_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 546 (all A (-$T -> (all B (m1_subset_1(B,A) -> k8_subset_1(A) = B)))) # label(d6_subset_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 547 (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]. 16.82/16.20 548 $T # label(t14_subset_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 549 $T # label(t1_subset_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 550 (all A exists B m1_subset_1(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 551 (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]. 16.82/16.20 552 (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]. 16.82/16.20 553 (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]. 16.82/16.20 554 (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]. 16.82/16.20 555 $T # label(t45_subset_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 556 (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]. 16.82/16.20 557 (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]. 16.82/16.20 558 $T # label(t12_subset_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 559 (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]. 16.82/16.20 560 (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]. 16.82/16.20 561 $T # label(t6_subset_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 562 (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]. 16.82/16.20 563 (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]. 16.82/16.20 564 $T # label(t9_subset_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 565 (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]. 16.82/16.20 566 (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]. 16.82/16.20 567 (all A k1_subset_1(A) = k1_xboole_0) # label(d3_subset_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 568 (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]. 16.82/16.20 569 (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]. 16.82/16.20 570 (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]. 16.82/16.20 571 (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]. 16.82/16.20 572 (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]. 16.82/16.20 573 (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]. 16.82/16.20 574 (all A k3_subset_1(A,k2_subset_1(A)) = k1_subset_1(A)) # label(t21_subset_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 575 (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]. 16.82/16.20 576 (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]. 16.82/16.20 577 (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]. 16.82/16.20 578 $T # label(dt_k1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 579 (all A (-v2_setfam_1(A) -> -v1_xboole_0(A))) # label(cc2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 580 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> -v1_xboole_0(k2_tarski(A,B)) & v1_setfam_1(k2_tarski(A,B)))) # label(fc3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 581 (all A all B -(k1_setfam_1(k2_xboole_0(A,B)) != k3_xboole_0(k1_setfam_1(A),k1_setfam_1(B)) & B != k1_xboole_0 & A != k1_xboole_0)) # label(t10_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 582 (all A (v2_setfam_1(A) <-> (all B (-v1_xboole_0(B) -> -r2_hidden(B,A))))) # label(d11_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 583 $T # label(dt_k2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 584 (all A all B all C (r2_hidden(A,B) & r1_xboole_0(A,C) -> r1_xboole_0(k1_setfam_1(B),C))) # label(t9_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 585 (all A (-v2_setfam_1(A) -> (exists B (-v1_xboole_0(B) & m1_subset_1(B,A))))) # label(rc3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 586 (all A all B (v1_setfam_1(A) & v1_setfam_1(B) -> v1_setfam_1(k2_xboole_0(A,B)))) # label(fc4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 587 $T # label(t26_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 588 (all A all B all C (r1_setfam_1(C,k2_tarski(A,B)) -> (all D -(-r1_tarski(D,B) & -r1_tarski(D,A) & r2_hidden(D,C))))) # label(t25_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 589 (all A all B k3_tarski(k3_setfam_1(A,B)) = k3_xboole_0(k3_tarski(A),k3_tarski(B))) # label(t39_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 590 (all A all B k3_xboole_0(A,B) = k1_setfam_1(k2_tarski(A,B))) # label(t12_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 591 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> m1_subset_1(k8_setfam_1(A,B),k1_zfmisc_1(A)))) # label(dt_k8_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 592 (all A all B (r1_setfam_1(A,B) <-> (all C -((all D -(r1_tarski(C,D) & r2_hidden(D,B))) & r2_hidden(C,A))))) # label(d2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 593 (all A all B all C ((all D ((exists E exists F (r2_hidden(E,A) & D = k4_xboole_0(E,F) & r2_hidden(F,B))) <-> r2_hidden(D,C))) <-> C = k4_setfam_1(A,B))) # label(d6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 594 (all A all B -(A != k1_xboole_0 & k1_xboole_0 != B & -r1_tarski(k2_xboole_0(k1_setfam_1(A),k1_setfam_1(B)),k1_setfam_1(k2_setfam_1(A,B))))) # label(t40_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 595 $T # label(t14_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 596 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k1_xboole_0 = B -> A = k8_setfam_1(A,B)) & (B != k1_xboole_0 -> k8_setfam_1(A,B) = k6_setfam_1(A,B)))) # label(d10_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 597 (all A all B all C (r1_setfam_1(B,C) & r1_setfam_1(A,B) -> r1_setfam_1(A,C))) # label(t23_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 598 (all A (v1_setfam_1(A) <-> -r2_hidden(k1_xboole_0,A))) # label(d9_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 599 $T # label(t32_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 600 (all A all B (r2_hidden(A,B) -> r1_tarski(k1_setfam_1(B),A))) # label(t4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 601 (all A all B k2_setfam_1(A,B) = k2_setfam_1(B,A)) # label(commutativity_k2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 602 $T # label(t15_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 603 $T # label(t16_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 604 (all A all B (-r1_xboole_0(A,B) -> k1_setfam_1(k3_setfam_1(A,B)) = k3_xboole_0(k1_setfam_1(A),k1_setfam_1(B)))) # label(t34_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 605 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r1_tarski(k7_setfam_1(A,B),k7_setfam_1(A,C)) -> r1_tarski(B,C)))))) # label(t51_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 606 (all A all B ((k1_xboole_0 != A -> (B = k1_setfam_1(A) <-> (all C (r2_hidden(C,B) <-> (all D (r2_hidden(D,A) -> r2_hidden(C,D))))))) & (A = k1_xboole_0 -> (B = k1_setfam_1(A) <-> B = k1_xboole_0)))) # label(d1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 607 (all A (r1_setfam_1(A,k1_xboole_0) -> A = k1_xboole_0)) # label(t21_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 608 (all A r1_setfam_1(k4_setfam_1(A,A),A)) # label(t31_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 609 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> k3_tarski(B) = k5_setfam_1(A,B))) # label(redefinition_k5_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 610 (all A all B (v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> v1_xboole_0(k7_setfam_1(A,B)))) # label(fc1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.20 611 (all A all B all C (r1_tarski(k3_tarski(A),B) & r2_hidden(C,A) -> r1_tarski(C,B))) # label(t56_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 612 (all A k1_setfam_1(k1_tarski(A)) = A) # label(t11_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 613 $T # label(t1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 614 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> m1_subset_1(k6_setfam_1(A,B),k1_zfmisc_1(A)))) # label(dt_k6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 615 (all A r1_setfam_1(k3_setfam_1(A,A),A)) # label(t30_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 616 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r2_hidden(B,A) -> ((all D (r2_hidden(D,C) -> r2_hidden(B,D))) <-> r2_hidden(B,k8_setfam_1(A,C)))))) # label(t58_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 617 $T # label(t22_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 618 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k1_tarski(A) = B -> k1_tarski(k1_xboole_0) = k7_setfam_1(A,B)))) # label(t55_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 619 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k7_setfam_1(A,B) = k7_setfam_1(A,C) -> C = B))))) # label(t53_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 620 (all A r1_tarski(k1_setfam_1(A),k3_tarski(A))) # label(t3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 621 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> k1_setfam_1(B) = k6_setfam_1(A,B))) # label(redefinition_k6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 622 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r1_tarski(B,C) -> r1_tarski(k8_setfam_1(A,C),k8_setfam_1(A,B))))))) # label(t59_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 623 (all A all B r1_tarski(k1_setfam_1(k4_setfam_1(A,B)),k4_xboole_0(k1_setfam_1(A),k1_setfam_1(B)))) # label(t41_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 624 (all A (-v1_xboole_0(A) -> v1_setfam_1(k1_tarski(A)) & -v1_xboole_0(k1_tarski(A)))) # label(fc2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 625 $T # label(t28_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 626 (all A all B (r1_tarski(A,B) -> r1_setfam_1(A,B))) # label(t17_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 627 (all A all B k3_xboole_0(A,k3_tarski(B)) = k3_tarski(k3_setfam_1(k1_tarski(A),B))) # label(t36_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 628 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k7_setfam_1(A,B) = C <-> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(D,C) <-> r2_hidden(k3_subset_1(A,D),B))))))))) # label(d8_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 629 (all A all B r1_setfam_1(A,A)) # label(reflexivity_r1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 630 $T # label(t27_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 631 (all A (-v1_xboole_0(A) & v1_setfam_1(A) -> (all B (m1_subset_1(B,A) -> -v1_xboole_0(B))))) # label(cc1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 632 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r2_hidden(C,B) <-> r2_hidden(k3_subset_1(A,C),k7_setfam_1(A,B))))))) # label(t49_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 633 (all A all B (r1_setfam_1(B,k1_tarski(A)) -> (all C (r2_hidden(C,B) -> r1_tarski(C,A))))) # label(t24_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 634 $T # label(t45_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 635 (all A all B (k1_xboole_0 != B -> k1_setfam_1(k4_setfam_1(k1_tarski(A),B)) = k4_xboole_0(A,k3_tarski(B)))) # label(t37_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 636 (all A all B (r2_setfam_1(A,B) <-> (all C -(r2_hidden(C,B) & (all D -(r1_tarski(D,C) & r2_hidden(D,A))))))) # label(d3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 637 (all A all B (B != k1_xboole_0 -> k3_tarski(k4_setfam_1(k1_tarski(A),B)) = k4_xboole_0(A,k1_setfam_1(B)))) # label(t38_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 638 (all A all B (k1_xboole_0 != B -> k1_setfam_1(k2_setfam_1(k1_tarski(A),B)) = k2_xboole_0(A,k1_setfam_1(B)))) # label(t35_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 639 $T # label(dt_k4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 640 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r1_tarski(k7_setfam_1(A,B),C) <-> r1_tarski(B,k7_setfam_1(A,C))))))) # label(t52_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 641 (all A all B (r2_setfam_1(B,A) -> A = k1_xboole_0 | r1_tarski(k1_setfam_1(B),k1_setfam_1(A)))) # label(t19_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 642 (all A all B all C (r2_hidden(A,B) & r1_tarski(A,C) -> r1_tarski(k1_setfam_1(B),C))) # label(t8_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 643 $T # label(t13_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 644 (all A all B (r1_tarski(A,B) -> k1_xboole_0 = A | r1_tarski(k1_setfam_1(B),k1_setfam_1(A)))) # label(t7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 645 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> k7_setfam_1(A,k4_subset_1(k1_zfmisc_1(A),B,C)) = k4_subset_1(k1_zfmisc_1(A),k7_setfam_1(A,B),k7_setfam_1(A,C)))))) # label(t54_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 646 (all A r1_setfam_1(A,k2_setfam_1(A,A))) # label(t29_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 647 $T # label(t50_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 648 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> -(k1_xboole_0 != B & k1_xboole_0 = k7_setfam_1(A,B)))) # label(t46_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 649 (all A all B k3_setfam_1(A,B) = k3_setfam_1(B,A)) # label(commutativity_k3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 650 (all A all B all C (k2_setfam_1(A,B) = C <-> (all D (r2_hidden(D,C) <-> (exists E exists F (r2_hidden(E,A) & r2_hidden(F,B) & D = k2_xboole_0(E,F))))))) # label(d4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 651 (all A all B r2_setfam_1(B,B)) # label(reflexivity_r2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 652 (all A all B all C ((all D ((exists E exists F (D = k3_xboole_0(E,F) & r2_hidden(F,B) & r2_hidden(E,A))) <-> r2_hidden(D,C))) <-> C = k3_setfam_1(A,B))) # label(d5_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 653 (all A all B all C ((all D (r2_hidden(D,B) -> r1_xboole_0(D,C))) & r1_tarski(C,k3_tarski(k2_xboole_0(A,B))) -> r1_tarski(C,k3_tarski(A)))) # label(t57_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 654 (all A all B (r1_setfam_1(A,B) -> r1_tarski(k3_tarski(A),k3_tarski(B)))) # label(t18_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 655 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> ((all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(D,C) <-> r2_hidden(D,B)))) -> C = B))))) # label(t44_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 656 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> m1_subset_1(k5_setfam_1(A,B),k1_zfmisc_1(A)))) # label(dt_k5_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 657 $T # label(dt_k3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 658 $T # label(t43_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 659 (all A (r2_hidden(k1_xboole_0,A) -> k1_setfam_1(A) = k1_xboole_0)) # label(t5_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 660 $T # label(d7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 661 (exists A -v2_setfam_1(A)) # label(rc2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 662 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> m1_subset_1(k7_setfam_1(A,B),k1_zfmisc_1(k1_zfmisc_1(A))))) # label(dt_k7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 663 $T # label(t33_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 664 (all A r1_setfam_1(k1_xboole_0,A)) # label(t20_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 665 (exists A (v1_setfam_1(A) & -v1_xboole_0(A))) # label(rc1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 666 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (B != k1_xboole_0 -> k6_setfam_1(A,k7_setfam_1(A,B)) = k6_subset_1(A,k2_subset_1(A),k5_setfam_1(A,B))))) # label(t47_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 667 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> k7_setfam_1(A,k7_setfam_1(A,B)) = B)) # label(involutiveness_k7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 668 $T # label(t42_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 669 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (B != k1_xboole_0 -> k6_subset_1(A,k2_subset_1(A),k6_setfam_1(A,B)) = k5_setfam_1(A,k7_setfam_1(A,B))))) # label(t48_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 670 (all A all B ((all C (r2_hidden(C,A) -> r1_tarski(B,C))) -> A = k1_xboole_0 | r1_tarski(B,k1_setfam_1(A)))) # label(t6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 671 (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]. 16.82/16.21 672 (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]. 16.82/16.21 673 (all A all B (r2_hidden(A,B) -> m1_subset_1(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 674 (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]. 16.82/16.21 675 (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]. 16.82/16.21 676 (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]. 16.82/16.21 677 $T # label(t83_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 678 $T # label(t142_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 679 (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]. 16.82/16.21 680 (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]. 16.82/16.21 681 (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]. 16.82/16.21 682 (exists A (-v1_xboole_0(A) & v1_relat_1(A))) # label(rc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 683 $T # label(t61_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 684 (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]. 16.82/16.21 685 $T # label(t35_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 686 (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]. 16.82/16.21 687 (exists A (v3_relat_1(A) & v1_relat_1(A))) # label(rc3_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 688 (all A (v1_relat_1(A) -> k10_relat_1(A,k1_xboole_0) = k1_xboole_0)) # label(t171_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 689 $T # label(t36_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 690 (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]. 16.82/16.21 691 (all A k1_xboole_0 = k10_relat_1(k1_xboole_0,A)) # label(t172_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 692 (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]. 16.82/16.21 693 (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]. 16.82/16.21 694 (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]. 16.82/16.21 695 (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]. 16.82/16.21 696 (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]. 16.82/16.21 697 $T # label(t59_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 698 (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]. 16.82/16.21 699 (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]. 16.82/16.21 700 (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]. 16.82/16.21 701 (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]. 16.82/16.21 702 (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]. 16.82/16.21 703 $T # label(dt_k3_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 704 $T # label(t84_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 705 (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]. 16.82/16.21 706 (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]. 16.82/16.21 707 (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]. 16.82/16.21 708 (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]. 16.82/16.21 709 (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]. 16.82/16.21 710 (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]. 16.82/16.21 711 (all A all B v1_relat_1(k2_zfmisc_1(A,B))) # label(t6_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.82/16.21 712 (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]. 16.82/16.21 713 (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]. 16.84/16.21 714 (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]. 16.84/16.21 715 (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]. 16.84/16.21 716 $T # label(t2_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.21 717 (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]. 16.84/16.21 718 (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]. 16.84/16.21 719 (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]. 16.84/16.21 720 (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]. 16.84/16.21 721 (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]. 16.84/16.21 722 $T # label(t113_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.21 723 (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]. 16.84/16.21 724 (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]. 16.84/16.21 725 (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]. 16.84/16.21 726 (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]. 16.84/16.21 727 (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]. 16.84/16.21 728 $T # label(dt_k9_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.21 729 (all A v1_relat_1(k6_relat_1(A))) # label(dt_k6_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.21 730 (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]. 16.84/16.21 731 (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]. 16.84/16.21 732 (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]. 16.84/16.21 733 (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]. 16.84/16.21 734 (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]. 16.84/16.21 735 (all A k1_xboole_0 = k7_relat_1(k1_xboole_0,A)) # label(t111_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.21 736 $T # label(t68_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.21 737 (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]. 16.84/16.21 738 (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]. 16.84/16.21 739 (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]. 16.84/16.21 740 $T # label(t43_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.21 741 (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]. 16.84/16.21 742 (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]. 16.84/16.21 743 (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]. 16.84/16.21 744 (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]. 16.84/16.21 745 (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]. 16.84/16.21 746 (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]. 16.84/16.21 747 (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]. 16.84/16.21 748 (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]. 16.84/16.21 749 (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]. 16.84/16.21 750 (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]. 16.84/16.21 751 (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]. 16.84/16.21 752 (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]. 16.84/16.21 753 (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]. 16.84/16.21 754 (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]. 16.84/16.21 755 (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]. 16.84/16.21 756 (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]. 16.84/16.21 757 (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]. 16.84/16.21 758 (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]. 16.84/16.21 759 (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]. 16.84/16.21 760 (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]. 16.84/16.21 761 (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]. 16.84/16.21 762 (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]. 16.84/16.21 763 (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]. 16.84/16.21 764 $T # label(t8_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.21 765 (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]. 16.84/16.21 766 $T # label(t85_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.21 767 (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]. 16.84/16.21 768 (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]. 16.84/16.21 769 (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]. 16.84/16.21 770 (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]. 16.84/16.21 771 (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]. 16.84/16.21 772 (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]. 16.84/16.21 773 (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]. 16.84/16.21 774 (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]. 16.84/16.21 775 (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]. 16.84/16.21 776 (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]. 16.84/16.21 777 (exists A (v1_relat_1(A) & v1_xboole_0(A))) # label(rc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.21 778 $T # label(t58_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.21 779 (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]. 16.84/16.21 780 (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]. 16.84/16.21 781 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.21 782 (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]. 16.84/16.21 783 (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]. 16.84/16.21 784 (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]. 16.84/16.21 785 $T # label(t63_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.21 786 $T # label(t42_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.21 787 (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]. 16.84/16.21 788 (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]. 16.84/16.21 789 (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]. 16.84/16.21 790 (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]. 16.84/16.21 791 (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]. 16.84/16.21 792 (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]. 16.84/16.21 793 (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]. 16.84/16.21 794 (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]. 16.84/16.21 795 $T # label(t114_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.21 796 (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]. 16.84/16.21 797 (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]. 16.84/16.21 798 (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]. 16.84/16.21 799 (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]. 16.84/16.21 800 (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]. 16.84/16.21 801 (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]. 16.84/16.21 802 (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]. 16.84/16.21 803 (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]. 16.84/16.21 804 (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]. 16.84/16.21 805 (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]. 16.84/16.21 806 (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]. 16.84/16.21 807 (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]. 16.84/16.21 808 (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]. 16.84/16.21 809 (all A (v1_relat_1(A) -> v1_relat_1(k4_relat_1(A)))) # label(dt_k4_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.21 810 (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]. 16.84/16.21 811 (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]. 16.84/16.21 812 (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]. 16.84/16.21 813 $T # label(t69_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.21 814 (all A k1_xboole_0 = k8_relat_1(A,k1_xboole_0)) # label(t138_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.21 815 (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]. 16.84/16.21 816 (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]. 16.84/16.21 817 (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]. 16.84/16.21 818 (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]. 16.84/16.21 819 (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]. 16.84/16.21 820 (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]. 16.84/16.21 821 (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]. 16.84/16.21 822 (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]. 16.84/16.21 823 (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]. 16.84/16.21 824 (all A all B v1_relat_1(k1_tarski(k4_tarski(A,B)))) # label(t4_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.21 825 (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]. 16.84/16.21 826 (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]. 16.84/16.21 827 (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]. 16.84/16.21 828 (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]. 16.84/16.21 829 (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]. 16.84/16.21 830 (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]. 16.84/16.21 831 (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]. 16.84/16.21 832 (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]. 16.84/16.21 833 (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]. 16.84/16.21 834 (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]. 16.84/16.21 835 (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]. 16.84/16.21 836 (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]. 16.84/16.21 837 (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]. 16.84/16.21 838 (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]. 16.84/16.21 839 (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]. 16.84/16.21 840 $T # label(t164_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.21 841 (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]. 16.84/16.21 842 $T # label(dt_k10_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.21 843 (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]. 16.84/16.21 844 (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]. 16.84/16.21 845 (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]. 16.84/16.21 846 (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]. 16.84/16.21 847 (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]. 16.84/16.21 848 $T # label(t1_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.21 849 (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]. 16.84/16.21 850 (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]. 16.84/16.21 851 (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]. 16.84/16.21 852 (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]. 16.84/16.21 853 $T # label(t70_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.21 854 (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]. 16.84/16.21 855 (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]. 16.84/16.21 856 $T # label(t162_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.21 857 (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]. 16.84/16.21 858 (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]. 16.84/16.21 859 (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]. 16.84/16.21 860 $T # label(t141_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.21 861 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.21 862 (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]. 16.84/16.22 863 (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]. 16.84/16.22 864 (all A k1_xboole_0 = k9_relat_1(k1_xboole_0,A)) # label(t150_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 865 (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]. 16.84/16.22 866 (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]. 16.84/16.22 867 (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]. 16.84/16.22 868 (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]. 16.84/16.22 869 $T # label(t16_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 870 (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]. 16.84/16.22 871 $T # label(t57_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 872 (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]. 16.84/16.22 873 (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]. 16.84/16.22 874 (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]. 16.84/16.22 875 (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]. 16.84/16.22 876 (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]. 16.84/16.22 877 (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]. 16.84/16.22 878 $T # label(t7_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 879 (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]. 16.84/16.22 880 (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]. 16.84/16.22 881 (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]. 16.84/16.22 882 (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]. 16.84/16.22 883 (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]. 16.84/16.22 884 (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]. 16.84/16.22 885 $T # label(t17_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 886 (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]. 16.84/16.22 887 (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]. 16.84/16.22 888 (all A (v1_xboole_0(A) -> v1_relat_1(A))) # label(cc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 889 (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]. 16.84/16.22 890 (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]. 16.84/16.22 891 (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]. 16.84/16.22 892 (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]. 16.84/16.22 893 $T # label(t12_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 894 (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]. 16.84/16.22 895 $T # label(t11_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 896 (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]. 16.84/16.22 897 (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]. 16.84/16.22 898 (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]. 16.84/16.22 899 (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]. 16.84/16.22 900 $T # label(t165_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 901 (all A k4_relat_1(k6_relat_1(A)) = k6_relat_1(A)) # label(t72_relat_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 902 (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]. 16.84/16.22 903 (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]. 16.84/16.22 904 (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]. 16.84/16.22 905 (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]. 16.84/16.22 906 (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]. 16.84/16.22 907 $T # label(t135_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 908 (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]. 16.84/16.22 909 (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]. 16.84/16.22 910 $T # label(t107_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 911 $T # label(t91_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 912 $T # label(t132_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 913 $T # label(t95_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 914 (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]. 16.84/16.22 915 $T # label(t5_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 916 (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]. 16.84/16.22 917 (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]. 16.84/16.22 918 (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]. 16.84/16.22 919 (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]. 16.84/16.22 920 (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]. 16.84/16.22 921 $T # label(t114_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 922 (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]. 16.84/16.22 923 (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]. 16.84/16.22 924 $T # label(t74_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 925 (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]. 16.84/16.22 926 (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]. 16.84/16.22 927 $T # label(t130_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 928 (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]. 16.84/16.22 929 (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]. 16.84/16.22 930 $T # label(d6_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 931 $T # label(t129_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 932 (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]. 16.84/16.22 933 (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]. 16.84/16.22 934 (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]. 16.84/16.22 935 $T # label(t93_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 936 (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]. 16.84/16.22 937 $T # label(t101_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 938 (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]. 16.84/16.22 939 (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]. 16.84/16.22 940 (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]. 16.84/16.22 941 $T # label(t11_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 942 (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]. 16.84/16.22 943 (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]. 16.84/16.22 944 (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]. 16.84/16.22 945 (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]. 16.84/16.22 946 (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]. 16.84/16.22 947 (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]. 16.84/16.22 948 $T # label(t109_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 949 (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]. 16.84/16.22 950 (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]. 16.84/16.22 951 $T # label(t141_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 952 (exists A (v1_relat_1(A) & v1_funct_1(A) & v1_xboole_0(A))) # label(rc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 953 (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]. 16.84/16.22 954 (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]. 16.84/16.22 955 $T # label(t24_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 956 (all A (v1_xboole_0(A) -> v1_funct_1(A))) # label(cc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 957 $T # label(t102_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 958 (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]. 16.84/16.22 959 (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]. 16.84/16.22 960 (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]. 16.84/16.22 961 (all A k2_funct_1(k6_relat_1(A)) = k6_relat_1(A)) # label(t67_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 962 $T # label(t6_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 963 (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]. 16.84/16.22 964 (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]. 16.84/16.22 965 (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]. 16.84/16.22 966 $T # label(t133_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 967 $T # label(t39_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 968 $T # label(t41_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 969 (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]. 16.84/16.22 970 (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]. 16.84/16.22 971 $T # label(d2_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 972 (all A v2_funct_1(k6_relat_1(A))) # label(t52_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 973 $T # label(t113_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 974 $T # label(t94_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 975 $T # label(t10_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 976 $T # label(t30_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 977 (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]. 16.84/16.22 978 (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]. 16.84/16.22 979 (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]. 16.84/16.22 980 (exists A (v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A))) # label(rc3_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 981 (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]. 16.84/16.22 982 (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]. 16.84/16.22 983 (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]. 16.84/16.22 984 (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]. 16.84/16.22 985 (exists A (v3_relat_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc4_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 986 $T # label(dt_k1_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 987 $T # label(t77_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 988 (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]. 16.84/16.22 989 (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]. 16.84/16.22 990 $T # label(t26_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 991 (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]. 16.84/16.22 992 $T # label(t83_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 993 (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]. 16.84/16.22 994 $T # label(t90_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 995 $T # label(t88_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 996 (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]. 16.84/16.22 997 (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]. 16.84/16.22 998 (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]. 16.84/16.22 999 (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]. 16.84/16.22 1000 $T # label(t3_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1001 $T # label(t105_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1002 (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]. 16.84/16.22 1003 $T # label(t79_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1004 (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]. 16.84/16.22 1005 (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]. 16.84/16.22 1006 (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]. 16.84/16.22 1007 (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]. 16.84/16.22 1008 $T # label(t119_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1009 $T # label(t7_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1010 (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]. 16.84/16.22 1011 (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]. 16.84/16.22 1012 (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]. 16.84/16.22 1013 $T # label(d3_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1014 $T # label(t29_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1015 $T # label(d10_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1016 (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]. 16.84/16.22 1017 $T # label(t80_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1018 $T # label(t31_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1019 (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]. 16.84/16.22 1020 (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]. 16.84/16.22 1021 $T # label(t1_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1022 $T # label(t110_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1023 (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]. 16.84/16.22 1024 $T # label(t134_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1025 $T # label(t112_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1026 (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]. 16.84/16.22 1027 (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]. 16.84/16.22 1028 $T # label(t104_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1029 (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]. 16.84/16.22 1030 (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]. 16.84/16.22 1031 $T # label(t92_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1032 (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]. 16.84/16.22 1033 (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]. 16.84/16.22 1034 $T # label(t4_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1035 $T # label(t45_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1036 (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]. 16.84/16.22 1037 $T # label(t75_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1038 $T # label(t115_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1039 (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]. 16.84/16.22 1040 $T # label(t28_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1041 (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]. 16.84/16.22 1042 (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]. 16.84/16.22 1043 $T # label(t111_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1044 $T # label(t69_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1045 (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]. 16.84/16.22 1046 $T # label(t32_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1047 $T # label(t13_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1048 $T # label(t103_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1049 (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]. 16.84/16.22 1050 (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]. 16.84/16.22 1051 $T # label(t36_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1052 (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]. 16.84/16.22 1053 $T # label(t108_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1054 (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]. 16.84/16.22 1055 (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]. 16.84/16.22 1056 $T # label(d7_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1057 (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]. 16.84/16.22 1058 $T # label(t98_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1059 $T # label(t78_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1060 $T # label(t96_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1061 (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]. 16.84/16.22 1062 $T # label(t127_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1063 $T # label(t136_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1064 (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]. 16.84/16.22 1065 (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]. 16.84/16.22 1066 (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]. 16.84/16.22 1067 (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]. 16.84/16.22 1068 (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]. 16.84/16.22 1069 (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]. 16.84/16.22 1070 (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]. 16.84/16.22 1071 (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]. 16.84/16.22 1072 (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]. 16.84/16.22 1073 $T # label(t140_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1074 (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]. 16.84/16.22 1075 $T # label(t100_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1076 $T # label(t106_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1077 (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]. 16.84/16.22 1078 (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]. 16.84/16.22 1079 (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]. 16.84/16.22 1080 (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]. 16.84/16.22 1081 (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]. 16.84/16.22 1082 (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]. 16.84/16.22 1083 $T # label(t131_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1084 (exists A (v1_funct_1(A) & v2_relat_1(A) & v1_relat_1(A))) # label(rc5_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1085 (exists A (v1_funct_1(A) & v1_relat_1(A))) # label(rc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1086 (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]. 16.84/16.22 1087 $T # label(t128_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1088 (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]. 16.84/16.22 1089 (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]. 16.84/16.22 1090 $T # label(d11_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1091 $T # label(t81_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1092 (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]. 16.84/16.22 1093 (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]. 16.84/16.22 1094 (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]. 16.84/16.22 1095 (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]. 16.84/16.22 1096 (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]. 16.84/16.22 1097 (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]. 16.84/16.22 1098 $T # label(t116_funct_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.22 1099 (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]. 16.84/16.23 1100 (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]. 16.84/16.23 1101 (all A (v1_relat_1(A) -> (k4_relat_1(A) = A <-> v3_relat_2(A)))) # label(t30_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1102 $T # label(t10_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1103 (all A (v1_relat_1(A) -> (all B (r6_relat_2(A,B) <-> (all C all D -(r2_hidden(C,B) & D != C & -r2_hidden(k4_tarski(C,D),A) & -r2_hidden(k4_tarski(D,C),A) & r2_hidden(D,B))))))) # label(d6_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1104 (all A (v1_relat_1(A) -> (v2_relat_2(A) -> v2_relat_2(k4_relat_1(A))))) # label(t28_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1105 (all A (v1_relat_1(A) -> (v3_relat_2(A) -> v3_relat_2(k4_relat_1(A))))) # label(t34_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1106 (all A (v1_relat_1(A) -> (v1_relat_2(A) -> k1_relat_1(A) = k1_relat_1(k4_relat_1(A)) & k2_relat_1(A) = k2_relat_1(k4_relat_1(A))))) # label(t29_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1107 $T # label(t2_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1108 $T # label(t21_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1109 $T # label(t13_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1110 (all A (v1_relat_1(A) -> (all B (r1_relat_2(A,B) <-> (all C (r2_hidden(C,B) -> r2_hidden(k4_tarski(C,C),A))))))) # label(d1_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1111 $T # label(t16_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1112 (all A (v1_relat_1(A) -> (v8_relat_2(A) <-> r8_relat_2(A,k3_relat_1(A))))) # label(d16_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1113 $T # label(t12_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1114 (all A (v1_relat_1(A) -> (v4_relat_2(A) <-> r1_tarski(k3_xboole_0(A,k4_relat_1(A)),k6_relat_1(k1_relat_1(A)))))) # label(t39_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1115 (all A (v8_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)))) # label(t23_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1116 $T # label(t9_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1117 $T # label(t11_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1118 $T # label(t4_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1119 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v3_relat_2(A) & v3_relat_2(B) -> v3_relat_2(k3_xboole_0(A,B)) & v3_relat_2(k4_xboole_0(A,B)) & v3_relat_2(k2_xboole_0(A,B))))))) # label(t35_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1120 (all A (v1_relat_1(A) -> (v3_relat_2(A) <-> r3_relat_2(A,k3_relat_1(A))))) # label(d11_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1121 (all A (v1_relat_1(A) -> (v7_relat_2(A) -> v6_relat_2(A) & v1_relat_2(A)))) # label(t46_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1122 $T # label(t3_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1123 (all A all B (v1_relat_1(B) -> (r4_relat_2(B,A) <-> r5_relat_2(k4_xboole_0(B,k6_relat_1(A)),A)))) # label(t19_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1124 (all A (v1_relat_1(A) -> (v8_relat_2(A) <-> r1_tarski(k5_relat_1(A,A),A)))) # label(t44_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1125 (all A (v1_relat_1(A) -> (k2_xboole_0(A,k4_relat_1(A)) = k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A)) <-> v7_relat_2(A)))) # label(t47_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1126 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v8_relat_2(B) & v8_relat_2(A) -> v8_relat_2(k3_xboole_0(A,B))))))) # label(t43_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1127 (all A (v1_relat_1(A) -> (all B (r5_relat_2(A,B) <-> (all C all D -(r2_hidden(D,B) & r2_hidden(k4_tarski(C,D),A) & r2_hidden(k4_tarski(D,C),A) & r2_hidden(C,B))))))) # label(d5_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1128 (all A (v1_relat_1(A) -> (v1_relat_2(A) <-> r1_relat_2(A,k3_relat_1(A))))) # label(d9_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1129 (all A (v1_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)))) # label(t24_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1130 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v1_relat_2(A) & v1_relat_2(B) -> v1_relat_2(k2_xboole_0(A,B)) & v1_relat_2(k3_xboole_0(A,B))))))) # label(t31_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1131 $T # label(t8_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1132 $T # label(t14_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1133 (all A (v1_relat_1(A) -> (all B ((all C all D all E (r2_hidden(D,B) & r2_hidden(k4_tarski(C,D),A) & r2_hidden(k4_tarski(D,E),A) & r2_hidden(E,B) & r2_hidden(C,B) -> r2_hidden(k4_tarski(C,E),A))) <-> r8_relat_2(A,B))))) # label(d8_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1134 (all A (v1_relat_1(A) -> (v8_relat_2(A) & v3_relat_2(A) -> v1_relat_2(A)))) # label(t22_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1135 (all A (v1_relat_1(A) -> (r2_relat_2(A,k3_relat_1(A)) <-> v2_relat_2(A)))) # label(d10_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1136 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v4_relat_2(A) -> v4_relat_2(k4_xboole_0(A,B)) & v4_relat_2(k3_xboole_0(A,B))))))) # label(t41_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1137 (all A (v1_relat_1(A) -> (v4_relat_2(A) -> v4_relat_2(k4_relat_1(A))))) # label(t40_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1138 (all A (v1_relat_1(A) -> (r5_relat_2(A,k3_relat_1(A)) <-> v5_relat_2(A)))) # label(d13_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1139 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v5_relat_2(B) & v5_relat_2(A) -> v5_relat_2(k3_xboole_0(A,B))))))) # label(t37_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1140 (all A (v1_relat_1(A) -> (all B ((all C all D -(r2_hidden(D,B) & -r2_hidden(k4_tarski(D,C),A) & -r2_hidden(k4_tarski(C,D),A) & r2_hidden(C,B))) <-> r7_relat_2(A,B))))) # label(d7_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1141 (all A (v1_relat_1(A) -> (v5_relat_2(A) -> v2_relat_2(A) & v4_relat_2(A)))) # label(t26_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1142 (all A (v1_relat_1(A) -> (v8_relat_2(A) & v2_relat_2(A) -> v5_relat_2(A)))) # label(t25_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1143 $T # label(t5_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1144 (all A (v1_relat_1(A) -> (all B (r2_relat_2(A,B) <-> (all C -(r2_hidden(C,B) & r2_hidden(k4_tarski(C,C),A))))))) # label(d2_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1145 $T # label(t1_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1146 $T # label(t15_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1147 (all A (v1_relat_1(A) -> (v5_relat_2(A) -> v5_relat_2(k4_relat_1(A))))) # label(t36_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1148 (all A (v1_relat_1(A) -> (v4_relat_2(A) <-> r4_relat_2(A,k3_relat_1(A))))) # label(d12_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1149 (all A (v1_relat_1(A) -> (v1_relat_2(A) -> v1_relat_2(k4_relat_1(A))))) # label(t27_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1150 (all A all B (v1_relat_1(B) -> (r5_relat_2(B,A) -> r4_relat_2(k2_xboole_0(B,k6_relat_1(A)),A)))) # label(t20_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1151 (all A (v1_relat_1(A) -> (r1_tarski(k6_relat_1(k3_relat_1(A)),A) <-> v1_relat_2(A)))) # label(t17_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1152 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v2_relat_2(A) & v2_relat_2(B) -> v2_relat_2(k2_xboole_0(A,B)) & v2_relat_2(k3_xboole_0(A,B))))))) # label(t32_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1153 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v2_relat_2(A) -> v2_relat_2(k4_xboole_0(A,B))))))) # label(t33_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1154 (all A (v1_relat_1(A) -> (v7_relat_2(A) <-> r7_relat_2(A,k3_relat_1(A))))) # label(d15_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1155 (all A (v1_relat_1(A) -> (r1_xboole_0(k6_relat_1(k3_relat_1(A)),A) <-> v2_relat_2(A)))) # label(t18_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1156 (all A (v1_relat_1(A) -> (v8_relat_2(A) -> v8_relat_2(k4_relat_1(A))))) # label(t42_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1157 (all A (v1_relat_1(A) -> (all B ((all C all D (r2_hidden(C,B) & r2_hidden(D,B) & r2_hidden(k4_tarski(C,D),A) -> r2_hidden(k4_tarski(D,C),A))) <-> r3_relat_2(A,B))))) # label(d3_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1158 $T # label(t6_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1159 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v5_relat_2(A) -> v5_relat_2(k4_xboole_0(A,B))))))) # label(t38_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1160 (all A (v1_relat_1(A) -> (v6_relat_2(A) <-> r6_relat_2(A,k3_relat_1(A))))) # label(d14_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1161 (all A (v1_relat_1(A) -> (all B (r4_relat_2(A,B) <-> (all C all D (r2_hidden(C,B) & r2_hidden(k4_tarski(D,C),A) & r2_hidden(k4_tarski(C,D),A) & r2_hidden(D,B) -> C = D)))))) # label(d4_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1162 (all A (v1_relat_1(A) -> (r1_tarski(k4_xboole_0(k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A)),k6_relat_1(k3_relat_1(A))),k2_xboole_0(A,k4_relat_1(A))) <-> v6_relat_2(A)))) # label(t45_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1163 $T # label(t7_relat_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1164 (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]. 16.84/16.23 1165 (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]. 16.84/16.23 1166 $T # label(t17_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1167 (all A m1_ordinal1(k1_xboole_0,A)) # label(t45_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1168 (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]. 16.84/16.23 1169 (all A r2_hidden(A,k1_ordinal1(A))) # label(t10_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1170 (all A all B (k1_ordinal1(B) = k1_ordinal1(A) -> B = A)) # label(t12_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1171 (all A (v1_xboole_0(A) -> v3_ordinal1(A) & v2_ordinal1(A) & v1_ordinal1(A))) # label(cc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1172 (all A all B (v3_ordinal1(B) -> (r2_hidden(A,B) -> v3_ordinal1(A)))) # label(t23_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1173 (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]. 16.84/16.23 1174 (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]. 16.84/16.23 1175 (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]. 16.84/16.23 1176 $T # label(t20_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1177 (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]. 16.84/16.23 1178 (all A -(all B (r2_hidden(B,A) <-> v3_ordinal1(B)))) # label(t37_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1179 $T # label(d5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1180 (all A ((all B (r2_hidden(B,A) -> r1_tarski(B,A))) <-> v1_ordinal1(A))) # label(d2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1181 (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]. 16.84/16.23 1182 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> r3_xboole_0(A,B))))) # label(t25_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1183 (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]. 16.84/16.23 1184 (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]. 16.84/16.23 1185 $T # label(t1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1186 (all A (v3_ordinal1(A) <-> v1_ordinal1(A) & v2_ordinal1(A))) # label(d4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1187 $T # label(t18_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1188 (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]. 16.84/16.23 1189 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]. 16.84/16.23 1190 (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]. 16.84/16.23 1191 $T # label(t9_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1192 $T # label(t8_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1193 (all A (v3_ordinal1(A) -> v3_ordinal1(k3_tarski(A)))) # label(t30_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1194 (all A (v3_ordinal1(A) -> v1_ordinal1(A) & v2_ordinal1(A))) # label(cc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1195 (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]. 16.84/16.23 1196 (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]. 16.84/16.23 1197 (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]. 16.84/16.23 1198 (all A (v3_ordinal1(A) -> v3_ordinal1(k1_ordinal1(A)))) # label(t29_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1199 $T # label(t11_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1200 (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]. 16.84/16.23 1201 $T # label(t28_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1202 $T # label(t16_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1203 (all A all B -(r2_hidden(A,B) & r1_tarski(B,A))) # label(t7_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1204 (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]. 16.84/16.23 1205 (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]. 16.84/16.23 1206 (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]. 16.84/16.23 1207 (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]. 16.84/16.23 1208 (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]. 16.84/16.23 1209 $T # label(dt_k1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1210 (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]. 16.84/16.23 1211 (all A -v1_xboole_0(k1_ordinal1(A))) # label(fc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1212 (all A -(all B (v3_ordinal1(B) -> r2_hidden(B,A)))) # label(t38_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1213 (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]. 16.84/16.23 1214 (all A (v4_ordinal1(A) <-> k3_tarski(A) = A)) # label(d6_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1215 (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]. 16.84/16.23 1216 (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]. 16.84/16.23 1217 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> r1_ordinal1(A,A))) # label(reflexivity_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1218 (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]. 16.84/16.23 1219 $T # label(t2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1220 (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]. 16.84/16.23 1221 (exists A (v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & -v1_xboole_0(A))) # label(rc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1222 (all A k1_ordinal1(A) != A) # label(t14_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1223 (all A exists B m1_ordinal1(B,A)) # label(existence_m1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1224 (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]. 16.84/16.23 1225 (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]. 16.84/16.23 1226 (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]. 16.84/16.23 1227 (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]. 16.84/16.23 1228 $T # label(t15_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1229 (all A k2_xboole_0(A,k1_tarski(A)) = k1_ordinal1(A)) # label(d1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1230 (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]. 16.84/16.23 1231 (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]. 16.84/16.23 1232 $T # label(t40_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1233 (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]. 16.84/16.23 1234 (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]. 16.84/16.23 1235 (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]. 16.84/16.23 1236 (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]. 16.84/16.23 1237 $T # label(t43_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1238 (exists A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A))) # label(rc4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1239 (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]. 16.84/16.23 1240 $T # label(t44_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1241 (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]. 16.84/16.23 1242 (exists A (v3_ordinal1(A) & v2_ordinal1(A) & v1_ordinal1(A))) # label(rc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1243 (all A (v2_ordinal1(A) & v1_ordinal1(A) -> v3_ordinal1(A))) # label(cc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1244 (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]. 16.84/16.23 1245 (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]. 16.84/16.23 1246 (all A all B all C (v1_relat_1(C) -> (r2_hidden(B,k3_relat_1(C)) & r2_hidden(A,k3_relat_1(C)) & v2_wellord1(C) -> (r1_tarski(k1_wellord1(C,A),k1_wellord1(C,B)) <-> r2_hidden(k4_tarski(A,B),C))))) # label(t37_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1247 (all A all B (v1_relat_1(B) -> k2_wellord1(k2_wellord1(B,A),A) = k2_wellord1(B,A))) # label(t28_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1248 (all A all B (v1_relat_1(B) -> (v4_relat_2(B) -> v4_relat_2(k2_wellord1(B,A))))) # label(t25_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1249 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_wellord1(A) & r3_wellord1(A,B,C) -> v2_wellord1(B)))))))) # label(t54_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1250 $T # label(t46_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1251 (all A all B all C (v1_relat_1(C) -> (v2_wellord1(C) -> r3_xboole_0(k1_wellord1(C,A),k1_wellord1(C,B))))) # label(t33_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1252 (all A all B all C all D (v1_relat_1(D) -> (all E (v1_relat_1(E) -> (v2_wellord1(D) & v2_wellord1(E) & r4_wellord1(k2_wellord1(D,k1_wellord1(D,A)),k2_wellord1(E,k1_wellord1(E,C))) & r4_wellord1(D,k2_wellord1(E,k1_wellord1(E,B))) & r2_hidden(C,k3_relat_1(E)) & r2_hidden(B,k3_relat_1(E)) & r2_hidden(A,k3_relat_1(D)) -> r1_tarski(k1_wellord1(E,C),k1_wellord1(E,B)) & r2_hidden(k4_tarski(C,B),E)))))) # label(t62_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1253 (all A all B (v1_relat_1(B) -> k2_wellord1(B,A) = k7_relat_1(k8_relat_1(A,B),A))) # label(t17_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1254 $T # label(dt_k1_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1255 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> (all B -(r2_hidden(B,k3_relat_1(A)) & r4_wellord1(A,k2_wellord1(A,k1_wellord1(A,B)))))))) # label(t57_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1256 $T # label(t56_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1257 (all A all B (v1_relat_1(B) -> k8_relat_1(A,k7_relat_1(B,A)) = k2_wellord1(B,A))) # label(t18_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1258 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r4_wellord1(A,B) <-> (exists C (v1_relat_1(C) & v1_funct_1(C) & r3_wellord1(A,B,C)))))))) # label(d8_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1259 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k3_relat_1(k2_wellord1(C,B))) -> r2_hidden(A,k3_relat_1(C)) & r2_hidden(A,B)))) # label(t19_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1260 (all A all B (v1_relat_1(B) -> (r2_wellord1(B,A) -> (all C -(r1_tarski(C,A) & k1_xboole_0 != C & (all D -(r2_hidden(D,C) & (all E (r2_hidden(E,C) -> r2_hidden(k4_tarski(D,E),B)))))))))) # label(t9_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1261 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r3_wellord1(A,B,C) -> (v8_relat_2(A) -> v8_relat_2(B)) & (v1_wellord1(A) -> v1_wellord1(B)) & (v4_relat_2(A) -> v4_relat_2(B)) & (v6_relat_2(A) -> v6_relat_2(B)) & (v1_relat_2(A) -> v1_relat_2(B))))))))) # label(t53_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1262 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k2_wellord1(C,A) = k2_wellord1(k2_wellord1(C,B),A)))) # label(t29_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1263 (all A all B all C (v1_relat_1(C) -> ((all D (r2_hidden(D,k1_wellord1(C,A)) -> r2_hidden(k4_tarski(D,B),C) & B != D)) & r2_hidden(B,k3_relat_1(C)) & r2_hidden(A,k3_relat_1(C)) & v2_wellord1(C) -> r2_hidden(k4_tarski(A,B),C)))) # label(t42_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1264 (all A all B (v1_relat_1(A) -> v1_relat_1(k2_wellord1(A,B)))) # label(dt_k2_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1265 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (v2_wellord1(A) & r3_wellord1(A,B,C) -> (all D -((all E -(r4_wellord1(k2_wellord1(A,k1_wellord1(A,D)),k2_wellord1(B,k1_wellord1(B,E))) & r2_hidden(E,k3_relat_1(B)))) & r2_hidden(D,k3_relat_1(A))))))))))) # label(t61_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1266 (all A all B (v1_relat_1(B) -> r1_tarski(k2_wellord1(B,A),B) & r1_tarski(k2_wellord1(B,A),k2_zfmisc_1(A,A)))) # label(t15_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1267 (all A (v1_relat_1(A) -> (all B ((all C -(r1_tarski(C,B) & C != k1_xboole_0 & (all D -(r2_hidden(D,C) & r1_xboole_0(k1_wellord1(A,D),C))))) <-> r1_wellord1(A,B))))) # label(d3_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1268 (all A (v1_relat_1(A) -> (v1_wellord1(A) <-> (all B -(B != k1_xboole_0 & (all C -(r2_hidden(C,B) & r1_xboole_0(k1_wellord1(A,C),B))) & r1_tarski(B,k3_relat_1(A))))))) # label(d2_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1269 $T # label(t44_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1270 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r3_wellord1(A,B,C) & v2_wellord1(A) -> (all D -(r2_hidden(D,k3_relat_1(A)) & (all E -(r2_hidden(E,k3_relat_1(B)) & k9_relat_1(C,k1_wellord1(A,D)) = k1_wellord1(B,E)))))))))))) # label(t60_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1271 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k3_relat_1(A) = k1_relat_1(B) & r1_tarski(k2_relat_1(B),k3_relat_1(A)) & (all C all D (r2_hidden(k4_tarski(C,D),A) -> r2_hidden(k4_tarski(k1_funct_1(B,C),k1_funct_1(B,D)),A) & k1_funct_1(B,D) != k1_funct_1(B,C) | D = C)) & v2_wellord1(A) -> (all C (r2_hidden(C,k3_relat_1(A)) -> r2_hidden(k4_tarski(C,k1_funct_1(B,C)),A)))))))) # label(t43_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1272 (all A all B all C (v1_relat_1(C) -> r1_tarski(k1_wellord1(k2_wellord1(C,A),B),k1_wellord1(C,B)))) # label(t21_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1273 $T # label(t4_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1274 (all A all B (v1_relat_1(B) -> r1_tarski(k3_relat_1(k2_wellord1(B,A)),A) & r1_tarski(k3_relat_1(k2_wellord1(B,A)),k3_relat_1(B)))) # label(t20_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1275 (all A all B all C (v1_relat_1(C) -> -(v2_wellord1(C) & r2_hidden(A,k3_relat_1(C)) & r4_wellord1(k2_wellord1(C,k1_wellord1(C,A)),k2_wellord1(C,k1_wellord1(C,B))) & B != A & r2_hidden(B,k3_relat_1(C))))) # label(t58_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1276 (all A (v1_relat_1(A) -> r3_wellord1(A,A,k6_relat_1(k3_relat_1(A))))) # label(t47_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1277 (all A all B all C (v1_relat_1(C) -> k2_wellord1(k2_wellord1(C,A),B) = k2_wellord1(C,k3_xboole_0(A,B)))) # label(t26_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1278 $T # label(t6_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1279 (all A all B all C (v1_relat_1(C) -> k2_wellord1(k2_wellord1(C,B),A) = k2_wellord1(k2_wellord1(C,A),B))) # label(t27_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1280 (all A (v1_relat_1(A) -> A = k2_wellord1(A,k3_relat_1(A)))) # label(t30_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1281 (all A (v1_relat_1(A) -> -((all B -(r2_hidden(B,k3_relat_1(A)) & (all C (r2_hidden(C,k3_relat_1(A)) -> r2_hidden(k4_tarski(B,C),A))))) & k3_relat_1(A) != k1_xboole_0 & v2_wellord1(A)))) # label(t11_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1282 $T # label(t34_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1283 (all A all B (v1_relat_1(B) -> (v6_relat_2(B) -> v6_relat_2(k2_wellord1(B,A))))) # label(t23_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1284 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v2_wellord1(A) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r3_wellord1(A,B,D) & r3_wellord1(A,B,C) -> D = C)))))))))) # label(t55_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1285 $T # label(t14_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1286 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k2_relat_1(C) = k3_relat_1(B) & v2_funct_1(C) & (all D all E (r2_hidden(k4_tarski(k1_funct_1(C,D),k1_funct_1(C,E)),B) & r2_hidden(E,k3_relat_1(A)) & r2_hidden(D,k3_relat_1(A)) <-> r2_hidden(k4_tarski(D,E),A))) & k3_relat_1(A) = k1_relat_1(C) <-> r3_wellord1(A,B,C)))))))) # label(d7_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1287 $T # label(t3_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1288 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> (all B ((all C (r2_hidden(C,k3_relat_1(A)) & r1_tarski(k1_wellord1(A,C),B) -> r2_hidden(C,B))) -> r1_tarski(k3_relat_1(A),B)))))) # label(t41_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1289 (all A all B (v1_relat_1(B) -> k1_wellord1(B,A) = k1_xboole_0 | r2_hidden(A,k3_relat_1(B)))) # label(t2_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1290 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r4_wellord1(B,C) & r4_wellord1(A,B) -> r4_wellord1(A,C)))))))) # label(t52_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1291 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k2_zfmisc_1(B,B)) & r2_hidden(A,C) <-> r2_hidden(A,k2_wellord1(C,B))))) # label(t16_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1292 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> -(v2_wellord1(B) & (all C -(r4_wellord1(k2_wellord1(A,k1_wellord1(A,C)),B) & r2_hidden(C,k3_relat_1(A)))) & (all C -(r2_hidden(C,k3_relat_1(B)) & r4_wellord1(A,k2_wellord1(B,k1_wellord1(B,C))))) & -r4_wellord1(A,B) & v2_wellord1(A)))))) # label(t63_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1293 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r1_tarski(A,k3_relat_1(B)) & r3_wellord1(B,C,D) & v2_wellord1(B) -> r4_wellord1(k2_wellord1(B,A),k2_wellord1(C,k9_relat_1(D,A))) & r3_wellord1(k2_wellord1(B,A),k2_wellord1(C,k9_relat_1(D,A)),k7_relat_1(D,A))))))))) # label(t59_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1294 (all A all B (v1_relat_1(B) -> (v1_relat_2(B) -> v1_relat_2(k2_wellord1(B,A))))) # label(t22_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1295 (all A all B (v1_relat_1(B) -> (v2_wellord1(B) -> v2_wellord1(k2_wellord1(B,A))))) # label(t32_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1296 (all A (v1_relat_1(A) -> (v1_wellord1(A) <-> r1_wellord1(A,k3_relat_1(A))))) # label(t5_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1297 (all A all B (v1_relat_1(A) & v1_relat_1(B) -> v1_relat_1(k3_wellord1(A,B)) & v1_funct_1(k3_wellord1(A,B)))) # label(dt_k3_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1298 (all A all B all C (v1_relat_1(C) -> (v2_wellord1(C) & r2_hidden(B,k3_relat_1(C)) & r2_hidden(A,k3_relat_1(C)) -> (r1_tarski(k1_wellord1(C,A),k1_wellord1(C,B)) <-> B = A | r2_hidden(A,k1_wellord1(C,B)))))) # label(t38_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1299 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (all E (v1_relat_1(E) & v1_funct_1(E) -> (r3_wellord1(B,C,E) & r3_wellord1(A,B,D) -> r3_wellord1(A,C,k5_relat_1(D,E))))))))))))) # label(t51_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1300 (all A all B (v1_relat_1(B) -> -(v2_wellord1(B) & (all C -(r2_hidden(C,k3_relat_1(B)) & r4_wellord1(k2_wellord1(B,k1_wellord1(B,C)),k2_wellord1(B,A)))) & -r4_wellord1(B,k2_wellord1(B,A)) & r1_tarski(A,k3_relat_1(B))))) # label(t64_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1301 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r3_wellord1(A,B,C) -> (all D all E (r2_hidden(k4_tarski(D,E),A) -> r2_hidden(k4_tarski(k1_funct_1(C,D),k1_funct_1(C,E)),B) & k1_funct_1(C,E) != k1_funct_1(C,D) | E = D))))))))) # label(t45_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1302 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r3_wellord1(A,B,C) -> r3_wellord1(B,A,k2_funct_1(C))))))))) # label(t49_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1303 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k3_relat_1(C)) & r2_hidden(B,k1_wellord1(C,A)) & v2_wellord1(C) -> k1_wellord1(C,B) = k1_wellord1(k2_wellord1(C,k1_wellord1(C,A)),B)))) # label(t35_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1304 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> (all B -(r2_hidden(B,k3_relat_1(A)) & (exists C (-r2_hidden(k4_tarski(C,B),A) & r2_hidden(C,k3_relat_1(A)))) & (all C -(r2_hidden(C,k3_relat_1(A)) & (all D -(r2_hidden(D,k3_relat_1(A)) & -r2_hidden(k4_tarski(C,D),A) & D != B & r2_hidden(k4_tarski(B,D),A))) & r2_hidden(k4_tarski(B,C),A))))) | k3_relat_1(A) = k1_xboole_0))) # label(t12_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1305 (all A all B (v1_relat_1(B) -> r1_tarski(k1_wellord1(B,A),k3_relat_1(B)))) # label(t13_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1306 (all A all B (v1_relat_1(B) -> (v1_wellord1(B) -> v1_wellord1(k2_wellord1(B,A))))) # label(t31_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1307 (all A all B (v1_relat_1(B) -> (r1_tarski(A,k3_relat_1(B)) & v2_wellord1(B) -> (-(k3_relat_1(B) != A & (all C -(k1_wellord1(B,C) = A & r2_hidden(C,k3_relat_1(B))))) <-> (all C (r2_hidden(C,A) -> (all D (r2_hidden(k4_tarski(D,C),B) -> r2_hidden(D,A))))))))) # label(t36_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1308 $T # label(t7_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1309 (all A (v1_relat_1(A) -> (all B k2_wellord1(A,B) = k3_xboole_0(A,k2_zfmisc_1(B,B))))) # label(d6_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1310 (all A (v1_relat_1(A) -> (v2_wellord1(A) <-> r2_wellord1(A,k3_relat_1(A))))) # label(t8_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1311 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r4_wellord1(A,B) -> r4_wellord1(B,A)))))) # label(t50_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1312 (all A all B (v1_relat_1(B) -> (r1_tarski(A,k3_relat_1(B)) & v2_wellord1(B) -> k3_relat_1(k2_wellord1(B,A)) = A))) # label(t39_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1313 $T # label(t1_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1314 (all A (v1_relat_1(A) -> (v2_wellord1(A) <-> v8_relat_2(A) & v4_relat_2(A) & v1_wellord1(A) & v6_relat_2(A) & v1_relat_2(A)))) # label(d4_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1315 (all A all B (v1_relat_1(B) -> (v2_wellord1(B) -> k1_wellord1(B,A) = k3_relat_1(k2_wellord1(B,k1_wellord1(B,A)))))) # label(t40_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1316 (all A (v1_relat_1(A) -> (all B (r1_relat_2(A,B) & r4_relat_2(A,B) & r1_wellord1(A,B) & r6_relat_2(A,B) & r8_relat_2(A,B) <-> r2_wellord1(A,B))))) # label(d5_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1317 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> (all B -(r1_tarski(B,k3_relat_1(A)) & (all C -((all D (r2_hidden(D,B) -> r2_hidden(k4_tarski(C,D),A))) & r2_hidden(C,B))) & B != k1_xboole_0))))) # label(t10_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1318 (all A all B (v1_relat_1(B) -> (v8_relat_2(B) -> v8_relat_2(k2_wellord1(B,A))))) # label(t24_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1319 (all A (v1_relat_1(A) -> r4_wellord1(A,A))) # label(t48_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1320 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v2_wellord1(A) & r4_wellord1(A,B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k3_wellord1(A,B) = C <-> r3_wellord1(A,B,C))))))))) # label(d9_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1321 (all A (v1_relat_1(A) -> (all B all C (k1_wellord1(A,B) = C <-> (all D (r2_hidden(D,C) <-> r2_hidden(k4_tarski(D,B),A) & B != D)))))) # label(d1_wellord1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1322 (all A all B exists C m2_relset_1(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1323 (all A all B exists C m1_relset_1(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.23 1324 (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]. 16.84/16.23 1325 (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]. 16.84/16.23 1326 (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]. 16.84/16.23 1327 $T # label(t1_relset_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1328 (all A m2_relset_1(k6_relat_1(A),A,A)) # label(t29_relset_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1329 (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]. 16.84/16.24 1330 (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]. 16.84/16.24 1331 (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]. 16.84/16.24 1332 (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]. 16.84/16.24 1333 $T # label(t41_relset_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1334 (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]. 16.84/16.24 1335 (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]. 16.84/16.24 1336 (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]. 16.84/16.24 1337 (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]. 16.84/16.24 1338 (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]. 16.84/16.24 1339 (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]. 16.84/16.24 1340 (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]. 16.84/16.24 1341 (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]. 16.84/16.24 1342 (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]. 16.84/16.24 1343 (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]. 16.84/16.24 1344 (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]. 16.84/16.24 1345 (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]. 16.84/16.24 1346 (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]. 16.84/16.24 1347 (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]. 16.84/16.24 1348 (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]. 16.84/16.24 1349 $T # label(t3_relset_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1350 (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]. 16.84/16.24 1351 (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]. 16.84/16.24 1352 $T # label(t37_relset_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1353 $T # label(t2_relset_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1354 $T # label(t21_relset_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1355 (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]. 16.84/16.24 1356 (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]. 16.84/16.24 1357 $T # label(t18_relset_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1358 (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]. 16.84/16.24 1359 (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]. 16.84/16.24 1360 (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]. 16.84/16.24 1361 (all A all B m2_relset_1(k1_xboole_0,A,B)) # label(t25_relset_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1362 (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]. 16.84/16.24 1363 (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]. 16.84/16.24 1364 (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]. 16.84/16.24 1365 (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]. 16.84/16.24 1366 (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]. 16.84/16.24 1367 (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]. 16.84/16.24 1368 (all A r1_tarski(k6_relat_1(A),k2_zfmisc_1(A,A))) # label(t28_relset_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1369 $T # label(t7_relset_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1370 (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]. 16.84/16.24 1371 (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]. 16.84/16.24 1372 (all A (-v1_xboole_0(A) -> k6_relat_1(A) != k1_xboole_0)) # label(t46_relset_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1373 $T # label(t40_relset_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1374 (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]. 16.84/16.24 1375 (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]. 16.84/16.24 1376 $T # label(t20_relset_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1377 (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]. 16.84/16.24 1378 (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]. 16.84/16.24 1379 (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]. 16.84/16.24 1380 $T # label(t5_relset_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1381 $T # label(t44_relset_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1382 (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]. 16.84/16.24 1383 (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]. 16.84/16.24 1384 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1385 (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]. 16.84/16.24 1386 (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]. 16.84/16.24 1387 (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]. 16.84/16.24 1388 (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]. 16.84/16.24 1389 $T # label(t42_relset_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1390 (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]. 16.84/16.24 1391 (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]. 16.84/16.24 1392 (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]. 16.84/16.24 1393 (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]. 16.84/16.24 1394 (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]. 16.84/16.24 1395 (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]. 16.84/16.24 1396 (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]. 16.84/16.24 1397 (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]. 16.84/16.24 1398 (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]. 16.84/16.24 1399 $T # label(t43_relset_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1400 (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]. 16.84/16.24 1401 (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]. 16.84/16.24 1402 (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]. 16.84/16.24 1403 (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]. 16.84/16.24 1404 (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]. 16.84/16.24 1405 (all A all B all C all D all E all F (m1_relset_1(E,A,B) & m1_relset_1(F,C,D) -> 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]. 16.84/16.24 1406 (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]. 16.84/16.24 1407 (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]. 16.84/16.24 1408 (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]. 16.84/16.24 1409 (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]. 16.84/16.24 1410 (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]. 16.84/16.24 1411 $T # label(t100_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1412 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> k3_partfun1(D,B,k3_xboole_0(A,C)) = k9_relset_1(B,C,A,k3_partfun1(D,B,C)))) # label(t97_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1413 (all A all B all C (m2_relset_1(C,A,k1_xboole_0) & v1_funct_1(C) -> k10_relat_1(C,B) = k1_xboole_0)) # label(t68_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1414 $T # label(t177_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1415 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,k1_xboole_0) -> v2_funct_1(B))) # label(t66_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1416 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((exists C (v1_relat_1(C) & v1_funct_1(C) & C = k2_xboole_0(A,B))) <-> r1_partfun1(A,B)))))) # label(t130_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1417 (all A all B all C all D all E all F (v1_funct_1(E) & m1_relset_1(E,A,B) & v1_funct_1(F) & m1_relset_1(F,C,D) -> v1_funct_1(k1_partfun1(A,B,C,D,E,F)) & m2_relset_1(k1_partfun1(A,B,C,D,E,F),A,D))) # label(dt_k1_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1418 $T # label(t111_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1419 $T # label(t98_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1420 (all A all B all C (r2_hidden(C,k4_partfun1(A,B)) -> v1_funct_1(C) & m2_relset_1(C,A,B))) # label(t120_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1421 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,k1_relat_1(C)) & r1_tarski(k2_relat_1(C),B) -> v1_partfun1(k3_partfun1(C,A,B),A,B)))) # label(t115_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1422 (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) -> (r2_hidden(D,k5_partfun1(A,B,C)) -> v1_partfun1(D,A,B)))))) # label(t169_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1423 (all A all B (m2_relset_1(k1_xboole_0,A,B) & v1_funct_1(k1_xboole_0))) # label(t56_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1424 (all A all B all C all D all E (v1_funct_1(E) & m2_relset_1(E,A,B) -> (r1_tarski(A,C) & r1_tarski(B,D) -> m2_relset_1(E,C,D) & v1_funct_1(E)))) # label(t32_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1425 $T # label(t17_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1426 $T # label(t5_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1427 (all A all B all C (C = k4_partfun1(A,B) <-> (all D (r2_hidden(D,C) <-> (exists E (v1_funct_1(E) & r1_tarski(k2_relat_1(E),B) & r1_tarski(k1_relat_1(E),A) & E = D & v1_relat_1(E))))))) # label(d5_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1428 $T # label(t11_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1429 $T # label(t88_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1430 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_partfun1(k8_relat_1(A,B),B))) # label(t145_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1431 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> -(r2_hidden(C,k9_relat_1(D,A)) & (all E (m1_subset_1(E,A) -> -(k1_funct_1(D,E) = C & r2_hidden(E,k4_relset_1(A,B,D)))))))) # label(t49_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1432 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k4_partfun1(C,A),k4_partfun1(C,B)))) # label(t127_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1433 $T # label(t170_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1434 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> k10_relat_1(C,B) = k4_relset_1(A,B,C))) # label(t53_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1435 $T # label(t173_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1436 $T # label(t137_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1437 $T # label(t103_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1438 $T # label(t108_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1439 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,k1_tarski(A),B) -> r1_tarski(k9_relat_1(D,C),k1_tarski(k1_funct_1(D,A))))) # label(t71_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1440 (all A all B all C (m2_relset_1(C,A,B) -> (v1_partfun1(C,A,B) <-> k4_relset_1(A,B,C) = A))) # label(d4_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1441 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_tarski(B)) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,k1_tarski(B)) -> (k4_relset_1(A,k1_tarski(B),C) = k4_relset_1(A,k1_tarski(B),D) -> D = C))))) # label(t74_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1442 $T # label(t163_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1443 (all A all B all C (m2_relset_1(C,k1_tarski(A),B) & v1_funct_1(C) -> v2_funct_1(C))) # label(t70_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1444 $T # label(t150_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1445 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) -> v2_funct_1(k3_partfun1(C,A,B))))) # label(t94_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1446 $T # label(t151_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1447 $T # label(t183_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1448 $T # label(t159_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1449 $T # label(t152_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1450 (all A all B (v1_funct_1(B) & m2_relset_1(B,k1_xboole_0,A) -> k1_tarski(k1_xboole_0) = k5_partfun1(k1_xboole_0,A,B))) # label(t176_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1451 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_xboole_0) -> (all D (m2_relset_1(D,B,k1_xboole_0) & v1_funct_1(D) -> C = D)))) # label(t65_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1452 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> k3_partfun1(D,k3_xboole_0(A,C),B) = k2_partfun1(A,B,k3_partfun1(D,A,B),C))) # label(t96_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1453 $T # label(t6_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1454 (all A (v1_relat_1(A) & v3_relat_2(A) & v8_relat_2(A) -> v1_relat_2(A) & v1_relat_1(A))) # label(cc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1455 (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) -> k2_xboole_0(A,B) != C)) & (all C (r2_hidden(C,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(A,C) = k1_funct_1(B,C)))))))) # label(t2_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1456 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> v1_funct_1(k9_relset_1(A,B,C,D)) & m2_relset_1(k9_relset_1(A,B,C,D),A,C))) # label(t45_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1457 $T # label(t90_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1458 (all A all B all C all D all E all F (m1_relset_1(F,C,D) & v1_funct_1(F) & m1_relset_1(E,A,B) & v1_funct_1(E) -> k5_relat_1(E,F) = k1_partfun1(A,B,C,D,E,F))) # label(redefinition_k1_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1459 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_tarski(k3_partfun1(C,A,B),C))) # label(t76_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1460 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(A,B) & r2_hidden(k1_funct_1(D,A),C) & r2_hidden(A,k1_relat_1(D)) -> k1_funct_1(D,A) = k1_funct_1(k3_partfun1(D,B,C),A)))) # label(t79_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1461 (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_xboole_0(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) & r1_partfun1(C,D) & (B = k1_xboole_0 -> k1_xboole_0 = A)))))) # label(t186_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1462 (all A k6_relat_1(A) = k6_partfun1(A)) # label(redefinition_k6_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1463 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> v1_funct_1(k7_relat_1(k8_relat_1(A,C),B)) & m2_relset_1(k7_relat_1(k8_relat_1(A,C),B),B,A))) # label(t47_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1464 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> v1_funct_1(k8_relset_1(A,B,D,C)) & m2_relset_1(k8_relset_1(A,B,D,C),C,B))) # label(t43_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1465 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k1_relat_1(C),A) & r1_tarski(k2_relat_1(C),B) -> k3_partfun1(C,A,B) = C))) # label(t85_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1466 (all A all B all C all D all E (v1_relat_1(E) & v1_funct_1(E) -> (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k3_partfun1(E,A,C),k3_partfun1(E,B,D))))) # label(t84_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1467 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (D = k5_partfun1(A,B,C) <-> (all E (r2_hidden(E,D) <-> (exists F (v1_funct_1(F) & E = F & v1_partfun1(F,A,B) & r1_partfun1(C,F) & m2_relset_1(F,A,B))))))))) # label(d7_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1468 (all A all B all C (m1_subset_1(C,k4_partfun1(A,B)) -> v1_funct_1(C) & m2_relset_1(C,A,B))) # label(t121_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1469 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,k1_relat_1(C)) & r1_tarski(k9_relat_1(C,A),B) -> v1_partfun1(k3_partfun1(C,A,B),A,B)))) # label(t117_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1470 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,k1_xboole_0,A) -> k1_xboole_0 = k9_relat_1(C,B))) # label(t60_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1471 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (v1_partfun1(C,A,B) <-> k1_tarski(C) = k5_partfun1(A,B,C)))) # label(t174_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1472 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r1_tarski(C,D) -> r1_tarski(k3_partfun1(C,A,B),k3_partfun1(D,A,B))))))) # label(t81_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1473 (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_relat_1(E) & v1_funct_1(E) -> (r1_partfun1(C,E) & r1_tarski(D,C) -> r1_partfun1(D,E)))))))) # label(t140_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1474 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> r1_partfun1(k3_partfun1(k1_xboole_0,A,B),C))) # label(t142_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1475 (all A all B (v1_funct_1(B) & m2_relset_1(B,k1_xboole_0,A) -> v1_partfun1(B,k1_xboole_0,A))) # label(t112_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1476 $T # label(t14_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1477 $T # label(t22_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1478 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> -(r2_hidden(C,k2_relat_1(D)) & (all E (m1_subset_1(E,A) -> -(r2_hidden(E,k4_relset_1(A,B,D)) & C = k1_funct_1(D,E))))))) # label(t26_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1479 $T # label(t4_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1480 (all A all B (v1_funct_1(B) & m2_relset_1(B,k1_xboole_0,A) -> k4_relset_1(k1_xboole_0,A,B) = k1_xboole_0 & k1_xboole_0 = k2_relat_1(B))) # label(t54_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1481 $T # label(t105_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1482 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> v1_funct_1(k8_relset_1(A,B,D,C)) & m2_relset_1(k8_relset_1(A,B,D,C),A,B))) # label(t44_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1483 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r1_tarski(A,B) -> r1_tarski(k3_partfun1(D,A,C),k3_partfun1(D,B,C))))) # label(t82_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1484 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((exists C (r1_tarski(B,C) & r1_tarski(A,C) & v1_funct_1(C) & v1_relat_1(C))) <-> r1_partfun1(A,B)))))) # label(t131_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1485 $T # label(dt_k5_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1486 $T # label(t157_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1487 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(A,C) -> v1_funct_1(D) & m2_relset_1(D,C,B)))) # label(t30_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1488 $T # label(t161_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1489 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> m2_relset_1(k9_relset_1(A,B,C,D),A,B) & v1_funct_1(k9_relset_1(A,B,C,D)))) # label(t46_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1490 (all A all B all C all D (m2_relset_1(D,A,k1_tarski(B)) & v1_funct_1(D) -> (r2_hidden(C,k4_relset_1(A,k1_tarski(B),D)) -> k1_funct_1(D,C) = B))) # label(t73_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1491 (all A all B all C all D (r2_hidden(A,f1_s4_partfun1) & r2_hidden(B,f2_s4_partfun1) & p1_s4_partfun1(A,B,C) & p1_s4_partfun1(A,B,D) -> D = C)) & (all A all B all C (r2_hidden(B,f2_s4_partfun1) & p1_s4_partfun1(A,B,C) & r2_hidden(A,f1_s4_partfun1) -> r2_hidden(C,f3_s4_partfun1))) -> (exists A (v1_funct_1(A) & (all B all C (r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1,A)) <-> (exists D p1_s4_partfun1(B,C,D)) & r2_hidden(C,f2_s4_partfun1) & r2_hidden(B,f1_s4_partfun1))) & (all B all C (r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1,A)) -> p1_s4_partfun1(B,C,k1_funct_1(A,k4_tarski(B,C))))) & m2_relset_1(A,k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1))) # label(s4_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1492 (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) -> (k4_relset_1(A,B,C) = k4_relset_1(A,B,D) & (all E (m1_subset_1(E,A) -> (r2_hidden(E,k4_relset_1(A,B,C)) -> k1_funct_1(D,E) = k1_funct_1(C,E)))) -> C = D))))) # label(t34_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1493 $T # label(t165_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1494 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,B) -> r1_partfun1(A,B)))))) # label(t135_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1495 $T # label(t89_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1496 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(C,D) -> m2_relset_1(C,A,B) & v1_funct_1(C)))))) # label(t33_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1497 (all A all B exists C (m1_relset_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C))) # label(rc2_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1498 (all A all B (v1_funct_1(B) & m2_relset_1(B,k1_xboole_0,A) -> v2_funct_1(B))) # label(t59_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1499 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_tarski(B)) -> (all D (m2_relset_1(D,A,k1_tarski(B)) & v1_funct_1(D) -> r1_partfun1(C,D))))) # label(t143_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1500 (all A all B all C (m2_relset_1(C,k1_xboole_0,A) & v1_funct_1(C) -> (all D (m2_relset_1(D,k1_xboole_0,B) & v1_funct_1(D) -> D = C)))) # label(t58_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1501 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (all E (v1_relat_1(E) & v1_funct_1(E) -> r1_tarski(k1_partfun1(C,A,A,B,k3_partfun1(D,C,A),k3_partfun1(E,A,B)),k3_partfun1(k5_relat_1(D,E),C,B)))))) # label(t92_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1502 $T # label(t107_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1503 $T # label(t15_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1504 (exists A (v2_funct_1(A) & v1_xboole_0(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1505 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r1_tarski(A,B) -> r1_tarski(k3_partfun1(D,C,A),k3_partfun1(D,C,B))))) # label(t83_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1506 $T # label(t104_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1507 $T # label(t166_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1508 $T # label(t21_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1509 (all A k1_tarski(k1_xboole_0) = k4_partfun1(A,k1_xboole_0)) # label(t123_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1510 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_xboole_0 = k2_relat_1(C) -> m2_relset_1(C,A,B) & v1_funct_1(C)))) # label(t63_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1511 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> C = k3_partfun1(C,A,B))) # label(t87_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1512 $T # label(t118_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1513 (exists A (v1_relat_1(A) & (all B (r2_hidden(B,f1_s1_partfun1) -> (-p1_s1_partfun1(B) -> k1_funct_1(A,B) = f3_s1_partfun1(B)) & (p1_s1_partfun1(B) -> f2_s1_partfun1(B) = k1_funct_1(A,B)))) & f1_s1_partfun1 = k1_relat_1(A) & v1_funct_1(A))) # label(s1_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1514 (all A all B all C (m2_relset_1(C,A,B) -> C = k5_relat_1(C,k6_relat_1(B)))) # label(t37_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1515 $T # label(t12_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1516 (all A (v1_partfun1(k6_partfun1(A),A,A) & m2_relset_1(k6_partfun1(A),A,A))) # label(dt_k6_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1517 (all A all B all C (p1_s2_partfun1(A,C) & p1_s2_partfun1(A,B) & r2_hidden(A,f1_s2_partfun1) -> C = B)) & (all A all B (p1_s2_partfun1(A,B) & r2_hidden(A,f1_s2_partfun1) -> r2_hidden(B,f2_s2_partfun1))) -> (exists A (v1_funct_1(A) & m2_relset_1(A,f1_s2_partfun1,f2_s2_partfun1) & (all B (r2_hidden(B,k4_relset_1(f1_s2_partfun1,f2_s2_partfun1,A)) -> p1_s2_partfun1(B,k1_funct_1(A,B)))) & (all B (r2_hidden(B,k4_relset_1(f1_s2_partfun1,f2_s2_partfun1,A)) <-> (exists C p1_s2_partfun1(B,C)) & r2_hidden(B,f1_s2_partfun1))))) # label(s2_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1518 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) -> k3_partfun1(k2_funct_1(C),B,A) = k2_funct_1(k3_partfun1(C,A,B))))) # label(t95_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1519 $T # label(t9_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1520 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> k9_relat_1(C,A) = k2_relat_1(C))) # label(t51_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1521 $T # label(t154_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1522 (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) -> (C = k2_xboole_0(A,B) -> (all D (r2_hidden(D,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(A,D) = k1_funct_1(B,D)))))))))) # label(t3_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1523 $T # label(t160_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1524 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(D,k5_partfun1(A,B,C)) -> r1_partfun1(C,D)))))) # label(t171_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1525 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(C) = k1_xboole_0 -> m2_relset_1(C,A,B) & v1_funct_1(C)))) # label(t55_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1526 $T # label(t181_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1527 $T # label(d2_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1528 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r1_tarski(k4_relset_1(A,B,D),C) -> v1_funct_1(D) & m2_relset_1(D,C,B)))) # label(t28_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1529 $T # label(dt_k4_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1530 (all A all B (p1_s5_partfun1(A,B) -> r2_hidden(f4_s5_partfun1(A,B),f3_s5_partfun1))) -> (exists A ((all B all C (r2_hidden(B,f1_s5_partfun1) & p1_s5_partfun1(B,C) & r2_hidden(C,f2_s5_partfun1) <-> r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1,A)))) & (all B all C (r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1,A)) -> k1_funct_1(A,k4_tarski(B,C)) = f4_s5_partfun1(B,C))) & m2_relset_1(A,k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1) & v1_funct_1(A))) # label(s5_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1531 (all A (v1_relat_1(A) & v1_funct_1(A) -> k3_partfun1(A,k1_relat_1(A),k2_relat_1(A)) = A)) # label(t86_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1532 (all A all B -v1_xboole_0(k4_partfun1(A,B))) # label(fc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1533 $T # label(t124_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1534 (all A all B (v1_funct_1(B) & m2_relset_1(B,k1_xboole_0,A) -> B = k1_xboole_0)) # label(t57_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1535 $T # label(t182_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1536 (all A (v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)) & v8_relat_2(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_1(k6_relat_1(A)))) # label(fc2_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1537 (all A all B all C all D all E all F (r1_tarski(A,k2_zfmisc_1(B,C)) & r1_tarski(D,k2_zfmisc_1(E,F)) -> r1_tarski(k2_xboole_0(A,D),k2_zfmisc_1(k2_xboole_0(B,E),k2_xboole_0(C,F))))) # label(t1_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1538 $T # label(t110_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1539 (all A all B all C (m2_relset_1(C,A,B) -> C = k5_relat_1(k6_relat_1(A),C))) # label(t36_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1540 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (v2_funct_1(C) -> m2_relset_1(k2_funct_1(C),B,A) & v1_funct_1(k2_funct_1(C))))) # label(t39_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1541 (all A (v1_relat_1(A) & v1_funct_1(A) -> r1_partfun1(k1_xboole_0,A))) # label(t141_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1542 $T # label(t18_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1543 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> r1_partfun1(k7_relat_1(k8_relat_1(A,C),B),C))) # label(t146_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1544 $T # label(t48_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1545 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> r2_hidden(C,k4_partfun1(A,B)))) # label(t119_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1546 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k4_partfun1(A,C),k4_partfun1(B,C)))) # label(t125_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1547 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> r1_partfun1(A,B)))))) # label(t138_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1548 $T # label(t8_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1549 (all A all B (m2_relset_1(B,A,k1_xboole_0) & v1_funct_1(B) -> B = k1_xboole_0)) # label(t64_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1550 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> k5_partfun1(k1_xboole_0,A,B) = k1_tarski(B))) # label(t175_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1551 $T # label(t155_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1552 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (r2_hidden(D,k4_relset_1(A,B,C)) & k1_funct_1(C,D) = k1_funct_1(C,E) & r2_hidden(E,k4_relset_1(A,B,C)) -> E = D))))) -> v2_funct_1(C)))) # label(t38_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1553 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(A) & m2_relset_1(A,k1_relat_1(A),k2_relat_1(A)))) # label(t24_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1554 $T # label(t50_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1555 $T # label(t184_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1556 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(A,k4_relset_1(B,C,k3_partfun1(D,B,C))) -> k1_funct_1(D,A) = k1_funct_1(k3_partfun1(D,B,C),A)))) # label(t80_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1557 (all A all B k1_xboole_0 = k3_partfun1(k1_xboole_0,A,B)) # label(t91_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1558 (all A all B (v1_relat_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_funct_1(A) -> r1_partfun1(A,A))) # label(reflexivity_r1_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1559 $T # label(t75_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.24 1560 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (v1_partfun1(k3_partfun1(C,A,B),A,B) -> r1_tarski(k9_relat_1(C,A),B)))) # label(t116_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1561 $T # label(t133_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1562 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(B,C) -> v1_funct_1(D) & m2_relset_1(D,A,C)))) # label(t31_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1563 $T # label(t13_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1564 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (k1_xboole_0 = B & v1_partfun1(C,A,B) -> k1_xboole_0 = A))) # label(t99_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1565 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r2_hidden(C,k4_relset_1(A,B,D)) -> r2_hidden(k1_funct_1(D,C),B)))) # label(t27_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1566 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(k2_relat_1(D),C) -> m2_relset_1(D,A,C) & v1_funct_1(D)))) # label(t29_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1567 (all A all B all C all D (m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(A,B),C) -> (k4_relset_1(k2_zfmisc_1(A,B),C,D) = k4_relset_1(k2_zfmisc_1(A,B),C,E) & (all F all G (r2_hidden(k4_tarski(F,G),k4_relset_1(k2_zfmisc_1(A,B),C,D)) -> k1_funct_1(D,k4_tarski(F,G)) = k1_funct_1(E,k4_tarski(F,G)))) -> D = E))))) # label(t35_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1568 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> -((all E (m2_relset_1(E,A,B) & v1_funct_1(E) -> -(v1_partfun1(E,A,B) & r1_partfun1(C,E) & r1_partfun1(D,E)))) & r1_partfun1(C,D) & (k1_xboole_0 = B -> A = k1_xboole_0)))))) # label(t162_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1569 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,k1_tarski(A),B) -> r1_tarski(k2_relat_1(C),k1_tarski(k1_funct_1(C,A))))) # label(t69_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1570 $T # label(t40_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1571 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (-r1_xboole_0(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) -> r1_partfun1(C,D)))))) # label(t185_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1572 $T # label(d1_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1573 $T # label(t109_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1574 $T # label(t179_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1575 $T # label(t102_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1576 $T # label(t129_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1577 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,k1_xboole_0) -> (k1_xboole_0 != A -> k5_partfun1(A,k1_xboole_0,B) = k1_xboole_0))) # label(t172_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1578 $T # label(t23_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1579 (all A all B (v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(B) & v1_relat_1(A) -> (r1_partfun1(A,B) -> r1_partfun1(B,A)))) # label(symmetry_r1_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1580 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(B,C) & r1_tarski(A,C) -> r1_partfun1(A,B)))))))) # label(t139_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1581 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C (r2_hidden(C,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(A,C) = k1_funct_1(B,C))) <-> r1_partfun1(A,B)))))) # label(d6_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1582 (all A all B (v1_partfun1(k3_partfun1(k1_xboole_0,A,B),A,B) -> k1_xboole_0 = A)) # label(t114_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1583 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_xboole_0) -> k9_relat_1(C,B) = k1_xboole_0)) # label(t67_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1584 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (v1_partfun1(D,A,B) & r1_partfun1(C,D) & v1_partfun1(C,A,B) -> D = C))))) # label(t148_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1585 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (all E (v1_funct_1(E) & v1_relat_1(E) -> (r1_tarski(k3_xboole_0(k2_relat_1(D),k1_relat_1(E)),A) -> k3_partfun1(k5_relat_1(D,E),C,B) = k1_partfun1(C,A,A,B,k3_partfun1(D,C,A),k3_partfun1(E,A,B))))))) # label(t93_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1586 (all A k4_partfun1(k1_xboole_0,A) = k1_tarski(k1_xboole_0)) # label(t122_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1587 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_partfun1(A,B) & k1_relat_1(A) = k1_relat_1(B) -> B = A))))) # label(t136_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1588 $T # label(t164_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1589 (all A all B all C (v1_relat_1(A) & v1_funct_1(A) -> m2_relset_1(k3_partfun1(A,B,C),B,C) & v1_funct_1(k3_partfun1(A,B,C)))) # label(dt_k3_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1590 (all A all B all C (m2_relset_1(C,k1_xboole_0,A) & v1_funct_1(C) -> k1_xboole_0 = k10_relat_1(C,B))) # label(t61_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1591 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (k1_relat_1(D) = k1_tarski(A) & r2_hidden(k1_funct_1(D,A),C) & r2_hidden(A,B) -> m2_relset_1(D,B,C) & v1_funct_1(D)))) # label(t72_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1592 $T # label(t134_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1593 $T # label(t180_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1594 $T # label(t52_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1595 (all A all B r1_tarski(k4_partfun1(k1_xboole_0,A),k4_partfun1(B,A))) # label(t126_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1596 (all A all B all C all D (m1_relset_1(C,A,B) & v1_funct_1(C) -> v1_funct_1(k2_partfun1(A,B,C,D)) & m2_relset_1(k2_partfun1(A,B,C,D),A,B))) # label(dt_k2_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1597 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C k7_relat_1(k8_relat_1(C,A),B) = k3_partfun1(A,B,C)))) # label(d3_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1598 $T # label(t42_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1599 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (r2_hidden(D,k5_partfun1(A,B,C)) -> m2_relset_1(D,A,B) & v1_funct_1(D))))) # label(t168_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1600 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_partfun1(k3_partfun1(C,A,B),C))) # label(t147_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1601 $T # label(t178_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1602 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k2_relat_1(B),A) -> m2_relset_1(B,k1_relat_1(B),A) & v1_funct_1(B)))) # label(t25_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1603 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,A,B) -> k7_relat_1(C,D) = k2_partfun1(A,B,C,D))) # label(redefinition_k2_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1604 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v1_partfun1(k3_partfun1(C,A,B),A,B) -> r1_tarski(A,k1_relat_1(C))))) # label(t113_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1605 $T # label(t7_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1606 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_tarski(k2_relat_1(k3_partfun1(C,A,B)),k2_relat_1(C)) & r1_tarski(k4_relset_1(A,B,k3_partfun1(C,A,B)),k1_relat_1(C)))) # label(t77_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1607 $T # label(t101_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1608 (all A all B (m2_relset_1(B,A,k1_xboole_0) & v1_funct_1(B) -> k1_xboole_0 = k4_relset_1(A,k1_xboole_0,B) & k2_relat_1(B) = k1_xboole_0)) # label(t62_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1609 $T # label(t19_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1610 (all A all B all C all D (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k4_partfun1(A,C),k4_partfun1(B,D)))) # label(t128_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1611 $T # label(t156_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1612 (all A (p1_s3_partfun1(A) -> r2_hidden(f3_s3_partfun1(A),f2_s3_partfun1))) -> (exists A ((all B (r2_hidden(B,k4_relset_1(f1_s3_partfun1,f2_s3_partfun1,A)) -> f3_s3_partfun1(B) = k1_funct_1(A,B))) & (all B (r2_hidden(B,f1_s3_partfun1) & p1_s3_partfun1(B) <-> r2_hidden(B,k4_relset_1(f1_s3_partfun1,f2_s3_partfun1,A)))) & m2_relset_1(A,f1_s3_partfun1,f2_s3_partfun1) & v1_funct_1(A))) # label(s3_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1613 $T # label(t41_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1614 $T # label(t16_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1615 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(A,k4_relset_1(B,C,k3_partfun1(D,B,C))) <-> r2_hidden(A,k1_relat_1(D)) & r2_hidden(k1_funct_1(D,A),C) & r2_hidden(A,B)))) # label(t78_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1616 $T # label(t106_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1617 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_partfun1(k7_relat_1(B,A),B))) # label(t144_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1618 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(k1_relat_1(A),k1_relat_1(B)) -> (r1_partfun1(A,B) <-> (all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(B,C) = k1_funct_1(A,C))))))))) # label(t132_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1619 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m2_relset_1(E,A,B) & v1_funct_1(E) -> (v1_partfun1(E,A,B) & r1_partfun1(D,E) & r1_partfun1(C,E) -> r1_partfun1(C,D)))))))) # label(t158_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1620 $T # label(t153_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1621 $T # label(t149_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1622 $T # label(t167_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1623 (all A exists B (v1_relat_2(B) & v3_relat_2(B) & v4_relat_2(B) & v1_partfun1(B,A,A) & v8_relat_2(B) & v1_relat_1(B) & m1_relset_1(B,A,A))) # label(rc3_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1624 $T # label(t20_partfun1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1625 (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]. 16.84/16.25 1626 (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]. 16.84/16.25 1627 (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]. 16.84/16.25 1628 (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]. 16.84/16.25 1629 (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]. 16.84/16.25 1630 (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]. 16.84/16.25 1631 (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]. 16.84/16.25 1632 (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]. 16.84/16.25 1633 (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]. 16.84/16.25 1634 (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]. 16.84/16.25 1635 (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]. 16.84/16.25 1636 (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]. 16.84/16.25 1637 (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]. 16.84/16.25 1638 (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]. 16.84/16.25 1639 (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]. 16.84/16.25 1640 (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]. 16.84/16.25 1641 $T # label(t27_mcart_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1642 (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]. 16.84/16.25 1643 (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]. 16.84/16.25 1644 $T # label(dt_k18_mcart_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1645 (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]. 16.84/16.25 1646 (all A k17_mcart_1(A) = k1_mcart_1(k1_mcart_1(A))) # label(d14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1647 (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]. 16.84/16.25 1648 (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]. 16.84/16.25 1649 (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]. 16.84/16.25 1650 (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]. 16.84/16.25 1651 (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]. 16.84/16.25 1652 $T # label(dt_k4_mcart_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1653 (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]. 16.84/16.25 1654 (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]. 16.84/16.25 1655 (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]. 16.84/16.25 1656 (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]. 16.84/16.25 1657 (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]. 16.84/16.25 1658 (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]. 16.84/16.25 1659 (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]. 16.84/16.25 1660 (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]. 16.84/16.25 1661 (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]. 16.84/16.25 1662 (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]. 16.84/16.25 1663 (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]. 16.84/16.25 1664 (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]. 16.84/16.25 1665 (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]. 16.84/16.25 1666 $T # label(t22_mcart_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1667 (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]. 16.84/16.25 1668 (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]. 16.84/16.25 1669 (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]. 16.84/16.25 1670 $T # label(dt_k17_mcart_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1671 (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]. 16.84/16.25 1672 (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]. 16.84/16.25 1673 (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]. 16.84/16.25 1674 (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]. 16.84/16.25 1675 $T # label(dt_k1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1676 (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]. 16.84/16.25 1677 (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]. 16.84/16.25 1678 (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]. 16.84/16.25 1679 (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]. 16.84/16.25 1680 (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]. 16.84/16.25 1681 (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]. 16.84/16.25 1682 (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]. 16.84/16.25 1683 (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]. 16.84/16.25 1684 (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]. 16.84/16.25 1685 (all A k1_mcart_1(k2_mcart_1(A)) = k19_mcart_1(A)) # label(d16_mcart_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1686 $T # label(t21_mcart_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1687 (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]. 16.84/16.25 1688 (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]. 16.84/16.25 1689 (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]. 16.84/16.25 1690 (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]. 16.84/16.25 1691 (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]. 16.84/16.25 1692 (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]. 16.84/16.25 1693 $T # label(dt_k19_mcart_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1694 (all A k20_mcart_1(A) = k2_mcart_1(k2_mcart_1(A))) # label(d17_mcart_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1695 (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]. 16.84/16.25 1696 (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]. 16.84/16.25 1697 (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]. 16.84/16.25 1698 (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]. 16.84/16.25 1699 (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]. 16.84/16.25 1700 (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]. 16.84/16.25 1701 (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]. 16.84/16.25 1702 (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]. 16.84/16.25 1703 (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]. 16.84/16.25 1704 (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]. 16.84/16.25 1705 (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]. 16.84/16.25 1706 (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]. 16.84/16.25 1707 (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]. 16.84/16.25 1708 (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]. 16.84/16.25 1709 (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]. 16.84/16.25 1710 (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]. 16.84/16.25 1711 (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]. 16.84/16.25 1712 (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]. 16.84/16.25 1713 (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]. 16.84/16.25 1714 (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]. 16.84/16.25 1715 (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]. 16.84/16.25 1716 (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]. 16.84/16.25 1717 (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]. 16.84/16.25 1718 (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]. 16.84/16.25 1719 (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]. 16.84/16.25 1720 $T # label(dt_k3_mcart_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1721 (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]. 16.84/16.25 1722 (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]. 16.84/16.25 1723 (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]. 16.84/16.25 1724 (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]. 16.84/16.25 1725 (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]. 16.84/16.25 1726 (all A k18_mcart_1(A) = k2_mcart_1(k1_mcart_1(A))) # label(d15_mcart_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1727 (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]. 16.84/16.25 1728 $T # label(dt_k2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1729 (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]. 16.84/16.25 1730 (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]. 16.84/16.25 1731 (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]. 16.84/16.25 1732 (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]. 16.84/16.25 1733 (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]. 16.84/16.25 1734 (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]. 16.84/16.25 1735 $T # label(dt_k20_mcart_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1736 (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]. 16.84/16.25 1737 (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]. 16.84/16.25 1738 (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]. 16.84/16.25 1739 (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]. 16.84/16.25 1740 (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]. 16.84/16.25 1741 $T # label(t30_mcart_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.25 1742 (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]. 16.84/16.25 1743 (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]. 16.84/16.25 1744 (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]. 16.84/16.25 1745 (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]. 16.84/16.25 1746 (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]. 16.84/16.25 1747 (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]. 16.84/16.25 1748 (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]. 16.84/16.25 1749 (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]. 16.84/16.25 1750 (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]. 16.84/16.26 1751 (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]. 16.84/16.26 1752 (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]. 16.84/16.26 1753 (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]. 16.84/16.26 1754 (all A -(r2_hidden(A,f1_s1_wellord2) & (all B -(p1_s1_wellord2(A,B) & r2_hidden(B,f2_s1_wellord2))))) -> (exists A (v1_relat_1(A) & v1_funct_1(A) & k1_relat_1(A) = f1_s1_wellord2 & (all B (r2_hidden(B,f1_s1_wellord2) -> p1_s1_wellord2(B,k1_funct_1(A,B)))) & r1_tarski(k2_relat_1(A),f2_s1_wellord2))) # label(s1_wellord2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1755 (all A (v3_ordinal1(A) -> v2_wellord1(k1_wellord2(A)))) # label(t7_wellord2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1756 $T # label(t1_wellord2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1757 $T # label(t18_wellord2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1758 $T # label(t15_wellord2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1759 (all A all B (v3_ordinal1(B) -> (r1_tarski(A,B) -> r1_ordinal1(k2_wellord2(k1_wellord2(A)),B)))) # label(t17_wellord2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1760 $T # label(t24_wellord2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1761 (all A (v1_relat_1(A) -> v3_ordinal1(k2_wellord2(A)))) # label(dt_k2_wellord2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1762 (all A all B all C (r2_wellord2(A,B) & r2_wellord2(B,C) -> r2_wellord2(A,C))) # label(t22_wellord2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1763 (all A (v1_relat_1(A) -> -(v2_wellord1(A) & (all B (v3_ordinal1(B) -> -r4_wellord1(A,k1_wellord2(B)))) & (all B -(r2_hidden(B,k3_relat_1(A)) & (all C (v3_ordinal1(C) -> -r4_wellord1(k2_wellord1(A,k1_wellord1(A,B)),k1_wellord2(C))))))))) # label(t13_wellord2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1764 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) -> (k2_wellord2(B) = A <-> r1_wellord2(A,B)))))) # label(d3_wellord2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1765 (all A all B (r1_tarski(A,B) -> k1_wellord2(A) = k2_wellord1(k1_wellord2(B),A))) # label(t8_wellord2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1766 (all A all B ((exists C (v1_relat_1(C) & k2_relat_1(C) = B & k1_relat_1(C) = A & v2_funct_1(C) & v1_funct_1(C))) <-> r2_wellord2(A,B))) # label(d4_wellord2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1767 (all A v8_relat_2(k1_wellord2(A))) # label(t3_wellord2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1768 (all A exists B (v1_relat_1(B) & r2_wellord1(B,A))) # label(t26_wellord2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1769 (all A v4_relat_2(k1_wellord2(A))) # label(t5_wellord2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1770 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r4_wellord1(k1_wellord2(A),k1_wellord2(B)) -> B = A))))) # label(t11_wellord2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1771 $T # label(t19_wellord2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1772 (all A all B (r2_wellord2(A,B) -> r2_wellord2(B,A))) # label(symmetry_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1773 (all A (v3_ordinal1(A) -> v1_wellord1(k1_wellord2(A)))) # label(t6_wellord2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1774 (all A (v3_ordinal1(A) -> (all B (r1_tarski(B,A) -> v2_wellord1(k1_wellord2(B)))))) # label(t9_wellord2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1775 (all A all B r2_wellord2(A,A)) # label(reflexivity_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1776 (all A (v1_relat_1(A) -> -((all B (v3_ordinal1(B) -> -r4_wellord1(A,k1_wellord2(B)))) & v2_wellord1(A)))) # label(t14_wellord2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1777 (all A -(r2_hidden(A,f1_s2_wellord2) & (all B all C -(p1_s2_wellord2(A,B,C) & r2_hidden(C,f3_s2_wellord2) & r2_hidden(B,f2_s2_wellord2))))) -> (exists A (v1_funct_1(A) & (exists B (v1_relat_1(B) & (all C (r2_hidden(C,f1_s2_wellord2) -> p1_s2_wellord2(C,k1_funct_1(A,C),k1_funct_1(B,C)))) & k1_relat_1(B) = f1_s2_wellord2 & k1_relat_1(A) = f1_s2_wellord2 & v1_funct_1(B))) & v1_relat_1(A))) # label(s2_wellord2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1778 (all A v1_relat_2(k1_wellord2(A))) # label(t2_wellord2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1779 (all A (-v1_xboole_0(A) -> -((all B exists C ((all D k1_tarski(D) != k3_xboole_0(B,C)) & r2_hidden(C,A))) & (all B all C (r2_hidden(B,A) & r2_hidden(C,A) -> B = C | r1_xboole_0(B,C))) & (all B -(r2_hidden(B,A) & k1_xboole_0 = B))))) # label(t27_wellord2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1780 (all A all B (v1_relat_1(B) -> ((all C all D (r2_hidden(D,A) & r2_hidden(C,A) -> (r2_hidden(k4_tarski(C,D),B) <-> r1_tarski(C,D)))) & A = k3_relat_1(B) <-> B = k1_wellord2(A)))) # label(d1_wellord2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1781 (all A (v3_ordinal1(A) -> v6_relat_2(k1_wellord2(A)))) # label(t4_wellord2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1782 (all A all B (r2_tarski(A,B) <-> r2_wellord2(A,B))) # label(redefinition_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1783 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(A,B) -> k1_wellord1(k1_wellord2(B),A) = A))))) # label(t10_wellord2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1784 (all A v1_relat_1(k1_wellord2(A))) # label(dt_k1_wellord2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1785 (all A all B (v1_relat_1(B) -> (r2_wellord1(B,A) -> A = k3_relat_1(k2_wellord1(B,A)) & v2_wellord1(k2_wellord1(B,A))))) # label(t25_wellord2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1786 $T # label(t16_wellord2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1787 (all A (v1_relat_1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r4_wellord1(A,k1_wellord2(C)) & r4_wellord1(A,k1_wellord2(B)) -> C = B))))))) # label(t12_wellord2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1788 $T # label(t23_wellord2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1789 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> (all B (v3_ordinal1(B) -> (r4_wellord1(A,k1_wellord2(B)) <-> B = k2_wellord2(A))))))) # label(d2_wellord2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1790 $T # label(t21_wellord2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1791 (all A (-v1_xboole_0(A) -> -((all B (v1_relat_1(B) & v1_funct_1(B) -> -(A = k1_relat_1(B) & (all C (r2_hidden(C,A) -> r2_hidden(k1_funct_1(B,C),C)))))) & (all B -(r2_hidden(B,A) & B = k1_xboole_0))))) # label(t28_wellord2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1792 $T # label(t20_wellord2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1793 (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]. 16.84/16.26 1794 (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]. 16.84/16.26 1795 (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]. 16.84/16.26 1796 (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]. 16.84/16.26 1797 (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]. 16.84/16.26 1798 (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]. 16.84/16.26 1799 (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]. 16.84/16.26 1800 (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]. 16.84/16.26 1801 (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]. 16.84/16.26 1802 (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]. 16.84/16.26 1803 $T # label(t140_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1804 $T # label(t52_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1805 $T # label(t33_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1806 (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]. 16.84/16.26 1807 (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]. 16.84/16.26 1808 (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]. 16.84/16.26 1809 (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]. 16.84/16.26 1810 $T # label(t91_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1811 $T # label(t124_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1812 (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]. 16.84/16.26 1813 (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]. 16.84/16.26 1814 (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]. 16.84/16.26 1815 $T # label(t96_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1816 $T # label(t84_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1817 (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]. 16.84/16.26 1818 $T # label(t98_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1819 (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]. 16.84/16.26 1820 (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]. 16.84/16.26 1821 $T # label(t78_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1822 (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]. 16.84/16.26 1823 (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]. 16.84/16.26 1824 (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]. 16.84/16.26 1825 $T # label(t112_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1826 (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]. 16.84/16.26 1827 (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]. 16.84/16.26 1828 (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]. 16.84/16.26 1829 $T # label(t153_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1830 (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]. 16.84/16.26 1831 $T # label(t2_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1832 (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]. 16.84/16.26 1833 (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]. 16.84/16.26 1834 (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]. 16.84/16.26 1835 (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]. 16.84/16.26 1836 (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]. 16.84/16.26 1837 (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]. 16.84/16.26 1838 (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]. 16.84/16.26 1839 (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]. 16.84/16.26 1840 $T # label(t114_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1841 $T # label(t110_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1842 (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]. 16.84/16.26 1843 (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]. 16.84/16.26 1844 (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]. 16.84/16.26 1845 (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]. 16.84/16.26 1846 (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]. 16.84/16.26 1847 (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]. 16.84/16.26 1848 (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]. 16.84/16.26 1849 (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]. 16.84/16.26 1850 (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]. 16.84/16.26 1851 (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]. 16.84/16.26 1852 (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]. 16.84/16.26 1853 $T # label(t54_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1854 $T # label(t105_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1855 (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]. 16.84/16.26 1856 $T # label(t122_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1857 $T # label(t102_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1858 (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]. 16.84/16.26 1859 (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]. 16.84/16.26 1860 $T # label(t109_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1861 $T # label(t56_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1862 $T # label(t94_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1863 (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]. 16.84/16.26 1864 $T # label(t147_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1865 (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]. 16.84/16.26 1866 $T # label(t1_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1867 $T # label(t89_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1868 $T # label(t100_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1869 (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]. 16.84/16.26 1870 $T # label(t123_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1871 (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]. 16.84/16.26 1872 $T # label(t90_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1873 (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]. 16.84/16.26 1874 (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]. 16.84/16.26 1875 (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]. 16.84/16.26 1876 (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]. 16.84/16.26 1877 $T # label(t69_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1878 $T # label(t157_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1879 $T # label(t139_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1880 $T # label(t68_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1881 (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]. 16.84/16.26 1882 (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]. 16.84/16.26 1883 (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]. 16.84/16.26 1884 $T # label(t93_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1885 (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]. 16.84/16.26 1886 (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]. 16.84/16.26 1887 (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]. 16.84/16.26 1888 $T # label(t10_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1889 (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]. 16.84/16.26 1890 (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]. 16.84/16.26 1891 $T # label(t42_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1892 (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]. 16.84/16.26 1893 $T # label(t127_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1894 (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]. 16.84/16.26 1895 (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]. 16.84/16.26 1896 $T # label(t129_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1897 (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]. 16.84/16.26 1898 $T # label(t135_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1899 (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]. 16.84/16.26 1900 (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]. 16.84/16.26 1901 $T # label(t104_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1902 $T # label(dt_k1_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1903 (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]. 16.84/16.26 1904 $T # label(t39_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1905 (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]. 16.84/16.26 1906 (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]. 16.84/16.26 1907 (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]. 16.84/16.26 1908 (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]. 16.84/16.26 1909 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]. 16.84/16.26 1910 $T # label(t128_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1911 (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]. 16.84/16.26 1912 (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]. 16.84/16.26 1913 (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]. 16.84/16.26 1914 (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]. 16.84/16.26 1915 $T # label(t15_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1916 $T # label(t63_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1917 (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]. 16.84/16.26 1918 (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]. 16.84/16.26 1919 $T # label(t101_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1920 $T # label(t97_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1921 $T # label(t125_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1922 (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]. 16.84/16.26 1923 (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]. 16.84/16.26 1924 (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]. 16.84/16.26 1925 $T # label(t13_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1926 (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]. 16.84/16.26 1927 (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]. 16.84/16.26 1928 (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]. 16.84/16.26 1929 $T # label(t144_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1930 $T # label(t81_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1931 (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]. 16.84/16.26 1932 (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]. 16.84/16.26 1933 (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]. 16.84/16.26 1934 $T # label(t103_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1935 (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]. 16.84/16.26 1936 $T # label(t117_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1937 (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]. 16.84/16.26 1938 $T # label(t126_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1939 $T # label(t71_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1940 (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]. 16.84/16.26 1941 (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]. 16.84/16.26 1942 (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]. 16.84/16.26 1943 $T # label(t57_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.26 1944 (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]. 16.84/16.26 1945 (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]. 16.84/16.26 1946 (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]. 16.84/16.26 1947 (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]. 16.84/16.26 1948 (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]. 16.84/16.27 1949 (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]. 16.84/16.27 1950 (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]. 16.84/16.27 1951 $T # label(t138_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.27 1952 $T # label(t163_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.27 1953 (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]. 16.84/16.27 1954 $T # label(t95_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.27 1955 $T # label(t58_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.27 1956 (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]. 16.84/16.27 1957 (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]. 16.84/16.27 1958 (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]. 16.84/16.27 1959 $T # label(t150_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.27 1960 $T # label(t111_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.27 1961 (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]. 16.84/16.27 1962 (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]. 16.84/16.27 1963 (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]. 16.84/16.27 1964 (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]. 16.84/16.27 1965 $T # label(t106_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.27 1966 (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]. 16.84/16.27 1967 $T # label(t72_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.27 1968 (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]. 16.84/16.27 1969 (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]. 16.84/16.27 1970 (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]. 16.84/16.27 1971 (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]. 16.84/16.27 1972 (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]. 16.84/16.27 1973 (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]. 16.84/16.27 1974 (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]. 16.84/16.27 1975 (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]. 16.84/16.27 1976 $T # label(t107_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.27 1977 (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]. 16.84/16.27 1978 $T # label(t137_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.27 1979 (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]. 16.84/16.27 1980 (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]. 16.84/16.27 1981 (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]. 16.84/16.27 1982 (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]. 16.84/16.27 1983 (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]. 16.84/16.27 1984 (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]. 16.84/16.27 1985 (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]. 16.84/16.27 1986 (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]. 16.84/16.27 1987 (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]. 16.84/16.27 1988 (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]. 16.84/16.27 1989 (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]. 16.84/16.27 1990 (all A -v1_xboole_0(k1_funct_2(A,A))) # label(fc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.27 1991 $T # label(t108_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.27 1992 (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]. 16.84/16.27 1993 (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]. 16.84/16.27 1994 $T # label(t80_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.27 1995 (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]. 16.84/16.27 1996 (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]. 16.84/16.27 1997 (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]. 16.84/16.27 1998 (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]. 16.84/16.27 1999 (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]. 16.84/16.27 2000 (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]. 16.84/16.27 2001 (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]. 16.84/16.27 2002 (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]. 16.84/16.27 2003 $T # label(t99_funct_2) # label(axiom) # label(non_clause). [assumption]. 16.84/16.27 2004 (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]. 16.84/16.27 2005 (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]. 16.84/16.27 2006 (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]. 16.84/16.27 2007 (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]. 16.84/16.27 2008 (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]. 16.84/16.27 2009 (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]. 16.84/16.27 2010 $T # label(t67_funct_3) # label(axiom) # label(non_clause). [assumption]. 16.84/16.27 2011 (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]. 16.84/16.27 2012 (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]. 16.84/16.27 2013 (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]. 16.84/16.27 2014 (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]. 16.84/16.27 2015 $T # label(t23_funct_3) # label(axiom) # label(non_clause). [assumption]. 16.84/16.27 2016 (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]. 16.84/16.27 2017 (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]. 16.84/16.27 2018 (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]. 16.84/16.27 2019 (all A k12_funct_3(A) = k11_funct_3(A)) # label(redefinition_k12_funct_3) # label(axiom) # label(non_clause). [assumption]. 16.84/16.27 2020 $T # label(t55_funct_3) # label(axiom) # label(non_clause). [assumption]. 16.84/16.27 2021 (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]. 16.84/16.27 2022 $T # label(t51_funct_3) # label(axiom) # label(non_clause). [assumption]. 16.84/16.27 2023 (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]. 16.84/16.27 2024 (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]. 16.84/16.27 2025 $T # label(t54_funct_3) # label(axiom) # label(non_clause). [assumption]. 16.84/16.27 2026 (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]. 16.84/16.27 2027 $T # label(t52_funct_3) # label(axiom) # label(non_clause). [assumption]. 16.84/16.27 2028 (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]. 16.84/16.27 2029 (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]. 16.84/16.27 2030 (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]. 16.84/16.27 2031 (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]. 16.84/16.27 2032 (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]. 16.84/16.27 2033 $T # label(t7_funct_3) # label(axiom) # label(non_clause). [assumption]. 16.84/16.27 2034 (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]. 16.84/16.27 2035 (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]. 16.84/16.27 2036 (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]. 16.84/16.27 2037 (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]. 16.84/16.27 2038 (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]. 16.84/16.27 2039 (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]. 16.84/16.27 2040 $T # label(t26_funct_3) # label(axiom) # label(non_clause). [assumption]. 16.84/16.27 2041 (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]. 16.84/16.27 2042 $T # label(t65_funct_3) # label(axiom) # label(non_clause). [assumption]. 16.84/16.27 2043 (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]. 16.84/16.27 2044 (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]. 16.84/16.27 2045 $T # label(t63_funct_3) # label(axiom) # label(non_clause). [assumption]. 16.84/16.27 2046 (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]. 16.84/16.27 2047 (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]. 16.84/16.27 2048 (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]. 16.84/16.27 2049 (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]. 16.84/16.27 2050 (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]. 16.84/16.27 2051 (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]. 16.84/16.27 2052 (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]. 16.84/16.27 2053 (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]. 16.84/16.27 2054 (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]. 16.84/16.27 2055 (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]. 16.84/16.27 2056 (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]. 16.84/16.27 2057 $T # label(t11_funct_3) # label(axiom) # label(non_clause). [assumption]. 16.84/16.27 2058 (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]. 16.84/16.27 2059 (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]. 16.84/16.27 2060 (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]. 16.84/16.27 2061 (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]. 16.84/16.27 2062 (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]. 16.84/16.27 2063 (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]. 16.84/16.27 2064 (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]. 16.84/16.27 2065 (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]. 16.84/16.27 2066 (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]. 16.84/16.27 2067 (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]. 16.84/16.27 2068 (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]. 16.84/16.27 2069 $T # label(d4_funct_3) # label(axiom) # label(non_clause). [assumption]. 16.84/16.27 2070 (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]. 16.84/16.27 2071 (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]. 16.84/16.27 2072 (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]. 16.84/16.27 2073 $T # label(t40_funct_3) # label(axiom) # label(non_clause). [assumption]. 16.84/16.27 2074 (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]. 16.84/16.27 2075 (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]. 16.84/16.27 2076 $T # label(t64_funct_3) # label(axiom) # label(non_clause). [assumption]. 16.84/16.27 2077 (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]. 16.84/16.27 2078 (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]. 16.84/16.27 2079 (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]. 16.84/16.27 2080 (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]. 16.84/16.27 2081 (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]. 16.84/16.27 2082 (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]. 16.84/16.27 2083 (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]. 16.84/16.27 2084 (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]. 16.84/16.27 2085 (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]. 16.84/16.27 2086 (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]. 16.84/16.27 2087 (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]. 16.84/16.27 2088 (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]. 16.84/16.27 2089 (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]. 16.84/16.27 2090 (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]. 16.84/16.27 2091 (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]. 16.84/16.27 2092 (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]. 16.84/16.27 2093 (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]. 16.84/16.27 2094 (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]. 16.84/16.27 2095 (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]. 16.84/16.27 2096 (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]. 16.84/16.27 2097 $T # label(t44_funct_3) # label(axiom) # label(non_clause). [assumption]. 16.84/16.27 2098 (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]. 16.84/16.27 2099 (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]. 16.84/16.27 2100 $T # label(t50_funct_3) # label(axiom) # label(non_clause). [assumption]. 16.84/16.27 2101 (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]. 16.84/16.27 2102 (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]. 16.84/16.27 2103 (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]. 16.84/16.27 2104 (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]. 16.84/16.27 2105 (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]. 16.84/16.27 2106 (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]. 16.84/16.27 2107 (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]. 16.84/16.27 2108 $T # label(t41_funct_3) # label(axiom) # label(non_clause). [assumption]. 16.84/16.27 2109 (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]. 16.84/16.27 2110 (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]. 16.84/16.27 2111 (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]. 16.84/16.27 2112 (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]. 16.84/16.27 2113 (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]. 16.84/16.27 2114 (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]. 16.84/16.27 2115 (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]. 16.84/16.27 2116 $T # label(t85_funct_3) # label(axiom) # label(non_clause). [assumption]. 16.84/16.27 2117 (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]. 16.84/16.27 2118 (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]. 16.84/16.27 2119 (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]. 16.84/16.27 2120 (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]. 16.84/16.27 2121 (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]. 16.84/16.27 2122 (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]. 16.84/16.27 2123 (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]. 16.84/16.27 2124 (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]. 16.84/16.28 2125 (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]. 16.84/16.28 2126 (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]. 16.84/16.28 2127 (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]. 16.84/16.28 2128 (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]. 16.84/16.28 2129 (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]. 16.84/16.28 2130 (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]. 16.84/16.28 2131 (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]. 16.84/16.28 2132 $T # label(t57_funct_3) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2133 (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]. 16.84/16.28 2134 $T # label(t46_funct_3) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2135 (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]. 16.84/16.28 2136 (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]. 16.84/16.28 2137 (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]. 16.84/16.28 2138 $T # label(t58_funct_3) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2139 (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]. 16.84/16.28 2140 $T # label(t45_funct_3) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2141 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k9_relat_1(B,A),k1_relat_1(C)) & r1_tarski(A,k1_relat_1(B)) -> r1_tarski(A,k1_relat_1(k5_relat_1(B,C)))))))) # label(t3_funct_3) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2142 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k7_subset_1(A,B,C) = a_3_7_domain_1(A,B,C))))))) # label(t64_domain_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2143 (all A all B (-v1_xboole_0(B) -> ((exists C (C = A & -$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]. 16.84/16.28 2144 (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]. 16.84/16.28 2145 (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]. 16.84/16.28 2146 $T # label(t6_domain_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2147 (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]. 16.84/16.28 2148 (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]. 16.84/16.28 2149 (all A (-v1_xboole_0(A) -> a_1_0_domain_1(A) = A)) # label(t48_domain_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2150 (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]. 16.84/16.28 2151 (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]. 16.84/16.28 2152 (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]. 16.84/16.28 2153 (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]. 16.84/16.28 2154 (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]. 16.84/16.28 2155 (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]. 16.84/16.28 2156 (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]. 16.84/16.28 2157 (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]. 16.84/16.28 2158 (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]. 16.84/16.28 2159 (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]. 16.84/16.28 2160 (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]. 16.84/16.28 2161 (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]. 16.84/16.28 2162 $T # label(t1_domain_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2163 (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]. 16.84/16.28 2164 $T # label(t21_domain_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2165 (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]. 16.84/16.28 2166 (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]. 16.84/16.28 2167 (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]. 16.84/16.28 2168 $T # label(t34_domain_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2169 $T # label(t3_domain_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2170 $T # label(t8_domain_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2171 $T # label(t36_domain_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2172 (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]. 16.84/16.28 2173 (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]. 16.84/16.28 2174 (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]. 16.84/16.28 2175 (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]. 16.84/16.28 2176 $T # label(t18_domain_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2177 (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]. 16.84/16.28 2178 $T # label(t5_domain_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2179 (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]. 16.84/16.28 2180 (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]. 16.84/16.28 2181 $T # label(t13_domain_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2182 (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]. 16.84/16.28 2183 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (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]. 16.84/16.28 2184 (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]. 16.84/16.28 2185 $T # label(t22_domain_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2186 $T # label(t2_domain_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2187 (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]. 16.84/16.28 2188 $T # label(t44_domain_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2189 (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]. 16.84/16.28 2190 (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]. 16.84/16.28 2191 (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]. 16.84/16.28 2192 (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]. 16.84/16.28 2193 (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]. 16.84/16.28 2194 (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]. 16.84/16.28 2195 (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]. 16.84/16.28 2196 (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]. 16.84/16.28 2197 (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]. 16.84/16.28 2198 (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]. 16.84/16.28 2199 (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]. 16.84/16.28 2200 (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]. 16.84/16.28 2201 (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]. 16.84/16.28 2202 $T # label(t14_domain_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2203 (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]. 16.84/16.28 2204 (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]. 16.84/16.28 2205 (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]. 16.84/16.28 2206 $T # label(t11_domain_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2207 (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]. 16.84/16.28 2208 (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]. 16.84/16.28 2209 (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]. 16.84/16.28 2210 (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]. 16.84/16.28 2211 (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]. 16.84/16.28 2212 (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]. 16.84/16.28 2213 (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]. 16.84/16.28 2214 (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]. 16.84/16.28 2215 (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]. 16.84/16.28 2216 (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]. 16.84/16.28 2217 $T # label(t37_domain_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2218 $T # label(t39_domain_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2219 $T # label(t23_domain_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2220 (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]. 16.84/16.28 2221 (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]. 16.84/16.28 2222 (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]. 16.84/16.28 2223 (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]. 16.84/16.28 2224 (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]. 16.84/16.28 2225 (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]. 16.84/16.28 2226 $T # label(t7_domain_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2227 (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]. 16.84/16.28 2228 (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]. 16.84/16.28 2229 (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]. 16.84/16.28 2230 (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]. 16.84/16.28 2231 (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]. 16.84/16.28 2232 (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]. 16.84/16.28 2233 (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]. 16.84/16.28 2234 (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]. 16.84/16.28 2235 (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]. 16.84/16.28 2236 (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]. 16.84/16.28 2237 (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]. 16.84/16.28 2238 (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]. 16.84/16.28 2239 (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]. 16.84/16.28 2240 $T # label(t29_domain_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2241 (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]. 16.84/16.28 2242 (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]. 16.84/16.28 2243 $T # label(t4_domain_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2244 $T # label(t20_domain_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2245 (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]. 16.84/16.28 2246 (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]. 16.84/16.28 2247 (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]. 16.84/16.28 2248 (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]. 16.84/16.28 2249 $T # label(t46_domain_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2250 (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]. 16.84/16.28 2251 (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]. 16.84/16.28 2252 $T # label(t38_domain_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2253 (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]. 16.84/16.28 2254 (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]. 16.84/16.28 2255 $T # label(t35_domain_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2256 $T # label(t19_domain_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2257 (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]. 16.84/16.28 2258 (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]. 16.84/16.28 2259 $T # label(t30_domain_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2260 (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]. 16.84/16.28 2261 (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]. 16.84/16.28 2262 (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]. 16.84/16.28 2263 (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]. 16.84/16.28 2264 (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]. 16.84/16.28 2265 $T # label(t10_domain_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2266 (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]. 16.84/16.28 2267 (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]. 16.84/16.28 2268 (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]. 16.84/16.28 2269 (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]. 16.84/16.28 2270 (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]. 16.84/16.28 2271 $T # label(t27_domain_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2272 (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]. 16.84/16.28 2273 (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]. 16.84/16.28 2274 $T # label(t47_domain_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2275 (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]. 16.84/16.28 2276 (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]. 16.84/16.28 2277 (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]. 16.84/16.28 2278 (all A (-v1_xboole_0(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (v1_binop_1(C,A) -> (r4_binop_1(A,C,B) <-> r6_binop_1(A,C,B))))))))) # label(t26_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2279 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (r3_binop_1(A,C,B) <-> (all D (m1_subset_1(D,A) -> D = k1_binop_1(B,D,C) & k1_binop_1(B,C,D) = D))))))) # label(t11_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2280 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (v1_binop_1(B,A) -> (r1_binop_1(A,C,B) <-> r3_binop_1(A,C,B))))))) # label(t14_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2281 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (v1_binop_1(C,A) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k2_binop_1(A,A,A,B,k2_binop_1(A,A,A,C,D,E),k2_binop_1(A,A,A,C,D,F)) = k2_binop_1(A,A,A,C,D,k2_binop_1(A,A,A,B,E,F)))))))) <-> r6_binop_1(A,C,B))))))))) # label(t24_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2282 $T # label(t19_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2283 (exists A (m2_relset_1(A,k2_zfmisc_1(f1_s2_binop_1,f1_s2_binop_1),f1_s2_binop_1) & (all B (m1_subset_1(B,f1_s2_binop_1) -> (all C (m1_subset_1(C,f1_s2_binop_1) -> k2_binop_1(f1_s2_binop_1,f1_s2_binop_1,f1_s2_binop_1,A,B,C) = f2_s2_binop_1(B,C))))) & v1_funct_2(A,k2_zfmisc_1(f1_s2_binop_1,f1_s2_binop_1),f1_s2_binop_1) & v1_funct_1(A))) # label(s2_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2284 $T # label(t8_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2285 (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) -> (v2_binop_1(B,A) <-> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> k2_binop_1(A,A,A,B,k2_binop_1(A,A,A,B,C,D),E) = k2_binop_1(A,A,A,B,C,k2_binop_1(A,A,A,B,D,E))))))))))))) # label(d14_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2286 (all A all B (v1_funct_1(B) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> m1_subset_1(k3_binop_1(A,B),A))) # label(dt_k3_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2287 $T # label(dt_k1_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2288 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> (v1_binop_1(B,A) -> (r3_binop_1(A,C,B) <-> r2_binop_1(A,C,B))))))) # label(t15_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2289 $T # label(t9_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2290 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (v2_binop_1(B,A) <-> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> k1_binop_1(B,C,k1_binop_1(B,D,E)) = k1_binop_1(B,k1_binop_1(B,C,D),E)))))))))) # label(d3_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2291 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k1_binop_1(C,k1_binop_1(B,D,F),k1_binop_1(B,E,F)) = k1_binop_1(B,k1_binop_1(C,D,E),F) & k1_binop_1(B,D,k1_binop_1(C,E,F)) = k1_binop_1(C,k1_binop_1(B,D,E),k1_binop_1(B,D,F)))))))) <-> r6_binop_1(A,B,C)))))) # label(t23_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.28 2292 (all A (m1_subset_1(A,f1_s1_binop_1) -> (all B (m1_subset_1(B,f1_s1_binop_1) -> (exists C (p1_s1_binop_1(A,B,C) & m1_subset_1(C,f1_s1_binop_1))))))) -> (exists A (v1_funct_2(A,k2_zfmisc_1(f1_s1_binop_1,f1_s1_binop_1),f1_s1_binop_1) & m2_relset_1(A,k2_zfmisc_1(f1_s1_binop_1,f1_s1_binop_1),f1_s1_binop_1) & (all B (m1_subset_1(B,f1_s1_binop_1) -> (all C (m1_subset_1(C,f1_s1_binop_1) -> p1_s1_binop_1(B,C,k2_binop_1(f1_s1_binop_1,f1_s1_binop_1,f1_s1_binop_1,A,B,C)))))) & v1_funct_1(A))) # label(s1_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2293 $T # label(t22_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2294 $T # label(t1_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2295 (all A all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (r2_binop_1(A,D,B) & r1_binop_1(A,C,B) -> C = D))))))) # label(t17_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2296 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> ((all D (m1_subset_1(D,A) -> D = k2_binop_1(A,A,A,C,B,D))) <-> r1_binop_1(A,B,C)))))))) # label(d16_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2297 (all A all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> (v1_binop_1(B,A) -> (r3_binop_1(A,C,B) <-> (all D (m1_subset_1(D,A) -> D = k1_binop_1(B,D,C))))))))) # label(t13_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2298 (all A (-v1_xboole_0(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (v1_binop_1(C,A) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k2_binop_1(A,A,A,C,k2_binop_1(A,A,A,B,D,E),F) = k2_binop_1(A,A,A,B,k2_binop_1(A,A,A,C,D,F),k2_binop_1(A,A,A,C,E,F)))))))) <-> r6_binop_1(A,C,B))))))))) # label(t25_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2299 (all A (m1_relset_1(A,k2_zfmisc_1(k1_xboole_0,k1_xboole_0),k1_xboole_0) -> (v1_funct_2(A,k2_zfmisc_1(k1_xboole_0,k1_xboole_0),k1_xboole_0) & v1_funct_1(A) -> v1_funct_1(A) & v1_xboole_0(A) & v1_funct_2(A,k2_zfmisc_1(k1_xboole_0,k1_xboole_0),k1_xboole_0) & v1_binop_1(A,k1_xboole_0) & v2_binop_1(A,k1_xboole_0)))) # label(cc1_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2300 $T # label(t4_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2301 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> k2_binop_1(A,A,A,C,k8_funct_2(A,A,B,D),k8_funct_2(A,A,B,E)) = k8_funct_2(A,A,B,k2_binop_1(A,A,A,C,D,E)))))) <-> r7_binop_1(A,B,C)))))))) # label(d20_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2302 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> ((exists C (r3_binop_1(A,C,B) & m1_subset_1(C,A))) -> (all C (m1_subset_1(C,A) -> (r3_binop_1(A,C,B) <-> k3_binop_1(A,B) = C)))))) # label(d8_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2303 (all A all B (m1_subset_1(B,A) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (r1_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> k1_binop_1(C,B,D) = D))))))) # label(d5_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2304 $T # label(t21_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2305 (all A all B (m1_subset_1(B,A) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> ((all D (m1_subset_1(D,A) -> k1_binop_1(C,D,B) = D)) <-> r2_binop_1(A,B,C)))))) # label(d6_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2306 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k2_binop_1(A,A,A,B,D,k2_binop_1(A,A,A,C,E,F)) = k2_binop_1(A,A,A,C,k2_binop_1(A,A,A,B,D,E),k2_binop_1(A,A,A,B,D,F)))))))) <-> r4_binop_1(A,B,C)))))))) # label(d18_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2307 (all A all B all C all D all E all F (-v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m1_subset_1(E,A) & m1_subset_1(F,B) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & -v1_xboole_0(A) -> k1_binop_1(D,E,F) = k2_binop_1(A,B,C,D,E,F))) # label(redefinition_k2_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2308 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (v1_binop_1(B,A) -> ((all D (m1_subset_1(D,A) -> k1_binop_1(B,C,D) = D)) <-> r3_binop_1(A,C,B))))))) # label(t12_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2309 (all A all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (r3_binop_1(A,D,B) & r3_binop_1(A,C,B) -> C = D))))))) # label(t18_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2310 $T # label(t5_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2311 (all A all B (m1_subset_1(B,A) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (r2_binop_1(A,B,C) & r1_binop_1(A,B,C) <-> r3_binop_1(A,B,C)))))) # label(d7_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2312 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> ((all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> k1_binop_1(B,D,C) = k1_binop_1(B,C,D))))) <-> v1_binop_1(B,A)))) # label(d2_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2313 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (r5_binop_1(A,B,C) & r4_binop_1(A,B,C) <-> r6_binop_1(A,B,C)))))) # label(d11_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2314 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m2_relset_1(D,k2_zfmisc_1(A,B),C) -> (all E (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 (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> k2_binop_1(A,B,C,E,F,G) = k2_binop_1(A,B,C,D,F,G))))) -> D = E))))))))))) # label(t2_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2315 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (r2_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> k2_binop_1(A,A,A,C,D,B) = D))))))))) # label(d17_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2316 $T # label(t3_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2317 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C k1_binop_1(A,B,C) = k1_funct_1(A,k4_tarski(B,C))))) # label(d1_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2318 $T # label(t7_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2319 (all A (-v1_xboole_0(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (v1_binop_1(B,A) <-> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> k2_binop_1(A,A,A,B,D,C) = k2_binop_1(A,A,A,B,C,D)))))))))) # label(d13_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2320 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k1_binop_1(C,k1_binop_1(B,D,F),k1_binop_1(B,E,F)) = k1_binop_1(B,k1_binop_1(C,D,E),F))))))) <-> r5_binop_1(A,B,C)))))) # label(d10_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2321 (all A all B all C all D all E all F (-v1_xboole_0(B) & m1_subset_1(F,B) & m1_subset_1(E,A) & 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(A) -> m1_subset_1(k2_binop_1(A,B,C,D,E,F),C))) # label(dt_k2_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2322 $T # label(t10_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2323 (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) -> C = k2_binop_1(A,A,A,B,C,C))) <-> v3_binop_1(B,A)))))) # label(d15_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2324 (all A (-v1_xboole_0(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (r5_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k2_binop_1(A,A,A,C,k2_binop_1(A,A,A,B,D,F),k2_binop_1(A,A,A,B,E,F)) = k2_binop_1(A,A,A,B,k2_binop_1(A,A,A,C,D,E),F)))))))))))))) # label(d19_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2325 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (v1_binop_1(B,A) -> (r2_binop_1(A,C,B) <-> r1_binop_1(A,C,B))))))) # label(t16_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2326 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> k1_funct_1(B,k1_binop_1(C,D,E)) = k1_binop_1(C,k1_funct_1(B,D),k1_funct_1(B,E)))))) <-> r7_binop_1(A,B,C)))))) # label(d12_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2327 $T # label(t20_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2328 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (r4_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k1_binop_1(B,D,k1_binop_1(C,E,F)) = k1_binop_1(C,k1_binop_1(B,D,E),k1_binop_1(B,D,F))))))))))))) # label(d9_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2329 $T # label(t6_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2330 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (v1_binop_1(C,A) -> (r5_binop_1(A,C,B) <-> r4_binop_1(A,C,B))))))))) # label(t28_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2331 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (v1_binop_1(C,A) -> (r6_binop_1(A,C,B) <-> r5_binop_1(A,C,B))))))))) # label(t27_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2332 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> ((all C (m1_subset_1(C,A) -> k1_binop_1(B,C,C) = C)) <-> v3_binop_1(B,A)))) # label(d4_binop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2333 (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]. 16.84/16.29 2334 (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]. 16.84/16.29 2335 (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]. 16.84/16.29 2336 (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]. 16.84/16.29 2337 $T # label(dt_k3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2338 (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]. 16.84/16.29 2339 (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]. 16.84/16.29 2340 (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]. 16.84/16.29 2341 (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]. 16.84/16.29 2342 (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]. 16.84/16.29 2343 (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]. 16.84/16.29 2344 (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]. 16.84/16.29 2345 (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]. 16.84/16.29 2346 (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]. 16.84/16.29 2347 (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]. 16.84/16.29 2348 (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]. 16.84/16.29 2349 (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]. 16.84/16.29 2350 $T # label(t50_funcop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2351 (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]. 16.84/16.29 2352 (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]. 16.84/16.29 2353 (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]. 16.84/16.29 2354 (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]. 16.84/16.29 2355 (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]. 16.84/16.29 2356 (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]. 16.84/16.29 2357 (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]. 16.84/16.29 2358 (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]. 16.84/16.29 2359 (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]. 16.84/16.29 2360 (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]. 16.84/16.29 2361 (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]. 16.84/16.29 2362 (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]. 16.84/16.29 2363 (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]. 16.84/16.29 2364 (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]. 16.84/16.29 2365 (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]. 16.84/16.29 2366 (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]. 16.84/16.29 2367 (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]. 16.84/16.29 2368 (exists A (v1_relat_1(A) & v1_funcop_1(A) & v1_funct_1(A))) # label(rc1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2369 (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]. 16.84/16.29 2370 (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]. 16.84/16.29 2371 (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]. 16.84/16.29 2372 (all A k1_funcop_1(k12_funct_3(A)) = k12_funct_3(A)) # label(t9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2373 (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]. 16.84/16.29 2374 (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]. 16.84/16.29 2375 (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]. 16.84/16.29 2376 (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]. 16.84/16.29 2377 $T # label(dt_k5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2378 (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]. 16.84/16.29 2379 (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]. 16.84/16.29 2380 (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]. 16.84/16.29 2381 (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]. 16.84/16.29 2382 (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]. 16.84/16.29 2383 (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]. 16.84/16.29 2384 $T # label(t8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2385 (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]. 16.84/16.29 2386 $T # label(t68_funcop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2387 (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]. 16.84/16.29 2388 (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]. 16.84/16.29 2389 (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]. 16.84/16.29 2390 (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]. 16.84/16.29 2391 $T # label(dt_k2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2392 (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]. 16.84/16.29 2393 (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]. 16.84/16.29 2394 (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]. 16.84/16.29 2395 (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]. 16.84/16.29 2396 $T # label(dt_k4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2397 $T # label(t62_funcop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2398 (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]. 16.84/16.29 2399 (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]. 16.84/16.29 2400 (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]. 16.84/16.29 2401 (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]. 16.84/16.29 2402 (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]. 16.84/16.29 2403 (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]. 16.84/16.29 2404 (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]. 16.84/16.29 2405 (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]. 16.84/16.29 2406 (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]. 16.84/16.29 2407 (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]. 16.84/16.29 2408 $T # label(t5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2409 (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]. 16.84/16.29 2410 (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]. 16.84/16.29 2411 (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]. 16.84/16.29 2412 (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]. 16.84/16.29 2413 (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]. 16.84/16.29 2414 (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]. 16.84/16.29 2415 (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]. 16.84/16.29 2416 (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]. 16.84/16.29 2417 (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]. 16.84/16.29 2418 (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]. 16.84/16.29 2419 (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]. 16.84/16.29 2420 (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]. 16.84/16.29 2421 (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]. 16.84/16.29 2422 (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]. 16.84/16.29 2423 $T # label(t12_funcop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.29 2424 (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]. 16.84/16.29 2425 (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]. 16.84/16.29 2426 (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]. 16.84/16.29 2427 (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]. 16.84/16.29 2428 (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]. 16.84/16.29 2429 (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]. 16.84/16.29 2430 (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]. 16.84/16.29 2431 (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]. 16.84/16.29 2432 (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]. 16.84/16.29 2433 (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]. 16.84/16.29 2434 (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]. 16.84/16.29 2435 (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]. 16.84/16.30 2436 $T # label(t40_funcop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.30 2437 (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]. 16.84/16.30 2438 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (all E (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]. 16.84/16.30 2439 (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]. 16.84/16.30 2440 (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]. 16.84/16.30 2441 $T # label(t33_funcop_1) # label(axiom) # label(non_clause). [assumption]. 16.84/16.30 2442 (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]. 16.84/16.30 2443 (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]. 16.84/16.30 2444 (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]. 16.84/16.30 2445 (all A (-v1_xboole_0(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (all D (m2_relset_1(D,A,A) & v1_funct_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]. 16.84/16.30 2446 (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]. 16.84/16.30 2447 (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]. 16.84/16.30 2448 (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]. 16.84/16.30 2449 (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]. 16.84/16.30 2450 (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]. 16.84/16.30 2451 (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]. 16.84/16.30 2452 (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]. 16.84/16.30 2453 (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]. 16.84/16.30 2454 (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]. 16.84/16.30 2455 (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]. 16.84/16.30 2456 (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]. 16.84/16.30 2457 (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]. 16.84/16.30 2458 $T # label(dt_k4_funct_4) # label(axiom) # label(non_clause). [assumption]. 16.84/16.30 2459 (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]. 16.84/16.30 2460 (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]. 16.84/16.30 2461 (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]. 16.84/16.30 2462 (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]. 16.84/16.30 2463 (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]. 16.84/16.30 2464 (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]. 16.84/16.30 2465 (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]. 16.84/16.30 2466 (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]. 16.84/16.30 2467 (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]. 16.84/16.30 2468 (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]. 16.84/16.30 2469 (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]. 16.84/16.30 2470 (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]. 16.84/16.30 2471 (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]. 16.84/16.30 2472 (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]. 16.84/16.30 2473 (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]. 16.84/16.30 2474 (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]. 16.84/16.30 2475 (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]. 16.84/16.30 2476 (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]. 16.84/16.30 2477 (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]. 16.84/16.30 2478 (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]. 16.84/16.30 2479 (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]. 16.84/16.30 2480 (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]. 16.84/16.30 2481 (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]. 16.84/16.30 2482 (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]. 16.84/16.30 2483 (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]. 16.84/16.30 2484 (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]. 16.84/16.30 2485 (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]. 16.84/16.30 2486 (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]. 16.84/16.30 2487 (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]. 16.84/16.30 2488 (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]. 16.84/16.30 2489 (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]. 16.84/16.30 2490 (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]. 16.84/16.30 2491 (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]. 16.84/16.30 2492 (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]. 16.84/16.30 2493 (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]. 16.84/16.30 2494 (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]. 16.84/16.30 2495 (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]. 16.84/16.30 2496 (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]. 16.84/16.30 2497 (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]. 16.95/16.30 2498 (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]. 16.95/16.30 2499 (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]. 16.95/16.30 2500 (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]. 16.95/16.30 2501 (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]. 16.95/16.30 2502 (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]. 16.95/16.30 2503 (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]. 16.95/16.30 2504 (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]. 16.95/16.30 2505 (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]. 16.95/16.30 2506 (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]. 16.95/16.30 2507 (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]. 16.95/16.30 2508 (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]. 16.95/16.30 2509 (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]. 16.95/16.30 2510 (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]. 16.95/16.30 2511 (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]. 16.95/16.30 2512 (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]. 16.95/16.30 2513 (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]. 16.95/16.30 2514 (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]. 16.95/16.30 2515 (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]. 16.95/16.30 2516 (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]. 16.95/16.30 2517 (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]. 16.95/16.30 2518 $T # label(t3_funct_4) # label(axiom) # label(non_clause). [assumption]. 16.95/16.30 2519 (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]. 16.95/16.30 2520 (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]. 16.95/16.30 2521 (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]. 16.95/16.30 2522 (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]. 16.95/16.30 2523 (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]. 16.95/16.30 2524 (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]. 16.95/16.30 2525 (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]. 16.95/16.30 2526 (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]. 16.95/16.30 2527 (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]. 16.95/16.30 2528 (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]. 16.95/16.30 2529 (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]. 16.95/16.30 2530 (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]. 16.95/16.30 2531 (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]. 16.95/16.30 2532 (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]. 16.95/16.30 2533 (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]. 16.95/16.30 2534 (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]. 16.95/16.30 2535 (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]. 16.95/16.30 2536 (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]. 16.95/16.30 2537 (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]. 16.95/16.30 2538 (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]. 16.95/16.30 2539 (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]. 16.95/16.30 2540 (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]. 16.95/16.30 2541 (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]. 16.95/16.30 2542 (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]. 16.95/16.30 2543 (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]. 16.95/16.30 2544 (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]. 16.95/16.30 2545 $T # label(t43_ordinal2) # label(axiom) # label(non_clause). [assumption]. 16.95/16.30 2546 (all A (v3_ordinal1(A) -> k1_ordinal1(A) = k14_ordinal2(A,k4_ordinal2))) # label(t48_ordinal2) # label(axiom) # label(non_clause). [assumption]. 16.95/16.30 2547 (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]. 16.95/16.30 2548 (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]. 16.95/16.32 2549 (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]. 16.95/16.32 2550 (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]. 16.95/16.32 2551 (exists A (v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal1(A) & v1_ordinal1(A))) # label(rc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 16.95/16.32 2552 (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]. 16.95/16.32 2553 (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]. 16.95/16.32 2554 $T # label(t36_ordinal2) # label(axiom) # label(non_clause). [assumption]. 16.95/16.32 2555 (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]. 16.95/16.32 2556 (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]. 16.95/16.32 2557 (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]. 16.95/16.32 2558 (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]. 16.95/16.32 2559 (all A k1_setfam_1(k2_ordinal2(A)) = k6_ordinal2(A)) # label(d6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 16.95/16.32 2560 (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]. 16.95/16.32 2561 (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]. 16.95/16.32 2562 (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]. 16.95/16.32 2563 (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]. 16.95/16.32 2564 $T # label(t40_ordinal2) # label(axiom) # label(non_clause). [assumption]. 16.95/16.32 2565 (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]. 16.95/16.32 2566 (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]. 16.95/16.32 2567 (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]. 16.95/16.32 2568 $T # label(t42_ordinal2) # label(axiom) # label(non_clause). [assumption]. 16.95/16.32 2569 (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]. 16.95/16.32 2570 (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]. 16.95/16.32 2571 (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]. 16.95/16.32 2572 (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]. 16.95/16.32 2573 $T # label(dt_k1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 16.95/16.32 2574 (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]. 16.95/16.32 2575 (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]. 16.95/16.32 2576 (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]. 16.95/16.32 2577 (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]. 16.95/16.32 2578 (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]. 16.95/16.32 2579 (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]. 16.95/16.32 2580 (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]. 16.95/16.32 2581 (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]. 16.95/16.32 2582 $T # label(t20_ordinal2) # label(axiom) # label(non_clause). [assumption]. 16.95/16.32 2583 $T # label(t38_ordinal2) # label(axiom) # label(non_clause). [assumption]. 16.95/16.32 2584 (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]. 16.95/16.32 2585 $T # label(t64_ordinal2) # label(axiom) # label(non_clause). [assumption]. 16.95/16.32 2586 $T # label(t39_ordinal2) # label(axiom) # label(non_clause). [assumption]. 16.95/16.32 2587 (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]. 16.95/16.32 2588 $T # label(t6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 16.95/16.32 2589 (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]. 16.95/16.32 2590 (all A (v3_ordinal1(A) -> k7_ordinal2(k1_tarski(A)) = k1_ordinal1(A))) # label(t31_ordinal2) # label(axiom) # label(non_clause). [assumption]. 16.95/16.32 2591 (all A (r2_hidden(A,k5_ordinal2) <-> v4_ordinal2(A))) # label(d21_ordinal2) # label(axiom) # label(non_clause). [assumption]. 16.95/16.32 2592 (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]. 16.95/16.32 2593 (all A (v3_ordinal1(A) -> k2_ordinal2(A) = A)) # label(t10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 16.95/16.32 2594 (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]. 17.03/16.39 2595 (all A r1_ordinal1(k6_ordinal2(A),k7_ordinal2(A))) # label(t32_ordinal2) # label(axiom) # label(non_clause). [assumption]. 17.03/16.39 2596 (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]. 17.03/16.39 2597 $T # label(t12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 17.03/16.39 2598 (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]. 17.03/16.39 2599 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]. 17.03/16.39 2600 (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]. 17.03/16.39 2601 (all A r1_tarski(k3_ordinal2(A),A)) # label(t13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 17.03/16.39 2602 (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]. 17.03/16.39 2603 (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]. 17.03/16.39 2604 (all A (v3_ordinal1(A) -> k1_xboole_0 = k15_ordinal2(k1_xboole_0,A))) # label(t52_ordinal2) # label(axiom) # label(non_clause). [assumption]. 17.03/16.39 2605 (all A (v3_ordinal1(A) -> (all B (m1_ordinal1(B,A) -> v1_ordinal2(B))))) # label(cc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 17.03/16.39 2606 (all A (v3_ordinal1(A) -> k3_tarski(k1_ordinal1(A)) = A)) # label(t2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 17.03/16.39 2607 (all A r1_tarski(k3_ordinal2(A),k2_ordinal2(A))) # label(t15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 17.03/16.39 2608 (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]. 17.03/16.39 2609 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]. 17.03/16.42 2610 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]. 17.03/16.42 2611 (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]. 17.03/16.42 2612 (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]. 17.03/16.42 2613 (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]. 17.03/16.42 2614 (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]. 17.03/16.42 2615 $T # label(dt_k5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 17.03/16.42 2616 (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]. 17.03/16.42 2617 $T # label(t21_ordinal2) # label(axiom) # label(non_clause). [assumption]. 17.03/16.42 2618 (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]. 17.03/16.42 2619 (all A (v3_ordinal1(A) -> A = k14_ordinal2(k1_xboole_0,A))) # label(t47_ordinal2) # label(axiom) # label(non_clause). [assumption]. 17.03/16.43 2620 (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]. 17.03/16.43 2621 (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]. 17.03/16.43 2622 $T # label(t18_ordinal2) # label(axiom) # label(non_clause). [assumption]. 17.03/16.43 2623 (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]. 17.03/16.43 2624 (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]. 17.03/16.43 2625 (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]. 17.03/16.43 2626 (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]. 17.03/16.43 2627 (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]. 17.03/16.43 2628 (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]. 17.03/16.43 2629 (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]. 17.03/16.43 2630 (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]. 17.03/16.43 2631 (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]. 17.16/16.55 2632 (all A (v3_ordinal1(A) -> A = k14_ordinal2(A,k1_xboole_0))) # label(t44_ordinal2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2633 (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]. 17.16/16.55 2634 (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]. 17.16/16.55 2635 (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]. 17.16/16.55 2636 (all A (v3_ordinal1(A) -> k4_ordinal2 = k16_ordinal2(A,k1_xboole_0))) # label(t60_ordinal2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2637 (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]. 17.16/16.55 2638 (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]. 17.16/16.55 2639 (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]. 17.16/16.55 2640 (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]. 17.16/16.55 2641 (all A (v3_ordinal1(A) -> r1_tarski(k1_ordinal1(A),k1_zfmisc_1(A)))) # label(t3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2642 (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]. 17.16/16.55 2643 (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]. 17.16/16.55 2644 (all A (v3_ordinal1(A) -> k1_xboole_0 = k15_ordinal2(A,k1_xboole_0))) # label(t55_ordinal2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2645 (all A v3_ordinal1(k6_ordinal2(A))) # label(dt_k6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2646 (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]. 17.16/16.55 2647 (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]. 17.16/16.55 2648 (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]. 17.16/16.55 2649 $T # label(dt_k3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2650 $T # label(t8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2651 $T # label(t41_ordinal2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2652 (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]. 17.16/16.55 2653 (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]. 17.16/16.55 2654 (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]. 17.16/16.55 2655 (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]. 17.16/16.55 2656 $T # label(t33_ordinal2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2657 $T # label(t37_ordinal2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2658 (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]. 17.16/16.55 2659 (all A r1_tarski(k2_ordinal2(A),A)) # label(t9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2660 (all A (v3_ordinal1(A) -> A = k7_ordinal2(A))) # label(t26_ordinal2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2661 (all A (v3_ordinal1(A) -> r1_ordinal1(k3_tarski(A),A))) # label(t5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2662 (all A v3_ordinal1(k7_ordinal2(A))) # label(dt_k7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2663 (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]. 17.16/16.55 2664 (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]. 17.16/16.55 2665 (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]. 17.16/16.55 2666 (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]. 17.16/16.55 2667 $T # label(dt_k2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2668 $T # label(t8_finset_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2669 (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]. 17.16/16.55 2670 (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]. 17.16/16.55 2671 (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]. 17.16/16.55 2672 (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]. 17.16/16.55 2673 (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]. 17.16/16.55 2674 $T # label(t4_finset_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2675 (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]. 17.16/16.55 2676 (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]. 17.16/16.55 2677 $T # label(t6_finset_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2678 (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]. 17.16/16.55 2679 (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]. 17.16/16.55 2680 (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]. 17.16/16.55 2681 (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]. 17.16/16.55 2682 $T # label(t12_finset_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2683 (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]. 17.16/16.55 2684 (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]. 17.16/16.55 2685 (exists A (v1_finset_1(A) & -v1_xboole_0(A))) # label(rc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2686 $T # label(t9_finset_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2687 (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]. 17.16/16.55 2688 (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]. 17.16/16.55 2689 $T # label(t3_finset_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2690 (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]. 17.16/16.55 2691 (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]. 17.16/16.55 2692 $T # label(t2_finset_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2693 (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]. 17.16/16.55 2694 $T # label(t7_finset_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2695 (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]. 17.16/16.55 2696 $T # label(t10_finset_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2697 (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]. 17.16/16.55 2698 (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]. 17.16/16.55 2699 (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]. 17.16/16.55 2700 (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]. 17.16/16.55 2701 (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]. 17.16/16.55 2702 (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]. 17.16/16.55 2703 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]. 17.16/16.55 2704 (all A all B all C all D (v1_finset_1(A) & v1_finset_1(D) & v1_finset_1(C) & v1_finset_1(B) -> v1_finset_1(k4_zfmisc_1(A,B,C,D)))) # label(fc16_finset_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2705 $T # label(t1_finset_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2706 (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]. 17.16/16.55 2707 (all A all B all C v1_finset_1(k1_enumset1(A,B,C))) # label(fc3_finset_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2708 (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]. 17.16/16.55 2709 $T # label(t11_finset_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2710 (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]. 17.16/16.55 2711 (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]. 17.16/16.55 2712 (all A (-v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)))) # label(fc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2713 $T # label(t5_finset_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2714 (all A (v1_finset_1(k1_zfmisc_1(A)) <-> v1_finset_1(A))) # label(t24_finset_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2715 (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]. 17.16/16.55 2716 (all A (v1_xboole_0(A) -> v1_finset_1(A))) # label(cc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2717 (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]. 17.16/16.55 2718 (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]. 17.16/16.55 2719 (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]. 17.16/16.55 2720 (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]. 17.16/16.55 2721 (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]. 17.16/16.55 2722 (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]. 17.16/16.55 2723 (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]. 17.16/16.55 2724 (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]. 17.16/16.55 2725 (all A all B (m1_subset_1(B,k5_finsub_1(A)) -> m1_subset_1(B,k1_zfmisc_1(A)))) # label(t32_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2726 (exists A (-v1_xboole_0(A) & v1_finsub_1(A) & v4_finsub_1(A) & v3_finsub_1(A) & v2_finsub_1(A))) # label(rc1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2727 (all A all B all C (-v1_xboole_0(A) & v4_finsub_1(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> k3_finsub_1(A,B,B) = B)) # label(idempotence_k3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2728 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (v1_finset_1(A) -> m1_subset_1(B,k5_finsub_1(A))))) # label(t34_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2729 $T # label(t31_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2730 (all A all B all C (v4_finsub_1(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k4_finsub_1(A,B,C) = k5_xboole_0(B,C))) # label(redefinition_k4_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2731 (all A r1_tarski(k5_finsub_1(A),k1_zfmisc_1(A))) # label(t26_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2732 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & v4_finsub_1(A) -> k1_finsub_1(A,B,C) = k1_finsub_1(A,C,B))) # label(commutativity_k1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2733 $T # label(t2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2734 (all A all B all C (m1_subset_1(C,A) & m1_subset_1(B,A) & v4_finsub_1(A) & -v1_xboole_0(A) -> k2_finsub_1(A,B,C) = k4_xboole_0(B,C))) # label(redefinition_k2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2735 $T # label(t19_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2736 (all A (v4_finsub_1(A) <-> (all B all C (r2_hidden(B,A) & r2_hidden(C,A) -> r2_hidden(k2_xboole_0(B,C),A) & r2_hidden(k4_xboole_0(B,C),A))))) # label(t10_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2737 (all A (-v1_xboole_0(A) & v4_finsub_1(A) -> r2_hidden(k1_xboole_0,A))) # label(t18_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2738 $T # label(t33_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2739 $T # label(t3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2740 (all A (v2_finsub_1(A) <-> (all B all C (r2_hidden(C,A) & r2_hidden(B,A) -> r2_hidden(k3_xboole_0(B,C),A))))) # label(d2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2741 $T # label(t9_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2742 (all A all B (r1_tarski(A,B) -> r1_tarski(k5_finsub_1(A),k5_finsub_1(B)))) # label(t23_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2743 (all A (-v1_xboole_0(k5_finsub_1(A)) & v3_finsub_1(k5_finsub_1(A)) & v4_finsub_1(k5_finsub_1(A)) & v1_finsub_1(k5_finsub_1(A)))) # label(fc2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2744 (all A all B (m1_subset_1(B,k5_finsub_1(A)) -> v1_finset_1(B))) # label(cc3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2745 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> r2_hidden(k5_xboole_0(B,C),A) & r2_hidden(k3_xboole_0(B,C),A))))) -> v4_finsub_1(A)))) # label(t16_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2746 (all A (v1_finset_1(A) -> k5_finsub_1(A) = k1_zfmisc_1(A))) # label(t27_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2747 $T # label(t1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2748 (all A all B all C (m1_subset_1(C,A) & m1_subset_1(B,A) & v4_finsub_1(A) & -v1_xboole_0(A) -> m1_subset_1(k3_finsub_1(A,B,C),A))) # label(dt_k3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2749 (all A (v4_finsub_1(A) & -v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & v4_finsub_1(B) -> -v1_xboole_0(k3_xboole_0(A,B)) & v4_finsub_1(k3_xboole_0(A,B)))))) # label(t21_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2750 $T # label(t11_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2751 (all A ((all B all C (r2_hidden(B,A) & r2_hidden(C,A) -> r2_hidden(k2_xboole_0(B,C),A))) <-> v1_finsub_1(A))) # label(d1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2752 (all A (-v1_xboole_0(k1_zfmisc_1(A)) & v3_finsub_1(k1_zfmisc_1(A)) & v4_finsub_1(k1_zfmisc_1(A)) & v1_finsub_1(k1_zfmisc_1(A)))) # label(fc1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2753 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> r2_hidden(k4_xboole_0(B,C),A) & r2_hidden(k5_xboole_0(B,C),A))))) -> v4_finsub_1(A)))) # label(t15_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2754 $T # label(t22_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2755 $T # label(t6_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2756 (all A (v4_finsub_1(A) -> v3_finsub_1(A) & v1_finsub_1(A))) # label(cc1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2757 (all A (v3_finsub_1(A) <-> (all B all C (r2_hidden(C,A) & r2_hidden(B,A) -> r2_hidden(k4_xboole_0(B,C),A))))) # label(d3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2758 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> r2_hidden(k5_xboole_0(B,C),A) & r2_hidden(k2_xboole_0(B,C),A))))) -> v4_finsub_1(A)))) # label(t17_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2759 (all A all B (m1_subset_1(B,k5_finsub_1(A)) -> v1_finset_1(B))) # label(t30_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2760 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & v4_finsub_1(A) -> m1_subset_1(k2_finsub_1(A,B,C),A))) # label(dt_k2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2761 $T # label(t5_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2762 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & v4_finsub_1(A) & -v1_xboole_0(A) -> k1_finsub_1(A,B,B) = B)) # label(idempotence_k1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2763 $T # label(t4_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2764 (all A v4_finsub_1(k5_finsub_1(A))) # label(dt_k5_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2765 $T # label(t12_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2766 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & v4_finsub_1(A) -> k4_finsub_1(A,B,C) = k4_finsub_1(A,C,B))) # label(commutativity_k4_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2767 (all A all B all C (-v1_xboole_0(C) & v4_finsub_1(C) -> (m1_subset_1(B,C) & m1_subset_1(A,C) -> m1_subset_1(k5_xboole_0(A,B),C)))) # label(t14_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2768 $T # label(t7_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2769 (all A all B all C (-v1_xboole_0(A) & v4_finsub_1(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> k2_xboole_0(B,C) = k1_finsub_1(A,B,C))) # label(redefinition_k1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2770 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & v4_finsub_1(A) -> k3_finsub_1(A,C,B) = k3_finsub_1(A,B,C))) # label(commutativity_k3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2771 $T # label(t8_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2772 (all A all B all C (-v1_xboole_0(A) & v4_finsub_1(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> m1_subset_1(k1_finsub_1(A,B,C),A))) # label(dt_k1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2773 (all A (v3_finsub_1(A) & v1_finsub_1(A) <-> v4_finsub_1(A))) # label(d4_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2774 $T # label(t29_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2775 (all A v4_finsub_1(k1_zfmisc_1(A))) # label(t20_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2776 (all A (v3_finsub_1(A) & v1_finsub_1(A) -> v4_finsub_1(A))) # label(cc2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2777 (all A all B all C (-v1_xboole_0(A) & v4_finsub_1(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> m1_subset_1(k4_finsub_1(A,B,C),A))) # label(dt_k4_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2778 (all A all B k5_finsub_1(k3_xboole_0(A,B)) = k3_xboole_0(k5_finsub_1(A),k5_finsub_1(B))) # label(t24_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2779 (all A all B r1_tarski(k2_xboole_0(k5_finsub_1(A),k5_finsub_1(B)),k5_finsub_1(k2_xboole_0(A,B)))) # label(t25_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2780 (all A all B all C (v4_finsub_1(C) & -v1_xboole_0(C) -> (m1_subset_1(B,C) & m1_subset_1(A,C) -> m1_subset_1(k3_xboole_0(A,B),C)))) # label(t13_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2781 (all A all B (v4_finsub_1(B) -> ((all C (v1_finset_1(C) & r1_tarski(C,A) <-> r2_hidden(C,B))) <-> B = k5_finsub_1(A)))) # label(d5_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2782 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & v4_finsub_1(A) & -v1_xboole_0(A) -> k3_xboole_0(B,C) = k3_finsub_1(A,B,C))) # label(redefinition_k3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2783 (all A (-v1_xboole_0(A) -> (all B all C (m2_relset_1(C,A,k5_finsub_1(B)) & v1_funct_2(C,A,k5_finsub_1(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,k5_finsub_1(A)) -> k3_tarski(k8_setwiseo(A,k5_finsub_1(B),C,D)) = k10_setwiseo(A,B,D,C))))))) # label(t61_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2784 $T # label(t9_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2785 (all A v1_setwiseo(k9_setwiseo(A),k5_finsub_1(A))) # label(t53_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2786 (all A all B all C -(-r2_hidden(C,A) & -r1_tarski(A,B) & r1_tarski(A,k2_xboole_0(B,k1_tarski(C))))) # label(t5_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.55 2787 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C all D (v1_funct_2(D,k2_zfmisc_1(A,A),A) & m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) -> (v1_binop_1(D,A) & v2_binop_1(D,A) & v3_binop_1(D,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (E != k1_xboole_0 -> (all F (v1_funct_1(F) & m2_relset_1(F,B,k5_finsub_1(C)) & v1_funct_2(F,B,k5_finsub_1(C)) -> (all G (v1_funct_1(G) & m2_relset_1(G,k5_finsub_1(C),A) & v1_funct_2(G,k5_finsub_1(C),A) -> ((all H (m1_subset_1(H,k5_finsub_1(C)) -> (all I (m1_subset_1(I,k5_finsub_1(C)) -> k8_funct_2(k5_finsub_1(C),A,G,k5_setwiseo(C,H,I)) = k2_binop_1(A,A,A,D,k8_funct_2(k5_finsub_1(C),A,G,H),k8_funct_2(k5_finsub_1(C),A,G,I)))))) -> k8_funct_2(k5_finsub_1(C),A,G,k10_setwiseo(B,C,E,F)) = k7_setwiseo(B,A,D,E,k7_funct_2(B,k5_finsub_1(C),A,F,G))))))))))))))))) # label(t64_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.56 2788 $T # label(t1_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.56 2789 (all A (-v1_xboole_0(A) -> (all B all C (v1_funct_1(C) & v1_funct_2(C,A,k5_finsub_1(B)) & m2_relset_1(C,A,k5_finsub_1(B)) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> k10_setwiseo(A,B,k3_setwiseo(A,D,E),C) = k5_setwiseo(B,k8_funct_2(A,k5_finsub_1(B),C,D),k8_funct_2(A,k5_finsub_1(B),C,E)))))))))) # label(t57_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.56 2790 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(A)) -> (all C (r2_hidden(C,B) -> m1_subset_1(C,A))))))) # label(t14_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.56 2791 (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) -> (v1_setwiseo(B,A) <-> r3_binop_1(A,k3_binop_1(A,B),B)))))) # label(t22_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.56 2792 $T # label(t17_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.56 2793 (all A r3_binop_1(k5_finsub_1(A),k1_setwiseo(A),k9_setwiseo(A))) # label(t52_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.56 2794 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) -> m1_subset_1(k2_setwiseo(A,B),k5_finsub_1(A)))) # label(dt_k2_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.56 2795 (all A all B all C all D (m1_subset_1(C,A) & m1_subset_1(D,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k4_setwiseo(A,B,C,D) = k1_enumset1(B,C,D))) # label(redefinition_k4_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.56 2796 (all A all B all C r1_tarski(k2_tarski(A,B),k1_enumset1(A,B,C))) # label(t4_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.56 2797 (all A all B all C (m1_subset_1(C,k5_finsub_1(A)) & m1_subset_1(B,k5_finsub_1(A)) -> m1_subset_1(k6_setwiseo(A,B,C),k5_finsub_1(A)))) # label(dt_k6_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.56 2798 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,B,A) & m2_relset_1(C,B,A) -> (all D (m1_subset_1(D,B) -> r2_hidden(D,k3_funct_2(B,A,C,k1_tarski(k8_funct_2(B,A,C,D)))))))))))) # label(t12_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.56 2799 (all A all B all C all D all E (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(D,k5_finsub_1(A)) & v1_funct_1(E) & v1_funct_2(E,A,B) & m1_relset_1(E,A,B) & m1_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> m1_subset_1(k7_setwiseo(A,B,C,D,E),B))) # label(dt_k7_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.56 2800 (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 (m1_subset_1(D,k5_finsub_1(A)) -> (all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (v2_binop_1(C,B) & v1_binop_1(C,B) -> (all F (m1_subset_1(F,B) -> ((exists G (v1_funct_1(G) & v1_funct_2(G,k5_finsub_1(A),B) & (all H (m1_subset_1(H,k5_finsub_1(A)) -> (r1_tarski(H,D) -> (all I (m1_subset_1(I,A) -> (r2_hidden(I,k6_setwiseo(A,D,H)) -> k8_funct_2(k5_finsub_1(A),B,G,k5_setwiseo(A,H,k2_setwiseo(A,I))) = k2_binop_1(B,B,B,C,k8_funct_2(k5_finsub_1(A),B,G,H),k8_funct_2(A,B,E,I))))) | k1_xboole_0 = H))) & (all H (m1_subset_1(H,A) -> k8_funct_2(A,B,E,H) = k8_funct_2(k5_finsub_1(A),B,G,k2_setwiseo(A,H)))) & (all H (m1_subset_1(H,B) -> (r3_binop_1(B,H,C) -> H = k1_funct_1(G,k1_xboole_0)))) & k8_funct_2(k5_finsub_1(A),B,G,D) = F & m2_relset_1(G,k5_finsub_1(A),B))) <-> k7_setwiseo(A,B,C,D,E) = F))) | -v1_setwiseo(C,B) & k1_xboole_0 = D))))))))))) # label(d3_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.56 2801 (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) -> (v1_binop_1(C,B) & v2_binop_1(C,B) & v3_binop_1(C,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (all F (m1_subset_1(F,k5_finsub_1(A)) -> (all G (m1_subset_1(G,k5_finsub_1(A)) -> (k2_funct_2(A,B,D,F) = k2_funct_2(A,B,E,G) -> F = k1_xboole_0 | k7_setwiseo(A,B,C,G,E) = k7_setwiseo(A,B,C,F,D))))))))))))))))) # label(t35_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.56 2802 (all A (m1_subset_1(A,f1_s3_setwiseo) -> p1_s3_setwiseo(k2_setwiseo(f1_s3_setwiseo,A)))) & (all A (m1_subset_1(A,k5_finsub_1(f1_s3_setwiseo)) -> (all B (m1_subset_1(B,k5_finsub_1(f1_s3_setwiseo)) -> (p1_s3_setwiseo(B) & p1_s3_setwiseo(A) -> A = k1_xboole_0 | p1_s3_setwiseo(k5_setwiseo(f1_s3_setwiseo,A,B)) | B = k1_xboole_0))))) -> (all A (m1_subset_1(A,k5_finsub_1(f1_s3_setwiseo)) -> (A != k1_xboole_0 -> p1_s3_setwiseo(A)))) # label(s3_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.56 2803 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (v1_setwiseo(B,A) <-> (exists C (r3_binop_1(A,C,B) & m1_subset_1(C,A)))))))) # label(d2_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.56 2804 (all A (m2_relset_1(k9_setwiseo(A),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k5_finsub_1(A)) & v1_funct_2(k9_setwiseo(A),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k5_finsub_1(A)) & v1_funct_1(k9_setwiseo(A)))) # label(dt_k9_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.56 2805 (all A all B (v1_funct_2(B,A,k5_finsub_1(A)) & m2_relset_1(B,A,k5_finsub_1(A)) & v1_funct_1(B) -> (k11_setwiseo(A) = B <-> (all C (r2_hidden(C,A) -> k1_tarski(C) = k1_funct_1(B,C)))))) # label(d6_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.56 2806 (all A all B (m2_relset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k5_finsub_1(A)) & v1_funct_2(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k5_finsub_1(A)) & v1_funct_1(B) -> (k9_setwiseo(A) = B <-> (all C (m1_subset_1(C,k5_finsub_1(A)) -> (all D (m1_subset_1(D,k5_finsub_1(A)) -> k2_binop_1(k5_finsub_1(A),k5_finsub_1(A),k5_finsub_1(A),B,C,D) = k5_setwiseo(A,C,D)))))))) # label(d4_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.56 2807 (all A all B all C r1_tarski(k1_tarski(A),k1_enumset1(A,B,C))) # label(t3_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.56 2808 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) -> k1_tarski(B) = k2_setwiseo(A,B))) # label(redefinition_k2_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.56 2809 (all A (-v1_xboole_0(A) -> (all B all C (v1_funct_1(C) & v1_funct_2(C,A,k5_finsub_1(B)) & m2_relset_1(C,A,k5_finsub_1(B)) -> (all D (m1_subset_1(D,k5_finsub_1(A)) -> (all E (r2_hidden(E,k10_setwiseo(A,B,D,C)) <-> (exists F (m1_subset_1(F,A) & r2_hidden(E,k8_funct_2(A,k5_finsub_1(B),C,F)) & r2_hidden(F,D))))))))))) # label(t70_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.56 2810 (all A (-v1_xboole_0(A) -> (all B all C (v1_funct_1(C) & m2_relset_1(C,A,k5_finsub_1(B)) & v1_funct_2(C,A,k5_finsub_1(B)) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k10_setwiseo(A,B,k4_setwiseo(A,D,E,F),C) = k5_setwiseo(B,k5_setwiseo(B,k8_funct_2(A,k5_finsub_1(B),C,D),k8_funct_2(A,k5_finsub_1(B),C,E)),k8_funct_2(A,k5_finsub_1(B),C,F)))))))))))) # label(t58_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.56 2811 (all A (-v1_xboole_0(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (v1_setwiseo(B,A) -> (all C (m1_subset_1(C,A) -> k2_binop_1(A,A,A,B,k3_binop_1(A,B),C) = C & k2_binop_1(A,A,A,B,C,k3_binop_1(A,B)) = C))))))) # label(t23_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.56 2812 $T # label(t46_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.56 2813 (all A v2_binop_1(k9_setwiseo(A),k5_finsub_1(A))) # label(t51_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.56 2814 (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,A),A) & m2_relset_1(D,k2_zfmisc_1(A,A),A) -> (v1_binop_1(D,A) & v2_binop_1(D,A) & v3_binop_1(D,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (E != k1_xboole_0 -> (all F (m2_relset_1(F,B,C) & v1_funct_2(F,B,C) & v1_funct_1(F) -> (all G (v1_funct_1(G) & v1_funct_2(G,C,A) & m2_relset_1(G,C,A) -> k7_setwiseo(C,A,D,k8_setwiseo(B,C,F,E),G) = k7_setwiseo(B,A,D,E,k7_funct_2(B,C,A,F,G)))))))))))))))))) # label(t38_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.57 2815 (all A exists B (m1_subset_1(B,k5_finsub_1(A)) & v1_finset_1(B) & v1_xboole_0(B))) # label(rc1_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.57 2816 (all A all B all C all D (-v1_xboole_0(A) & v1_funct_2(C,A,B) & m1_subset_1(D,k5_finsub_1(A)) & m1_relset_1(C,A,B) & v1_funct_1(C) & -v1_xboole_0(B) -> k9_relat_1(C,D) = k8_setwiseo(A,B,C,D))) # label(redefinition_k8_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.57 2817 (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,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) -> (v1_binop_1(C,A) & v2_binop_1(C,A) & r6_binop_1(A,D,C) & v3_binop_1(C,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (E != k1_xboole_0 -> (all F (m2_relset_1(F,B,A) & v1_funct_2(F,B,A) & v1_funct_1(F) -> (all G (m1_subset_1(G,A) -> k2_binop_1(A,A,A,D,k7_setwiseo(B,A,C,E,F),G) = k7_setwiseo(B,A,C,E,k7_funcop_1(A,B,D,F,G)))))))))))))))))) # label(t37_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.57 2818 (all A (-v1_xboole_0(A) -> (all B all C (v1_funct_2(C,A,k5_finsub_1(B)) & m2_relset_1(C,A,k5_finsub_1(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,k5_finsub_1(A)) -> k10_setwiseo(A,B,k5_setwiseo(A,E,k2_setwiseo(A,D)),C) = k5_setwiseo(B,k10_setwiseo(A,B,E,C),k8_funct_2(A,k5_finsub_1(B),C,D)))))))))) # label(t60_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.57 2819 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C all D (m1_subset_1(D,k5_finsub_1(A)) -> (all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (all F (v1_funct_2(F,B,k5_finsub_1(C)) & m2_relset_1(F,B,k5_finsub_1(C)) & v1_funct_1(F) -> k10_setwiseo(A,C,D,k7_funct_2(A,B,k5_finsub_1(C),E,F)) = k10_setwiseo(B,C,k8_setwiseo(A,B,E,D),F))))))))))) # label(t63_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.57 2820 (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 (m1_subset_1(D,k5_finsub_1(B)) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,A) & m2_relset_1(E,B,A) -> (v3_binop_1(C,A) & v2_binop_1(C,A) & v1_binop_1(C,A) -> (all F (m1_subset_1(F,A) -> ((all G (m1_subset_1(G,B) -> (r2_hidden(G,D) -> k8_funct_2(B,A,E,G) = F))) -> k7_setwiseo(B,A,C,D,E) = F))) | k1_xboole_0 = D))))))))))) # label(t33_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.57 2821 (all A (v1_funct_1(k11_setwiseo(A)) & v1_funct_2(k11_setwiseo(A),A,k5_finsub_1(A)) & m2_relset_1(k11_setwiseo(A),A,k5_finsub_1(A)))) # label(dt_k11_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.57 2822 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (v1_binop_1(C,A) & v2_binop_1(C,A) -> (all E (m1_subset_1(E,B) -> k7_setwiseo(B,A,C,k2_setwiseo(B,E),D) = k8_funct_2(B,A,D,E)))))))))))) # label(t26_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.57 2823 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (all D (m1_subset_1(D,k5_finsub_1(B)) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,A) & m2_relset_1(E,B,A) -> (v2_binop_1(C,A) & v1_setwiseo(C,A) & v1_binop_1(C,A) & v3_binop_1(C,A) -> (all F (m1_subset_1(F,B) -> k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,D,E),k8_funct_2(B,A,E,F)) = k7_setwiseo(B,A,C,k5_setwiseo(B,D,k2_setwiseo(B,F)),E)))))))))))))) # label(t41_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.57 2824 (all A (-v1_xboole_0(A) -> (all B (v1_funct_2(B,A,k5_finsub_1(A)) & m2_relset_1(B,A,k5_finsub_1(A)) & v1_funct_1(B) -> ((all C (m1_subset_1(C,A) -> k8_funct_2(A,k5_finsub_1(A),B,C) = k2_setwiseo(A,C))) <-> B = k11_setwiseo(A)))))) # label(t67_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2825 (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) -> (v1_binop_1(C,A) & v1_setwiseo(C,A) & v2_binop_1(C,A) -> (all D (v1_funct_1(D) & v1_funct_2(D,B,A) & m2_relset_1(D,B,A) -> k3_binop_1(A,C) = k7_setwiseo(B,A,C,k1_setwiseo(B),D)))))))))) # label(t40_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2826 (all A all B all C (m1_subset_1(B,k5_finsub_1(A)) & m1_subset_1(C,k5_finsub_1(A)) -> m1_subset_1(k5_setwiseo(A,B,C),k5_finsub_1(A)))) # label(dt_k5_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2827 $T # label(t10_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2828 (all A r3_binop_1(k5_finsub_1(A),k3_binop_1(k5_finsub_1(A),k9_setwiseo(A)),k9_setwiseo(A))) # label(t54_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2829 (all A (-v1_xboole_0(A) -> (all B all C (v1_funct_2(C,A,k5_finsub_1(B)) & m2_relset_1(C,A,k5_finsub_1(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,A) -> k10_setwiseo(A,B,k2_setwiseo(A,D),C) = k8_funct_2(A,k5_finsub_1(B),C,D))))))) # label(t56_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2830 $T # label(t7_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2831 (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 (m1_subset_1(D,k5_finsub_1(A)) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> (v2_binop_1(C,B) & v1_binop_1(C,B) & v3_binop_1(C,B) -> (all F (m1_subset_1(F,B) -> ((exists G (v1_funct_1(G) & m2_relset_1(G,k5_finsub_1(A),B) & F = k8_funct_2(k5_finsub_1(A),B,G,D) & (all H (m1_subset_1(H,B) -> (r3_binop_1(B,H,C) -> H = k1_funct_1(G,k1_xboole_0)))) & (all H (m1_subset_1(H,A) -> k8_funct_2(k5_finsub_1(A),B,G,k2_setwiseo(A,H)) = k8_funct_2(A,B,E,H))) & (all H (m1_subset_1(H,k5_finsub_1(A)) -> (r1_tarski(H,D) -> (all I (m1_subset_1(I,A) -> (r2_hidden(I,D) -> k8_funct_2(k5_finsub_1(A),B,G,k5_setwiseo(A,H,k2_setwiseo(A,I))) = k2_binop_1(B,B,B,C,k8_funct_2(k5_finsub_1(A),B,G,H),k8_funct_2(A,B,E,I))))) | k1_xboole_0 = H))) & v1_funct_2(G,k5_finsub_1(A),B))) <-> F = k7_setwiseo(A,B,C,D,E)))) | D = k1_xboole_0 & -v1_setwiseo(C,B)))))))))))) # label(t25_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2832 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (v1_binop_1(C,B) & v3_binop_1(C,B) & v1_setwiseo(C,B) & v2_binop_1(C,B) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(D,D),D) & m2_relset_1(E,k2_zfmisc_1(D,D),D) -> (v2_binop_1(E,D) & v3_binop_1(E,D) & v1_setwiseo(E,D) & v1_binop_1(E,D) -> (all F (v1_funct_2(F,A,B) & m2_relset_1(F,A,B) & v1_funct_1(F) -> (all G (v1_funct_2(G,B,D) & m2_relset_1(G,B,D) & v1_funct_1(G) -> (k3_binop_1(D,E) = k8_funct_2(B,D,G,k3_binop_1(B,C)) & (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,B) -> k8_funct_2(B,D,G,k2_binop_1(B,B,B,C,H,I)) = k2_binop_1(D,D,D,E,k8_funct_2(B,D,G,H),k8_funct_2(B,D,G,I)))))) -> (all H (m1_subset_1(H,k5_finsub_1(A)) -> k7_setwiseo(A,D,E,H,k7_funct_2(A,B,D,F,G)) = k8_funct_2(B,D,G,k7_setwiseo(A,B,C,H,F))))))))))))))))))))) # label(t45_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2833 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(A)) -> k10_setwiseo(A,A,B,k11_setwiseo(A)) = B)))) # label(t71_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2834 (all A v3_binop_1(k9_setwiseo(A),k5_finsub_1(A))) # label(t49_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2835 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_relset_1(C,A,B) & m1_subset_1(D,k5_finsub_1(A)) & v1_funct_2(C,A,B) & v1_funct_1(C) -> m1_subset_1(k8_setwiseo(A,B,C,D),k5_finsub_1(B)))) # label(dt_k8_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2836 (all A all B (m1_subset_1(B,k5_finsub_1(A)) -> (all C (r1_tarski(C,B) -> m1_subset_1(C,k5_finsub_1(A)))))) # label(t16_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2837 (all A all B all C all D (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(D,A) & m1_subset_1(C,A) -> m1_subset_1(k4_setwiseo(A,B,C,D),k5_finsub_1(A)))) # label(dt_k4_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2838 (all A all B all C (m1_subset_1(B,k5_finsub_1(A)) & m1_subset_1(C,k5_finsub_1(A)) -> k4_xboole_0(B,C) = k6_setwiseo(A,B,C))) # label(redefinition_k6_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2839 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (v2_binop_1(C,A) & v1_binop_1(C,A) & v3_binop_1(C,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (all F (m1_subset_1(F,k5_finsub_1(B)) -> -(E != k1_xboole_0 & k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,E,D),k7_setwiseo(B,A,C,F,D)) != k7_setwiseo(B,A,C,k5_setwiseo(B,E,F),D) & F != k1_xboole_0)))))))))))))) # label(t30_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2840 (all A all B all C (C = A | r2_hidden(A,B) <-> r2_hidden(A,k2_xboole_0(B,k1_tarski(C))))) # label(t6_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2841 (all A all B all C all D (-v1_xboole_0(A) & m1_subset_1(C,k5_finsub_1(A)) & m1_relset_1(D,A,k5_finsub_1(B)) & v1_funct_2(D,A,k5_finsub_1(B)) & v1_funct_1(D) -> m1_subset_1(k10_setwiseo(A,B,C,D),k5_finsub_1(B)))) # label(dt_k10_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2842 (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 (m1_subset_1(D,k5_finsub_1(A)) -> (all E (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> (v1_binop_1(C,B) & v3_binop_1(C,B) & v2_binop_1(C,B) -> (all F (m1_subset_1(F,B) -> (k2_funct_2(A,B,E,D) = k2_setwiseo(B,F) -> k7_setwiseo(A,B,C,D,E) = F)))))))))))))) # label(t34_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2843 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k3_setwiseo(A,C,B) = k3_setwiseo(A,B,C))) # label(commutativity_k3_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2844 $T # label(t20_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2845 $T # label(t24_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2846 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k5_finsub_1(A)) -> (all D all E (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> ((all F (m1_subset_1(F,A) -> (r2_hidden(F,C) -> r2_hidden(k8_funct_2(A,B,E,F),D)))) -> r1_tarski(k2_funct_2(A,B,E,C),D)))))))))) # label(t15_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2847 (all A (m1_subset_1(k1_setwiseo(A),k5_finsub_1(A)) & v1_xboole_0(k1_setwiseo(A)))) # label(dt_k1_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2848 (all A v1_binop_1(k9_setwiseo(A),k5_finsub_1(A))) # label(t50_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2849 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C all D (v1_funct_2(D,k2_zfmisc_1(B,B),B) & m2_relset_1(D,k2_zfmisc_1(B,B),B) & v1_funct_1(D) -> (v2_binop_1(D,B) & v1_setwiseo(D,B) & v3_binop_1(D,B) & v1_binop_1(D,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,k5_finsub_1(C)) & m2_relset_1(E,A,k5_finsub_1(C)) -> (all F (m2_relset_1(F,k5_finsub_1(C),B) & v1_funct_2(F,k5_finsub_1(C),B) & v1_funct_1(F) -> (k3_binop_1(B,D) = k8_funct_2(k5_finsub_1(C),B,F,k1_setwiseo(C)) & (all G (m1_subset_1(G,k5_finsub_1(C)) -> (all H (m1_subset_1(H,k5_finsub_1(C)) -> k2_binop_1(B,B,B,D,k8_funct_2(k5_finsub_1(C),B,F,G),k8_funct_2(k5_finsub_1(C),B,F,H)) = k8_funct_2(k5_finsub_1(C),B,F,k5_setwiseo(C,G,H)))))) -> (all G (m1_subset_1(G,k5_finsub_1(A)) -> k8_funct_2(k5_finsub_1(C),B,F,k10_setwiseo(A,C,G,E)) = k7_setwiseo(A,B,D,G,k7_funct_2(A,k5_finsub_1(C),B,E,F)))))))))))))))) # label(t65_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2850 (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 (m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) -> (v3_binop_1(C,A) & v2_binop_1(C,A) & r6_binop_1(A,D,C) & v1_binop_1(C,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (E != k1_xboole_0 -> (all F (v1_funct_1(F) & m2_relset_1(F,B,A) & v1_funct_2(F,B,A) -> (all G (m1_subset_1(G,A) -> k7_setwiseo(B,A,C,E,k8_funcop_1(A,B,D,G,F)) = k2_binop_1(A,A,A,D,G,k7_setwiseo(B,A,C,E,F)))))))))))))))))) # label(t36_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2851 $T # label(t66_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2852 $T # label(t48_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2853 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> k9_relat_1(C,k4_xboole_0(B,k10_relat_1(C,A))) = k4_xboole_0(k9_relat_1(C,B),A))) # label(t11_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2854 (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,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) -> (v3_binop_1(D,A) & v1_setwiseo(D,A) & v2_binop_1(D,A) & v1_binop_1(D,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (all F (m2_relset_1(F,B,C) & v1_funct_2(F,B,C) & v1_funct_1(F) -> (all G (v1_funct_1(G) & m2_relset_1(G,C,A) & v1_funct_2(G,C,A) -> k7_setwiseo(C,A,D,k8_setwiseo(B,C,F,E),G) = k7_setwiseo(B,A,D,E,k7_funct_2(B,C,A,F,G))))))))))))))))) # label(t44_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2855 (all A (-v1_xboole_0(A) -> (all B all C (v1_funct_1(C) & v1_funct_2(C,A,k5_finsub_1(B)) & m2_relset_1(C,A,k5_finsub_1(B)) -> (all D (m1_subset_1(D,k5_finsub_1(A)) -> (all E (m1_subset_1(E,k5_finsub_1(A)) -> k5_setwiseo(B,k10_setwiseo(A,B,D,C),k10_setwiseo(A,B,E,C)) = k10_setwiseo(A,B,k5_setwiseo(A,D,E),C))))))))) # label(t62_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2856 (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 (m1_subset_1(D,k5_finsub_1(B)) -> (all E (v1_funct_1(E) & m2_relset_1(E,B,A) & v1_funct_2(E,B,A) -> (v1_binop_1(C,A) & v3_binop_1(C,A) & v2_binop_1(C,A) -> (all F (m1_subset_1(F,B) -> (r2_hidden(F,D) -> k2_binop_1(A,A,A,C,k8_funct_2(B,A,E,F),k7_setwiseo(B,A,C,D,E)) = k7_setwiseo(B,A,C,D,E))))))))))))))) # label(t31_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2857 (all A (-v1_xboole_0(A) -> (all B all C (m1_subset_1(C,A) -> (C = B <-> r2_hidden(B,k8_funct_2(A,k5_finsub_1(A),k11_setwiseo(A),C))))))) # label(t68_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2858 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,B,A) & v1_funct_2(C,B,A) -> (all D (m1_subset_1(D,B) -> k1_tarski(k8_funct_2(B,A,C,D)) = k2_funct_2(B,A,C,k1_tarski(D)))))))))) # label(t13_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2859 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> k2_tarski(B,C) = k3_setwiseo(A,B,C))) # label(redefinition_k3_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2860 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (v3_binop_1(C,A) & v2_binop_1(C,A) & v1_binop_1(C,A) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,E),k8_funct_2(B,A,D,F)) = k7_setwiseo(B,A,C,k3_setwiseo(B,E,F),D)))))))))))))) # label(t27_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2861 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (r2_hidden(C,k8_funct_2(A,k5_finsub_1(A),k11_setwiseo(A),D)) & r2_hidden(B,k8_funct_2(A,k5_finsub_1(A),k11_setwiseo(A),D)) -> B = C))))))))) # label(t69_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2862 (all A all B all C (r1_tarski(k2_xboole_0(A,k1_tarski(B)),C) <-> r1_tarski(A,C) & r2_hidden(B,C))) # label(t8_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2863 (all A k1_xboole_0 = k3_binop_1(k5_finsub_1(A),k9_setwiseo(A))) # label(t55_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2864 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,B,A) & v1_funct_2(C,B,A) -> (all D (m1_subset_1(D,k5_finsub_1(B)) -> (k2_funct_2(B,A,C,D) = k1_xboole_0 -> k1_xboole_0 = D))))))))) # label(t19_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2865 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_1(D) & v1_funct_2(D,B,A) & m2_relset_1(D,B,A) -> (v2_binop_1(C,A) & v1_binop_1(C,A) & v3_binop_1(C,A) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,B) -> k7_setwiseo(B,A,C,k4_setwiseo(B,E,F,G),D) = k2_binop_1(A,A,A,C,k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,E),k8_funct_2(B,A,D,F)),k8_funct_2(B,A,D,G))))))))))))))))) # label(t28_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2866 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (m2_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_1(D) -> (v2_binop_1(C,A) & v1_setwiseo(C,A) & v1_binop_1(C,A) & v3_binop_1(C,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (all F (m1_subset_1(F,k5_finsub_1(B)) -> k7_setwiseo(B,A,C,k5_setwiseo(B,E,F),D) = k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,E,D),k7_setwiseo(B,A,C,F,D))))))))))))))) # label(t42_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2867 (all A (-v1_xboole_0(A) -> (exists B (v1_finset_1(B) & -v1_xboole_0(B) & m1_subset_1(B,k5_finsub_1(A)))))) # label(rc2_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2868 (all A all B all C (m1_subset_1(B,k5_finsub_1(A)) & m1_subset_1(C,k5_finsub_1(A)) -> k5_setwiseo(A,B,C) = k5_setwiseo(A,C,B))) # label(commutativity_k5_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2869 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> m1_subset_1(k3_setwiseo(A,B,C),k5_finsub_1(A)))) # label(dt_k3_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2870 (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) -> (v2_binop_1(C,A) & v3_binop_1(C,A) & v1_binop_1(C,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (all F (m1_subset_1(F,k5_finsub_1(B)) -> (r1_tarski(E,F) -> E = k1_xboole_0 | k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,E,D),k7_setwiseo(B,A,C,F,D)) = k7_setwiseo(B,A,C,F,D))))))))))))))) # label(t32_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2871 (all A (-v1_xboole_0(A) -> (all B all C (v1_funct_1(C) & v1_funct_2(C,A,k5_finsub_1(B)) & m2_relset_1(C,A,k5_finsub_1(B)) -> k10_setwiseo(A,B,k1_setwiseo(A),C) = k1_xboole_0)))) # label(t59_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2872 $T # label(t21_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2873 (all A (m1_subset_1(A,k5_finsub_1(f1_s4_setwiseo)) -> (all B (m1_subset_1(B,f1_s4_setwiseo) -> (p1_s4_setwiseo(A) -> p1_s4_setwiseo(k5_setwiseo(f1_s4_setwiseo,A,k2_setwiseo(f1_s4_setwiseo,B)))))))) & p1_s4_setwiseo(k1_setwiseo(f1_s4_setwiseo)) -> (all A (m1_subset_1(A,k5_finsub_1(f1_s4_setwiseo)) -> p1_s4_setwiseo(A))) # label(s4_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2874 p1_s2_setwiseo(k1_setwiseo(f1_s2_setwiseo)) & (all A (m1_subset_1(A,k5_finsub_1(f1_s2_setwiseo)) -> (all B (m1_subset_1(B,f1_s2_setwiseo) -> (p1_s2_setwiseo(A) -> p1_s2_setwiseo(k5_setwiseo(f1_s2_setwiseo,A,k2_setwiseo(f1_s2_setwiseo,B))) | r2_hidden(B,A)))))) -> (all A (m1_subset_1(A,k5_finsub_1(f1_s2_setwiseo)) -> p1_s2_setwiseo(A))) # label(s2_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2875 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (m1_subset_1(D,k5_finsub_1(B)) -> (all E (m2_relset_1(E,B,A) & v1_funct_2(E,B,A) & v1_funct_1(E) -> (v1_binop_1(C,A) & v2_binop_1(C,A) & v3_binop_1(C,A) -> k1_xboole_0 = D | (all F (m1_subset_1(F,B) -> k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,D,E),k8_funct_2(B,A,E,F)) = k7_setwiseo(B,A,C,k5_setwiseo(B,D,k2_setwiseo(B,F)),E)))))))))))))) # label(t29_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2876 (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) -> (v3_binop_1(C,B) & v2_binop_1(C,B) & v1_binop_1(C,B) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_2(E,k2_zfmisc_1(D,D),D) & m2_relset_1(E,k2_zfmisc_1(D,D),D) & v1_funct_1(E) -> (v2_binop_1(E,D) & v3_binop_1(E,D) & v1_binop_1(E,D) -> (all F (v1_funct_2(F,A,B) & m2_relset_1(F,A,B) & v1_funct_1(F) -> (all G (v1_funct_1(G) & v1_funct_2(G,B,D) & m2_relset_1(G,B,D) -> ((all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,B) -> k2_binop_1(D,D,D,E,k8_funct_2(B,D,G,H),k8_funct_2(B,D,G,I)) = k8_funct_2(B,D,G,k2_binop_1(B,B,B,C,H,I)))))) -> (all H (m1_subset_1(H,k5_finsub_1(A)) -> (k1_xboole_0 != H -> k8_funct_2(B,D,G,k7_setwiseo(A,B,C,H,F)) = k7_setwiseo(A,D,E,H,k7_funct_2(A,B,D,F,G)))))))))))))))))))))) # label(t39_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2877 (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) -> (v2_binop_1(C,B) & v3_binop_1(C,B) & v1_setwiseo(C,B) & v1_binop_1(C,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (all F (m1_subset_1(F,k5_finsub_1(A)) -> (all G (m1_subset_1(G,k5_finsub_1(A)) -> (k8_setwiseo(A,B,E,G) = k8_setwiseo(A,B,D,F) -> k7_setwiseo(A,B,C,F,D) = k7_setwiseo(A,B,C,G,E))))))))))))))))) # label(t43_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2878 (all A (-v1_xboole_0(A) -> (all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,k5_finsub_1(B)) & v1_funct_2(D,A,k5_finsub_1(B)) -> (all E (m2_relset_1(E,k5_finsub_1(B),k5_finsub_1(C)) & v1_funct_2(E,k5_finsub_1(B),k5_finsub_1(C)) & v1_funct_1(E) -> (k1_setwiseo(C) = k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,k1_setwiseo(B)) & (all F (m1_subset_1(F,k5_finsub_1(B)) -> (all G (m1_subset_1(G,k5_finsub_1(B)) -> k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,k5_setwiseo(B,F,G)) = k5_setwiseo(C,k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,F),k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,G)))))) -> (all F (m1_subset_1(F,k5_finsub_1(A)) -> k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,k10_setwiseo(A,B,F,D)) = k10_setwiseo(A,C,F,k7_funct_2(A,k5_finsub_1(B),k5_finsub_1(C),D,E))))))))))) # label(t72_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2879 $T # label(t47_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2880 (all A all B all C (m1_subset_1(B,k5_finsub_1(A)) & m1_subset_1(C,k5_finsub_1(A)) -> k5_setwiseo(A,B,B) = B)) # label(idempotence_k5_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2881 (all A k1_setwiseo(A) = k1_xboole_0) # label(d1_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2882 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(A)) -> -(B != k1_xboole_0 & (all C (m1_subset_1(C,A) -> -r2_hidden(C,B)))))))) # label(t18_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2883 (all A (-v1_xboole_0(A) -> (all B all C (m1_subset_1(C,k5_finsub_1(A)) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,k5_finsub_1(B)) & m2_relset_1(D,A,k5_finsub_1(B)) -> k10_setwiseo(A,B,C,D) = k7_setwiseo(A,k5_finsub_1(B),k9_setwiseo(B),C,D))))))) # label(d5_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2884 $T # label(t2_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2885 (all A all B all C (m1_subset_1(C,k5_finsub_1(A)) & m1_subset_1(B,k5_finsub_1(A)) -> k5_setwiseo(A,B,C) = k2_xboole_0(B,C))) # label(redefinition_k5_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2886 (exists A (m2_relset_1(A,f1_s1_setwiseo,k5_finsub_1(f1_s1_setwiseo)) & (all B (m1_subset_1(B,f1_s1_setwiseo) -> (all C (m1_subset_1(C,f1_s1_setwiseo) -> (r2_hidden(C,f2_s1_setwiseo) & p1_s1_setwiseo(C,B) <-> r2_hidden(C,k8_funct_2(f1_s1_setwiseo,k5_finsub_1(f1_s1_setwiseo),A,B))))))) & v1_funct_2(A,f1_s1_setwiseo,k5_finsub_1(f1_s1_setwiseo)) & v1_funct_1(A))) # label(s1_setwiseo) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2887 (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]. 17.16/16.58 2888 (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]. 17.16/16.58 2889 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]. 17.16/16.58 2890 (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]. 17.16/16.58 2891 (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]. 17.16/16.58 2892 (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]. 17.16/16.58 2893 (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]. 17.16/16.58 2894 (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]. 17.16/16.58 2895 (exists A (v1_fraenkel(A) & -v1_xboole_0(A))) # label(rc1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2896 (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]. 17.16/16.58 2897 $T # label(t1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2898 (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]. 17.16/16.58 2899 (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]. 17.16/16.58 2900 $T # label(t7_fraenkel) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2901 (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]. 17.16/16.58 2902 (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]. 17.16/16.58 2903 (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]. 17.16/16.58 2904 (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]. 17.16/16.58 2905 (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]. 17.16/16.58 2906 (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]. 17.16/16.58 2907 (all A (v1_fraenkel(A) -> (all B (r1_tarski(B,A) -> v1_fraenkel(B))))) # label(t17_fraenkel) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2908 (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]. 17.16/16.58 2909 (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]. 17.16/16.58 2910 (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]. 17.16/16.58 2911 (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]. 17.16/16.58 2912 (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]. 17.16/16.58 2913 (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]. 17.16/16.58 2914 (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]. 17.16/16.58 2915 (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]. 17.16/16.58 2916 (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]. 17.16/16.58 2917 (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]. 17.16/16.58 2918 (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]. 17.16/16.58 2919 (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]. 17.16/16.58 2920 (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]. 17.16/16.58 2921 (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]. 17.16/16.58 2922 (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]. 17.16/16.58 2923 (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]. 17.16/16.58 2924 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]. 17.16/16.58 2925 (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]. 17.16/16.58 2926 (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]. 17.16/16.58 2927 (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]. 17.16/16.58 2928 (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]. 17.16/16.58 2929 (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]. 17.16/16.58 2930 (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]. 17.16/16.58 2931 (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]. 17.16/16.58 2932 (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]. 17.16/16.58 2933 v1_finset_1(f2_s21_fraenkel) -> v1_finset_1(a_0_38_fraenkel) # label(s21_fraenkel) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2934 (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]. 17.16/16.58 2935 $T # label(t2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 17.16/16.58 2936 (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]. 17.16/16.58 2937 (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]. 17.16/16.58 2938 (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]. 17.16/16.58 2939 (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]. 17.16/16.58 2940 (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]. 17.16/16.58 2941 (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]. 17.16/16.58 2942 (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]. 17.16/16.58 2943 (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]. 17.16/16.58 2944 (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]. 17.16/16.58 2945 (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]. 17.16/16.58 2946 (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]. 17.16/16.58 2947 (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]. 17.16/16.58 2948 (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]. 17.16/16.58 2949 (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]. 17.16/16.58 2950 (all A all B v1_fraenkel(k1_funct_2(A,B))) # label(fc1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 2951 (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]. 17.16/16.59 2952 (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]. 17.16/16.59 2953 (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]. 17.16/16.59 2954 (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]. 17.16/16.59 2955 (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]. 17.16/16.59 2956 (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]. 17.16/16.59 2957 (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]. 17.16/16.59 2958 (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]. 17.16/16.59 2959 (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]. 17.16/16.59 2960 (all A all B exists C m1_fraenkel(C,A,B)) # label(existence_m1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 2961 (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]. 17.16/16.59 2962 (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]. 17.16/16.59 2963 (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]. 17.16/16.59 2964 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_fraenkel(k1_tarski(A)))) # label(t8_fraenkel) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 2965 (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]. 17.16/16.59 2966 $T # label(t9_fraenkel) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 2967 (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]. 17.16/16.59 2968 (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]. 17.16/16.59 2969 (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]. 17.16/16.59 2970 $T # label(t13_fraenkel) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 2971 $T # label(t12_fraenkel) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 2972 $T # label(t4_fraenkel) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 2973 (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]. 17.16/16.59 2974 (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]. 17.16/16.59 2975 (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]. 17.16/16.59 2976 (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]. 17.16/16.59 2977 (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]. 17.16/16.59 2978 $T # label(dt_k4_numbers) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 2979 $T # label(dt_k1_numbers) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 2980 (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]. 17.16/16.59 2981 $T # label(dt_k2_numbers) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 2982 $T # label(dt_k3_numbers) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 2983 (exists A (-v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & -v3_xreal_0(A) & v2_xreal_0(A))) # label(rc2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 2984 (exists A (v1_xcmplx_0(A) & v1_xreal_0(A) & v3_xreal_0(A) & -v2_xreal_0(A) & -v1_xboole_0(A))) # label(rc3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 2985 (all A all B (v1_xreal_0(A) & -v2_xreal_0(B) & v1_xreal_0(B) & -v3_xreal_0(A) -> -v2_xreal_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) & v1_xcmplx_0(k7_xcmplx_0(A,B)))) # label(fc27_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 2986 (all A all B (v1_xreal_0(A) & -v2_xreal_0(B) & v1_xreal_0(B) & -v2_xreal_0(A) -> v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & -v3_xreal_0(k3_xcmplx_0(A,B)))) # label(fc23_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 2987 (all A (v1_xreal_0(A) -> v1_xreal_0(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)))) # label(fc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 2988 (all A all B (v3_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) & v1_xreal_0(A) -> -v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & -v2_xreal_0(k2_xcmplx_0(A,B)) & v3_xreal_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)))) # label(fc11_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 2989 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & -v3_xreal_0(B) & -v2_xreal_0(A) -> v1_xreal_0(k3_xcmplx_0(A,B)) & -v2_xreal_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc21_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 2990 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> v1_xreal_0(k7_xcmplx_0(A,B)) & v1_xcmplx_0(k7_xcmplx_0(A,B)))) # label(fc6_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 2991 (all A (v1_xreal_0(A) -> v1_xcmplx_0(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(A)))) # label(fc2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 2992 (all A (v4_ordinal2(A) -> v1_xreal_0(A))) # label(cc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 2993 (all A (-v3_xreal_0(A) & -v2_xreal_0(A) & v1_xreal_0(A) -> v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A))) # label(cc8_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 2994 (all A (v2_xreal_0(A) & v1_xreal_0(A) -> -v1_xboole_0(A) & v1_xreal_0(A) & -v3_xreal_0(A) & v1_xcmplx_0(A))) # label(cc3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 2995 (all A all B (v1_xreal_0(B) & -v2_xreal_0(B) & v2_xreal_0(A) & v1_xreal_0(A) -> -v1_xboole_0(k6_xcmplx_0(B,A)) & v3_xreal_0(k6_xcmplx_0(B,A)) & -v2_xreal_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)))) # label(fc18_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 2996 (all A all B (v1_xreal_0(A) & -v3_xreal_0(A) & v1_xreal_0(B) & -v3_xreal_0(B) -> v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) & -v3_xreal_0(k7_xcmplx_0(A,B)))) # label(fc29_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 2997 (all A (v1_xreal_0(A) -> (v2_xreal_0(A) <-> -r1_xreal_0(A,np__0)))) # label(d3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 2998 (exists A (v1_xreal_0(A) & -v2_xreal_0(A) & -v3_xreal_0(A) & v1_xcmplx_0(A) & v1_xboole_0(A))) # label(rc4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 2999 (all A all B (v1_xreal_0(A) & v2_xreal_0(A) & -v3_xreal_0(B) & v1_xreal_0(B) -> v1_xreal_0(k2_xcmplx_0(A,B)) & v2_xreal_0(k2_xcmplx_0(A,B)) & -v3_xreal_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & -v1_xboole_0(k2_xcmplx_0(A,B)))) # label(fc9_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3000 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & -v3_xreal_0(B) & -v3_xreal_0(A) -> v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & -v3_xreal_0(k3_xcmplx_0(A,B)))) # label(fc24_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3001 (all A all B (-v2_xreal_0(A) & -v3_xreal_0(B) & v1_xreal_0(B) & v1_xreal_0(A) -> -v2_xreal_0(k3_xcmplx_0(B,A)) & v1_xreal_0(k3_xcmplx_0(B,A)) & v1_xcmplx_0(k3_xcmplx_0(B,A)))) # label(fc22_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3002 (all A (v3_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(A) & v1_xreal_0(A) & -v2_xreal_0(A) & -v1_xboole_0(A))) # label(cc5_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3003 (all A all B (v1_xreal_0(A) & -v3_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) -> v1_xreal_0(k6_xcmplx_0(B,A)) & -v2_xreal_0(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)))) # label(fc16_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3004 (all A (v1_xreal_0(A) & -v3_xreal_0(A) & -v1_xboole_0(A) -> v1_xcmplx_0(A) & v2_xreal_0(A) & v1_xreal_0(A))) # label(cc4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3005 (all A all B (v1_xreal_0(B) & -v3_xreal_0(B) & v3_xreal_0(A) & v1_xreal_0(A) -> -v1_xboole_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v2_xreal_0(k6_xcmplx_0(B,A)) & -v3_xreal_0(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)))) # label(fc20_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3006 (all A (r2_hidden(A,k1_numbers) <-> v1_xreal_0(A))) # label(d1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3007 (all A all B (-v3_xreal_0(B) & v1_xreal_0(B) & v3_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & -v2_xreal_0(k6_xcmplx_0(A,B)) & v3_xreal_0(k6_xcmplx_0(A,B)) & -v1_xboole_0(k6_xcmplx_0(A,B)))) # label(fc19_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3008 (all A (v1_xreal_0(A) & -v2_xreal_0(A) & -v1_xboole_0(A) -> v1_xcmplx_0(A) & v1_xreal_0(A) & v3_xreal_0(A))) # label(cc6_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3009 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> r1_xreal_0(B,A) | r1_xreal_0(A,B))) # label(connectedness_r1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3010 (all A all B (v1_xreal_0(A) & -v2_xreal_0(B) & v1_xreal_0(B) & -v3_xreal_0(A) -> v1_xreal_0(k6_xcmplx_0(A,B)) & -v3_xreal_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)))) # label(fc15_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3011 (all A all B (v2_xreal_0(A) & -v3_xreal_0(B) & v1_xreal_0(B) & v1_xreal_0(A) -> -v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & -v3_xreal_0(k2_xcmplx_0(B,A)) & v2_xreal_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)))) # label(fc10_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3012 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) & v2_xreal_0(A) -> -v1_xboole_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & -v3_xreal_0(k6_xcmplx_0(A,B)) & v2_xreal_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)))) # label(fc17_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3013 (all A (-v3_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(A)) & -v3_xreal_0(k5_xcmplx_0(A)))) # label(fc26_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3014 (all A (-v2_xreal_0(A) & v1_xreal_0(A) -> v1_xreal_0(k4_xcmplx_0(A)) & -v3_xreal_0(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)))) # label(fc13_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3015 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)))) # label(fc4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3016 (all A (-v3_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(k4_xcmplx_0(A)) & -v2_xreal_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)))) # label(fc14_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3017 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r2_hidden(A,k2_arytm_2) & r2_hidden(B,k2_arytm_2) -> (r1_xreal_0(A,B) <-> (exists C ((exists D (m1_subset_1(D,k2_arytm_2) & A = C & r1_arytm_2(C,D) & D = B)) & m1_subset_1(C,k2_arytm_2))))) & (r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) -> ((exists C (m1_subset_1(C,k2_arytm_2) & (exists D (m1_subset_1(D,k2_arytm_2) & r1_arytm_2(D,C) & B = k4_tarski(np__0,D) & A = k4_tarski(np__0,C))))) <-> r1_xreal_0(A,B))) & -(-(r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_arytm_2)) & -(r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2))) & -(r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) <-> r1_xreal_0(A,B))))))) # label(d2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3018 (all A (-v2_xreal_0(A) & v1_xreal_0(A) -> -v2_xreal_0(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(A)) & v1_xcmplx_0(k5_xcmplx_0(A)))) # label(fc25_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3019 (exists A (v1_xreal_0(A) & v1_xcmplx_0(A))) # label(rc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3020 (all A all B (-v2_xreal_0(B) & v1_xreal_0(B) & -v3_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(k7_xcmplx_0(B,A)) & -v2_xreal_0(k7_xcmplx_0(B,A)) & v1_xreal_0(k7_xcmplx_0(B,A)))) # label(fc28_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3021 (all A (v1_xreal_0(A) -> v1_xcmplx_0(A))) # label(cc2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3022 (all A all B (v3_xreal_0(A) & -v2_xreal_0(B) & v1_xreal_0(B) & v1_xreal_0(A) -> -v2_xreal_0(k2_xcmplx_0(B,A)) & v3_xreal_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & -v1_xboole_0(k2_xcmplx_0(B,A)))) # label(fc12_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3023 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)))) # label(fc3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3024 (all A all B (v1_xreal_0(B) & -v2_xreal_0(B) & -v2_xreal_0(A) & v1_xreal_0(A) -> v1_xreal_0(k2_xcmplx_0(A,B)) & -v2_xreal_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)))) # label(fc8_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3025 (all A all B (-v3_xreal_0(A) & -v3_xreal_0(B) & v1_xreal_0(B) & v1_xreal_0(A) -> v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & -v3_xreal_0(k2_xcmplx_0(A,B)))) # label(fc7_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3026 (all A (v1_xreal_0(A) & v1_xboole_0(A) -> -v3_xreal_0(A) & -v2_xreal_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A))) # label(cc7_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3027 (all A (v1_xreal_0(A) -> (v3_xreal_0(A) <-> -r1_xreal_0(np__0,A)))) # label(d4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3028 (all A all B (v1_xreal_0(A) & -v2_xreal_0(B) & v1_xreal_0(B) & -v2_xreal_0(A) -> v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) & -v3_xreal_0(k7_xcmplx_0(A,B)))) # label(fc30_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3029 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> r1_xreal_0(A,A))) # label(reflexivity_r1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3030 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)))) # label(fc5_xreal_0) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3031 $T # label(t29_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3032 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (all D (v1_int_1(D) -> (all E (v1_int_1(E) -> (r1_int_1(A,B,C) & r1_int_1(D,E,C) -> r1_int_1(k6_xcmplx_0(A,D),k6_xcmplx_0(B,E),C)))))))))))) # label(t38_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3033 $T # label(t11_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3034 $T # label(t26_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3035 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (all D (v1_int_1(D) -> (r1_int_1(A,k6_xcmplx_0(C,B),D) <-> r1_int_1(k2_xcmplx_0(A,B),C,D)))))))))) # label(t40_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3036 (all A all B (v1_int_1(A) & v1_int_1(B) -> v1_int_1(k5_int_1(A,B)))) # label(dt_k5_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3037 (all A (v1_int_1(A) -> (-r1_xreal_0(np__0,A) -> r1_xreal_0(A,k1_real_1(np__1))))) # label(t21_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3038 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> r1_xreal_0(np__0,k5_int_1(A,B)))))) # label(t82_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3039 (all A (v1_xreal_0(A) -> r1_xreal_0(np__0,k4_int_1(A)) & -r1_xreal_0(np__1,k4_int_1(A)))) # label(t69_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3040 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (all D (v1_int_1(D) -> (all E (v1_int_1(E) -> (r1_int_1(D,E,C) & r1_int_1(A,B,C) -> r1_int_1(k3_xcmplx_0(A,D),k3_xcmplx_0(B,E),C)))))))))))) # label(t39_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3041 (all A (v1_xreal_0(A) -> v1_xreal_0(k3_int_1(A)) & v1_xcmplx_0(k3_int_1(A)))) # label(fc10_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3042 (all A (v1_int_1(A) -> (p1_s4_int_1(A) -> p1_s4_int_1(k2_xcmplx_0(A,np__1)) & p1_s4_int_1(k6_xcmplx_0(A,np__1))))) & p1_s4_int_1(f1_s4_int_1) -> (all A (v1_int_1(A) -> p1_s4_int_1(A))) # label(s4_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3043 $T # label(t31_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3044 $T # label(t12_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3045 (all A all B (v1_int_1(B) & m1_subset_1(A,k5_numbers) -> v1_xcmplx_0(k3_xcmplx_0(B,A)) & v1_xreal_0(k3_xcmplx_0(B,A)) & v1_int_1(k3_xcmplx_0(B,A)))) # label(fc7_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3046 (all A (v1_int_1(A) -> v1_xreal_0(A) & v1_xcmplx_0(A))) # label(cc4_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3047 $T # label(t46_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3048 $T # label(t1_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3049 (all A (v1_int_1(A) <-> r2_hidden(A,k4_numbers))) # label(d2_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3050 (all A (v1_int_1(A) -> r1_int_1(np__0,A,A) & r1_int_1(A,np__0,A))) # label(t33_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3051 (all A (v1_xreal_0(A) -> (all B (v4_ordinal2(B) -> (B = A | A = k4_xcmplx_0(B) -> v1_int_1(A)))))) # label(t7_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3052 (all A (v1_xreal_0(A) -> -(v1_int_1(A) & -r1_xreal_0(A,k1_int_1(A))) & -(r1_xreal_0(A,k1_int_1(A)) & -v1_int_1(A)))) # label(t48_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3053 $T # label(dt_k3_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3054 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (B != np__0 -> k6_int_1(A,B) = k6_xcmplx_0(A,k3_xcmplx_0(k5_int_1(A,B),B))) & (np__0 = B -> np__0 = k6_int_1(A,B)))))) # label(d8_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3055 (all A (v1_xreal_0(A) -> (k2_int_1(A) = k1_int_1(A) <-> v1_int_1(A)))) # label(t59_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3056 (all A (v1_int_1(A) -> v1_xreal_0(k4_xcmplx_0(A)) & v1_int_1(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)))) # label(fc3_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3057 (all A (v1_xreal_0(A) -> -(v1_int_1(A) & -r1_xreal_0(k2_int_1(A),A)) & -(-v1_int_1(A) & r1_xreal_0(k2_int_1(A),A)))) # label(t55_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3058 (all A (v1_xreal_0(A) -> k3_int_1(A) = k4_int_1(A))) # label(redefinition_k4_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3059 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> r1_int_1(A,A,B))))) # label(t32_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3060 (all A all B (v1_int_1(B) & m1_subset_1(A,k5_numbers) -> v1_xreal_0(k6_xcmplx_0(B,A)) & v1_int_1(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)))) # label(fc8_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3061 (all A (v1_xreal_0(A) -> v1_int_1(k2_int_1(A)))) # label(dt_k2_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3062 (all A (m1_subset_1(A,k4_numbers) -> v1_int_1(A))) # label(cc1_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3063 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> (k2_int_1(A) = B <-> r1_xreal_0(A,B) & -r1_xreal_0(k2_xcmplx_0(A,np__1),B)))))) # label(d5_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3064 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> r1_int_1(A,B,np__1))))) # label(t34_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3065 $T # label(t5_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3066 (all A (v1_xreal_0(A) -> k1_int_1(A) = k1_int_1(k1_int_1(A)))) # label(t63_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3067 (all A (v1_xreal_0(A) -> -r1_xreal_0(k2_xcmplx_0(k1_int_1(A),np__1),A))) # label(t52_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3068 (all A all B (v1_int_1(B) & v1_int_1(A) -> r2_int_1(A,A))) # label(reflexivity_r2_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3069 (all A (m1_subset_1(A,k5_numbers) -> v1_ordinal1(A) & v3_ordinal1(A) & v1_xcmplx_0(A) & -v3_xreal_0(A) & v1_int_1(A) & v1_xreal_0(A) & v4_ordinal2(A) & v2_ordinal1(A))) # label(cc2_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3070 (all A (v1_xreal_0(A) -> k1_int_1(k4_int_1(A)) = np__0)) # label(t70_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3071 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (C = k2_xcmplx_0(B,A) -> r1_xreal_0(B,C)))))))) # label(t19_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3072 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (r1_int_1(A,B,C) <-> r1_int_1(k2_xcmplx_0(A,C),B,C)))))))) # label(t42_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3073 (all A all B (v1_int_1(A) & v1_int_1(B) -> v1_xreal_0(k2_xcmplx_0(A,B)) & v1_int_1(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)))) # label(fc1_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3074 (all A (v1_xreal_0(A) -> k2_int_1(k1_int_1(A)) = k1_int_1(A))) # label(t65_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3075 $T # label(t3_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3076 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (r1_xreal_0(A,B) -> r2_hidden(k6_xcmplx_0(B,A),k5_numbers)))))) # label(t18_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3077 $T # label(t4_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3078 (exists A v1_int_1(A)) # label(rc2_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3079 (all A (v1_xreal_0(A) -> (v1_int_1(A) -> v1_int_1(k6_xcmplx_0(A,np__1)) & v1_int_1(k2_xcmplx_0(A,np__1))))) # label(t17_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3080 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> k2_xcmplx_0(k1_int_1(A),B) = k1_int_1(k2_xcmplx_0(A,B)))))) # label(t51_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3081 (all A (v1_xreal_0(A) -> (r1_xreal_0(np__0,A) -> r1_xreal_0(np__0,k1_int_1(A)) & m2_subset_1(k1_int_1(A),k1_numbers,k5_numbers) & m2_subset_1(k2_int_1(A),k1_numbers,k5_numbers) & r1_xreal_0(np__0,k2_int_1(A))))) # label(t80_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3082 (all A (v1_xreal_0(A) -> m1_subset_1(k4_int_1(A),k1_numbers))) # label(dt_k4_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3083 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> ((exists D (v1_int_1(D) & k6_xcmplx_0(A,B) = k3_xcmplx_0(C,D))) <-> r1_int_1(A,B,C)))))))) # label(d3_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3084 (all A all B (v1_int_1(A) & v1_int_1(B) -> v1_int_1(k6_int_1(A,B)))) # label(dt_k6_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3085 $T # label(t15_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3086 (all A all B (v1_int_1(B) & v1_int_1(A) -> v1_int_1(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc2_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3087 (exists A (m1_subset_1(A,k1_zfmisc_1(k4_numbers)) & (all B (v1_int_1(B) -> (p1_s1_int_1(B) <-> r2_hidden(B,A)))))) # label(s1_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3088 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (k3_xcmplx_0(A,B) = k1_real_1(np__1) <-> k1_real_1(np__1) = B & np__1 = A | B = np__1 & A = k1_real_1(np__1)))))) # label(t23_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3089 (all A (v1_xreal_0(A) -> -((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> A != B & k1_real_1(B) != A)) & v1_int_1(A)))) # label(t8_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3090 $T # label(t53_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3091 (all A all B (v1_int_1(B) & v1_int_1(A) -> v1_int_1(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)))) # label(fc4_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3092 (all A (v1_xreal_0(A) -> (A != np__0 -> k1_int_1(k7_xcmplx_0(A,A)) = np__1))) # label(t74_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3093 $T # label(t13_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3094 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (r1_xreal_0(A,C) & r1_xreal_0(A,B) -> r1_xreal_0(k2_xcmplx_0(A,np__1),B) | C = B | r1_xreal_0(k2_xcmplx_0(A,np__1),C)))))))) # label(t45_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3095 $T # label(t9_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3096 $T # label(t49_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3097 (all A (v1_xreal_0(A) -> k3_int_1(A) = k6_xcmplx_0(A,k1_int_1(A)))) # label(d6_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3098 (all A (v1_xreal_0(A) -> -(-v1_int_1(A) & r1_xreal_0(k2_int_1(A),k1_int_1(A))) & -(v1_int_1(A) & -r1_xreal_0(k2_int_1(A),k1_int_1(A))))) # label(t60_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3099 $T # label(t6_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3100 (all A (v4_ordinal2(A) -> v1_int_1(A))) # label(cc3_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3101 (all A (v1_int_1(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) -> r1_xreal_0(A,k1_int_1(B))))))) # label(t81_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3102 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (r1_int_1(A,B,C) -> r1_int_1(B,A,C)))))))) # label(t35_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3103 $T # label(t25_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3104 (all A (v1_xreal_0(A) -> r1_xreal_0(k1_int_1(A),k2_int_1(A)))) # label(t61_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3105 (all A (v1_xreal_0(A) -> (v1_int_1(A) <-> k1_int_1(A) = A))) # label(t47_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3106 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> k5_int_1(A,B) = k1_int_1(k7_xcmplx_0(A,B)))))) # label(d7_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3107 (all A all B (m1_subset_1(B,k5_numbers) & m1_subset_1(A,k5_numbers) -> v1_xreal_0(k6_xcmplx_0(A,B)) & v1_int_1(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)))) # label(fc9_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3108 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (k3_xcmplx_0(A,B) = np__1 <-> A = k1_real_1(np__1) & B = k1_real_1(np__1) | np__1 = A & B = np__1))))) # label(t22_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3109 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (-r1_xreal_0(B,A) -> r1_xreal_0(A,k6_xcmplx_0(B,np__1))))))) # label(t79_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3110 (all A (v1_int_1(A) -> (p1_s3_int_1(A) & r1_xreal_0(A,f1_s3_int_1) -> p1_s3_int_1(k6_xcmplx_0(A,np__1))))) & p1_s3_int_1(f1_s3_int_1) -> (all A (v1_int_1(A) -> (r1_xreal_0(A,f1_s3_int_1) -> p1_s3_int_1(A)))) # label(s3_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3111 (all A (k4_numbers = A <-> (all B (r2_hidden(B,A) <-> -(all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k1_real_1(C) != B & C != B)))))) # label(d1_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3112 $T # label(t56_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3113 (all A (v1_xreal_0(A) -> v1_int_1(k1_int_1(A)))) # label(dt_k1_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3114 (all A (v1_int_1(A) -> (p1_s2_int_1(A) & r1_xreal_0(f1_s2_int_1,A) -> p1_s2_int_1(k2_xcmplx_0(A,np__1))))) & p1_s2_int_1(f1_s2_int_1) -> (all A (v1_int_1(A) -> (r1_xreal_0(f1_s2_int_1,A) -> p1_s2_int_1(A)))) # label(s2_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3115 (all A (v1_int_1(A) -> (p1_s5_int_1(A) -> r1_xreal_0(f1_s5_int_1,A)))) & (exists A (v1_int_1(A) & p1_s5_int_1(A))) -> (exists A (v1_int_1(A) & (all B (v1_int_1(B) -> (p1_s5_int_1(B) -> r1_xreal_0(A,B)))) & p1_s5_int_1(A))) # label(s5_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3116 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (r2_int_1(A,B) <-> (exists C (B = k3_xcmplx_0(A,C) & v1_int_1(C)))))))) # label(d9_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3117 (all A (v1_xreal_0(A) -> k1_int_1(k2_int_1(A)) = k2_int_1(A))) # label(t62_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3118 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (all D (v1_int_1(D) -> (r1_int_1(A,B,C) & r1_int_1(B,D,C) -> r1_int_1(A,D,C)))))))))) # label(t36_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3119 (exists A (v1_int_1(A) & p1_s6_int_1(A))) & (all A (v1_int_1(A) -> (p1_s6_int_1(A) -> r1_xreal_0(A,f1_s6_int_1)))) -> (exists A ((all B (v1_int_1(B) -> (p1_s6_int_1(B) -> r1_xreal_0(B,A)))) & p1_s6_int_1(A) & v1_int_1(A))) # label(s6_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3120 $T # label(t27_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3121 $T # label(t30_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3122 (all A (v1_int_1(A) -> (r1_xreal_0(np__0,A) -> r2_hidden(A,k5_numbers)))) # label(t16_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3123 (all A (v1_int_1(A) -> (A != np__0 -> np__1 = k5_int_1(A,A)))) # label(t76_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3124 $T # label(t14_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3125 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> k2_xcmplx_0(k2_int_1(A),B) = k2_int_1(k2_xcmplx_0(A,B)))))) # label(t58_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3126 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (-r1_xreal_0(B,A) -> r1_xreal_0(k2_xcmplx_0(A,np__1),B)))))) # label(t20_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3127 (all A (v1_xreal_0(A) -> -r1_xreal_0(k2_xcmplx_0(A,np__1),k1_int_1(A)) & -r1_xreal_0(A,k6_xcmplx_0(k1_int_1(A),np__1)))) # label(t50_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3128 (all A (v1_xreal_0(A) -> k2_int_1(A) = k2_int_1(k2_int_1(A)))) # label(t64_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3129 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> (B = k1_int_1(A) <-> r1_xreal_0(B,A) & -r1_xreal_0(B,k6_xcmplx_0(A,np__1))))))) # label(d4_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3130 $T # label(t10_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3131 (all A (v1_xreal_0(A) -> k2_xcmplx_0(k1_int_1(A),k4_int_1(A)) = A)) # label(t68_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3132 (all A (v1_xreal_0(A) -> (k1_int_1(A) = k2_int_1(A) <-> k2_int_1(A) != k2_xcmplx_0(k1_int_1(A),np__1)))) # label(t66_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3133 (exists A (v1_xreal_0(A) & v1_int_1(A) & v1_xcmplx_0(A) & m1_subset_1(A,k1_numbers))) # label(rc1_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3134 (all A (v1_xreal_0(A) -> (k4_int_1(A) = np__0 <-> v1_int_1(A)))) # label(t71_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3135 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (r1_xreal_0(B,A) & r1_xreal_0(C,A) -> r1_xreal_0(B,k6_xcmplx_0(A,np__1)) | C = B | r1_xreal_0(C,k6_xcmplx_0(A,np__1))))))))) # label(t44_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3136 $T # label(t67_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3137 (all A (v1_xreal_0(A) -> -(-v1_int_1(A) & r1_xreal_0(k4_int_1(A),np__0)) & -(v1_int_1(A) & -r1_xreal_0(k4_int_1(A),np__0)))) # label(t72_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3138 (all A (v1_int_1(A) -> np__0 = k5_int_1(A,np__0))) # label(t75_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3139 (all A all B (v1_int_1(B) & m1_subset_1(A,k5_numbers) -> v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v1_int_1(k2_xcmplx_0(B,A)))) # label(fc6_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3140 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (r1_int_1(A,B,C) <-> r1_int_1(k6_xcmplx_0(A,C),B,C)))))))) # label(t43_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3141 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> -(-r1_xreal_0(B,A) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(r1_xreal_0(np__1,C) & C = k6_xcmplx_0(B,A))))))))) # label(t78_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3142 $T # label(t2_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3143 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (all D (v1_int_1(D) -> (all E (v1_int_1(E) -> (r1_int_1(A,B,C) & r1_int_1(D,E,C) -> r1_int_1(k2_xcmplx_0(A,D),k2_xcmplx_0(B,E),C)))))))))))) # label(t37_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3144 (all A (v1_int_1(A) -> k6_int_1(A,A) = np__0)) # label(t77_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3145 $T # label(t24_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3146 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (all D (v1_int_1(D) -> (all E (v1_int_1(E) -> (k3_xcmplx_0(A,B) = C & r1_int_1(D,E,C) -> r1_int_1(D,E,A)))))))))))) # label(t41_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3147 $T # label(t73_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3148 $T # label(t28_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3149 (all A (v1_xreal_0(A) -> (k2_int_1(A) = A <-> v1_int_1(A)))) # label(t54_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3150 (all A (v1_xreal_0(A) -> -r1_xreal_0(k2_int_1(A),k6_xcmplx_0(A,np__1)) & -r1_xreal_0(k2_xcmplx_0(k2_int_1(A),np__1),A))) # label(t57_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3151 (all A (m1_subset_1(A,k5_numbers) -> v1_xcmplx_0(k4_xcmplx_0(A)) & v1_int_1(k4_xcmplx_0(A)) & -v2_xreal_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)))) # label(fc5_int_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3152 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> k7_xcmplx_0(A,B) = k6_binop_2(A,B))) # label(redefinition_k6_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3153 (all A (m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & v1_funct_1(A) -> ((all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> k2_binop_1(k1_numbers,k1_numbers,k1_numbers,A,B,C) = k11_binop_2(B,C))))) <-> A = k35_binop_2))) # label(d11_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3154 (all A (v1_funct_2(A,f1_s1_binop_2,f2_s1_binop_2) & m2_relset_1(A,f1_s1_binop_2,f2_s1_binop_2) & v1_funct_1(A) -> (all B (v1_funct_2(B,f1_s1_binop_2,f2_s1_binop_2) & m2_relset_1(B,f1_s1_binop_2,f2_s1_binop_2) & v1_funct_1(B) -> ((all C (m1_subset_1(C,f1_s1_binop_2) -> k8_funct_2(f1_s1_binop_2,f2_s1_binop_2,B,C) = f3_s1_binop_2(C))) & (all C (m1_subset_1(C,f1_s1_binop_2) -> f3_s1_binop_2(C) = k8_funct_2(f1_s1_binop_2,f2_s1_binop_2,A,C))) -> B = A))))) # label(s1_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3155 (all A (m1_subset_1(A,k1_numbers) -> m1_subset_1(k7_binop_2(A),k1_numbers))) # label(dt_k7_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3156 (all A all B (m1_subset_1(B,k5_numbers) & m1_subset_1(A,k5_numbers) -> k3_xcmplx_0(A,B) = k24_binop_2(A,B))) # label(redefinition_k24_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3157 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> k6_xcmplx_0(A,B) = k4_binop_2(A,B))) # label(redefinition_k4_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3158 (all A (v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) & v1_funct_2(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) -> ((all B (m1_subset_1(B,k3_numbers) -> (all C (m1_subset_1(C,k3_numbers) -> k2_binop_1(k3_numbers,k3_numbers,k3_numbers,A,B,C) = k18_binop_2(B,C))))) <-> k42_binop_2 = A))) # label(d18_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3159 (all A (v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) & v1_funct_2(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) -> (k27_binop_2 = A <-> (all B (m1_subset_1(B,k2_numbers) -> (all C (m1_subset_1(C,k2_numbers) -> k2_binop_1(k2_numbers,k2_numbers,k2_numbers,A,B,C) = k3_binop_2(B,C)))))))) # label(d3_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3160 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> m1_subset_1(k6_binop_2(A,B),k2_numbers))) # label(dt_k6_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3161 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k12_binop_2(A,B) = k7_xcmplx_0(A,B))) # label(redefinition_k12_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3162 (all A all B (m1_subset_1(B,k3_numbers) & m1_subset_1(A,k3_numbers) -> k16_binop_2(A,B) = k6_xcmplx_0(A,B))) # label(redefinition_k16_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3163 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> k3_binop_2(A,B) = k3_binop_2(B,A))) # label(commutativity_k3_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3164 (all A (m1_subset_1(A,k3_numbers) -> m1_subset_1(k14_binop_2(A),k3_numbers))) # label(dt_k14_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3165 (all A (m1_subset_1(A,k3_numbers) -> A = k14_binop_2(k14_binop_2(A)))) # label(involutiveness_k14_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3166 (all A (v1_funct_1(A) & v1_funct_2(A,k1_numbers,k1_numbers) & m2_relset_1(A,k1_numbers,k1_numbers) -> (A = k32_binop_2 <-> (all B (m1_subset_1(B,k1_numbers) -> k8_funct_2(k1_numbers,k1_numbers,A,B) = k8_binop_2(B)))))) # label(d8_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3167 (all A (v1_funct_1(A) & m2_relset_1(A,k2_numbers,k2_numbers) & v1_funct_2(A,k2_numbers,k2_numbers) -> ((all B (m1_subset_1(B,k2_numbers) -> k1_binop_2(B) = k8_funct_2(k2_numbers,k2_numbers,A,B))) <-> k25_binop_2 = A))) # label(d1_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3168 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> k5_binop_2(B,A) = k5_binop_2(A,B))) # label(commutativity_k5_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3169 (all A all B (m1_subset_1(B,k4_numbers) & m1_subset_1(A,k4_numbers) -> m1_subset_1(k21_binop_2(A,B),k4_numbers))) # label(dt_k21_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3170 (all A (v1_funct_2(A,k1_numbers,k1_numbers) & m2_relset_1(A,k1_numbers,k1_numbers) & v1_funct_1(A) -> (A = k31_binop_2 <-> (all B (m1_subset_1(B,k1_numbers) -> k7_binop_2(B) = k8_funct_2(k1_numbers,k1_numbers,A,B)))))) # label(d7_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3171 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> m2_subset_1(k24_binop_2(A,B),k1_numbers,k5_numbers))) # label(dt_k24_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3172 (all A (v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) -> ((all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> k2_binop_1(k1_numbers,k1_numbers,k1_numbers,A,B,C) = k9_binop_2(B,C))))) <-> k33_binop_2 = A))) # label(d9_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3173 (all A (m1_subset_1(A,k1_numbers) -> k7_binop_2(A) = k4_xcmplx_0(A))) # label(redefinition_k7_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3174 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> k24_binop_2(B,A) = k24_binop_2(A,B))) # label(commutativity_k24_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3175 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> m1_subset_1(k5_binop_2(A,B),k2_numbers))) # label(dt_k5_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3176 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> m1_subset_1(k10_binop_2(A,B),k1_numbers))) # label(dt_k10_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3177 (all A (v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) & v1_funct_2(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) -> (A = k48_binop_2 <-> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k2_binop_1(k5_numbers,k5_numbers,k5_numbers,A,B,C) = k24_binop_2(B,C)))))))) # label(d24_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3178 (all A (m1_subset_1(A,k3_numbers) -> v1_xreal_0(A) & v1_rat_1(A) & v1_xcmplx_0(A))) # label(cc1_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3179 (all A all B (m1_subset_1(B,k3_numbers) & m1_subset_1(A,k3_numbers) -> m1_subset_1(k18_binop_2(A,B),k3_numbers))) # label(dt_k18_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3180 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> k2_xcmplx_0(A,B) = k9_binop_2(A,B))) # label(redefinition_k9_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3181 (all A (v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) -> ((all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> k12_binop_2(B,C) = k2_binop_1(k1_numbers,k1_numbers,k1_numbers,A,B,C))))) <-> A = k36_binop_2))) # label(d12_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3182 (all A (v1_funct_2(A,k4_numbers,k4_numbers) & m2_relset_1(A,k4_numbers,k4_numbers) & v1_funct_1(A) -> ((all B (m1_subset_1(B,k4_numbers) -> k19_binop_2(B) = k8_funct_2(k4_numbers,k4_numbers,A,B))) <-> k43_binop_2 = A))) # label(d19_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3183 (all A all B (m1_subset_1(A,k3_numbers) & m1_subset_1(B,k3_numbers) -> k17_binop_2(A,B) = k17_binop_2(B,A))) # label(commutativity_k17_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3184 (all A (v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) -> (k34_binop_2 = A <-> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> k10_binop_2(B,C) = k2_binop_1(k1_numbers,k1_numbers,k1_numbers,A,B,C)))))))) # label(d10_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3185 (all A (m1_subset_1(A,k1_numbers) -> k7_binop_2(k7_binop_2(A)) = A)) # label(involutiveness_k7_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3186 (all A all B (m1_subset_1(B,k4_numbers) & m1_subset_1(A,k4_numbers) -> k20_binop_2(A,B) = k20_binop_2(B,A))) # label(commutativity_k20_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3187 (all A all B (m1_subset_1(B,k5_numbers) & m1_subset_1(A,k5_numbers) -> k23_binop_2(A,B) = k2_xcmplx_0(A,B))) # label(redefinition_k23_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3188 (all A (m1_subset_1(A,k1_numbers) -> A = k8_binop_2(k8_binop_2(A)))) # label(involutiveness_k8_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3189 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> m1_subset_1(k3_binop_2(A,B),k2_numbers))) # label(dt_k3_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3190 (all A (m1_subset_1(A,k2_numbers) -> m1_subset_1(k2_binop_2(A),k2_numbers))) # label(dt_k2_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3191 (all A (m2_relset_1(A,k2_zfmisc_1(f1_s2_binop_2,f1_s2_binop_2),f1_s2_binop_2) & v1_funct_2(A,k2_zfmisc_1(f1_s2_binop_2,f1_s2_binop_2),f1_s2_binop_2) & v1_funct_1(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(f1_s2_binop_2,f1_s2_binop_2),f1_s2_binop_2) & v1_funct_2(B,k2_zfmisc_1(f1_s2_binop_2,f1_s2_binop_2),f1_s2_binop_2) & v1_funct_1(B) -> ((all C (m1_subset_1(C,f1_s2_binop_2) -> (all D (m1_subset_1(D,f1_s2_binop_2) -> f2_s2_binop_2(C,D) = k2_binop_1(f1_s2_binop_2,f1_s2_binop_2,f1_s2_binop_2,B,C,D))))) & (all C (m1_subset_1(C,f1_s2_binop_2) -> (all D (m1_subset_1(D,f1_s2_binop_2) -> k2_binop_1(f1_s2_binop_2,f1_s2_binop_2,f1_s2_binop_2,A,C,D) = f2_s2_binop_2(C,D))))) -> A = B))))) # label(s2_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3192 (all A all B (m1_subset_1(A,k3_numbers) & m1_subset_1(B,k3_numbers) -> m1_subset_1(k17_binop_2(A,B),k3_numbers))) # label(dt_k17_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3193 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> k2_xcmplx_0(A,B) = k3_binop_2(A,B))) # label(redefinition_k3_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3194 (all A (v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) & m2_relset_1(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) -> (A = k28_binop_2 <-> (all B (m1_subset_1(B,k2_numbers) -> (all C (m1_subset_1(C,k2_numbers) -> k2_binop_1(k2_numbers,k2_numbers,k2_numbers,A,B,C) = k4_binop_2(B,C)))))))) # label(d4_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3195 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> m1_subset_1(k4_binop_2(A,B),k2_numbers))) # label(dt_k4_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3196 (all A all B (m1_subset_1(A,k3_numbers) & m1_subset_1(B,k3_numbers) -> k2_xcmplx_0(A,B) = k15_binop_2(A,B))) # label(redefinition_k15_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.59 3197 (all A all B (m1_subset_1(B,k4_numbers) & m1_subset_1(A,k4_numbers) -> k20_binop_2(A,B) = k2_xcmplx_0(A,B))) # label(redefinition_k20_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3198 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> k10_binop_2(A,B) = k6_xcmplx_0(A,B))) # label(redefinition_k10_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3199 (all A all B (m1_subset_1(A,k3_numbers) & m1_subset_1(B,k3_numbers) -> k17_binop_2(A,B) = k3_xcmplx_0(A,B))) # label(redefinition_k17_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3200 (all A all B (m1_subset_1(A,k3_numbers) & m1_subset_1(B,k3_numbers) -> m1_subset_1(k15_binop_2(A,B),k3_numbers))) # label(dt_k15_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3201 (all A (v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) & v1_funct_2(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) -> (k46_binop_2 = A <-> (all B (m1_subset_1(B,k4_numbers) -> (all C (m1_subset_1(C,k4_numbers) -> k2_binop_1(k4_numbers,k4_numbers,k4_numbers,A,B,C) = k22_binop_2(B,C)))))))) # label(d22_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3202 (all A (m1_subset_1(A,k2_numbers) -> k2_binop_2(A) = k5_xcmplx_0(A))) # label(redefinition_k2_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3203 (all A (m1_subset_1(A,k1_numbers) -> k5_xcmplx_0(A) = k8_binop_2(A))) # label(redefinition_k8_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3204 (all A (m1_subset_1(A,k1_numbers) -> m1_subset_1(k8_binop_2(A),k1_numbers))) # label(dt_k8_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3205 (all A all B (m1_subset_1(A,k4_numbers) & m1_subset_1(B,k4_numbers) -> k22_binop_2(B,A) = k22_binop_2(A,B))) # label(commutativity_k22_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3206 (all A (m1_subset_1(A,k2_numbers) -> k2_binop_2(k2_binop_2(A)) = A)) # label(involutiveness_k2_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3207 (all A (m1_subset_1(A,k2_numbers) -> k1_binop_2(A) = k4_xcmplx_0(A))) # label(redefinition_k1_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3208 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> k23_binop_2(A,B) = k23_binop_2(B,A))) # label(commutativity_k23_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3209 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> k11_binop_2(A,B) = k11_binop_2(B,A))) # label(commutativity_k11_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3210 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> m1_subset_1(k11_binop_2(A,B),k1_numbers))) # label(dt_k11_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3211 (all A (m1_subset_1(A,k4_numbers) -> m1_subset_1(k19_binop_2(A),k4_numbers))) # label(dt_k19_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3212 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> m1_subset_1(k12_binop_2(A,B),k1_numbers))) # label(dt_k12_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3213 (all A (m1_subset_1(A,k4_numbers) -> k19_binop_2(k19_binop_2(A)) = A)) # label(involutiveness_k19_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3214 (all A all B (m1_subset_1(B,k3_numbers) & m1_subset_1(A,k3_numbers) -> k7_xcmplx_0(A,B) = k18_binop_2(A,B))) # label(redefinition_k18_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3215 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> k3_xcmplx_0(A,B) = k5_binop_2(A,B))) # label(redefinition_k5_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3216 (all A all B (m1_subset_1(B,k4_numbers) & m1_subset_1(A,k4_numbers) -> m1_subset_1(k22_binop_2(A,B),k4_numbers))) # label(dt_k22_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3217 (all A (v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) & m2_relset_1(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) -> (A = k44_binop_2 <-> (all B (m1_subset_1(B,k4_numbers) -> (all C (m1_subset_1(C,k4_numbers) -> k20_binop_2(B,C) = k2_binop_1(k4_numbers,k4_numbers,k4_numbers,A,B,C)))))))) # label(d20_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3218 (all A (m2_relset_1(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) & v1_funct_2(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) & v1_funct_1(A) -> (A = k45_binop_2 <-> (all B (m1_subset_1(B,k4_numbers) -> (all C (m1_subset_1(C,k4_numbers) -> k2_binop_1(k4_numbers,k4_numbers,k4_numbers,A,B,C) = k21_binop_2(B,C)))))))) # label(d21_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3219 (all A (m1_subset_1(A,k4_numbers) -> k19_binop_2(A) = k4_xcmplx_0(A))) # label(redefinition_k19_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3220 (all A (m2_relset_1(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) & v1_funct_2(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) & v1_funct_1(A) -> ((all B (m1_subset_1(B,k3_numbers) -> (all C (m1_subset_1(C,k3_numbers) -> k2_binop_1(k3_numbers,k3_numbers,k3_numbers,A,B,C) = k17_binop_2(B,C))))) <-> k41_binop_2 = A))) # label(d17_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3221 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k3_xcmplx_0(A,B) = k11_binop_2(A,B))) # label(redefinition_k11_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3222 (all A all B (m1_subset_1(B,k4_numbers) & m1_subset_1(A,k4_numbers) -> k3_xcmplx_0(A,B) = k22_binop_2(A,B))) # label(redefinition_k22_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3223 (all A (m1_subset_1(A,k2_numbers) -> A = k1_binop_2(k1_binop_2(A)))) # label(involutiveness_k1_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3224 (all A (m1_subset_1(A,k3_numbers) -> A = k13_binop_2(k13_binop_2(A)))) # label(involutiveness_k13_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3225 (all A all B (m1_subset_1(B,k3_numbers) & m1_subset_1(A,k3_numbers) -> k15_binop_2(B,A) = k15_binop_2(A,B))) # label(commutativity_k15_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3226 (all A all B (m1_subset_1(A,k4_numbers) & m1_subset_1(B,k4_numbers) -> m1_subset_1(k20_binop_2(A,B),k4_numbers))) # label(dt_k20_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3227 (all A (v1_funct_2(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) & m2_relset_1(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) & v1_funct_1(A) -> ((all B (m1_subset_1(B,k3_numbers) -> (all C (m1_subset_1(C,k3_numbers) -> k15_binop_2(B,C) = k2_binop_1(k3_numbers,k3_numbers,k3_numbers,A,B,C))))) <-> k39_binop_2 = A))) # label(d15_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3228 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> m1_subset_1(k9_binop_2(A,B),k1_numbers))) # label(dt_k9_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3229 (all A (m1_subset_1(A,k3_numbers) -> m1_subset_1(k13_binop_2(A),k3_numbers))) # label(dt_k13_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3230 (all A (v1_funct_1(A) & m2_relset_1(A,k3_numbers,k3_numbers) & v1_funct_2(A,k3_numbers,k3_numbers) -> ((all B (m1_subset_1(B,k3_numbers) -> k13_binop_2(B) = k8_funct_2(k3_numbers,k3_numbers,A,B))) <-> A = k37_binop_2))) # label(d13_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3231 (all A (v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) & m2_relset_1(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) -> ((all B (m1_subset_1(B,k2_numbers) -> (all C (m1_subset_1(C,k2_numbers) -> k2_binop_1(k2_numbers,k2_numbers,k2_numbers,A,B,C) = k6_binop_2(B,C))))) <-> A = k30_binop_2))) # label(d6_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3232 (all A (m1_subset_1(A,k3_numbers) -> k5_xcmplx_0(A) = k14_binop_2(A))) # label(redefinition_k14_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3233 (all A (m1_subset_1(A,k3_numbers) -> k4_xcmplx_0(A) = k13_binop_2(A))) # label(redefinition_k13_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3234 (all A (v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) & m2_relset_1(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) -> (k29_binop_2 = A <-> (all B (m1_subset_1(B,k2_numbers) -> (all C (m1_subset_1(C,k2_numbers) -> k5_binop_2(B,C) = k2_binop_1(k2_numbers,k2_numbers,k2_numbers,A,B,C)))))))) # label(d5_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3235 (all A (v1_funct_2(A,k2_numbers,k2_numbers) & m2_relset_1(A,k2_numbers,k2_numbers) & v1_funct_1(A) -> (A = k26_binop_2 <-> (all B (m1_subset_1(B,k2_numbers) -> k8_funct_2(k2_numbers,k2_numbers,A,B) = k2_binop_2(B)))))) # label(d2_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3236 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> k9_binop_2(B,A) = k9_binop_2(A,B))) # label(commutativity_k9_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3237 (all A (m1_subset_1(A,k2_numbers) -> m1_subset_1(k1_binop_2(A),k2_numbers))) # label(dt_k1_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3238 (all A (v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) & m2_relset_1(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) -> (k47_binop_2 = A <-> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k2_binop_1(k5_numbers,k5_numbers,k5_numbers,A,B,C) = k23_binop_2(B,C)))))))) # label(d23_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3239 (all A all B (m1_subset_1(B,k4_numbers) & m1_subset_1(A,k4_numbers) -> k21_binop_2(A,B) = k6_xcmplx_0(A,B))) # label(redefinition_k21_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3240 (all A all B (m1_subset_1(B,k5_numbers) & m1_subset_1(A,k5_numbers) -> m2_subset_1(k23_binop_2(A,B),k1_numbers,k5_numbers))) # label(dt_k23_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3241 (all A all B (m1_subset_1(A,k3_numbers) & m1_subset_1(B,k3_numbers) -> m1_subset_1(k16_binop_2(A,B),k3_numbers))) # label(dt_k16_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3242 (all A (v1_funct_1(A) & m2_relset_1(A,k3_numbers,k3_numbers) & v1_funct_2(A,k3_numbers,k3_numbers) -> ((all B (m1_subset_1(B,k3_numbers) -> k14_binop_2(B) = k8_funct_2(k3_numbers,k3_numbers,A,B))) <-> A = k38_binop_2))) # label(d14_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3243 (all A (v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) & m2_relset_1(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) -> (k40_binop_2 = A <-> (all B (m1_subset_1(B,k3_numbers) -> (all C (m1_subset_1(C,k3_numbers) -> k16_binop_2(B,C) = k2_binop_1(k3_numbers,k3_numbers,k3_numbers,A,B,C)))))))) # label(d16_binop_2) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3244 (all A all B (v2_membered(A) -> v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)))) # label(fc30_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3245 (all A (v2_membered(A) -> v1_membered(A))) # label(cc4_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3246 (all A all B (r2_hidden(B,A) & v5_membered(B) -> v5_membered(k1_setfam_1(A)))) # label(t30_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3247 (all A (v2_membered(A) -> (all B (v2_membered(B) -> (A = B <-> (all C (v1_xreal_0(C) -> (r2_hidden(C,B) <-> r2_hidden(C,A))))))))) # label(d12_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3248 (all A all B (v1_membered(A) -> v1_membered(k3_xboole_0(B,A)))) # label(fc28_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3249 (exists A ((all B (v1_xcmplx_0(B) -> (r2_hidden(B,A) <-> p1_s1_membered(B)))) & v1_membered(A))) # label(s1_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3250 (all A all B (v5_membered(B) -> (r1_tarski(A,B) -> v5_membered(A)))) # label(t20_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3251 (all A (v5_membered(A) -> r1_tarski(A,k5_numbers))) # label(t5_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3252 (all A all B (v1_membered(A) & v1_membered(B) -> v1_membered(k5_xboole_0(A,B)))) # label(fc42_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3253 (all A (v4_membered(A) -> (all B (v4_membered(B) -> (r1_xboole_0(A,B) <-> (all C (v1_int_1(C) -> -(r2_hidden(C,B) & r2_hidden(C,A))))))))) # label(d19_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3254 (all A (v4_membered(A) -> (all B (v4_membered(B) -> (A = B <-> (all C (v1_int_1(C) -> (r2_hidden(C,B) <-> r2_hidden(C,A))))))))) # label(d14_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3255 (all A all B all C (v1_xreal_0(A) & v1_xreal_0(C) & v1_xreal_0(B) -> v2_membered(k1_enumset1(A,B,C)) & v1_membered(k1_enumset1(A,B,C)))) # label(fc18_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3256 (all A all B all C (v1_int_1(A) & v1_int_1(B) & v1_int_1(C) -> v1_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)) & v4_membered(k1_enumset1(A,B,C)))) # label(fc20_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3257 (all A (v5_membered(A) -> v4_membered(A))) # label(cc1_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3258 (all A (v1_membered(A) <-> (all B (r2_hidden(B,A) -> v1_xcmplx_0(B))))) # label(d1_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3259 (all A all B (r2_hidden(B,A) & v2_membered(B) -> v2_membered(k1_setfam_1(A)))) # label(t27_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3260 (all A all B (v1_membered(B) & v1_membered(A) -> v1_membered(k2_xboole_0(A,B)))) # label(fc22_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3261 (all A (v2_membered(A) -> (all B (v2_membered(B) -> (r1_xboole_0(A,B) <-> (all C (v1_xreal_0(C) -> -(r2_hidden(C,B) & r2_hidden(C,A))))))))) # label(d17_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3262 (all A (v3_membered(A) -> v2_membered(A))) # label(cc3_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3263 (all A (m1_subset_1(A,k1_zfmisc_1(k2_numbers)) -> v1_membered(A))) # label(cc5_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3264 (all A ((all B (r2_hidden(B,A) -> v5_membered(B))) -> v5_membered(k3_tarski(A)))) # label(t25_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3265 (all A all B (v1_membered(A) -> v1_membered(k3_xboole_0(A,B)))) # label(fc27_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3266 (all A all B (v4_membered(A) & v4_membered(B) -> v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)))) # label(fc25_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3267 (all A ((all B (r2_hidden(B,A) -> v4_membered(B))) -> v4_membered(k3_tarski(A)))) # label(t24_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3268 (all A all B (v2_membered(B) & v2_membered(A) -> v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)))) # label(fc23_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3269 (all A (v1_membered(A) -> ((all B (v1_xcmplx_0(B) -> r2_hidden(B,A))) -> k2_numbers = A))) # label(t11_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3270 (all A (v1_rat_1(A) -> v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v1_membered(k1_tarski(A)))) # label(fc9_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3271 (all A all B (v5_membered(A) -> v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v5_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)))) # label(fc35_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3272 (all A (v5_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v5_membered(B) & v4_membered(B) & v3_membered(B) & v2_membered(B) & v1_membered(B))))) # label(cc20_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3273 (all A (v4_ordinal2(A) -> v1_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) & v5_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)))) # label(fc11_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3274 (all A (v1_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v1_membered(B))))) # label(cc16_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3275 (exists A ((all B (v1_xreal_0(B) -> (r2_hidden(B,A) <-> p1_s2_membered(B)))) & v2_membered(A))) # label(s2_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3276 (all A all B (v2_membered(A) -> v2_membered(k3_xboole_0(A,B)) & v1_membered(k3_xboole_0(A,B)))) # label(fc29_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3277 (exists A (-v1_xboole_0(A) & v2_membered(A) & v3_membered(A) & v5_membered(A) & v4_membered(A) & v1_membered(A))) # label(rc1_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3278 (all A (v3_membered(A) -> (all B (m1_subset_1(B,A) -> v1_xcmplx_0(B) & v1_xreal_0(B) & v1_rat_1(B))))) # label(cc12_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3279 (all A (v5_membered(A) -> (all B (v5_membered(B) -> ((all C (v4_ordinal2(C) -> (r2_hidden(C,A) -> r2_hidden(C,B)))) <-> r1_tarski(A,B)))))) # label(d10_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3280 (all A all B (v3_membered(B) -> (r1_tarski(A,B) -> v3_membered(A)))) # label(t18_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3281 (all A (-v1_xboole_0(A) & v5_membered(A) -> (exists B (v4_ordinal2(B) & r2_hidden(B,A))))) # label(t10_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3282 (all A (v3_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v2_membered(B) & v3_membered(B) & v1_membered(B))))) # label(cc18_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3283 (all A (v4_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v1_membered(B) & v3_membered(B) & v4_membered(B) & v2_membered(B))))) # label(cc19_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3284 (exists A (v5_membered(A) & (all B (v4_ordinal2(B) -> (p1_s5_membered(B) <-> r2_hidden(B,A)))))) # label(s5_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3285 (all A (v4_membered(A) -> (all B (m1_subset_1(B,A) -> v1_xcmplx_0(B) & v1_xreal_0(B) & v1_rat_1(B) & v1_int_1(B))))) # label(cc13_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3286 (all A all B all C (v1_xcmplx_0(C) & v1_xcmplx_0(B) & v1_xcmplx_0(A) -> v1_membered(k1_enumset1(A,B,C)))) # label(fc17_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3287 (all A all B (v4_ordinal2(A) & v4_ordinal2(B) -> v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v5_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)))) # label(fc16_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3288 (all A ((all B (r2_hidden(B,A) -> v2_membered(B))) -> v2_membered(k3_tarski(A)))) # label(t22_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3289 (exists A ((all B (v1_int_1(B) -> (r2_hidden(B,A) <-> p1_s4_membered(B)))) & v4_membered(A))) # label(s4_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3290 (all A all B (v5_membered(B) & v5_membered(A) -> v5_membered(k5_xboole_0(A,B)) & v4_membered(k5_xboole_0(A,B)) & v3_membered(k5_xboole_0(A,B)) & v2_membered(k5_xboole_0(A,B)) & v1_membered(k5_xboole_0(A,B)))) # label(fc46_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3291 (all A (v1_int_1(A) -> v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v1_membered(k1_tarski(A)))) # label(fc10_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3292 (all A (v5_membered(A) -> (all B (v5_membered(B) -> (B = A <-> (all C (v4_ordinal2(C) -> (r2_hidden(C,B) <-> r2_hidden(C,A))))))))) # label(d15_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3293 (all A all B (v3_membered(A) & v3_membered(B) -> v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v1_membered(k2_xboole_0(A,B)))) # label(fc24_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3294 (all A (v1_xreal_0(A) -> v2_membered(k1_tarski(A)) & v1_membered(k1_tarski(A)))) # label(fc8_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3295 (all A (v2_membered(A) -> ((all B (v1_xreal_0(B) -> r2_hidden(B,A))) -> A = k1_numbers))) # label(t12_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3296 (all A all B (v3_membered(A) -> v3_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v1_membered(k4_xboole_0(A,B)))) # label(fc39_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3297 (all A (v2_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v1_membered(B) & v2_membered(B))))) # label(cc17_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3298 (all A (v1_membered(A) -> (all B (m1_subset_1(B,A) -> v1_xcmplx_0(B))))) # label(cc10_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3299 (all A all B (v2_membered(B) -> (r1_tarski(A,B) -> v2_membered(A)))) # label(t17_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3300 (all A all B (v4_membered(A) -> v2_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) & v1_membered(k4_xboole_0(A,B)))) # label(fc40_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3301 (all A all B (v3_membered(B) & v3_membered(A) -> v2_membered(k5_xboole_0(A,B)) & v3_membered(k5_xboole_0(A,B)) & v1_membered(k5_xboole_0(A,B)))) # label(fc44_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3302 (all A all B (v4_membered(A) -> v2_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) & v1_membered(k3_xboole_0(A,B)))) # label(fc33_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3303 (all A all B all C (v4_ordinal2(C) & v4_ordinal2(B) & v4_ordinal2(A) -> v3_membered(k1_enumset1(A,B,C)) & v4_membered(k1_enumset1(A,B,C)) & v5_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)) & v1_membered(k1_enumset1(A,B,C)))) # label(fc21_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3304 (all A all B (v1_membered(B) & r2_hidden(B,A) -> v1_membered(k1_setfam_1(A)))) # label(t26_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3305 (all A (v2_membered(A) -> r1_tarski(A,k1_numbers))) # label(t2_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3306 (all A all B (v1_membered(B) -> (r1_tarski(A,B) -> v1_membered(A)))) # label(t16_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3307 (all A (v1_membered(A) -> (all B (v1_membered(B) -> (r1_tarski(A,B) <-> (all C (v1_xcmplx_0(C) -> (r2_hidden(C,A) -> r2_hidden(C,B))))))))) # label(d6_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3308 (all A (v5_membered(A) <-> (all B (r2_hidden(B,A) -> v4_ordinal2(B))))) # label(d5_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3309 (all A (v3_membered(A) -> (all B (v3_membered(B) -> (A = B <-> (all C (v1_rat_1(C) -> (r2_hidden(C,A) <-> r2_hidden(C,B))))))))) # label(d13_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3310 (all A (v5_membered(A) -> (all B (v5_membered(B) -> ((all C (v4_ordinal2(C) -> -(r2_hidden(C,A) & r2_hidden(C,B)))) <-> r1_xboole_0(A,B)))))) # label(d20_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3311 (all A (-v1_xboole_0(A) & v3_membered(A) -> (exists B (r2_hidden(B,A) & v1_rat_1(B))))) # label(t8_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3312 (all A (v1_xboole_0(A) -> v1_membered(A) & v5_membered(A) & v4_membered(A) & v3_membered(A) & v2_membered(A))) # label(cc15_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3313 (all A (v2_membered(A) -> (all B (v2_membered(B) -> ((all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r2_hidden(C,B)))) <-> r1_tarski(A,B)))))) # label(d7_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3314 (all A (m1_subset_1(A,k1_zfmisc_1(k4_numbers)) -> v4_membered(A) & v3_membered(A) & v2_membered(A) & v1_membered(A))) # label(cc8_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3315 (all A all B (v4_membered(A) -> v1_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)))) # label(fc34_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3316 (all A ((all B (r2_hidden(B,A) -> v1_membered(B))) -> v1_membered(k3_tarski(A)))) # label(t21_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3317 (all A all B (v4_membered(B) & v4_membered(A) -> v2_membered(k5_xboole_0(A,B)) & v3_membered(k5_xboole_0(A,B)) & v4_membered(k5_xboole_0(A,B)) & v1_membered(k5_xboole_0(A,B)))) # label(fc45_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3318 (all A (v4_membered(A) -> v3_membered(A))) # label(cc2_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3319 (all A (-v1_xboole_0(A) & v1_membered(A) -> (exists B (v1_xcmplx_0(B) & r2_hidden(B,A))))) # label(t6_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3320 (all A all B (v3_membered(A) -> v1_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)))) # label(fc31_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3321 (all A (v1_membered(A) -> r1_tarski(A,k2_numbers))) # label(t1_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3322 (all A all B (v2_membered(A) -> v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)))) # label(fc38_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3323 (all A all B (v1_rat_1(A) & v1_rat_1(B) -> v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v1_membered(k2_tarski(A,B)))) # label(fc14_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3324 (all A all B (v5_membered(A) -> v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)) & v5_membered(k4_xboole_0(A,B)))) # label(fc41_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3325 (all A all B (v2_membered(A) & v2_membered(B) -> v2_membered(k5_xboole_0(A,B)) & v1_membered(k5_xboole_0(A,B)))) # label(fc43_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3326 (all A (v2_membered(A) & -v1_xboole_0(A) -> (exists B (r2_hidden(B,A) & v1_xreal_0(B))))) # label(t7_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3327 (all A (v4_membered(A) -> (all B (v4_membered(B) -> ((all C (v1_int_1(C) -> (r2_hidden(C,A) -> r2_hidden(C,B)))) <-> r1_tarski(A,B)))))) # label(d9_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3328 (all A (v1_xcmplx_0(A) -> v1_membered(k1_tarski(A)))) # label(fc7_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3329 (all A all B all C (v1_rat_1(A) & v1_rat_1(B) & v1_rat_1(C) -> v1_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)))) # label(fc19_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3330 (all A (v4_membered(A) -> ((all B (v1_int_1(B) -> r2_hidden(B,A))) -> k4_numbers = A))) # label(t14_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3331 (all A (v3_membered(A) -> ((all B (v1_rat_1(B) -> r2_hidden(B,A))) -> k3_numbers = A))) # label(t13_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3332 (all A (m1_subset_1(A,k1_zfmisc_1(k5_numbers)) -> v1_membered(A) & v4_membered(A) & v5_membered(A) & v3_membered(A) & v2_membered(A))) # label(cc9_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3333 (all A (v5_membered(A) -> (all B (m1_subset_1(B,A) -> v1_xcmplx_0(B) & v4_ordinal2(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B))))) # label(cc14_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3334 (all A all B (v3_membered(B) & r2_hidden(B,A) -> v3_membered(k1_setfam_1(A)))) # label(t28_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3335 (all A ((all B (r2_hidden(B,A) -> v3_membered(B))) -> v3_membered(k3_tarski(A)))) # label(t23_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3336 (all A all B (v5_membered(B) & v5_membered(A) -> v2_membered(k2_xboole_0(A,B)) & v5_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v1_membered(k2_xboole_0(A,B)))) # label(fc26_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3337 (all A (v4_membered(A) -> r1_tarski(A,k4_numbers))) # label(t4_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3338 (all A all B (v1_membered(A) -> v1_membered(k4_xboole_0(A,B)))) # label(fc37_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3339 (all A ((all B (r2_hidden(B,A) -> v1_xreal_0(B))) <-> v2_membered(A))) # label(d2_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3340 (all A all B (v4_membered(B) -> (r1_tarski(A,B) -> v4_membered(A)))) # label(t19_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3341 (all A (v1_membered(A) -> (all B (v1_membered(B) -> ((all C (v1_xcmplx_0(C) -> -(r2_hidden(C,A) & r2_hidden(C,B)))) <-> r1_xboole_0(A,B)))))) # label(d16_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3342 (all A all B (v3_membered(A) -> v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v1_membered(k3_xboole_0(B,A)))) # label(fc32_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3343 (all A (v2_membered(A) -> (all B (m1_subset_1(B,A) -> v1_xreal_0(B) & v1_xcmplx_0(B))))) # label(cc11_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3344 (all A all B (v5_membered(A) -> v4_membered(k3_xboole_0(B,A)) & v5_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v1_membered(k3_xboole_0(B,A)))) # label(fc36_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3345 (exists A (v3_membered(A) & (all B (v1_rat_1(B) -> (r2_hidden(B,A) <-> p1_s3_membered(B)))))) # label(s3_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3346 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> v2_membered(k2_tarski(A,B)) & v1_membered(k2_tarski(A,B)))) # label(fc13_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3347 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> v1_membered(A) & v2_membered(A))) # label(cc6_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3348 (all A (v3_membered(A) <-> (all B (r2_hidden(B,A) -> v1_rat_1(B))))) # label(d3_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3349 (all A all B (r2_hidden(B,A) & v4_membered(B) -> v4_membered(k1_setfam_1(A)))) # label(t29_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3350 (all A all B (v1_xcmplx_0(B) & v1_xcmplx_0(A) -> v1_membered(k2_tarski(A,B)))) # label(fc12_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3351 (all A all B (v1_int_1(A) & v1_int_1(B) -> v4_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v1_membered(k2_tarski(A,B)))) # label(fc15_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3352 (all A (v4_membered(A) <-> (all B (r2_hidden(B,A) -> v1_int_1(B))))) # label(d4_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3353 (all A (m1_subset_1(A,k1_zfmisc_1(k3_numbers)) -> v2_membered(A) & v3_membered(A) & v1_membered(A))) # label(cc7_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3354 (all A (v1_membered(A) -> (all B (v1_membered(B) -> ((all C (v1_xcmplx_0(C) -> (r2_hidden(C,A) <-> r2_hidden(C,B)))) <-> B = A))))) # label(d11_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3355 (all A (v3_membered(A) -> (all B (v3_membered(B) -> ((all C (v1_rat_1(C) -> -(r2_hidden(C,A) & r2_hidden(C,B)))) <-> r1_xboole_0(A,B)))))) # label(d18_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3356 (all A (v4_membered(A) & -v1_xboole_0(A) -> (exists B (r2_hidden(B,A) & v1_int_1(B))))) # label(t9_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3357 (all A (v3_membered(A) -> (all B (v3_membered(B) -> (r1_tarski(A,B) <-> (all C (v1_rat_1(C) -> (r2_hidden(C,A) -> r2_hidden(C,B))))))))) # label(d8_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3358 (all A (v3_membered(A) -> r1_tarski(A,k3_numbers))) # label(t3_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3359 (all A (v5_membered(A) -> ((all B (v4_ordinal2(B) -> r2_hidden(B,A))) -> k5_numbers = A))) # label(t15_membered) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3360 (all A k1_card_1(k1_tarski(A)) = k4_ordinal2) # label(t50_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3361 (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]. 17.16/16.60 3362 $T # label(t15_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3363 $T # label(t77_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3364 (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]. 17.16/16.60 3365 (all A (r2_hidden(A,k5_ordinal2) -> v1_card_1(A))) # label(t65_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3366 (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]. 17.16/16.60 3367 $T # label(t62_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3368 (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]. 17.16/16.60 3369 $T # label(d2_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3370 (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]. 17.16/16.60 3371 (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]. 17.16/16.60 3372 (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]. 17.16/16.60 3373 (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]. 17.16/16.60 3374 $T # label(t53_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3375 (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]. 17.16/16.60 3376 $T # label(t9_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3377 $T # label(t10_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3378 (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]. 17.16/16.60 3379 (all A (v1_card_1(A) -> r2_hidden(A,k2_card_1(A)))) # label(t32_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3380 (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]. 17.16/16.60 3381 (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]. 17.16/16.60 3382 (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]. 17.16/16.60 3383 (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]. 17.16/16.60 3384 $T # label(t70_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3385 $T # label(t31_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3386 $T # label(t37_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3387 (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]. 17.16/16.60 3388 (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]. 17.16/16.60 3389 (all A r2_hidden(k1_card_1(k1_xboole_0),k2_card_1(A))) # label(t33_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3390 (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]. 17.16/16.60 3391 $T # label(t63_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3392 $T # label(t18_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3393 (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]. 17.16/16.60 3394 (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]. 17.16/16.60 3395 (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]. 17.16/16.60 3396 $T # label(t20_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3397 $T # label(t1_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3398 (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]. 17.16/16.60 3399 (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]. 17.16/16.60 3400 (all A (v3_ordinal1(A) -> r1_ordinal1(k1_card_1(A),A))) # label(t24_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3401 (exists A v1_card_1(A)) # label(rc1_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3402 (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]. 17.16/16.60 3403 $T # label(t67_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3404 $T # label(t5_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3405 (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]. 17.16/16.60 3406 $T # label(t75_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3407 (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]. 17.16/16.60 3408 $T # label(t12_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3409 $T # label(d10_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3410 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]. 17.16/16.60 3411 (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]. 17.16/16.60 3412 (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]. 17.16/16.60 3413 (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]. 17.16/16.60 3414 $T # label(t54_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3415 (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]. 17.16/16.60 3416 (all A v1_card_1(k1_card_1(A))) # label(dt_k1_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3417 $T # label(t6_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3418 (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]. 17.16/16.60 3419 $T # label(d4_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3420 (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]. 17.16/16.60 3421 (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]. 17.16/16.60 3422 (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]. 17.16/16.60 3423 (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]. 17.16/16.60 3424 (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]. 17.16/16.60 3425 $T # label(t19_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3426 (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]. 17.16/16.60 3427 (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]. 17.16/16.60 3428 (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]. 17.16/16.60 3429 $T # label(t17_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3430 (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]. 17.16/16.60 3431 $T # label(dt_k3_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3432 (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]. 17.16/16.60 3433 (all A np__1 = k4_card_1(k1_tarski(A))) # label(t79_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3434 (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]. 17.16/16.60 3435 (all A (k1_xboole_0 = A <-> r2_wellord2(A,k1_xboole_0))) # label(t46_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3436 (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]. 17.16/16.60 3437 $T # label(t57_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3438 (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]. 17.16/16.60 3439 $T # label(d9_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3440 $T # label(t3_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3441 (all A (v1_finset_1(A) -> v1_finset_1(k2_card_1(A)))) # label(t82_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3442 $T # label(t2_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.60 3443 (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]. 17.16/16.60 3444 (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]. 17.16/16.61 3445 (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]. 17.16/16.61 3446 (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]. 17.16/16.61 3447 (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]. 17.16/16.61 3448 $T # label(t11_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3449 (all A v1_card_1(k2_card_1(A))) # label(dt_k2_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3450 (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]. 17.16/16.61 3451 (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]. 17.16/16.61 3452 (all A exists B (r2_wellord2(A,B) & v3_ordinal1(B))) # label(t4_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3453 (all A -r2_wellord2(A,k1_zfmisc_1(A))) # label(t29_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3454 (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]. 17.16/16.61 3455 (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]. 17.16/16.61 3456 $T # label(t55_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3457 (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]. 17.16/16.61 3458 $T # label(t16_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3459 $T # label(d3_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3460 (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]. 17.16/16.61 3461 (all A (v3_ordinal1(A) -> r2_hidden(A,k2_card_1(A)))) # label(t36_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3462 $T # label(t7_card_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3463 (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]. 17.16/16.61 3464 $T # label(t28_finseq_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3465 $T # label(t54_finseq_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3466 (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]. 17.16/16.61 3467 (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]. 17.16/16.61 3468 (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]. 17.16/16.61 3469 $T # label(t2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3470 (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]. 17.16/16.61 3471 (all A (v4_ordinal2(A) -> v1_finset_1(k1_finseq_1(A)))) # label(fc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3472 (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]. 17.16/16.61 3473 (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]. 17.16/16.61 3474 (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]. 17.16/16.61 3475 (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]. 17.16/16.61 3476 (all A k1_tarski(k4_tarski(np__1,A)) = k5_finseq_1(A)) # label(d5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3477 (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]. 17.16/16.61 3478 (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]. 17.16/16.61 3479 (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]. 17.16/16.61 3480 (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]. 17.16/16.61 3481 (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]. 17.16/16.61 3482 (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]. 17.16/16.61 3483 (all A m2_finseq_1(k14_finseq_1(A),k5_numbers)) # label(dt_k14_finseq_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3484 (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]. 17.16/16.61 3485 (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]. 17.16/16.61 3486 (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]. 17.16/16.61 3487 (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]. 17.16/16.61 3488 (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]. 17.16/16.61 3489 (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]. 17.16/16.61 3490 (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]. 17.16/16.61 3491 (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]. 17.16/16.61 3492 (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]. 17.16/16.61 3493 (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]. 17.16/16.61 3494 (all A (v4_ordinal2(A) -> A = k4_card_1(k2_finseq_1(A)))) # label(t78_finseq_1_AndRHS) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3495 (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]. 17.16/16.61 3496 (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]. 17.16/16.61 3497 (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]. 17.16/16.61 3498 (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]. 17.16/16.61 3499 (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]. 17.16/16.61 3500 (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]. 17.16/16.61 3501 $T # label(dt_k13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3502 (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]. 17.16/16.61 3503 (exists A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A))) # label(rc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3504 (all A exists B m1_finseq_1(B,A)) # label(existence_m1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3505 $T # label(t22_finseq_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3506 $T # label(dt_k5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3507 $T # label(t1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3508 (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]. 17.16/16.61 3509 (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]. 17.16/16.61 3510 (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]. 17.16/16.61 3511 (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]. 17.16/16.61 3512 $T # label(t67_finseq_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3513 (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]. 17.16/16.61 3514 (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]. 17.16/16.61 3515 (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]. 17.16/16.61 3516 (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]. 17.16/16.61 3517 (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]. 17.16/16.61 3518 (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]. 17.16/16.61 3519 (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]. 17.16/16.61 3520 (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]. 17.16/16.61 3521 $T # label(t53_finseq_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3522 (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]. 17.16/16.61 3523 (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]. 17.16/16.61 3524 (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]. 17.16/16.61 3525 (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]. 17.16/16.61 3526 (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]. 17.16/16.61 3527 (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]. 17.16/16.61 3528 $T # label(t30_finseq_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3529 (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]. 17.16/16.61 3530 (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]. 17.16/16.61 3531 (all A (v1_relat_1(A) -> v1_relat_1(k17_finseq_1(A)))) # label(dt_k17_finseq_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3532 (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]. 17.16/16.61 3533 (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]. 17.16/16.61 3534 (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]. 17.16/16.61 3535 $T # label(t34_finseq_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3536 (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]. 17.16/16.61 3537 (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]. 17.16/16.61 3538 (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]. 17.16/16.61 3539 (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]. 17.16/16.61 3540 (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]. 17.16/16.61 3541 (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]. 17.16/16.61 3542 (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]. 17.16/16.61 3543 (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]. 17.16/16.61 3544 (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]. 17.16/16.61 3545 (all A -v1_xboole_0(k13_finseq_1(A))) # label(fc9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3546 (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]. 17.16/16.61 3547 (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]. 17.16/16.61 3548 (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]. 17.16/16.61 3549 (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]. 17.16/16.61 3550 (exists A (v1_relat_1(A) & v1_funct_1(A) & v2_finseq_1(A))) # label(rc5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3551 (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]. 17.16/16.61 3552 (all A (v4_ordinal2(A) -> k1_finseq_1(A) = k2_finseq_1(A))) # label(redefinition_k2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3553 (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]. 17.16/16.61 3554 (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]. 17.16/16.61 3555 (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]. 17.16/16.61 3556 (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]. 17.16/16.61 3557 $T # label(t51_finseq_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3558 (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]. 17.16/16.61 3559 (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]. 17.16/16.61 3560 $T # label(dt_k10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3561 (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]. 17.16/16.61 3562 (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]. 17.16/16.61 3563 (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]. 17.16/16.61 3564 (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]. 17.16/16.61 3565 (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]. 17.16/16.61 3566 (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]. 17.16/16.61 3567 (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]. 17.16/16.61 3568 (all A exists B m2_finseq_1(B,A)) # label(existence_m2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3569 (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]. 17.16/16.61 3570 (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]. 17.16/16.61 3571 (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]. 17.16/16.61 3572 (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]. 17.16/16.61 3573 (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]. 17.16/16.61 3574 $T # label(t31_finseq_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3575 (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]. 17.16/16.61 3576 (all A r2_hidden(k1_xboole_0,k13_finseq_1(A))) # label(t66_finseq_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3577 (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]. 17.16/16.61 3578 $T # label(t49_finseq_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3579 $T # label(t13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3580 (all A k1_tarski(k4_tarski(np__1,A)) = k9_finseq_1(A)) # label(t52_finseq_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3581 (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]. 17.16/16.61 3582 (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]. 17.16/16.61 3583 (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]. 17.16/16.61 3584 (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]. 17.16/16.61 3585 (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]. 17.16/16.61 3586 (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]. 17.16/16.61 3587 (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]. 17.16/16.61 3588 (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]. 17.16/16.61 3589 (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]. 17.16/16.61 3590 (all A m2_finseq_1(k1_xboole_0,A)) # label(t29_finseq_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3591 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]. 17.16/16.61 3592 (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]. 17.16/16.61 3593 (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]. 17.16/16.61 3594 (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]. 17.16/16.61 3595 (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]. 17.16/16.61 3596 (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]. 17.16/16.61 3597 $T # label(t70_finseq_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3598 (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]. 17.16/16.61 3599 (all A k1_xboole_0 = k6_finseq_1(A)) # label(d6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3600 (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]. 17.16/16.61 3601 (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]. 17.16/16.61 3602 (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]. 17.16/16.61 3603 $T # label(dt_k11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3604 (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]. 17.16/16.61 3605 (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]. 17.16/16.61 3606 $T # label(dt_k1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3607 (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]. 17.16/16.61 3608 (all A k5_finseq_1(A) = k9_finseq_1(A)) # label(redefinition_k9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 17.16/16.61 3609 (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]. 17.16/16.61 3610 (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]. 17.16/16.61 3611 (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]. 17.16/16.61 3612 (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]. 17.16/16.61 3613 (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]. 17.16/16.61 3614 (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]. 17.16/16.61 3615 (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]. 17.16/16.61 3616 (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]. 17.16/16.61 3617 (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]. 17.16/16.61 3618 (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]. 17.16/16.61 3619 (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]. 17.16/16.61 3620 (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]. 17.16/16.61 3621 (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]. 17.16/16.61 3622 (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]. 17.28/16.64 3623 (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]. 17.28/16.64 3624 (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]. 17.28/16.64 3625 (all A -(A != k1_xboole_0 & (all B -(r2_hidden(B,A) & (all C -(r1_tarski(C,B) & B != C & r2_hidden(C,A))))) & (all B -((all C -(r2_hidden(C,A) & (all D (r2_hidden(D,B) -> r1_tarski(C,D))))) & v6_ordinal1(B) & r1_tarski(B,A))))) # label(t176_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3626 $T # label(t102_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3627 $T # label(t85_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3628 $T # label(t33_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3629 $T # label(t62_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3630 (all A all B all C (v1_relat_1(C) -> (r1_tarski(B,A) & r8_relat_2(C,A) -> r8_relat_2(C,B)))) # label(t95_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3631 (all A (-v1_xboole_0(A) -> (-r2_hidden(k1_xboole_0,A) -> (all B (v1_funct_1(B) & v1_funct_2(B,A,k3_tarski(A)) & m2_relset_1(B,A,k3_tarski(A)) -> ((all C (r2_hidden(C,A) -> r2_hidden(k1_funct_1(B,C),C))) <-> m1_orders_1(B,A))))))) # label(d1_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3632 (all A all B (v1_relat_2(B) & v4_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> A = k5_relset_1(A,A,B) & k4_relset_1(A,A,B) = A)) # label(t99_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3633 (all A (v1_relat_1(A) -> (v2_orders_1(A) -> v2_orders_1(k4_relat_1(A))))) # label(t105_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3634 (all A (v1_relat_1(A) -> (all B (v4_relat_2(A) & r8_orders_1(A,B) -> r6_orders_1(A,B))))) # label(t158_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3635 $T # label(t31_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3636 (all A (v1_relat_1(A) -> (all B all C (r1_tarski(C,B) & r3_orders_1(A,B) -> r3_orders_1(A,C))))) # label(t134_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3637 (all A (v1_relat_1(A) -> (all B (r2_hidden(B,k3_relat_1(A)) & (all C -(r2_hidden(C,k3_relat_1(A)) & C != B & r2_hidden(k4_tarski(B,C),A))) <-> r6_orders_1(A,B))))) # label(d11_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3638 $T # label(t116_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3639 (all A (m1_subset_1(A,f1_s1_orders_1) -> (all B (m1_subset_1(B,f1_s1_orders_1) -> (p1_s1_orders_1(A,B) & p1_s1_orders_1(B,A) -> A = B))))) & (all A -((all B (m1_subset_1(B,f1_s1_orders_1) -> (exists C (r2_hidden(C,A) & -p1_s1_orders_1(C,B) & m1_subset_1(C,f1_s1_orders_1))))) & (all B (m1_subset_1(B,f1_s1_orders_1) -> (all C (m1_subset_1(C,f1_s1_orders_1) -> -(r2_hidden(C,A) & -p1_s1_orders_1(C,B) & -p1_s1_orders_1(B,C) & r2_hidden(B,A)))))) & r1_tarski(A,f1_s1_orders_1))) & (all A (m1_subset_1(A,f1_s1_orders_1) -> (all B (m1_subset_1(B,f1_s1_orders_1) -> (all C (m1_subset_1(C,f1_s1_orders_1) -> (p1_s1_orders_1(A,B) & p1_s1_orders_1(B,C) -> p1_s1_orders_1(A,C)))))))) & (all A (m1_subset_1(A,f1_s1_orders_1) -> p1_s1_orders_1(A,A))) -> (exists A ((all B (m1_subset_1(B,f1_s1_orders_1) -> -(p1_s1_orders_1(A,B) & B != A))) & m1_subset_1(A,f1_s1_orders_1))) # label(s1_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3640 (all A (v1_relat_1(A) -> (all B (r7_orders_1(k4_relat_1(A),B) <-> r6_orders_1(A,B))))) # label(t164_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3641 (all A (v1_relat_1(A) -> (all B -(B = k3_relat_1(A) & r5_orders_1(A,B) & (all C -r7_orders_1(A,C)) & r2_orders_1(A,B))))) # label(t174_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3642 (all A (v2_orders_1(k6_partfun1(A)) & v1_orders_1(k6_partfun1(A)))) # label(t120_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3643 $T # label(t42_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3644 $T # label(t148_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3645 $T # label(t52_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3646 $T # label(t32_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3647 (all A all B all C (v1_relat_1(C) -> (r1_tarski(B,A) & r4_relat_2(C,A) -> r4_relat_2(C,B)))) # label(t94_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3648 (all A (v1_relat_1(A) -> (all B (r5_orders_1(k4_relat_1(A),B) <-> r4_orders_1(A,B))))) # label(t151_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3649 (all A all B (v1_relat_1(B) -> (r6_relat_2(B,A) & r1_relat_2(B,A) <-> r7_relat_2(B,A)))) # label(t92_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3650 $T # label(t38_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3651 (all A (-v1_xboole_0(A) -> -v1_xboole_0(k1_orders_1(A)))) # label(fc1_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3652 $T # label(t22_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3653 $T # label(t90_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3654 $T # label(t117_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3655 $T # label(t68_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3656 $T # label(t18_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3657 $T # label(t156_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3658 $T # label(t81_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3659 $T # label(t172_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3660 (all A (v1_relat_1(A) -> (v2_orders_1(A) -> r2_orders_1(A,k3_relat_1(A))))) # label(t130_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3661 $T # label(t74_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3662 (all A (v1_relat_1(A) -> (v1_orders_1(A) -> v1_orders_1(k4_relat_1(A))))) # label(t104_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3663 (all A (v1_relat_1(A) -> (all B (r2_orders_1(A,B) -> v1_relat_2(k2_wellord1(A,B)) & v1_partfun1(k2_wellord1(A,B),B,B) & m2_relset_1(k2_wellord1(A,B),B,B) & v8_relat_2(k2_wellord1(A,B)) & v4_relat_2(k2_wellord1(A,B)))))) # label(t141_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3664 (all A (v1_relat_1(A) -> (all B (r2_orders_1(A,B) -> r2_orders_1(k4_relat_1(A),B))))) # label(t137_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3665 $T # label(t29_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3666 $T # label(t89_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3667 (all A all B (v1_relat_2(B) & v4_relat_2(B) & v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) -> v1_orders_1(B))) # label(t111_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3668 (all A (v1_relat_1(A) -> (all B (r5_orders_1(A,B) <-> r4_orders_1(k4_relat_1(A),B))))) # label(t152_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3669 $T # label(dt_k1_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3670 (all A (v1_relat_1(A) -> (all B (r9_orders_1(k4_relat_1(A),B) <-> r8_orders_1(A,B))))) # label(t166_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3671 (all A (v1_relat_1(A) -> (all B (r1_relat_2(A,B) & r8_relat_2(A,B) <-> r1_orders_1(A,B))))) # label(d6_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3672 $T # label(t16_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3673 (all A (-(k1_xboole_0 = k3_tarski(A) & (exists B (B != k1_xboole_0 & r2_hidden(B,A)))) & -(k1_xboole_0 != k3_tarski(A) & (all B -(k1_xboole_0 != B & r2_hidden(B,A)))))) # label(t91_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3674 (all A (v1_relat_1(A) -> (all B (r3_orders_1(A,B) -> r1_orders_1(A,B) & r2_orders_1(A,B))))) # label(t125_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3675 (all A (v1_relat_1(A) -> (all B all C (r6_relat_2(A,B) & r1_tarski(C,B) -> r6_relat_2(A,C))))) # label(t186_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3676 $T # label(t57_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3677 (all A (v1_relat_1(A) -> (v6_relat_2(A) -> v6_relat_2(k4_relat_1(A))))) # label(t188_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3678 $T # label(t37_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3679 $T # label(t28_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3680 $T # label(t70_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3681 (all A (r1_orders_1(k6_partfun1(A),A) & r2_orders_1(k6_partfun1(A),A))) # label(t146_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3682 $T # label(t168_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3683 $T # label(t73_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3684 (all A (v1_relat_1(A) -> (all B (r5_orders_1(A,B) <-> (all C -(v3_orders_1(k2_wellord1(A,C)) & (all D -((all E (r2_hidden(E,C) -> r2_hidden(k4_tarski(D,E),A))) & r2_hidden(D,B))) & r1_tarski(C,B))))))) # label(d10_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3685 (all A (v1_relat_1(A) -> (all B (r9_orders_1(A,B) <-> r2_hidden(B,k3_relat_1(A)) & (all C (r2_hidden(C,k3_relat_1(A)) -> C = B | r2_hidden(k4_tarski(B,C),A))))))) # label(d14_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3686 (all A (v1_relat_1(A) -> (v3_orders_1(A) -> v2_orders_1(A) & v1_orders_1(A)))) # label(t108_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3687 (all A k1_orders_1(A) = k4_xboole_0(k1_zfmisc_1(A),k1_tarski(k1_xboole_0))) # label(d2_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3688 $T # label(t87_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3689 $T # label(t8_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3690 (all A all B all C (v1_relat_1(C) -> (r1_tarski(B,A) & r7_relat_2(C,A) -> r7_relat_2(C,B)))) # label(t96_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3691 $T # label(t40_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3692 (all A (v1_relat_1(A) -> (all B -(r5_orders_1(A,B) & k1_xboole_0 = B)))) # label(t150_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3693 $T # label(t79_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3694 $T # label(t47_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3695 $T # label(t48_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3696 $T # label(t72_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3697 (all A (v1_relat_1(A) -> (all B (r2_hidden(B,k3_relat_1(A)) & (all C (r2_hidden(C,k3_relat_1(A)) -> r2_hidden(k4_tarski(C,B),A) | C = B)) <-> r8_orders_1(A,B))))) # label(d13_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3698 $T # label(t64_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3699 $T # label(t67_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3700 $T # label(t17_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3701 $T # label(t11_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3702 (all A (v1_relat_1(A) -> (all B (v1_orders_1(A) -> v1_orders_1(k2_wellord1(A,B)))))) # label(t113_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3703 $T # label(t65_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3704 (all A (-v1_xboole_0(A) -> -r2_hidden(k1_xboole_0,k1_orders_1(A)))) # label(t4_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3705 (all A (v1_relat_1(A) -> (all B (r7_orders_1(A,B) <-> r2_hidden(B,k3_relat_1(A)) & (all C -(B != C & r2_hidden(k4_tarski(C,B),A) & r2_hidden(C,k3_relat_1(A)))))))) # label(d12_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3706 $T # label(t30_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3707 (all A all B all C all D (v4_relat_2(D) & v8_relat_2(D) & m2_relset_1(D,A,A) & v1_partfun1(D,A,A) & v1_relat_2(D) -> (r2_hidden(B,A) & r2_hidden(C,A) & r2_hidden(k4_tarski(B,C),D) & r2_hidden(k4_tarski(C,B),D) -> C = B))) # label(t13_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3708 $T # label(t53_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3709 $T # label(t101_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3710 $T # label(t121_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3711 $T # label(t66_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3712 $T # label(t155_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3713 $T # label(t19_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3714 (all A (v1_relat_1(A) -> (all B all C (r2_wellord1(A,B) & r1_tarski(C,B) -> r2_wellord1(A,C))))) # label(t187_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3715 (all A (v1_relat_1(A) -> (all B all C (r8_orders_1(A,B) & v1_relat_2(A) & r1_tarski(C,k3_relat_1(A)) & r2_hidden(B,C) -> r4_orders_1(A,C))))) # label(t161_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3716 $T # label(t36_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3717 (all A (v1_relat_1(A) -> (all B (v3_orders_1(A) -> v3_orders_1(k2_wellord1(A,B)))))) # label(t115_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3718 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (r2_hidden(A,k1_orders_1(B)) <-> r1_tarski(A,B)))))) # label(t5_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3719 $T # label(t3_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3720 (all A (v1_relat_1(A) -> (all B (r7_orders_1(A,B) <-> r6_orders_1(k4_relat_1(A),B))))) # label(t163_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3721 $T # label(t24_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3722 $T # label(t77_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3723 $T # label(t1_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3724 (all A (v1_relat_1(A) -> k2_wellord1(A,k1_xboole_0) = k1_xboole_0)) # label(t194_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3725 (all A all B (v1_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v4_relat_2(B) -> A = k3_relat_1(B))) # label(t100_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3726 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> v1_orders_1(A) & v2_orders_1(A) & v3_orders_1(A)))) # label(t107_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3727 $T # label(t75_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3728 $T # label(t144_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3729 $T # label(t82_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3730 (all A (v1_relat_1(A) -> (all B (r6_relat_2(A,B) -> r6_relat_2(k4_relat_1(A),B))))) # label(t192_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3731 $T # label(t2_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3732 $T # label(t44_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3733 (all A (v1_relat_1(A) -> (all B (r2_orders_1(A,B) -> r1_orders_1(A,B))))) # label(t126_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3734 (all A (v1_relat_1(A) -> (all B (r8_relat_2(A,B) -> v8_relat_2(k2_wellord1(A,B)))))) # label(t183_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3735 $T # label(t21_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3736 (all A (v1_relat_1(A) -> (v1_orders_1(A) <-> v1_relat_2(A) & v8_relat_2(A)))) # label(d3_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3737 (all A (v1_relat_1(A) -> (all B (r2_wellord1(A,B) -> r1_orders_1(A,B) & r3_orders_1(A,B) & r2_orders_1(A,B))))) # label(t124_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3738 (all A (v1_relat_1(A) -> (all B all C (r2_orders_1(A,B) & r1_tarski(C,B) -> r2_orders_1(A,C))))) # label(t131_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.64 3739 $T # label(t50_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3740 (all A all B all C (v4_relat_2(C) & v8_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v1_relat_2(C) -> (r2_hidden(B,A) -> r2_hidden(k4_tarski(B,B),C)))) # label(t12_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3741 $T # label(t10_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3742 (all A (v1_relat_1(A) -> (all B (r7_orders_1(A,B) & v6_relat_2(A) -> r9_orders_1(A,B))))) # label(t159_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3743 $T # label(t84_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3744 $T # label(t118_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3745 $T # label(t80_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3746 (all A (m1_subset_1(A,f1_s2_orders_1) -> p1_s2_orders_1(A,A))) & (all A (m1_subset_1(A,f1_s2_orders_1) -> (all B (m1_subset_1(B,f1_s2_orders_1) -> (p1_s2_orders_1(B,A) & p1_s2_orders_1(A,B) -> A = B))))) & (all A (m1_subset_1(A,f1_s2_orders_1) -> (all B (m1_subset_1(B,f1_s2_orders_1) -> (all C (m1_subset_1(C,f1_s2_orders_1) -> (p1_s2_orders_1(A,B) & p1_s2_orders_1(B,C) -> p1_s2_orders_1(A,C)))))))) & (all A -((all B (m1_subset_1(B,f1_s2_orders_1) -> (all C (m1_subset_1(C,f1_s2_orders_1) -> -(r2_hidden(B,A) & -p1_s2_orders_1(B,C) & -p1_s2_orders_1(C,B) & r2_hidden(C,A)))))) & (all B (m1_subset_1(B,f1_s2_orders_1) -> (exists C (r2_hidden(C,A) & -p1_s2_orders_1(B,C) & m1_subset_1(C,f1_s2_orders_1))))) & r1_tarski(A,f1_s2_orders_1))) -> (exists A (m1_subset_1(A,f1_s2_orders_1) & (all B (m1_subset_1(B,f1_s2_orders_1) -> -(p1_s2_orders_1(B,A) & B != A))))) # label(s2_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3747 (all A (v1_relat_1(A) -> (all B (r1_orders_1(A,B) -> v1_orders_1(k2_wellord1(A,B)))))) # label(t129_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3748 $T # label(t20_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3749 $T # label(t171_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3750 (all A all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v4_relat_2(B) & v1_relat_2(B) -> v2_orders_1(B))) # label(t110_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3751 (all A (v1_relat_1(A) -> (v2_orders_1(A) <-> v8_relat_2(A) & v4_relat_2(A) & v1_relat_2(A)))) # label(d4_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3752 (all A (v1_relat_1(A) -> (v3_orders_1(A) -> r3_orders_1(A,k3_relat_1(A))))) # label(t133_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3753 (all A all B all C (v1_relat_1(C) -> (r1_tarski(B,A) & r1_relat_2(C,A) -> r1_relat_2(C,B)))) # label(t93_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3754 (all A (v1_relat_1(A) -> (all B (r2_orders_1(A,B) -> v2_orders_1(k2_wellord1(A,B)))))) # label(t132_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3755 $T # label(t147_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3756 $T # label(t69_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3757 (all A (v1_relat_1(A) -> (all B (v1_relat_2(A) & r1_tarski(B,k3_relat_1(A)) -> k3_relat_1(k2_wellord1(A,B)) = B)))) # label(t181_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3758 (all A all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v4_relat_2(B) & v1_relat_2(B) -> r1_orders_1(B,A))) # label(t139_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3759 (all A (v1_relat_1(A) -> (all B (r8_relat_2(A,B) -> r8_relat_2(k4_relat_1(A),B))))) # label(t190_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3760 (all A all B (v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v4_relat_2(B) & v1_relat_2(B) -> r2_orders_1(B,A))) # label(t140_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3761 $T # label(t63_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3762 (all A (v1_relat_1(A) -> (all B (v6_relat_2(A) & r6_orders_1(A,B) -> r8_orders_1(A,B))))) # label(t160_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3763 $T # label(t59_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3764 $T # label(t103_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3765 $T # label(t55_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3766 $T # label(t43_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3767 (all A (v1_relat_1(A) -> (all B -(k3_relat_1(A) = B & (all C (v1_relat_1(C) -> -(r1_tarski(A,C) & B = k3_relat_1(C) & r3_orders_1(C,B)))) & r2_orders_1(A,B))))) # label(t179_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3768 (all A all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) -> A = k3_relat_1(B))) # label(t97_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3769 $T # label(t39_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3770 $T # label(t51_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3771 (all A (v1_relat_1(A) -> (all B (r1_orders_1(A,B) -> r1_orders_1(k4_relat_1(A),B))))) # label(t136_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3772 $T # label(t88_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3773 $T # label(t60_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3774 (all A (-v1_xboole_0(A) -> (all B (m1_orders_1(B,A) -> v1_funct_2(B,A,k3_tarski(A)) & m2_relset_1(B,A,k3_tarski(A)) & v1_funct_1(B))))) # label(dt_m1_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3775 (all A -((all B -(r2_hidden(B,A) & (all C -(r2_hidden(C,A) & C != B & r1_tarski(B,C))))) & (all B (r1_tarski(B,A) & v6_ordinal1(B) -> k1_xboole_0 = B | r2_hidden(k3_tarski(B),A))) & A != k1_xboole_0)) # label(t177_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3776 (all A all B (m2_relset_1(B,A,A) -> (r1_relat_2(B,A) -> k3_relat_1(B) = A & A = k4_relset_1(A,A,B)))) # label(t98_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3777 $T # label(t170_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3778 (all A (v1_relat_1(A) -> (all B -(k1_xboole_0 = B & r4_orders_1(A,B))))) # label(t149_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3779 $T # label(t122_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3780 $T # label(t45_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3781 $T # label(t46_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3782 $T # label(t71_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3783 (all A (v1_relat_1(A) -> (all B (r3_orders_1(A,B) -> v1_relat_2(k2_wellord1(A,B)) & v4_relat_2(k2_wellord1(A,B)) & v8_relat_2(k2_wellord1(A,B)) & m2_relset_1(k2_wellord1(A,B),B,B) & v1_partfun1(k2_wellord1(A,B),B,B))))) # label(t142_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3784 (all A (v1_relat_1(A) -> (all B all C (r9_orders_1(A,B) & v1_relat_2(A) & r1_tarski(C,k3_relat_1(A)) & r2_hidden(B,C) -> r5_orders_1(A,C))))) # label(t162_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3785 $T # label(t41_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3786 (all A (v1_relat_1(A) -> (all B (r4_relat_2(A,B) -> v4_relat_2(k2_wellord1(A,B)))))) # label(t184_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3787 (all A (v1_relat_1(A) -> (v1_relat_2(A) & v6_relat_2(A) & v4_relat_2(A) & v8_relat_2(A) <-> v3_orders_1(A)))) # label(d5_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3788 (all A (-v1_xboole_0(A) -> (exists B m1_orders_1(B,A)))) # label(existence_m1_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3789 (all A all B all C all D all E (v1_partfun1(E,A,A) & m2_relset_1(E,A,A) & v8_relat_2(E) & v4_relat_2(E) & v1_relat_2(E) -> (r2_hidden(D,A) & r2_hidden(k4_tarski(B,C),E) & r2_hidden(k4_tarski(C,D),E) & r2_hidden(C,A) & r2_hidden(B,A) -> r2_hidden(k4_tarski(B,D),E)))) # label(t14_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3790 (all A (v1_relat_1(A) -> (all B (v2_orders_1(A) -> v2_orders_1(k2_wellord1(A,B)))))) # label(t114_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3791 $T # label(t145_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3792 (all A (v1_relat_1(A) -> (all B -(r2_orders_1(A,B) & (all C -r6_orders_1(A,C)) & r4_orders_1(A,B) & B = k3_relat_1(A))))) # label(t173_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3793 $T # label(t169_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3794 (all A (v1_relat_1(A) -> (all B (r4_relat_2(A,B) -> r4_relat_2(k4_relat_1(A),B))))) # label(t191_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3795 (all A (v1_relat_1(A) -> (all B (r3_orders_1(A,B) -> r3_orders_1(k4_relat_1(A),B))))) # label(t138_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3796 $T # label(t34_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3797 (all A (v1_relat_1(A) -> (all B (r1_relat_2(A,B) -> r1_relat_2(k4_relat_1(A),B))))) # label(t189_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3798 (all A (v1_relat_1(A) -> (all B ((all C -(r1_tarski(C,B) & (all D -((all E (r2_hidden(E,C) -> r2_hidden(k4_tarski(E,D),A))) & r2_hidden(D,B))) & v3_orders_1(k2_wellord1(A,C)))) <-> r4_orders_1(A,B))))) # label(d9_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3799 $T # label(t83_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3800 $T # label(t61_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3801 (all A (-v1_xboole_0(A) -> r2_hidden(A,k1_orders_1(A)))) # label(t7_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3802 (all A (v1_relat_1(A) -> (all B all C (r1_tarski(C,B) & r1_orders_1(A,B) -> r1_orders_1(A,C))))) # label(t128_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3803 $T # label(t23_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3804 $T # label(t9_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3805 (all A all B (v1_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v4_relat_2(B) -> (v6_relat_2(B) -> v3_orders_1(B)))) # label(t112_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3806 (all A (v1_relat_1(A) -> (all B (r3_orders_1(A,B) -> v3_orders_1(k2_wellord1(A,B)))))) # label(t135_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3807 (all A (v1_relat_1(A) -> (v2_orders_1(A) -> v1_orders_1(A)))) # label(t109_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3808 (all A (v1_relat_1(A) -> (all B k2_wellord1(k4_relat_1(A),B) = k4_relat_1(k2_wellord1(A,B))))) # label(t193_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3809 $T # label(t56_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3810 $T # label(t49_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3811 $T # label(t35_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3812 $T # label(t167_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3813 (all A (v1_relat_1(A) -> (all B (r9_orders_1(A,B) & v4_relat_2(A) -> r7_orders_1(A,B))))) # label(t157_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3814 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (m1_subset_1(A,k1_zfmisc_1(B)) <-> r2_hidden(A,k1_orders_1(B))))))) # label(t6_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3815 (all A (v1_relat_1(A) -> (v1_orders_1(A) -> r1_orders_1(A,k3_relat_1(A))))) # label(t127_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3816 $T # label(t154_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3817 (all A -((all B -(r1_tarski(B,A) & v6_ordinal1(B) & (all C -(r2_hidden(C,A) & (all D (r2_hidden(D,B) -> r1_tarski(D,C))))))) & (all B -(r2_hidden(B,A) & (all C -(r2_hidden(C,A) & r1_tarski(B,C) & B != C)))) & k1_xboole_0 != A)) # label(t175_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3818 $T # label(t78_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3819 (all A (v1_relat_1(A) -> (all B (r1_relat_2(A,B) -> v1_relat_2(k2_wellord1(A,B)))))) # label(t182_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3820 (all A (v1_relat_1(A) -> (all B (r6_relat_2(A,B) -> v6_relat_2(k2_wellord1(A,B)))))) # label(t185_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3821 (all A (v1_relat_1(A) -> (v3_orders_1(A) -> v3_orders_1(k4_relat_1(A))))) # label(t106_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3822 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B -((all C -(r1_tarski(C,k1_relat_1(A)) & k9_relat_1(A,C) = B & v1_finset_1(C))) & r1_tarski(B,k2_relat_1(A)) & v1_finset_1(B))))) # label(t195_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3823 $T # label(t26_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3824 (all A -(A != k1_xboole_0 & (all B -(r2_hidden(B,A) & (all C -(r1_tarski(C,B) & C != B & r2_hidden(C,A))))) & (all B (r1_tarski(B,A) & v6_ordinal1(B) -> B = k1_xboole_0 | r2_hidden(k1_setfam_1(B),A))))) # label(t178_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3825 $T # label(t54_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3826 (all A (v1_relat_1(A) -> (all B (r8_orders_1(k4_relat_1(A),B) <-> r9_orders_1(A,B))))) # label(t165_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3827 $T # label(t58_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3828 (all A (v1_relat_1(A) -> (all B (r2_orders_1(A,B) <-> r4_relat_2(A,B) & r8_relat_2(A,B) & r1_relat_2(A,B))))) # label(d7_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3829 (all A (v1_relat_1(A) -> (all B (r3_orders_1(A,B) <-> r8_relat_2(A,B) & r4_relat_2(A,B) & r6_relat_2(A,B) & r1_relat_2(A,B))))) # label(d8_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3830 $T # label(t27_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3831 $T # label(t123_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3832 (all A (v1_relat_1(A) -> (all B (r2_wellord1(A,B) -> v8_relat_2(k2_wellord1(A,B)) & m2_relset_1(k2_wellord1(A,B),B,B) & v1_partfun1(k2_wellord1(A,B),B,B) & v4_relat_2(k2_wellord1(A,B)) & v1_relat_2(k2_wellord1(A,B)))))) # label(t143_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3833 $T # label(t86_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3834 $T # label(t25_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3835 $T # label(t15_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3836 $T # label(t153_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3837 $T # label(t76_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3838 (all A (v1_relat_1(A) -> r1_tarski(A,k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A))))) # label(t180_orders_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3839 (all A all B all C all D (v1_partfun1(D,B,B) & m2_relset_1(D,B,B) & v8_relat_2(D) & v3_relat_2(D) -> (all E (v3_relat_2(E) & v1_partfun1(E,B,B) & m2_relset_1(E,B,B) & v8_relat_2(E) -> (r2_hidden(A,B) -> ((exists F (v1_relat_1(F) & r1_xreal_0(np__1,k3_finseq_1(F)) & C = k1_funct_1(F,k3_finseq_1(F)) & (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,G) -> r1_xreal_0(k3_finseq_1(F),G) | r2_hidden(k4_tarski(k1_funct_1(F,G),k1_funct_1(F,k1_nat_1(G,np__1))),k3_eqrel_1(B,D,E))))) & A = k1_funct_1(F,np__1) & v1_finseq_1(F) & v1_funct_1(F))) <-> r2_hidden(k4_tarski(A,C),k5_eqrel_1(B,D,E)))))))) # label(t36_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3840 (all A all B (r2_hidden(B,A) -> A = k6_eqrel_1(A,k1_eqrel_1(A),B))) # label(t34_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3841 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(A,A)))) -> ((all C (r2_hidden(C,B) -> v8_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v3_relat_2(C))) -> v3_relat_2(k6_setfam_1(k2_zfmisc_1(A,A),B)) & v8_relat_2(k6_setfam_1(k2_zfmisc_1(A,A),B)) & m2_relset_1(k6_setfam_1(k2_zfmisc_1(A,A),B),A,A) & v1_partfun1(k6_setfam_1(k2_zfmisc_1(A,A),B),A,A) | B = k1_xboole_0))) # label(t19_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3842 (all A (r2_hidden(A,f1_s1_eqrel_1) -> p1_s1_eqrel_1(A,A))) & (all A all B all C (p1_s1_eqrel_1(A,B) & p1_s1_eqrel_1(B,C) -> p1_s1_eqrel_1(A,C))) & (all A all B (p1_s1_eqrel_1(A,B) -> p1_s1_eqrel_1(B,A))) -> (exists A (v3_relat_2(A) & v8_relat_2(A) & v1_partfun1(A,f1_s1_eqrel_1,f1_s1_eqrel_1) & m2_relset_1(A,f1_s1_eqrel_1,f1_s1_eqrel_1) & (all B all C (r2_hidden(k4_tarski(B,C),A) <-> p1_s1_eqrel_1(B,C) & r2_hidden(C,f1_s1_eqrel_1) & r2_hidden(B,f1_s1_eqrel_1))))) # label(s1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3843 (all A exists B m1_eqrel_1(B,A)) # label(existence_m1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3844 (all A all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> (all C (v8_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v3_relat_2(C) -> (all D (v3_relat_2(D) & v1_partfun1(D,A,A) & m2_relset_1(D,A,A) & v8_relat_2(D) -> (r1_tarski(k3_eqrel_1(A,B,C),D) & (all E (v3_relat_2(E) & m2_relset_1(E,A,A) & v1_partfun1(E,A,A) & v8_relat_2(E) -> (r1_tarski(k3_eqrel_1(A,B,C),E) -> r1_tarski(D,E)))) <-> D = k5_eqrel_1(A,B,C)))))))) # label(d3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3845 (all A all B (v3_relat_2(B) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & -v1_xboole_0(A) -> v1_setfam_1(k7_eqrel_1(A,B)) & -v1_xboole_0(k7_eqrel_1(A,B)))) # label(fc4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3846 (all A all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> (k1_xboole_0 = A -> k1_xboole_0 = k7_eqrel_1(A,B)))) # label(t40_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3847 (all A all B all C (m1_relset_1(C,A,A) & m1_relset_1(B,A,A) -> B = k3_eqrel_1(A,B,B))) # label(idempotence_k3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3848 $T # label(d2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3849 (all A (v3_relat_2(k6_partfun1(A)) & v8_relat_2(k6_partfun1(A)) & v1_partfun1(k6_partfun1(A),A,A) & m2_relset_1(k6_partfun1(A),A,A))) # label(t6_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3850 (all A all B all C (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v8_relat_2(C) & v1_partfun1(C,A,A) & m1_relset_1(C,A,A) & v3_relat_2(C) -> k5_eqrel_1(A,C,B) = k5_eqrel_1(A,B,C))) # label(commutativity_k5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3851 (all A all B (v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v1_relat_2(B) -> -((exists C r2_hidden(C,A)) & B = k1_xboole_0))) # label(t14_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3852 (all A all B all C (v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v8_relat_2(C) & v3_relat_2(C) -> (all D (r2_hidden(D,A) -> (r2_hidden(k4_tarski(D,B),C) <-> k6_eqrel_1(A,C,B) = k6_eqrel_1(A,C,D)))))) # label(t44_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3853 (all A all B (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> (all C all D -(r2_hidden(D,A) & -r1_xboole_0(k6_eqrel_1(A,B,C),k6_eqrel_1(A,B,D)) & k6_eqrel_1(A,B,C) != k6_eqrel_1(A,B,D) & r2_hidden(C,A))))) # label(t32_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3854 (all A all B (m2_relset_1(B,A,A) -> k2_eqrel_1(A,k1_eqrel_1(A),B) = B)) # label(t18_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3855 (all A all B all C all D all E (v8_relat_2(E) & m2_relset_1(E,A,A) & v1_partfun1(E,A,A) -> (r2_hidden(k4_tarski(B,C),E) & r2_hidden(k4_tarski(C,D),E) -> r2_hidden(k4_tarski(B,D),E)))) # label(t13_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3856 (all A all B all C (v1_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) -> (r2_hidden(B,A) -> r2_hidden(k4_tarski(B,B),C)))) # label(t11_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3857 (all A all B (v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v3_relat_2(B) -> m1_subset_1(k7_eqrel_1(A,B),k1_zfmisc_1(k1_zfmisc_1(A))))) # label(dt_k7_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3858 $T # label(t1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3859 (all A all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> k4_eqrel_1(A,k6_partfun1(A),B) = k6_partfun1(A))) # label(t17_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3860 (all A all B all C (v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v8_relat_2(C) & v3_relat_2(C) -> (all D (r2_hidden(D,A) -> (k6_eqrel_1(A,C,D) = k6_eqrel_1(A,C,B) <-> r2_hidden(B,k6_eqrel_1(A,C,D))))))) # label(t31_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3861 (all A all B (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & -v1_xboole_0(A) -> -v1_xboole_0(k7_eqrel_1(A,B)))) # label(fc3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3862 $T # label(t10_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3863 (all A (v3_relat_2(k1_eqrel_1(A)) & v8_relat_2(k1_eqrel_1(A)) & m2_relset_1(k1_eqrel_1(A),A,A) & v1_partfun1(k1_eqrel_1(A),A,A))) # label(t7_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3864 (all A all B (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> (all C (v3_relat_2(C) & v8_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) -> (all D (v3_relat_2(D) & v8_relat_2(D) & v1_partfun1(D,A,A) & m2_relset_1(D,A,A) -> (k3_eqrel_1(A,B,C) = D -> (all E -(r2_hidden(E,A) & k6_eqrel_1(A,B,E) != k6_eqrel_1(A,D,E) & k6_eqrel_1(A,C,E) != k6_eqrel_1(A,D,E)))))))))) # label(t37_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3865 (all A k2_zfmisc_1(A,A) = k1_eqrel_1(A)) # label(d1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3866 $T # label(t15_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3867 (all A all B (v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v1_relat_2(B) -> (all C (r2_hidden(C,A) -> r2_hidden(C,k6_eqrel_1(A,B,C)))))) # label(t28_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3868 $T # label(t8_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3869 (all A all B (m2_relset_1(B,A,A) -> (exists C (v1_partfun1(C,A,A) & (all D (m2_relset_1(D,A,A) & v1_partfun1(D,A,A) & v8_relat_2(D) & v3_relat_2(D) -> (r1_tarski(B,D) -> r1_tarski(C,D)))) & r1_tarski(B,C) & m2_relset_1(C,A,A) & v8_relat_2(C) & v3_relat_2(C))))) # label(t20_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3870 (all A all B (m1_eqrel_1(B,A) -> m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))))) # label(dt_m1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3871 (all A all B all C (v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v3_relat_2(C) & m1_relset_1(C,A,A) & v1_partfun1(C,A,A) & v8_relat_2(C) & v8_relat_2(B) & v3_relat_2(B) -> m2_relset_1(k4_eqrel_1(A,B,C),A,A) & v1_partfun1(k4_eqrel_1(A,B,C),A,A) & v8_relat_2(k4_eqrel_1(A,B,C)) & v3_relat_2(k4_eqrel_1(A,B,C)))) # label(dt_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3872 $T # label(t2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3873 (all A all B all C (v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v8_relat_2(C) & v1_partfun1(C,A,A) & m1_relset_1(C,A,A) & v3_relat_2(C) & v3_relat_2(B) -> k5_eqrel_1(A,B,B) = B)) # label(idempotence_k5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3874 (all A m2_relset_1(k1_eqrel_1(A),A,A)) # label(dt_k1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3875 (all A all B all C all D all E (v3_relat_2(E) & v1_partfun1(E,A,A) & m2_relset_1(E,A,A) & v8_relat_2(E) & v1_relat_2(E) -> (r2_hidden(D,k6_eqrel_1(A,E,C)) & r2_hidden(B,k6_eqrel_1(A,E,C)) -> r2_hidden(k4_tarski(B,D),E)))) # label(t30_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3876 (all A all B all C (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v1_partfun1(C,A,A) & m1_relset_1(C,A,A) & v8_relat_2(C) & v3_relat_2(C) -> v1_partfun1(k5_eqrel_1(A,B,C),A,A) & m2_relset_1(k5_eqrel_1(A,B,C),A,A) & v8_relat_2(k5_eqrel_1(A,B,C)) & v3_relat_2(k5_eqrel_1(A,B,C)))) # label(dt_k5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3877 (all A all B (v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v3_relat_2(B) -> k5_eqrel_1(A,B,B) = B)) # label(t22_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.67 3878 (all A all B (m2_relset_1(B,A,A) -> (v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v3_relat_2(B) <-> v3_relat_2(B) & v8_relat_2(B) & k3_relat_1(B) = A & v1_relat_2(B)))) # label(t16_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3879 (all A (-v1_xboole_0(A) -> (all B (m1_eqrel_1(B,A) -> -v1_xboole_0(B))))) # label(cc1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3880 (all A all B all C (v3_relat_2(C) & v1_partfun1(C,B,B) & m2_relset_1(C,B,B) & v8_relat_2(C) -> -((all D (m1_subset_1(D,B) -> k6_eqrel_1(B,C,D) != A)) & r2_hidden(A,k7_eqrel_1(B,C))))) # label(t45_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3881 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k1_xboole_0 = A -> (B = k1_xboole_0 <-> m1_eqrel_1(B,A))) & (A != k1_xboole_0 -> (m1_eqrel_1(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r2_hidden(C,B) -> k1_xboole_0 != C & (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> -(r2_hidden(D,B) & C != D & -r1_xboole_0(C,D))))))) & A = k5_setfam_1(A,B))))) # label(d6_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3882 (all A all B (v3_relat_2(B) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) -> k7_eqrel_1(A,B) = k8_eqrel_1(A,B))) # label(redefinition_k8_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3883 (all A all B (v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> m1_eqrel_1(k8_eqrel_1(A,B),A))) # label(dt_k8_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3884 (all A all B (v3_relat_2(B) & v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) -> (all C (v8_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v3_relat_2(C) -> B = k5_eqrel_1(A,B,k4_eqrel_1(A,B,C)))))) # label(t25_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3885 (all A all B all C all D (v3_relat_2(D) & v1_partfun1(D,A,A) & m2_relset_1(D,A,A) -> (r2_hidden(k4_tarski(B,C),D) -> r2_hidden(k4_tarski(C,B),D)))) # label(t12_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3886 (all A all B all C (v8_relat_2(B) & v1_partfun1(B,A,A) & v8_relat_2(C) & m1_relset_1(C,A,A) & v1_partfun1(C,A,A) & v3_relat_2(C) & m1_relset_1(B,A,A) & v3_relat_2(B) -> B = k4_eqrel_1(A,B,B))) # label(idempotence_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3887 (all A all B all C (v1_relat_2(B) & v3_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) -> m1_subset_1(k6_eqrel_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k6_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3888 $T # label(t5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3889 (all A all B (v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v8_relat_2(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k7_eqrel_1(A,B) = C <-> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(D,C) <-> (exists E (k6_eqrel_1(A,B,E) = D & r2_hidden(E,A))))))))))) # label(d5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3890 (all A all B all C (m1_relset_1(C,A,A) & m1_relset_1(B,A,A) -> k2_eqrel_1(A,B,C) = k2_eqrel_1(A,C,B))) # label(commutativity_k2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3891 (all A all B all C (v3_relat_2(B) & v8_relat_2(B) & v3_relat_2(C) & v8_relat_2(C) & m1_relset_1(C,A,A) & v1_partfun1(C,A,A) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) -> k4_eqrel_1(A,B,C) = k4_eqrel_1(A,C,B))) # label(commutativity_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3892 (all A all B (v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) -> (all C (v3_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v8_relat_2(C) -> -(k1_eqrel_1(A) != B & C != k1_eqrel_1(A) & k1_eqrel_1(A) = k3_eqrel_1(A,B,C)))))) # label(t38_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3893 (all A (v1_relat_1(k1_eqrel_1(A)) & v1_partfun1(k1_eqrel_1(A),A,A) & v1_relat_2(k1_eqrel_1(A)))) # label(fc1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3894 (all A all B all C (m1_relset_1(C,A,A) & m1_relset_1(B,A,A) -> k3_eqrel_1(A,C,B) = k3_eqrel_1(A,B,C))) # label(commutativity_k3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3895 (all A all B (v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v8_relat_2(B) -> ((exists C k6_eqrel_1(A,B,C) = A) -> B = k1_eqrel_1(A)))) # label(t35_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3896 $T # label(t39_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3897 (all A all B (v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) -> (all C (v8_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v3_relat_2(C) -> k5_eqrel_1(A,C,B) = k5_eqrel_1(A,B,C))))) # label(t23_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3898 $T # label(t9_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3899 (all A all B (m1_eqrel_1(B,A) -> v1_setfam_1(B))) # label(cc2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3900 (all A all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) & v1_relat_2(B) -> (all C -(r2_hidden(C,A) & (all D -r2_hidden(C,k6_eqrel_1(A,B,D))))))) # label(t29_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3901 (all A all B (v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v8_relat_2(B) -> (all C (v3_relat_2(C) & v8_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) -> k4_eqrel_1(A,B,k5_eqrel_1(A,B,C)) = B)))) # label(t24_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3902 (all A all B (m1_eqrel_1(B,A) -> (exists C (v1_partfun1(C,A,A) & B = k7_eqrel_1(A,C) & m2_relset_1(C,A,A) & v8_relat_2(C) & v3_relat_2(C))))) # label(t43_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3903 (all A all B all C (m1_relset_1(C,A,A) & m1_relset_1(B,A,A) -> k3_xboole_0(B,C) = k2_eqrel_1(A,B,C))) # label(redefinition_k2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3904 (all A all B all C (m1_relset_1(B,A,A) & m1_relset_1(C,A,A) -> B = k2_eqrel_1(A,B,B))) # label(idempotence_k2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3905 $T # label(t21_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3906 (all A all B all C (v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v8_relat_2(C) & m1_relset_1(C,A,A) & v1_partfun1(C,A,A) & v3_relat_2(C) & v3_relat_2(B) -> k3_xboole_0(B,C) = k4_eqrel_1(A,B,C))) # label(redefinition_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3907 (all A all B all C (m1_relset_1(C,A,A) & m1_relset_1(B,A,A) -> m2_relset_1(k3_eqrel_1(A,B,C),A,A))) # label(dt_k3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3908 (all A all B (r2_hidden(B,A) -> k1_tarski(B) = k6_eqrel_1(A,k6_partfun1(A),B))) # label(t33_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3909 $T # label(t26_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3910 (all A all B (v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) -> m1_eqrel_1(k7_eqrel_1(A,B),A))) # label(t42_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3911 (all A (r3_relat_2(k6_partfun1(A),A) & r8_relat_2(k6_partfun1(A),A) & r1_relat_2(k6_partfun1(A),A))) # label(t4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3912 $T # label(t41_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3913 (all A all B all C all D (v1_partfun1(D,A,A) & m2_relset_1(D,A,A) & v3_relat_2(D) & v1_relat_2(D) -> (r2_hidden(k4_tarski(B,C),D) <-> r2_hidden(B,k6_eqrel_1(A,D,C))))) # label(t27_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3914 (all A all B (v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v1_relat_2(B) -> (all C k10_relset_1(A,A,B,k1_tarski(C)) = k6_eqrel_1(A,B,C)))) # label(d4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3915 (all A all B all C (m1_relset_1(B,A,A) & m1_relset_1(C,A,A) -> m2_relset_1(k2_eqrel_1(A,B,C),A,A))) # label(dt_k2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3916 (all A all B all C (m1_relset_1(C,A,A) & m1_relset_1(B,A,A) -> k3_eqrel_1(A,B,C) = k2_xboole_0(B,C))) # label(redefinition_k3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3917 $T # label(t3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3918 (all A (v3_relat_2(k1_eqrel_1(A)) & v1_partfun1(k1_eqrel_1(A),A,A) & v8_relat_2(k1_eqrel_1(A)) & v1_relat_2(k1_eqrel_1(A)) & v1_relat_1(k1_eqrel_1(A)))) # label(fc2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3919 (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]. 17.28/16.68 3920 (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]. 17.28/16.68 3921 (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]. 17.28/16.68 3922 (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]. 17.28/16.68 3923 (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]. 17.28/16.68 3924 $T # label(t25_funct_5) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3925 (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]. 17.28/16.68 3926 (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]. 17.28/16.68 3927 (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]. 17.28/16.68 3928 (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]. 17.28/16.68 3929 (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]. 17.28/16.68 3930 (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]. 17.28/16.68 3931 (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]. 17.28/16.68 3932 (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]. 17.28/16.68 3933 (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]. 17.28/16.68 3934 (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]. 17.28/16.68 3935 (all A k1_tarski(k1_xboole_0) = k1_funct_2(k1_xboole_0,A)) # label(t64_funct_5) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3936 $T # label(t14_funct_5) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3937 (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]. 17.28/16.68 3938 (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]. 17.28/16.68 3939 (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]. 17.28/16.68 3940 (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]. 17.28/16.68 3941 (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]. 17.28/16.68 3942 (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]. 17.28/16.68 3943 (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]. 17.28/16.68 3944 (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]. 17.28/16.68 3945 (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]. 17.28/16.68 3946 (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]. 17.28/16.68 3947 (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]. 17.28/16.68 3948 (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]. 17.28/16.68 3949 $T # label(t2_funct_5) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3950 (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]. 17.28/16.68 3951 (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]. 17.28/16.68 3952 (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]. 17.28/16.68 3953 (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]. 17.28/16.68 3954 (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]. 17.28/16.68 3955 (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]. 17.28/16.68 3956 (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]. 17.28/16.68 3957 (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]. 17.28/16.68 3958 (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]. 17.28/16.68 3959 (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]. 17.28/16.68 3960 (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]. 17.28/16.68 3961 $T # label(t22_funct_5) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3962 (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]. 17.28/16.68 3963 (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]. 17.28/16.68 3964 (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]. 17.28/16.68 3965 (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]. 17.28/16.68 3966 (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]. 17.28/16.68 3967 (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]. 17.28/16.68 3968 (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]. 17.28/16.68 3969 (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]. 17.28/16.68 3970 (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]. 17.28/16.68 3971 (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]. 17.28/16.68 3972 (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]. 17.28/16.68 3973 (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]. 17.28/16.68 3974 (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]. 17.28/16.68 3975 (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]. 17.28/16.68 3976 (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]. 17.28/16.68 3977 (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]. 17.28/16.68 3978 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (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]. 17.28/16.68 3979 (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]. 17.28/16.68 3980 (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]. 17.28/16.68 3981 $T # label(t3_funct_5) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3982 (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]. 17.28/16.68 3983 (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]. 17.28/16.68 3984 (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]. 17.28/16.68 3985 (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]. 17.28/16.68 3986 (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]. 17.28/16.68 3987 (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]. 17.28/16.68 3988 (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]. 17.28/16.68 3989 (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]. 17.28/16.68 3990 (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]. 17.28/16.68 3991 $T # label(dt_k2_funct_5) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3992 (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]. 17.28/16.68 3993 (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]. 17.28/16.68 3994 (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]. 17.28/16.68 3995 $T # label(dt_k1_funct_5) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3996 $T # label(t23_funct_5) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 3997 (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]. 17.28/16.68 3998 (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]. 17.28/16.68 3999 (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]. 17.28/16.68 4000 $T # label(t24_funct_5) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 4001 (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]. 17.28/16.68 4002 (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]. 17.28/16.68 4003 (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]. 17.28/16.68 4004 (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]. 17.28/16.68 4005 (all A k13_finseq_1(A) = k3_finseq_2(A)) # label(redefinition_k3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 4006 (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]. 17.28/16.68 4007 (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]. 17.28/16.68 4008 (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]. 17.28/16.68 4009 (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]. 17.28/16.68 4010 (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]. 17.28/16.68 4011 (all A exists B (m1_finseq_2(B,A) & -v1_xboole_0(B))) # label(rc1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 4012 (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]. 17.28/16.68 4013 (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]. 17.28/16.68 4014 (all A k2_finseq_2(np__2,A) = k10_finseq_1(A,A)) # label(t75_finseq_2) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 4015 (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]. 17.28/16.68 4016 (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]. 17.28/16.68 4017 (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]. 17.28/16.68 4018 (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]. 17.28/16.68 4019 (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]. 17.28/16.68 4020 (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]. 17.28/16.68 4021 (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]. 17.28/16.68 4022 (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]. 17.28/16.68 4023 (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]. 17.28/16.68 4024 (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]. 17.28/16.68 4025 (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]. 17.28/16.68 4026 (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]. 17.28/16.68 4027 (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]. 17.28/16.68 4028 (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]. 17.28/16.68 4029 (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]. 17.28/16.68 4030 (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]. 17.28/16.68 4031 (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]. 17.28/16.68 4032 (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]. 17.28/16.68 4033 (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]. 17.28/16.68 4034 (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]. 17.28/16.68 4035 (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]. 17.28/16.68 4036 (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]. 17.28/16.68 4037 $T # label(t29_finseq_2) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 4038 (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]. 17.28/16.68 4039 (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]. 17.28/16.68 4040 (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]. 17.28/16.68 4041 $T # label(t12_finseq_2) # label(axiom) # label(non_clause). [assumption]. 17.28/16.68 4042 (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]. 17.28/16.68 4043 (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]. 17.28/16.68 4044 (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]. 17.28/16.68 4045 (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]. 17.28/16.68 4046 (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]. 17.28/16.68 4047 (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]. 17.28/16.68 4048 (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]. 17.28/16.69 4049 (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]. 17.28/16.69 4050 (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]. 17.28/16.69 4051 (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]. 17.28/16.69 4052 (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]. 17.28/16.69 4053 (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]. 17.28/16.69 4054 (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]. 17.28/16.69 4055 (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]. 17.28/16.69 4056 (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]. 17.28/16.69 4057 $T # label(t108_finseq_2) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4058 (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]. 17.28/16.69 4059 (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]. 17.28/16.69 4060 (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]. 17.28/16.69 4061 (all A (v4_ordinal2(A) -> A = k3_finseq_1(k1_finseq_2(A)))) # label(t55_finseq_2) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4062 (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]. 17.28/16.69 4063 (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]. 17.28/16.69 4064 (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]. 17.28/16.69 4065 $T # label(t103_finseq_2) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4066 (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]. 17.28/16.69 4067 (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]. 17.28/16.69 4068 (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]. 17.28/16.69 4069 (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]. 17.28/16.69 4070 (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]. 17.28/16.69 4071 (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]. 17.28/16.69 4072 (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]. 17.28/16.69 4073 (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]. 17.28/16.69 4074 (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]. 17.28/16.69 4075 (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]. 17.28/16.69 4076 (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]. 17.28/16.69 4077 $T # label(dt_m1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4078 $T # label(t106_finseq_2) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4079 (all A exists B m1_finseq_2(B,A)) # label(existence_m1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4080 (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]. 17.28/16.69 4081 (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]. 17.28/16.69 4082 (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]. 17.28/16.69 4083 (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]. 17.28/16.69 4084 (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]. 17.28/16.69 4085 (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]. 17.28/16.69 4086 (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]. 17.28/16.69 4087 (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]. 17.28/16.69 4088 (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]. 17.28/16.69 4089 (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]. 17.28/16.69 4090 $T # label(t7_finseq_2) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4091 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (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]. 17.28/16.69 4092 (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]. 17.28/16.69 4093 (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]. 17.28/16.69 4094 (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]. 17.28/16.69 4095 (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]. 17.28/16.69 4096 (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]. 17.28/16.69 4097 (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]. 17.28/16.69 4098 (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]. 17.28/16.69 4099 (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]. 17.28/16.69 4100 (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]. 17.28/16.69 4101 (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]. 17.28/16.69 4102 (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]. 17.28/16.69 4103 $T # label(t17_finseq_2) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4104 (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]. 17.28/16.69 4105 (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]. 17.28/16.69 4106 (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]. 17.28/16.69 4107 (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]. 17.28/16.69 4108 (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]. 17.28/16.69 4109 (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]. 17.28/16.69 4110 (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]. 17.28/16.69 4111 (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]. 17.28/16.69 4112 (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]. 17.28/16.69 4113 (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]. 17.28/16.69 4114 $T # label(t53_finseq_2) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4115 (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]. 17.28/16.69 4116 (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]. 17.28/16.69 4117 (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]. 17.28/16.69 4118 (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]. 17.28/16.69 4119 (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]. 17.28/16.69 4120 $T # label(t67_finseq_2) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4121 (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]. 17.28/16.69 4122 (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]. 17.28/16.69 4123 (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]. 17.28/16.69 4124 (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]. 17.28/16.69 4125 (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]. 17.28/16.69 4126 (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]. 17.28/16.69 4127 (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]. 17.28/16.69 4128 (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]. 17.28/16.69 4129 (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]. 17.28/16.69 4130 (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]. 17.28/16.69 4131 (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]. 17.28/16.69 4132 (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]. 17.28/16.69 4133 (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]. 17.28/16.69 4134 (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]. 17.28/16.69 4135 (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]. 17.28/16.69 4136 (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]. 17.28/16.69 4137 (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]. 17.28/16.69 4138 (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]. 17.28/16.69 4139 (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]. 17.28/16.69 4140 (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]. 17.28/16.69 4141 (all A k11_finseq_1(A,A,A) = k2_finseq_2(np__3,A)) # label(t76_finseq_2) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4142 (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]. 17.28/16.69 4143 (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]. 17.28/16.69 4144 (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]. 17.28/16.69 4145 (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]. 17.28/16.69 4146 (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]. 17.28/16.69 4147 (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]. 17.28/16.69 4148 (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]. 17.28/16.69 4149 (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]. 17.28/16.69 4150 (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]. 17.28/16.69 4151 (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]. 17.28/16.69 4152 (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]. 17.28/16.69 4153 (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]. 17.28/16.69 4154 (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]. 17.28/16.69 4155 (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]. 17.28/16.69 4156 (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]. 17.28/16.69 4157 (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]. 17.28/16.69 4158 (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]. 17.28/16.69 4159 (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]. 17.28/16.69 4160 (all A k2_finseq_2(np__1,A) = k9_finseq_1(A)) # label(t73_finseq_2) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4161 (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]. 17.28/16.69 4162 (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]. 17.28/16.69 4163 (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]. 17.28/16.69 4164 (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]. 17.28/16.69 4165 (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]. 17.28/16.69 4166 (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]. 17.28/16.69 4167 (all A k2_finseq_2(np__0,A) = k1_xboole_0) # label(t72_finseq_2) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4168 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (-v1_xboole_0(C) -> (all D (m2_finseq_1(D,C) -> (all E (v1_funct_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]. 17.28/16.69 4169 (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]. 17.28/16.69 4170 (all A k1_tarski(A) = k3_classes1(A,k1_xboole_0)) # label(t10_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4171 (all A exists B (v3_ordinal1(B) & r1_tarski(A,k4_classes1(B)))) # label(t69_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4172 (all A all B all C (v3_ordinal1(C) -> (r2_hidden(A,k3_classes1(B,C)) -> r2_hidden(k1_zfmisc_1(A),k3_classes1(B,k1_ordinal1(C)))))) # label(t15_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4173 (all A (v1_ordinal1(A) -> v1_ordinal1(k1_classes1(A)))) # label(t27_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4174 (all A all B (v3_ordinal1(B) -> ((all C (r2_hidden(C,A) -> r2_hidden(k6_classes1(C),B))) <-> r1_ordinal1(k6_classes1(A),B)))) # label(t77_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4175 (all A k1_ordinal1(k6_classes1(A)) = k6_classes1(k1_zfmisc_1(A))) # label(t71_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4176 (all A all B r1_tarski(k5_classes1(k3_xboole_0(A,B)),k3_xboole_0(k5_classes1(A),k5_classes1(B)))) # label(t68_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4177 (all A all B (k1_classes1(A) = B <-> r1_classes1(A,B) & (all C (r1_classes1(A,C) -> r1_tarski(B,C))))) # label(d4_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4178 (all A all B (v3_ordinal1(B) -> k2_xboole_0(k2_xboole_0(a_2_0_classes1(A,B),a_2_1_classes1(A,B)),k3_xboole_0(k1_zfmisc_1(k3_classes1(A,B)),k1_classes1(A))) = k3_classes1(A,k1_ordinal1(B)))) # label(t11_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4179 (all A (v3_ordinal1(A) -> (all B (r2_hidden(B,k4_classes1(A)) -> -r2_tarski(B,k4_classes1(A)) & r2_hidden(k1_card_1(B),k1_card_1(k4_classes1(A))))))) # label(t45_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4180 (all A (v3_ordinal1(A) -> r1_tarski(A,k4_classes1(A)))) # label(t44_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4181 (all A r2_hidden(A,k1_classes1(A))) # label(t5_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4182 (all A all B ((all C (v1_ordinal1(C) & r1_tarski(A,C) -> r1_tarski(B,C))) & r1_tarski(A,B) & v1_ordinal1(B) -> B = k5_classes1(A))) # label(t61_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4183 (all A (r2_hidden(k3_classes1(A,k1_xboole_0),k3_classes1(A,k4_ordinal2)) & k3_classes1(A,k4_ordinal2) != k3_classes1(A,k1_xboole_0))) # label(t26_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4184 (all A all B (r2_hidden(A,k1_classes1(B)) -> r2_hidden(k1_card_1(A),k1_card_1(k1_classes1(B))))) # label(t28_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4185 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r1_tarski(k4_classes1(A),k4_classes1(B)) <-> r1_ordinal1(A,B)))))) # label(t43_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4186 (all A all B all C (v3_ordinal1(C) -> (r2_hidden(A,k3_classes1(B,k1_ordinal1(C))) <-> -((all D -(r2_hidden(D,k3_classes1(B,C)) & (A = k1_zfmisc_1(D) | r1_tarski(A,D)))) & -(r2_hidden(A,k1_classes1(B)) & r1_tarski(A,k3_classes1(B,C))))))) # label(t13_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4187 (all A -v1_xboole_0(k1_classes1(A))) # label(fc1_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4188 (all A all B (v3_ordinal1(B) -> (k3_classes1(A,B) = k3_classes1(A,k1_ordinal1(B)) -> k1_classes1(A) = k3_classes1(A,B)))) # label(t21_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4189 (all A all B ((all C (r2_hidden(C,B) <-> (exists D (v1_relat_1(D) & v1_funct_1(D) & (exists E (r2_hidden(C,k1_funct_1(D,E)) & k5_numbers = k1_relat_1(D) & A = k1_funct_1(D,np__0) & (all F (m2_subset_1(F,k1_numbers,k5_numbers) -> k3_tarski(k1_funct_1(D,F)) = k1_funct_1(D,k1_nat_1(F,np__1)))) & m2_subset_1(E,k1_numbers,k5_numbers))))))) <-> k5_classes1(A) = B)) # label(d7_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4190 (all A (v1_ordinal1(A) -> r1_tarski(k3_tarski(A),A))) # label(t54_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4191 (all A -(v1_ordinal1(A) & (all B (v3_ordinal1(B) -> -r1_tarski(k1_classes1(A),k4_classes1(B)))))) # label(t53_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4192 $T # label(t1_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4193 (all A (v3_ordinal1(A) -> k6_classes1(A) = A)) # label(t81_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4194 (all A all B all C all D (v3_ordinal1(D) -> (r2_hidden(B,k3_classes1(C,D)) & r1_tarski(A,B) -> r2_hidden(A,k3_classes1(C,k1_ordinal1(D)))))) # label(t14_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4195 (all A all B (r2_hidden(A,k1_classes1(B)) -> r2_hidden(k1_zfmisc_1(A),k1_classes1(B)))) # label(t7_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4196 $T # label(dt_k4_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4197 (all A (v3_ordinal1(A) -> r1_tarski(k3_tarski(k4_classes1(A)),k4_classes1(A)))) # label(t40_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4198 (all A all B all C (v3_ordinal1(C) -> (v4_ordinal1(C) -> C = k1_xboole_0 | (r2_hidden(B,k3_classes1(A,C)) <-> (exists D (v3_ordinal1(D) & r2_hidden(D,C) & r2_hidden(B,k3_classes1(A,D)))))))) # label(t16_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4199 (all A (v1_ordinal1(A) -> (all B (v3_ordinal1(B) -> (B != k1_xboole_0 -> v1_ordinal1(k3_classes1(A,B))))))) # label(t25_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.69 4200 (all A v1_ordinal1(k5_classes1(A))) # label(t58_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4201 (all A all B (v3_ordinal1(B) -> (r1_tarski(A,k4_classes1(B)) <-> r1_ordinal1(k6_classes1(A),B)))) # label(t73_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4202 (all A r1_tarski(A,k5_classes1(A))) # label(t59_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4203 (all A all B (v3_ordinal1(B) -> (r2_hidden(k1_zfmisc_1(A),k4_classes1(k1_ordinal1(B))) <-> r2_hidden(A,k4_classes1(B))))) # label(t48_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4204 (all A all B all C all D (v1_funct_1(C) & v5_ordinal1(C) & v3_ordinal1(D) & v1_relat_1(C) -> (r2_hidden(A,a_3_0_classes1(B,C,D)) <-> (exists E (m1_subset_1(E,k1_classes1(B)) & (exists F (m1_subset_1(F,k1_classes1(B)) & r2_hidden(F,k1_funct_1(C,D)) & r1_tarski(E,F))) & A = E))))) # label(fraenkel_a_3_0_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4205 (all A (v3_ordinal1(A) -> k6_classes1(k4_classes1(A)) = A)) # label(t72_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4206 (all A all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal1(B,C) -> r1_tarski(k3_classes1(A,B),k3_classes1(A,C))))))) # label(t19_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4207 (all A all B (r1_tarski(A,B) -> r1_tarski(k5_classes1(A),k5_classes1(B)))) # label(t65_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4208 (all A all B all C (v3_ordinal1(C) -> (r2_hidden(A,a_2_2_classes1(B,C)) <-> (exists D (m1_subset_1(D,k1_classes1(B)) & A = D & (exists E (v3_ordinal1(E) & r2_hidden(E,C) & r2_hidden(D,k3_classes1(B,E))))))))) # label(fraenkel_a_2_2_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4209 (all A all B (v3_ordinal1(B) -> (r2_hidden(A,k4_classes1(B)) <-> r2_hidden(k6_classes1(A),B)))) # label(t74_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4210 (all A all B (v3_ordinal1(B) -> (v4_ordinal1(B) -> B = k1_xboole_0 | a_2_2_classes1(A,B) = k3_classes1(A,B)))) # label(t12_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4211 (all A all B -(-r2_hidden(A,k1_classes1(B)) & -r2_tarski(A,k1_classes1(B)) & r1_tarski(A,k1_classes1(B)))) # label(t8_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4212 $T # label(dt_k1_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4213 (all A k5_classes1(A) = k5_classes1(k5_classes1(A))) # label(t66_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4214 (all A (v3_ordinal1(A) -> (v4_ordinal1(A) -> (all B (r2_hidden(B,k4_classes1(A)) <-> (exists C (r2_hidden(B,k4_classes1(C)) & r2_hidden(C,A) & v3_ordinal1(C))))) | A = k1_xboole_0))) # label(t35_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4215 (all A all B (v1_ordinal1(B) & r1_tarski(A,B) -> r1_tarski(k5_classes1(A),B))) # label(t60_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4216 (all A (v3_ordinal1(A) -> r1_tarski(k4_classes1(A),k4_classes1(k1_ordinal1(A))))) # label(t39_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4217 (all A (v3_ordinal1(A) -> (all B ((exists C (v5_ordinal1(C) & B = k1_ordinal2(C) & k1_ordinal1(A) = k1_relat_1(C) & k1_funct_1(C,k1_xboole_0) = k1_xboole_0 & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = k1_zfmisc_1(k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> D = k1_xboole_0 | k3_tarski(k2_relat_1(k2_ordinal1(C,D))) = k1_funct_1(C,D)))) & v1_funct_1(C) & v1_relat_1(C))) <-> B = k4_classes1(A))))) # label(d6_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4218 (all A exists B (v3_ordinal1(B) & k1_classes1(A) = k3_classes1(A,B) & (all C (v3_ordinal1(C) -> -(k1_classes1(A) = k3_classes1(A,C) & r2_hidden(C,B)))))) # label(t23_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4219 (all A all B k2_xboole_0(k5_classes1(A),k5_classes1(B)) = k5_classes1(k2_xboole_0(A,B))) # label(t67_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4220 (all A (v2_classes1(A) <-> v1_classes1(A) & (all B (r2_hidden(B,A) -> r2_hidden(k1_zfmisc_1(B),A))) & (all B -(-r2_hidden(B,A) & -r2_tarski(B,A) & r1_tarski(B,A))))) # label(d2_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4221 (all A all B (v3_ordinal1(B) -> (r1_tarski(A,k4_classes1(B)) <-> r1_tarski(k1_zfmisc_1(A),k4_classes1(k1_ordinal1(B)))))) # label(t46_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4222 (all A all B (v3_ordinal1(B) -> (r1_ordinal1(B,k6_classes1(A)) <-> (all C (v3_ordinal1(C) -> -((all D -(r1_ordinal1(C,k6_classes1(D)) & r2_hidden(D,A))) & r2_hidden(C,B))))))) # label(t78_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4223 (all A all B (v1_ordinal1(A) & v1_ordinal1(B) -> v1_ordinal1(k3_xboole_0(A,B)))) # label(t56_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4224 (all A all B all C (v3_ordinal1(C) -> (r2_hidden(B,k4_classes1(C)) & r1_tarski(A,B) -> r2_hidden(A,k4_classes1(C))))) # label(t47_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4225 (all A (k1_xboole_0 = k6_classes1(A) <-> A = k1_xboole_0)) # label(t79_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4226 (all A all B (r2_hidden(k1_card_1(A),k1_card_1(k1_classes1(B))) & r1_tarski(A,k1_classes1(B)) -> r2_hidden(A,k1_classes1(B)))) # label(t9_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4227 (all A all B (v3_ordinal1(B) -> -((all C -(k6_classes1(C) = B & r2_hidden(C,A))) & k1_ordinal1(B) = k6_classes1(A)))) # label(t80_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4228 (all A all B (v3_ordinal1(B) -> (r2_hidden(A,k4_classes1(B)) -> r1_tarski(A,k4_classes1(B))))) # label(t38_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4229 $T # label(t70_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4230 (all A (v3_ordinal1(A) -> k1_zfmisc_1(k4_classes1(A)) = k4_classes1(k1_ordinal1(A)))) # label(t34_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4231 (all A (v1_classes1(A) <-> (all B all C (r2_hidden(B,A) & r1_tarski(C,B) -> r2_hidden(C,A))))) # label(d1_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4232 (all A all B (v3_ordinal1(B) -> (r2_hidden(A,k4_classes1(B)) <-> r2_hidden(k1_tarski(A),k4_classes1(k1_ordinal1(B)))))) # label(t49_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4233 (all A all B (v3_ordinal1(B) -> r1_tarski(k3_classes1(A,B),k3_classes1(A,k1_ordinal1(B))))) # label(t18_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4234 (all A (v3_ordinal1(A) -> v1_ordinal1(k4_classes1(A)))) # label(t37_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4235 (all A all B (v3_ordinal1(B) -> ((all C (v3_ordinal1(C) -> (r1_tarski(A,k4_classes1(C)) -> r1_ordinal1(B,C)))) & r1_tarski(A,k4_classes1(B)) <-> k6_classes1(A) = B))) # label(d8_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4236 (all A all B -(r2_hidden(A,k1_classes1(B)) & (all C (v3_ordinal1(C) -> -(-r2_hidden(A,k3_classes1(B,C)) & r2_hidden(A,k3_classes1(B,k1_ordinal1(C)))))) & B != A)) # label(t24_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4237 (all A all B (v3_ordinal1(B) -> (r1_tarski(A,k4_classes1(B)) <-> r2_hidden(A,k4_classes1(k1_ordinal1(B)))))) # label(t36_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4238 (all A all B all C all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(A,k3_classes1(B,D)) -> r2_hidden(C,k3_classes1(B,D)) | -r1_tarski(C,A) & C != k1_zfmisc_1(A) | D = k1_xboole_0))) # label(t17_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4239 (all A all B (v3_ordinal1(B) -> k2_classes1(A,B) = k3_classes1(A,B))) # label(redefinition_k3_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4240 (all A (v4_ordinal1(k6_classes1(k1_classes1(A))) & k6_classes1(k1_classes1(A)) != k1_xboole_0)) # label(t82_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4241 (all A v3_ordinal1(k6_classes1(A))) # label(dt_k6_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4242 (all A all B all C all D (v1_relat_1(C) & v5_ordinal1(C) & v3_ordinal1(D) & v1_funct_1(C) -> (r2_hidden(A,a_3_1_classes1(B,C,D)) <-> (exists E (m1_subset_1(E,k1_classes1(B)) & A = k1_zfmisc_1(E) & r2_hidden(E,k1_funct_1(C,D))))))) # label(fraenkel_a_3_1_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4243 (all A all B (v3_ordinal1(B) -> (r2_hidden(A,k4_classes1(B)) -> r2_hidden(k3_tarski(A),k4_classes1(B))))) # label(t41_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4244 (all A (v1_classes1(A) & (all B (r2_hidden(k1_card_1(B),k1_card_1(A)) & r1_tarski(B,A) -> r2_hidden(B,A))) & (all B (r2_hidden(B,A) -> r2_hidden(k1_zfmisc_1(B),A))) <-> v2_classes1(A))) # label(t2_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4245 (all A all B (v1_ordinal1(A) & v1_ordinal1(B) -> v1_ordinal1(k2_xboole_0(A,B)))) # label(t55_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4246 (all A all B all C (v3_ordinal1(C) -> (r2_hidden(B,k4_classes1(C)) & r2_hidden(A,k4_classes1(C)) <-> r2_hidden(k4_tarski(A,B),k4_classes1(k1_ordinal1(k1_ordinal1(C))))))) # label(t51_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4247 (all A all B (r2_hidden(A,B) -> r2_hidden(k6_classes1(A),k6_classes1(B)))) # label(t76_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4248 (all A all B all C (v3_ordinal1(C) -> ((exists D (D = A & (exists E (m1_subset_1(E,k1_classes1(B)) & r2_hidden(E,k3_classes1(B,C)) & r1_tarski(D,E))) & m1_subset_1(D,k1_classes1(B)))) <-> r2_hidden(A,a_2_0_classes1(B,C))))) # label(fraenkel_a_2_0_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4249 (all A all B -(r2_hidden(A,k1_classes1(B)) & r2_tarski(A,k1_classes1(B)))) # label(t29_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4250 $T # label(t4_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4251 (all A exists B (k1_classes1(A) = k3_classes1(A,B) & v3_ordinal1(B))) # label(t22_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4252 (all A all B all C (r2_hidden(A,k1_classes1(B)) & r1_tarski(C,A) -> r2_hidden(C,k1_classes1(B)))) # label(t6_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4253 $T # label(dt_k2_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4254 (all A all B all C (r1_tarski(C,k1_classes1(B)) & r1_tarski(A,k1_classes1(B)) -> r1_tarski(k2_zfmisc_1(A,C),k1_classes1(B)))) # label(t32_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4255 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(A,B) <-> r2_hidden(k4_classes1(A),k4_classes1(B))))))) # label(t42_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4256 (all A (v1_ordinal1(A) -> A = k5_classes1(A))) # label(t62_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4257 (all A all B (r1_classes1(A,B) <-> v2_classes1(B) & r2_hidden(A,B))) # label(d3_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4258 (all A all B all C (v3_ordinal1(C) -> (r2_hidden(A,a_2_1_classes1(B,C)) <-> (exists D (r2_hidden(D,k3_classes1(B,C)) & k1_zfmisc_1(D) = A & m1_subset_1(D,k1_classes1(B))))))) # label(fraenkel_a_2_1_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4259 $T # label(dt_k5_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4260 (all A all B all C (r2_hidden(C,k1_classes1(A)) & r2_hidden(B,k1_classes1(A)) -> r2_hidden(k2_tarski(B,C),k1_classes1(A)) & r2_hidden(k1_tarski(B),k1_classes1(A)))) # label(t30_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4261 $T # label(t57_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4262 (all A (v3_ordinal1(A) -> A = k5_classes1(A))) # label(t64_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4263 (all A all B (v3_ordinal1(B) -> (k3_xboole_0(k4_classes1(B),k1_classes1(A)) = k3_xboole_0(k4_classes1(k1_ordinal1(B)),k1_classes1(A)) & v1_ordinal1(A) -> r1_tarski(k1_classes1(A),k4_classes1(B))))) # label(t52_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4264 (all A all B (v3_ordinal1(B) -> m1_subset_1(k3_classes1(A,B),k1_zfmisc_1(k1_classes1(A))))) # label(dt_k3_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4265 (all A all B (r1_tarski(A,B) -> r1_ordinal1(k6_classes1(A),k6_classes1(B)))) # label(t75_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4266 (all A all B (v3_ordinal1(B) -> (all C ((exists D (v1_relat_1(D) & v5_ordinal1(D) & k1_ordinal2(D) = C & (all E (v3_ordinal1(E) -> (r2_hidden(E,k1_ordinal1(B)) & v4_ordinal1(E) -> k1_xboole_0 = E | k3_xboole_0(k3_tarski(k2_relat_1(k2_ordinal1(D,E))),k1_classes1(A)) = k1_funct_1(D,E)))) & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(B)) -> k2_xboole_0(k2_xboole_0(a_3_0_classes1(A,D,E),a_3_1_classes1(A,D,E)),k3_xboole_0(k1_zfmisc_1(k1_funct_1(D,E)),k1_classes1(A))) = k1_funct_1(D,k1_ordinal1(E))))) & k1_funct_1(D,k1_xboole_0) = k1_tarski(A) & k1_ordinal1(B) = k1_relat_1(D) & v1_funct_1(D))) <-> C = k2_classes1(A,B))))) # label(d5_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4267 $T # label(t3_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4268 (all A all B all C (v3_ordinal1(C) -> (r2_hidden(B,k4_classes1(C)) & r2_hidden(A,k4_classes1(C)) <-> r2_hidden(k2_tarski(A,B),k4_classes1(k1_ordinal1(C)))))) # label(t50_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4269 (all A all B all C (r2_hidden(C,k1_classes1(A)) & r2_hidden(B,k1_classes1(A)) -> r2_hidden(k4_tarski(B,C),k1_classes1(A)))) # label(t31_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4270 (all A exists B (k3_classes1(A,k1_ordinal1(B)) = k3_classes1(A,B) & v3_ordinal1(B))) # label(t20_classes1) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4271 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k2_card_3(A)) & v1_funct_1(k2_card_3(A)))) # label(dt_k2_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4272 (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)) -> r1_xboole_0(k1_funct_1(k2_card_3(C),A),k1_funct_1(k2_card_3(C),B)) | B = A))) # label(t13_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4273 $T # label(t23_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4274 (all A all B k1_card_3(k2_funcop_1(A,B)) = k2_funcop_1(A,k1_card_1(B))) # label(t10_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4275 f1_s3_card_3 != k1_xboole_0 & (all A all B (p1_s3_card_3(A,B) | p1_s3_card_3(B,A))) & (all A all B all C (p1_s3_card_3(A,B) & p1_s3_card_3(B,C) -> p1_s3_card_3(A,C))) -> (exists A ((all B (r2_hidden(B,f1_s3_card_3) -> p1_s3_card_3(A,B))) & r2_hidden(A,f1_s3_card_3))) # label(s3_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4276 (all A all B k2_funcop_1(k1_tarski(A),k2_zfmisc_1(B,k1_tarski(A))) = k2_card_3(k2_funcop_1(k1_tarski(A),B))) # label(t12_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4277 (all A all B k2_zfmisc_1(B,A) = k3_card_3(k2_card_3(k2_funcop_1(A,B)))) # label(t36_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4278 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> k1_tarski(k1_funct_1(B,A)) = k5_card_3(A,k1_tarski(B)))) # label(t25_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4279 (all A (v1_card_1(A) -> (all B (v6_ordinal1(B) & (all C (r2_hidden(C,B) -> r2_hidden(k1_card_1(C),A))) -> r1_tarski(k1_card_1(k3_tarski(B)),A))))) # label(t62_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4280 (all A (v1_funct_1(A) & v1_card_3(A) & v1_relat_1(A) -> v1_card_1(k6_card_3(A)))) # label(dt_k6_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4281 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(k1_card_1(A),k1_card_1(B)) -> r2_hidden(A,B)))))) # label(t59_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4282 $T # label(t7_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4283 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,B) -> r1_tarski(k3_card_3(A),k3_card_3(B))))))) # label(t35_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4284 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_fraenkel(k4_card_3(A)))) # label(fc3_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4285 (all A k5_card_3(A,k1_xboole_0) = k1_xboole_0) # label(t24_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4286 (all A (v1_finset_1(A) -> r2_hidden(k1_card_1(A),k1_card_1(k5_ordinal2)))) # label(t58_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4287 (all A all B all C r1_tarski(k5_xboole_0(k5_card_3(B,A),k5_card_3(B,C)),k5_card_3(B,k5_xboole_0(A,C)))) # label(t30_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4288 $T # label(dt_k3_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4289 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> k7_card_3(k2_funcop_1(A,B)) = k3_card_2(B,A))))) # label(t53_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4290 (all A all B k1_funct_2(A,B) = k4_card_3(k2_funcop_1(A,B))) # label(t20_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4291 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) -> k1_card_3(A) = A)) # label(t8_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4292 (exists A (v1_card_3(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc1_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4293 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) -> k1_card_1(k3_card_3(k2_card_3(A))) = k6_card_3(A))) # label(d7_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4294 $T # label(t5_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4295 (all A (v1_card_1(A) -> (all B k7_card_3(k2_funcop_1(k1_tarski(B),A)) = A))) # label(t51_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4296 (all A (v1_card_1(A) -> (all B k6_card_3(k2_funcop_1(k1_tarski(B),A)) = A))) # label(t50_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4297 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> -((all C all D A != k4_tarski(C,D)) & r2_hidden(A,k3_card_3(k2_card_3(B)))))) # label(t32_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4298 (all A all B r1_tarski(k3_card_3(k2_funcop_1(A,B)),B)) # label(t15_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4299 (all A (v1_card_3(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_card_3(B) -> (r1_tarski(A,B) -> r1_tarski(k7_card_3(A),k7_card_3(B)) | r2_hidden(np__0,k2_relat_1(B))))))) # label(t47_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4300 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> v1_finset_1(k4_classes1(A)))) # label(t57_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4301 f1_s2_card_3 != k1_xboole_0 & (all A all B all C (p1_s2_card_3(A,B) & p1_s2_card_3(B,C) -> p1_s2_card_3(A,C))) & (all A all B (p1_s2_card_3(A,B) & p1_s2_card_3(B,A) -> A = B)) -> (exists A ((all B -(r2_hidden(B,f1_s2_card_3) & A != B & p1_s2_card_3(B,A))) & r2_hidden(A,f1_s2_card_3))) # label(s2_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4302 (all A (v3_ordinal1(A) -> (all B (v1_card_1(B) -> (r2_hidden(k1_card_1(A),B) -> r2_hidden(A,B)))))) # label(t60_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4303 $T # label(dt_k4_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4304 (all A (v1_funct_1(A) & v1_card_3(A) & v1_relat_1(A) -> (all B (v1_card_3(B) & v1_funct_1(B) & v1_relat_1(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> r2_hidden(k1_funct_1(A,C),k1_funct_1(B,C)))) & k1_relat_1(A) = k1_relat_1(B) -> r2_hidden(k6_card_3(A),k7_card_3(B))))))) # label(t56_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4305 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_card_3(B) & v1_funct_1(B) & v1_relat_1(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> k1_card_1(k1_funct_1(A,C)) = k1_funct_1(B,C))) & k1_relat_1(A) = k1_relat_1(B) <-> B = k1_card_3(A)))))) # label(d2_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4306 (exists A (v1_relat_1(A) & f1_s4_card_3 = k1_relat_1(A) & (all B (r2_hidden(B,f1_s4_card_3) -> (all C (r2_hidden(C,k1_funct_1(A,B)) <-> p1_s4_card_3(B,C) & r2_hidden(C,f2_s4_card_3(B)))))) & v1_funct_1(A))) # label(s4_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4307 $T # label(t1_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4308 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) -> v1_card_1(k7_card_3(A)))) # label(dt_k7_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4309 (all A all B (A != k1_xboole_0 -> B = k3_card_3(k2_funcop_1(A,B)))) # label(t16_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4310 (all A (v1_card_3(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (r2_hidden(B,k1_relat_1(A)) -> k1_funct_1(A,B) = k1_card_1(k1_funct_1(k2_card_3(A),B)))))) # label(t40_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4311 (all A (v1_funct_1(A) & v1_card_3(A) & v1_relat_1(A) -> r1_tarski(k1_card_1(k3_card_3(A)),k6_card_3(A)))) # label(t55_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4312 (all A all B r1_tarski(k1_card_1(k5_card_3(B,A)),k1_card_1(A))) # label(t31_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4313 $T # label(t4_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4314 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> k4_card_3(B) = k1_xboole_0 | k1_funct_1(B,A) = k5_card_3(A,k4_card_3(B))))) # label(t22_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4315 (all A all B k3_card_3(k2_funcop_1(k1_tarski(A),B)) = B) # label(t17_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4316 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(B) = k1_relat_1(A) & (all C (r2_hidden(C,k1_relat_1(A)) -> r1_tarski(k1_funct_1(A,C),k1_funct_1(B,C)))) -> r1_tarski(k4_card_3(A),k4_card_3(B))))))) # label(t38_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4317 (all A (v1_relat_1(A) & v1_funct_1(A) -> k3_card_3(A) = k3_tarski(k2_relat_1(A)))) # label(d4_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4318 (all A -((all B -(r1_tarski(B,A) & k3_tarski(A) = k3_tarski(B) & (all C -(r1_tarski(C,B) & k1_xboole_0 != C & (all D -((all E (r2_hidden(E,C) -> r1_tarski(D,E))) & r2_hidden(D,C))))))) & v6_ordinal1(A))) # label(t61_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4319 (all A (v1_funct_1(A) & v1_relat_1(A) -> (k4_card_3(A) = k1_xboole_0 <-> r2_hidden(k1_xboole_0,k2_relat_1(A))))) # label(t37_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4320 (all A all B all C r1_tarski(k5_card_3(C,k3_xboole_0(A,B)),k3_xboole_0(k5_card_3(C,A),k5_card_3(C,B)))) # label(t28_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4321 (all A all B all C (v1_setfam_1(B) & m1_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> v1_fraenkel(k4_card_3(C)) & -v1_xboole_0(k4_card_3(C)))) # label(fc4_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4322 (all A (v1_funct_1(A) & v1_card_3(A) & v1_relat_1(A) -> (k7_card_3(A) = np__0 <-> r2_hidden(k1_xboole_0,k2_relat_1(A))))) # label(t44_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4323 (all A (v1_card_1(A) -> k7_card_3(k2_funcop_1(k1_xboole_0,A)) = np__1)) # label(t49_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4324 (all A all B (v1_card_3(A) & v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k7_relat_1(A,B)) & v1_card_3(k7_relat_1(A,B)) & v1_relat_1(k7_relat_1(A,B)))) # label(fc1_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4325 (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_relat_1(A) & (all C (r2_hidden(C,k1_relat_1(A)) -> k2_zfmisc_1(k1_funct_1(A,C),k1_tarski(C)) = k1_funct_1(B,C))) <-> B = k2_card_3(A)))))) # label(d3_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4326 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,B) -> r1_tarski(k2_card_3(A),k2_card_3(B))))))) # label(t34_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4327 $T # label(t21_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4328 (all A (v1_relat_1(A) & v1_funct_1(A) -> r1_tarski(k1_card_1(k3_card_3(A)),k6_card_3(k1_card_3(A))))) # label(t54_card_3) # label(axiom) # label(non_clause). [assumption]. 17.28/16.70 4329 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B ((all C (r2_hidden(C,B) <-> (exists D (k1_relat_1(A) = k1_relat_1(D) & (all E (r2_hidden(E,k1_relat_1(A)) -> r2_hidden(k1_funct_1(D,E),k1_funct_1(A,E)))) & D = C & v1_funct_1(D) & v1_relat_1(D))))) <-> B = k4_card_3(A))))) # label(d5_card_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4330 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k3_card_3(k2_card_3(B))) <-> A = k4_tarski(k1_mcart_1(A),k2_mcart_1(A)) & r2_hidden(k1_mcart_1(A),k1_funct_1(B,k2_mcart_1(A))) & r2_hidden(k2_mcart_1(A),k1_relat_1(B))))) # label(t33_card_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4331 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) -> (all B (v1_funct_1(B) & v1_card_3(B) & v1_relat_1(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> r1_tarski(k1_funct_1(A,C),k1_funct_1(B,C)))) & k1_relat_1(B) = k1_relat_1(A) -> r1_tarski(k7_card_3(A),k7_card_3(B))))))) # label(t45_card_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4332 $T # label(t41_card_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4333 (all A (v1_relat_1(A) & v1_card_3(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_card_3(B) -> (r1_tarski(A,B) -> r1_tarski(k6_card_3(A),k6_card_3(B))))))) # label(t46_card_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4334 (all A (v1_card_1(A) -> k6_card_3(k2_funcop_1(k1_xboole_0,A)) = np__0)) # label(t48_card_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4335 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B (r2_hidden(B,k1_relat_1(A)) -> v1_card_1(k1_funct_1(A,B)))) <-> v1_card_3(A)))) # label(d1_card_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4336 $T # label(t2_card_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4337 (all A (v1_funct_1(A) & v2_relat_1(A) & v1_relat_1(A) -> -v1_xboole_0(k4_card_3(A)) & v1_fraenkel(k4_card_3(A)))) # label(fc5_card_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4338 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> k5_card_3(A,k2_tarski(B,C)) = k2_tarski(k1_funct_1(B,A),k1_funct_1(C,A)))))) # label(t26_card_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4339 (all A (v1_relat_1(A) & v1_card_3(A) & v1_funct_1(A) -> (all B (r2_hidden(B,k1_relat_1(A)) -> k1_funct_1(A,B) = k1_card_1(k1_funct_1(A,B)))))) # label(t39_card_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4340 (all A all B all C r1_tarski(k4_xboole_0(k5_card_3(B,A),k5_card_3(B,C)),k5_card_3(B,k4_xboole_0(A,C)))) # label(t29_card_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4341 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k1_card_3(A)) & v1_funct_1(k1_card_3(A)) & v1_card_3(k1_card_3(A)))) # label(dt_k1_card_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4342 (all A all B (v1_card_1(B) -> v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v1_card_3(k2_funcop_1(A,B)) & v1_ordinal2(k2_funcop_1(A,B)))) # label(fc2_card_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4343 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> k2_card_2(A,B) = k6_card_3(k2_funcop_1(A,B)))))) # label(t52_card_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4344 (exists A (v1_funct_1(A) & (all B (r2_hidden(B,f1_s1_card_3) -> k1_funct_1(A,B) = f2_s1_card_3(B))) & f1_s1_card_3 = k1_relat_1(A) & v1_card_3(A) & v1_relat_1(A))) # label(s1_card_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4345 (all A all B all C ((all D ((exists E (v1_relat_1(E) & D = k1_funct_1(E,A) & r2_hidden(E,B) & v1_funct_1(E))) <-> r2_hidden(D,C))) <-> C = k5_card_3(A,B))) # label(d6_card_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4346 $T # label(t42_card_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4347 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_card_3(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> r1_tarski(k1_funct_1(A,C),k1_funct_1(B,C)))) & k1_relat_1(B) = k1_relat_1(A) -> r1_tarski(k6_card_3(A),k6_card_3(B))))))) # label(t43_card_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4348 $T # label(dt_k5_card_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4349 $T # label(t6_card_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4350 (all A all B all C k5_card_3(C,k2_xboole_0(A,B)) = k2_xboole_0(k5_card_3(C,A),k5_card_3(C,B))) # label(t27_card_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4351 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) -> k7_card_3(A) = k1_card_1(k4_card_3(A)))) # label(d8_card_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4352 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(A,k4_card_3(B)) <-> (all C (r2_hidden(C,k1_relat_1(B)) -> r2_hidden(k1_funct_1(A,C),k1_funct_1(B,C)))) & k1_relat_1(A) = k1_relat_1(B)))))) # label(t18_card_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4353 (all A all B (r2_hidden(B,A) & v2_classes1(A) -> r1_tarski(k1_classes1(B),A))) # label(t5_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4354 (all A (v2_classes1(A) -> v1_classes1(A))) # label(cc1_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4355 (all A (v3_ordinal1(A) -> (all B (k16_classes2(A) = B <-> (exists C (v1_relat_1(C) & v5_ordinal1(C) & k1_ordinal1(A) = k1_relat_1(C) & k13_classes2 = k1_funct_1(C,k1_xboole_0) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_classes1(k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> D = k1_xboole_0 | k1_funct_1(C,D) = k15_classes2(k3_card_3(k2_ordinal1(C,D)))))) & k1_ordinal2(C) = B & v1_funct_1(C))))))) # label(d5_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4356 (all A (v3_ordinal1(A) -> v1_ordinal1(k1_classes1(A)) & v2_classes1(k1_classes1(A)) & v1_classes2(k1_classes1(A)) & v1_classes1(k1_classes1(A)) & -v1_xboole_0(k1_classes1(A)))) # label(fc4_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4357 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (v1_classes2(B) & -v1_xboole_0(B) -> (all C (v1_classes2(C) & -v1_xboole_0(C) -> (r2_hidden(A,B) & r2_hidden(B,C) -> r2_hidden(A,C)))))))) # label(t59_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4358 (all A (v1_ordinal1(A) & v2_classes1(A) -> v1_classes2(A))) # label(cc3_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4359 $T # label(t49_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4360 (all A (-v1_xboole_0(A) & v1_classes2(A) -> r1_tarski(k16_classes2(k1_xboole_0),A) & r1_tarski(k1_classes1(k1_xboole_0),A) & r1_tarski(k13_classes2,A))) # label(t79_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4361 (all A (v2_classes1(A) -> k1_card_1(A) = k2_ordinal2(A))) # label(t10_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4362 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (-v1_xboole_0(B) & v1_classes2(B) -> r3_xboole_0(A,B))))) # label(t58_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4363 (all A all B all C (v1_classes2(C) & -v1_xboole_0(C) -> (r2_hidden(B,C) & r2_hidden(A,C) -> r2_hidden(k2_tarski(A,B),C) & r2_hidden(k4_tarski(A,B),C)))) # label(t64_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4364 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) & v1_classes2(A) -> k2_classes2(A,B) = k1_zfmisc_1(B))) # label(redefinition_k2_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4365 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (exists B (m1_subset_1(B,A) & -v1_xboole_0(B))))) # label(rc2_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4366 (all A all B all C (v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k2_xboole_0(B,C) = k7_classes2(A,B,C))) # label(redefinition_k7_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4367 $T # label(t48_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4368 (all A (v1_classes2(A) & -v1_xboole_0(A) -> v4_ordinal1(k2_ordinal2(A)) & k1_xboole_0 != k2_ordinal2(A))) # label(t55_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4369 (all A all B all C (v1_classes2(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k4_tarski(B,C) = k6_classes2(A,B,C))) # label(redefinition_k6_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4370 (all A all B all C (v2_classes1(A) & r2_hidden(B,A) & r2_hidden(C,A) -> r2_hidden(k1_tarski(B),A) & r2_hidden(k2_tarski(B,C),A))) # label(t3_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4371 (all A (v1_ordinal1(A) -> -v1_xboole_0(k1_classes1(A)) & v1_classes2(k1_classes1(A)) & v2_classes1(k1_classes1(A)) & v1_classes1(k1_classes1(A)) & v1_ordinal1(k1_classes1(A)))) # label(fc6_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4372 (all A (v3_ordinal1(A) -> (all B (r2_hidden(A,k2_ordinal2(k1_classes1(B))) -> r2_hidden(k4_classes1(A),k1_classes1(B)) & r2_hidden(k1_card_1(k4_classes1(A)),k1_card_1(k1_classes1(B))))))) # label(t27_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4373 (all A (v1_ordinal1(A) & v2_classes1(A) -> k4_classes1(k1_card_1(A)) = A)) # label(t32_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4374 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (v1_classes2(B) & -v1_xboole_0(B) -> r2_hidden(B,A) | r1_tarski(A,B))))) # label(t57_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4375 (all A all B (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(B,A) -> k1_classes2(A,B) = k1_tarski(B))) # label(redefinition_k1_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4376 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (k16_classes2(A) = k16_classes2(B) -> B = A))))) # label(t81_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4377 (all A (v1_card_1(A) -> (all B (r2_hidden(A,k1_classes1(B)) -> r1_tarski(A,k1_classes1(B)))))) # label(t19_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4378 (all A all B (r2_hidden(A,k1_card_1(k1_classes1(B))) -> r2_hidden(A,k1_classes1(B)))) # label(t15_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4379 (all A all B all C (v2_classes1(A) & r2_hidden(B,A) & r2_hidden(C,A) -> r2_hidden(k4_tarski(B,C),A))) # label(t4_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4380 (all A (v2_classes1(A) -> v4_ordinal1(k1_card_1(A)) & k1_xboole_0 != k1_card_1(A) & k1_card_1(A) != np__0 | A = k1_xboole_0)) # label(t21_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4381 $T # label(t47_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4382 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(A,B) <-> r2_hidden(k16_classes2(A),k16_classes2(B))))))) # label(t80_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4383 (all A all B (v2_classes1(A) -> r1_tarski(k1_funct_2(B,A),A) | -(r2_hidden(B,A) & v1_ordinal1(A)) & -(r1_tarski(B,A) & r2_hidden(k1_card_1(B),k1_card_1(A))) & -(r1_tarski(B,A) & r2_hidden(B,A)))) # label(t23_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4384 (all A all B all C (v1_classes2(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k4_xboole_0(B,C) = k9_classes2(A,B,C))) # label(redefinition_k9_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4385 (all A all B all C (v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k11_classes2(A,B,C) = k2_zfmisc_1(B,C))) # label(redefinition_k11_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4386 (all A all B (r2_hidden(B,A) & v2_classes1(A) -> r2_hidden(k1_card_1(B),A))) # label(t12_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4387 (all A all B (r2_hidden(B,A) & v1_classes1(A) -> r2_hidden(k1_card_1(B),k1_card_1(A)) & -r2_wellord2(B,A))) # label(t1_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4388 (all A all B (v1_ordinal1(A) & r2_hidden(A,k1_classes1(B)) -> r1_tarski(A,k1_classes1(B)))) # label(t9_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4389 (all A all B all C (v1_classes2(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> m1_subset_1(k10_classes2(A,B,C),A))) # label(dt_k10_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4390 (all A (v3_ordinal1(A) -> (all B (r2_hidden(A,k1_classes1(B)) -> r2_hidden(k1_ordinal1(A),k1_classes1(B)) & r1_tarski(A,k1_classes1(B)))))) # label(t7_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4391 (all A all B all C (v1_classes2(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k7_classes2(A,B,B) = B)) # label(idempotence_k7_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4392 (all A (v2_classes1(A) -> v2_classes1(k4_classes1(k1_card_1(A))))) # label(t39_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4393 (all A (v3_ordinal1(A) -> (all B (r2_hidden(A,k2_ordinal2(k1_classes1(B))) -> r1_tarski(k1_card_1(k4_classes1(A)),k1_card_1(k1_classes1(B))))))) # label(t34_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4394 (all A (v1_card_1(A) -> (all B (r2_hidden(A,B) & v2_classes1(B) -> r1_tarski(A,B))))) # label(t18_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4395 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & v1_classes2(A) -> k3_xboole_0(B,C) = k8_classes2(A,B,C))) # label(redefinition_k8_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4396 (all A all B all C (v1_classes2(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k1_funct_2(B,C) = k12_classes2(A,B,C))) # label(redefinition_k12_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4397 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (v1_classes2(B) & -v1_xboole_0(B) -> -v1_xboole_0(k2_xboole_0(A,B)) & v1_classes2(k2_xboole_0(A,B)) & v1_classes2(k3_xboole_0(A,B)) & -v1_xboole_0(k3_xboole_0(A,B)))))) # label(t61_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4398 (all A all B all C (-v1_xboole_0(C) & v1_classes2(C) -> (r2_hidden(B,C) & r2_hidden(A,C) -> r2_hidden(k2_zfmisc_1(A,B),C) & r2_hidden(k1_funct_2(A,B),C)))) # label(t67_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4399 (all A (v3_ordinal1(A) -> -v1_xboole_0(k16_classes2(A)) & v1_classes2(k16_classes2(A)) & v2_classes1(k16_classes2(A)) & v1_classes1(k16_classes2(A)) & v1_ordinal1(k16_classes2(A)))) # label(fc8_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4400 (all A all B (v1_classes2(B) & -v1_xboole_0(B) -> (r2_hidden(A,B) -> r2_hidden(k1_zfmisc_1(A),B) & r2_hidden(k3_tarski(A),B) & r2_hidden(k1_setfam_1(A),B)))) # label(t65_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4401 (all A all B all C (v1_classes2(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k8_classes2(A,C,B) = k8_classes2(A,B,C))) # label(commutativity_k8_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4402 (all A all B (v1_classes2(B) & -v1_xboole_0(B) -> (r2_hidden(A,B) -> r2_hidden(k1_tarski(A),B)))) # label(t63_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4403 (all A all B (-(-(r1_tarski(A,k1_classes1(B)) & r2_hidden(A,k1_classes1(B))) & -(r2_hidden(k1_card_1(A),k1_card_1(k1_classes1(B))) & r1_tarski(A,k1_classes1(B))) & -(r2_hidden(A,k1_classes1(B)) & v1_ordinal1(B))) -> r1_tarski(k1_funct_2(A,k1_classes1(B)),k1_classes1(B)))) # label(t24_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4404 (all A (v2_classes1(A) -> v4_ordinal1(k1_card_1(A)))) # label(t20_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4405 (all A (-v1_xboole_0(A) & v1_classes2(A) -> r2_hidden(k1_xboole_0,A))) # label(t62_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4406 (all A (v3_ordinal1(A) -> v1_ordinal1(k4_classes1(A)))) # label(fc7_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4407 (all A all B -(v2_classes1(A) & -r2_wellord2(B,k4_classes1(k1_card_1(A))) & -r2_hidden(B,k4_classes1(k1_card_1(A))) & r1_tarski(B,k4_classes1(k1_card_1(A))))) # label(t37_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4408 (all A (v3_ordinal1(A) -> (all B -(r2_hidden(A,k6_classes1(B)) & (all C -(r2_hidden(C,B) & A = k6_classes1(C))) & v1_ordinal1(B))))) # label(t41_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4409 (all A (v3_ordinal1(A) -> (all B (r2_hidden(A,k2_ordinal2(B)) & v2_classes1(B) -> r1_tarski(k1_card_1(k4_classes1(A)),k1_card_1(B)))))) # label(t33_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4410 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & v1_classes2(A) -> m1_subset_1(k5_classes2(A,B,C),A))) # label(dt_k5_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4411 (all A k1_card_1(k1_classes1(A)) = k2_ordinal2(k1_classes1(A))) # label(t11_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4412 (all A (v1_classes2(k15_classes2(A)) & -v1_xboole_0(k15_classes2(A)))) # label(dt_k15_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4413 (all A v1_ordinal1(k5_classes1(A))) # label(fc5_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4414 (all A all B (v1_classes2(B) & -v1_xboole_0(B) -> ((all C (-v1_xboole_0(C) & v1_classes2(C) -> (r1_tarski(A,C) -> r1_tarski(B,C)))) & r1_tarski(A,B) <-> B = k15_classes2(A)))) # label(d4_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4415 (all A all B (m1_subset_1(B,A) & v1_classes2(A) & -v1_xboole_0(A) -> k1_setfam_1(B) = k4_classes2(A,B))) # label(redefinition_k4_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4416 $T # label(t2_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4417 $T # label(t74_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4418 (all A (v1_classes2(A) & -v1_xboole_0(A) -> v3_ordinal1(k2_ordinal2(A)) & v2_ordinal1(k2_ordinal2(A)) & v1_ordinal1(k2_ordinal2(A)))) # label(fc2_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4419 (all A r1_tarski(k4_classes1(k1_card_1(k1_classes1(A))),k1_classes1(A))) # label(t29_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4420 (all A (v1_ordinal1(A) & v2_classes1(A) -> r1_tarski(A,k4_classes1(k1_card_1(A))))) # label(t31_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4421 (all A all B all C (v1_classes2(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k5_xboole_0(B,C) = k10_classes2(A,B,C))) # label(redefinition_k10_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4422 (all A (v1_classes2(A) -> v2_classes1(A) & v1_classes1(A) & v1_ordinal1(A))) # label(cc2_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4423 (all A all B (r2_hidden(A,k1_classes1(B)) -> r2_hidden(k1_card_1(A),k1_classes1(B)))) # label(t13_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4424 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & v1_classes2(A) & -v1_xboole_0(A) -> k7_classes2(A,C,B) = k7_classes2(A,B,C))) # label(commutativity_k7_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4425 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r1_tarski(k16_classes2(A),k16_classes2(B)) <-> r1_ordinal1(A,B)))))) # label(t82_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4426 (all A all B (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(B,A) -> m1_subset_1(k2_classes2(A,B),A) & -v1_xboole_0(k2_classes2(A,B)))) # label(dt_k2_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4427 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) -> (v4_ordinal1(k1_relat_1(A)) & (all B (v3_ordinal1(B) -> (r2_hidden(B,k1_relat_1(A)) -> k4_classes1(B) = k1_funct_1(A,B)))) -> k4_classes1(k1_relat_1(A)) = k3_card_3(A)))) # label(t25_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4428 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & v1_classes2(A) -> k10_classes2(A,B,C) = k10_classes2(A,C,B))) # label(commutativity_k10_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4429 (exists A (v1_classes2(A) & v2_classes1(A) & v1_classes1(A) & -v1_xboole_0(A) & v1_ordinal1(A))) # label(rc1_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4430 (all A (k1_card_1(k1_classes1(A)) != k1_xboole_0 & v4_ordinal1(k1_card_1(k1_classes1(A))) & np__0 != k1_card_1(k1_classes1(A)))) # label(t22_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.70 4431 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & v1_classes2(A) -> k5_classes2(A,C,B) = k5_classes2(A,B,C))) # label(commutativity_k5_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4432 (all A (v1_card_1(A) -> (all B (r2_hidden(A,k1_card_1(k1_classes1(B))) -> r2_hidden(A,k1_classes1(B)))))) # label(t17_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4433 (all A (v2_classes1(A) -> k1_card_1(k4_classes1(k1_card_1(A))) = k1_card_1(A))) # label(t35_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4434 (all A all B (m1_subset_1(B,A) & v1_classes2(A) & -v1_xboole_0(A) -> m1_subset_1(k4_classes2(A,B),A))) # label(dt_k4_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4435 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & v1_classes2(A) -> m1_subset_1(k6_classes2(A,B,C),A))) # label(dt_k6_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4436 (all A (v3_ordinal1(A) -> (all B (v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B) -> (v4_ordinal1(A) & (all C (v3_ordinal1(C) -> (r2_hidden(C,A) -> k1_funct_1(B,C) = k16_classes2(C)))) & A = k1_relat_1(B) -> k16_classes2(A) = k15_classes2(k3_card_3(B)) | A = k1_xboole_0))))) # label(t78_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4437 (all A all B (v1_classes2(A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> m1_subset_1(k3_classes2(A,B),A))) # label(dt_k3_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4438 (all A (v1_classes2(A) <-> v1_ordinal1(A) & v2_classes1(A))) # label(d1_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4439 (all A all B (v2_classes1(A) & r2_hidden(B,k1_card_1(A)) -> r2_hidden(B,A))) # label(t14_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4440 $T # label(t60_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4441 (all A (v1_card_1(A) -> (all B (v2_classes1(B) & r2_hidden(A,k1_card_1(B)) -> r2_hidden(A,B))))) # label(t16_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4442 (all A (v2_classes1(A) -> r1_tarski(k4_classes1(k1_card_1(A)),A))) # label(t28_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4443 (all A (v1_classes2(A) & -v1_xboole_0(A) -> v1_classes2(k1_classes1(A)) & v2_classes1(k1_classes1(A)) & v1_classes1(k1_classes1(A)) & -v1_xboole_0(k1_classes1(A)) & v1_ordinal1(k1_classes1(A)))) # label(fc3_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4444 (all A all B all C (v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> m1_subset_1(k11_classes2(A,B,C),A))) # label(dt_k11_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4445 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & v1_classes2(B) -> -(-r2_hidden(A,B) & -r2_hidden(B,A) & A != B))))) # label(t56_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4446 (all A all B -(-r2_wellord2(A,k4_classes1(k1_card_1(k1_classes1(B)))) & -r2_hidden(A,k4_classes1(k1_card_1(k1_classes1(B)))) & r1_tarski(A,k4_classes1(k1_card_1(k1_classes1(B)))))) # label(t38_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4447 (all A (v1_ordinal1(A) -> r1_tarski(k1_card_1(k6_classes1(A)),k1_card_1(A)))) # label(t42_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4448 (all A (v3_ordinal1(A) -> (all B (r2_hidden(A,k2_ordinal2(B)) & v2_classes1(B) -> r2_hidden(k4_classes1(A),B) & r2_hidden(k1_card_1(k4_classes1(A)),k1_card_1(B)))))) # label(t26_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4449 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & v1_classes2(A) -> k8_classes2(A,B,B) = B)) # label(idempotence_k8_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4450 $T # label(t72_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4451 (all A all B (r2_hidden(B,A) & v1_ordinal1(A) & v2_classes1(A) -> r2_hidden(k6_classes1(B),A))) # label(t30_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4452 (all A all B all C (v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> m1_subset_1(k9_classes2(A,B,C),A))) # label(dt_k9_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4453 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> m1_subset_1(k12_classes2(A,B,C),A))) # label(dt_k12_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4454 (all A all B all C (v1_classes2(C) & -v1_xboole_0(C) -> (r2_hidden(B,C) & r2_hidden(A,C) -> r2_hidden(k4_xboole_0(A,B),C) & r2_hidden(k5_xboole_0(A,B),C) & r2_hidden(k3_xboole_0(A,B),C) & r2_hidden(k2_xboole_0(A,B),C)))) # label(t66_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4455 (all A all B (v1_classes1(A) & v1_ordinal1(B) & r2_hidden(B,A) -> r1_tarski(B,A))) # label(t8_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4456 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & v1_classes2(A) & -v1_xboole_0(A) -> m1_subset_1(k8_classes2(A,B,C),A))) # label(dt_k8_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4457 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> m1_subset_1(k7_classes2(A,B,C),A))) # label(dt_k7_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4458 (all A all B (r2_hidden(B,A) & v1_ordinal1(B) & v2_classes1(A) -> r2_hidden(B,k4_classes1(k1_card_1(A))))) # label(t43_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4459 (all A all B all C (m1_subset_1(C,A) & m1_subset_1(B,A) & v1_classes2(A) & -v1_xboole_0(A) -> k5_classes2(A,B,C) = k2_tarski(B,C))) # label(redefinition_k5_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4460 (all A all B (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(B,A) -> m1_subset_1(k1_classes2(A,B),A))) # label(dt_k1_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4461 (all A (v3_ordinal1(A) -> k16_classes2(k1_ordinal1(A)) = k1_classes1(k16_classes2(A)))) # label(t76_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4462 (all A (v1_ordinal1(A) -> r1_classes1(A,k4_classes1(k1_card_1(k1_classes1(A)))))) # label(t45_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4463 $T # label(t73_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4464 (all A (-v1_xboole_0(A) & v1_classes2(A) -> v3_ordinal1(k2_ordinal2(A)))) # label(t50_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4465 (all A (v1_ordinal1(A) -> v1_classes2(k1_classes1(A)))) # label(t51_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4466 (all A k1_card_1(k1_classes1(A)) = k1_card_1(k4_classes1(k1_card_1(k1_classes1(A))))) # label(t36_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4467 (all A all B (v1_classes2(A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k3_classes2(A,B) = k3_tarski(B))) # label(redefinition_k3_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4468 (all A v2_classes1(k4_classes1(k1_card_1(k1_classes1(A))))) # label(t40_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4469 $T # label(dt_k16_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4470 (all A (-v1_xboole_0(k1_classes1(A)) & v1_classes1(k1_classes1(A)) & v2_classes1(k1_classes1(A)))) # label(fc1_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4471 (all A all B (v1_ordinal1(A) & r2_hidden(A,k1_classes1(B)) -> r2_hidden(A,k4_classes1(k1_card_1(k1_classes1(B)))))) # label(t44_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4472 (all A (v1_ordinal1(A) -> k1_classes1(A) = k4_classes1(k1_card_1(k1_classes1(A))))) # label(t46_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4473 $T # label(t68_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4474 (all A (v3_ordinal1(A) -> v1_classes2(k1_classes1(A)))) # label(t53_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4475 (all A (v3_ordinal1(A) -> (all B (v2_classes1(B) & r2_hidden(A,B) -> r1_tarski(A,B) & r2_hidden(k1_ordinal1(A),B))))) # label(t6_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4476 (all A (-v1_xboole_0(A) & v1_classes2(A) -> -v1_xboole_0(k1_classes1(A)) & v1_classes2(k1_classes1(A)))) # label(t52_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4477 (all A (v1_classes2(A) & -v1_xboole_0(A) -> k4_classes1(k2_ordinal2(A)) = A)) # label(t54_classes2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4478 $T # label(t101_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4479 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C k7_finseq_1(k1_finseq_3(A,C),k1_finseq_3(B,C)) = k1_finseq_3(k7_finseq_1(A,B),C)))))) # label(t80_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4480 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (k4_finseq_1(B) = k4_finseq_1(A) <-> k3_finseq_1(B) = k3_finseq_1(A)))))) # label(t31_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4481 (all A (v4_ordinal2(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> k5_relat_1(k14_finseq_1(k4_xboole_0(k4_finseq_1(B),k1_tarski(A))),B) = k2_finseq_3(A,B))))) # label(d2_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4482 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> k1_finseq_3(A,k2_relat_1(A)) = k1_xboole_0)) # label(t79_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4483 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> r1_tarski(k2_finseq_1(A),k2_finseq_1(k2_xcmplx_0(A,B))))))) # label(t19_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4484 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B all C (v4_ordinal2(C) -> (r2_hidden(C,k4_finseq_1(A)) -> (all D (v1_finset_1(D) -> -(-r2_hidden(k1_funct_1(A,C),B) & k1_funct_1(A,C) != k1_funct_1(k1_finseq_3(A,B),k6_xcmplx_0(C,k4_card_1(D))) & D = a_3_0_finseq_3(A,B,C))))))))) # label(t92_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4485 (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_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> ((all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(C)) -> k1_funct_1(C,D) = k1_funct_1(A,k1_nat_1(k3_finseq_1(B),D))))) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(B)) -> k1_funct_1(B,D) = k1_funct_1(A,D)))) & k3_finseq_1(A) = k1_nat_1(k3_finseq_1(B),k3_finseq_1(C)) -> A = k7_finseq_1(B,C)))))))) # label(t43_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4486 (all A all B k10_finseq_1(A,B) != k1_xboole_0) # label(t38_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4487 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (k2_finseq_1(k2_xcmplx_0(A,B)) = k2_finseq_1(A) -> B = np__0))))) # label(t18_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4488 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r2_hidden(A,k2_finseq_1(B)) -> r2_hidden(k6_xcmplx_0(A,C),k2_finseq_1(B)) | r1_xreal_0(A,C)))))))) # label(t13_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4489 (all A (v4_ordinal2(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_1(C,B) -> m2_finseq_1(k2_finseq_3(A,C),B))))))) # label(t114_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4490 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (k3_finseq_1(A) = k1_nat_1(C,np__1) -> r1_xreal_0(B,D) | k1_funct_1(A,D) = k1_funct_1(k2_finseq_3(B,A),D)))))))))) # label(t119_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4491 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_xreal_0(A,B) <-> k7_relat_1(k1_finseq_2(A),k2_finseq_1(B)) = k1_finseq_2(A)))))) # label(t58_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4492 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (k3_finseq_1(A) = k2_xcmplx_0(C,np__1) & r2_hidden(B,k4_finseq_1(A)) -> k3_finseq_1(k2_finseq_3(B,A)) = C))))))) # label(t118_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4493 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v4_ordinal2(C) -> (all D (v4_ordinal2(D) -> (k7_relat_1(A,k2_finseq_1(C)) = B & k2_xcmplx_0(C,D) = k3_finseq_1(A) -> k3_finseq_1(B) = C))))))))) # label(t59_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4494 (all A v2_funct_1(k9_finseq_1(A))) # label(t102_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4495 (all A all B (v4_ordinal2(B) -> (r1_tarski(A,k2_finseq_1(B)) -> v2_funct_1(k14_finseq_1(A))))) # label(t99_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4496 $T # label(t8_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4497 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (r2_hidden(C,k4_finseq_1(A)) -> r2_hidden(C,k4_finseq_1(k7_finseq_1(A,B))))))))) # label(t24_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4498 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (r2_hidden(B,k2_relat_1(A)) -> r2_hidden(np__1,k4_finseq_1(A)))))) # label(t33_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4499 (all A all B all C k1_xboole_0 != k11_finseq_1(A,B,C)) # label(t39_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4500 (all A all B all C k9_finseq_1(A) != k10_finseq_1(B,C)) # label(t40_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4501 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(B,k4_finseq_1(A)) & r1_xreal_0(D,C) & r1_xreal_0(B,D) & k1_nat_1(C,np__1) = k3_finseq_1(A) -> k1_funct_1(k2_finseq_3(B,A),D) = k1_funct_1(A,k1_nat_1(D,np__1))))))))))) # label(t120_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4502 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (k4_finseq_1(k1_finseq_3(A,B)) = k4_finseq_1(A) -> r1_xboole_0(B,k2_relat_1(A)))))) # label(t71_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4503 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B k4_xboole_0(k2_relat_1(A),B) = k2_relat_1(k1_finseq_3(A,B))))) # label(t72_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4504 (all A (v4_ordinal2(A) -> v2_funct_1(k1_finseq_2(A)))) # label(t100_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4505 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> k1_finseq_2(A) = k7_relat_1(k1_finseq_2(k2_xcmplx_0(A,B)),k2_finseq_1(A)))))) # label(t56_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4506 (all A (v4_ordinal2(A) -> (all B all C (m2_finseq_1(C,B) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r1_xreal_0(D,A) -> k1_funct_1(k16_finseq_1(B,C,A),D) = k1_funct_1(C,D)))))))) # label(t121_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4507 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> r3_xboole_0(k2_finseq_1(A),k2_finseq_1(B)))))) # label(t20_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4508 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (r2_hidden(B,k4_finseq_1(A)) -> m2_subset_1(B,k1_numbers,k5_numbers))))) # label(t25_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4509 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v4_ordinal2(B) -> (m2_subset_1(k6_xcmplx_0(B,np__1),k1_numbers,k5_numbers) & m2_subset_1(k6_xcmplx_0(k3_finseq_1(A),B),k1_numbers,k5_numbers) <-> r2_hidden(B,k4_finseq_1(A))))))) # label(t28_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4510 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v2_funct_1(A) & r2_hidden(B,k2_relat_1(A)) -> k6_xcmplx_0(k3_finseq_1(A),np__1) = k3_finseq_1(k1_finseq_3(A,k1_tarski(B))))))) # label(t97_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4511 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B r1_xreal_0(k3_finseq_1(k1_finseq_3(A,B)),k3_finseq_1(A))))) # label(t67_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4512 (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(k4_finseq_1(A),k4_finseq_1(B)) <-> r1_xreal_0(k3_finseq_1(A),k3_finseq_1(B))))))) # label(t32_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4513 (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 k1_nat_1(k4_card_1(k10_relat_1(A,C)),k4_card_1(k10_relat_1(B,C))) = k4_card_1(k10_relat_1(k7_finseq_1(A,B),C))))))) # label(t63_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4514 (all A all B k2_finseq_1(np__2) = k4_finseq_1(k10_finseq_1(A,B))) # label(t29_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4515 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B all C all D (v2_funct_1(A) & k1_enumset1(B,C,D) = k2_relat_1(A) -> k3_finseq_1(A) = np__3 | D = B | D = C | B = C)))) # label(t110_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4516 (all A all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) & v4_ordinal2(A) -> v1_funct_1(k2_finseq_3(A,B)) & v1_finseq_1(k2_finseq_3(A,B)) & v1_relat_1(k2_finseq_3(A,B)))) # label(dt_k2_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4517 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (k7_relat_1(k1_finseq_2(A),k2_finseq_1(B)) = k1_finseq_2(B) <-> r1_xreal_0(B,A)))))) # label(t57_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4518 (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 (v4_ordinal2(C) -> (all D (v4_ordinal2(D) -> (k2_xcmplx_0(C,D) = k3_finseq_1(A) & k7_relat_1(A,k2_finseq_1(C)) = B -> k4_finseq_1(B) = k2_finseq_1(C)))))))))) # label(t60_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4519 (all A k1_finseq_3(k1_xboole_0,A) = k1_xboole_0) # label(t81_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4520 (all A all B all C all D all E k10_finseq_1(A,B) != k11_finseq_1(C,D,E)) # label(t42_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4521 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C r1_tarski(k10_relat_1(A,C),k10_relat_1(k7_finseq_1(A,B),C))))))) # label(t64_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4522 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (k2_relat_1(k1_finseq_3(A,B)) = k2_relat_1(A) -> r1_xboole_0(B,k2_relat_1(A)))))) # label(t74_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4523 $T # label(t35_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4524 (all A all B (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> v1_relat_1(k1_finseq_3(A,B)) & v1_finseq_1(k1_finseq_3(A,B)) & v1_funct_1(k1_finseq_3(A,B)))) # label(dt_k1_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4525 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v4_ordinal2(B) -> (r1_xreal_0(np__1,B) & r1_xreal_0(B,k3_finseq_1(A)) <-> r2_hidden(B,k4_finseq_1(A))))))) # label(t27_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4526 (all A all B (k1_finseq_3(k9_finseq_1(A),B) = k1_xboole_0 <-> r2_hidden(A,B))) # label(t83_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4527 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B all C (m2_finseq_1(A,B) -> m2_finseq_1(k1_finseq_3(A,C),B))))) # label(t93_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4528 (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 all D (v4_ordinal2(D) -> (B = k7_relat_1(A,k2_finseq_1(D)) & k2_xcmplx_0(D,np__1) = k3_finseq_1(A) -> (r2_hidden(k1_funct_1(A,k2_xcmplx_0(D,np__1)),C) <-> k1_finseq_3(B,C) = k1_finseq_3(A,C))))))))) # label(t90_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4529 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (k2_relat_1(A) != k1_xboole_0 -> r2_hidden(np__1,k4_finseq_1(A))))) # label(t34_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4530 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r2_hidden(k2_xcmplx_0(A,B),k2_finseq_1(A)) -> B = np__0))))) # label(t11_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4531 (all A all B (v4_ordinal2(B) -> (k1_tarski(A) = k2_finseq_1(B) -> np__1 = A & B = np__1))) # label(t22_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4532 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (k1_tarski(B) = k2_relat_1(A) & v2_funct_1(A) -> np__1 = k3_finseq_1(A))))) # label(t105_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4533 $T # label(t47_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4534 (all A all B all C (k9_finseq_1(B) = k1_finseq_3(k10_finseq_1(A,B),C) -> B = A | r2_hidden(A,C) & -r2_hidden(B,C))) # label(t86_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4535 (all A (v4_ordinal2(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(k2_finseq_3(A,B)),k2_relat_1(B)))))) # label(t115_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4536 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r2_hidden(k6_xcmplx_0(A,B),k2_finseq_1(A)) <-> -r1_xreal_0(A,B)))))) # label(t14_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4537 (all A (v4_ordinal2(A) -> k6_subset_1(k5_numbers,k2_finseq_1(k2_xcmplx_0(A,np__1)),k2_finseq_1(A)) = k1_tarski(k2_xcmplx_0(A,np__1)))) # label(t16_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4538 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B r1_tarski(k4_finseq_1(k1_finseq_3(A,B)),k4_finseq_1(A))))) # label(t70_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4539 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v2_funct_1(A) -> v2_funct_1(k1_finseq_3(A,B)))))) # label(t94_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4540 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (k3_finseq_1(A) = k3_finseq_1(k1_finseq_3(A,B)) -> r1_xboole_0(B,k2_relat_1(A)))))) # label(t68_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4541 (all A all B all C (r2_hidden(C,B) -> r2_hidden(A,B) | k1_finseq_3(k10_finseq_1(A,C),B) = k9_finseq_1(A))) # label(t87_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4542 $T # label(t65_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4543 (all A all B (v2_funct_1(k10_finseq_1(A,B)) <-> B != A)) # label(t103_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4544 (all A all B all C (k1_finseq_3(k10_finseq_1(A,B),C) = k9_finseq_1(A) -> A = B | r2_hidden(B,C) & -r2_hidden(A,C))) # label(t88_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4545 (all A (v4_ordinal2(A) -> k2_finseq_1(k2_xcmplx_0(A,np__1)) != k2_finseq_1(A))) # label(t17_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4546 (all A all B all C k2_finseq_1(np__3) = k4_finseq_1(k11_finseq_1(A,B,C))) # label(t30_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4547 (all A all B all C (v4_ordinal2(C) -> (all D (v4_ordinal2(D) -> (r1_tarski(A,k2_finseq_1(C)) & r1_tarski(B,k2_finseq_1(D)) -> (k8_finseq_1(k5_numbers,k14_finseq_1(A),k14_finseq_1(B)) = k14_finseq_1(k2_xboole_0(A,B)) <-> (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (all F (m2_subset_1(F,k1_numbers,k5_numbers) -> -(r2_hidden(E,A) & r2_hidden(F,B) & r1_xreal_0(F,E)))))))))))) # label(t48_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4548 (all A (v4_ordinal2(A) -> -r2_hidden(k2_xcmplx_0(A,np__1),k2_finseq_1(A)))) # label(t9_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4549 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (k1_nat_1(C,np__1) = D & r2_hidden(B,k2_finseq_1(D)) & r2_hidden(A,k2_finseq_1(C)) -> (r1_xreal_0(B,A) & r1_xreal_0(A,C) -> k1_nat_1(A,np__1) = k1_funct_1(k14_finseq_1(k4_xboole_0(k2_finseq_1(D),k1_tarski(B))),A)) & (r1_xreal_0(np__1,A) -> k1_funct_1(k14_finseq_1(k4_xboole_0(k2_finseq_1(D),k1_tarski(B))),A) = A | r1_xreal_0(B,A))))))))))) # label(t117_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4550 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B ((exists C (m2_subset_1(C,k1_numbers,k5_numbers) & k3_xboole_0(B,k4_finseq_1(A)) = k2_finseq_1(C))) <-> v1_relat_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)) & v1_finseq_1(k7_relat_1(A,B)))))) # label(t62_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4551 (all A (v4_ordinal2(A) -> (np__0 != A -> k14_finseq_1(k1_tarski(A)) = k9_finseq_1(A)))) # label(t50_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4552 (all A (v4_ordinal2(A) -> k1_finseq_2(A) = k14_finseq_1(k2_finseq_1(A)))) # label(t54_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4553 (all A all B all C (r2_hidden(A,B) -> r2_hidden(C,B) | k1_finseq_3(k10_finseq_1(A,C),B) = k9_finseq_1(C))) # label(t85_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4554 (all A (v4_ordinal2(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (r2_hidden(A,k4_finseq_1(B)) -> k1_funct_1(B,A) = k1_funct_1(k7_finseq_1(k9_finseq_1(C),B),k2_xcmplx_0(A,np__1)))))))) # label(t112_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4555 (all A all B all C all D (v1_relat_1(B) & v4_ordinal2(D) & v1_finseq_1(B) & v1_funct_1(B) -> ((exists E (E = A & r2_hidden(k1_funct_1(B,E),C) & r1_xreal_0(E,D) & r2_hidden(E,k4_finseq_1(B)) & m2_subset_1(E,k1_numbers,k5_numbers))) <-> r2_hidden(A,a_3_0_finseq_3(B,C,D))))) # label(fraenkel_a_3_0_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4556 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> -(-v1_xboole_0(B) & (all C (m1_subset_1(C,A) -> (all D (m2_finseq_1(D,A) -> -(k8_finseq_1(A,k12_finseq_1(A,C),D) = B & C = k1_funct_1(B,np__1))))))))))) # label(t111_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4557 (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) -> (v2_funct_1(A) & v2_funct_1(B) & r1_xboole_0(k2_relat_1(A),k2_relat_1(B)) <-> v2_funct_1(k7_finseq_1(A,B))))))) # label(t98_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4558 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (-r1_xreal_0(B,A) -> r2_hidden(k2_xcmplx_0(A,np__1),k2_finseq_1(B))))))) # label(t12_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4559 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B all C (v4_ordinal2(C) -> (k6_xcmplx_0(k3_finseq_1(A),k4_card_1(k10_relat_1(A,B))) = C -> k4_finseq_1(k1_finseq_3(A,B)) = k2_finseq_1(C)))))) # label(t69_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4560 (all A (v4_ordinal2(A) -> (-r2_hidden(A,k2_finseq_1(A)) <-> k1_xboole_0 = k2_finseq_1(A)))) # label(t7_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4561 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C all D (v4_ordinal2(D) -> (k7_relat_1(A,k2_finseq_1(D)) = B & k2_xcmplx_0(D,np__1) = k3_finseq_1(A) -> (k1_finseq_3(A,C) = k7_finseq_1(k1_finseq_3(B,C),k9_finseq_1(k1_funct_1(A,k2_xcmplx_0(D,np__1)))) <-> -r2_hidden(k1_funct_1(A,k2_xcmplx_0(D,np__1)),C))))))))) # label(t91_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4562 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_finset_1(B) -> (r1_tarski(B,k2_relat_1(A)) & v2_funct_1(A) -> k3_finseq_1(k1_finseq_3(A,B)) = k6_xcmplx_0(k3_finseq_1(A),k4_card_1(B))))))) # label(t96_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4563 $T # label(t21_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4564 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B r1_tarski(k2_relat_1(k1_finseq_3(A,B)),k2_relat_1(A))))) # label(t73_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4565 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (A != np__0 -> r2_hidden(A,k2_finseq_1(k2_xcmplx_0(A,B)))))))) # label(t10_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4566 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> -(-r1_xreal_0(A,np__0) & -r1_xreal_0(B,A) & k10_finseq_1(A,B) != k14_finseq_1(k2_tarski(A,B))))))) # label(t51_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4567 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (A = k1_finseq_3(A,k1_tarski(B)) <-> -r2_hidden(B,k2_relat_1(A)))))) # label(t77_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4568 (all A (v4_ordinal2(A) -> k3_finseq_1(k14_finseq_1(k2_finseq_1(A))) = A)) # label(t52_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4569 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (k2_relat_1(A) = k1_tarski(B) & v2_funct_1(A) -> A = k9_finseq_1(B))))) # label(t106_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4570 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (k2_xcmplx_0(B,np__1) = A & r2_hidden(C,k2_finseq_1(A)) -> B = k3_finseq_1(k14_finseq_1(k4_xboole_0(k2_finseq_1(A),k1_tarski(C))))))))))) # label(t116_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4571 (all A all B all C (B != A & C != A & C != B <-> v2_funct_1(k11_finseq_1(A,B,C)))) # label(t104_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4572 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v4_ordinal2(C) -> (k3_finseq_1(A) = k2_xcmplx_0(C,np__1) & B = k7_relat_1(A,k2_finseq_1(C)) -> k7_finseq_1(B,k9_finseq_1(k1_funct_1(A,k2_xcmplx_0(C,np__1)))) = A))))))) # label(t61_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4573 (all A (v4_ordinal2(A) -> (all B (v1_finset_1(B) -> (r1_tarski(B,k2_finseq_1(A)) -> k4_card_1(B) = k3_finseq_1(k14_finseq_1(B))))))) # label(t44_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4574 (all A all B all C (k1_finseq_3(k10_finseq_1(A,B),C) = k10_finseq_1(A,B) <-> -r2_hidden(B,C) & -r2_hidden(A,C))) # label(t89_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4575 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> k1_finseq_3(A,k1_xboole_0) = A)) # label(t78_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4576 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B all C (k2_tarski(B,C) = k2_relat_1(A) & v2_funct_1(A) -> B = C | k3_finseq_1(A) = np__2)))) # label(t107_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4577 (all A all B all C all D k11_finseq_1(B,C,D) != k9_finseq_1(A)) # label(t41_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4578 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> k7_relat_1(k14_finseq_1(k2_finseq_1(k2_xcmplx_0(A,B))),k2_finseq_1(A)) = k14_finseq_1(k2_finseq_1(A)))))) # label(t53_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4579 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B k3_finseq_1(k1_finseq_3(A,B)) = k6_xcmplx_0(k3_finseq_1(A),k4_card_1(k10_relat_1(A,B)))))) # label(t66_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4580 (all A all B all C (k1_finseq_3(k10_finseq_1(A,B),C) = k1_xboole_0 <-> r2_hidden(A,C) & r2_hidden(B,C))) # label(t84_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4581 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v4_ordinal2(B) -> (A = k7_relat_1(A,k2_finseq_1(B)) <-> r1_xreal_0(k3_finseq_1(A),B)))))) # label(t55_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4582 (all A all B (k1_finseq_3(k9_finseq_1(A),B) = k9_finseq_1(A) <-> -r2_hidden(A,B))) # label(t82_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4583 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v2_funct_1(A) -> k3_finseq_1(k1_finseq_3(A,B)) = k6_xcmplx_0(k3_finseq_1(A),k4_card_1(k3_xboole_0(B,k2_relat_1(A)))))))) # label(t95_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4584 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (r1_xboole_0(B,k2_relat_1(A)) <-> k1_finseq_3(A,B) = A)))) # label(t76_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4585 (all A (v4_ordinal2(A) -> r1_xboole_0(k2_finseq_1(A),k1_tarski(k2_xcmplx_0(A,np__1))))) # label(t15_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4586 $T # label(t36_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4587 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (r1_tarski(k2_relat_1(A),B) <-> k1_xboole_0 = k1_finseq_3(A,B))))) # label(t75_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4588 (all A all B all C (v4_ordinal2(C) -> (k2_tarski(A,B) = k2_finseq_1(C) -> A = B | C = np__2 & k2_tarski(np__1,np__2) = k2_tarski(A,B)))) # label(t23_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4589 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B k5_relat_1(k14_finseq_1(k4_xboole_0(k4_finseq_1(A),k10_relat_1(A,B))),A) = k1_finseq_3(A,B)))) # label(d1_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4590 $T # label(t37_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4591 (all A (v4_ordinal2(A) -> (all B (v1_finset_1(B) -> (r1_tarski(B,k2_finseq_1(A)) -> k2_finseq_1(k4_card_1(B)) = k4_finseq_1(k14_finseq_1(B))))))) # label(t45_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4592 (all A (v4_ordinal2(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> -(r2_hidden(A,k4_finseq_1(B)) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(C = k3_finseq_1(k2_finseq_3(A,B)) & k1_nat_1(C,np__1) = k3_finseq_1(B))))) & (-r2_hidden(A,k4_finseq_1(B)) -> k2_finseq_3(A,B) = B))))) # label(t113_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4593 (all A all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (all D (v4_ordinal2(D) -> (all E (v4_ordinal2(E) -> (all F (v4_ordinal2(F) -> -(r1_tarski(A,k2_finseq_1(B)) & r1_xreal_0(np__1,E) & r1_xreal_0(E,F) & D = k1_funct_1(k14_finseq_1(A),E) & C = k1_funct_1(k14_finseq_1(A),F) & r1_xreal_0(F,k3_finseq_1(k14_finseq_1(A))) & -r1_xreal_0(D,C)))))))))))) # label(t46_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4594 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B all C -(k2_relat_1(A) = k2_tarski(B,C) & k10_finseq_1(B,C) != A & k10_finseq_1(C,B) != A & B != C & v2_funct_1(A))))) # label(t108_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4595 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B all C all D (v2_funct_1(A) & k2_relat_1(A) = k1_enumset1(B,C,D) & v2_funct_1(k11_finseq_1(B,C,D)) -> k3_finseq_1(A) = np__3)))) # label(t109_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4596 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B -(np__0 = B & r2_hidden(B,k4_finseq_1(A)))))) # label(t26_finseq_3) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4597 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v1_relat_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & v1_funct_1(C) -> k2_ordinal1(k1_ordinal3(A,C),B) = k1_ordinal3(A,k2_ordinal1(C,B)))))))) # label(t16_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4598 (all A (v1_relat_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_1(A) -> r1_tarski(k2_relat_1(A),k8_ordinal2(A)))) # label(t20_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4599 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (m1_ordinal4(B,A) -> r2_hidden(k4_classes1(B),A))))) # label(t33_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4600 $T # label(dt_k1_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4601 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (m1_ordinal4(B,A) -> -r4_zfrefle1(k2_ordinal2(A),B))))) # label(t29_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4602 (all A (v3_ordinal1(A) -> (all B (v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) & v1_relat_1(B) -> (v4_ordinal1(k1_relat_1(B)) & v2_ordinal2(B) & r1_ordinal2(A,B) -> r4_zfrefle1(A,k1_relat_1(B)) | k1_relat_1(B) = k1_xboole_0))))) # label(t24_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.71 4603 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (r2_zfrefle1(A,B) <-> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (k1_xboole_0 = k2_zf_model(C) -> (r2_zf_model(A,C) <-> r2_zf_model(B,C)))))))))) # label(d2_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4604 (all A -((all B -p1_s1_zfrefle1(A,B)) & r2_hidden(A,f1_s1_zfrefle1))) -> (exists A (f1_s1_zfrefle1 = k1_relat_1(A) & (all B (r2_hidden(B,f1_s1_zfrefle1) -> p1_s1_zfrefle1(B,k1_funct_1(A,B)))) & v1_funct_1(A) & v1_relat_1(A))) # label(s1_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4605 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r4_zfrefle1(B,A) & r4_zfrefle1(A,B) -> B = A))))) # label(t23_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4606 (all A (-v1_xboole_0(A) & v1_classes2(A) -> -((all B (m1_ordinal4(B,A) -> (all C (-v1_xboole_0(C) -> -(k4_classes1(B) = C & r3_zfrefle1(C,A) & r4_zfrefle1(B,k5_ordinal2)))))) & r2_hidden(k5_ordinal2,A)))) # label(t37_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4607 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,B,k1_funct_2(k2_ordinal2(A),k2_ordinal2(A))) & v1_funct_2(C,B,k1_funct_2(k2_ordinal2(A),k2_ordinal2(A))) & v1_funct_1(C) -> -((all D (m2_ordinal4(D,A) -> -(v2_ordinal2(D) & v3_ordinal2(D) & (all E (m1_ordinal4(E,A) -> k4_ordinal4(A,D,k6_ordinal4(A,E)) = k7_ordinal2(k2_xboole_0(k1_tarski(k4_ordinal4(A,D,E)),k9_relat_1(k4_funct_5(C),k2_zfmisc_1(B,k1_tarski(k6_ordinal4(A,E)))))))) & (all E (m1_ordinal4(E,A) -> (v4_ordinal1(E) -> k8_ordinal2(k2_ordinal1(D,E)) = k4_ordinal4(A,D,E) | k2_ordinal4(A) = E))) & k4_ordinal4(A,D,k2_ordinal4(A)) = k2_ordinal4(A)))) & r2_hidden(k1_card_1(B),k1_card_1(A))))))))) # label(t14_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4608 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (r3_zfrefle1(A,B) -> r2_zfrefle1(A,B)))))) # label(t9_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4609 (all A (v3_ordinal1(A) -> (all B (v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) & v1_relat_1(B) -> (v2_ordinal2(B) & v3_ordinal2(B) -> v3_ordinal2(k1_ordinal3(A,B))))))) # label(t17_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4610 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r4_zfrefle1(A,B) <-> (exists C (v1_relat_1(C) & v1_funct_1(C) & r1_tarski(k2_relat_1(C),A) & v2_ordinal2(C) & k8_ordinal2(C) = A & B = k1_relat_1(C) & v1_ordinal2(C) & v5_ordinal1(C)))))))) # label(d5_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4611 (all A (-v1_xboole_0(A) -> r1_zfrefle1(A,k1_subset_1(k9_zf_lang)))) # label(t1_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4612 (all A (-v1_xboole_0(A) & v1_classes2(A) -> -((all B (m1_ordinal4(B,A) -> (all C (-v1_xboole_0(C) -> -(v1_zf_model(C) & C = k4_classes1(B) & r4_zfrefle1(B,k5_ordinal2)))))) & r2_hidden(k5_ordinal2,A)))) # label(t42_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4613 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (v2_relat_1(B) & v1_zf_refle(B,A) & m1_ordinal1(B,A) -> -(r2_hidden(k5_ordinal2,A) & (all C (m1_ordinal4(C,A) -> (all D (m1_ordinal4(D,A) -> (r2_hidden(C,D) -> r1_tarski(k5_zf_refle(A,B,C),k5_zf_refle(A,B,D))))))) & (all C (m2_ordinal4(C,A) -> -((all D (m1_ordinal4(D,A) -> (D = k4_ordinal4(A,C,D) -> k1_xboole_0 = D | r2_zfrefle1(k5_zf_refle(A,B,D),k4_zf_refle(A,B))))) & v3_ordinal2(C) & v2_ordinal2(C)))) & (all C (m1_ordinal4(C,A) -> (v4_ordinal1(C) -> C = k1_xboole_0 | k3_card_3(k2_ordinal1(B,C)) = k5_zf_refle(A,B,C))))))))) # label(t38_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4614 (all A (v3_ordinal1(A) -> r4_zfrefle1(k1_ordinal1(A),k4_ordinal2))) # label(t25_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4615 (all A (-v1_xboole_0(A) & v1_classes2(A) -> -((all B (m2_ordinal4(B,A) -> -((all C (m1_ordinal4(C,A) -> (all D (-v1_xboole_0(D) -> (D = k4_classes1(C) & k4_ordinal4(A,B,C) = C -> r2_zfrefle1(D,A) | C = k1_xboole_0))))) & v3_ordinal2(B) & v2_ordinal2(B)))) & r2_hidden(k5_ordinal2,A)))) # label(t39_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4616 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r4_zfrefle1(B,C) & r4_zfrefle1(A,B) -> r4_zfrefle1(A,C)))))))) # label(t21_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4617 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -((all C (v3_ordinal1(C) -> A != k1_ordinal1(C))) & r4_zfrefle1(A,k1_ordinal1(B))))))) # label(t26_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4618 (all A (v3_ordinal1(A) -> (all B (v1_funct_1(B) & v1_ordinal2(B) & v5_ordinal1(B) & v1_relat_1(B) -> (v2_ordinal2(B) -> v2_ordinal2(k1_ordinal3(A,B))))))) # label(t15_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4619 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> r3_zfrefle1(A,A))) # label(reflexivity_r3_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4620 $T # label(t11_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4621 $T # label(t18_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4622 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> (r2_zfrefle1(A,B) -> r2_zfrefle1(B,A)))) # label(symmetry_r2_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4623 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (exists B (m2_finseq_1(B,k5_numbers) & (all C (-v1_xboole_0(C) -> (r2_zf_model(C,A) <-> r2_zf_model(C,B)))) & k1_xboole_0 = k2_zf_model(B) & v1_zf_lang(B))))) # label(t6_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4624 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> r2_zfrefle1(A,A))) # label(reflexivity_r2_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4625 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (v1_zf_model(A) & v1_ordinal1(B) & r2_zfrefle1(A,B) -> v1_zf_model(B)))))) # label(t10_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4626 (all A (-v1_xboole_0(A) -> (v1_zf_model(A) -> r1_zfrefle1(A,k2_zfrefle1)))) # label(t4_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4627 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r4_zfrefle1(A,B) -> (v4_ordinal1(A) <-> v4_ordinal1(B))))))) # label(t27_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4628 (all A (-v1_xboole_0(A) -> (v1_ordinal1(A) & r1_zfrefle1(A,k2_zfrefle1) -> v1_zf_model(A)))) # label(t5_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4629 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (-v1_xboole_0(B) & v1_classes2(B) -> (r1_tarski(k2_relat_1(A),B) & r2_hidden(k1_relat_1(A),B) -> r2_hidden(k2_relat_1(A),B)))))) # label(t12_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4630 (all A (v3_ordinal1(A) -> (r4_zfrefle1(A,k1_xboole_0) -> k1_xboole_0 = A))) # label(t28_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4631 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k9_zf_lang)) -> (all C (m1_subset_1(C,k1_zfmisc_1(k9_zf_lang)) -> (r1_zfrefle1(A,C) & r1_zfrefle1(A,B) -> r1_zfrefle1(A,k4_subset_1(k9_zf_lang,B,C))))))))) # label(t3_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4632 (all A all B (k1_card_1(A) = k1_card_1(B) | r2_wellord2(A,B) -> k1_card_1(k1_zfmisc_1(B)) = k1_card_1(k1_zfmisc_1(A)) & r2_wellord2(k1_zfmisc_1(A),k1_zfmisc_1(B)))) # label(t13_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4633 (all A all B (v1_funct_1(B) & v1_ordinal2(B) & v5_ordinal1(B) & v1_relat_1(B) -> (r2_hidden(A,k2_relat_1(B)) -> v3_ordinal1(A)))) # label(t19_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4634 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (r3_zfrefle1(A,B) <-> r1_tarski(A,B) & (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (all D (m2_relset_1(D,k1_zf_lang,A) & v1_funct_2(D,k1_zf_lang,A) & v1_funct_1(D) -> (r1_zf_model(A,D,C) <-> r1_zf_model(B,k2_zf_lang1(k1_zf_lang,A,B,D),C))))))))))) # label(d3_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4635 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (m1_ordinal4(B,A) -> -((all C (m1_ordinal4(C,A) -> (all D (-v1_xboole_0(D) -> -(r2_hidden(B,C) & r2_zfrefle1(D,A) & k4_classes1(C) = D))))) & r2_hidden(k5_ordinal2,A)))))) # label(t40_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4636 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (m1_ordinal4(B,A) -> (all C (m2_ordinal4(C,A) -> -(r2_hidden(k5_ordinal2,A) & (all D (m1_ordinal4(D,A) -> -(r2_hidden(B,D) & k4_ordinal4(A,C,D) = D & r4_zfrefle1(D,k5_ordinal2)))) & v3_ordinal2(C) & v2_ordinal2(C)))))))) # label(t31_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4637 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k9_zf_lang)) -> (all C (m1_subset_1(C,k1_zfmisc_1(k9_zf_lang)) -> (r1_zfrefle1(A,C) & r1_tarski(B,C) -> r1_zfrefle1(A,B)))))))) # label(t2_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4638 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> r4_zfrefle1(A,A))) # label(reflexivity_r4_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4639 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (v1_zf_refle(B,A) & m1_ordinal1(B,A) & v2_relat_1(B) -> -((all C (m1_ordinal4(C,A) -> (all D (m1_ordinal4(D,A) -> (r2_hidden(C,D) -> r1_tarski(k5_zf_refle(A,B,C),k5_zf_refle(A,B,D))))))) & (all C (m2_ordinal4(C,A) -> -(v3_ordinal2(C) & (all D (m1_ordinal4(D,A) -> (k4_ordinal4(A,C,D) = D -> D = k1_xboole_0 | r3_zfrefle1(k5_zf_refle(A,B,D),k4_zf_refle(A,B))))) & v2_ordinal2(C)))) & (all C (m1_ordinal4(C,A) -> (v4_ordinal1(C) -> C = k1_xboole_0 | k3_card_3(k2_ordinal1(B,C)) = k5_zf_refle(A,B,C)))) & r2_hidden(k5_ordinal2,A)))))) # label(t32_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4640 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (r2_zfrefle1(A,B) <-> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (r2_zf_model(B,C) <-> r2_zf_model(A,C))))))))) # label(t7_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4641 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (m1_ordinal4(B,A) -> (k1_xboole_0 != B -> m1_subset_1(k4_classes1(B),A) & -v1_xboole_0(k4_classes1(B))))))) # label(t34_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4642 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (m1_ordinal4(B,A) -> (all C (m2_ordinal4(C,A) -> -(v2_ordinal2(C) & (all D (m1_ordinal4(D,A) -> -(k4_ordinal4(A,C,D) = D & r2_hidden(B,D)))) & v3_ordinal2(C) & r2_hidden(k5_ordinal2,A)))))))) # label(t30_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4643 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (m1_ordinal4(B,A) -> -(r2_hidden(k5_ordinal2,A) & (all C (m1_ordinal4(C,A) -> (all D (-v1_xboole_0(D) -> -(r2_hidden(B,C) & r3_zfrefle1(D,A) & D = k4_classes1(C))))))))))) # label(t36_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4644 (all A (v1_classes2(A) & -v1_xboole_0(A) -> -((all B (m2_ordinal4(B,A) -> -(v3_ordinal2(B) & (all C (m1_ordinal4(C,A) -> (all D (-v1_xboole_0(D) -> (k4_classes1(C) = D & k4_ordinal4(A,B,C) = C -> k1_xboole_0 = C | r3_zfrefle1(D,A)))))) & v2_ordinal2(B)))) & r2_hidden(k5_ordinal2,A)))) # label(t35_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4645 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k9_zf_lang)) -> ((all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> (r2_hidden(C,B) -> r2_zf_model(A,C)))) <-> r1_zfrefle1(A,B)))))) # label(d1_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4646 (all A ((all B (-(B != k6_zf_model & B != k10_zf_model & (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> -(r1_xboole_0(k1_enumset1(k2_zf_lang(np__0),k2_zf_lang(np__1),k2_zf_lang(np__2)),k2_zf_model(C)) & B = k11_zf_model(C)))) & k9_zf_model != B & B != k8_zf_model & k7_zf_model != B) & r2_hidden(B,k9_zf_lang) <-> r2_hidden(B,A))) <-> k1_zfrefle1 = A)) # label(d4_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4647 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r4_zfrefle1(A,B) -> r1_tarski(B,A)))))) # label(t22_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4648 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (r2_zfrefle1(A,B) <-> (all C (m1_subset_1(C,k1_zfmisc_1(k9_zf_lang)) -> (r1_zfrefle1(A,C) <-> r1_zfrefle1(B,C))))))))) # label(t8_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4649 (all A all B (v1_classes2(B) & -v1_xboole_0(B) -> -(r2_hidden(k5_ordinal2,B) & r2_hidden(A,B) & (all C (-v1_xboole_0(C) -> -(r2_hidden(A,C) & r2_hidden(C,B) & v1_zf_model(C))))))) # label(t43_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4650 (all A (-v1_xboole_0(A) & v1_classes2(A) -> -(r2_hidden(k5_ordinal2,A) & (all B (m1_ordinal4(B,A) -> (all C (-v1_xboole_0(C) -> -(r4_zfrefle1(B,k5_ordinal2) & r2_zfrefle1(C,A) & C = k4_classes1(B))))))))) # label(t41_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4651 (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]. 17.36/16.72 4652 $T # label(t7_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4653 (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]. 17.36/16.72 4654 (all A (m1_subset_1(A,k8_qc_lang1) -> A = k10_qc_lang1(A))) # label(d12_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4655 (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]. 17.36/16.72 4656 $T # label(t6_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4657 (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]. 17.36/16.72 4658 $T # label(t26_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4659 $T # label(t39_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4660 (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]. 17.36/16.72 4661 $T # label(t43_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4662 (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]. 17.36/16.72 4663 $T # label(t19_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4664 $T # label(t42_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4665 (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]. 17.36/16.72 4666 $T # label(t8_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4667 $T # label(t18_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4668 (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]. 17.36/16.72 4669 $T # label(t14_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4670 $T # label(t44_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4671 (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]. 17.36/16.72 4672 (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]. 17.36/16.72 4673 (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]. 17.36/16.72 4674 $T # label(t28_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4675 (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]. 17.36/16.72 4676 (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]. 17.36/16.72 4677 (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]. 17.36/16.72 4678 (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]. 17.36/16.72 4679 (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]. 17.36/16.72 4680 $T # label(t15_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4681 (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]. 17.36/16.72 4682 $T # label(t20_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4683 (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]. 17.36/16.72 4684 $T # label(t32_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4685 $T # label(t11_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4686 $T # label(t12_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4687 (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]. 17.36/16.72 4688 (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]. 17.36/16.72 4689 (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]. 17.36/16.72 4690 (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]. 17.36/16.72 4691 $T # label(t25_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4692 $T # label(t9_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.72 4693 (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]. 17.36/16.73 4694 $T # label(t3_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.73 4695 (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]. 17.36/16.73 4696 $T # label(t41_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.73 4697 $T # label(dt_k1_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.73 4698 (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]. 17.36/16.73 4699 (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]. 17.36/16.73 4700 $T # label(t29_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.73 4701 (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]. 17.36/16.73 4702 (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]. 17.36/16.73 4703 (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]. 17.36/16.73 4704 $T # label(t17_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.73 4705 (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]. 17.36/16.73 4706 $T # label(t38_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.73 4707 (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]. 17.36/16.73 4708 (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]. 17.36/16.73 4709 (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]. 17.36/16.73 4710 (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]. 17.36/16.73 4711 (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]. 17.36/16.73 4712 $T # label(t16_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.73 4713 (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]. 17.36/16.73 4714 $T # label(t27_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.73 4715 (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]. 17.36/16.73 4716 (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]. 17.36/16.73 4717 (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]. 17.36/16.73 4718 (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]. 17.36/16.73 4719 (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]. 17.36/16.73 4720 $T # label(t13_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.73 4721 (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]. 17.36/16.73 4722 (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]. 17.36/16.73 4723 (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]. 17.36/16.73 4724 (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]. 17.36/16.73 4725 (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]. 17.36/16.73 4726 (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]. 17.36/16.73 4727 $T # label(t24_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.73 4728 $T # label(t22_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.73 4729 (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]. 17.36/16.73 4730 (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]. 17.36/16.73 4731 (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]. 17.36/16.74 4732 (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]. 17.36/16.74 4733 (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]. 17.36/16.74 4734 (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]. 17.36/16.74 4735 $T # label(t31_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.74 4736 (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]. 17.36/16.74 4737 $T # label(t30_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.74 4738 (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]. 17.36/16.74 4739 $T # label(t5_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.74 4740 (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]. 17.36/16.74 4741 (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]. 17.36/16.74 4742 $T # label(dt_k5_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.74 4743 $T # label(t40_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.74 4744 (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]. 17.36/16.74 4745 (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]. 17.36/16.74 4746 (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]. 17.36/16.74 4747 (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]. 17.36/16.74 4748 (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]. 17.36/16.74 4749 (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]. 17.36/16.74 4750 (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]. 17.36/16.74 4751 (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]. 17.36/16.74 4752 (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]. 17.36/16.74 4753 (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]. 17.36/16.74 4754 (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]. 17.36/16.74 4755 (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]. 17.36/16.74 4756 (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]. 17.36/16.74 4757 (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]. 17.36/16.74 4758 (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]. 17.36/16.74 4759 (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]. 17.36/16.74 4760 (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]. 17.36/16.74 4761 (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]. 17.36/16.74 4762 (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]. 17.36/16.74 4763 $T # label(t15_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.74 4764 (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]. 17.36/16.74 4765 (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]. 17.36/16.74 4766 (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]. 17.36/16.74 4767 (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]. 17.36/16.74 4768 (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]. 17.36/16.74 4769 (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]. 17.36/16.74 4770 $T # label(t41_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.74 4771 $T # label(t69_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.74 4772 $T # label(t36_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.74 4773 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> 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]. 17.36/16.74 4774 (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]. 17.36/16.74 4775 $T # label(t57_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.74 4776 (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]. 17.36/16.74 4777 (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]. 17.36/16.74 4778 (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]. 17.36/16.74 4779 (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]. 17.36/16.74 4780 (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]. 17.36/16.74 4781 (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]. 17.36/16.74 4782 (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]. 17.36/16.74 4783 (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]. 17.36/16.74 4784 (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]. 17.36/16.74 4785 (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]. 17.36/16.74 4786 (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]. 17.36/16.74 4787 (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]. 17.36/16.74 4788 (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]. 17.36/16.74 4789 (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]. 17.36/16.74 4790 (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]. 17.36/16.74 4791 $T # label(t68_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.74 4792 (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]. 17.36/16.74 4793 (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]. 17.36/16.74 4794 (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]. 17.36/16.74 4795 (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]. 17.36/16.74 4796 $T # label(t37_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.74 4797 (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]. 17.36/16.74 4798 (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]. 17.36/16.74 4799 (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]. 17.36/16.74 4800 (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]. 17.36/16.74 4801 (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]. 17.36/16.74 4802 (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]. 17.36/16.74 4803 (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]. 17.36/16.74 4804 (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]. 17.36/16.74 4805 (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]. 17.36/16.74 4806 (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]. 17.36/16.74 4807 (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]. 17.36/16.74 4808 (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]. 17.36/16.74 4809 (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]. 17.36/16.74 4810 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (-(-(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]. 17.36/16.74 4811 $T # label(t40_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.74 4812 $T # label(t35_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.74 4813 (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]. 17.36/16.74 4814 (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]. 17.36/16.74 4815 (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]. 17.36/16.74 4816 (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]. 17.36/16.74 4817 (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]. 17.36/16.74 4818 (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]. 17.36/16.74 4819 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (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]. 17.36/16.74 4820 $T # label(d17_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.74 4821 (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]. 17.36/16.74 4822 (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]. 17.36/16.74 4823 (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]. 17.36/16.74 4824 (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]. 17.36/16.74 4825 (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]. 17.36/16.74 4826 (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]. 17.36/16.74 4827 (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]. 17.36/16.74 4828 (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]. 17.36/16.74 4829 (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]. 17.36/16.74 4830 (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]. 17.36/16.74 4831 (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]. 17.36/16.74 4832 $T # label(t10_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.74 4833 (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]. 17.36/16.74 4834 (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]. 17.36/16.74 4835 $T # label(t12_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.74 4836 (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]. 17.36/16.74 4837 (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]. 17.36/16.74 4838 $T # label(dt_k15_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.74 4839 (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]. 17.36/16.74 4840 (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]. 17.36/16.74 4841 (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]. 17.36/16.74 4842 $T # label(t44_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.74 4843 (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]. 17.36/16.74 4844 (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]. 17.36/16.74 4845 (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]. 17.36/16.74 4846 (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]. 17.36/16.74 4847 (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]. 17.36/16.74 4848 (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]. 17.36/16.74 4849 (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]. 17.36/16.74 4850 (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]. 17.36/16.74 4851 (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]. 17.36/16.74 4852 (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]. 17.36/16.74 4853 (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]. 17.36/16.74 4854 (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]. 17.36/16.74 4855 $T # label(t11_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.74 4856 (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]. 17.36/16.74 4857 (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]. 17.36/16.74 4858 (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]. 17.36/16.74 4859 (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]. 17.36/16.74 4860 (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]. 17.36/16.74 4861 $T # label(t43_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.74 4862 (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]. 17.36/16.74 4863 (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]. 17.36/16.74 4864 (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]. 17.36/16.74 4865 (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]. 17.36/16.74 4866 (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]. 17.36/16.74 4867 (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]. 17.36/16.74 4868 (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]. 17.36/16.74 4869 $T # label(t34_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.74 4870 (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]. 17.36/16.74 4871 (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]. 17.36/16.74 4872 (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]. 17.36/16.74 4873 $T # label(t70_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.74 4874 (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]. 17.36/16.74 4875 (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]. 17.36/16.74 4876 (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]. 17.36/16.74 4877 (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]. 17.36/16.74 4878 (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]. 17.36/16.74 4879 (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]. 17.36/16.74 4880 $T # label(t9_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.74 4881 (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]. 17.36/16.74 4882 $T # label(t106_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.74 4883 (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]. 17.36/16.74 4884 $T # label(t102_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.74 4885 (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]. 17.36/16.74 4886 (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]. 17.36/16.74 4887 (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]. 17.36/16.74 4888 (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]. 17.36/16.74 4889 (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]. 17.36/16.74 4890 (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]. 17.36/16.74 4891 (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]. 17.36/16.74 4892 (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]. 17.36/16.74 4893 (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]. 17.36/16.74 4894 (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]. 17.36/16.74 4895 (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]. 17.36/16.74 4896 (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]. 17.36/16.74 4897 (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]. 17.36/16.74 4898 (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]. 17.36/16.74 4899 (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]. 17.36/16.74 4900 (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]. 17.36/16.74 4901 $T # label(t42_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.74 4902 (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]. 17.36/16.74 4903 (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]. 17.36/16.74 4904 (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]. 17.36/16.74 4905 (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]. 17.36/16.74 4906 $T # label(t39_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 17.36/16.74 4907 (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]. 17.36/16.74 4908 (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]. 17.36/16.74 4909 (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]. 17.36/16.74 4910 $T # label(t4_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 17.36/16.74 4911 (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]. 17.36/16.74 4912 (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]. 17.36/16.74 4913 (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]. 17.36/16.74 4914 (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]. 17.36/16.74 4915 (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]. 17.36/16.75 4916 (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]. 17.36/16.75 4917 $T # label(t12_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 17.36/16.75 4918 $T # label(dt_k3_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 17.36/16.75 4919 (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]. 17.36/16.75 4920 (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]. 17.36/16.75 4921 $T # label(t8_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 17.36/16.75 4922 (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]. 17.36/16.75 4923 (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]. 17.36/16.75 4924 (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]. 17.36/16.75 4925 (all A all B B = k1_funct_1(k3_cqc_lang(A,B),A)) # label(t6_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 17.36/16.75 4926 (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]. 17.36/16.75 4927 (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]. 17.36/16.75 4928 (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]. 17.36/16.75 4929 (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]. 17.36/16.75 4930 (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]. 17.36/16.75 4931 (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]. 17.36/16.75 4932 (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]. 17.36/16.75 4933 (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]. 17.36/16.75 4934 (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]. 17.36/16.75 4935 (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]. 17.36/16.75 4936 $T # label(dt_k1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 17.36/16.75 4937 (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]. 17.36/16.75 4938 (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]. 17.36/16.75 4939 (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]. 17.36/16.75 4940 (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]. 17.36/16.75 4941 (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]. 17.36/16.75 4942 $T # label(t14_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 17.36/16.75 4943 (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]. 17.36/16.75 4944 $T # label(t27_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 17.36/16.75 4945 (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]. 17.36/16.75 4946 (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]. 17.36/16.75 4947 (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]. 17.36/16.75 4948 (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]. 17.36/16.75 4949 (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]. 17.36/16.75 4950 (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]. 17.36/16.75 4951 (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]. 17.36/16.75 4952 (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]. 17.36/16.75 4953 (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]. 17.36/16.75 4954 (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]. 17.36/16.75 4955 (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]. 17.36/16.75 4956 $T # label(t26_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 17.36/16.75 4957 $T # label(t2_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 17.36/16.75 4958 (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]. 17.36/16.75 4959 $T # label(t3_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 17.36/16.75 4960 (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]. 17.36/16.75 4961 (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]. 17.36/16.75 4962 (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]. 17.36/16.75 4963 (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]. 17.36/16.75 4964 (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]. 17.36/16.75 4965 (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]. 17.36/16.75 4966 (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]. 17.36/16.75 4967 (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]. 17.36/16.75 4968 (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]. 17.36/16.75 4969 (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]. 17.36/16.75 4970 (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]. 17.36/16.75 4971 (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]. 17.36/16.75 4972 (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]. 17.36/16.75 4973 (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]. 17.36/16.75 4974 (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]. 17.36/16.75 4975 (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]. 17.36/16.75 4976 (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]. 17.36/16.75 4977 (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]. 17.36/16.75 4978 (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]. 17.36/16.75 4979 (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]. 17.36/16.75 4980 (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]. 17.36/16.75 4981 (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]. 17.36/16.75 4982 $T # label(t1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 17.36/16.75 4983 (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]. 17.36/16.75 4984 (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]. 17.36/16.75 4985 (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]. 17.36/16.75 4986 (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]. 17.36/16.75 4987 $T # label(t9_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 17.36/16.75 4988 (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]. 17.36/16.75 4989 (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]. 17.36/16.75 4990 (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]. 17.36/16.75 4991 (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]. 17.36/16.75 4992 (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]. 17.36/16.75 4993 (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]. 17.36/16.75 4994 $T # label(t25_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 17.36/16.75 4995 (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]. 17.36/16.75 4996 (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]. 17.36/16.75 4997 (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]. 17.36/16.75 4998 (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]. 17.36/16.75 4999 (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]. 17.36/16.75 5000 (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]. 17.36/16.75 5001 (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]. 17.36/16.75 5002 (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]. 17.36/16.75 5003 $T # label(t93_pboole) # label(axiom) # label(non_clause). [assumption]. 17.36/16.75 5004 (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]. 17.36/16.75 5005 (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]. 17.36/16.75 5006 (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]. 17.36/16.75 5007 (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]. 17.36/16.75 5008 (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]. 17.36/16.75 5009 (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]. 17.36/16.75 5010 (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]. 17.36/16.75 5011 (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]. 17.36/16.75 5012 (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]. 17.36/16.75 5013 (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]. 17.36/16.75 5014 (all A (m1_pboole(A,k1_xboole_0) -> A = k1_xboole_0)) # label(t134_pboole) # label(axiom) # label(non_clause). [assumption]. 17.36/16.75 5015 (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]. 17.36/16.75 5016 (all A k1_pboole(A) = k2_funcop_1(A,k1_xboole_0)) # label(d6_pboole) # label(axiom) # label(non_clause). [assumption]. 17.36/16.75 5017 $T # label(t107_pboole) # label(axiom) # label(non_clause). [assumption]. 17.36/16.75 5018 (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]. 17.36/16.75 5019 (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]. 17.36/16.75 5020 (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]. 17.36/16.75 5021 (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]. 17.36/16.75 5022 (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]. 17.36/16.75 5023 (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]. 17.36/16.75 5024 (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]. 17.36/16.75 5025 (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]. 17.36/16.75 5026 (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]. 17.36/16.75 5027 (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]. 17.36/16.75 5028 (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]. 17.36/16.75 5029 (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]. 17.36/16.75 5030 (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]. 17.36/16.75 5031 (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]. 17.36/16.75 5032 (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]. 17.36/16.75 5033 (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]. 17.36/16.75 5034 (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]. 17.36/16.75 5035 (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]. 17.36/16.75 5036 (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]. 17.36/16.75 5037 (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]. 17.36/16.75 5038 (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]. 17.36/16.75 5039 (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]. 17.36/16.75 5040 (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]. 17.36/16.75 5041 (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]. 17.36/16.75 5042 (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]. 17.36/16.75 5043 (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]. 17.36/16.75 5044 (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]. 17.36/16.75 5045 (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]. 17.36/16.75 5046 (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]. 17.36/16.75 5047 (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]. 17.36/16.75 5048 (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]. 17.36/16.76 5049 (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]. 17.36/16.76 5050 (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]. 17.36/16.76 5051 (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]. 17.36/16.76 5052 (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]. 17.36/16.76 5053 (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]. 17.36/16.76 5054 $T # label(t31_pboole) # label(axiom) # label(non_clause). [assumption]. 17.36/16.76 5055 (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]. 17.36/16.76 5056 (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]. 17.36/16.76 5057 (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]. 17.36/16.76 5058 (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]. 17.36/16.76 5059 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r1_pboole(A,B,D) & r1_pboole(A,B,C) -> r4_pboole(A,C,D)))))))) # label(t10_pboole) # label(axiom) # label(non_clause). [assumption]. 17.36/16.76 5060 (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]. 17.36/16.76 5061 (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]. 17.36/16.76 5062 (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]. 17.36/16.76 5063 (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]. 17.36/16.76 5064 (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]. 17.36/16.76 5065 (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]. 17.36/16.76 5066 (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]. 17.36/16.76 5067 (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]. 17.36/16.76 5068 (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]. 17.36/16.76 5069 (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]. 17.36/16.76 5070 (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]. 17.36/16.76 5071 (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]. 17.36/16.76 5072 (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]. 17.36/16.76 5073 (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]. 17.36/16.76 5074 (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]. 17.36/16.76 5075 (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]. 17.36/16.76 5076 $T # label(t125_pboole) # label(axiom) # label(non_clause). [assumption]. 17.36/16.76 5077 (all A m1_pboole(k1_pboole(A),A)) # label(dt_k1_pboole) # label(axiom) # label(non_clause). [assumption]. 17.36/16.76 5078 (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]. 17.36/16.76 5079 (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]. 17.36/16.76 5080 (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]. 17.36/16.76 5081 (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]. 17.36/16.76 5082 (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]. 17.36/16.76 5083 (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]. 17.36/16.76 5084 (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]. 17.36/16.76 5085 (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]. 17.36/16.76 5086 (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]. 17.36/16.76 5087 (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]. 17.36/16.76 5088 (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]. 17.36/16.76 5089 (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]. 17.36/16.76 5090 (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]. 17.36/16.76 5091 (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]. 17.36/16.76 5092 (all A all B k1_funct_1(k1_pboole(B),A) = k1_xboole_0) # label(t5_pboole) # label(axiom) # label(non_clause). [assumption]. 17.36/16.76 5093 (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]. 17.36/16.76 5094 (exists A (v1_relat_1(A) & v1_funct_1(A) & v3_relat_1(A))) # label(rc1_pboole) # label(axiom) # label(non_clause). [assumption]. 17.36/16.76 5095 (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]. 17.36/16.76 5096 (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]. 17.36/16.76 5097 (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]. 17.36/16.76 5098 (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]. 17.36/16.76 5099 (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]. 17.36/16.76 5100 (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]. 17.36/16.76 5101 (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]. 17.36/16.76 5102 $T # label(t117_pboole) # label(axiom) # label(non_clause). [assumption]. 17.36/16.76 5103 (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]. 17.36/16.76 5104 (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]. 17.36/16.76 5105 (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]. 17.36/16.76 5106 (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]. 17.36/16.76 5107 (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]. 17.36/16.76 5108 (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]. 17.36/16.76 5109 (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]. 17.36/16.76 5110 $T # label(t13_pboole) # label(axiom) # label(non_clause). [assumption]. 17.36/16.76 5111 (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]. 17.36/16.76 5112 (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]. 17.36/16.76 5113 (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]. 17.36/16.76 5114 (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]. 17.36/16.76 5115 (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]. 17.36/16.76 5116 (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]. 17.36/16.76 5117 $T # label(d1_pboole) # label(axiom) # label(non_clause). [assumption]. 17.36/16.76 5118 (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]. 17.36/16.76 5119 (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]. 17.36/16.76 5120 (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]. 17.36/16.76 5121 $T # label(t90_pboole) # label(axiom) # label(non_clause). [assumption]. 17.36/16.76 5122 $T # label(t131_pboole) # label(axiom) # label(non_clause). [assumption]. 17.36/16.76 5123 (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]. 17.36/16.76 5124 (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]. 17.36/16.76 5125 (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]. 17.36/16.76 5126 (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]. 17.36/16.76 5127 (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]. 17.36/16.76 5128 (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]. 17.36/16.76 5129 (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]. 17.36/16.76 5130 (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]. 17.36/16.76 5131 (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]. 17.36/16.76 5132 (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]. 17.36/16.76 5133 (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]. 17.36/16.76 5134 (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]. 17.36/16.76 5135 (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]. 17.36/16.76 5136 (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]. 17.36/16.76 5137 (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]. 17.36/16.76 5138 $T # label(t33_pboole) # label(axiom) # label(non_clause). [assumption]. 17.36/16.76 5139 (all A exists B m1_pboole(B,A)) # label(existence_m1_pboole) # label(axiom) # label(non_clause). [assumption]. 17.36/16.76 5140 (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]. 17.36/16.76 5141 (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]. 17.36/16.76 5142 (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]. 17.36/16.76 5143 (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]. 17.36/16.76 5144 $T # label(t14_pboole) # label(axiom) # label(non_clause). [assumption]. 17.36/16.76 5145 (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]. 17.36/16.76 5146 (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]. 17.36/16.76 5147 (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]. 17.36/16.76 5148 (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]. 17.36/16.76 5149 $T # label(d2_pboole) # label(axiom) # label(non_clause). [assumption]. 17.36/16.76 5150 (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]. 17.36/16.76 5151 (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]. 17.36/16.76 5152 (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]. 17.36/16.76 5153 $T # label(t32_pboole) # label(axiom) # label(non_clause). [assumption]. 17.36/16.76 5154 (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]. 17.36/16.76 5155 (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]. 17.36/16.76 5156 (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]. 17.36/16.76 5157 (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]. 17.36/16.76 5158 (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]. 17.36/16.76 5159 (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]. 17.36/16.76 5160 (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]. 17.36/16.76 5161 (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]. 17.36/16.76 5162 (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]. 17.36/16.76 5163 (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]. 17.36/16.76 5164 (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]. 17.36/16.76 5165 (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]. 17.36/16.76 5166 (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]. 17.36/16.76 5167 (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]. 17.36/16.76 5168 (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]. 17.36/16.76 5169 (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]. 17.36/16.76 5170 (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]. 17.36/16.76 5171 (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]. 17.36/16.76 5172 (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]. 17.36/16.76 5173 (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]. 17.36/16.76 5174 (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]. 17.36/16.76 5175 (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]. 17.36/16.76 5176 (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]. 17.36/16.76 5177 (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]. 17.36/16.76 5178 (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]. 17.36/16.76 5179 (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]. 17.36/16.76 5180 (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]. 17.36/16.76 5181 (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]. 17.36/16.76 5182 (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]. 17.36/16.76 5183 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B all C k2_finseq_2(A,C) = k5_relat_1(k2_finseq_2(A,B),k2_funcop_1(k1_tarski(B),C))))) # label(t152_pboole) # label(axiom) # label(non_clause). [assumption]. 17.36/16.76 5184 (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]. 17.36/16.76 5185 (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]. 17.36/16.76 5186 (all A all B (m1_pboole(B,A) -> r2_pboole(A,k1_pboole(A),B))) # label(t49_pboole) # label(axiom) # label(non_clause). [assumption]. 17.36/16.76 5187 (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]. 17.36/16.76 5188 (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]. 17.36/16.76 5189 (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]. 17.36/16.76 5190 (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]. 17.36/16.76 5191 (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]. 17.36/16.76 5192 (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]. 17.36/16.76 5193 (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]. 17.36/16.76 5194 (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]. 17.36/16.76 5195 (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]. 17.36/16.76 5196 (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]. 17.36/16.76 5197 (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]. 17.36/16.76 5198 (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]. 17.36/16.76 5199 (all A all B k2_funcop_1(A,B) = k10_pboole(A,B)) # label(redefinition_k10_pboole) # label(axiom) # label(non_clause). [assumption]. 17.36/16.76 5200 (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]. 17.36/16.76 5201 (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]. 17.36/16.76 5202 (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]. 17.36/16.76 5203 (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]. 17.36/16.76 5204 (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]. 17.36/16.76 5205 (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]. 17.36/16.76 5206 (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]. 17.36/16.76 5207 (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]. 17.36/16.76 5208 (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]. 17.36/16.76 5209 (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]. 17.36/16.76 5210 (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]. 17.36/16.76 5211 (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]. 17.36/16.76 5212 (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]. 17.36/16.76 5213 (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]. 17.36/16.76 5214 (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]. 17.36/16.76 5215 (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]. 17.36/16.76 5216 (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]. 17.36/16.76 5217 (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]. 17.36/16.76 5218 (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]. 17.36/16.76 5219 (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]. 17.36/16.76 5220 (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]. 17.36/16.76 5221 (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]. 17.36/16.76 5222 (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]. 17.36/16.76 5223 (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]. 17.36/16.76 5224 $T # label(t30_pboole) # label(axiom) # label(non_clause). [assumption]. 17.36/16.76 5225 (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]. 17.36/16.76 5226 (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]. 17.36/16.76 5227 (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]. 17.36/16.76 5228 (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]. 17.36/16.76 5229 (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]. 17.36/16.76 5230 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> m1_subset_1(k5_seq_4(A),k1_numbers))) # label(dt_k5_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.76 5231 (all A (v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> (v4_seq_2(A) -> v4_seq_2(k22_seq_1(A))))) # label(t26_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.76 5232 $T # label(t12_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.76 5233 (all A (v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) -> (v1_seq_2(A) & v3_seqm_3(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> r1_xreal_0(k8_funct_2(k5_numbers,k1_numbers,A,B),k2_seq_2(A))))))) # label(t54_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.76 5234 (all A (v2_membered(A) -> v1_xreal_0(k2_seq_4(A)))) # label(dt_k2_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.76 5235 (all A (v1_xreal_0(A) -> k1_seq_4(A) = k1_tarski(A))) # label(redefinition_k1_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.76 5236 (all A (v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> (exists B (v1_funct_2(B,k5_numbers,k1_numbers) & v1_seqm_3(B) & m2_relset_1(B,k5_numbers,k1_numbers) & v6_seqm_3(k3_seqm_3(B,A)) & v7_seqm_3(B) & v1_funct_1(B))))) # label(t56_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.76 5237 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> (v3_seq_4(A) -> r1_xreal_0(k5_seq_4(A),k4_seq_4(A)) | v1_xboole_0(A)))) # label(t24_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.76 5238 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_funct_1(B) & m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_2(B,k5_numbers,k1_numbers) -> (v4_seq_2(B) -> k2_seq_2(B) = k2_seq_2(k1_seqm_3(B,A)) & v4_seq_2(k1_seqm_3(B,A))))))) # label(t33_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.76 5239 (all A (-v1_xboole_0(A) & v2_membered(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> ((all D (v1_xreal_0(D) -> (r2_hidden(D,A) -> r1_xreal_0(D,C)))) -> r1_xreal_0(k2_seq_4(A),C)))))))) # label(t62_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.76 5240 (all A (v2_membered(A) -> ((exists B ((all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r1_xreal_0(B,C)))) & v1_xreal_0(B))) <-> v2_seq_4(A)))) # label(d2_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.76 5241 (all A (v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) -> (v4_seq_2(A) <-> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(B,np__0) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (exists D (m2_subset_1(D,k1_numbers,k5_numbers) & r1_xreal_0(B,k18_complex1(k5_real_1(k8_funct_2(k5_numbers,k1_numbers,A,D),k8_funct_2(k5_numbers,k1_numbers,A,C)))) & r1_xreal_0(C,D))))))))))) # label(t58_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.76 5242 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> k5_seq_4(A) = k3_seq_4(A))) # label(redefinition_k5_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5243 (all A (m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_2(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> (v2_seq_2(A) & v4_seqm_3(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> r1_xreal_0(k2_seq_2(A),k8_funct_2(k5_numbers,k1_numbers,A,B))))))) # label(t55_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5244 (all A (v1_funct_1(A) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_2(A,k5_numbers,k1_numbers) -> -((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> -v2_relat_1(k1_seqm_3(A,B)))) & np__0 != k2_seq_2(A) & v4_seq_2(A)))) # label(t37_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5245 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (m2_relset_1(C,k5_numbers,k1_numbers) & v1_funct_2(C,k5_numbers,k1_numbers) & v1_funct_1(C) -> ((all D (m2_subset_1(D,k1_numbers,k5_numbers) -> k7_xcmplx_0(B,k2_xcmplx_0(k2_nat_1(D,D),A)) = k8_funct_2(k5_numbers,k1_numbers,C,D))) -> v4_seq_2(C) & k2_seq_2(C) = np__0 | r1_xreal_0(A,np__0)))))))) # label(t50_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5246 (all A (v1_funct_1(A) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_2(A,k5_numbers,k1_numbers) -> (v5_seqm_3(A) -> v4_seq_2(A)))) # label(t39_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5247 (all A (v2_membered(A) & -v1_xboole_0(A) -> (all B (v2_membered(B) -> (r1_tarski(A,B) & v2_seq_4(B) -> r1_xreal_0(k3_seq_4(B),k3_seq_4(A))))))) # label(t64_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5248 (all A (v2_membered(A) & -v1_xboole_0(A) -> (all B (v1_xreal_0(B) -> ((all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r1_xreal_0(C,B)))) & (all C (v1_xreal_0(C) -> ((all D (v1_xreal_0(D) -> (r2_hidden(D,A) -> r1_xreal_0(D,C)))) -> r1_xreal_0(B,C)))) -> k2_seq_4(A) = B))))) # label(t63_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5249 (all A (v1_xreal_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_2(B,k5_numbers,k1_numbers) -> (v5_seqm_3(B) & r2_hidden(A,k2_relat_1(B)) | (exists C (A = k8_funct_2(k5_numbers,k1_numbers,B,C) & m2_subset_1(C,k1_numbers,k5_numbers))) & v5_seqm_3(B) -> A = k2_seq_2(B)))))) # label(t40_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5250 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> (v2_seq_4(A) & v1_seq_4(A) <-> v3_seq_4(A)))) # label(d3_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5251 (all A (v1_xreal_0(A) -> (all B (v2_membered(B) & -v1_xboole_0(B) -> ((all C (v1_xreal_0(C) -> (r2_hidden(C,B) -> r1_xreal_0(A,C)))) & (all C (v1_xreal_0(C) -> ((all D (v1_xreal_0(D) -> (r2_hidden(D,B) -> r1_xreal_0(C,D)))) -> r1_xreal_0(C,A)))) -> k3_seq_4(B) = A))))) # label(t61_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5252 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v2_membered(C) -> ((all D (v1_xreal_0(D) -> (r2_hidden(D,C) -> r1_xreal_0(D,A)))) & (all D (v1_xreal_0(D) -> -((all E (v1_xreal_0(E) -> -(r2_hidden(E,C) & -r1_xreal_0(E,k6_xcmplx_0(A,D))))) & -r1_xreal_0(D,np__0)))) & (all D (v1_xreal_0(D) -> (r2_hidden(D,C) -> r1_xreal_0(D,B)))) & (all D (v1_xreal_0(D) -> -(-r1_xreal_0(D,np__0) & (all E (v1_xreal_0(E) -> -(-r1_xreal_0(E,k6_xcmplx_0(B,D)) & r2_hidden(E,C))))))) -> B = A))))))) # label(t17_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5253 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_funct_2(C,k5_numbers,k1_numbers) & m2_relset_1(C,k5_numbers,k1_numbers) & v1_funct_1(C) -> ((all D (m2_subset_1(D,k1_numbers,k5_numbers) -> k7_xcmplx_0(B,k2_xcmplx_0(D,A)) = k8_funct_2(k5_numbers,k1_numbers,C,D))) -> v4_seq_2(C) & k2_seq_2(C) = np__0 | r1_xreal_0(A,np__0)))))))) # label(t46_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5254 (all A (v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) -> (v6_seqm_3(A) & v3_seq_2(A) -> v4_seq_2(A)))) # label(t53_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5255 (all A (v2_membered(A) -> -(-v1_xboole_0(A) & v1_seq_4(A) & (all B (v1_xreal_0(B) -> -((all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r1_xreal_0(C,B)))) & (all C (v1_xreal_0(C) -> -(-r1_xreal_0(C,np__0) & (all D (v1_xreal_0(D) -> -(-r1_xreal_0(D,k6_xcmplx_0(B,C)) & r2_hidden(D,A))))))))))))) # label(t16_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5256 $T # label(t7_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5257 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> k4_seq_4(A) = k2_seq_4(A))) # label(redefinition_k4_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5258 (all A (v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> ((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k6_real_1(np__1,k1_nat_1(k2_nat_1(B,B),np__1)) = k8_funct_2(k5_numbers,k1_numbers,A,B))) -> np__0 = k2_seq_2(A) & v4_seq_2(A)))) # label(t49_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5259 (all A (v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_2(B,k5_numbers,k1_numbers) -> (v4_seq_2(A) -> v4_seq_2(B) | (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (exists D (k8_funct_2(k5_numbers,k1_numbers,A,D) != k8_funct_2(k5_numbers,k1_numbers,B,D) & r1_xreal_0(C,D) & m2_subset_1(D,k1_numbers,k5_numbers)))))))))) # label(t31_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5260 (all A (v1_xreal_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_numbers) & m2_relset_1(B,k5_numbers,k1_numbers) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k7_xcmplx_0(np__1,k2_xcmplx_0(k2_nat_1(C,C),A)) = k8_funct_2(k5_numbers,k1_numbers,B,C))) -> r1_xreal_0(A,np__0) | v4_seq_2(B)))))) # label(t47_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5261 (all A (v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) -> (v4_seq_2(A) -> k18_complex1(k2_seq_2(A)) = k2_seq_2(k22_seq_1(A))))) # label(t27_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5262 (all A (v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_2(B,k5_numbers,k1_numbers) -> (v4_seq_2(B) & m1_seqm_3(A,B) -> v4_seq_2(A)))))) # label(t29_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5263 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> (v3_seq_4(A) -> v1_xboole_0(A) | -((exists B (v1_xreal_0(B) & (exists C (C != B & r2_hidden(C,A) & r2_hidden(B,A) & v1_xreal_0(C))))) & r1_xreal_0(k4_seq_4(A),k5_seq_4(A))) & -(-r1_xreal_0(k4_seq_4(A),k5_seq_4(A)) & (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(r2_hidden(B,A) & C != B & r2_hidden(C,A)))))))))) # label(t25_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5264 $T # label(t34_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5265 $T # label(t3_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5266 $T # label(t6_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5267 (all A (v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> -(v4_seq_2(A) & (all B (m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_2(B,k5_numbers,k1_numbers) & v1_funct_1(B) -> -(v2_relat_1(B) & m1_seqm_3(B,A)))) & k2_seq_2(A) != np__0))) # label(t38_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5268 $T # label(t13_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5269 $T # label(t4_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5270 (all A (v1_xreal_0(A) -> m1_subset_1(k1_seq_4(A),k1_zfmisc_1(k1_numbers)))) # label(dt_k1_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5271 (all A (v1_funct_1(A) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_2(A,k5_numbers,k1_numbers) -> (all B (v1_funct_2(B,k5_numbers,k1_numbers) & m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_1(B) -> (v5_seqm_3(A) & v4_seq_2(B) -> k3_real_1(k8_funct_2(k5_numbers,k1_numbers,A,np__0),k2_seq_2(B)) = k2_seq_2(k9_seq_1(A,B)) & k2_seq_2(k10_seq_1(A,B)) = k5_real_1(k8_funct_2(k5_numbers,k1_numbers,A,np__0),k2_seq_2(B)) & k4_real_1(k8_funct_2(k5_numbers,k1_numbers,A,np__0),k2_seq_2(B)) = k2_seq_2(k11_seq_1(A,B)) & k2_seq_2(k10_seq_1(B,A)) = k5_real_1(k2_seq_2(B),k8_funct_2(k5_numbers,k1_numbers,A,np__0))))))) # label(t59_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5272 $T # label(t21_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5273 (all A (v2_membered(A) & -v1_xboole_0(A) -> (all B (v1_xreal_0(B) -> ((all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r1_xreal_0(B,C)))) -> r1_xreal_0(B,k3_seq_4(A))))))) # label(t60_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5274 (all A (v2_membered(A) -> -(-v1_xboole_0(A) & v2_seq_4(A) & (all B (v1_xreal_0(B) -> -((all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r1_xreal_0(B,C)))) & (all C (v1_xreal_0(C) -> -((all D (v1_xreal_0(D) -> -(-r1_xreal_0(k2_xcmplx_0(B,C),D) & r2_hidden(D,A)))) & -r1_xreal_0(C,np__0)))))))))) # label(t18_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5275 (all A (v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) -> (all B (m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_2(B,k5_numbers,k1_numbers) & v1_funct_1(B) -> (v4_seq_2(B) & m1_seqm_3(A,B) -> k2_seq_2(B) = k2_seq_2(A)))))) # label(t30_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5276 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> m1_subset_1(k4_seq_4(A),k1_numbers))) # label(dt_k4_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5277 (all A (v1_xreal_0(A) -> v3_seq_4(k1_seq_4(A)))) # label(t15_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5278 $T # label(t20_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5279 $T # label(t11_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5280 $T # label(t5_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5281 (all A (v1_xreal_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_numbers)) -> ((all C (v1_xreal_0(C) -> (r2_hidden(C,B) -> r2_hidden(k2_xcmplx_0(C,A),B)))) -> r1_xreal_0(A,np__0) | (all C (v1_xreal_0(C) -> (exists D (v1_xreal_0(D) & -r1_xreal_0(D,C) & r2_hidden(D,B))))) | (all C (v1_xreal_0(C) -> -r2_hidden(C,B)))))))) # label(t9_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5282 (all A (v1_xreal_0(A) -> k4_seq_4(k1_seq_4(A)) = A & k5_seq_4(k1_seq_4(A)) = A)) # label(t22_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5283 (all A (m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_2(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> (all B (v1_funct_2(B,k5_numbers,k1_numbers) & m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_1(B) -> (v4_seq_2(A) -> v4_seq_2(B) | (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k1_seqm_3(B,C) != A))))))) # label(t35_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5284 (all A (m1_relset_1(A,k5_numbers,k1_numbers) -> (v1_funct_1(A) & v5_seqm_3(A) & v1_funct_2(A,k5_numbers,k1_numbers) -> v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & v1_seq_1(A) & v4_seq_2(A)))) # label(cc1_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5285 (all A (v2_membered(A) -> (v1_seq_4(A) -> (all B (v1_xreal_0(B) -> ((all C (v1_xreal_0(C) -> -(-r1_xreal_0(C,np__0) & (all D (v1_xreal_0(D) -> -(-r1_xreal_0(D,k6_xcmplx_0(B,C)) & r2_hidden(D,A))))))) & (all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r1_xreal_0(C,B)))) <-> k2_seq_4(A) = B))) | v1_xboole_0(A)))) # label(d4_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5286 (all A (m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_2(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> (all B (v1_funct_2(B,k5_numbers,k1_numbers) & m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_1(B) -> (v4_seq_2(A) -> k2_seq_2(B) = k2_seq_2(A) | (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> A != k1_seqm_3(B,C)))))))) # label(t36_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5287 (all A (v2_membered(A) -> (v2_seq_4(A) -> v1_xboole_0(A) | (all B (v1_xreal_0(B) -> (k3_seq_4(A) = B <-> (all C (v1_xreal_0(C) -> -((all D (v1_xreal_0(D) -> -(-r1_xreal_0(k2_xcmplx_0(B,C),D) & r2_hidden(D,A)))) & -r1_xreal_0(C,np__0)))) & (all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r1_xreal_0(B,C)))))))))) # label(d5_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5288 (all A (v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) -> (all B (v1_funct_2(B,k5_numbers,k1_numbers) & m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_1(B) -> (v4_seq_2(A) -> k2_seq_2(B) = k2_seq_2(A) | (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (exists D (m2_subset_1(D,k1_numbers,k5_numbers) & r1_xreal_0(C,D) & k8_funct_2(k5_numbers,k1_numbers,B,D) != k8_funct_2(k5_numbers,k1_numbers,A,D)))))))))) # label(t32_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5289 (all A (v2_membered(A) & -v1_xboole_0(A) -> (all B (v2_membered(B) -> (r1_tarski(A,B) & v1_seq_4(B) -> r1_xreal_0(k2_seq_4(A),k2_seq_4(B))))))) # label(t65_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5290 (all A (v1_xreal_0(A) -> k4_seq_4(k1_seq_4(A)) = k5_seq_4(k1_seq_4(A)))) # label(t23_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5291 (all A (v2_membered(A) -> v1_xreal_0(k3_seq_4(A)))) # label(dt_k3_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5292 (all A (v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) -> (v5_seqm_3(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k8_funct_2(k5_numbers,k1_numbers,A,B) = k2_seq_2(A)))))) # label(t41_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5293 (all A (v1_funct_1(A) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_2(A,k5_numbers,k1_numbers) -> (v4_seq_2(k22_seq_1(A)) & np__0 = k2_seq_2(k22_seq_1(A)) -> k2_seq_2(A) = np__0 & v4_seq_2(A)))) # label(t28_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5294 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v2_membered(C) -> ((all D (v1_xreal_0(D) -> (r2_hidden(D,C) -> r1_xreal_0(A,D)))) & (all D (v1_xreal_0(D) -> -((all E (v1_xreal_0(E) -> -(r2_hidden(E,C) & -r1_xreal_0(k2_xcmplx_0(A,D),E)))) & -r1_xreal_0(D,np__0)))) & (all D (v1_xreal_0(D) -> -((all E (v1_xreal_0(E) -> -(-r1_xreal_0(k2_xcmplx_0(B,D),E) & r2_hidden(E,C)))) & -r1_xreal_0(D,np__0)))) & (all D (v1_xreal_0(D) -> (r2_hidden(D,C) -> r1_xreal_0(B,D)))) -> A = B))))))) # label(t19_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5295 (all A (v2_membered(A) -> (v1_seq_4(A) <-> (exists B (v1_xreal_0(B) & (all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r1_xreal_0(C,B))))))))) # label(d1_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5296 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> (v3_seq_4(A) <-> (exists B (-r1_xreal_0(B,np__0) & (all C (v1_xreal_0(C) -> -(r1_xreal_0(B,k18_complex1(C)) & r2_hidden(C,A)))) & v1_xreal_0(B)))))) # label(t14_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5297 (all A (v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> (v1_seq_2(A) & v3_seqm_3(A) -> v4_seq_2(A)))) # label(t51_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5298 (all A (v1_xreal_0(A) -> -(all B (m2_subset_1(B,k1_numbers,k5_numbers) -> r1_xreal_0(B,A))))) # label(t10_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5299 (all A (v1_funct_1(A) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_2(A,k5_numbers,k1_numbers) -> (v4_seqm_3(A) & v2_seq_2(A) -> v4_seq_2(A)))) # label(t52_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5300 (all A (v1_xreal_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_numbers) & m2_relset_1(B,k5_numbers,k1_numbers) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k8_funct_2(k5_numbers,k1_numbers,B,C) = k7_xcmplx_0(np__1,k2_xcmplx_0(k2_nat_1(C,C),A)))) -> r1_xreal_0(A,np__0) | np__0 = k2_seq_2(B)))))) # label(t48_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5301 (all A (v1_xreal_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_numbers) & m2_relset_1(B,k5_numbers,k1_numbers) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k8_funct_2(k5_numbers,k1_numbers,B,C) = k7_xcmplx_0(np__1,k2_xcmplx_0(C,A)))) -> k2_seq_2(B) = np__0 | r1_xreal_0(A,np__0)))))) # label(t44_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5302 (all A (v1_xreal_0(A) -> (all B (v1_funct_2(B,k5_numbers,k1_numbers) & m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_1(B) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k8_funct_2(k5_numbers,k1_numbers,B,C) = k7_xcmplx_0(np__1,k2_xcmplx_0(C,A)))) -> v4_seq_2(B) | r1_xreal_0(A,np__0)))))) # label(t43_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5303 (all A (v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) -> ((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k6_real_1(np__1,k1_nat_1(B,np__1)) = k8_funct_2(k5_numbers,k1_numbers,A,B))) -> np__0 = k2_seq_2(A) & v4_seq_2(A)))) # label(t45_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5304 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_numbers)) -> -((all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(r2_hidden(C,A) & r1_xreal_0(D,C) & r2_hidden(D,B)))))) & (all C (v1_xreal_0(C) -> (exists D ((exists E (v1_xreal_0(E) & r2_hidden(D,A) & -(r1_xreal_0(D,C) & r1_xreal_0(C,E)) & r2_hidden(E,B))) & v1_xreal_0(D)))))))))) # label(t8_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5305 (all A (m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_2(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> (v4_seq_2(A) -> np__0 = k2_seq_2(A) | (all B (v1_funct_1(B) & m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_2(B,k5_numbers,k1_numbers) -> (m1_seqm_3(B,A) & v2_relat_1(B) -> k2_seq_2(k18_seq_1(B)) = k2_real_1(k2_seq_2(A)))))))) # label(t42_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5306 (all A (m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_2(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> -((all B (v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_numbers) & m2_relset_1(B,k5_numbers,k1_numbers) -> -(v4_seq_2(B) & m1_seqm_3(B,A)))) & v3_seq_2(A)))) # label(t57_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5307 $T # label(t2_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5308 $T # label(t1_seq_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5309 $T # label(dt_k3_multop_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5310 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_2(E,k3_zfmisc_1(A,B,C),D) & m2_relset_1(E,k3_zfmisc_1(A,B,C),D) & v1_funct_1(E) -> (all F (m2_relset_1(F,k3_zfmisc_1(A,B,C),D) & v1_funct_2(F,k3_zfmisc_1(A,B,C),D) & v1_funct_1(F) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> k2_multop_1(A,B,C,D,E,G,H,I) = k2_multop_1(A,B,C,D,F,G,H,I))))))) -> E = F))))))))))))) # label(t4_multop_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5311 $T # label(t1_multop_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5312 $T # label(dt_k1_multop_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5313 (exists A (v1_funct_1(A) & (all B (m1_subset_1(B,f1_s4_multop_1) -> (all C (m1_subset_1(C,f2_s4_multop_1) -> (all D (m1_subset_1(D,f3_s4_multop_1) -> k2_multop_1(f1_s4_multop_1,f2_s4_multop_1,f3_s4_multop_1,f4_s4_multop_1,A,B,C,D) = f5_s4_multop_1(B,C,D))))))) & m2_relset_1(A,k3_zfmisc_1(f1_s4_multop_1,f2_s4_multop_1,f3_s4_multop_1),f4_s4_multop_1) & v1_funct_2(A,k3_zfmisc_1(f1_s4_multop_1,f2_s4_multop_1,f3_s4_multop_1),f4_s4_multop_1))) # label(s4_multop_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5314 (all A (m1_subset_1(A,f1_s2_multop_1) -> (all B (m1_subset_1(B,f1_s2_multop_1) -> (all C (m1_subset_1(C,f1_s2_multop_1) -> (exists D (m1_subset_1(D,f1_s2_multop_1) & p1_s2_multop_1(A,B,C,D))))))))) -> (exists A (v1_funct_2(A,k3_zfmisc_1(f1_s2_multop_1,f1_s2_multop_1,f1_s2_multop_1),f1_s2_multop_1) & m2_relset_1(A,k3_zfmisc_1(f1_s2_multop_1,f1_s2_multop_1,f1_s2_multop_1),f1_s2_multop_1) & (all B (m1_subset_1(B,f1_s2_multop_1) -> (all C (m1_subset_1(C,f1_s2_multop_1) -> (all D (m1_subset_1(D,f1_s2_multop_1) -> p1_s2_multop_1(B,C,D,k2_multop_1(f1_s2_multop_1,f1_s2_multop_1,f1_s2_multop_1,f1_s2_multop_1,A,B,C,D)))))))) & v1_funct_1(A))) # label(s2_multop_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5315 (all A (-v1_xboole_0(A) -> (all B all C all D all E all F (m2_relset_1(F,k4_zfmisc_1(B,C,D,E),A) & v1_funct_2(F,k4_zfmisc_1(B,C,D,E),A) & v1_funct_1(F) -> (all G (m2_relset_1(G,k4_zfmisc_1(B,C,D,E),A) & v1_funct_2(G,k4_zfmisc_1(B,C,D,E),A) & v1_funct_1(G) -> ((all H all I all J all K (r2_hidden(J,D) & r2_hidden(K,E) & r2_hidden(I,C) & r2_hidden(H,B) -> k1_funct_1(F,k4_mcart_1(H,I,J,K)) = k1_funct_1(G,k4_mcart_1(H,I,J,K)))) -> F = G))))))) # label(t6_multop_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5316 $T # label(t5_multop_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5317 (all A (-v1_xboole_0(A) -> (all B all C all D all E (v1_funct_1(E) & v1_funct_2(E,k3_zfmisc_1(B,C,D),A) & m2_relset_1(E,k3_zfmisc_1(B,C,D),A) -> (all F (v1_funct_2(F,k3_zfmisc_1(B,C,D),A) & m2_relset_1(F,k3_zfmisc_1(B,C,D),A) & v1_funct_1(F) -> ((all G all H all I (r2_hidden(G,B) & r2_hidden(I,D) & r2_hidden(H,C) -> k1_funct_1(F,k3_mcart_1(G,H,I)) = k1_funct_1(E,k3_mcart_1(G,H,I)))) -> E = F))))))) # label(t2_multop_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5318 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (v1_funct_2(F,k4_zfmisc_1(A,B,C,D),E) & m2_relset_1(F,k4_zfmisc_1(A,B,C,D),E) & v1_funct_1(F) -> (all G (v1_funct_1(G) & v1_funct_2(G,k4_zfmisc_1(A,B,C,D),E) & m2_relset_1(G,k4_zfmisc_1(A,B,C,D),E) -> ((all H (m1_subset_1(H,A) -> (all I (m1_subset_1(I,B) -> (all J (m1_subset_1(J,C) -> (all K (m1_subset_1(K,D) -> k8_funct_2(k4_zfmisc_1(A,B,C,D),E,G,k5_domain_1(A,B,C,D,H,I,J,K)) = k8_funct_2(k4_zfmisc_1(A,B,C,D),E,F,k5_domain_1(A,B,C,D,H,I,J,K)))))))))) -> F = G))))))))))))))) # label(t7_multop_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5319 (exists A (v1_funct_1(A) & v1_funct_2(A,k3_zfmisc_1(f1_s3_multop_1,f2_s3_multop_1,f3_s3_multop_1),f4_s3_multop_1) & (all B (m1_subset_1(B,f1_s3_multop_1) -> (all C (m1_subset_1(C,f2_s3_multop_1) -> (all D (m1_subset_1(D,f3_s3_multop_1) -> k8_funct_2(k3_zfmisc_1(f1_s3_multop_1,f2_s3_multop_1,f3_s3_multop_1),f4_s3_multop_1,A,k4_domain_1(f1_s3_multop_1,f2_s3_multop_1,f3_s3_multop_1,B,C,D)) = f5_s3_multop_1(B,C,D))))))) & m2_relset_1(A,k3_zfmisc_1(f1_s3_multop_1,f2_s3_multop_1,f3_s3_multop_1),f4_s3_multop_1))) # label(s3_multop_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5320 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C all D all E k1_funct_1(A,k4_mcart_1(B,C,D,E)) = k3_multop_1(A,B,C,D,E)))) # label(d2_multop_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5321 (all A (m1_subset_1(A,f1_s6_multop_1) -> (all B (m1_subset_1(B,f1_s6_multop_1) -> (all C (m1_subset_1(C,f1_s6_multop_1) -> (all D (m1_subset_1(D,f1_s6_multop_1) -> (exists E (p1_s6_multop_1(A,B,C,D,E) & m1_subset_1(E,f1_s6_multop_1))))))))))) -> (exists A (v1_funct_1(A) & v1_funct_2(A,k4_zfmisc_1(f1_s6_multop_1,f1_s6_multop_1,f1_s6_multop_1,f1_s6_multop_1),f1_s6_multop_1) & m2_relset_1(A,k4_zfmisc_1(f1_s6_multop_1,f1_s6_multop_1,f1_s6_multop_1,f1_s6_multop_1),f1_s6_multop_1) & (all B (m1_subset_1(B,f1_s6_multop_1) -> (all C (m1_subset_1(C,f1_s6_multop_1) -> (all D (m1_subset_1(D,f1_s6_multop_1) -> (all E (m1_subset_1(E,f1_s6_multop_1) -> p1_s6_multop_1(B,C,D,E,k4_multop_1(f1_s6_multop_1,f1_s6_multop_1,f1_s6_multop_1,f1_s6_multop_1,f1_s6_multop_1,A,B,C,D,E)))))))))))) # label(s6_multop_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5322 (all A all B all C all D all E all F all G all H (-v1_xboole_0(A) & -v1_xboole_0(C) & -v1_xboole_0(D) & v1_funct_1(E) & v1_funct_2(E,k3_zfmisc_1(A,B,C),D) & m1_relset_1(E,k3_zfmisc_1(A,B,C),D) & m1_subset_1(H,C) & m1_subset_1(G,B) & m1_subset_1(F,A) & -v1_xboole_0(B) -> k2_multop_1(A,B,C,D,E,F,G,H) = k1_multop_1(E,F,G,H))) # label(redefinition_k2_multop_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5323 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (v1_funct_1(F) & m2_relset_1(F,k4_zfmisc_1(A,B,C,D),E) & v1_funct_2(F,k4_zfmisc_1(A,B,C,D),E) -> (all G (v1_funct_2(G,k4_zfmisc_1(A,B,C,D),E) & m2_relset_1(G,k4_zfmisc_1(A,B,C,D),E) & v1_funct_1(G) -> ((all H (m1_subset_1(H,A) -> (all I (m1_subset_1(I,B) -> (all J (m1_subset_1(J,C) -> (all K (m1_subset_1(K,D) -> k4_multop_1(A,B,C,D,E,F,H,I,J,K) = k4_multop_1(A,B,C,D,E,G,H,I,J,K))))))))) -> G = F))))))))))))))) # label(t8_multop_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5324 (all A all B all C all D all E all F all G all H (-v1_xboole_0(A) & m1_subset_1(G,B) & m1_subset_1(H,C) & m1_subset_1(F,A) & m1_relset_1(E,k3_zfmisc_1(A,B,C),D) & v1_funct_2(E,k3_zfmisc_1(A,B,C),D) & v1_funct_1(E) & -v1_xboole_0(D) & -v1_xboole_0(C) & -v1_xboole_0(B) -> m1_subset_1(k2_multop_1(A,B,C,D,E,F,G,H),D))) # label(dt_k2_multop_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5325 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C all D k1_multop_1(A,B,C,D) = k1_funct_1(A,k3_mcart_1(B,C,D))))) # label(d1_multop_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5326 (all A (m1_subset_1(A,f1_s1_multop_1) -> (all B (m1_subset_1(B,f2_s1_multop_1) -> (all C (m1_subset_1(C,f3_s1_multop_1) -> (exists D (m1_subset_1(D,f4_s1_multop_1) & p1_s1_multop_1(A,B,C,D))))))))) -> (exists A (v1_funct_2(A,k3_zfmisc_1(f1_s1_multop_1,f2_s1_multop_1,f3_s1_multop_1),f4_s1_multop_1) & m2_relset_1(A,k3_zfmisc_1(f1_s1_multop_1,f2_s1_multop_1,f3_s1_multop_1),f4_s1_multop_1) & (all B (m1_subset_1(B,f1_s1_multop_1) -> (all C (m1_subset_1(C,f2_s1_multop_1) -> (all D (m1_subset_1(D,f3_s1_multop_1) -> p1_s1_multop_1(B,C,D,k8_funct_2(k3_zfmisc_1(f1_s1_multop_1,f2_s1_multop_1,f3_s1_multop_1),f4_s1_multop_1,A,k4_domain_1(f1_s1_multop_1,f2_s1_multop_1,f3_s1_multop_1,B,C,D))))))))) & v1_funct_1(A))) # label(s1_multop_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5327 (exists A (m2_relset_1(A,k4_zfmisc_1(f1_s7_multop_1,f2_s7_multop_1,f3_s7_multop_1,f4_s7_multop_1),f5_s7_multop_1) & (all B (m1_subset_1(B,f1_s7_multop_1) -> (all C (m1_subset_1(C,f2_s7_multop_1) -> (all D (m1_subset_1(D,f3_s7_multop_1) -> (all E (m1_subset_1(E,f4_s7_multop_1) -> f6_s7_multop_1(B,C,D,E) = k8_funct_2(k4_zfmisc_1(f1_s7_multop_1,f2_s7_multop_1,f3_s7_multop_1,f4_s7_multop_1),f5_s7_multop_1,A,k5_domain_1(f1_s7_multop_1,f2_s7_multop_1,f3_s7_multop_1,f4_s7_multop_1,B,C,D,E)))))))))) & v1_funct_2(A,k4_zfmisc_1(f1_s7_multop_1,f2_s7_multop_1,f3_s7_multop_1,f4_s7_multop_1),f5_s7_multop_1) & v1_funct_1(A))) # label(s7_multop_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5328 (exists A (v1_funct_1(A) & m2_relset_1(A,k4_zfmisc_1(f1_s8_multop_1,f1_s8_multop_1,f1_s8_multop_1,f1_s8_multop_1),f1_s8_multop_1) & (all B (m1_subset_1(B,f1_s8_multop_1) -> (all C (m1_subset_1(C,f1_s8_multop_1) -> (all D (m1_subset_1(D,f1_s8_multop_1) -> (all E (m1_subset_1(E,f1_s8_multop_1) -> k4_multop_1(f1_s8_multop_1,f1_s8_multop_1,f1_s8_multop_1,f1_s8_multop_1,f1_s8_multop_1,A,B,C,D,E) = f2_s8_multop_1(B,C,D,E))))))))) & v1_funct_2(A,k4_zfmisc_1(f1_s8_multop_1,f1_s8_multop_1,f1_s8_multop_1,f1_s8_multop_1),f1_s8_multop_1))) # label(s8_multop_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5329 (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,k3_zfmisc_1(A,B,C),D) & v1_funct_2(E,k3_zfmisc_1(A,B,C),D) -> (all F (v1_funct_1(F) & v1_funct_2(F,k3_zfmisc_1(A,B,C),D) & m2_relset_1(F,k3_zfmisc_1(A,B,C),D) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> k8_funct_2(k3_zfmisc_1(A,B,C),D,F,k4_domain_1(A,B,C,G,H,I)) = k8_funct_2(k3_zfmisc_1(A,B,C),D,E,k4_domain_1(A,B,C,G,H,I)))))))) -> F = E))))))))))))) # label(t3_multop_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5330 (all A (m1_subset_1(A,f1_s5_multop_1) -> (all B (m1_subset_1(B,f2_s5_multop_1) -> (all C (m1_subset_1(C,f3_s5_multop_1) -> (all D (m1_subset_1(D,f4_s5_multop_1) -> (exists E (m1_subset_1(E,f5_s5_multop_1) & p1_s5_multop_1(A,B,C,D,E))))))))))) -> (exists A (v1_funct_2(A,k4_zfmisc_1(f1_s5_multop_1,f2_s5_multop_1,f3_s5_multop_1,f4_s5_multop_1),f5_s5_multop_1) & m2_relset_1(A,k4_zfmisc_1(f1_s5_multop_1,f2_s5_multop_1,f3_s5_multop_1,f4_s5_multop_1),f5_s5_multop_1) & (all B (m1_subset_1(B,f1_s5_multop_1) -> (all C (m1_subset_1(C,f2_s5_multop_1) -> (all D (m1_subset_1(D,f3_s5_multop_1) -> (all E (m1_subset_1(E,f4_s5_multop_1) -> p1_s5_multop_1(B,C,D,E,k8_funct_2(k4_zfmisc_1(f1_s5_multop_1,f2_s5_multop_1,f3_s5_multop_1,f4_s5_multop_1),f5_s5_multop_1,A,k5_domain_1(f1_s5_multop_1,f2_s5_multop_1,f3_s5_multop_1,f4_s5_multop_1,B,C,D,E))))))))))) & v1_funct_1(A))) # label(s5_multop_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5331 (all A all B all C all D all E all F all G all H all I all J (-v1_xboole_0(A) & -v1_xboole_0(C) & -v1_xboole_0(E) & v1_funct_1(F) & v1_funct_2(F,k4_zfmisc_1(A,B,C,D),E) & m1_subset_1(G,A) & m1_subset_1(J,D) & m1_subset_1(I,C) & m1_subset_1(H,B) & m1_relset_1(F,k4_zfmisc_1(A,B,C,D),E) & -v1_xboole_0(D) & -v1_xboole_0(B) -> k4_multop_1(A,B,C,D,E,F,G,H,I,J) = k3_multop_1(F,G,H,I,J))) # label(redefinition_k4_multop_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5332 (all A all B all C all D all E all F all G all H all I all J (-v1_xboole_0(D) & -v1_xboole_0(E) & v1_funct_1(F) & v1_funct_2(F,k4_zfmisc_1(A,B,C,D),E) & m1_relset_1(F,k4_zfmisc_1(A,B,C,D),E) & m1_subset_1(I,C) & m1_subset_1(J,D) & m1_subset_1(H,B) & m1_subset_1(G,A) & -v1_xboole_0(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> m1_subset_1(k4_multop_1(A,B,C,D,E,F,G,H,I,J),E))) # label(dt_k4_multop_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5333 (all A all B (m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (exists C m1_realset1(C,A,B)))) # label(existence_m1_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5334 (all A (v1_finset_1(A) -> (-r1_xreal_0(np__2,k4_card_1(A)) <-> v1_realset1(A)))) # label(t13_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5335 (all A all B (-v1_realset1(A) & m1_subset_1(B,A) -> k1_tarski(B) = k5_realset1(A,B))) # label(redefinition_k5_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5336 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m2_realset1(C,A,B) -> v1_funct_1(k1_realset1(C,B)) & v1_funct_2(k1_realset1(C,B),k2_zfmisc_1(B,B),B) & m2_relset_1(k1_realset1(C,B),k2_zfmisc_1(B,B),B))))) # label(t9_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5337 (all A (-v1_xboole_0(A) -> -((all B (m1_subset_1(B,A) -> -v1_xboole_0(k4_xboole_0(A,k1_tarski(B))))) & v1_realset1(A)))) # label(t6_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5338 (all A (-v1_realset1(A) -> (exists B m4_realset1(B,A)))) # label(existence_m4_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5339 (all A (-v1_realset1(A) -> -v1_xboole_0(A))) # label(cc1_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5340 $T # label(dt_k1_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5341 (all A all B (m1_subset_1(B,A) -> (exists C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & (all D (r2_hidden(D,k2_zfmisc_1(k4_xboole_0(A,k1_tarski(B)),k4_xboole_0(A,k1_tarski(B)))) -> r2_hidden(k1_funct_1(C,D),k4_xboole_0(A,k1_tarski(B))))))))) # label(t10_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5342 (all A (-v1_realset1(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (r2_realset1(A,B,C) <-> m1_realset1(k4_xboole_0(A,k1_tarski(C)),A,B) & v1_funct_1(k4_xboole_0(k1_realset1(B,A),k1_tarski(C))) & v1_funct_2(k4_xboole_0(k1_realset1(B,A),k1_tarski(C)),k2_zfmisc_1(k4_xboole_0(A,k1_tarski(C)),k4_xboole_0(A,k1_tarski(C))),k4_xboole_0(A,k1_tarski(C))) & m2_relset_1(k4_xboole_0(k1_realset1(B,A),k1_tarski(C)),k2_zfmisc_1(k4_xboole_0(A,k1_tarski(C)),k4_xboole_0(A,k1_tarski(C))),k4_xboole_0(A,k1_tarski(C)))))))))) # label(d5_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5343 $T # label(dt_m4_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5344 (all A (v1_relat_1(A) -> (all B k7_relat_1(A,k2_zfmisc_1(B,B)) = k1_realset1(A,B)))) # label(d3_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5345 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_realset1(C,A,B) -> v1_funct_2(k1_realset1(B,C),k2_zfmisc_1(C,C),C) & m2_relset_1(k1_realset1(B,C),k2_zfmisc_1(C,C),C) & v1_funct_1(k1_realset1(B,C)))))) # label(t3_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5346 (all A all B all C (m1_realset1(C,A,B) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> v1_funct_2(k2_realset1(A,B,C),k2_zfmisc_1(C,C),C) & m2_relset_1(k2_realset1(A,B,C),k2_zfmisc_1(C,C),C) & v1_funct_1(k2_realset1(A,B,C)))) # label(dt_k2_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5347 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (exists C (v1_funct_1(C) & (all D (r2_hidden(D,k2_zfmisc_1(B,B)) -> r2_hidden(k1_funct_1(C,D),B))) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A))))) # label(t8_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5348 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> -((exists C (m1_subset_1(C,A) & (exists D (m1_subset_1(D,A) & r2_hidden(D,B) & D != C & r2_hidden(C,B))))) & v1_realset1(B)) & -((all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> -(r2_hidden(D,B) & C != D & r2_hidden(C,B)))))) & -v1_realset1(B)))) # label(t15_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5349 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m2_realset1(C,A,B) -> k1_realset1(C,B) = k3_realset1(A,B,C))))) # label(d7_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5350 (all A all B (m1_subset_1(B,A) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> ((all D (r2_hidden(D,k2_zfmisc_1(k4_xboole_0(A,k1_tarski(B)),k4_xboole_0(A,k1_tarski(B)))) -> r2_hidden(k1_funct_1(C,D),k4_xboole_0(A,k1_tarski(B))))) <-> m3_realset1(C,A,B)))))) # label(d8_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5351 (all A (-v1_realset1(A) -> (all B ((exists C (k1_tarski(C) = B & m1_subset_1(C,A))) <-> m4_realset1(B,A))))) # label(d10_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5352 (all A (-v1_realset1(A) -> (all B (m1_subset_1(B,A) -> (all C (m3_realset1(C,A,B) -> k1_realset1(C,k4_xboole_0(A,k1_tarski(B))) = k4_realset1(A,B,C))))))) # label(d9_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5353 (all A all B all C (m2_realset1(C,A,B) & m1_subset_1(B,k1_zfmisc_1(A)) -> v1_funct_1(k3_realset1(A,B,C)) & v1_funct_2(k3_realset1(A,B,C),k2_zfmisc_1(B,B),B) & m2_relset_1(k3_realset1(A,B,C),k2_zfmisc_1(B,B),B))) # label(dt_k3_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5354 (all A (-(v1_realset1(A) & (exists B exists C (r2_hidden(B,A) & r2_hidden(C,A) & C != B))) & -(-v1_realset1(A) & (all B all C -(r2_hidden(B,A) & B != C & r2_hidden(C,A)))))) # label(t14_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5355 (all A all 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) -> (r2_hidden(B,k2_zfmisc_1(A,A)) -> r2_hidden(k1_funct_1(C,B),A)))) # label(t1_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5356 (all A (-v1_realset1(A) -> (all B (m4_realset1(B,A) -> -v1_xboole_0(k4_xboole_0(A,B)))))) # label(t12_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5357 (all A all B all C (m1_subset_1(B,A) & m3_realset1(C,A,B) & -v1_realset1(A) -> v1_funct_1(k4_realset1(A,B,C)) & m2_relset_1(k4_realset1(A,B,C),k2_zfmisc_1(k4_xboole_0(A,k1_tarski(B)),k4_xboole_0(A,k1_tarski(B))),k4_xboole_0(A,k1_tarski(B))) & v1_funct_2(k4_realset1(A,B,C),k2_zfmisc_1(k4_xboole_0(A,k1_tarski(B)),k4_xboole_0(A,k1_tarski(B))),k4_xboole_0(A,k1_tarski(B))))) # label(dt_k4_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.77 5358 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> ((all D (r2_hidden(D,k2_zfmisc_1(B,B)) -> r2_hidden(k1_funct_1(C,D),B))) <-> m2_realset1(C,A,B)))))) # label(d6_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5359 (all A (-v1_realset1(A) -> (all B (m1_subset_1(B,A) -> (all C (m3_realset1(C,A,B) -> v1_funct_2(k1_realset1(C,k4_xboole_0(A,k1_tarski(B))),k2_zfmisc_1(k4_xboole_0(A,k1_tarski(B)),k4_xboole_0(A,k1_tarski(B))),k4_xboole_0(A,k1_tarski(B))) & m2_relset_1(k1_realset1(C,k4_xboole_0(A,k1_tarski(B))),k2_zfmisc_1(k4_xboole_0(A,k1_tarski(B)),k4_xboole_0(A,k1_tarski(B))),k4_xboole_0(A,k1_tarski(B))) & v1_funct_1(k1_realset1(C,k4_xboole_0(A,k1_tarski(B)))))))))) # label(t11_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5360 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (exists C (m1_subset_1(C,k1_zfmisc_1(A)) & (all D (r2_hidden(D,k2_zfmisc_1(C,C)) -> r2_hidden(k1_funct_1(B,D),C))))))) # label(t2_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5361 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> -v1_xboole_0(k4_xboole_0(A,k1_tarski(B))))) -> -v1_realset1(A)))) # label(t7_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5362 (all A all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (r2_hidden(D,k2_zfmisc_1(C,C)) -> r2_hidden(k1_funct_1(B,D),C))) <-> m1_realset1(C,A,B)))))) # label(d2_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5363 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m2_realset1(C,A,B) -> v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C))))) # label(dt_m2_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5364 (all A all B (m1_subset_1(B,A) -> (exists C m3_realset1(C,A,B)))) # label(existence_m3_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5365 (all A (v1_realset1(A) <-> -(-v1_xboole_0(A) & (all B k1_tarski(B) != A)))) # label(d4_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5366 (all A all B all C (m1_relset_1(B,k2_zfmisc_1(A,A),A) & m1_realset1(C,A,B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> k2_realset1(A,B,C) = k1_realset1(B,C))) # label(redefinition_k2_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5367 (exists A (-v1_xboole_0(A) & v1_realset1(A))) # label(rc1_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5368 (all A all B (v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k1_realset1(A,B)) & v1_funct_1(k1_realset1(A,B)))) # label(fc2_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5369 (all A all B (m1_subset_1(B,A) & -v1_realset1(A) -> m4_realset1(k5_realset1(A,B),A))) # label(dt_k5_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5370 (all A all B (m1_subset_1(B,A) -> (all C (m3_realset1(C,A,B) -> v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A))))) # label(dt_m3_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5371 (all A all B (-v1_realset1(A) & m4_realset1(B,A) -> -v1_xboole_0(k4_xboole_0(A,B)))) # label(fc4_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5372 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (exists C m2_realset1(C,A,B)))) # label(existence_m2_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5373 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_realset1(C,A,B) -> m1_subset_1(C,k1_zfmisc_1(A)))))) # label(dt_m1_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5374 (all A all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_realset1(A,B,C) <-> (all D (r2_hidden(D,k2_zfmisc_1(C,C)) -> r2_hidden(k1_funct_1(B,D),C)))))))) # label(d1_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5375 (all A (v1_realset1(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) & -v1_xboole_0(k1_tarski(A)))) # label(fc3_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5376 (exists A ((all B (m1_subset_1(B,A) -> -v1_xboole_0(k4_xboole_0(A,k1_tarski(B))))) & -v1_xboole_0(A))) # label(t5_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5377 (all A all B (v1_relat_1(A) -> v1_relat_1(k1_realset1(A,B)))) # label(fc1_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5378 (all A (-v1_xboole_0(A) -> ((all B -v1_xboole_0(k4_xboole_0(A,k1_tarski(B)))) <-> -v1_realset1(A)))) # label(t4_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5379 (exists A (-v1_realset1(A) & -v1_xboole_0(A))) # label(rc2_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5380 (all A (-v1_realset1(A) -> (exists B (-v1_xboole_0(B) & m4_realset1(B,A))))) # label(rc3_realset1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5381 (all A (v1_funct_1(A) & v1_funcop_1(A) & v1_relat_1(A) -> k1_relat_1(k2_funct_6(A)) = k1_relat_1(A))) # label(t89_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5382 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (v1_funct_1(C) & v1_relat_1(C) -> ((all D (r2_hidden(D,k1_relat_1(A)) -> k1_funct_1(C,D) = k1_funct_2(k1_funct_1(A,D),B))) & k1_relat_1(C) = k1_relat_1(A) <-> k8_funct_6(A,B) = C))))) # label(d8_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5383 $T # label(d10_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5384 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C k5_funct_6(A,B,C) = k1_funct_1(k4_funct_5(A),k4_tarski(B,C))))) # label(d5_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5385 (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(k6_funct_6(B))) & C = k1_funct_1(k6_funct_6(B),A) -> (all D (r2_hidden(D,k1_relat_1(C)) -> r2_hidden(k4_tarski(D,A),k1_relat_1(k4_funct_5(B))) & k1_funct_1(C,D) = k1_funct_1(k4_funct_5(B),k4_tarski(D,A)))) & k1_relat_1(C) = k10_relat_1(B,k1_funct_6(k2_relat_1(B)))))))) # label(t51_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5386 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(A,k1_relat_1(C)) & r2_hidden(B,k1_relat_1(D)) -> (all E all F (k4_tarski(E,F) = k1_funct_1(k15_funct_3(C,D),k4_tarski(A,B)) <-> k10_finseq_1(E,F) = k1_funct_1(k7_funct_6(k10_finseq_1(C,D)),k10_finseq_1(A,B))))))))) # label(t68_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5387 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> k3_funct_6(k2_funcop_1(A,B)) = k2_funcop_1(A,k2_relat_1(B)) & k2_funct_6(k2_funcop_1(A,B)) = k2_funcop_1(A,k1_relat_1(B)))) # label(t36_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5388 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (r2_hidden(B,k1_relat_1(k10_funct_6(A))) -> v1_relat_1(k1_funct_1(k10_funct_6(A),B)) & v1_funct_1(k1_funct_1(k10_funct_6(A),B)))))) # label(t84_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5389 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> k2_zfmisc_1(A,k1_relat_1(B)) = k1_relat_1(k4_funct_5(k2_funcop_1(A,B))) & k1_relat_1(k6_funct_5(k2_funcop_1(A,B))) = k2_zfmisc_1(k1_relat_1(B),A) & r1_tarski(k2_relat_1(k6_funct_5(k2_funcop_1(A,B))),k2_relat_1(B)) & r1_tarski(k2_relat_1(k4_funct_5(k2_funcop_1(A,B))),k2_relat_1(B)))) # label(t17_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5390 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> k4_card_3(k2_finseq_2(A,B)) = k4_finseq_2(A,B))))) # label(t9_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5391 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k10_relat_1(A,k1_funct_6(k2_relat_1(A))) = k1_relat_1(B) & (all C (r2_hidden(C,k10_relat_1(A,k1_funct_6(k2_relat_1(A)))) -> k2_funct_5(k1_funct_1(A,C)) = k1_funct_1(B,C))) <-> B = k3_funct_6(A)))))) # label(d3_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5392 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(A,k1_relat_1(C)) & D = k1_funct_1(C,A) & r2_hidden(B,k1_relat_1(D)) -> k5_funct_6(C,A,B) = k1_funct_1(D,B)))))) # label(t44_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5393 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_2(C,A,A) & m2_relset_1(C,A,A) & v3_funct_2(C,A,A) & v1_funct_1(C) -> (A = k1_relat_1(B) -> r2_wellord2(k4_card_3(B),k4_card_3(k5_relat_1(C,B)))))))) # label(t71_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5394 (all A all B all C all D all E all F (v1_relat_1(F) & v1_funct_1(F) -> (k1_relat_1(F) = A & r1_tarski(k2_relat_1(F),k4_partfun1(D,E)) -> -r2_hidden(k6_funct_5(F),k1_funct_2(k2_zfmisc_1(B,A),C)) & -r2_hidden(k4_funct_5(F),k1_funct_2(k2_zfmisc_1(A,B),C)) | r2_hidden(F,k1_funct_2(A,k1_funct_2(B,C)))))) # label(t22_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5395 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k4_card_3(k2_funct_6(C))) & r2_hidden(A,k1_relat_1(B)) -> k5_funct_6(k7_funct_6(C),B,A) = k5_funct_6(C,A,k1_funct_1(B,A))))))) # label(t56_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5396 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (A != k1_xboole_0 -> k1_relat_1(k6_funct_6(k2_funcop_1(A,B))) = k1_relat_1(B) & (all C (r2_hidden(C,k1_relat_1(B)) -> k2_funcop_1(A,k1_funct_1(B,C)) = k1_funct_1(k6_funct_6(k2_funcop_1(A,B)),C)))))) # label(t63_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5397 (all A (-v1_xboole_0(A) -> k4_card_3(k9_finseq_1(A)) = k4_finseq_2(np__1,A))) # label(t4_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5398 (all A all B (k1_xboole_0 != A -> k3_card_3(k2_funcop_1(A,B)) = B & k4_funct_6(k2_funcop_1(A,B)) = B)) # label(t43_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5399 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(B)) & k1_funct_1(B,A) = C -> r1_tarski(k2_relat_1(C),k2_relat_1(k6_funct_5(B))) & r1_tarski(k2_relat_1(C),k2_relat_1(k4_funct_5(B)))))))) # label(t16_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5400 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> k4_card_3(k10_finseq_1(A,B)) = a_2_0_funct_6(A,B))))) # label(t5_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5401 (all A (v1_relat_1(A) & v1_funct_1(A) -> k2_funct_6(k9_finseq_1(A)) = k9_finseq_1(k1_relat_1(A)) & k9_finseq_1(k2_relat_1(A)) = k3_funct_6(k9_finseq_1(A)))) # label(t33_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5402 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> ((all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(D,k2_relat_1(C)) -> r2_hidden(A,k1_relat_1(D))))) & r2_hidden(B,k2_relat_1(C)) -> r2_hidden(A,k1_relat_1(k6_funct_6(C)))))))) # label(t53_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5403 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(C) & -v1_xboole_0(D) -> (r2_hidden(A,a_3_0_funct_6(B,C,D)) <-> (exists E exists F exists G (m1_subset_1(F,C) & m1_subset_1(G,D) & A = k11_finseq_1(E,F,G) & m1_subset_1(E,B)))))) # label(fraenkel_a_3_0_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5404 (all A (-v1_xboole_0(A) -> k4_card_3(k11_finseq_1(A,A,A)) = k4_finseq_2(np__3,A))) # label(t8_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5405 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_xboole_0 != B -> ((all C (r2_hidden(C,k1_relat_1(B)) -> r2_hidden(A,k1_funct_1(B,C)))) <-> r2_hidden(A,k4_funct_6(B)))))) # label(t37_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5406 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> k4_card_3(k10_finseq_1(k1_relat_1(A),k1_relat_1(B))) = k1_relat_1(k7_funct_6(k10_finseq_1(A,B))) & k4_card_3(k10_finseq_1(k2_relat_1(A),k2_relat_1(B))) = k2_relat_1(k7_funct_6(k10_finseq_1(A,B))) & (all C all D (r2_hidden(D,k1_relat_1(B)) & r2_hidden(C,k1_relat_1(A)) -> k10_finseq_1(k1_funct_1(A,C),k1_funct_1(B,D)) = k1_funct_1(k7_funct_6(k10_finseq_1(A,B)),k10_finseq_1(C,D)))))))) # label(t65_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5407 (all A all B (B = k1_funct_6(A) <-> (all C (r2_hidden(C,B) <-> v1_relat_1(C) & v1_funct_1(C) & r2_hidden(C,A))))) # label(d1_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5408 (all A all B all C k2_funcop_1(A,k1_funct_2(B,C)) = k8_funct_6(k2_funcop_1(A,B),C)) # label(t76_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5409 (all A (A = k4_funct_6(k9_finseq_1(A)) & k3_card_3(k9_finseq_1(A)) = A)) # label(t39_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5410 (all A all B all C k9_funct_6(A,k10_finseq_1(B,C)) = k10_finseq_1(k1_funct_2(A,B),k1_funct_2(A,C))) # label(t81_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5411 (all A k8_funct_6(k1_xboole_0,A) = k1_xboole_0) # label(t73_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5412 (all A (v1_relat_1(A) & v1_funct_1(A) -> r1_tarski(k2_relat_1(k6_funct_6(A)),k4_card_3(k3_funct_6(A))) & k1_relat_1(k6_funct_6(A)) = k4_funct_6(k2_funct_6(A)))) # label(t49_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5413 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(B,A) = k5_funct_6(k11_finseq_1(C,D,B),np__3,A)))))))) # label(t47_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5414 (all A all B k9_finseq_1(k1_funct_2(A,B)) = k9_funct_6(A,k9_finseq_1(B))) # label(t80_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5415 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(B) = k4_card_3(k2_funct_6(A)) & (all C (v1_relat_1(C) & v1_funct_1(C) -> -((all D (v1_relat_1(D) & v1_funct_1(D) -> -(k1_funct_1(B,C) = D & k1_relat_1(D) = k10_relat_1(A,k1_funct_6(k2_relat_1(A))) & (all E (r2_hidden(E,k1_relat_1(D)) -> k1_funct_1(k4_funct_5(A),k4_tarski(E,k1_funct_1(C,E))) = k1_funct_1(D,E)))))) & r2_hidden(C,k4_card_3(k2_funct_6(A)))))) <-> k7_funct_6(A) = B))))) # label(d7_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5416 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(D,k1_funct_2(A,k1_funct_2(B,C))) -> r2_hidden(k6_funct_5(D),k1_funct_2(k2_zfmisc_1(B,A),C)) & r2_hidden(k4_funct_5(D),k1_funct_2(k2_zfmisc_1(A,B),C))))) # label(t20_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5417 (all A all B all C k8_funct_6(k10_finseq_1(A,B),C) = k10_finseq_1(k1_funct_2(A,C),k1_funct_2(B,C))) # label(t75_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5418 (all A (-v1_xboole_0(A) -> k4_finseq_2(np__2,A) = k4_card_3(k10_finseq_1(A,A)))) # label(t6_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5419 (all A all B all C all D all E all F (v1_relat_1(F) & v1_funct_1(F) -> (r1_tarski(k1_relat_1(F),k2_zfmisc_1(D,E)) -> r2_hidden(F,k4_partfun1(k2_zfmisc_1(A,B),C)) | -r2_hidden(k3_funct_5(F),k4_partfun1(A,k4_partfun1(B,C))) & -r2_hidden(k5_funct_5(F),k4_partfun1(B,k4_partfun1(A,C)))))) # label(t25_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5420 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k3_funct_6(A)) & v1_relat_1(k3_funct_6(A)))) # label(dt_k3_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5421 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(C,k1_relat_1(D)) & r2_hidden(A,B) -> k1_funct_1(D,C) = k5_funct_6(k2_funcop_1(B,D),A,C)))) # label(t48_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5422 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (r2_hidden(B,k1_relat_1(A)) -> k1_funct_1(k7_funct_6(k9_finseq_1(A)),k9_finseq_1(B)) = k9_finseq_1(k1_funct_1(A,B)))) & k2_relat_1(k7_funct_6(k9_finseq_1(A))) = k4_card_3(k9_finseq_1(k2_relat_1(A))) & k1_relat_1(k7_funct_6(k9_finseq_1(A))) = k4_card_3(k9_finseq_1(k1_relat_1(A))))) # label(t64_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5423 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(D,k1_funct_2(A,k1_funct_2(B,C))) -> B = k1_xboole_0 | (all E (v1_relat_1(E) & v1_funct_1(E) -> (all F (v1_relat_1(F) & v1_funct_1(F) -> (all G all H (r2_hidden(H,B) & E = k1_funct_1(D,G) & k1_funct_1(k10_funct_6(D),H) = F & r2_hidden(G,A) -> k1_funct_1(F,G) = k1_funct_1(E,H) & k1_relat_1(F) = A & k1_relat_1(E) = B & r1_tarski(k2_relat_1(F),C) & r1_tarski(k2_relat_1(E),C))))))) | k1_xboole_0 = A))) # label(t86_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5424 (all A all B all C (k4_funct_5(k2_funcop_1(A,k2_funcop_1(B,C))) = k2_funcop_1(k2_zfmisc_1(A,B),C) & k2_funcop_1(k2_zfmisc_1(B,A),C) = k6_funct_5(k2_funcop_1(A,k2_funcop_1(B,C))))) # label(t15_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5425 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(D,k1_funct_2(A,k1_funct_2(B,C))) -> k1_xboole_0 = B | r2_hidden(k10_funct_6(D),k1_funct_2(B,k1_funct_2(A,C))) | A = k1_xboole_0))) # label(t85_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5426 (all A (v1_funct_1(A) & v1_relat_1(A) -> (-r2_hidden(k1_xboole_0,k2_relat_1(A)) -> k8_funct_6(A,k1_xboole_0) = k2_funcop_1(k1_relat_1(A),k1_xboole_0)))) # label(t72_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5427 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(A,k1_relat_1(B)) & v1_relat_1(k1_funct_1(B,A)) & v1_funct_1(k1_funct_1(B,A)) <-> r2_hidden(A,k10_relat_1(B,k1_funct_6(k2_relat_1(B))))))) # label(t28_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5428 (all A k9_funct_6(A,k1_xboole_0) = k1_xboole_0) # label(t79_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5429 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(D,k1_funct_2(A,k1_funct_2(B,C))) -> D = k10_funct_6(k10_funct_6(D)) | B = k1_xboole_0 | A = k1_xboole_0))) # label(t87_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5430 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_funct_1(B,A) = C & r2_hidden(A,k1_relat_1(B)) -> r2_hidden(A,k1_relat_1(k3_funct_6(B))) & k2_relat_1(C) = k1_funct_1(k3_funct_6(B),A) & k1_relat_1(C) = k1_funct_1(k2_funct_6(B),A) & r2_hidden(A,k1_relat_1(k2_funct_6(B)))))))) # label(t31_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5431 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> a_3_0_funct_6(A,B,C) = k4_card_3(k11_finseq_1(A,B,C)))))))) # label(t7_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5432 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(B,A) = k5_funct_6(k9_finseq_1(B),np__1,A) & k5_funct_6(k11_finseq_1(B,C,D),np__1,A) = k1_funct_1(B,A) & k5_funct_6(k10_finseq_1(B,C),np__1,A) = k1_funct_1(B,A)))))))) # label(t45_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5433 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(k6_funct_6(B))) -> v1_funct_1(k1_funct_1(k6_funct_6(B),A)) & v1_relat_1(k1_funct_1(k6_funct_6(B),A))))) # label(t50_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5434 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (all E (v1_relat_1(E) & v1_funct_1(E) -> (r2_hidden(B,k1_relat_1(k6_funct_6(C))) & E = k1_funct_1(k6_funct_6(C),B) & D = k1_funct_1(C,A) & r2_hidden(A,k1_relat_1(C)) -> k1_funct_1(D,B) = k1_funct_1(E,A)))))))) # label(t54_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5435 (all A all B all C (-v1_xboole_0(B) & -v1_xboole_0(C) -> ((exists D exists E (A = k10_finseq_1(D,E) & m1_subset_1(E,C) & m1_subset_1(D,B))) <-> r2_hidden(A,a_2_0_funct_6(B,C))))) # label(fraenkel_a_2_0_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5436 (all A (v1_funct_1(A) & v1_relat_1(A) -> k3_funct_5(k7_relat_1(k6_funct_5(A),k2_zfmisc_1(k4_funct_6(k2_funct_6(A)),k1_relat_1(A)))) = k6_funct_6(A))) # label(d6_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5437 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (r2_hidden(B,k1_relat_1(A)) -> k1_funct_1(k6_funct_6(k9_finseq_1(A)),B) = k9_finseq_1(k1_funct_1(A,B)))) & k1_relat_1(k6_funct_6(k9_finseq_1(A))) = k1_relat_1(A))) # label(t61_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5438 (all A (v1_funct_1(A) & v1_relat_1(A) -> k3_funct_5(A) = k5_funct_5(k2_funct_4(A)) & k2_funct_4(k6_funct_5(A)) = k4_funct_5(A))) # label(t13_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5439 (all A all B all C k2_funct_4(k2_funcop_1(k2_zfmisc_1(A,B),C)) = k2_funcop_1(k2_zfmisc_1(B,A),C)) # label(t12_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5440 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> k2_funct_6(k10_finseq_1(A,B)) = k10_finseq_1(k1_relat_1(A),k1_relat_1(B)) & k3_funct_6(k10_finseq_1(A,B)) = k10_finseq_1(k2_relat_1(A),k2_relat_1(B)))))) # label(t34_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5441 (all A all B all C all D ((exists E exists F exists G (r2_hidden(F,C) & r2_hidden(G,D) & k11_finseq_1(E,F,G) = A & r2_hidden(E,B))) <-> r2_hidden(A,k4_card_3(k11_finseq_1(B,C,D))))) # label(t3_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5442 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k6_funct_6(A)) & v1_funct_1(k6_funct_6(A)))) # label(dt_k6_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5443 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> v1_relat_1(k9_funct_6(A,B)) & v1_funct_1(k9_funct_6(A,B)))) # label(dt_k9_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5444 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(B)) & r2_hidden(A,k1_relat_1(C)) -> (all D all E (k1_funct_1(k6_funct_6(k10_finseq_1(B,C)),A) = k10_finseq_1(D,E) <-> k4_tarski(D,E) = k1_funct_1(k13_funct_3(B,C),A)))))))) # label(t67_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5445 (all A all B all C ((exists D exists E (r2_hidden(D,B) & r2_hidden(E,C) & k10_finseq_1(D,E) = A)) <-> r2_hidden(A,k4_card_3(k10_finseq_1(B,C))))) # label(t2_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5446 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> -((all C all D A != k4_tarski(C,D)) & r2_hidden(A,k1_relat_1(k2_funct_4(B)))))) # label(t11_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5447 (all A all B (k3_xboole_0(A,B) = k4_funct_6(k10_finseq_1(A,B)) & k3_card_3(k10_finseq_1(A,B)) = k2_xboole_0(A,B))) # label(t40_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5448 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(D,k1_funct_2(k2_zfmisc_1(A,B),C)) -> k2_zfmisc_1(A,B) = k1_xboole_0 | r2_hidden(k5_funct_5(D),k1_funct_2(B,k1_funct_2(A,C))) & r2_hidden(k3_funct_5(D),k1_funct_2(A,k1_funct_2(B,C)))))) # label(t19_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5449 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k10_funct_6(A)) & v1_funcop_1(k10_funct_6(A)) & v1_funct_1(k10_funct_6(A)))) # label(dt_k10_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5450 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k2_funct_6(A)) & v1_relat_1(k2_funct_6(A)))) # label(dt_k2_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5451 (all A all B all C all D all E all F (v1_relat_1(F) & v1_funct_1(F) -> (r1_tarski(k1_relat_1(F),A) & r1_tarski(k2_relat_1(F),k4_partfun1(D,E)) -> r2_hidden(F,k4_partfun1(A,k4_partfun1(B,C))) | -r2_hidden(k6_funct_5(F),k4_partfun1(k2_zfmisc_1(B,A),C)) & -r2_hidden(k4_funct_5(F),k4_partfun1(k2_zfmisc_1(A,B),C))))) # label(t26_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5452 (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(B) = k1_relat_1(A) & v2_funct_1(B) & (all D (r2_hidden(D,k1_relat_1(B)) -> r2_wellord2(k1_funct_1(A,D),k1_funct_1(C,k1_funct_1(B,D))))) & k2_relat_1(B) = k1_relat_1(C) -> r2_wellord2(k4_card_3(A),k4_card_3(C))))))))) # label(t70_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5453 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> k3_xboole_0(k1_relat_1(A),k1_relat_1(B)) = k1_relat_1(k6_funct_6(k10_finseq_1(A,B))) & (all C (r2_hidden(C,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k10_finseq_1(k1_funct_1(A,C),k1_funct_1(B,C)) = k1_funct_1(k6_funct_6(k10_finseq_1(A,B)),C))))))) # label(t62_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5454 (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) -> k2_funct_6(k11_finseq_1(A,B,C)) = k11_finseq_1(k1_relat_1(A),k1_relat_1(B),k1_relat_1(C)) & k11_finseq_1(k2_relat_1(A),k2_relat_1(B),k2_relat_1(C)) = k3_funct_6(k11_finseq_1(A,B,C)))))))) # label(t35_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5455 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> k1_enumset1(A,B,C) = k1_funct_6(k1_enumset1(A,B,C)) & k1_funct_6(k2_tarski(A,B)) = k2_tarski(A,B) & k1_tarski(A) = k1_funct_6(k1_tarski(A)) & k1_funct_6(k1_xboole_0) = k1_xboole_0)))))) # label(t29_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5456 $T # label(dt_k5_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5457 (all A all B k9_finseq_1(k1_funct_2(A,B)) = k8_funct_6(k9_finseq_1(A),B)) # label(t74_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5458 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r2_wellord2(k1_funct_2(k3_card_3(k2_card_3(B)),A),k4_card_3(k8_funct_6(B,A))))) # label(t77_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5459 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(D,k4_partfun1(A,k4_partfun1(B,C))) -> r2_hidden(k6_funct_5(D),k4_partfun1(k2_zfmisc_1(B,A),C)) & r2_hidden(k4_funct_5(D),k4_partfun1(k2_zfmisc_1(A,B),C))))) # label(t24_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5460 $T # label(dt_k1_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5461 (all A all B all C (k4_funct_6(k11_finseq_1(A,B,C)) = k3_xboole_0(k3_xboole_0(A,B),C) & k3_card_3(k11_finseq_1(A,B,C)) = k2_xboole_0(k2_xboole_0(A,B),C))) # label(t41_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5462 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (all E (v1_relat_1(E) & v1_funct_1(E) -> (r2_hidden(A,k1_relat_1(B)) & r2_hidden(D,k4_card_3(k2_funct_6(B))) & k1_funct_1(k7_funct_6(B),D) = E & k1_funct_1(B,A) = C -> r2_hidden(E,k4_card_3(k3_funct_6(B))) & k1_funct_1(E,A) = k1_funct_1(C,k1_funct_1(D,A)) & r2_hidden(k1_funct_1(D,A),k1_relat_1(C))))))))))) # label(t57_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5463 (all A (k3_card_3(k2_funcop_1(k1_xboole_0,A)) = k1_xboole_0 & k4_funct_6(k2_funcop_1(k1_xboole_0,A)) = k1_xboole_0)) # label(t42_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5464 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(k6_funct_6(B))) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(C,k2_relat_1(B)) -> r2_hidden(A,k1_relat_1(C)))))))) # label(t52_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5465 (all A r1_tarski(k1_funct_6(A),A)) # label(t27_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5466 $T # label(dt_k4_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5467 (all A (v1_relat_1(A) & v1_funct_1(A) -> k4_card_3(k3_funct_6(A)) = k2_relat_1(k7_funct_6(A)))) # label(t58_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5468 (all A all B all C all D all E all F (v1_funct_1(F) & v1_relat_1(F) -> (r1_tarski(k1_relat_1(F),k2_zfmisc_1(D,E)) -> -r2_hidden(k3_funct_5(F),k1_funct_2(A,k1_funct_2(B,C))) & -r2_hidden(k5_funct_5(F),k1_funct_2(B,k1_funct_2(A,C))) | r2_hidden(F,k1_funct_2(k2_zfmisc_1(A,B),C))))) # label(t21_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5469 (all A (v1_relat_1(A) & v1_funct_1(A) -> k9_funct_6(k1_xboole_0,A) = k2_funcop_1(k1_relat_1(A),k1_tarski(k1_xboole_0)))) # label(t78_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5470 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_xboole_0 != A -> k2_relat_1(B) = k2_relat_1(k6_funct_5(k2_funcop_1(A,B))) & k2_relat_1(B) = k2_relat_1(k4_funct_5(k2_funcop_1(A,B)))))) # label(t18_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5471 $T # label(d11_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5472 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k2_funct_6(A) = B <-> (all C (r2_hidden(C,k10_relat_1(A,k1_funct_6(k2_relat_1(A)))) -> k1_funct_5(k1_funct_1(A,C)) = k1_funct_1(B,C))) & k10_relat_1(A,k1_funct_6(k2_relat_1(A))) = k1_relat_1(B)))))) # label(d2_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5473 (all A all B (v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k8_funct_6(A,B)) & v1_funct_1(k8_funct_6(A,B)))) # label(dt_k8_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5474 (all A (v1_funct_1(A) & v1_relat_1(A) -> r1_tarski(k4_card_3(A),k1_funct_2(k1_relat_1(A),k3_card_3(A))))) # label(t10_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5475 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> k2_relat_1(k7_funct_6(k2_funcop_1(A,B))) = k1_funct_2(A,k2_relat_1(B)) & (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(C,k1_funct_2(A,k1_relat_1(B))) -> k1_funct_1(k7_funct_6(k2_funcop_1(A,B)),C) = k5_relat_1(C,B)))) & k1_relat_1(k7_funct_6(k2_funcop_1(A,B))) = k1_funct_2(A,k1_relat_1(B)))) # label(t66_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5476 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(D,k4_partfun1(k2_zfmisc_1(A,B),C)) -> r2_hidden(k3_funct_5(D),k4_partfun1(A,k4_partfun1(B,C))) & r2_hidden(k5_funct_5(D),k4_partfun1(B,k4_partfun1(A,C)))))) # label(t23_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5477 (all A (v1_funct_1(A) & v1_relat_1(A) -> k4_funct_6(A) = k1_setfam_1(k2_relat_1(A)))) # label(d4_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5478 (all A all B all C k9_funct_6(A,k2_funcop_1(B,C)) = k2_funcop_1(B,k1_funct_2(A,C))) # label(t82_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5479 (all A (v1_relat_1(A) & v1_funcop_1(A) & v1_funct_1(A) -> k1_relat_1(A) = k1_relat_1(k3_funct_6(A)))) # label(t90_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5480 (all A (v1_relat_1(A) & v1_funct_1(A) -> (-r2_hidden(k1_xboole_0,k2_relat_1(A)) -> (v2_funct_1(k7_funct_6(A)) <-> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(B,k2_relat_1(A)) -> v2_funct_1(B)))))))) # label(t59_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5481 (all A all B (r1_tarski(A,k1_funct_6(B)) -> A = k1_funct_6(A))) # label(t30_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5482 (all A (v1_funct_1(A) & v1_relat_1(A) -> k10_funct_6(A) = k5_funct_5(k4_funct_5(A)))) # label(d12_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5483 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v1_funct_1(k1_funct_1(C,A)) & r2_hidden(B,k1_relat_1(k6_funct_6(C))) & v1_relat_1(k1_funct_1(C,A)) & r2_hidden(A,k1_relat_1(C)) -> k5_funct_6(C,A,B) = k5_funct_6(k6_funct_6(C),B,A)))) # label(t55_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5484 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r2_wellord2(k4_card_3(k9_funct_6(A,B)),k1_funct_2(A,k4_card_3(B))))) # label(t83_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5485 (all A all B all C (k2_zfmisc_1(A,B) != k1_xboole_0 -> k2_funcop_1(A,k2_funcop_1(B,C)) = k3_funct_5(k2_funcop_1(k2_zfmisc_1(A,B),C)) & k2_funcop_1(B,k2_funcop_1(A,C)) = k5_funct_5(k2_funcop_1(k2_zfmisc_1(A,B),C)))) # label(t14_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5486 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> ((all D (r2_hidden(D,k1_relat_1(B)) -> k1_funct_2(A,k1_funct_1(B,D)) = k1_funct_1(C,D))) & k1_relat_1(C) = k1_relat_1(B) <-> k9_funct_6(A,B) = C))))) # label(d9_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5487 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> ((all D (r2_hidden(D,A) -> r2_wellord2(k1_funct_1(B,D),k1_funct_1(C,D)))) & k1_relat_1(C) = A & A = k1_relat_1(B) -> r2_wellord2(k4_card_3(B),k4_card_3(C))))))) # label(t69_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5488 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(B,A) = k5_funct_6(k10_finseq_1(C,B),np__2,A) & k5_funct_6(k11_finseq_1(C,B,D),np__2,A) = k1_funct_1(B,A)))))))) # label(t46_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5489 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k7_funct_6(A)) & v1_relat_1(k7_funct_6(A)))) # label(dt_k7_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5490 (all A all B ((exists C (r2_hidden(C,B) & A = k9_finseq_1(C))) <-> r2_hidden(A,k4_card_3(k9_finseq_1(B))))) # label(t1_funct_6) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5491 $T # label(t17_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5492 (all A (v1_relat_1(A) -> r1_tarski(k6_relat_1(k1_relat_1(k1_sysrel(A))),k6_relat_1(k1_relat_1(A))) & r1_tarski(k6_relat_1(k2_relat_1(k1_sysrel(A))),k6_relat_1(k1_relat_1(A))))) # label(t52_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5493 $T # label(t11_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5494 (all A (v1_relat_1(A) -> (k5_relat_1(k4_xboole_0(A,k6_relat_1(k2_relat_1(k1_sysrel(A)))),k6_relat_1(k2_relat_1(k1_sysrel(A)))) = k1_xboole_0 -> k6_relat_1(k2_relat_1(k1_sysrel(A))) = k8_relat_1(k2_relat_1(k1_sysrel(A)),A) & k8_relat_1(k1_relat_1(k1_sysrel(A)),A) = k6_relat_1(k1_relat_1(k1_sysrel(A)))) & (k5_relat_1(k6_relat_1(k1_relat_1(k1_sysrel(A))),k4_xboole_0(A,k6_relat_1(k1_relat_1(k1_sysrel(A))))) = k1_xboole_0 -> k6_relat_1(k1_relat_1(k1_sysrel(A))) = k7_relat_1(A,k2_relat_1(k1_sysrel(A))) & k6_relat_1(k1_relat_1(k1_sysrel(A))) = k7_relat_1(A,k1_relat_1(k1_sysrel(A)))))) # label(t55_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5495 (all A all B all C (v1_relat_1(C) -> (r1_tarski(C,k2_zfmisc_1(A,B)) -> r1_tarski(k2_relat_1(C),B) & r1_tarski(k1_relat_1(C),A)))) # label(t15_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5496 (all A k6_relat_1(k1_tarski(A)) = k1_tarski(k4_tarski(A,A))) # label(t30_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5497 (all A all B (v1_relat_1(B) -> (r1_tarski(k6_relat_1(A),B) -> r1_tarski(k6_relat_1(A),k4_relat_1(B))))) # label(t37_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5498 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (k1_xboole_0 = k5_relat_1(k4_xboole_0(A,k6_relat_1(k1_relat_1(A))),A) & B = k5_relat_1(A,B) & k1_xboole_0 = k5_relat_1(k4_xboole_0(B,k6_relat_1(k1_relat_1(B))),B) & A = k5_relat_1(B,A) -> k1_sysrel(A) = k1_sysrel(B)) & (A = k5_relat_1(A,B) & k5_relat_1(B,k4_xboole_0(B,k6_relat_1(k1_relat_1(B)))) = k1_xboole_0 & k5_relat_1(B,A) = B & k5_relat_1(A,k4_xboole_0(A,k6_relat_1(k1_relat_1(A)))) = k1_xboole_0 -> k1_sysrel(B) = k1_sysrel(A)))))) # label(t59_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5499 (all A (v1_relat_1(A) -> r1_tarski(k6_relat_1(k2_relat_1(k1_sysrel(A))),A) & r1_tarski(k6_relat_1(k1_relat_1(k1_sysrel(A))),A))) # label(t53_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5500 (all A all B all C all D all E (v1_relat_1(E) -> (k2_xboole_0(C,D) = A & r1_tarski(E,k2_zfmisc_1(A,B)) -> k2_xboole_0(k7_relat_1(E,C),k7_relat_1(E,D)) = E))) # label(t25_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5501 (all A all B all C (v1_relat_1(C) -> (r1_xboole_0(A,B) & r1_tarski(C,k2_xboole_0(k2_zfmisc_1(A,B),k2_zfmisc_1(B,A))) -> r1_tarski(k7_relat_1(C,A),k2_zfmisc_1(A,B))))) # label(t26_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5502 (all A (v1_relat_1(A) -> (k1_xboole_0 = k5_relat_1(A,k4_xboole_0(A,k6_relat_1(k1_relat_1(A)))) -> k5_relat_1(k6_relat_1(k1_relat_1(k1_sysrel(A))),k4_xboole_0(A,k6_relat_1(k1_relat_1(k1_sysrel(A))))) = k1_xboole_0) & (k5_relat_1(k4_xboole_0(A,k6_relat_1(k1_relat_1(A))),A) = k1_xboole_0 -> k5_relat_1(k4_xboole_0(A,k6_relat_1(k1_relat_1(k1_sysrel(A)))),k6_relat_1(k1_relat_1(k1_sysrel(A)))) = k1_xboole_0))) # label(t56_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5503 (all A (v1_relat_1(A) -> v1_relat_1(k1_sysrel(A)))) # label(dt_k1_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5504 (all A all B (v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(k1_sysrel(B))) -> r2_hidden(k4_tarski(A,A),B) & r2_hidden(A,k1_relat_1(B))) & (r2_hidden(A,k2_relat_1(k1_sysrel(B))) -> r2_hidden(A,k1_relat_1(B)) & r2_hidden(k4_tarski(A,A),B)) & (r2_hidden(A,k1_relat_1(B)) & r2_hidden(k4_tarski(A,A),B) -> r2_hidden(A,k2_relat_1(k1_sysrel(B)))) & (r2_hidden(A,k2_relat_1(k1_sysrel(B))) -> r2_hidden(A,k2_relat_1(B)) & r2_hidden(k4_tarski(A,A),B)) & (r2_hidden(k4_tarski(A,A),B) & r2_hidden(A,k2_relat_1(B)) -> r2_hidden(A,k2_relat_1(k1_sysrel(B)))) & (r2_hidden(A,k1_relat_1(k1_sysrel(B))) -> r2_hidden(A,k2_relat_1(B)) & r2_hidden(k4_tarski(A,A),B)) & (r2_hidden(k4_tarski(A,A),B) & r2_hidden(A,k2_relat_1(B)) -> r2_hidden(A,k1_relat_1(k1_sysrel(B)))) & (r2_hidden(A,k1_relat_1(B)) & r2_hidden(k4_tarski(A,A),B) -> r2_hidden(A,k1_relat_1(k1_sysrel(B)))))) # label(t46_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5505 (all A (v1_relat_1(A) -> (r1_tarski(A,k5_relat_1(A,A)) & k5_relat_1(k4_xboole_0(A,k6_relat_1(k1_relat_1(A))),A) = k1_xboole_0 -> k6_relat_1(k1_relat_1(A)) = k3_xboole_0(A,k6_relat_1(k1_relat_1(A)))) & (r1_tarski(A,k5_relat_1(A,A)) & k5_relat_1(A,k4_xboole_0(A,k6_relat_1(k2_relat_1(A)))) = k1_xboole_0 -> k6_relat_1(k2_relat_1(A)) = k3_xboole_0(A,k6_relat_1(k2_relat_1(A)))))) # label(t41_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5506 (all A all B (v1_relat_1(B) -> (k5_relat_1(k6_relat_1(A),k4_xboole_0(B,k6_relat_1(A))) = k1_xboole_0 -> k4_xboole_0(k1_relat_1(B),k1_relat_1(k6_relat_1(A))) = k1_relat_1(k4_xboole_0(B,k6_relat_1(A)))) & (k5_relat_1(k4_xboole_0(B,k6_relat_1(A)),k6_relat_1(A)) = k1_xboole_0 -> k4_xboole_0(k2_relat_1(B),k2_relat_1(k6_relat_1(A))) = k2_relat_1(k4_xboole_0(B,k6_relat_1(A)))))) # label(t39_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5507 (all A all B k1_xboole_0 = k4_xboole_0(k6_relat_1(k4_xboole_0(A,B)),k6_relat_1(A))) # label(t34_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5508 (all A all B (v1_relat_1(B) -> (r1_tarski(k6_relat_1(A),k2_xboole_0(B,k4_relat_1(B))) -> r1_tarski(k6_relat_1(A),B) & r1_tarski(k6_relat_1(A),k4_relat_1(B))))) # label(t36_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5509 (all A all B all C (v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),C) & k5_relat_1(C,k4_xboole_0(C,k1_sysrel(C))) = k1_xboole_0 & k5_relat_1(C,C) = C -> A = B | r2_hidden(B,k1_relat_1(k1_sysrel(C))) & r2_hidden(A,k4_xboole_0(k1_relat_1(C),k1_relat_1(k1_sysrel(C))))) & (k1_xboole_0 = k5_relat_1(k4_xboole_0(C,k1_sysrel(C)),C) & r2_hidden(k4_tarski(A,B),C) & k5_relat_1(C,C) = C -> r2_hidden(B,k4_xboole_0(k2_relat_1(C),k1_relat_1(k1_sysrel(C)))) & r2_hidden(A,k1_relat_1(k1_sysrel(C))) | B = A))) # label(t48_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5510 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (k1_xboole_0 = k5_relat_1(k4_xboole_0(B,k6_relat_1(k1_relat_1(B))),B) & A = k5_relat_1(B,A) -> r1_tarski(k1_sysrel(A),k1_sysrel(B))) & (k5_relat_1(B,k4_xboole_0(B,k6_relat_1(k1_relat_1(B)))) = k1_xboole_0 & A = k5_relat_1(A,B) -> r1_tarski(k1_sysrel(A),k1_sysrel(B))))))) # label(t58_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5511 (all A all B (v1_relat_1(B) -> (r1_tarski(B,k2_zfmisc_1(A,A)) -> k4_xboole_0(B,k6_relat_1(A)) = k4_xboole_0(B,k6_relat_1(k1_relat_1(B))) & k4_xboole_0(B,k6_relat_1(A)) = k4_xboole_0(B,k6_relat_1(k2_relat_1(B)))))) # label(t38_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5512 $T # label(t8_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5513 (all A (v1_relat_1(A) -> r1_tarski(k1_relat_1(k1_sysrel(A)),k2_relat_1(A)) & r1_tarski(k2_relat_1(k1_sysrel(A)),k1_relat_1(A)) & r1_tarski(k2_relat_1(k1_sysrel(A)),k2_relat_1(A)) & r1_tarski(k1_relat_1(k1_sysrel(A)),k1_relat_1(A)))) # label(t51_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5514 (all A all B all C (v1_relat_1(C) -> (k1_xboole_0 = k5_relat_1(k4_xboole_0(C,k6_relat_1(k1_relat_1(C))),C) & r2_hidden(k4_tarski(A,B),C) & C = k5_relat_1(C,C) -> r2_hidden(B,k4_xboole_0(k2_relat_1(C),k1_relat_1(k1_sysrel(C)))) & r2_hidden(A,k1_relat_1(k1_sysrel(C))) | B = A) & (k5_relat_1(C,C) = C & k1_xboole_0 = k5_relat_1(C,k4_xboole_0(C,k6_relat_1(k1_relat_1(C)))) & r2_hidden(k4_tarski(A,B),C) -> r2_hidden(B,k1_relat_1(k1_sysrel(C))) & r2_hidden(A,k4_xboole_0(k1_relat_1(C),k1_relat_1(k1_sysrel(C)))) | A = B))) # label(t49_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5515 (all A all B (v1_relat_1(B) -> (r1_tarski(k6_relat_1(A),B) & k1_xboole_0 = k5_relat_1(k6_relat_1(A),k4_xboole_0(B,k6_relat_1(A))) -> k6_relat_1(A) = k7_relat_1(B,A)) & (r1_tarski(k6_relat_1(A),B) & k1_xboole_0 = k5_relat_1(k4_xboole_0(B,k6_relat_1(A)),k6_relat_1(A)) -> k6_relat_1(A) = k8_relat_1(A,B)))) # label(t54_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5516 (all A all B (r1_tarski(A,B) -> r1_tarski(k6_relat_1(A),k6_relat_1(B)))) # label(t33_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5517 (all A (v1_relat_1(A) -> k1_sysrel(A) = k3_xboole_0(A,k6_relat_1(k1_relat_1(A))))) # label(d1_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5518 $T # label(t21_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5519 (all A all B all C (v1_relat_1(C) -> r1_tarski(k1_relat_1(k3_xboole_0(C,k2_zfmisc_1(A,B))),A) & r1_tarski(k2_relat_1(k3_xboole_0(C,k2_zfmisc_1(A,B))),B))) # label(t13_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5520 (all A (v1_relat_1(A) -> (r1_tarski(A,k6_relat_1(k1_relat_1(A))) -> A = k6_relat_1(k1_relat_1(A))))) # label(t35_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5521 $T # label(t19_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5522 (all A (v1_relat_1(A) -> k2_relat_1(k1_sysrel(A)) = k1_relat_1(k1_sysrel(A)))) # label(t45_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5523 (all A all B all C (r2_hidden(k4_tarski(A,B),k6_relat_1(C)) <-> r2_hidden(k4_tarski(B,A),k6_relat_1(C)))) # label(t31_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5524 $T # label(t7_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5525 (all A all B k2_zfmisc_1(B,A) = k4_relat_1(k2_zfmisc_1(A,B))) # label(t18_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5526 (all A (v1_relat_1(A) -> (r1_tarski(A,k5_relat_1(A,A)) & k5_relat_1(A,k4_xboole_0(A,k6_relat_1(k2_relat_1(A)))) = k1_xboole_0 -> r1_tarski(k6_relat_1(k2_relat_1(A)),A)) & (r1_tarski(A,k5_relat_1(A,A)) & k5_relat_1(k4_xboole_0(A,k6_relat_1(k1_relat_1(A))),A) = k1_xboole_0 -> r1_tarski(k6_relat_1(k1_relat_1(A)),A)))) # label(t40_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5527 $T # label(t3_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5528 $T # label(t23_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5529 $T # label(t6_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5530 (all A all B (v1_relat_1(B) -> (k5_relat_1(B,k4_xboole_0(B,k6_relat_1(A))) = k1_xboole_0 & r1_tarski(k2_relat_1(B),A) -> k5_relat_1(B,k4_xboole_0(B,k6_relat_1(k2_relat_1(B)))) = k1_xboole_0) & (r1_tarski(k1_relat_1(B),A) & k1_xboole_0 = k5_relat_1(k4_xboole_0(B,k6_relat_1(A)),B) -> k5_relat_1(k4_xboole_0(B,k6_relat_1(k1_relat_1(B))),B) = k1_xboole_0))) # label(t42_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5531 (all A all B v1_relat_1(k2_zfmisc_1(A,B))) # label(fc1_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5532 (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)) & k5_relat_1(k2_xboole_0(A,B),C) = k2_xboole_0(k5_relat_1(A,C),k5_relat_1(B,C)))))))) # label(t20_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5533 $T # label(t2_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5534 (all A all B -(k1_xboole_0 != A & B != k1_xboole_0 & -(k1_relat_1(k2_zfmisc_1(A,B)) = A & B = k2_relat_1(k2_zfmisc_1(A,B))))) # label(t12_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.78 5535 (all A all B all C all D all E (v1_relat_1(E) -> (r1_xboole_0(A,B) & r1_tarski(E,k2_xboole_0(k2_zfmisc_1(A,B),k2_zfmisc_1(B,A))) & r2_hidden(k4_tarski(C,D),E) & r2_hidden(D,A) -> -r2_hidden(C,A) & r2_hidden(C,B) & -r2_hidden(D,B)) & (r1_xboole_0(A,B) & r1_tarski(E,k2_xboole_0(k2_zfmisc_1(A,B),k2_zfmisc_1(B,A))) & r2_hidden(k4_tarski(C,D),E) & r2_hidden(C,B) -> -r2_hidden(C,A) & -r2_hidden(D,B) & r2_hidden(D,A)) & (r1_xboole_0(A,B) & r2_hidden(D,B) & r2_hidden(k4_tarski(C,D),E) & r1_tarski(E,k2_xboole_0(k2_zfmisc_1(A,B),k2_zfmisc_1(B,A))) -> r2_hidden(C,A) & -r2_hidden(C,B) & -r2_hidden(D,A)) & (r1_xboole_0(A,B) & r2_hidden(k4_tarski(C,D),E) & r2_hidden(C,A) & r1_tarski(E,k2_xboole_0(k2_zfmisc_1(A,B),k2_zfmisc_1(B,A))) -> -r2_hidden(D,A) & r2_hidden(D,B) & -r2_hidden(C,B)))) # label(t22_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5536 (all A (v1_relat_1(A) -> (k1_xboole_0 = k5_relat_1(k4_xboole_0(A,k6_relat_1(k1_relat_1(A))),A) & k5_relat_1(A,A) = A -> k1_relat_1(A) = k1_relat_1(k1_sysrel(A)) & k1_relat_1(A) = k2_relat_1(k1_sysrel(A))) & (A = k5_relat_1(A,A) & k5_relat_1(A,k4_xboole_0(A,k6_relat_1(k1_relat_1(A)))) = k1_xboole_0 -> k2_relat_1(A) = k1_relat_1(k1_sysrel(A)) & k2_relat_1(A) = k2_relat_1(k1_sysrel(A))))) # label(t50_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5537 $T # label(t10_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5538 $T # label(t5_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5539 (all A all B (k6_relat_1(k4_xboole_0(A,B)) = k4_xboole_0(k6_relat_1(A),k6_relat_1(B)) & k6_relat_1(k3_xboole_0(A,B)) = k3_xboole_0(k6_relat_1(A),k6_relat_1(B)) & k2_xboole_0(k6_relat_1(A),k6_relat_1(B)) = k6_relat_1(k2_xboole_0(A,B)))) # label(t32_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5540 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (k5_relat_1(A,B) = A & k5_relat_1(B,k4_xboole_0(B,k6_relat_1(k1_relat_1(B)))) = k1_xboole_0 -> k1_xboole_0 = k5_relat_1(A,k4_xboole_0(B,k6_relat_1(k1_relat_1(B))))) & (k5_relat_1(k4_xboole_0(B,k6_relat_1(k1_relat_1(B))),B) = k1_xboole_0 & A = k5_relat_1(B,A) -> k5_relat_1(k4_xboole_0(B,k6_relat_1(k1_relat_1(B))),A) = k1_xboole_0))))) # label(t57_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5541 (all A (v1_relat_1(A) -> r1_tarski(k1_sysrel(A),A) & r1_tarski(k1_sysrel(A),k6_relat_1(k1_relat_1(A))))) # label(t43_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5542 $T # label(t1_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5543 (all A k5_relat_1(k6_relat_1(A),k6_relat_1(A)) = k6_relat_1(A)) # label(t29_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5544 $T # label(t9_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5545 (all A all B all C all D (v1_relat_1(D) -> (r1_tarski(C,B) & r1_tarski(D,k2_zfmisc_1(A,B)) -> k3_xboole_0(D,k2_zfmisc_1(A,C)) = k8_relat_1(C,D)) & (r1_tarski(D,k2_zfmisc_1(A,B)) & r1_tarski(C,A) -> k7_relat_1(D,C) = k3_xboole_0(D,k2_zfmisc_1(C,B))))) # label(t24_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5546 (all A all B all C (v1_relat_1(C) -> (r1_xboole_0(A,B) -> r1_xboole_0(k1_relat_1(k3_xboole_0(k4_relat_1(C),k2_zfmisc_1(A,B))),k2_relat_1(k3_xboole_0(k4_relat_1(C),k2_zfmisc_1(A,B)))) & r1_xboole_0(k1_relat_1(k3_xboole_0(C,k2_zfmisc_1(A,B))),k2_relat_1(k3_xboole_0(C,k2_zfmisc_1(A,B))))))) # label(t14_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5547 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(A,B) -> r1_tarski(k4_relat_1(A),k4_relat_1(B))))))) # label(t27_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5548 (all A all B all C (v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),k1_sysrel(C)) -> A = B & r2_hidden(A,k1_relat_1(k1_sysrel(C)))))) # label(t44_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5549 $T # label(t4_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5550 $T # label(t28_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5551 (all A all B all C (v1_relat_1(C) -> (r1_tarski(C,k2_zfmisc_1(A,B)) -> r1_tarski(k4_relat_1(C),k2_zfmisc_1(B,A))))) # label(t16_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5552 (all A (v1_relat_1(A) -> k6_relat_1(k1_relat_1(k1_sysrel(A))) = k1_sysrel(A))) # label(t47_sysrel) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5553 (all A (v3_ordinal1(A) -> (r1_ordinal1(k5_ordinal2,A) -> A = k14_ordinal2(k4_ordinal2,A)))) # label(t31_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5554 (all A all B (v1_finset_1(B) -> v1_finset_1(A) | k1_card_1(k2_xboole_0(A,B)) = k1_card_1(A) & r2_wellord2(k2_xboole_0(A,B),A))) # label(t36_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5555 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> r1_tarski(k2_card_2(k3_card_1(np__0),k1_card_1(A)),k3_card_1(np__0)) & r1_tarski(k2_card_2(k1_card_1(A),k3_card_1(np__0)),k3_card_1(np__0)))) # label(t67_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5556 (all A (v3_ordinal1(A) -> ((all B (v3_ordinal1(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(B,A) -> r2_hidden(k14_ordinal2(B,C),A)))))) <-> v4_ordinal1(A)))) # label(t27_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5557 (all A (-v1_xboole_0(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (v1_card_4(A) -> v1_card_4(k4_finseq_2(B,A))))))) # label(t58_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5558 (all A (-v1_xboole_0(A) -> r1_tarski(k3_card_1(np__0),k1_card_1(k3_finseq_2(A))))) # label(t66_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5559 (all A all B (v1_finset_1(B) -> v1_finset_1(A) | r2_wellord2(k2_zfmisc_1(A,B),A) & k1_card_1(A) = k1_card_1(k2_zfmisc_1(A,B)) | k1_xboole_0 = B)) # label(t81_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5560 (all A all B (k1_card_2(k1_card_1(A),k1_card_1(B)) = k1_card_1(A) & r2_hidden(k1_card_1(B),k1_card_1(A)) -> k1_card_1(k4_xboole_0(A,B)) = k1_card_1(A))) # label(t76_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5561 (all A all B (v1_card_4(A) & v1_card_4(B) -> v1_card_4(k2_xboole_0(A,B)))) # label(t47_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5562 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (v1_finset_1(A) -> v1_finset_1(B) | -r2_hidden(B,A) & -r1_tarski(B,A)))))) # label(t26_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5563 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_card_1(C) -> (all D (v1_card_1(D) -> (-(-(r2_hidden(C,D) & r2_hidden(A,B)) & -(r2_hidden(C,D) & r1_tarski(A,B)) & -(r1_tarski(C,D) & r1_tarski(A,B)) & -(r2_hidden(A,B) & r1_tarski(C,D))) -> r1_tarski(k2_card_2(A,C),k2_card_2(B,D)) & r1_tarski(k2_card_2(C,A),k2_card_2(B,D))))))))))) # label(t68_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5564 $T # label(t16_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5565 (all A (v1_card_1(A) -> (-v1_finset_1(A) -> A = k2_card_2(A,A)))) # label(t77_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5566 $T # label(t12_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5567 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (-v1_finset_1(A) -> -v1_finset_1(k1_card_2(B,A)) & -v1_finset_1(k1_card_2(A,B))))))) # label(t39_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5568 (all A (v3_ordinal1(A) -> (exists B (m2_subset_1(B,k1_numbers,k5_numbers) & k14_ordinal2(A,B) = k15_ordinal2(A,k1_ordinal1(k4_ordinal2)))))) # label(t29_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5569 (all A (v1_card_1(A) -> (-v1_finset_1(A) <-> r1_ordinal1(k3_card_1(np__0),A)))) # label(t11_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5570 $T # label(t10_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5571 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> -(-v1_finset_1(A) & (r1_tarski(B,A) | r2_hidden(B,A)) & -(A = k1_card_2(A,B) & k1_card_2(B,A) = A)))))) # label(t34_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5572 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (r2_hidden(A,B) <-> r1_tarski(k2_card_1(A),B)))))) # label(t22_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5573 (all A (A = k1_xboole_0 <-> k1_card_1(A) = np__0)) # label(t17_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5574 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (B = A <-> k2_card_1(B) = k2_card_1(A)))))) # label(t21_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5575 (all A all B (v1_card_4(B) & v1_card_4(A) -> v1_card_4(k5_xboole_0(A,B)))) # label(t50_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5576 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_card_1(C) -> (r2_hidden(k1_card_2(A,B),k1_card_2(A,C)) -> r2_hidden(B,C)))))))) # label(t75_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5577 (all A all B (v1_finset_1(A) -> A = k1_xboole_0 | k1_card_1(B) = k2_card_2(k1_card_1(B),k1_card_1(A)) | v1_finset_1(B))) # label(t85_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5578 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> m2_subset_1(k1_card_4(A,B),k1_numbers,k5_numbers))) # label(dt_k1_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5579 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_card_1(C) -> (all D (v1_card_1(D) -> (r2_hidden(A,B) & r2_hidden(C,D) -> r2_hidden(k1_card_2(C,A),k1_card_2(B,D)) & r2_hidden(k1_card_2(A,C),k1_card_2(B,D))))))))))) # label(t74_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5580 (all A (v1_finset_1(A) <-> (exists B (m2_subset_1(B,k1_numbers,k5_numbers) & k1_card_1(A) = k1_card_1(B))))) # label(t4_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5581 (all A all B -(-(r2_wellord2(k2_xboole_0(A,B),A) & k1_card_1(k2_xboole_0(A,B)) = k1_card_1(A)) & (r2_hidden(k1_card_1(B),k1_card_1(A)) | r1_tarski(k1_card_1(B),k1_card_1(A))) & -v1_finset_1(A))) # label(t37_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5582 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v3_ordinal1(B) -> (r2_wellord2(B,A) -> A = B))))) # label(t6_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5583 (all A (v1_card_4(A) & (all B (r2_hidden(B,A) -> v1_card_4(B))) -> v1_card_4(k3_tarski(A)))) # label(t62_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5584 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> r1_tarski(A,k1_card_2(A,B)) & r1_tarski(B,k1_card_2(A,B)))))) # label(t72_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5585 (all A (r2_hidden(k1_card_1(A),k3_card_1(np__0)) <-> v1_finset_1(A))) # label(t2_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5586 (all A (v3_ordinal1(A) -> (r2_hidden(A,k5_ordinal2) <-> v1_finset_1(A)))) # label(t7_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5587 (all A ((exists B exists C (f1_s2_card_4(B,C) = A & p1_s2_card_4(B,C) & m2_subset_1(C,k1_numbers,k5_numbers) & m2_subset_1(B,k1_numbers,k5_numbers))) <-> r2_hidden(A,a_0_1_card_4))) # label(fraenkel_a_0_1_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5588 (all A (v3_ordinal1(A) -> (v4_ordinal1(A) -> A = k15_ordinal2(A,k1_ordinal1(k4_ordinal2))))) # label(t30_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5589 (all A all B (v1_card_1(B) -> (all C (v1_card_1(C) -> ((all D (r2_hidden(D,A) -> r1_tarski(k1_card_1(D),C))) & r1_tarski(k1_card_1(A),B) -> r1_tarski(k1_card_1(k3_tarski(A)),k2_card_2(B,C))))))) # label(t60_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5590 $T # label(t18_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5591 (all A (v1_card_1(A) -> (-v1_finset_1(A) -> v4_ordinal1(A)))) # label(t32_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5592 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_card_1(C) -> -(C != np__0 & -(r1_tarski(k3_card_2(A,C),k3_card_2(B,C)) & r1_tarski(k3_card_2(C,A),k3_card_2(C,B))) & (r1_tarski(A,B) | r2_hidden(A,B))))))))) # label(t71_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5593 (all A (-v1_finset_1(A) -> k1_card_1(A) = k2_card_2(k3_card_1(np__0),k1_card_1(A)))) # label(t84_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5594 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> -(-v1_finset_1(A) & -(r1_tarski(k2_card_2(A,B),A) & r1_tarski(k2_card_2(B,A),A)) & (r2_hidden(B,A) | r1_tarski(B,A))))))) # label(t79_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5595 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B (r2_hidden(B,k1_relat_1(A)) -> v1_finset_1(k1_funct_1(A,B)))) & v1_finset_1(k1_relat_1(A)) -> v1_finset_1(k3_card_3(A))))) # label(t63_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5596 (all A all B (r1_tarski(A,B) & v1_card_4(B) -> v1_card_4(A))) # label(t46_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5597 (all A (v1_card_1(A) & v1_finset_1(A) -> (all B (v1_finset_1(B) & v1_card_1(B) -> v1_finset_1(k2_card_2(A,B)))))) # label(t40_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5598 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (k2_nat_1(k1_card_4(np__2,C),k1_nat_1(k2_nat_1(np__2,D),np__1)) = k2_nat_1(k1_card_4(np__2,A),k1_nat_1(k2_nat_1(np__2,B),np__1)) -> B = D & C = A))))))))) # label(t52_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5599 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_card_1(C) -> (r2_hidden(A,B) | r1_tarski(A,B) -> r1_tarski(k1_card_2(A,C),k1_card_2(C,B)) & r1_tarski(k1_card_2(A,C),k1_card_2(B,C)) & r1_tarski(k1_card_2(C,A),k1_card_2(B,C)) & r1_tarski(k1_card_2(C,A),k1_card_2(C,B))))))))) # label(t42_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5600 (all A ((exists B (v1_relat_1(B) & v1_funct_1(B) & r1_tarski(A,k2_relat_1(B)) & k1_relat_1(B) = k5_numbers)) <-> v1_card_4(A))) # label(t45_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5601 (all A (-v1_xboole_0(A) -> k1_card_1(A) = k1_card_1(k4_finseq_2(np__1,A)) & r2_wellord2(k4_finseq_2(np__1,A),A))) # label(t56_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5602 (all A all B (k1_card_1(A) = k1_card_1(B) <-> k2_card_1(A) = k2_card_1(B))) # label(t20_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5603 (all A (v1_finset_1(A) -> v1_card_4(A))) # label(t43_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5604 (all A (r1_tarski(k1_card_1(A),k3_card_1(np__0)) <-> v1_card_4(A))) # label(d1_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5605 (all A (v1_card_1(A) -> (r2_hidden(np__0,A) <-> r1_tarski(np__1,A)))) # label(t24_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5606 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> k1_card_4(A,B) = k2_newton(A,B))) # label(redefinition_k1_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5607 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v3_ordinal1(B) -> k14_ordinal2(k1_ordinal1(B),A) = k14_ordinal2(B,k1_nat_1(A,np__1)) & k14_ordinal2(k1_ordinal1(B),A) = k14_ordinal2(B,k1_ordinal1(A)))))) # label(t28_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5608 (all A (v1_finset_1(A) -> r2_hidden(k1_card_1(A),k3_card_1(np__0)) & r2_hidden(k1_card_1(A),k5_ordinal2))) # label(t3_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5609 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k1_card_1(k1_relat_1(C)),A) & (all D (r2_hidden(D,k1_relat_1(C)) -> r1_tarski(k1_card_1(k1_funct_1(C,D)),B))) -> r1_tarski(k1_card_1(k3_card_3(C)),k2_card_2(A,B))))))))) # label(t59_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5610 (all A all B -(-v1_finset_1(A) & -(r2_wellord2(k2_xboole_0(A,B),A) & k1_card_1(A) = k1_card_1(k2_xboole_0(A,B))) & (r2_wellord2(A,B) | r2_wellord2(B,A)))) # label(t35_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5611 (all A (-v1_xboole_0(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> -(-v1_finset_1(A) & np__0 != B & -(r2_wellord2(k4_finseq_2(B,A),A) & k1_card_1(k4_finseq_2(B,A)) = k1_card_1(A))))))) # label(t86_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5612 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_card_1(C) -> (r2_hidden(A,B) | r1_tarski(A,B) -> r1_tarski(k2_card_2(C,A),k2_card_2(C,B)) & r1_tarski(k2_card_2(A,C),k2_card_2(C,B)) & r1_tarski(k2_card_2(A,C),k2_card_2(B,C)) & r1_tarski(k2_card_2(C,A),k2_card_2(B,C))))))))) # label(t69_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5613 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (r2_hidden(A,k2_card_1(B)) <-> r1_tarski(A,B)))))) # label(t23_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5614 $T # label(t64_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5615 (all A (v1_card_1(A) -> r1_tarski(np__0,A))) # label(t19_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5616 (all A ((exists B exists C exists D (m2_subset_1(B,k1_numbers,k5_numbers) & m2_subset_1(C,k1_numbers,k5_numbers) & p1_s3_card_4(B,C,D) & A = f1_s3_card_4(B,C,D) & m2_subset_1(D,k1_numbers,k5_numbers))) <-> r2_hidden(A,a_0_2_card_4))) # label(fraenkel_a_0_2_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5617 (all A (v1_card_1(A) & v1_finset_1(A) -> (all B (v1_finset_1(B) & v1_card_1(B) -> v1_finset_1(k1_card_2(A,B)))))) # label(t38_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5618 (all A (v1_card_1(A) -> (r2_hidden(A,k3_card_1(np__0)) <-> v1_finset_1(A)))) # label(t9_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5619 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_card_1(C) -> (all D (v1_card_1(D) -> -(np__0 != A & -r1_tarski(k3_card_2(A,C),k3_card_2(B,D)) & -(-(r2_hidden(C,D) & r2_hidden(A,B)) & -(r2_hidden(C,D) & r1_tarski(A,B)) & -(r1_tarski(C,D) & r1_tarski(A,B)) & -(r1_tarski(C,D) & r2_hidden(A,B)))))))))))) # label(t70_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5620 (all A (-v1_finset_1(A) -> r2_wellord2(k2_zfmisc_1(A,A),A) & k1_card_1(A) = k1_card_1(k2_zfmisc_1(A,A)))) # label(t80_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5621 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (v1_finset_1(A) -> r2_hidden(A,B) & r1_tarski(A,B) | v1_finset_1(B)))))) # label(t13_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5622 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_card_1(C) -> (r2_hidden(k2_card_2(A,B),k2_card_2(A,C)) -> r2_hidden(B,C)))))))) # label(t83_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5623 (all A (-((all B -(r1_tarski(B,A) & k3_card_1(np__0) = k1_card_1(B))) & -v1_finset_1(A)) & -((exists B (k3_card_1(np__0) = k1_card_1(B) & r1_tarski(B,A))) & v1_finset_1(A)))) # label(t14_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5624 (all A all B (v1_card_4(A) -> v1_card_4(k4_xboole_0(A,B)))) # label(t49_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5625 (all A ((exists B (f1_s1_card_4(B) = A & p1_s1_card_4(B) & m2_subset_1(B,k1_numbers,k5_numbers))) <-> r2_hidden(A,a_0_0_card_4))) # label(fraenkel_a_0_0_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5626 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_card_1(C) -> (all D (v1_card_1(D) -> (r2_hidden(C,D) & r2_hidden(A,B) -> r2_hidden(k2_card_2(C,A),k2_card_2(B,D)) & r2_hidden(k2_card_2(A,C),k2_card_2(B,D))))))))))) # label(t82_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5627 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_card_1(C) -> (all D (v1_card_1(D) -> (-(-(r1_tarski(C,D) & r1_tarski(A,B)) & -(r1_tarski(C,D) & r2_hidden(A,B)) & -(r1_tarski(A,B) & r2_hidden(C,D)) & -(r2_hidden(C,D) & r2_hidden(A,B))) -> r1_tarski(k1_card_2(A,C),k1_card_2(B,D)) & r1_tarski(k1_card_2(C,A),k1_card_2(B,D))))))))))) # label(t41_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5628 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B (r2_hidden(B,k1_relat_1(A)) -> v1_card_4(k1_funct_1(A,B)))) & v1_card_4(k1_relat_1(A)) -> v1_card_4(k3_card_3(A))))) # label(t61_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5629 (all A (v1_finset_1(k1_card_1(A)) <-> v1_finset_1(A))) # label(t1_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5630 (all A all B (v1_card_4(B) & v1_card_4(A) -> v1_card_4(k2_zfmisc_1(A,B)))) # label(t55_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5631 (all A (v1_card_1(A) -> (r1_tarski(np__2,A) <-> r2_hidden(np__1,A)))) # label(t25_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5632 (all A (v1_card_1(A) -> (-v1_finset_1(A) -> A = k1_card_2(A,A)))) # label(t33_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5633 (all A (v3_ordinal1(A) -> (-v1_finset_1(A) <-> r1_ordinal1(k5_ordinal2,A)))) # label(t8_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5634 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (r2_hidden(np__0,B) -> v1_finset_1(A) | -r2_hidden(B,A) & -r1_tarski(B,A) | k2_card_2(A,B) = A & A = k2_card_2(B,A)))))) # label(t78_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5635 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (np__0 != A -> r1_tarski(B,k2_card_2(A,B)) & r1_tarski(B,k2_card_2(B,A))))))) # label(t73_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5636 (all A (v3_ordinal1(A) -> A = k4_xboole_0(k1_ordinal1(A),k1_tarski(A)))) # label(t5_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5637 (all A (-v1_xboole_0(A) -> (v1_card_4(A) -> v1_card_4(k3_finseq_2(A))))) # label(t65_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5638 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> -(np__0 != A & B = np__0 & np__0 != k3_newton(B,A)) & -(np__0 = k3_newton(B,A) & -(A != np__0 & B = np__0)))))) # label(t51_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5639 (all A all B (v1_card_4(A) -> v1_card_4(k3_xboole_0(A,B)) & v1_card_4(k3_xboole_0(B,A)))) # label(t48_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5640 (all A (-v1_xboole_0(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> r2_wellord2(k2_zfmisc_1(k4_finseq_2(B,A),k4_finseq_2(C,A)),k4_finseq_2(k1_nat_1(B,C),A)) & k1_card_1(k2_zfmisc_1(k4_finseq_2(B,A),k4_finseq_2(C,A))) = k1_card_1(k4_finseq_2(k1_nat_1(B,C),A)))))))) # label(t57_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5641 (all A (-v1_xboole_0(A) -> (-v1_finset_1(A) -> k1_card_1(k3_finseq_2(A)) = k1_card_1(A)))) # label(t87_card_4) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5642 $T # label(d5_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5643 (all A all B (v1_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) -> (all C all D (m1_toler_1(D,A,B) & v1_toler_1(D,A,B) -> (r2_hidden(C,D) -> r1_tarski(D,k6_eqrel_1(A,B,C))))))) # label(t70_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5644 (all A all B (v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v1_relat_2(B) -> r1_tarski(k6_partfun1(A),B))) # label(t50_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5645 $T # label(t24_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5646 (all A all B all C (r2_hidden(B,k3_relat_1(k1_eqrel_1(A))) & r2_hidden(C,k3_relat_1(k1_eqrel_1(A))) -> r2_hidden(k4_tarski(B,C),k1_eqrel_1(A)))) # label(t16_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5647 (all A all B all C (v1_relat_2(B) & m1_subset_1(C,k1_zfmisc_1(A)) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) -> k2_wellord1(B,C) = k2_toler_1(A,B,C))) # label(redefinition_k2_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5648 (all A all B (v1_relat_2(B) & v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) -> r1_tarski(B,k7_relset_1(A,A,A,A,B,B)))) # label(t74_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5649 (all A all B (v1_relat_2(B) & v3_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) -> (exists C (m1_toler_1(C,A,B) & v1_toler_1(C,A,B))))) # label(rc1_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5650 $T # label(t14_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5651 $T # label(t48_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5652 (all A all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) & v1_relat_2(B) -> k3_tarski(k4_toler_1(A,B)) = A)) # label(t66_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5653 $T # label(t23_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5654 $T # label(t62_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5655 (all A all B all C (r2_hidden(C,A) & r2_hidden(B,A) -> r2_hidden(k4_tarski(B,C),k1_eqrel_1(A)))) # label(t15_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5656 (all A v7_relat_2(k1_eqrel_1(A))) # label(t19_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5657 (all A all B (v1_relat_2(B) & v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> (all C all D (r2_hidden(k4_tarski(C,D),B) -> m1_toler_1(k2_tarski(C,D),A,B))))) # label(t40_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5658 (all A all B (v1_relat_2(B) & v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> (all C -((all D (m1_toler_1(D,A,B) & v1_toler_1(D,A,B) -> -r2_hidden(C,D))) & r2_hidden(C,A))))) # label(t47_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5659 (all A all B all C (v1_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) -> (r2_hidden(B,A) <-> r2_hidden(k4_tarski(B,B),C)))) # label(t27_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5660 (all A all B (v1_relat_1(A) -> k1_toler_1(A,B) = k2_wellord1(A,B))) # label(redefinition_k1_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5661 (all A all B (v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v1_relat_2(B) -> m1_toler_1(k1_xboole_0,A,B))) # label(t34_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5662 (all A all B all C (v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v3_relat_2(C) & v1_relat_2(C) -> (all D ((all E (m1_toler_1(E,A,C) & v1_toler_1(E,A,C) & r2_hidden(B,E) <-> r2_hidden(E,D))) -> k6_eqrel_1(A,C,B) = k3_tarski(D))))) # label(t58_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5663 (all A k5_relset_1(A,A,k1_eqrel_1(A)) = A) # label(t13_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5664 $T # label(t10_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5665 (all A all B (v1_relat_1(A) -> m2_relset_1(k1_toler_1(A,B),B,B))) # label(dt_k1_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5666 $T # label(t22_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5667 $T # label(d2_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5668 $T # label(t12_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5669 (all A all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) & v1_relat_2(B) -> (all C (m1_toler_1(C,A,B) -> (v1_toler_1(C,A,B) <-> (all D -(-r2_hidden(D,C) & r2_hidden(D,A) & (all E -(-r2_hidden(k4_tarski(D,E),B) & r2_hidden(E,C)))))))))) # label(d4_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5670 $T # label(t57_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5671 $T # label(dt_m1_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5672 (all A all B (v1_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) -> A = k3_tarski(k3_toler_1(A,B)))) # label(t67_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5673 $T # label(t63_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5674 (all A all B (v1_relat_2(B) & v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> r1_tarski(B,k1_eqrel_1(A)))) # label(t49_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5675 $T # label(t60_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5676 (all A all B all C (v3_relat_2(C) & m2_relset_1(C,B,B) & v1_partfun1(C,B,B) & v1_relat_2(C) -> (m1_toler_1(A,B,C) -> r1_tarski(A,B)))) # label(t43_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5677 (all A all B all C (v1_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v3_relat_2(C) -> (all D ((all E (r2_hidden(E,D) <-> m1_toler_1(E,A,C) & r2_hidden(B,E))) -> k3_tarski(D) = k6_eqrel_1(A,C,B))))) # label(t59_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5678 $T # label(t17_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5679 $T # label(t20_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5680 (all A all B (v1_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) -> (v1_toler_1(k1_xboole_0,A,B) & m1_toler_1(k1_xboole_0,A,B) -> k1_xboole_0 = B))) # label(t38_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5681 $T # label(dt_k4_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5682 (all A all B (v1_relat_2(B) & v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> (all C (v3_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v1_relat_2(C) -> (r1_tarski(k4_toler_1(A,B),k4_toler_1(A,C)) -> r1_tarski(B,C)))))) # label(t64_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5683 $T # label(d1_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5684 (all A all B (v1_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) -> (all C all D -(r2_hidden(k4_tarski(C,D),B) & (all E (m1_toler_1(E,A,B) & v1_toler_1(E,A,B) -> -(r2_hidden(D,E) & r2_hidden(C,E)))))))) # label(t46_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5685 $T # label(t36_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5686 (all A all B (v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v3_relat_2(B) & v1_relat_2(B) -> (all C all D (m1_toler_1(C,A,B) & m1_toler_1(D,A,B) -> m1_toler_1(k3_xboole_0(C,D),A,B))))) # label(t42_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5687 (all A all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) & v1_relat_2(B) -> (v8_relat_2(B) -> (all C (r2_hidden(C,A) -> v1_toler_1(k6_eqrel_1(A,B,C),A,B) & m1_toler_1(k6_eqrel_1(A,B,C),A,B)))))) # label(t69_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5688 $T # label(t61_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5689 (all A all B all C (v1_relat_2(B) & v3_relat_2(B) & v1_partfun1(B,A,A) & m1_subset_1(C,k1_zfmisc_1(A)) & m1_relset_1(B,A,A) -> v1_relat_2(k2_toler_1(A,B,C)) & m2_relset_1(k2_toler_1(A,B,C),C,C) & v1_partfun1(k2_toler_1(A,B,C),C,C) & v3_relat_2(k2_toler_1(A,B,C)))) # label(dt_k2_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5690 $T # label(t55_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5691 $T # label(t56_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5692 $T # label(t26_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5693 (all A all B all C (v1_relat_2(C) & v3_relat_2(C) & v1_partfun1(C,B,B) & m2_relset_1(C,B,B) -> (r1_tarski(A,B) -> m2_relset_1(k1_toler_1(C,A),A,A) & v1_partfun1(k1_toler_1(C,A),A,A) & v3_relat_2(k1_toler_1(C,A)) & v1_relat_2(k1_toler_1(C,A))))) # label(t33_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5694 (all A all B (v1_relat_2(B) & v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> ((all C (r2_hidden(C,A) -> m1_toler_1(k6_eqrel_1(A,B,C),A,B))) -> v8_relat_2(B)))) # label(t68_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5695 (all A all B (r2_hidden(A,f1_s1_toler_1) & r2_hidden(B,f1_s1_toler_1) & p1_s1_toler_1(A,B) -> p1_s1_toler_1(B,A))) & (all A (r2_hidden(A,f1_s1_toler_1) -> p1_s1_toler_1(A,A))) -> (exists A (v3_relat_2(A) & v1_partfun1(A,f1_s1_toler_1,f1_s1_toler_1) & (all B all C (r2_hidden(B,f1_s1_toler_1) & r2_hidden(C,f1_s1_toler_1) -> (p1_s1_toler_1(B,C) <-> r2_hidden(k4_tarski(B,C),A)))) & m2_relset_1(A,f1_s1_toler_1,f1_s1_toler_1) & v1_relat_2(A))) # label(s1_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5696 (all A all B (v1_relat_2(B) & v3_relat_2(B) & v1_partfun1(B,k3_tarski(A),k3_tarski(A)) & m2_relset_1(B,k3_tarski(A),k3_tarski(A)) -> (all C (m2_relset_1(C,k3_tarski(A),k3_tarski(A)) & v1_partfun1(C,k3_tarski(A),k3_tarski(A)) & v3_relat_2(C) & v1_relat_2(C) -> ((all D all E (r2_hidden(k4_tarski(D,E),B) <-> (exists F (r2_hidden(F,A) & r2_hidden(E,F) & r2_hidden(D,F))))) & (all D all E (r2_hidden(k4_tarski(D,E),C) <-> (exists F (r2_hidden(F,A) & r2_hidden(D,F) & r2_hidden(E,F))))) -> B = C))))) # label(t52_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5697 (all A all B (v1_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) -> (all C (m1_toler_1(C,A,B) -> (exists D (r1_tarski(C,D) & m1_toler_1(D,A,B) & v1_toler_1(D,A,B))))))) # label(t45_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5698 $T # label(t11_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5699 $T # label(t35_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5700 $T # label(t44_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5701 $T # label(t18_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5702 (all A all B all C all D (m2_relset_1(D,A,B) -> (v3_relat_2(D) -> v3_relat_2(k1_toler_1(D,C))))) # label(t32_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5703 (all A all B (v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v1_relat_2(B) -> r1_tarski(k4_toler_1(A,B),k3_toler_1(A,B)))) # label(t72_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5704 (all A all B (v1_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v3_relat_2(B) -> (all C (v3_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v1_relat_2(C) -> ((all D (v1_toler_1(D,A,B) & m1_toler_1(D,A,B) <-> v1_toler_1(D,A,C) & m1_toler_1(D,A,C))) -> B = C))))) # label(t53_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5705 (all A all B (v1_relat_2(B) & v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) -> (all C ((all D (v1_toler_1(D,A,B) & m1_toler_1(D,A,B) <-> r2_hidden(D,C))) <-> C = k4_toler_1(A,B))))) # label(d7_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5706 $T # label(t30_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5707 (all A all B (v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v1_relat_2(B) -> A = k5_relset_1(A,A,B))) # label(t25_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5708 (all A all B (v1_relat_2(B) & v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> r1_relat_2(B,A))) # label(t28_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5709 (all A all B (v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v1_relat_2(B) -> (all C ((all D all E (r2_hidden(D,C) & r2_hidden(E,C) -> r2_hidden(k4_tarski(D,E),B))) <-> m1_toler_1(C,A,B))))) # label(d3_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5710 (all A exists B (v1_relat_2(B) & v3_relat_2(B) & v1_partfun1(B,k3_tarski(A),k3_tarski(A)) & (all C (r2_hidden(C,A) -> m1_toler_1(C,k3_tarski(A),B))) & m2_relset_1(B,k3_tarski(A),k3_tarski(A)))) # label(t51_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5711 (all A all B (v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v3_relat_2(B) & v1_relat_2(B) -> (all C (r2_hidden(C,A) -> m1_toler_1(k1_tarski(C),A,B))))) # label(t41_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5712 (all A all B (v1_relat_2(B) & v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) -> (all C (v1_relat_2(C) & v3_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) -> (r1_tarski(k3_toler_1(A,B),k3_toler_1(A,C)) <-> r1_tarski(B,C)))))) # label(t71_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5713 (all A all B all C (v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v3_relat_2(C) & v1_relat_2(C) -> (all D (r2_hidden(D,k6_eqrel_1(A,C,B)) <-> r2_hidden(k4_tarski(B,D),C))))) # label(t54_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5714 (all A v6_relat_2(k1_eqrel_1(A))) # label(t21_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5715 (all A all B (v1_relat_2(B) & v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) -> (all C ((all D (r2_hidden(D,C) <-> m1_toler_1(D,A,B))) <-> C = k3_toler_1(A,B))))) # label(d6_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5716 (all A all B (v1_relat_2(B) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) -> (exists C m1_toler_1(C,A,B)))) # label(existence_m1_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5717 $T # label(t31_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5718 (all A all B (v1_relat_2(B) & v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) -> r3_relat_2(B,A))) # label(t29_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5719 (all A all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) & v1_relat_2(B) -> (all C (m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v3_relat_2(C) & v1_relat_2(C) -> ((all D (r2_hidden(D,A) -> r1_tarski(k6_eqrel_1(A,B,D),k6_eqrel_1(A,C,D)))) -> r1_tarski(B,C)))))) # label(t73_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5720 $T # label(t37_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5721 (all A all B (v1_relat_2(B) & v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) -> (all C (v1_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v3_relat_2(C) -> (k4_toler_1(A,C) = k4_toler_1(A,B) -> C = B))))) # label(t65_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5722 $T # label(dt_k3_toler_1) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5723 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(A) = k1_relat_1(B) -> (r1_rfinseq(A,B) <-> (exists C (m2_relset_1(C,k1_relat_1(A),k1_relat_1(A)) & k5_relat_1(C,B) = A & v3_funct_2(C,k1_relat_1(A),k1_relat_1(A)) & v1_funct_2(C,k1_relat_1(A),k1_relat_1(A)) & v1_funct_1(C))))))))) # label(t6_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5724 (all A (m2_finseq_1(A,k1_numbers) -> (exists B (r1_rfinseq(A,B) & m2_finseq_1(B,k1_numbers) & v1_rfinseq(B))))) # label(t35_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5725 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> B = k8_finseq_1(A,k16_finseq_1(A,B,C),k1_rfinseq(A,B,C)))))))) # label(t21_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5726 (all A (m2_finseq_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (C = k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(D,np__2)) & B = k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(D,np__1)) & k1_nat_1(D,np__2) = k3_finseq_1(A) -> k2_rfinseq(A) = k8_finseq_1(k1_numbers,k16_finseq_1(k1_numbers,k2_rfinseq(A),D),k2_finseq_4(k1_numbers,k5_real_1(B,C),C))))))))))) # label(t24_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5727 (all A (m2_finseq_1(A,k1_numbers) -> (v1_rfinseq(A) <-> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(C,k4_finseq_1(A)) & r2_hidden(B,k4_finseq_1(A)) -> r1_xreal_0(C,B) | r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,C),k2_seq_1(k5_numbers,k1_numbers,A,B)))))))))) # label(t32_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5728 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_finset_1(B) -> (exists C (v1_funct_1(C) & r1_rfinseq(k7_relat_1(A,B),C) & v1_finseq_1(C) & v1_relat_1(C))))))) # label(t18_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5729 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> ((all C k1_card_1(k10_relat_1(A,k1_tarski(C))) = k1_card_1(k10_relat_1(B,k1_tarski(C)))) <-> r1_rfinseq(A,B)))))) # label(d1_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5730 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (r1_rfinseq(A,B) <-> r1_rfinseq(k7_finseq_1(A,C),k7_finseq_1(B,C))))))))) # label(t14_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5731 (all A all B (v1_finset_1(B) & v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k7_relat_1(A,B)) & v1_finset_1(k7_relat_1(A,B)) & v1_relat_1(k7_relat_1(A,B)))) # label(fc1_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5732 (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 k4_card_1(k10_relat_1(B,C)) = k4_card_1(k10_relat_1(A,C))) <-> r1_rfinseq(A,B)))))) # label(t13_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5733 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_rfinseq(A,B) -> k1_card_1(k1_relat_1(A)) = k1_card_1(k1_relat_1(B))))))) # label(t7_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.79 5734 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_rfinseq(A,B) -> k2_relat_1(A) = k2_relat_1(B)))))) # label(t1_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5735 (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_rfinseq(A,C) & r1_rfinseq(A,B) -> r1_rfinseq(B,C)))))))) # label(t2_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5736 (all A (m2_finseq_1(A,k1_numbers) -> (v1_rfinseq(A) <-> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(k1_nat_1(B,np__1),k4_finseq_1(A)) & r2_hidden(B,k4_finseq_1(A)) -> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(B,np__1)),k2_seq_1(k5_numbers,k1_numbers,A,B)))))))) # label(d4_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5737 (all A (m2_finseq_1(A,k1_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,B) -> r1_xreal_0(k3_finseq_1(A),B) | k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(B,np__1)) = k15_rvsum_1(k2_rfinseq(k1_rfinseq(k1_numbers,A,B)))))))) # label(t30_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5738 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (r1_rfinseq(A,B) <-> (exists C (m2_relset_1(C,k4_finseq_1(B),k4_finseq_1(B)) & A = k5_relat_1(C,B) & v3_funct_2(C,k4_finseq_1(B),k4_finseq_1(B)) & v1_funct_2(C,k4_finseq_1(B),k4_finseq_1(B)) & v1_funct_1(C)))))))) # label(t17_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5739 (all A (-v1_xboole_0(A) -> (all B (v1_relat_1(B) & v1_finset_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finset_1(C) -> (r1_tarski(k2_relat_1(C),A) & r1_tarski(k2_relat_1(B),A) -> ((all D (m1_subset_1(D,A) -> k4_card_1(k10_relat_1(C,k1_tarski(D))) = k4_card_1(k10_relat_1(B,k1_tarski(D))))) <-> r1_rfinseq(B,C))))))))) # label(t11_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5740 (all A (v1_rfinseq(A) & m2_finseq_1(A,k1_numbers) -> (all B (m2_finseq_1(B,k1_numbers) & v1_rfinseq(B) -> (r1_rfinseq(A,B) -> B = A))))) # label(t36_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5741 (all A (v1_relat_1(A) & v1_finset_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_finset_1(B) & v1_relat_1(B) -> (r1_rfinseq(A,B) -> k4_card_1(k1_relat_1(B)) = k4_card_1(k1_relat_1(A))))))) # label(t10_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5742 (all A (m2_finseq_1(A,k1_numbers) -> k3_funct_2(k5_numbers,k1_numbers,k9_rvsum_1(np__0,A),k1_tarski(np__0)) = k4_finseq_1(A))) # label(t38_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5743 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> r1_rfinseq(k7_finseq_1(A,B),k7_finseq_1(B,A)))))) # label(t15_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5744 (all A (v1_finset_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) -> ((all C k4_card_1(k10_relat_1(A,C)) = k4_card_1(k10_relat_1(B,C))) <-> r1_rfinseq(A,B)))))) # label(t9_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5745 $T # label(t8_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5746 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (r1_rfinseq(A,B) -> k3_finseq_1(B) = k3_finseq_1(A) & k4_finseq_1(A) = k4_finseq_1(B)))))) # label(t16_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5747 (all A (-v1_xboole_0(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),A) & r1_tarski(k2_relat_1(C),A) -> (r1_rfinseq(B,C) <-> (all D (m1_subset_1(D,A) -> k1_card_1(k10_relat_1(B,k1_tarski(D))) = k1_card_1(k10_relat_1(C,k1_tarski(D))))))))))))) # label(t5_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5748 (all A (m1_finseq_1(A,k1_numbers) -> m2_finseq_1(k2_rfinseq(A),k1_numbers))) # label(dt_k2_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5749 (all A (m2_finseq_1(A,k1_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k1_rfinseq(k1_numbers,k2_rfinseq(A),B) = k2_rfinseq(k1_rfinseq(k1_numbers,A,B)))))) # label(t28_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5750 (all A all B all C (m1_subset_1(C,k5_numbers) & m1_finseq_1(B,A) -> m2_finseq_1(k1_rfinseq(A,B,C),A))) # label(dt_k1_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5751 (all A (m2_finseq_1(A,k1_numbers) -> (k3_finseq_1(A) = np__1 | k3_finseq_1(A) = np__0 -> v1_rfinseq(A)))) # label(t31_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5752 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C k1_card_1(k10_relat_1(A,C)) = k1_card_1(k10_relat_1(B,C))) <-> r1_rfinseq(A,B)))))) # label(t4_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5753 (all A (m2_finseq_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (np__0 != B -> k3_funct_2(k5_numbers,k1_numbers,A,k1_tarski(k6_real_1(C,B))) = k3_funct_2(k5_numbers,k1_numbers,k9_rvsum_1(B,A),k1_tarski(C))))))))) # label(t37_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5754 (all A (m2_finseq_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (k3_finseq_1(A) = k1_nat_1(C,np__2) & B = k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(C,np__1)) -> k8_finseq_1(k1_numbers,k16_finseq_1(k1_numbers,k2_rfinseq(A),C),k12_finseq_1(k1_numbers,B)) = k2_rfinseq(k16_finseq_1(k1_numbers,A,k1_nat_1(C,np__1)))))))))) # label(t23_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5755 (all A (m2_finseq_1(A,k1_numbers) -> (all B (m2_finseq_1(B,k1_numbers) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(C,k5_real_1(k3_finseq_1(B),np__1)) & r1_xreal_0(np__1,C) -> k5_real_1(k2_seq_1(k5_numbers,k1_numbers,A,C),k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(C,np__1))) = k2_seq_1(k5_numbers,k1_numbers,B,C)))) & k2_seq_1(k5_numbers,k1_numbers,A,k3_finseq_1(A)) = k2_seq_1(k5_numbers,k1_numbers,B,k3_finseq_1(B)) & k3_finseq_1(B) = k3_finseq_1(A) <-> k2_rfinseq(A) = B))))) # label(d3_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5756 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (k1_funct_1(B,k1_nat_1(C,np__1)) = D & k1_nat_1(C,np__1) = k3_finseq_1(B) -> B = k7_finseq_1(k16_finseq_1(A,B,C),k9_finseq_1(D)))))))))) # label(t20_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5757 (all A all B (m2_finseq_1(B,A) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_finseq_1(D,A) -> (r1_xreal_0(C,k3_finseq_1(B)) -> (k1_rfinseq(A,B,C) = D <-> k3_finseq_1(D) = k5_real_1(k3_finseq_1(B),C) & (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (r2_hidden(E,k4_finseq_1(D)) -> k1_funct_1(D,E) = k1_funct_1(B,k1_nat_1(E,C))))))) & (-r1_xreal_0(C,k3_finseq_1(B)) -> (D = k6_finseq_1(A) <-> k1_rfinseq(A,B,C) = D)))))))) # label(d2_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5758 (all A (m2_finseq_1(A,k1_numbers) & v1_rfinseq(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> v1_rfinseq(k16_finseq_1(k1_numbers,A,B)) & m2_finseq_1(k16_finseq_1(k1_numbers,A,B),k1_numbers))))) # label(t33_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5759 $T # label(t12_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5760 (all A (m2_finseq_1(A,k1_numbers) -> (np__0 != k3_finseq_1(A) -> k15_rvsum_1(k2_rfinseq(A)) = k2_seq_1(k5_numbers,k1_numbers,A,np__1)))) # label(t29_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5761 (exists A (m1_finseq_1(A,k1_numbers) & v1_relat_1(A) & v1_rfinseq(A) & v1_finseq_1(A) & v1_finset_1(A) & v1_funct_1(A))) # label(rc1_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5762 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_rfinseq(A,B) <-> (exists C (k1_relat_1(A) = k1_relat_1(C) & v2_funct_1(C) & A = k5_relat_1(C,B) & k2_relat_1(C) = k1_relat_1(B) & v1_funct_1(C) & v1_relat_1(C)))))))) # label(t3_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5763 (all A (m2_finseq_1(A,k1_numbers) -> (all B (m2_finseq_1(B,k1_numbers) -> (r1_rfinseq(A,B) -> k15_rvsum_1(B) = k15_rvsum_1(A)))))) # label(t22_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5764 (all A all B (v1_relat_1(A) & v1_relat_1(B) -> r1_rfinseq(A,A))) # label(reflexivity_r1_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5765 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> k2_rfinseq(k2_finseq_4(k1_numbers,A,B)) = k2_finseq_4(k1_numbers,k5_real_1(A,B),B))))) # label(t27_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5766 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k2_finseq_1(C)) & r2_hidden(C,k4_finseq_1(B)) -> k1_funct_1(B,D) = k1_funct_1(k16_finseq_1(A,B,C),D) & r2_hidden(D,k4_finseq_1(B))))))))))) # label(t19_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5767 (all A all B (v1_relat_1(B) & v1_relat_1(A) -> (r1_rfinseq(A,B) -> r1_rfinseq(B,A)))) # label(symmetry_r1_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5768 (all A (v1_rfinseq(A) & m2_finseq_1(A,k1_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> m2_finseq_1(k1_rfinseq(k1_numbers,A,B),k1_numbers) & v1_rfinseq(k1_rfinseq(k1_numbers,A,B)))))) # label(t34_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5769 (all A (m1_subset_1(A,k1_numbers) -> k2_rfinseq(k12_finseq_1(k1_numbers,A)) = k12_finseq_1(k1_numbers,A))) # label(t26_rfinseq) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5770 (all A (-v2_card_1(A) & v1_card_1(A) -> (all B (v1_card_1(B) -> (k2_card_1(B) = A <-> k7_card_fil(A) = B))))) # label(d17_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5771 (all A (-v1_finset_1(A) & v1_card_1(A) -> (v2_card_1(A) & v1_card_5(A) <-> v4_card_fil(A)))) # label(d13_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5772 (all A (v6_card_fil(A) & v1_card_1(A) & -v1_finset_1(A) -> v1_ordinal1(A) & v2_ordinal1(A) & -v1_finset_1(A) & v4_card_fil(A) & v1_card_5(A) & v2_card_1(A) & v1_card_1(A) & -v1_xboole_0(A) & v3_ordinal1(A))) # label(cc5_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5773 (all A all B all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) & -v1_xboole_0(B) -> (r2_hidden(A,a_2_0_card_fil(B,C)) <-> (exists D (r2_hidden(k3_subset_1(B,D),C) & D = A & m1_subset_1(D,k1_zfmisc_1(B))))))) # label(fraenkel_a_2_0_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5774 (all A all B (m1_card_fil(B,A) & -v1_xboole_0(A) -> k7_setfam_1(A,B) = k2_card_fil(A,B))) # label(redefinition_k2_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5775 (all A all B all C (-v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) -> (r2_hidden(A,a_2_1_card_fil(B,C)) <-> (exists D (m1_subset_1(D,k1_zfmisc_1(B)) & k3_subset_1(B,D) = A & r2_hidden(D,C)))))) # label(fraenkel_a_2_1_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5776 (exists A (v3_ordinal1(A) & -v1_xboole_0(A) & -v1_finset_1(A) & -v2_card_1(A) & v1_card_1(A) & v2_ordinal1(A) & v1_ordinal1(A))) # label(rc2_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5777 (all A (-v1_finset_1(A) -> (all B (m1_card_fil(B,A) -> (r1_card_fil(A,k1_card_1(A),B) & v3_card_fil(B,A) -> v1_card_fil(B,A) | v2_card_fil(B,A)))))) # label(t23_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5778 (all A (-v1_xboole_0(A) -> (all B (m2_card_fil(B,A) -> m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) & -v1_xboole_0(B))))) # label(dt_m2_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5779 (all A (-v1_finset_1(A) -> (exists B (-v2_card_fil(B,A) & v3_card_fil(B,A) & -v1_xboole_0(B) & m1_card_fil(B,A))))) # label(rc1_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5780 (all A (-v1_finset_1(A) & v1_card_1(A) -> (v7_card_fil(A) -> v2_card_1(A)))) # label(t38_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.36/16.80 5781 (all A (-v1_xboole_0(A) -> (all B (m1_card_fil(B,A) -> (all C (m2_card_fil(C,A) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> -(r2_hidden(D,B) & r2_hidden(D,k2_card_fil(A,B))))) & (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> -(r2_hidden(D,k7_setfam_1(A,C)) & r2_hidden(D,C)))))))))) # label(t10_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5782 (all A (-v1_xboole_0(A) -> m1_subset_1(k1_tarski(A),k1_zfmisc_1(k1_zfmisc_1(A))) & (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(B,C) & r2_hidden(B,k1_tarski(A)) -> r2_hidden(C,k1_tarski(A))) & (r2_hidden(C,k1_tarski(A)) & r2_hidden(B,k1_tarski(A)) -> r2_hidden(k5_subset_1(A,B,C),k1_tarski(A))))))) & -r2_hidden(k1_xboole_0,k1_tarski(A)) & -v1_xboole_0(k1_tarski(A)))) # label(t2_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5783 (all A (-v1_finset_1(A) & v1_card_1(A) & v4_card_fil(A) -> v2_ordinal1(A) & v3_ordinal1(A) & -v1_xboole_0(A) & v2_card_1(A) & v1_card_5(A) & v1_card_1(A) & -v1_finset_1(A) & v1_ordinal1(A))) # label(cc2_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5784 (all A all B (m1_card_fil(B,A) & -v1_xboole_0(A) -> m2_card_fil(k2_card_fil(A,B),A))) # label(dt_k2_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5785 (all A (-v2_card_1(A) & v1_card_1(A) -> v1_card_1(k7_card_fil(A)))) # label(dt_k7_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5786 (all A (-v1_xboole_0(A) -> k4_card_fil(A) = a_1_0_card_fil(A))) # label(d9_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5787 (all A (v1_card_1(A) & -v1_finset_1(A) -> (v5_card_fil(A) -> v2_card_1(A)))) # label(t27_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5788 (all A (-v1_finset_1(A) -> v2_ordinal1(k1_card_1(A)) & -v1_xboole_0(k1_card_1(A)) & v1_card_1(k1_card_1(A)) & -v1_finset_1(k1_card_1(A)) & v3_ordinal1(k1_card_1(A)) & v1_ordinal1(k1_card_1(A)))) # label(fc1_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5789 (all A (-v1_finset_1(A) -> (all B (m1_card_fil(B,A) & v3_card_fil(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (-r2_hidden(C,k2_card_fil(A,B)) <-> r2_hidden(C,B)))))))) # label(t22_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5790 (all A (-v1_xboole_0(A) -> (all B (m1_card_fil(B,A) -> ((exists C (m1_subset_1(C,k1_zfmisc_1(A)) & (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(D,B) -> r1_tarski(C,D)))) & r2_hidden(C,B))) <-> v2_card_fil(B,A)))))) # label(d6_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5791 (all A (v1_card_1(A) & -v1_finset_1(A) -> (v4_card_fil(A) & r3_card_fil -> v6_card_fil(A)))) # label(t31_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5792 (all A (-v1_finset_1(A) & v1_card_1(A) -> (v7_card_fil(A) <-> (exists B (m1_card_fil(B,A) & -v2_card_fil(B,A) & v3_card_fil(B,A) & r1_card_fil(A,A,B)))))) # label(d16_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5793 (all A all B (-v1_finset_1(B) -> r2_hidden(k1_card_1(k1_tarski(A)),k1_card_1(B)))) # label(t1_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5794 (all A (v1_card_1(A) & -v1_finset_1(A) -> (v5_card_fil(A) & v1_card_5(A) <-> v6_card_fil(A)))) # label(d15_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5795 (all A (v1_card_1(A) & -v2_card_1(A) & -v1_finset_1(A) -> (exists B (v1_funct_2(B,k2_zfmisc_1(k7_card_fil(A),A),k1_zfmisc_1(A)) & m2_relset_1(B,k2_zfmisc_1(k7_card_fil(A),A),k1_zfmisc_1(A)) & r4_card_fil(A,B) & v1_funct_1(B))))) # label(t34_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5796 (all A (-v1_finset_1(A) -> k5_card_fil(A) = a_1_1_card_fil(A))) # label(d10_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5797 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k4_card_fil(A))) & -v1_xboole_0(B) -> (v6_ordinal1(B) -> m1_card_fil(k3_tarski(B),A)))))) # label(t16_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5798 (all A (-v1_finset_1(A) -> (all B (m1_card_fil(B,A) -> (v1_card_fil(B,A) & v3_card_fil(B,A) -> -v2_card_fil(B,A)))))) # label(cc1_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5799 (all A (-v2_card_1(A) & v1_card_1(A) & -v1_finset_1(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(k7_card_fil(A),A),k1_zfmisc_1(A)) & v1_funct_2(B,k2_zfmisc_1(k7_card_fil(A),A),k1_zfmisc_1(A)) & v1_funct_1(B) -> ((all C (m1_subset_1(C,k7_card_fil(A)) -> r1_tarski(k1_card_1(k1_card_fil(A,k3_tarski(a_3_2_card_fil(A,B,C)))),k7_card_fil(A)))) & (all C (m1_subset_1(C,A) -> r1_tarski(k1_card_1(k1_card_fil(A,k3_tarski(a_3_3_card_fil(A,B,C)))),k7_card_fil(A)))) & (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,k7_card_fil(A)) -> (all E (m1_subset_1(E,k7_card_fil(A)) -> (D != E -> v1_xboole_0(k5_subset_1(A,k2_binop_1(k7_card_fil(A),A,k1_zfmisc_1(A),B,D,C),k2_binop_1(k7_card_fil(A),A,k1_zfmisc_1(A),B,E,C)))))))))) & (all C (m1_subset_1(C,k7_card_fil(A)) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (D != E -> v1_xboole_0(k5_subset_1(A,k2_binop_1(k7_card_fil(A),A,k1_zfmisc_1(A),B,C,D),k2_binop_1(k7_card_fil(A),A,k1_zfmisc_1(A),B,C,E)))))))))) <-> r4_card_fil(A,B)))))) # label(d18_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5800 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) & -v1_xboole_0(B) -> k7_setfam_1(A,B) = a_2_0_card_fil(A,B))))) # label(t8_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5801 (all A all B all C (m1_card_fil(B,A) & m1_subset_1(C,k1_zfmisc_1(A)) & -v1_xboole_0(A) -> m1_subset_1(k3_card_fil(A,B,C),k1_zfmisc_1(k1_zfmisc_1(A))) & -v1_xboole_0(k3_card_fil(A,B,C)))) # label(dt_k3_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5802 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(D,k1_zfmisc_1(B)) & m1_card_fil(C,B) -> ((exists E (A = E & (exists F (m1_subset_1(F,k1_zfmisc_1(B)) & r2_hidden(F,a_3_1_card_fil(B,C,D)) & r1_tarski(F,E))) & m1_subset_1(E,k1_zfmisc_1(B)))) <-> r2_hidden(A,a_3_0_card_fil(B,C,D))))) # label(fraenkel_a_3_0_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5803 r3_card_fil <-> (all A (v1_card_1(A) & -v1_finset_1(A) -> k3_card_2(np__2,A) = k2_card_1(A))) # label(d12_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5804 (all A (-v1_finset_1(A) & v1_card_1(A) & -v2_card_1(A) -> (all B (m2_card_fil(B,A) -> -(r1_tarski(k6_card_fil(A),B) & (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> -(k1_card_1(C) = A & (all D -(r2_hidden(D,B) & r2_hidden(D,C))) & (all D all E (r2_hidden(D,C) & r2_hidden(E,C) -> E = D | r1_xboole_0(D,E)))))) & r2_card_fil(A,A,B)))))) # label(t35_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5805 (all A (-v1_xboole_0(A) -> (all B (m1_card_fil(B,A) -> ((all C (m1_subset_1(C,k1_zfmisc_1(A)) -> r2_hidden(k1_card_fil(A,C),B) | r2_hidden(C,B))) <-> v3_card_fil(B,A)))))) # label(d7_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5806 (all A all B (v1_card_1(B) -> -(r1_tarski(B,k1_card_1(A)) & (all C -(B = k1_card_1(C) & r1_tarski(C,A)))))) # label(t36_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5807 (all A (-v1_xboole_0(A) -> (all B (m1_card_fil(B,A) -> -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))))))) # label(dt_m1_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5808 (all A all B m1_subset_1(k1_card_fil(A,B),k1_zfmisc_1(A))) # label(dt_k1_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5809 (all A all B (-v1_finset_1(B) -> ((exists C (m1_subset_1(C,k1_zfmisc_1(B)) & C = A & r2_hidden(k1_card_1(k1_card_fil(B,C)),k1_card_1(B)))) <-> r2_hidden(A,a_1_1_card_fil(B))))) # label(fraenkel_a_1_1_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5810 (all A (-v1_xboole_0(A) -> (all B (m1_card_fil(B,A) <-> -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) & -r2_hidden(k1_xboole_0,B) & (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r1_tarski(C,D) & r2_hidden(C,B) -> r2_hidden(D,B)) & (r2_hidden(C,B) & r2_hidden(D,B) -> r2_hidden(k5_subset_1(A,C,D),B)))))))))) # label(t3_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5811 (all A (-v1_finset_1(A) & v1_card_1(A) -> (v7_card_fil(A) -> v5_card_fil(A)))) # label(t40_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5812 (all A (-v1_xboole_0(A) -> (all B (m1_card_fil(B,A) -> r2_hidden(A,B))))) # label(t5_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5813 (all A (v1_card_1(A) & -v1_finset_1(A) -> (v5_card_fil(A) <-> (all B (v1_card_1(B) -> (r2_hidden(B,A) -> r2_hidden(k3_card_2(np__2,B),A))))))) # label(d14_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5814 (all A (-v1_finset_1(A) & v1_card_1(A) & -v2_card_1(A) -> v3_ordinal1(k7_card_fil(A)) & v1_card_1(k7_card_fil(A)) & -v1_finset_1(k7_card_fil(A)) & -v1_xboole_0(k7_card_fil(A)) & v2_ordinal1(k7_card_fil(A)) & v1_ordinal1(k7_card_fil(A)))) # label(fc4_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5815 (all A all B all C all D (-v1_xboole_0(B) & m1_card_fil(C,B) & m1_subset_1(D,k1_zfmisc_1(B)) -> ((exists E (m1_subset_1(E,k1_zfmisc_1(B)) & r2_hidden(E,C) & k5_subset_1(B,E,D) = A)) <-> r2_hidden(A,a_3_1_card_fil(B,C,D))))) # label(fraenkel_a_3_1_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5816 (all A (-v1_xboole_0(A) -> (all B (m1_card_fil(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k3_card_fil(A,B,C) = a_3_0_card_fil(A,B,C))))))) # label(d8_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5817 (all A (r2_hidden(A,a_0_0_card_fil) <-> (exists B (m1_subset_1(B,f1_s1_card_fil) & p1_s1_card_fil(B) & B = A)))) # label(fraenkel_a_0_0_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5818 (all A (-v1_finset_1(A) -> k2_card_fil(A,k5_card_fil(A)) = k6_card_fil(A))) # label(d11_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5819 (all A (-v1_xboole_0(A) -> (all B (m2_card_fil(B,A) -> r2_hidden(k1_xboole_0,B))))) # label(t11_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5820 (all A (-v1_finset_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (r2_hidden(B,k5_card_fil(A)) <-> r2_hidden(k1_card_1(k1_card_fil(A,B)),k1_card_1(A))))))) # label(t18_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5821 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) & -v1_xboole_0(B) -> (m1_card_fil(B,A) <-> -r2_hidden(k1_xboole_0,B) & (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(C,B) & r1_tarski(C,D) -> r2_hidden(D,B)) & (r2_hidden(D,B) & r2_hidden(C,B) -> r2_hidden(k5_subset_1(A,C,D),B))))))))))) # label(d1_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5822 (all A (-v1_finset_1(A) -> m1_card_fil(k5_card_fil(A),A))) # label(dt_k5_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5823 (all A (-v1_finset_1(A) -> (all B (m1_card_fil(B,A) -> (r1_tarski(k5_card_fil(A),B) -> v1_card_fil(B,A)))))) # label(t20_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5824 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_card_fil(C,A) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(D,k3_card_fil(A,C,B)) <-> (exists E (m1_subset_1(E,k1_zfmisc_1(A)) & r2_hidden(E,C) & r1_tarski(k5_subset_1(A,E,B),D)))))))))))) # label(t13_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5825 (all A (-v1_xboole_0(A) -> (all B (m1_card_fil(B,A) -> (v1_card_fil(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r2_hidden(C,B) -> k1_card_1(C) = k1_card_1(A))))))))) # label(d5_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5826 (all A (-v1_finset_1(A) & v1_card_1(A) -> (v7_card_fil(A) -> v1_card_5(A)))) # label(t33_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5827 (all A (v1_card_1(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) & -v1_xboole_0(C) -> (r1_card_fil(B,A,C) -> r2_card_fil(B,A,k7_setfam_1(B,C))))))))) # label(t12_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.80 5828 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_card_fil(C,A) -> -(r2_hidden(B,C) & r2_hidden(k1_card_fil(A,B),C)))))))) # label(t6_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5829 (all A (-v1_finset_1(A) -> m2_card_fil(k6_card_fil(A),A))) # label(dt_k6_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5830 (all A (-v1_xboole_0(A) -> (all B (m1_card_fil(B,A) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> ((all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(k3_subset_1(A,D),B) <-> r2_hidden(D,C)))) -> -r2_hidden(A,C) & (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (all E (m1_subset_1(E,k1_zfmisc_1(A)) -> (r1_tarski(E,D) & r2_hidden(D,C) -> r2_hidden(E,C)) & (r2_hidden(E,C) & r2_hidden(D,C) -> r2_hidden(k4_subset_1(A,D,E),C))))))))))))) # label(t7_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5831 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_card_fil(C,A) -> ((all D (m1_subset_1(D,k1_zfmisc_1(A)) -> -(r1_xboole_0(D,B) & r2_hidden(D,C)))) -> m1_card_fil(k3_card_fil(A,C,B),A) & r1_tarski(C,k3_card_fil(A,C,B)) & r2_hidden(B,k3_card_fil(A,C,B))))))))) # label(t14_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5832 (all A (-v1_finset_1(A) & v1_card_1(A) -> (v7_card_fil(A) -> v4_card_fil(A)))) # label(t39_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5833 (all A (-v1_finset_1(A) & v1_card_1(A) -> -v1_xboole_0(k2_card_1(A)) & -v1_finset_1(k2_card_1(A)) & -v2_card_1(k2_card_1(A)) & v1_card_1(k2_card_1(A)) & v3_ordinal1(k2_card_1(A)) & v2_ordinal1(k2_card_1(A)) & v1_ordinal1(k2_card_1(A)))) # label(fc3_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5834 (all A (-v1_xboole_0(A) -> (exists B m2_card_fil(B,A)))) # label(existence_m2_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5835 (all A (-v1_finset_1(A) & v1_card_1(A) & v6_card_fil(A) -> v2_ordinal1(A) & v3_ordinal1(A) & v1_card_1(A) & v1_card_5(A) & v5_card_fil(A) & v2_card_1(A) & -v1_finset_1(A) & -v1_xboole_0(A) & v1_ordinal1(A))) # label(cc4_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5836 (all A all B k4_xboole_0(A,B) = k1_card_fil(A,B)) # label(redefinition_k1_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5837 (all A (v1_card_1(A) -> r1_tarski(k2_card_1(A),k3_card_2(np__2,A)))) # label(t24_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5838 (all A all B all C all D (v1_card_1(B) & m1_subset_1(D,B) & m2_relset_1(C,k2_zfmisc_1(k7_card_fil(B),B),k1_zfmisc_1(B)) & v1_funct_2(C,k2_zfmisc_1(k7_card_fil(B),B),k1_zfmisc_1(B)) & v1_funct_1(C) & -v2_card_1(B) & -v1_finset_1(B) -> ((exists E (r2_hidden(E,k7_card_fil(B)) & k2_binop_1(k7_card_fil(B),B,k1_zfmisc_1(B),C,E,D) = A & m1_subset_1(E,k7_card_fil(B)))) <-> r2_hidden(A,a_3_3_card_fil(B,C,D))))) # label(fraenkel_a_3_3_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5839 (all A (-v1_xboole_0(A) -> (all B (v1_card_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) & -v1_xboole_0(C) -> ((all D (-v1_xboole_0(D) -> (r2_hidden(k1_card_1(D),B) & r1_tarski(D,C) -> r2_hidden(k1_setfam_1(D),C)))) <-> r1_card_fil(A,B,C)))))))) # label(d3_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5840 (all A all B (m1_card_fil(B,A) & -v1_xboole_0(A) -> B = k2_card_fil(A,k2_card_fil(A,B)))) # label(involutiveness_k2_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5841 (all A (-v1_xboole_0(A) -> (all B (m1_card_fil(B,A) -> (exists C (m1_card_fil(C,A) & v3_card_fil(C,A) & r1_tarski(B,C))))))) # label(t17_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5842 (all A (-v1_xboole_0(A) -> -v1_xboole_0(k4_card_fil(A)) & m1_subset_1(k4_card_fil(A),k1_zfmisc_1(k1_zfmisc_1(k1_zfmisc_1(A)))))) # label(dt_k4_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5843 (all A (-v1_xboole_0(A) -> (exists B m1_card_fil(B,A)))) # label(existence_m1_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5844 r2_hidden(f2_s1_card_fil,a_0_0_card_fil) -> p1_s1_card_fil(f2_s1_card_fil) # label(s1_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5845 (all A all B (-v1_xboole_0(B) -> ((exists C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) & A = C & m1_card_fil(C,B))) <-> r2_hidden(A,a_1_0_card_fil(B))))) # label(fraenkel_a_1_0_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5846 (all A (-v1_finset_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (r2_hidden(B,k6_card_fil(A)) <-> r2_hidden(k1_card_1(B),k1_card_1(A))))))) # label(t19_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5847 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) & -v1_xboole_0(B) -> a_2_1_card_fil(A,B) = k7_setfam_1(A,B))))) # label(t9_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5848 (all A (v1_card_1(A) & -v1_finset_1(A) -> (r3_card_fil & v2_card_1(A) -> v5_card_fil(A)))) # label(t28_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5849 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) & -v1_xboole_0(B) -> ((all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(C,B) & r1_tarski(D,C) -> r2_hidden(D,B)) & (r2_hidden(D,B) & r2_hidden(C,B) -> r2_hidden(k4_subset_1(A,C,D),B)))))) & -r2_hidden(A,B) <-> m2_card_fil(B,A)))))) # label(d2_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5850 (all A (-v1_xboole_0(A) -> (all B (v1_card_1(B) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> ((all D (-v1_xboole_0(D) -> (r2_hidden(k1_card_1(D),B) & r1_tarski(D,C) -> r2_hidden(k3_tarski(D),C)))) <-> r2_card_fil(A,B,C)))))))) # label(d4_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5851 (all A (-v1_xboole_0(A) -> m1_card_fil(k1_tarski(A),A))) # label(t4_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5852 (all A (v1_card_1(A) & v5_card_fil(A) & -v1_finset_1(A) -> v1_ordinal1(A) & -v1_xboole_0(A) & -v1_finset_1(A) & v2_card_1(A) & v1_card_1(A) & v3_ordinal1(A) & v2_ordinal1(A))) # label(cc3_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5853 (all A (v1_card_1(A) & -v2_card_1(A) & -v1_finset_1(A) -> (all B (m1_card_fil(B,A) -> -(v3_card_fil(B,A) & r1_card_fil(A,A,B) & v1_card_fil(B,A)))))) # label(t37_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5854 (all A (v3_ordinal1(A) & v4_ordinal1(A) -> (all B (A = k7_ordinal2(B) & r1_tarski(B,A) -> k3_tarski(B) = A)))) # label(t32_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5855 (all A (v1_card_1(A) & -v1_finset_1(A) -> (v7_card_fil(A) -> v6_card_fil(A)))) # label(t41_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5856 (all A all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) & -v1_xboole_0(A) -> -v1_xboole_0(k7_setfam_1(A,B)))) # label(fc2_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5857 (all A (v1_card_1(A) & -v2_card_1(A) & -v1_finset_1(A) -> v3_ordinal1(A) & -v1_finset_1(A) & v1_card_1(A) & v1_card_5(A) & -v1_xboole_0(A) & v2_ordinal1(A) & v1_ordinal1(A))) # label(cc6_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5858 (all A all B all C all D (-v2_card_1(B) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(k7_card_fil(B),B),k1_zfmisc_1(B)) & m2_relset_1(C,k2_zfmisc_1(k7_card_fil(B),B),k1_zfmisc_1(B)) & m1_subset_1(D,k7_card_fil(B)) & v1_card_1(B) & -v1_finset_1(B) -> ((exists E (m1_subset_1(E,B) & A = k2_binop_1(k7_card_fil(B),B,k1_zfmisc_1(B),C,D,E) & r2_hidden(E,B))) <-> r2_hidden(A,a_3_2_card_fil(B,C,D))))) # label(fraenkel_a_3_2_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5859 (all A (-v1_finset_1(A) -> (all B (m1_card_fil(B,A) -> (v3_card_fil(B,A) & v1_card_fil(B,A) -> r1_tarski(k5_card_fil(A),B)))))) # label(t21_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5860 (all A (-v1_xboole_0(A) -> (all B (r2_hidden(B,k4_card_fil(A)) <-> m1_card_fil(B,A))))) # label(t15_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5861 (all A (-v1_finset_1(A) & v1_card_1(A) -> (v6_card_fil(A) -> v4_card_fil(A)))) # label(t30_card_fil) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5862 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) & v2_relat_1(B) -> -v1_xboole_0(k3_tarski(k2_relat_1(B))))))) # label(t6_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5863 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (k1_relat_1(A) = k1_tarski(B) & k2_relat_1(A) = k1_tarski(C) -> k1_tarski(k4_tarski(B,C)) = A)))) # label(t2_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5864 (all A all B k2_funcop_1(A,B) = k2_pre_circ(A,B)) # label(redefinition_k2_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5865 (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_tarski(A,B) -> r1_tarski(k1_funct_4(A,C),k1_funct_4(B,C))))))))) # label(t3_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5866 (all A all B all C all D (-v1_xboole_0(B) & v1_finset_1(B) & v1_trees_1(B) & v1_trees_1(C) & m1_trees_1(D,B) & v1_finset_1(C) & -v1_xboole_0(C) -> (r2_hidden(A,a_3_0_pre_circ(B,C,D)) <-> (exists E (m1_trees_1(E,C) & A = k8_finseq_1(k5_numbers,D,E)))))) # label(fraenkel_a_3_0_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5867 (all A k1_xboole_0 = k4_funct_5(k2_pre_circ(A,k1_xboole_0))) # label(t7_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5868 (all A (v1_funct_1(A) & v1_funct_2(A,k5_numbers,f1_s3_pre_circ) & m2_relset_1(A,k5_numbers,f1_s3_pre_circ) -> (all B (v1_funct_1(B) & v1_funct_2(B,k5_numbers,f1_s3_pre_circ) & m2_relset_1(B,k5_numbers,f1_s3_pre_circ) -> (f2_s3_pre_circ = k8_funct_2(k5_numbers,f1_s3_pre_circ,B,np__0) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> f3_s3_pre_circ(C,k8_funct_2(k5_numbers,f1_s3_pre_circ,B,C)) = k8_funct_2(k5_numbers,f1_s3_pre_circ,B,k1_nat_1(C,np__1)))) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> f3_s3_pre_circ(C,k8_funct_2(k5_numbers,f1_s3_pre_circ,A,C)) = k8_funct_2(k5_numbers,f1_s3_pre_circ,A,k1_nat_1(C,np__1)))) & f2_s3_pre_circ = k8_funct_2(k5_numbers,f1_s3_pre_circ,A,np__0) -> A = B))))) # label(s3_pre_circ_AndLHS) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5869 (exists A (v1_funct_2(A,k5_numbers,f1_s3_pre_circ) & m2_relset_1(A,k5_numbers,f1_s3_pre_circ) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> f3_s3_pre_circ(B,k8_funct_2(k5_numbers,f1_s3_pre_circ,A,B)) = k8_funct_2(k5_numbers,f1_s3_pre_circ,A,k1_nat_1(B,np__1)))) & f2_s3_pre_circ = k8_funct_2(k5_numbers,f1_s3_pre_circ,A,np__0) & v1_funct_1(A))) # label(s3_pre_circ_AndRHS) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5870 (all A exists B (m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_pre_circ(B,A) & v2_relat_1(B))) # label(rc2_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5871 (all A all B (v1_relat_1(A) & v3_trees_2(A) & m1_subset_1(B,k1_relat_1(A)) & v1_finset_1(A) & v1_funct_1(A) -> v1_relat_1(k5_trees_2(A,B)) & v1_funct_1(k5_trees_2(A,B)) & v1_finset_1(k5_trees_2(A,B)) & v3_trees_2(k5_trees_2(A,B)))) # label(fc4_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5872 (all A (v1_funct_1(A) & v1_finseq_1(A) & v6_trees_3(A) & v1_relat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(k1_nat_1(B,np__1),k4_finseq_1(A)) -> r2_hidden(k12_finseq_1(k5_numbers,B),k13_trees_3(k2_funct_6(A)))))))) # label(t17_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5873 (all A (v1_finset_1(A) & v3_trees_2(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v3_trees_2(B) & v1_finset_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (v1_relat_1(E) & v1_funct_1(E) & v6_trees_3(E) & v1_finseq_1(E) -> -(r2_hidden(k12_finseq_1(k5_numbers,D),k1_relat_1(A)) & A = k4_trees_4(C,E) & (all F (v1_funct_1(F) & v6_trees_3(F) & v1_finseq_1(F) & v1_relat_1(F) -> -(k4_trees_4(C,F) = k8_trees_2(A,k12_finseq_1(k5_numbers,D),B) & k3_finseq_1(E) = k3_finseq_1(F) & (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (r2_hidden(G,k4_finseq_1(E)) -> k1_funct_1(F,G) = k1_funct_1(E,G) | G = k1_nat_1(D,np__1)))) & B = k1_funct_1(F,k1_nat_1(D,np__1)))))))))))))) # label(t19_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5874 (all A (-v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) -> (all B (-v1_xboole_0(B) & v1_finset_1(B) & v1_trees_1(B) -> (all C (m1_trees_1(C,A) -> (all D (m2_finseq_1(D,k5_numbers) -> -(r2_hidden(D,k5_trees_1(A,C,B)) & (all E (m1_trees_1(E,B) -> D != k8_finseq_1(k5_numbers,C,E))) & r1_tarski(C,D)))))))))) # label(t15_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5875 (all A all B (m1_pboole(B,A) -> k1_funct_1(k6_pboole(A,B),k6_finseq_1(A)) = k1_tarski(k1_xboole_0))) # label(t5_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5876 (all A (-v1_xboole_0(A) & v1_trees_1(A) & v1_finset_1(A) -> (all B (m1_trees_1(B,A) -> -(r1_xreal_0(k4_card_1(A),k4_card_1(k4_trees_1(A,B))) & k1_xboole_0 != B))))) # label(t20_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5877 (all A all B all C (-v1_xboole_0(B) & v1_finset_1(B) & m1_trees_1(C,B) & v1_trees_1(B) -> (r2_hidden(A,a_2_1_pre_circ(B,C)) <-> (exists D (m1_trees_1(D,B) & -r1_tarski(C,D) & D = A))))) # label(fraenkel_a_2_1_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5878 (all A all B (v2_relat_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_funct_1(k5_relat_1(B,A)) & v2_relat_1(k5_relat_1(B,A)))) # label(fc3_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5879 $T # label(t1_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5880 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_pboole(B,A) -> m1_pboole(k3_pre_circ(A,B,C),C))) # label(dt_k3_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5881 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(C)) & r1_tarski(A,B) -> r1_tarski(A,k1_funct_4(B,C))))))))) # label(t4_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5882 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v2_relat_1(A) -> v1_relat_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)) & v2_relat_1(k7_relat_1(A,B)))) # label(fc2_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5883 (exists A (-v1_xboole_0(A) & v1_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) & v2_membered(A) & v1_finset_1(A))) # label(rc1_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5884 (all A (m1_subset_1(A,f1_s4_pre_circ) -> (r2_hidden(A,f2_s4_pre_circ) -> m2_relset_1(f5_s4_pre_circ(A),k1_funct_1(f3_s4_pre_circ,A),k1_funct_1(f4_s4_pre_circ,A)) & v1_funct_2(f5_s4_pre_circ(A),k1_funct_1(f3_s4_pre_circ,A),k1_funct_1(f4_s4_pre_circ,A)) & v1_funct_1(f5_s4_pre_circ(A))))) -> (exists A (m3_pboole(A,f2_s4_pre_circ,f3_s4_pre_circ,f4_s4_pre_circ) & (all B (m1_subset_1(B,f1_s4_pre_circ) -> (r2_hidden(B,f2_s4_pre_circ) -> k1_funct_1(A,B) = f5_s4_pre_circ(B)))))) # label(s4_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5885 (all A (v5_membered(A) & v1_finset_1(A) & -v1_xboole_0(A) -> v1_xreal_0(k2_seq_4(A)) & v1_xcmplx_0(k2_seq_4(A)) & v4_ordinal2(k2_seq_4(A)))) # label(fc1_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5886 (all A (v3_trees_2(A) & v1_finset_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_finset_1(B) & v3_trees_2(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (m1_trees_1(C,k1_relat_1(A)) -> k1_nat_1(k4_card_1(A),k4_card_1(B)) = k1_nat_1(k4_card_1(k8_trees_2(A,C,B)),k4_card_1(k5_trees_2(A,C))))))))) # label(t23_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5887 (all A all B (m1_pboole(B,A) -> ((all C (r2_hidden(C,A) -> v1_finset_1(k1_funct_1(B,C)))) <-> v1_pre_circ(B,A)))) # label(d3_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5888 (all A (v1_trees_1(A) & v1_finset_1(A) & -v1_xboole_0(A) -> (all B (v1_trees_1(B) & v1_finset_1(B) & -v1_xboole_0(B) -> (all C (m1_trees_1(C,A) -> k1_nat_1(k4_card_1(k5_trees_1(A,C,B)),k4_card_1(k4_trees_1(A,C))) = k1_nat_1(k4_card_1(A),k4_card_1(B)))))))) # label(t22_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5889 (all A (-v1_xboole_0(A) -> (all B all C (m1_pboole(C,A) & v2_relat_1(C) -> (all D (m3_pboole(D,A,k2_pre_circ(A,B),C) -> B = k1_relat_1(k10_funct_6(D)))))))) # label(t8_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5890 (all A np__1 = k4_card_1(k1_trees_4(A))) # label(t24_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5891 (all A (v1_relat_1(k1_trees_4(A)) & v1_funct_1(k1_trees_4(A)) & v3_trees_2(k1_trees_4(A)) & v1_finset_1(k1_trees_4(A)))) # label(fc6_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5892 (all A all B all C (m1_pboole(B,A) & m1_subset_1(C,k1_zfmisc_1(A)) -> k7_relat_1(B,C) = k3_pre_circ(A,B,C))) # label(redefinition_k3_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5893 (all A (v2_membered(A) & v1_finset_1(A) & -v1_xboole_0(A) -> (all B (v1_xreal_0(B) -> (B = k1_pre_circ(A) <-> (all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r1_xreal_0(C,B)))) & r2_hidden(B,A)))))) # label(d1_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5894 (all A (v2_membered(A) & v1_finset_1(A) & -v1_xboole_0(A) -> v1_xreal_0(k1_pre_circ(A)))) # label(dt_k1_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5895 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v4_trees_3(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(k1_nat_1(B,np__1),k4_finseq_1(A)) -> k1_funct_1(A,k1_nat_1(B,np__1)) = k4_trees_1(k13_trees_3(A),k12_finseq_1(k5_numbers,B))))))) # label(t16_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5896 (all A (v2_membered(A) & v1_finset_1(A) & -v1_xboole_0(A) -> k2_seq_4(A) = k1_pre_circ(A))) # label(redefinition_k1_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5897 (all A ((exists B (f2_s1_pre_circ(B) = A & p1_s1_pre_circ(B) & m1_subset_1(B,f1_s1_pre_circ))) <-> r2_hidden(A,a_0_0_pre_circ))) # label(fraenkel_a_0_0_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5898 (exists A (m1_pboole(A,f1_s2_pre_circ) & (all B (m1_subset_1(B,f1_s2_pre_circ) -> (r2_hidden(B,f1_s2_pre_circ) -> (-p1_s2_pre_circ(B) -> k1_funct_1(A,B) = f3_s2_pre_circ(B)) & (p1_s2_pre_circ(B) -> f2_s2_pre_circ(B) = k1_funct_1(A,B))))))) # label(s2_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5899 $T # label(d2_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5900 (all A all B all C (v1_relat_1(A) & v3_trees_2(A) & m1_subset_1(B,k1_relat_1(A)) & v1_relat_1(C) & v1_funct_1(C) & v3_trees_2(C) & v1_finset_1(C) & v1_finset_1(A) & v1_funct_1(A) -> v1_relat_1(k8_trees_2(A,B,C)) & v1_finset_1(k8_trees_2(A,B,C)) & v3_trees_2(k8_trees_2(A,B,C)) & v1_funct_1(k8_trees_2(A,B,C)))) # label(fc5_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5901 (all A (-v1_xboole_0(A) & v1_trees_1(A) & v1_finset_1(A) -> (all B (m1_trees_1(B,A) -> r2_tarski(k4_trees_1(A,B),a_2_0_pre_circ(A,B)))))) # label(t13_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5902 (all A all B (m1_pboole(B,A) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(C,k4_card_3(B)) -> r2_hidden(k5_relat_1(D,C),k4_card_3(k5_relat_1(D,B)))))))))) # label(t11_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5903 (all A (v1_relat_1(A) & v1_funct_1(A) -> k1_card_1(k1_relat_1(A)) = k1_card_1(A))) # label(t21_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5904 (all A (v1_funct_1(A) & v4_trees_3(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v4_trees_3(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (k3_finseq_1(A) = k3_finseq_1(B) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(A)) -> k1_nat_1(C,np__1) = D | k1_funct_1(A,D) = k1_funct_1(B,D)))) & r2_hidden(k1_nat_1(C,np__1),k4_finseq_1(A)) -> (all D (-v1_xboole_0(D) & v1_trees_1(D) -> (k1_funct_1(B,k1_nat_1(C,np__1)) = D -> k13_trees_3(B) = k5_trees_1(k13_trees_3(A),k12_finseq_1(k5_numbers,C),D))))))))))) # label(t18_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5905 (all A all B m1_pboole(k2_pre_circ(A,B),A)) # label(dt_k2_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5906 (all A (-v1_xboole_0(A) & v1_trees_1(A) & v1_finset_1(A) -> (all B (-v1_xboole_0(B) & v1_trees_1(B) & v1_finset_1(B) -> (all C (m1_trees_1(C,A) -> k5_trees_1(A,C,B) = k2_xboole_0(a_2_1_pre_circ(A,C),a_3_0_pre_circ(A,B,C)))))))) # label(t14_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5907 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_trees_3(A)) -> v1_finset_1(B))))) # label(cc1_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5908 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B k1_tarski(k2_finseq_2(A,B)) = k4_card_3(k2_finseq_2(A,k1_tarski(B)))))) # label(t12_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5909 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v2_relat_1(C) & m1_pboole(C,A) -> (all D (m3_pboole(D,A,k2_pre_circ(A,B),C) -> (all E (m1_subset_1(E,B) -> (exists F (m1_pboole(F,A) & k1_funct_1(k10_funct_6(D),E) = F & r3_pboole(A,F,C))))))))))))) # label(t10_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5910 (all A all B (m1_pboole(B,A) & v2_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (m1_subset_1(D,k4_card_3(B)) -> (r1_tarski(k1_relat_1(C),k1_relat_1(B)) & (all E (r2_hidden(E,k1_relat_1(C)) -> r2_hidden(k1_funct_1(C,E),k1_funct_1(B,E)))) -> m1_subset_1(k1_funct_4(D,C),k4_card_3(B))))))))) # label(t9_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5911 (all A all B all C (-v1_xboole_0(B) & v1_trees_1(B) & m1_trees_1(C,B) & v1_finset_1(B) -> (r2_hidden(A,a_2_0_pre_circ(B,C)) <-> (exists D (m1_trees_1(D,B) & r1_tarski(C,D) & A = D))))) # label(fraenkel_a_2_0_pre_circ) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5912 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> ((all D (m1_pboole(D,A) -> (r2_pboole(A,D,C) <-> r1_pboole(A,D,B)))) <-> r6_pboole(A,B,k1_mboolean(A,C))))))) # label(t1_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5913 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r2_pboole(A,k2_mboolean(A,k3_pboole(A,B,C)),k3_pboole(A,k2_mboolean(A,B),k2_mboolean(A,C))))))) # label(t29_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5914 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r6_pboole(A,k2_pboole(A,k1_mboolean(A,B),k1_mboolean(A,C)),k1_mboolean(A,k2_pboole(A,B,C))) -> (all D (r2_hidden(D,A) -> r3_xboole_0(k1_funct_1(B,D),k1_funct_1(C,D))))))))) # label(t8_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5915 (all A all B r6_pboole(A,k1_mboolean(A,k2_pre_circ(A,k1_tarski(B))),k2_pre_circ(A,k2_tarski(k1_xboole_0,k1_tarski(B))))) # label(t4_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5916 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (v2_relat_1(D) & m1_pboole(D,A) -> (r2_pboole(A,C,k2_mboolean(A,k2_pboole(A,B,D))) & (all E (m1_pboole(E,A) -> (r1_pboole(A,E,D) -> r6_pboole(A,k3_pboole(A,E,C),k1_pboole(A))))) -> r2_pboole(A,C,k2_mboolean(A,B))))))))) # label(t36_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5917 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> ((all D (r2_hidden(D,A) -> k1_zfmisc_1(k1_funct_1(B,D)) = k1_funct_1(C,D))) <-> k1_mboolean(A,B) = C))))) # label(d1_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5918 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) -> r2_pboole(A,k4_pboole(A,B,D),C)))))))) # label(t16_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5919 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r2_pboole(A,k12_pboole(A,B,C),k1_mboolean(A,k11_pboole(A,B,C))))))) # label(t20_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5920 (all A all B all C r6_pboole(A,k2_mboolean(A,k2_pre_circ(A,k2_tarski(k1_tarski(B),k1_tarski(C)))),k2_pre_circ(A,k2_tarski(B,C)))) # label(t25_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5921 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r1_pboole(A,B,C) -> r2_pboole(A,B,k2_mboolean(A,C))))))) # label(t26_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5922 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k2_mboolean(A,k2_pboole(A,B,C)),k2_pboole(A,k2_mboolean(A,B),k2_mboolean(A,C))))))) # label(t28_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5923 (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) -> r6_pboole(A,k3_pboole(A,D,B),k1_pboole(A))))) -> r6_pboole(A,k3_pboole(A,k2_mboolean(A,C),B),k1_pboole(A))))))) # label(t34_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5924 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) -> r2_pboole(A,k1_mboolean(A,B),k1_mboolean(A,C))))))) # label(t6_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5925 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) -> r2_pboole(A,k2_mboolean(A,B),k2_mboolean(A,C))))))) # label(t27_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5926 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r2_pboole(A,k1_mboolean(A,k4_pboole(A,B,C)),k2_pboole(A,k2_pre_circ(A,k1_tarski(k1_xboole_0)),k4_pboole(A,k1_mboolean(A,B),k1_mboolean(A,C)))))))) # label(t10_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5927 (all A all B (m1_pboole(B,A) -> r6_pboole(A,k2_mboolean(A,k1_mboolean(A,B)),B))) # label(t30_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5928 (all A (v3_relat_1(k2_mboolean(A,k1_pboole(A))) & v1_funct_1(k2_mboolean(A,k1_pboole(A))) & v1_relat_1(k2_mboolean(A,k1_pboole(A))))) # label(fc2_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5929 (all A all B (m1_pboole(B,A) -> r2_pboole(A,k1_pboole(A),B))) # label(t5_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5930 (all A all B (m1_pboole(B,A) -> r2_pboole(A,B,k1_mboolean(A,k2_mboolean(A,B))))) # label(t31_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5931 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> ((exists D (r1_pboole(A,D,C) & r1_pboole(A,B,D) & m1_pboole(D,A))) <-> r1_pboole(A,B,k2_mboolean(A,C))))))) # label(t21_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5932 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,k2_mboolean(A,B),C) & r1_pboole(A,D,B) -> r2_pboole(A,D,C)))))))) # label(t32_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5933 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (v2_relat_1(k2_pboole(A,B,C)) & (all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r1_pboole(A,D,k2_pboole(A,B,C)) & r1_pboole(A,E,k2_pboole(A,B,C)) -> E = D | r6_pboole(A,k3_pboole(A,D,E),k1_pboole(A))))))) -> r6_pboole(A,k2_mboolean(A,k3_pboole(A,B,C)),k3_pboole(A,k2_mboolean(A,B),k2_mboolean(A,C)))))))) # label(t35_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5934 (all A all B (m1_pboole(B,A) -> m1_pboole(k2_mboolean(A,B),A))) # label(dt_k2_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5935 (all A all B r6_pboole(A,k2_mboolean(A,k2_pre_circ(A,B)),k2_pre_circ(A,k3_tarski(B)))) # label(t23_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5936 (all A all B (m1_pboole(B,A) -> m1_pboole(k1_mboolean(A,B),A))) # label(dt_k1_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5937 (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)) & r5_pboole(A,B,k3_pboole(A,C,D)) <-> r2_pboole(A,B,k5_pboole(A,C,D))))))))) # label(t13_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5938 $T # label(t14_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5939 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r1_pboole(A,B,k1_mboolean(A,C)) <-> r2_pboole(A,B,C)))))) # label(t19_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5940 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r2_pboole(A,k11_pboole(A,B,C),k1_mboolean(A,k1_mboolean(A,k2_pboole(A,B,C)))))))) # label(t18_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5941 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r2_pboole(A,k2_pboole(A,k1_mboolean(A,B),k1_mboolean(A,C)),k1_mboolean(A,k2_pboole(A,B,C))))))) # label(t7_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5942 (all A all B (m1_pboole(B,A) & v1_pre_circ(B,A) & v2_relat_1(B) -> ((all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> -(r1_pboole(A,C,B) & -r2_pboole(A,D,C) & -r2_pboole(A,C,D) & r1_pboole(A,D,B)))))) -> r1_pboole(A,k2_mboolean(A,B),B)))) # label(t37_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5943 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k1_mboolean(A,k3_pboole(A,B,C)),k3_pboole(A,k1_mboolean(A,B),k1_mboolean(A,C))))))) # label(t9_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5944 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (C = k2_mboolean(A,B) <-> (all D (r2_hidden(D,A) -> k3_tarski(k1_funct_1(B,D)) = k1_funct_1(C,D)))))))) # label(d2_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5945 (all A r6_pboole(A,k2_mboolean(A,k1_pboole(A)),k1_pboole(A))) # label(t22_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5946 (all A all B (m1_pboole(B,A) -> v1_relat_1(k1_mboolean(A,B)) & v1_funct_1(k1_mboolean(A,B)) & v2_relat_1(k1_mboolean(A,B)))) # label(fc1_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5947 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) & r2_pboole(A,D,C) -> r2_pboole(A,k5_pboole(A,B,D),C)))))))) # label(t17_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5948 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) | r2_pboole(A,D,C) -> r2_pboole(A,k3_pboole(A,B,D),C)))))))) # label(t15_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5949 (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) & r5_pboole(A,B,D) <-> r2_pboole(A,B,k4_pboole(A,C,D))))))))) # label(t11_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5950 (all A all B r6_pboole(A,k1_mboolean(A,k2_pre_circ(A,B)),k2_pre_circ(A,k1_zfmisc_1(B)))) # label(t3_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5951 (all A r6_pboole(A,k1_mboolean(A,k1_pboole(A)),k2_pre_circ(A,k1_tarski(k1_xboole_0)))) # label(t2_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5952 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) & v2_relat_1(C) -> ((all D (m1_pboole(D,A) -> (r1_pboole(A,D,C) -> r2_pboole(A,D,B)))) -> r2_pboole(A,k2_mboolean(A,C),B)))))) # label(t33_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5953 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r2_pboole(A,k2_pboole(A,k1_mboolean(A,k4_pboole(A,B,C)),k1_mboolean(A,k4_pboole(A,C,B))),k1_mboolean(A,k5_pboole(A,B,C))))))) # label(t12_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5954 (all A all B r6_pboole(A,k2_mboolean(A,k2_pre_circ(A,k1_tarski(B))),k2_pre_circ(A,B))) # label(t24_mboolean) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5955 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (v4_mssubfam(C,A,B) -> v3_mssubfam(C,A,B)))))) # label(cc4_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5956 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (all D (m4_pboole(D,A,B) -> (all E (m4_pboole(E,A,B) -> (r6_pboole(A,C,k2_pzfmisc1(A,D,E)) -> r6_pboole(A,k6_mssubfam(A,B,C),k3_pboole(A,D,E))))))))))) # label(t51_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5957 (all A all B (m1_pboole(B,A) -> (exists C (v3_mssubfam(C,A,B) & v5_mssubfam(C,A,B) & v6_mssubfam(C,A,B) & v4_mssubfam(C,A,B) & v2_mssubfam(C,A,B) & v1_mssubfam(C,A,B) & v1_funct_1(C) & v2_relat_1(C) & v1_relat_1(C) & m4_pboole(C,A,k1_mboolean(A,B)))))) # label(rc5_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5958 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (all D (m1_pboole(D,A) -> ((all E -(r2_hidden(E,A) & (all F (m1_subset_1(F,k1_zfmisc_1(k1_zfmisc_1(k1_funct_1(B,E)))) -> -(k1_funct_1(D,E) = k8_setfam_1(k1_funct_1(B,E),F) & F = k1_funct_1(C,E)))))) <-> k5_mssubfam(A,B,C) = D))))))) # label(d2_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5959 (all A all B (m1_pboole(B,A) -> (v1_pre_circ(k1_mboolean(A,B),A) <-> v1_pre_circ(B,A)))) # label(t21_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5960 (all A all B (m1_pboole(B,A) -> (exists C (v3_relat_1(C) & v1_funct_1(C) & v1_pre_circ(C,A) & v1_relat_1(C) & m4_pboole(C,A,k1_mboolean(A,B)))))) # label(rc3_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5961 (all A all B (m1_pboole(B,A) & v2_relat_1(B) -> (all C (m3_pboole(C,A,B,k1_pboole(A)) -> r6_pboole(A,C,k1_pboole(A)))))) # label(t16_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5962 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m4_pboole(D,A,k1_mboolean(A,B)) -> (r1_pboole(A,C,D) -> r2_pboole(A,k6_mssubfam(A,B,D),C)))))))) # label(t43_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5963 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (v1_pre_circ(k11_pboole(A,B,C),A) & v2_relat_1(B) -> v1_pre_circ(C,A)))))) # label(t20_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5964 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r2_hidden(k1_xboole_0,B) -> k1_xboole_0 = k8_setfam_1(A,B)))) # label(t3_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5965 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (all D (m4_pboole(D,A,k1_mboolean(A,B)) -> (all E (m4_pboole(E,A,k1_mboolean(A,B)) -> (r6_pboole(A,C,k2_pboole(A,D,E)) -> r6_pboole(A,k6_mssubfam(A,B,C),k3_pboole(A,k6_mssubfam(A,B,D),k6_mssubfam(A,B,E)))))))))))) # label(t49_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5966 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r2_hidden(B,D) & r1_tarski(B,C) -> r1_tarski(k8_setfam_1(A,D),C)))) # label(t6_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5967 (all A all B (m1_pboole(B,A) -> (all C (v2_relat_1(C) & m4_pboole(C,A,k1_mboolean(A,B)) -> r2_pboole(A,k6_mssubfam(A,B,C),k2_mboolean(A,C)))))) # label(t42_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5968 (all A all B (v2_relat_1(B) & v1_pre_circ(B,A) & m1_pboole(B,A) -> -((all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> -(r1_pboole(A,C,B) & r1_pboole(A,D,B) & -r2_pboole(A,D,C) & -r2_pboole(A,C,D)))))) & (all C (m1_pboole(C,A) -> -((all D (m1_pboole(D,A) -> (r1_pboole(A,D,B) -> r2_pboole(A,D,C)))) & r1_pboole(A,C,B))))))) # label(t29_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5969 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (r2_hidden(D,B) -> r1_tarski(C,D))) -> r1_tarski(C,k8_setfam_1(A,B))))))) # label(t4_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5970 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,D,C) & r2_pboole(A,B,C) -> m4_pboole(k2_pzfmisc1(A,B,D),A,k1_mboolean(A,C))))))))) # label(t39_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5971 (all A all B (m1_pboole(B,A) -> k3_mssubfam(A,B) = k1_mboolean(A,B))) # label(redefinition_k3_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5972 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (v2_relat_1(B) & v1_pre_circ(k11_pboole(A,C,B),A) -> v1_pre_circ(C,A)))))) # label(t19_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5973 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r1_pboole(A,B,C) -> m2_pboole(B,A,C)))))) # label(t11_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5974 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) & v2_relat_1(C) -> (m2_pboole(B,A,C) -> r1_pboole(A,B,C)))))) # label(t12_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5975 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m4_pboole(D,A,k1_mboolean(A,C)) -> (r1_pboole(A,B,D) -> m4_pboole(B,A,C)))))))) # label(t33_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5976 (all A all B (m1_pboole(B,A) -> v3_relat_1(k1_pboole(A)) & m4_pboole(k1_pboole(A),A,k1_mboolean(A,B)) & v1_pre_circ(k1_pboole(A),A))) # label(t31_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5977 (all A (v1_relat_1(k1_pboole(A)) & v3_relat_1(k1_pboole(A)) & v1_pre_circ(k1_pboole(A),A) & v1_funct_1(k1_pboole(A)))) # label(fc1_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5978 $T # label(d1_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5979 (all A all B all C (m1_pboole(C,B) -> (all D (m4_pboole(D,B,k1_mboolean(B,C)) -> (r2_hidden(A,B) -> m1_subset_1(k1_funct_1(D,A),k1_zfmisc_1(k1_zfmisc_1(k1_funct_1(C,A))))))))) # label(t32_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5980 (all A all B (v1_funcop_1(B) & m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> -(v1_pre_circ(C,A) & r2_pboole(A,C,k2_mssubfam(A,B)) & (all D (m1_pboole(D,A) -> -(r6_pboole(A,k14_pboole(A,D,B),C) & v1_pre_circ(D,A) & r2_pboole(A,D,k1_mssubfam(A,B)))))))))) # label(t30_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5981 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m4_pboole(D,A,k1_mboolean(A,C)) & v2_relat_1(D) -> (r1_pboole(A,B,C) & (all E (m1_pboole(E,A) -> (r1_pboole(A,E,D) -> r1_pboole(A,B,E)))) -> r1_pboole(A,B,k6_mssubfam(A,C,D))))))))) # label(t53_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5982 (all A all B all C (v1_pre_circ(C,A) & m1_pboole(C,A) & m1_pboole(B,A) -> v1_funct_1(k3_pboole(A,C,B)) & v1_pre_circ(k3_pboole(A,C,B),A) & v1_relat_1(k3_pboole(A,C,B)))) # label(fc4_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5983 (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) -> -(v1_pre_circ(E,A) & r2_pboole(A,B,k11_pboole(A,E,C)) & r2_pboole(A,E,D)))) & r2_pboole(A,B,k11_pboole(A,D,C)) & v1_pre_circ(C,A) & v1_pre_circ(B,A)))))))) # label(t27_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5984 (all A all B (m1_pboole(B,A) -> (v1_pre_circ(k2_mboolean(A,B),A) -> v1_pre_circ(B,A) & (all C (m1_pboole(C,A) -> (r1_pboole(A,C,B) -> v1_pre_circ(C,A))))))) # label(t23_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5985 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (B != k1_xboole_0 -> r1_tarski(k8_setfam_1(A,B),k5_setfam_1(A,B))))) # label(t1_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5986 (all A all B (m1_pboole(B,A) -> (v3_relat_1(B) -> v1_pre_circ(B,A)))) # label(cc1_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5987 (all A all B all C (m1_pboole(B,A) & v1_pre_circ(C,A) & m1_pboole(C,A) & v1_funcop_1(B) -> v1_relat_1(k14_pboole(A,C,B)) & v1_pre_circ(k14_pboole(A,C,B),A) & v1_funct_1(k14_pboole(A,C,B)))) # label(fc6_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5988 (all A all B (v1_funcop_1(B) & m1_pboole(B,A) -> m1_pboole(k1_mssubfam(A,B),A))) # label(dt_k1_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5989 (all A all B (m1_pboole(B,A) -> m4_pboole(k3_mssubfam(A,B),A,k1_mboolean(A,B)))) # label(dt_k3_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5990 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (r1_pboole(A,k1_pboole(A),C) -> r6_pboole(A,k6_mssubfam(A,B,C),k1_pboole(A))))))) # label(t44_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5991 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r2_hidden(B,D) & r1_xboole_0(B,C) -> r1_xboole_0(k8_setfam_1(A,D),C)))) # label(t7_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5992 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (r1_pboole(A,B,C) <-> v5_mssubfam(C,A,B)))))) # label(d7_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5993 (all A all B (v1_funcop_1(B) & m1_pboole(B,A) -> m1_pboole(k2_mssubfam(A,B),A))) # label(dt_k2_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5994 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> r2_pboole(A,k2_mboolean(A,C),B))))) # label(t40_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.81 5995 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (all D (m4_pboole(D,A,k1_mboolean(A,B)) -> (r2_pboole(A,C,D) -> r2_pboole(A,k6_mssubfam(A,B,D),k6_mssubfam(A,B,C))))))))) # label(t46_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 5996 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (v1_mssubfam(C,A,B) <-> (all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r1_pboole(A,D,C) & r1_pboole(A,E,C) -> r1_pboole(A,k2_pboole(A,D,E),C))))))))))) # label(d3_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 5997 (all A all B (m1_pboole(B,A) & v1_funcop_1(B) -> (v1_pre_circ(k1_mssubfam(A,B),A) -> v1_pre_circ(k2_mssubfam(A,B),A)))) # label(t24_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 5998 (all A all B all C (m1_pboole(C,A) & v1_pre_circ(C,A) & m1_pboole(B,A) -> v1_pre_circ(k3_pboole(A,B,C),A) & v1_funct_1(k3_pboole(A,B,C)) & v1_relat_1(k3_pboole(A,B,C)))) # label(fc3_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 5999 (all A all B (m1_pboole(B,A) & v1_funcop_1(B) -> k2_mssubfam(A,B) = k3_funct_6(B))) # label(redefinition_k2_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6000 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m4_pboole(D,A,k1_mboolean(A,C)) -> m4_pboole(k4_pboole(A,D,B),A,k1_mboolean(A,C)))))))) # label(t36_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6001 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) & v1_pre_circ(C,A) & v1_pre_circ(B,A) -> v1_pre_circ(k12_pboole(A,B,C),A) & v1_funct_1(k12_pboole(A,B,C)) & v1_relat_1(k12_pboole(A,B,C)))) # label(fc9_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6002 (all A all B (m1_pboole(B,A) -> v1_mssubfam(k7_mssubfam(A,B),A,B) & m4_pboole(k7_mssubfam(A,B),A,k1_mboolean(A,B)) & v6_mssubfam(k7_mssubfam(A,B),A,B) & v5_mssubfam(k7_mssubfam(A,B),A,B) & v4_mssubfam(k7_mssubfam(A,B),A,B) & v3_mssubfam(k7_mssubfam(A,B),A,B) & v2_mssubfam(k7_mssubfam(A,B),A,B))) # label(dt_k7_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6003 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (v2_mssubfam(C,A,B) -> v1_mssubfam(C,A,B)))))) # label(cc3_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6004 (all A all B all C (v1_pre_circ(B,A) & v1_pre_circ(C,A) & m1_pboole(C,A) & m1_pboole(B,A) -> v1_pre_circ(k2_pboole(A,B,C),A) & v1_funct_1(k2_pboole(A,B,C)) & v1_relat_1(k2_pboole(A,B,C)))) # label(fc2_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6005 (all A all B all C (m4_pboole(C,A,k1_mboolean(A,B)) & m1_pboole(B,A) -> m4_pboole(k6_mssubfam(A,B,C),A,B))) # label(dt_k6_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6006 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m4_pboole(D,A,k1_mboolean(A,B)) -> (r1_pboole(A,C,k6_mssubfam(A,B,D)) -> (all E (m1_pboole(E,A) -> (r1_pboole(A,E,D) -> r1_pboole(A,C,E))))))))))) # label(t52_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6007 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (all D (m4_pboole(D,A,B) -> (r6_pboole(A,C,k1_pzfmisc1(A,D)) -> r6_pboole(A,k6_mssubfam(A,B,C),D)))))))) # label(t50_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6008 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> ((all D (r2_hidden(D,C) -> r1_tarski(B,D))) -> C = k1_xboole_0 | r1_tarski(B,k8_setfam_1(A,C))))) # label(t5_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6009 (all A all B all C (m1_pboole(B,A) & m4_pboole(C,A,k1_mboolean(A,B)) -> k6_mssubfam(A,B,C) = k5_mssubfam(A,B,C))) # label(redefinition_k6_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6010 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (B = k2_tarski(C,D) -> k8_setfam_1(A,B) = k5_subset_1(A,C,D)))))))) # label(t10_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6011 (all A all B (m1_pboole(B,A) -> k7_mssubfam(A,B) = k1_mboolean(A,B))) # label(redefinition_k7_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6012 (all A all B all C (v1_pre_circ(B,A) & v1_pre_circ(C,A) & m1_pboole(C,A) & m1_pboole(B,A) -> v1_pre_circ(k5_pboole(A,B,C),A) & v1_funct_1(k5_pboole(A,B,C)) & v1_relat_1(k5_pboole(A,B,C)))) # label(fc10_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6013 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (r1_pboole(A,k1_pboole(A),C) <-> v6_mssubfam(C,A,B)))))) # label(d8_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6014 (all A all B all C (v1_pre_circ(B,A) & m1_pboole(B,A) & m1_pboole(C,A) & v1_pre_circ(C,A) -> v1_pre_circ(k11_pboole(A,B,C),A) & v1_funct_1(k11_pboole(A,B,C)) & v1_relat_1(k11_pboole(A,B,C)))) # label(fc7_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6015 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (v2_mssubfam(C,A,B) -> v6_mssubfam(C,A,B)))))) # label(cc7_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6016 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (v4_mssubfam(C,A,B) <-> (all D (m4_pboole(D,A,k1_mboolean(A,B)) -> (r2_pboole(A,D,C) -> r1_pboole(A,k6_mssubfam(A,B,D),C))))))))) # label(d6_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6017 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> -(r2_pboole(A,B,k11_pboole(A,C,D)) & (all E (m1_pboole(E,A) -> (all F (m1_pboole(F,A) -> -(v1_pre_circ(E,A) & v1_pre_circ(F,A) & r2_pboole(A,B,k11_pboole(A,E,F)) & r2_pboole(A,F,D) & r2_pboole(A,E,C)))))) & v1_pre_circ(B,A)))))))) # label(t26_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6018 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> ((all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r1_pboole(A,E,C) & r1_pboole(A,D,C) -> r1_pboole(A,k3_pboole(A,D,E),C)))))) <-> v3_mssubfam(C,A,B)))))) # label(d5_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6019 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) & v1_funcop_1(C) -> ((all D all E (v1_funct_1(E) & v1_relat_1(E) -> (r2_hidden(D,A) & k1_funct_1(C,D) = E -> v1_finset_1(k10_relat_1(E,k1_funct_1(B,D)))))) & r2_pboole(A,B,k2_mssubfam(A,C)) -> v1_pre_circ(B,A)))))) # label(t25_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6020 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (v2_mssubfam(C,A,B) <-> (all D (m4_pboole(D,A,k1_mboolean(A,B)) -> (r2_pboole(A,D,C) -> r1_pboole(A,k2_mboolean(A,D),C))))))))) # label(d4_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6021 (all A all B (m1_pboole(B,A) & v1_funcop_1(B) -> k2_funct_6(B) = k1_mssubfam(A,B))) # label(redefinition_k1_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6022 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (v4_mssubfam(C,A,B) -> v5_mssubfam(C,A,B)))))) # label(cc5_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6023 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (all D (m4_pboole(D,A,k1_mboolean(A,B)) -> m4_pboole(k5_pboole(A,C,D),A,k1_mboolean(A,B)))))))) # label(t37_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6024 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r2_hidden(B,C) -> r1_tarski(k8_setfam_1(A,C),B)))) # label(t2_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6025 (all A all B (v2_relat_1(B) & m1_pboole(B,A) & v1_pre_circ(B,A) -> -((all C (m1_pboole(C,A) -> -((all D (m1_pboole(D,A) -> (r1_pboole(A,D,B) -> r2_pboole(A,C,D)))) & r1_pboole(A,C,B)))) & (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> -(r1_pboole(A,C,B) & r1_pboole(A,D,B) & -r2_pboole(A,C,D) & -r2_pboole(A,D,C))))))))) # label(t28_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6026 (all A (r2_hidden(A,f1_s1_mssubfam) -> (all B -((all C -(r2_hidden(C,k1_funct_1(f3_s1_mssubfam,A)) & p1_s1_mssubfam(C,B,A))) & r2_hidden(B,k1_funct_1(f2_s1_mssubfam,A)))))) -> (exists A (m3_pboole(A,f1_s1_mssubfam,f2_s1_mssubfam,f3_s1_mssubfam) & (all B -(r2_hidden(B,f1_s1_mssubfam) & (all C (m2_relset_1(C,k1_funct_1(f2_s1_mssubfam,B),k1_funct_1(f3_s1_mssubfam,B)) & v1_funct_2(C,k1_funct_1(f2_s1_mssubfam,B),k1_funct_1(f3_s1_mssubfam,B)) & v1_funct_1(C) -> -((all D (r2_hidden(D,k1_funct_1(f2_s1_mssubfam,B)) -> p1_s1_mssubfam(k1_funct_1(C,D),D,B))) & k1_funct_1(A,B) = C))))))) # label(s1_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6027 (all A all B (m1_pboole(B,A) & v1_pre_circ(B,A) -> v1_relat_1(k1_mboolean(A,B)) & v1_funct_1(k1_mboolean(A,B)) & v1_pre_circ(k1_mboolean(A,B),A) & v2_relat_1(k1_mboolean(A,B)))) # label(fc8_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6028 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) -> m4_pboole(k1_pzfmisc1(A,B),A,k1_mboolean(A,C))))))) # label(t38_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6029 (all A all B (m1_pboole(B,A) & v1_funcop_1(B) -> (all C (m1_pboole(C,A) & v1_funcop_1(C) -> m1_pboole(k13_pboole(B,C),A) & v1_funcop_1(k13_pboole(B,C)))))) # label(t15_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6030 (all A all B all C (m1_pboole(B,A) & m4_pboole(C,A,k1_mboolean(A,B)) -> m1_pboole(k5_mssubfam(A,B,C),A))) # label(dt_k5_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6031 (all A all B all C (m1_pboole(C,B) & v1_funcop_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(A,B) & k1_funct_1(C,A) = D -> k2_relat_1(D) = k1_funct_1(k2_mssubfam(B,C),A)))))) # label(t13_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6032 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) & v1_pre_circ(C,A) -> v1_pre_circ(B,A)))))) # label(t18_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6033 (all A all B all C all D (m1_subset_1(D,A) & m4_pboole(C,A,k1_mboolean(A,B)) & m1_pboole(B,A) & -v1_xboole_0(A) -> k4_mssubfam(A,B,C,D) = k1_funct_1(C,D))) # label(redefinition_k4_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6034 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (all D (m4_pboole(D,A,k1_mboolean(A,B)) -> m4_pboole(k2_pboole(A,C,D),A,k1_mboolean(A,B)))))))) # label(t34_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6035 (all A all B all C all D (m4_pboole(C,A,k1_mboolean(A,B)) & m1_subset_1(D,A) & m1_pboole(B,A) & -v1_xboole_0(A) -> m1_subset_1(k4_mssubfam(A,B,C,D),k1_zfmisc_1(k1_zfmisc_1(k1_funct_1(B,D)))))) # label(dt_k4_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6036 (all A all B (v2_relat_1(B) & m1_pboole(B,A) -> ((all C (m1_pboole(C,A) -> (r1_pboole(A,C,B) -> v1_pre_circ(C,A)))) & v1_pre_circ(B,A) -> v1_pre_circ(k2_mboolean(A,B),A)))) # label(t22_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6037 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (all E (m4_pboole(E,A,k1_mboolean(A,B)) -> (r2_pboole(A,C,D) & r1_pboole(A,C,E) -> r2_pboole(A,k6_mssubfam(A,B,E),D)))))))))) # label(t47_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6038 (all A all B all C (m1_pboole(B,A) & v1_pre_circ(C,A) & m1_pboole(C,A) -> v1_relat_1(k4_pboole(A,C,B)) & v1_pre_circ(k4_pboole(A,C,B),A) & v1_funct_1(k4_pboole(A,C,B)))) # label(fc5_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6039 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m4_pboole(D,A,k1_mboolean(A,C)) & v2_relat_1(D) -> ((all E (m1_pboole(E,A) -> (r1_pboole(A,E,D) -> r2_pboole(A,B,E)))) -> r2_pboole(A,B,k6_mssubfam(A,C,D))))))))) # label(t45_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6040 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (v5_mssubfam(C,A,B) -> v2_relat_1(C)))))) # label(cc6_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6041 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (v6_mssubfam(C,A,B) -> v2_relat_1(C)))))) # label(cc8_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6042 (all A all B (m1_pboole(B,A) & v1_pre_circ(B,A) -> (all C (m4_pboole(C,A,B) -> v1_pre_circ(C,A))))) # label(cc2_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6043 (all A all B (m1_pboole(B,A) -> (exists C (m4_pboole(C,A,k1_mboolean(A,B)) & v1_funct_1(C) & v2_relat_1(C) & v1_relat_1(C))))) # label(rc2_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6044 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (all D (m4_pboole(D,A,k1_mboolean(A,B)) -> m4_pboole(k3_pboole(A,C,D),A,k1_mboolean(A,B)))))))) # label(t35_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6045 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (all E (m4_pboole(E,A,k1_mboolean(A,B)) -> (r1_pboole(A,C,E) & r6_pboole(A,k3_pboole(A,C,D),k1_pboole(A)) -> r6_pboole(A,k3_pboole(A,k6_mssubfam(A,B,E),D),k1_pboole(A))))))))))) # label(t48_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6046 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (k1_tarski(C) = B -> C = k8_setfam_1(A,B)))))) # label(t9_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6047 (all A all B (m1_pboole(B,A) -> (exists C (v1_relat_1(C) & v3_relat_1(C) & v1_funct_1(C) & v1_pre_circ(C,A) & m4_pboole(C,A,B))))) # label(rc1_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6048 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (v1_funcop_1(D) & m1_pboole(D,A) -> (r1_pzfmisc1(A,B,C) & m3_pboole(D,A,B,C) -> r2_pboole(A,k2_mssubfam(A,D),C) & r6_pboole(A,k1_mssubfam(A,D),B)))))))) # label(t17_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6049 (all A all B all C (m1_pboole(C,B) & v1_funcop_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(A,B) & D = k1_funct_1(C,A) -> k1_relat_1(D) = k1_funct_1(k1_mssubfam(B,C),A)))))) # label(t14_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6050 (all A all B (m1_pboole(B,A) & v1_pre_circ(B,A) -> (exists C (m4_pboole(C,A,k1_mboolean(A,B)) & v1_relat_1(C) & v1_funct_1(C) & v1_pre_circ(C,A) & v2_relat_1(C))))) # label(rc4_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6051 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) -> (B = k4_subset_1(k1_zfmisc_1(A),C,D) -> k5_subset_1(A,k8_setfam_1(A,C),k8_setfam_1(A,D)) = k8_setfam_1(A,B)))))))) # label(t8_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6052 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (r6_pboole(A,C,k1_pboole(A)) -> r6_pboole(A,k6_mssubfam(A,B,C),B)))))) # label(t41_mssubfam) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6053 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r1_tarski(k2_relat_1(A),k1_relat_1(A)) -> r1_tarski(k2_relat_1(k9_funct_7(A,B)),k1_relat_1(A)) & k1_relat_1(k9_funct_7(A,B)) = k1_relat_1(A)))))) # label(t76_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6054 (all A (m1_subset_1(A,f1_s1_funct_7) -> (all B (m1_subset_1(B,f2_s1_funct_7) -> r2_hidden(f4_s1_funct_7(A,B),f3_s1_funct_7))))) -> (exists A (v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(f1_s1_funct_7,f2_s1_funct_7),f3_s1_funct_7) & (all B (m1_subset_1(B,f1_s1_funct_7) -> (all C (m1_subset_1(C,f2_s1_funct_7) -> k8_funct_2(k2_zfmisc_1(f1_s1_funct_7,f2_s1_funct_7),f3_s1_funct_7,A,k1_domain_1(f1_s1_funct_7,f2_s1_funct_7,B,C)) = f4_s1_funct_7(B,C))))) & v1_funct_2(A,k2_zfmisc_1(f1_s1_funct_7,f2_s1_funct_7),f3_s1_funct_7))) # label(s1_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6055 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (k1_nat_1(k3_finseq_1(B),np__1) = k3_finseq_1(A) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(k1_nat_1(C,np__1),k4_finseq_1(A)) & r2_hidden(C,k4_finseq_1(A)) <-> r2_hidden(C,k4_finseq_1(B)))))))))) # label(t24_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6056 p1_s5_funct_7(k1_xboole_0) & (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funcop_1(A) & v1_funct_1(A) -> (p1_s5_funct_7(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> p1_s5_funct_7(k7_finseq_1(A,k9_finseq_1(B)))))))) -> (all A (v1_funct_1(A) & v1_funcop_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> p1_s5_funct_7(A))) # label(s5_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6057 (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_funct_1(D) & v1_relat_1(D) -> k7_finseq_1(k9_finseq_1(A),k11_finseq_1(k1_funct_1(B,A),k1_funct_1(C,k1_funct_1(B,A)),k1_funct_1(D,k1_funct_1(C,k1_funct_1(B,A))))) = k5_funct_7(k11_finseq_1(B,C,D),A))))))) # label(t58_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6058 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_xboole_0(k2_relat_1(A),k1_relat_1(B)) -> k5_relat_1(A,C) = k5_relat_1(A,k1_funct_4(C,B))))))))) # label(t12_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6059 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> k6_partfun1(A) = k9_funct_7(B,np__0))) # label(t86_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6060 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k4_funct_7(k2_xboole_0(k1_relat_1(A),k2_relat_1(A)),k2_finseq_2(B,A)) = k9_funct_7(A,B))))) # label(t90_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6061 (all A all B (v1_funct_1(A) & v1_finseq_1(A) & v1_funcop_1(A) & v1_relat_1(A) -> v1_finseq_1(k5_funct_7(A,B)) & v1_funct_1(k5_funct_7(A,B)) & v1_relat_1(k5_funct_7(A,B)))) # label(dt_k5_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6062 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (r1_tarski(k1_relat_1(B),C) -> r1_funct_7(A,k1_funct_4(A,B),C))))))) # label(t31_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6063 v1_finset_1(f1_s2_funct_7) & (all A (m1_subset_1(A,f2_s2_funct_7) -> (all B (m1_subset_1(B,f2_s2_funct_7) -> (f4_s2_funct_7(B) = f4_s2_funct_7(A) -> A = B))))) -> v1_finset_1(a_0_0_funct_7) # label(s2_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6064 (all A (-v1_xboole_0(A) & v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) & v2_relat_1(A) -> (exists B m2_funct_7(B,A)))) # label(existence_m2_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6065 (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) -> k5_relat_1(A,k1_funct_4(B,C)) = k1_funct_4(k5_relat_1(A,B),k5_relat_1(A,C)))))))) # label(t11_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6066 r1_tarski(f1_s4_funct_7,f2_s4_funct_7) & (all A (m1_subset_1(A,f2_s4_funct_7) -> (all B (m1_subset_1(B,f2_s4_funct_7) -> (f3_s4_funct_7(A) = f3_s4_funct_7(B) -> B = A))))) -> r2_tarski(f1_s4_funct_7,a_0_2_funct_7) # label(s4_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6067 (all A (v1_finset_1(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (exists C ((all D (m2_subset_1(D,k1_zfmisc_1(A),B) -> (r1_tarski(D,C) -> D = C))) & m2_subset_1(C,k1_zfmisc_1(A),B))))))) # label(t23_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6068 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C all D (C != D -> k1_funct_1(k2_funct_7(A,C,B),D) = k1_funct_1(A,D))))) # label(t34_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6069 (all A (v1_funct_1(A) & v1_relat_1(A) -> k6_partfun1(k2_xboole_0(k1_relat_1(A),k2_relat_1(A))) = k9_funct_7(A,np__0))) # label(t70_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6070 (all A all B all C (-v1_xboole_0(A) & m1_funct_7(C,B,A) -> m2_relset_1(k8_funct_7(A,B,C),B,A) & v1_funct_2(k8_funct_7(A,B,C),B,A) & v1_funct_1(k8_funct_7(A,B,C)))) # label(dt_k8_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6071 (all A ((exists B (m1_subset_1(B,f2_s4_funct_7) & r2_hidden(B,f1_s4_funct_7) & A = f3_s4_funct_7(B))) <-> r2_hidden(A,a_0_2_funct_7))) # label(fraenkel_a_0_2_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6072 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (r2_hidden(E,k4_finseq_1(B)) -> E = D | k4_finseq_4(k5_numbers,A,B,E) = k4_finseq_4(k5_numbers,A,k3_funct_7(A,B,D,C),E)))))))))))) # label(t39_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6073 (all A all B (v1_relat_1(B) & v1_funct_1(B) & m1_subset_1(A,k5_numbers) -> v1_relat_1(k2_finseq_2(A,B)) & v1_finset_1(k2_finseq_2(A,B)) & v1_finseq_1(k2_finseq_2(A,B)) & v1_funcop_1(k2_finseq_2(A,B)) & v1_funct_1(k2_finseq_2(A,B)))) # label(fc7_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6074 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_funcop_1(B) & v1_finseq_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> ((exists D (m1_pboole(D,k5_numbers) & (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (r2_hidden(k1_nat_1(E,np__1),k4_finseq_1(B)) -> (all F (v1_funct_1(F) & v1_relat_1(F) -> (all G (v1_relat_1(G) & v1_funct_1(G) -> (k1_funct_1(D,E) = F & k1_funct_1(B,k1_nat_1(E,np__1)) = G -> k1_funct_1(D,k1_nat_1(E,np__1)) = k5_relat_1(F,G))))))))) & k6_partfun1(A) = k1_funct_1(D,np__0) & C = k1_funct_1(D,k3_finseq_1(B)) & v1_funcop_1(D))) <-> C = k4_funct_7(A,B)))))) # label(d4_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6075 (all A all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k9_funct_7(k6_partfun1(A),B) = k6_partfun1(A))) # label(t83_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6076 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> k3_funct_7(A,B,E,k4_finseq_4(k5_numbers,A,B,E)) = B)))))))))) # label(t40_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6077 $T # label(dt_k7_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6078 (all A (v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_funct_7(A) & v1_funcop_1(A) & v1_finseq_1(A))) # label(cc2_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6079 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k1_relat_1(B),A) -> B = k4_funct_7(A,k9_finseq_1(B))))) # label(t48_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6080 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_funct_7(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),k6_funct_7(A)) -> v1_relat_1(k7_finseq_1(k9_finseq_1(B),A)) & v1_funct_1(k7_finseq_1(k9_finseq_1(B),A)) & v1_funct_7(k7_finseq_1(k9_finseq_1(B),A)) & v1_finseq_1(k7_finseq_1(k9_finseq_1(B),A))))))) # label(t65_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6081 (all A all B all C (-v1_xboole_0(A) & m1_funct_7(C,B,A) -> k4_funct_7(B,C) = k8_funct_7(A,B,C))) # label(redefinition_k8_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6082 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C all D k2_funct_7(k2_funct_7(A,D,B),D,C) = k2_funct_7(A,D,C)))) # label(t36_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6083 (all A all B all C (v1_relat_1(A) & v1_funct_1(B) & v1_funct_1(C) & v1_relat_1(C) & v1_relat_1(B) & v1_funct_1(A) -> v1_funct_1(k11_finseq_1(A,B,C)) & v1_finset_1(k11_finseq_1(A,B,C)) & v1_finseq_1(k11_finseq_1(A,B,C)) & v1_funcop_1(k11_finseq_1(A,B,C)) & v1_relat_1(k11_finseq_1(A,B,C)))) # label(fc6_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6084 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_relat_1(A) & -v1_xboole_0(A) -> (all B (m2_funct_7(B,A) -> v1_funct_7(B) & v2_relat_1(B))))) # label(cc3_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6085 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) -> v1_relat_1(k10_finseq_1(A,B)) & v1_finset_1(k10_finseq_1(A,B)) & v1_finseq_1(k10_finseq_1(A,B)) & v1_funcop_1(k10_finseq_1(A,B)) & v1_funct_1(k10_finseq_1(A,B)))) # label(fc5_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6086 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> k4_funct_7(A,k10_finseq_1(B,C)) = k5_relat_1(k6_partfun1(A),k5_relat_1(B,C)))))) # label(t53_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6087 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(k2_funct_7(A,C,B),C) = B)))) # label(t33_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6088 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> k5_funct_7(k10_finseq_1(B,C),A) = k11_finseq_1(A,k1_funct_1(B,A),k1_funct_1(C,k1_funct_1(B,A))))))) # label(t55_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6089 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> ((exists B (v1_relat_1(B) & v1_finseq_1(B) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(C,k4_finseq_1(A)) -> r2_hidden(k1_funct_1(A,C),k1_funct_2(k1_funct_1(B,C),k1_funct_1(B,k1_nat_1(C,np__1))))))) & k3_finseq_1(B) = k1_nat_1(k3_finseq_1(A),np__1) & v1_funct_1(B))) <-> v1_funct_7(A)))) # label(d8_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6090 (exists A (v1_funct_1(A) & v1_funct_7(A) & v1_funcop_1(A) & v1_finseq_1(A) & v1_finset_1(A) & v2_relat_1(A) & v1_relat_1(A) & -v1_xboole_0(A))) # label(rc2_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6091 (all A all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) -> m2_relset_1(k9_funct_7(C,B),A,A) & v1_funct_2(k9_funct_7(C,B),A,A) & v1_funct_1(k9_funct_7(C,B)))))) # label(t85_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6092 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k9_funct_7(A,k1_nat_1(B,np__1)) = k5_relat_1(A,k9_funct_7(A,B)))))) # label(t71_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6093 (all A (v1_funct_7(A) & v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k7_funct_7(A),k1_relat_1(B)) -> v1_funct_7(k7_finseq_1(A,k9_finseq_1(B))) & v1_finseq_1(k7_finseq_1(A,k9_finseq_1(B))) & v1_funct_1(k7_finseq_1(A,k9_finseq_1(B))) & v1_relat_1(k7_finseq_1(A,k9_finseq_1(B)))))))) # label(t66_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6094 (all A all B all C (r2_hidden(A,k3_xboole_0(B,C)) -> k1_funct_7(A,C) = k1_funct_7(A,B))) # label(t26_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6095 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(C) = k2_xboole_0(A,k1_tarski(B)) -> k1_funct_4(k7_relat_1(C,A),k3_cqc_lang(B,k1_funct_1(C,B))) = C))) # label(t15_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6096 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_funcop_1(B) & v1_finseq_1(B) -> v1_relat_1(k4_funct_7(A,B)) & v1_funct_1(k4_funct_7(A,B)))) # label(dt_k4_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6097 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (B != np__0 -> r1_tarski(k1_relat_1(k9_funct_7(A,B)),k1_relat_1(A)) & r1_tarski(k2_relat_1(k9_funct_7(A,B)),k2_relat_1(A))))))) # label(t75_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6098 (all A (v1_funct_1(A) & v1_relat_1(A) -> -v1_xboole_0(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) & v1_funcop_1(k5_finseq_1(A)) & v1_funct_7(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_relat_1(k5_finseq_1(A)))) # label(fc10_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6099 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k5_relat_1(k6_partfun1(k2_xboole_0(k1_relat_1(A),k2_relat_1(A))),k9_funct_7(A,B)) = k9_funct_7(A,B))))) # label(t77_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6100 (all A all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,A) -> v1_funct_1(k9_funct_7(C,B)) & m2_relset_1(k9_funct_7(C,B),A,A))))) # label(t88_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6101 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> r1_tarski(k1_relat_1(k9_funct_7(A,B)),k2_xboole_0(k1_relat_1(A),k2_relat_1(A))) & r1_tarski(k2_relat_1(k9_funct_7(A,B)),k2_xboole_0(k1_relat_1(A),k2_relat_1(A))))))) # label(t74_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6102 (all A all B (m1_subset_1(B,k5_numbers) & v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k9_funct_7(A,B)) & v1_funct_1(k9_funct_7(A,B)))) # label(dt_k9_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6103 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (B != np__0 -> k9_funct_7(k9_funct_7(A,C),B) = k9_funct_7(A,k2_nat_1(C,B))))))))) # label(t80_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6104 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B k2_funct_7(A,B,k1_funct_1(A,B)) = A))) # label(t37_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6105 $T # label(dt_k6_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6106 (all A all B (r1_tarski(k3_finseq_2(A),k3_finseq_2(B)) -> r1_tarski(A,B))) # label(t21_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6107 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(B)) -> C = k4_finseq_4(k5_numbers,A,k3_funct_7(A,B,D,C),D)))))))))) # label(t38_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6108 (all A (v1_funct_1(A) & v1_relat_1(A) -> k9_funct_7(A,np__1) = A)) # label(t72_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6109 (all A (v1_finseq_1(A) & v1_funct_1(A) & v2_relat_1(A) & v1_relat_1(A) & -v1_xboole_0(A) -> (all B (m2_funct_7(B,A) -> v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B))))) # label(dt_m2_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6110 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B ((v1_xboole_0(A) -> (B = k6_funct_7(A) <-> v1_xboole_0(B))) & (-v1_xboole_0(A) -> (k1_funct_5(k1_funct_1(A,np__1)) = B <-> B = k6_funct_7(A))))))) # label(d6_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6111 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_funcop_1(A) -> (all B all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (C = k5_funct_7(A,B) <-> B = k1_funct_1(C,np__1) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (v1_relat_1(E) & v1_funct_1(E) -> (k1_funct_1(A,D) = E & r2_hidden(D,k4_finseq_1(A)) -> k1_funct_1(C,k1_nat_1(D,np__1)) = k1_funct_1(E,k1_funct_1(C,D))))))) & k3_finseq_1(C) = k1_nat_1(k3_finseq_1(A),np__1)))))) # label(d5_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6112 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_funcop_1(B) -> (all C (v1_finseq_1(C) & v1_funcop_1(C) & v1_funct_1(C) & v1_relat_1(C) -> k1_funct_1(k5_funct_7(C,k1_funct_1(k5_funct_7(B,A),k1_nat_1(k3_finseq_1(B),np__1))),k1_nat_1(k3_finseq_1(C),np__1)) = k1_funct_1(k5_funct_7(k7_finseq_1(B,C),A),k1_nat_1(k3_finseq_1(k7_finseq_1(B,C)),np__1)))))) # label(t51_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6113 (all A all B m1_subset_1(k1_funct_7(A,B),B)) # label(dt_k1_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6114 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_funcop_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> k4_funct_7(A,k7_finseq_1(B,k9_finseq_1(C))) = k5_relat_1(k4_funct_7(A,B),C))))) # label(t43_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6115 (all A all B (r2_hidden(A,B) -> A = k1_funct_7(A,B))) # label(d1_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6116 (all A (v1_relat_1(A) & v1_funct_7(A) & v1_finseq_1(A) & v1_funct_1(A) -> v1_finset_1(A) & v1_funcop_1(A) & v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(cc1_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6117 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B r1_funct_7(A,A,B)))) # label(t27_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6118 (all A all B all C (m1_subset_1(B,k5_numbers) & v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> v1_finseq_1(k2_funct_7(A,B,C)) & v1_finset_1(k2_funct_7(A,B,C)) & v1_funct_1(k2_funct_7(A,B,C)) & v1_relat_1(k2_funct_7(A,B,C)))) # label(fc9_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6119 (all A all B exists C m1_funct_7(C,A,B)) # label(existence_m1_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6120 (all A (r2_hidden(A,a_0_1_funct_7) <-> (exists B (B = A & r2_hidden(f3_s3_funct_7(B),f1_s3_funct_7) & m1_subset_1(B,f2_s3_funct_7))))) # label(fraenkel_a_0_1_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6121 (all A all B all C (-r1_xboole_0(A,k2_relat_1(k1_funct_4(k6_partfun1(B),k2_funcop_1(A,C)))) -> r2_hidden(C,A))) # label(t13_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6122 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> k5_funct_7(k9_finseq_1(B),A) = k10_finseq_1(A,k1_funct_1(B,A)))) # label(t49_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6123 (all A (v1_funct_1(A) & v1_funct_7(A) & v1_finseq_1(A) & v1_relat_1(A) -> k1_relat_1(k4_funct_7(k6_funct_7(A),A)) = k6_funct_7(A))) # label(t64_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6124 (all A all B all C (v1_funcop_1(C) & v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_funcop_1(D) & v1_finseq_1(D) & v1_relat_1(D) -> (r1_tarski(k2_relat_1(k4_funct_7(A,C)),B) -> k4_funct_7(A,k7_finseq_1(C,D)) = k5_relat_1(k4_funct_7(A,C),k4_funct_7(B,D))))))) # label(t50_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6125 (all A all B all C all D (-v1_xboole_0(k4_funct_4(A,B,C,D)) & v1_funct_1(k4_funct_4(A,B,C,D)) & v1_relat_1(k4_funct_4(A,B,C,D)))) # label(fc2_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6126 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_relat_1(B),k1_relat_1(A)) & r1_tarski(k2_relat_1(C),k1_relat_1(A)) -> k1_funct_4(k5_relat_1(B,A),k5_relat_1(C,A)) = k5_relat_1(k1_funct_4(B,C),A)))))))) # label(t10_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6127 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C ((r2_hidden(B,k1_relat_1(A)) -> k1_funct_4(A,k3_cqc_lang(B,C)) = k2_funct_7(A,B,C)) & (-r2_hidden(B,k1_relat_1(A)) -> A = k2_funct_7(A,B,C)))))) # label(d3_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6128 (exists A (-v1_xboole_0(A) & v2_relat_1(A) & v1_finset_1(A) & v1_funcop_1(A) & v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc1_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6129 (all A -((all B (m1_subset_1(B,f2_s3_funct_7) -> A != f3_s3_funct_7(B))) & r2_hidden(A,f1_s3_funct_7))) & (all A (m1_subset_1(A,f2_s3_funct_7) -> (all B (m1_subset_1(B,f2_s3_funct_7) -> (f3_s3_funct_7(A) = f3_s3_funct_7(B) -> A = B))))) -> r2_tarski(f1_s3_funct_7,a_0_1_funct_7) # label(s3_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6130 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k9_funct_7(A,k1_nat_1(B,C)) = k5_relat_1(k9_funct_7(A,C),k9_funct_7(A,B)))))))) # label(t79_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6131 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k5_relat_1(k9_funct_7(A,B),k6_partfun1(k2_xboole_0(k1_relat_1(A),k2_relat_1(A)))) = k9_funct_7(A,B))))) # label(t78_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6132 (all A all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,A) & m2_relset_1(D,A,A) -> k9_funct_7(k9_funct_7(D,B),C) = k9_funct_7(D,k2_nat_1(B,C)))))))) # label(t87_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6133 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (r1_tarski(k2_relat_1(A),B) -> k5_relat_1(A,k6_partfun1(B)) = A)))) # label(t1_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6134 (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 (r1_funct_7(A,B,D) & r1_funct_7(B,C,D) -> r1_funct_7(A,C,D))))))))) # label(t29_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6135 (all A (-v1_xboole_0(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) -> (v2_funct_1(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,k1_zfmisc_1(A)) -> (all F (m1_subset_1(F,k1_zfmisc_1(B)) -> (r2_hidden(k8_funct_2(A,B,C,D),k6_subset_1(B,k2_funct_2(A,B,C,E),F)) -> r2_hidden(D,k6_subset_1(A,E,k3_funct_2(A,B,C,F))))))))))))))))) # label(t4_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6136 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> k5_relat_1(k6_partfun1(A),B) = k4_funct_7(A,k9_finseq_1(B)))) # label(t47_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6137 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_funcop_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & -v1_xboole_0(k5_finseq_1(A)))) # label(fc4_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6138 (all A all B (m1_pboole(B,A) -> (all C (r2_hidden(C,A) -> k3_cqc_lang(C,k1_funct_1(B,C)) = k7_relat_1(B,k1_tarski(C)))))) # label(t7_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6139 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (v1_funcop_1(k7_finseq_1(A,B)) -> v1_funcop_1(A) & v1_funcop_1(B)))))) # label(t25_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6140 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k9_funct_7(A,B) = C <-> (exists D (v1_funct_1(D) & m2_relset_1(D,k5_numbers,k4_partfun1(k2_xboole_0(k1_relat_1(A),k2_relat_1(A)),k2_xboole_0(k1_relat_1(A),k2_relat_1(A)))) & k8_funct_2(k5_numbers,k4_partfun1(k2_xboole_0(k1_relat_1(A),k2_relat_1(A)),k2_xboole_0(k1_relat_1(A),k2_relat_1(A))),D,B) = C & (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (exists F (v1_funct_1(F) & F = k8_funct_2(k5_numbers,k4_partfun1(k2_xboole_0(k1_relat_1(A),k2_relat_1(A)),k2_xboole_0(k1_relat_1(A),k2_relat_1(A))),D,E) & k5_relat_1(A,F) = k8_funct_2(k5_numbers,k4_partfun1(k2_xboole_0(k1_relat_1(A),k2_relat_1(A)),k2_xboole_0(k1_relat_1(A),k2_relat_1(A))),D,k1_nat_1(E,np__1)) & v1_relat_1(F))))) & k6_partfun1(k2_xboole_0(k1_relat_1(A),k2_relat_1(A))) = k8_funct_2(k5_numbers,k4_partfun1(k2_xboole_0(k1_relat_1(A),k2_relat_1(A)),k2_xboole_0(k1_relat_1(A),k2_relat_1(A))),D,np__0) & v1_funct_2(D,k5_numbers,k4_partfun1(k2_xboole_0(k1_relat_1(A),k2_relat_1(A)),k2_xboole_0(k1_relat_1(A),k2_relat_1(A))))))))))))) # label(d11_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6141 (all A all B (v1_funcop_1(B) & v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (k1_xboole_0 != B -> r1_tarski(k2_relat_1(k4_funct_7(A,B)),k7_funct_7(B))))) # label(t61_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6142 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (v2_funct_1(C) -> (all D (m1_subset_1(D,B) -> (all E (m1_subset_1(E,k1_zfmisc_1(A)) -> (all F (m1_subset_1(F,k1_zfmisc_1(B)) -> (r2_hidden(D,k6_subset_1(B,k2_funct_2(A,B,C,E),F)) -> r2_hidden(k1_funct_1(k2_funct_1(C),D),k6_subset_1(A,E,k3_funct_2(A,B,C,F))))))))))))))))) # label(t5_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6143 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> k1_relat_1(A) = k6_funct_7(k7_finseq_1(k9_finseq_1(A),B)) & k2_relat_1(A) = k7_funct_7(k7_finseq_1(B,k9_finseq_1(A))))))) # label(t60_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.82 6144 (all A all B (v1_funct_1(B) & v1_funct_7(B) & v1_finseq_1(B) & v1_relat_1(B) -> (k1_xboole_0 != B -> k3_xboole_0(k6_funct_7(B),A) = k1_relat_1(k4_funct_7(A,B))))) # label(t63_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6145 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B ((v1_xboole_0(A) -> (v1_xboole_0(B) <-> B = k7_funct_7(A))) & (-v1_xboole_0(A) -> (B = k2_funct_5(k1_funct_1(A,k3_finseq_1(A))) <-> B = k7_funct_7(A))))))) # label(d7_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6146 $T # label(t9_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6147 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) & v2_relat_1(A) & -v1_xboole_0(A) -> (all B (m2_funct_7(B,A) -> r1_tarski(k2_relat_1(k4_funct_7(k1_funct_1(A,np__1),B)),k1_funct_1(A,k3_finseq_1(A))) & k1_funct_1(A,np__1) = k1_relat_1(k4_funct_7(k1_funct_1(A,np__1),B)))))) # label(t69_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6148 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (r1_funct_7(A,B,C) -> r1_funct_7(B,A,C))))))) # label(t28_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6149 (all A all B (v1_finseq_1(B) & v1_funcop_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> k5_funct_7(k7_finseq_1(k9_finseq_1(C),B),A) = k7_finseq_1(k9_finseq_1(A),k5_funct_7(B,k1_funct_1(C,A))))))) # label(t46_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6150 (all A all B all C all D (m1_finseq_1(B,A) & m1_subset_1(C,k5_numbers) & m1_subset_1(D,A) -> k2_funct_7(B,C,D) = k3_funct_7(A,B,C,D))) # label(redefinition_k3_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6151 (all A all B all C (m1_pboole(C,k2_zfmisc_1(A,B)) -> (all D all E (r2_hidden(D,A) & r2_hidden(E,B) -> k9_funct_2(D,E,k1_binop_1(C,D,E)) = k7_relat_1(C,k2_zfmisc_1(k1_tarski(D),k1_tarski(E))))))) # label(t8_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6152 (all A all B (v1_finseq_1(B) & v1_funcop_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> k4_funct_7(A,k7_finseq_1(k9_finseq_1(C),B)) = k5_relat_1(k7_relat_1(C,A),k4_funct_7(k9_relat_1(C,A),B)))))) # label(t45_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6153 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (C = k2_funcop_1(B,A) & r2_hidden(A,B) -> k9_funct_7(C,D) = C | D = np__0))))) # label(t89_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6154 (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) -> (v2_funct_1(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (all E (m1_subset_1(E,k1_zfmisc_1(B)) -> (r1_tarski(E,k2_funct_2(A,B,C,D)) -> r1_tarski(k3_funct_2(A,B,C,E),D))))))))))) # label(t2_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6155 (all A all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funcop_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> k7_finseq_1(k5_funct_7(B,A),k9_finseq_1(k1_funct_1(C,k1_funct_1(k5_funct_7(B,A),k1_nat_1(k3_finseq_1(B),np__1))))) = k5_funct_7(k7_finseq_1(B,k9_finseq_1(C)),A))))) # label(t44_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6156 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (v2_funct_1(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,k1_zfmisc_1(A)) -> (r2_hidden(k8_funct_2(A,B,C,D),k2_funct_2(A,B,C,E)) -> r2_hidden(D,E))))))))))))) # label(t3_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6157 $T # label(t17_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6158 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k9_funct_7(k1_xboole_0,A) = k1_xboole_0)) # label(t82_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6159 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C k1_relat_1(k2_funct_7(A,C,B)) = k1_relat_1(A)))) # label(t32_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6160 (all A all B (v1_funcop_1(B) & v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funcop_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> k1_rewrite1(k5_funct_7(B,A),k5_funct_7(C,k1_funct_1(k5_funct_7(B,A),k1_nat_1(k3_finseq_1(B),np__1)))) = k5_funct_7(k7_finseq_1(B,C),A))))) # label(t52_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6161 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_tarski(k2_relat_1(A),k1_relat_1(A)) -> k9_funct_7(A,k2_nat_1(B,C)) = k9_funct_7(k9_funct_7(A,B),C)))))))) # label(t81_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6162 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (-(-r1_tarski(k1_relat_1(k5_relat_1(B,C)),A) & -r1_tarski(k1_relat_1(k5_relat_1(B,k5_relat_1(C,D))),A) & -r1_tarski(k1_relat_1(B),A)) -> k5_relat_1(B,k5_relat_1(C,D)) = k4_funct_7(A,k11_finseq_1(B,C,D))))))))) # label(t57_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6163 (all A all B all C -(B != A & r2_hidden(A,k2_relat_1(k1_funct_4(k6_partfun1(C),k3_cqc_lang(A,B)))))) # label(t14_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6164 (all A all B (v1_finseq_1(A) & v1_funcop_1(A) & v1_relat_1(B) & v1_funcop_1(B) & v1_finseq_1(B) & v1_funct_1(B) & v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)) & v1_funcop_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)))) # label(fc8_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6165 (all A all B all C (v1_funct_1(C) & v1_funct_7(C) & v1_finseq_1(C) & v1_relat_1(C) -> (r2_hidden(A,B) & r2_hidden(A,k6_funct_7(C)) -> k1_funct_1(k4_funct_7(B,C),A) = k1_funct_1(k5_funct_7(C,A),k1_nat_1(k3_finseq_1(C),np__1))))) # label(t67_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6166 (all A (-v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_relat_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (m2_funct_7(B,A) <-> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(C,k4_finseq_1(B)) -> r2_hidden(k1_funct_1(B,C),k1_funct_2(k1_funct_1(A,C),k1_funct_1(A,k1_nat_1(C,np__1))))))) & k1_nat_1(k3_finseq_1(B),np__1) = k3_finseq_1(A)))))) # label(d10_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6167 (all A all B ((v1_xboole_0(B) -> v1_xboole_0(A)) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & v1_funct_7(C) -> (k6_funct_7(C) = A & r1_tarski(k7_funct_7(C),B) <-> m1_funct_7(C,A,B)))))) # label(d9_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6168 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (r1_funct_7(A,B,C) <-> k7_relat_1(B,k4_xboole_0(k1_relat_1(B),C)) = k7_relat_1(A,k4_xboole_0(k1_relat_1(A),C)))))))) # label(d2_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6169 (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) -> k4_funct_7(A,k11_finseq_1(B,C,D)) = k5_relat_1(k6_partfun1(A),k5_relat_1(B,k5_relat_1(C,D))))))))) # label(t56_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6170 (all A all B all C all D (m1_finseq_1(B,A) & m1_subset_1(C,k5_numbers) & m1_subset_1(D,A) -> m2_finseq_1(k3_funct_7(A,B,C,D),A))) # label(dt_k3_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6171 (all A all B all C (m1_funct_7(C,A,B) -> v1_funct_7(C) & v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C))) # label(dt_m1_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6172 (all A all B all C (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k2_funct_7(A,B,C)) & v1_relat_1(k2_funct_7(A,B,C)))) # label(dt_k2_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6173 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C all D k1_funct_4(k1_funct_4(A,k2_funcop_1(B,C)),k2_funcop_1(B,D)) = k1_funct_4(A,k2_funcop_1(B,D))))) # label(t16_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6174 (all A k5_funct_7(k1_xboole_0,A) = k9_finseq_1(A)) # label(t42_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6175 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (r1_funct_7(A,B,C) -> k4_xboole_0(k1_relat_1(A),C) = k4_xboole_0(k1_relat_1(B),C))))))) # label(t30_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6176 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k1_relat_1(k5_relat_1(B,C)),A) | r1_tarski(k1_relat_1(B),A) -> k4_funct_7(A,k10_finseq_1(B,C)) = k5_relat_1(B,C)))))) # label(t54_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6177 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (r2_hidden(B,k1_relat_1(A)) -> k3_cqc_lang(B,k1_funct_1(A,B)) = k7_relat_1(A,k1_tarski(B)))))) # label(t6_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6178 (all A all B (v1_funct_1(k3_cqc_lang(A,B)) & v1_relat_1(k3_cqc_lang(A,B)) & -v1_xboole_0(k3_cqc_lang(A,B)))) # label(fc1_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6179 (all A (m1_subset_1(A,k1_zfmisc_1(k5_numbers)) -> ((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(B,A) -> r2_hidden(C,A) | r1_xreal_0(B,C)))))) -> v1_card_1(A)))) # label(t22_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6180 (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) -> (v1_funct_7(k7_finseq_1(A,B)) -> v1_funct_7(A) & v1_funct_7(B)))))) # label(t62_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6181 (all A ((exists B (r2_hidden(f4_s2_funct_7(B),f1_s2_funct_7) & A = f3_s2_funct_7(B) & m1_subset_1(B,f2_s2_funct_7))) <-> r2_hidden(A,a_0_0_funct_7))) # label(fraenkel_a_0_0_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6182 (all A k6_partfun1(A) = k4_funct_7(A,k1_xboole_0)) # label(t41_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6183 (all A all B (r2_hidden(k9_finseq_1(A),k3_finseq_2(B)) <-> r2_hidden(A,B))) # label(t20_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6184 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C all D all E (D != E -> k2_funct_7(k2_funct_7(A,E,C),D,B) = k2_funct_7(k2_funct_7(A,D,B),E,C))))) # label(t35_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6185 (all A (-v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_relat_1(A) & v1_relat_1(A) -> (all B (m2_funct_7(B,A) -> (k1_xboole_0 != B -> r1_tarski(k7_funct_7(B),k1_funct_1(A,k3_finseq_1(A))) & k1_funct_1(A,np__1) = k6_funct_7(B)))))) # label(t68_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6186 (all A (v1_funct_1(A) & v1_relat_1(A) -> (r1_xboole_0(k2_relat_1(A),k1_relat_1(A)) -> k1_xboole_0 = k9_funct_7(A,np__2)))) # label(t84_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6187 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k9_funct_7(A,k1_nat_1(B,np__1)) = k5_relat_1(k9_funct_7(A,B),A))))) # label(t73_funct_7) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6188 (all A all B all C (m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_struct_0(A) & -v3_struct_0(A) -> m1_subset_1(k2_struct_0(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k2_struct_0) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6189 (all A all B (l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & -v3_struct_0(A) -> k1_struct_0(A,B) = k1_tarski(B))) # label(redefinition_k1_struct_0) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6190 (all A (l2_struct_0(A) -> (v2_struct_0(A) -> g2_struct_0(u1_struct_0(A),u2_struct_0(A)) = A))) # label(abstractness_v2_struct_0) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6191 (all A all B (m1_subset_1(B,A) -> (all C all D (g2_struct_0(C,D) = g2_struct_0(A,B) -> A = C & D = B)))) # label(free_g2_struct_0) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6192 (exists A (l2_struct_0(A) & v2_struct_0(A))) # label(rc2_struct_0) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6193 (all A all B (g1_struct_0(B) = g1_struct_0(A) -> B = A)) # label(free_g1_struct_0) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6194 (all A (l1_struct_0(A) -> (v3_struct_0(A) <-> v1_xboole_0(u1_struct_0(A))))) # label(d1_struct_0) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6195 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & l1_struct_0(A) & -v3_struct_0(A) -> (exists C m1_struct_0(C,A,B)))) # label(existence_m1_struct_0) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6196 (exists A l1_struct_0(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6197 (all A all B (m1_subset_1(B,A) -> v2_struct_0(g2_struct_0(A,B)) & l2_struct_0(g2_struct_0(A,B)))) # label(dt_g2_struct_0) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6198 (all A (l2_struct_0(A) -> l1_struct_0(A))) # label(dt_l2_struct_0) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6199 (all A all B (-v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & l1_struct_0(A) -> m1_subset_1(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k1_struct_0) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6200 (exists A l2_struct_0(A)) # label(existence_l2_struct_0) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6201 (exists A (v1_struct_0(A) & l1_struct_0(A))) # label(rc1_struct_0) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6202 (all A all B (-v3_struct_0(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & l1_struct_0(A) -> (all C (m1_struct_0(C,A,B) -> m1_subset_1(C,u1_struct_0(A)))))) # label(dt_m1_struct_0) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6203 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6204 (all A (l2_struct_0(A) -> m1_subset_1(u2_struct_0(A),u1_struct_0(A)))) # label(dt_u2_struct_0) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6205 (all A all B all C (-v3_struct_0(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_struct_0(A) -> k2_tarski(B,C) = k2_struct_0(A,B,C))) # label(redefinition_k2_struct_0) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6206 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6207 (all A all B all C (-v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_struct_0(A) -> k2_struct_0(A,C,B) = k2_struct_0(A,B,C))) # label(commutativity_k2_struct_0) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6208 (exists A (-v3_struct_0(A) & l1_struct_0(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6209 (exists A (l2_struct_0(A) & -v3_struct_0(A))) # label(rc4_struct_0) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6210 (all A (l1_struct_0(g1_struct_0(A)) & v1_struct_0(g1_struct_0(A)))) # label(dt_g1_struct_0) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6211 (all A (l1_struct_0(A) -> (v1_struct_0(A) -> g1_struct_0(u1_struct_0(A)) = A))) # label(abstractness_v1_struct_0) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6212 (all A (l1_struct_0(A) & -v3_struct_0(A) -> (exists B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc5_struct_0) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6213 (all A all B (l1_struct_0(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & -v3_struct_0(A) -> (all C (m1_subset_1(C,B) <-> m1_struct_0(C,A,B))))) # label(redefinition_m1_struct_0) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6214 (all A (-v3_struct_0(A) & l1_struct_0(A) -> -v1_xboole_0(u1_struct_0(A)))) # label(fc1_struct_0) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6215 (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]. 17.47/16.83 6216 $T # label(t28_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6217 (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]. 17.47/16.83 6218 (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]. 17.47/16.83 6219 (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]. 17.47/16.83 6220 $T # label(t106_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6221 (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]. 17.47/16.83 6222 $T # label(t5_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6223 (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]. 17.47/16.83 6224 (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]. 17.47/16.83 6225 (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]. 17.47/16.83 6226 (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]. 17.47/16.83 6227 (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]. 17.47/16.83 6228 (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]. 17.47/16.83 6229 (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]. 17.47/16.83 6230 (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]. 17.47/16.83 6231 (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]. 17.47/16.83 6232 (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]. 17.47/16.83 6233 (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]. 17.47/16.83 6234 (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]. 17.47/16.83 6235 (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]. 17.47/16.83 6236 (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]. 17.47/16.83 6237 $T # label(t119_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6238 (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]. 17.47/16.83 6239 (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]. 17.47/16.83 6240 (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]. 17.47/16.83 6241 (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]. 17.47/16.83 6242 (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]. 17.47/16.83 6243 (exists A (v2_cat_1(A) & v1_cat_1(A) & l1_cat_1(A))) # label(rc3_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6244 (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]. 17.47/16.83 6245 (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]. 17.47/16.83 6246 (all A (l1_cat_1(A) -> -v1_xboole_0(u2_cat_1(A)))) # label(dt_u2_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6247 (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]. 17.47/16.83 6248 (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]. 17.47/16.83 6249 (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]. 17.47/16.83 6250 (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]. 17.47/16.83 6251 $T # label(t3_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6252 (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]. 17.47/16.83 6253 (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]. 17.47/16.83 6254 (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]. 17.47/16.83 6255 (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]. 17.47/16.83 6256 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_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]. 17.47/16.83 6257 (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]. 17.47/16.83 6258 (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]. 17.47/16.83 6259 $T # label(t2_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6260 (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]. 17.47/16.83 6261 (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]. 17.47/16.83 6262 (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]. 17.47/16.83 6263 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,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]. 17.47/16.83 6264 (all A (l1_cat_1(A) -> -v1_xboole_0(u1_cat_1(A)))) # label(dt_u1_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6265 (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]. 17.47/16.83 6266 (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]. 17.47/16.83 6267 $T # label(t49_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6268 (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]. 17.47/16.83 6269 (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]. 17.47/16.83 6270 $T # label(t10_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6271 (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]. 17.47/16.83 6272 (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]. 17.47/16.83 6273 (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]. 17.47/16.83 6274 (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]. 17.47/16.83 6275 (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]. 17.47/16.83 6276 (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]. 17.47/16.83 6277 (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]. 17.47/16.83 6278 (exists A (v2_cat_1(A) & l1_cat_1(A))) # label(rc2_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6279 (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]. 17.47/16.83 6280 $T # label(t30_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.47/16.83 6281 (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]. 17.47/16.83 6282 (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]. 17.47/16.83 6283 (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]. 17.47/16.84 6284 $T # label(t114_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.47/16.84 6285 (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]. 17.47/16.84 6286 (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]. 17.47/16.84 6287 (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]. 17.47/16.84 6288 (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]. 17.47/16.84 6289 (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]. 17.47/16.84 6290 (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]. 17.47/16.84 6291 $T # label(t11_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.47/16.84 6292 $T # label(t15_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.47/16.84 6293 (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]. 17.47/16.84 6294 (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]. 17.47/16.84 6295 (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]. 17.47/16.84 6296 (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]. 17.47/16.84 6297 (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]. 17.47/16.84 6298 (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]. 17.47/16.84 6299 (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]. 17.47/16.84 6300 $T # label(t94_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.47/16.84 6301 (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]. 17.47/16.84 6302 (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]. 17.47/16.84 6303 (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]. 17.47/16.84 6304 $T # label(t121_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.47/16.84 6305 (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]. 17.47/16.84 6306 (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]. 17.47/16.84 6307 (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]. 17.47/16.84 6308 $T # label(dt_l1_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.47/16.84 6309 (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]. 17.47/16.84 6310 (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]. 17.47/16.84 6311 (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]. 17.47/16.84 6312 (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]. 17.47/16.84 6313 (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]. 17.47/16.84 6314 $T # label(t78_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.47/16.84 6315 (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]. 17.47/16.84 6316 (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]. 17.47/16.84 6317 (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]. 17.47/16.84 6318 $T # label(t101_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.47/16.84 6319 $T # label(t130_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.47/16.84 6320 (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]. 17.47/16.84 6321 (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]. 17.47/16.84 6322 (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]. 17.47/16.84 6323 $T # label(t20_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.47/16.84 6324 (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]. 17.47/16.84 6325 $T # label(t48_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.47/16.84 6326 (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]. 17.47/16.84 6327 (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]. 17.47/16.84 6328 (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]. 17.47/16.84 6329 (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]. 17.47/16.84 6330 (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]. 17.47/16.84 6331 (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]. 17.47/16.84 6332 (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]. 17.47/16.84 6333 (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]. 17.47/16.84 6334 $T # label(t79_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.47/16.84 6335 (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]. 17.47/16.84 6336 (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]. 17.47/16.84 6337 (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]. 17.47/16.84 6338 (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]. 17.47/16.84 6339 (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]. 17.47/16.84 6340 (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]. 17.47/16.84 6341 (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]. 17.47/16.84 6342 (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]. 17.47/16.84 6343 (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]. 17.47/16.84 6344 $T # label(t72_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.47/16.84 6345 (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]. 17.47/16.84 6346 (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]. 17.47/16.84 6347 (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]. 17.68/17.07 6348 $T # label(t53_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.68/17.07 6349 (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]. 17.68/17.07 6350 $T # label(t6_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.68/17.07 6351 (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]. 17.68/17.07 6352 (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]. 17.68/17.07 6353 (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]. 17.68/17.07 6354 (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]. 17.68/17.07 6355 (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]. 17.68/17.07 6356 $T # label(t95_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.68/17.07 6357 (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]. 17.68/17.07 6358 (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]. 17.78/17.14 6359 (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]. 17.78/17.14 6360 (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]. 17.78/17.14 6361 (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]. 17.78/17.14 6362 (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]. 17.78/17.14 6363 (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]. 17.78/17.14 6364 $T # label(t1_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.14 6365 $T # label(t80_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.14 6366 (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]. 17.78/17.14 6367 $T # label(t13_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.14 6368 (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]. 17.78/17.14 6369 (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]. 17.78/17.14 6370 (exists A l1_cat_1(A)) # label(existence_l1_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.14 6371 (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]. 17.78/17.14 6372 (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]. 17.78/17.14 6373 (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]. 17.78/17.14 6374 (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]. 17.78/17.14 6375 (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]. 17.78/17.14 6376 (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]. 17.78/17.14 6377 (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]. 17.78/17.14 6378 (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]. 17.78/17.14 6379 (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]. 17.78/17.14 6380 (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]. 17.78/17.14 6381 (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]. 17.78/17.14 6382 (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]. 17.78/17.14 6383 $T # label(t120_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.14 6384 (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]. 17.78/17.14 6385 (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]. 17.78/17.14 6386 (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]. 17.78/17.14 6387 (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]. 17.78/17.14 6388 (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]. 17.78/17.14 6389 (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]. 17.78/17.14 6390 $T # label(t12_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.14 6391 (exists A (v1_cat_1(A) & l1_cat_1(A))) # label(rc1_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.14 6392 $T # label(t17_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.14 6393 (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]. 17.78/17.14 6394 (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]. 17.78/17.14 6395 (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]. 17.78/17.14 6396 (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]. 17.78/17.14 6397 $T # label(t31_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.14 6398 (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]. 17.78/17.14 6399 $T # label(t16_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.14 6400 $T # label(t50_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.14 6401 (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]. 17.78/17.14 6402 (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]. 17.78/17.14 6403 (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]. 17.78/17.14 6404 (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]. 17.78/17.14 6405 (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]. 17.78/17.15 6406 (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]. 17.78/17.15 6407 $T # label(t14_cat_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6408 (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]. 17.78/17.15 6409 (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]. 17.78/17.15 6410 (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]. 17.78/17.15 6411 (exists A (l3_lattices(A) & v3_lattices(A))) # label(rc3_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6412 $T # label(t14_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6413 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v14_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k4_lattices(A,k6_lattices(A),B) = B)))) # label(t43_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6414 (all A (-v3_struct_0(A) & v6_lattices(A) & l3_lattices(A) & v8_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r1_lattices(A,k4_lattices(A,B,C),B))))))) # label(t23_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6415 (all A all B (-v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) -> v1_lattices(g1_lattices(A,B)) & -v3_struct_0(g1_lattices(A,B)))) # label(fc2_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6416 $T # label(t20_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6417 (all A all B all C (-v3_struct_0(A) & l3_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & v9_lattices(A) & v8_lattices(A) & v6_lattices(A) -> r3_lattices(A,B,B))) # label(reflexivity_r3_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6418 (exists A (l3_lattices(A) & -v3_struct_0(A) & v3_lattices(A))) # label(rc6_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6419 (all A all B all C (m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_lattices(A) & v6_lattices(A) & -v3_struct_0(A) -> m1_subset_1(k4_lattices(A,B,C),u1_struct_0(A)))) # label(dt_k4_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6420 $T # label(t42_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6421 (all A (-v3_struct_0(A) & l1_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_lattices(A),B,C) = k2_lattices(A,B,C))))))) # label(d2_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6422 (all A all B (-v1_xboole_0(A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> -v3_struct_0(g2_lattices(A,B)) & v2_lattices(g2_lattices(A,B)))) # label(fc1_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6423 (all A (l1_lattices(A) -> (v1_lattices(A) -> A = g1_lattices(u1_struct_0(A),u1_lattices(A))))) # label(abstractness_v1_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6424 (all A (-v3_struct_0(A) & v13_lattices(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k3_lattices(A,k5_lattices(A),B) = B)))) # label(t39_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6425 (all A (l2_lattices(A) -> l1_struct_0(A))) # label(dt_l2_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6426 (all A all B all C (m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l2_lattices(A) & v4_lattices(A) & -v3_struct_0(A) -> k3_lattices(A,C,B) = k3_lattices(A,B,C))) # label(commutativity_k3_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6427 $T # label(t16_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6428 (all A (-v3_struct_0(A) & l2_lattices(A) -> (v14_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> B = k1_lattices(A,C,B) & B = k1_lattices(A,B,C))) <-> B = k6_lattices(A))))))) # label(d17_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6429 $T # label(t7_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6430 (all A (l3_lattices(A) & -v3_struct_0(A) -> (v12_lattices(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattices(A,B,D) -> k1_lattices(A,B,k2_lattices(A,C,D)) = k2_lattices(A,k1_lattices(A,B,C),D))))))))))) # label(d12_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6431 (all A all B all C (v6_lattices(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l3_lattices(A) & v9_lattices(A) & v8_lattices(A) & -v3_struct_0(A) -> (r3_lattices(A,B,C) <-> r1_lattices(A,B,C)))) # label(redefinition_r3_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6432 (all A all B (v1_funct_1(B) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C all D (g1_lattices(C,D) = g1_lattices(A,B) -> B = D & A = C)))) # label(free_g1_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6433 (all A (l1_lattices(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_lattices(A,B,k2_lattices(A,C,D)) = k2_lattices(A,k2_lattices(A,B,C),D))))))) <-> v7_lattices(A)))) # label(d7_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6434 $T # label(t24_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6435 (all A (-v3_struct_0(A) & l1_lattices(A) -> (v13_lattices(A) <-> (exists B (m1_subset_1(B,u1_struct_0(A)) & (all C (m1_subset_1(C,u1_struct_0(A)) -> B = k2_lattices(A,B,C) & B = k2_lattices(A,C,B)))))))) # label(d13_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6436 (all A (-v3_struct_0(A) & l3_lattices(A) & v17_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r3_lattices(A,B,C) -> r3_lattices(A,k7_lattices(A,C),k7_lattices(A,B))))))))) # label(t53_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6437 (exists A (v3_lattices(A) & v5_lattices(A) & v7_lattices(A) & v9_lattices(A) & v10_lattices(A) & v15_lattices(A) & v14_lattices(A) & v13_lattices(A) & v8_lattices(A) & v6_lattices(A) & v4_lattices(A) & -v3_struct_0(A) & l3_lattices(A))) # label(rc11_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6438 (all A all B all C (-v1_xboole_0(A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> v3_lattices(g3_lattices(A,B,C)) & -v3_struct_0(g3_lattices(A,B,C)))) # label(fc3_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6439 $T # label(t11_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6440 (all A (l1_lattices(A) & -v3_struct_0(A) -> (v6_lattices(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_lattices(A,C,B) = k2_lattices(A,B,C)))))))) # label(d6_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6441 (exists A (l3_lattices(A) & v3_lattices(A) & v5_lattices(A) & v7_lattices(A) & v8_lattices(A) & v14_lattices(A) & v16_lattices(A) & v15_lattices(A) & v13_lattices(A) & v10_lattices(A) & v9_lattices(A) & v6_lattices(A) & v4_lattices(A) & -v3_struct_0(A))) # label(rc12_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6442 $T # label(t6_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6443 (all A all B (v1_funct_1(B) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> l2_lattices(g2_lattices(A,B)) & v2_lattices(g2_lattices(A,B)))) # label(dt_g2_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6444 (all A (v14_lattices(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k3_lattices(A,k6_lattices(A),B) = k6_lattices(A))))) # label(t44_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6445 (all A all B all C (v6_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_lattices(A) & -v3_struct_0(A) -> k4_lattices(A,B,C) = k2_lattices(A,B,C))) # label(redefinition_k4_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6446 (all A (-v3_struct_0(A) & l2_lattices(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_lattices(A,B,C) = k1_lattices(A,C,B))))) <-> v4_lattices(A)))) # label(d4_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6447 $T # label(t1_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6448 $T # label(t2_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6449 (all A (l3_lattices(A) & v17_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k3_lattices(A,k7_lattices(A,B),k7_lattices(A,C)) = k7_lattices(A,k4_lattices(A,B,C)))))))) # label(t50_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6450 (all A all B (v1_funct_1(B) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> v1_lattices(g1_lattices(A,B)) & l1_lattices(g1_lattices(A,B)))) # label(dt_g1_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6451 (all A all B all C (m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> v3_lattices(g3_lattices(A,B,C)) & l3_lattices(g3_lattices(A,B,C)))) # label(dt_g3_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6452 (all A (v10_lattices(A) & v17_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r3_lattices(A,B,k7_lattices(A,C)) <-> k5_lattices(A) = k4_lattices(A,B,C)))))))) # label(t52_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6453 (all A (l2_lattices(A) -> (v2_lattices(A) -> A = g2_lattices(u1_struct_0(A),u2_lattices(A))))) # label(abstractness_v2_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6454 (all A (l3_lattices(A) & v9_lattices(A) & v8_lattices(A) & v6_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_lattices(A,B,B) = B)))) # label(t17_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6455 (all A (-v3_struct_0(A) & l2_lattices(A) -> m1_subset_1(k6_lattices(A),u1_struct_0(A)))) # label(dt_k6_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6456 (all A all B all C (-v3_struct_0(A) & v6_lattices(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_lattices(A) -> k4_lattices(A,B,C) = k4_lattices(A,C,B))) # label(commutativity_k4_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6457 (all A (-v3_struct_0(A) & v11_lattices(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k3_lattices(A,B,k4_lattices(A,C,D)) = k4_lattices(A,k3_lattices(A,B,C),k3_lattices(A,B,D)))))))))) # label(t31_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6458 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v15_lattices(A) -> v14_lattices(A) & v13_lattices(A) & -v3_struct_0(A)))) # label(cc4_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6459 $T # label(t13_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6460 $T # label(t3_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6461 (all A (v10_lattices(A) & l3_lattices(A) & v17_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k4_lattices(A,k7_lattices(A,B),k7_lattices(A,C)) = k7_lattices(A,k3_lattices(A,B,C)))))))) # label(t51_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6462 (all A (l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_lattices(A,B,C) <-> k6_lattices(A) = k1_lattices(A,B,C) & k1_lattices(A,C,B) = k6_lattices(A) & k5_lattices(A) = k2_lattices(A,B,C) & k2_lattices(A,C,B) = k5_lattices(A)))))))) # label(d18_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6463 (all A (l3_lattices(A) -> l1_lattices(A) & l2_lattices(A))) # label(dt_l3_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6464 (all A (-v3_struct_0(A) & l1_lattices(A) -> m1_subset_1(k5_lattices(A),u1_struct_0(A)))) # label(dt_k5_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6465 (exists A (l2_lattices(A) & v2_lattices(A) & -v3_struct_0(A))) # label(rc4_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6466 (all A (l2_lattices(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_lattices(A,k1_lattices(A,B,C),D) = k1_lattices(A,B,k1_lattices(A,C,D)))))))) <-> v5_lattices(A)))) # label(d5_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6467 (all A all B (-v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & l3_lattices(A) -> m1_subset_1(k7_lattices(A,B),u1_struct_0(A)))) # label(dt_k7_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6468 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v10_lattices(A) & v11_lattices(A) -> v4_lattices(A) & v5_lattices(A) & v7_lattices(A) & v12_lattices(A) & v10_lattices(A) & v9_lattices(A) & v8_lattices(A) & v6_lattices(A) & -v3_struct_0(A)))) # label(cc7_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6469 (exists A l1_lattices(A)) # label(existence_l1_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6470 (all A (v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & v7_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattices(A,B,C) -> r1_lattices(A,k2_lattices(A,B,D),k2_lattices(A,C,D))))))))))) # label(t27_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6471 (all A (-v3_struct_0(A) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k3_lattices(A,k3_lattices(A,k4_lattices(A,B,C),k4_lattices(A,C,D)),k4_lattices(A,D,B)) = k4_lattices(A,k4_lattices(A,k3_lattices(A,B,C),k3_lattices(A,C,D)),k3_lattices(A,D,B)))))))))) # label(t34_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6472 (exists A (v1_lattices(A) & -v3_struct_0(A) & l1_lattices(A))) # label(rc5_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6473 (all A (l2_lattices(A) & v5_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattices(A,B,C) & r1_lattices(A,C,D) -> r1_lattices(A,B,D)))))))))) # label(t25_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6474 $T # label(t5_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6475 (all A (v13_lattices(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r3_lattices(A,k5_lattices(A),B))))) # label(t41_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6476 (all A (v10_lattices(A) & v14_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r3_lattices(A,B,k6_lattices(A)))))) # label(t45_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6477 (all A (l3_lattices(A) & v9_lattices(A) & v8_lattices(A) & v6_lattices(A) & v5_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r1_lattices(A,B,k1_lattices(A,B,C)))))))) # label(t22_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6478 (all A (-v3_struct_0(A) & l3_lattices(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_lattices(A,B,k1_lattices(A,B,C)) = B)))) <-> v9_lattices(A)))) # label(d9_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6479 $T # label(t33_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6480 (all A (l2_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_lattices(A,B,C) <-> C = k1_lattices(A,B,C)))))))) # label(d3_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6481 $T # label(t10_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6482 $T # label(t46_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6483 (all A (l1_lattices(A) -> v1_funct_1(u1_lattices(A)) & m2_relset_1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_2(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)))) # label(dt_u1_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6484 (all A all B all C (-v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_lattices(A) -> m1_subset_1(k2_lattices(A,B,C),u1_struct_0(A)))) # label(dt_k2_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6485 (all A (l3_lattices(A) & v9_lattices(A) & v8_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_lattices(A,B,C) <-> B = k2_lattices(A,B,C)))))))) # label(t21_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6486 (exists A (-v3_struct_0(A) & v2_lattices(A) & v4_lattices(A) & v5_lattices(A) & l2_lattices(A))) # label(rc7_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6487 $T # label(t15_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6488 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k4_lattices(A,k3_lattices(A,B,C),k3_lattices(A,B,D)) = k3_lattices(A,B,k4_lattices(A,C,D)))))))) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k3_lattices(A,k4_lattices(A,B,C),k4_lattices(A,B,D)) = k4_lattices(A,B,k3_lattices(A,C,D))))))))))) # label(t19_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6489 (all A (-v3_struct_0(A) & l3_lattices(A) -> (v11_lattices(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_lattices(A,k2_lattices(A,B,C),k2_lattices(A,B,D)) = k2_lattices(A,B,k1_lattices(A,C,D))))))))))) # label(d11_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6490 (all A (-v3_struct_0(A) & l3_lattices(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> C = k1_lattices(A,k2_lattices(A,B,C),C))))) <-> v8_lattices(A)))) # label(d8_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6491 (all A (-v3_struct_0(A) & l1_lattices(A) -> (v13_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k5_lattices(A) = B <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_lattices(A,B,C) = B & k2_lattices(A,C,B) = B)))))))) # label(d16_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6492 (all A (v10_lattices(A) & v17_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k7_lattices(A,k7_lattices(A,B)))))) # label(t49_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6493 (all A all B all C (-v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l2_lattices(A) -> m1_subset_1(k1_lattices(A,B,C),u1_struct_0(A)))) # label(dt_k1_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6494 (all A (l1_lattices(A) -> l1_struct_0(A))) # label(dt_l1_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6495 (all A all B all C (-v3_struct_0(A) & l2_lattices(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & v4_lattices(A) -> k1_lattices(A,B,C) = k3_lattices(A,B,C))) # label(redefinition_k3_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6496 (exists A l3_lattices(A)) # label(existence_l3_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6497 $T # label(t30_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6498 (all A (-v3_struct_0(A) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k4_lattices(A,k5_lattices(A),B) = k5_lattices(A))))) # label(t40_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6499 (all A (-v3_struct_0(A) & l2_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_lattices(A,B,C) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u2_lattices(A),B,C))))))) # label(d1_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6500 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C all D (g2_lattices(C,D) = g2_lattices(A,B) -> B = D & A = C)))) # label(free_g2_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6501 (all A (l3_lattices(A) & -v3_struct_0(A) -> (v16_lattices(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (exists C (r2_lattices(A,C,B) & m1_subset_1(C,u1_struct_0(A))))))))) # label(d19_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6502 $T # label(t36_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6503 (all A (l3_lattices(A) & -v3_struct_0(A) -> (v14_lattices(A) & v13_lattices(A) <-> v15_lattices(A)))) # label(d15_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6504 (all A (v10_lattices(A) & l3_lattices(A) & v17_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k5_lattices(A) = k4_lattices(A,k7_lattices(A,B),B))))) # label(t47_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6505 (exists A (l3_lattices(A) & -v3_struct_0(A) & v4_lattices(A) & v7_lattices(A) & v10_lattices(A) & v9_lattices(A) & v8_lattices(A) & v6_lattices(A) & v5_lattices(A) & v3_lattices(A))) # label(rc9_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6506 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k3_lattices(A,k3_lattices(A,k4_lattices(A,B,C),k4_lattices(A,C,D)),k4_lattices(A,D,B)) = k4_lattices(A,k4_lattices(A,k3_lattices(A,B,C),k3_lattices(A,C,D)),k3_lattices(A,D,B)))))))) -> v11_lattices(A)))) # label(t29_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6507 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v15_lattices(A) & v16_lattices(A) & v11_lattices(A) -> -v3_struct_0(A) & v17_lattices(A)))) # label(cc6_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6508 (all A (l3_lattices(A) -> (v10_lattices(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v7_lattices(A) & v9_lattices(A) & v8_lattices(A) & v6_lattices(A)))) # label(cc1_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6509 $T # label(t4_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6510 (all A (l3_lattices(A) -> (v17_lattices(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v13_lattices(A) & v16_lattices(A) & v15_lattices(A) & v14_lattices(A) & v11_lattices(A)))) # label(cc5_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6511 (all A (l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (-v3_struct_0(A) & l3_lattices(A) & v16_lattices(A) & v11_lattices(A) & v10_lattices(A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_lattices(A,C,B) <-> C = k7_lattices(A,B))))))))) # label(d21_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6512 (exists A (v2_lattices(A) & l2_lattices(A))) # label(rc2_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6513 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v11_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k4_lattices(A,B,C) = k4_lattices(A,B,D) & k3_lattices(A,B,D) = k3_lattices(A,B,C) -> C = D))))))))) # label(t32_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6514 $T # label(t9_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6515 (all A (l3_lattices(A) -> (v14_lattices(A) & v13_lattices(A) & -v3_struct_0(A) -> v15_lattices(A) & -v3_struct_0(A)))) # label(cc3_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6516 (exists A (v3_lattices(A) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v8_lattices(A) & v12_lattices(A) & v13_lattices(A) & v14_lattices(A) & v11_lattices(A) & v10_lattices(A) & v9_lattices(A) & v7_lattices(A) & -v3_struct_0(A) & l3_lattices(A))) # label(rc10_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6517 (all A (l3_lattices(A) & -v3_struct_0(A) -> (v10_lattices(A) <-> v4_lattices(A) & v8_lattices(A) & v7_lattices(A) & v9_lattices(A) & v6_lattices(A) & v5_lattices(A)))) # label(d10_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6518 $T # label(t28_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6519 (all A (l2_lattices(A) -> v1_funct_1(u2_lattices(A)) & m2_relset_1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_2(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)))) # label(dt_u2_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6520 (all A (-v3_struct_0(A) & l2_lattices(A) -> ((exists B (m1_subset_1(B,u1_struct_0(A)) & (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_lattices(A,C,B) = B & B = k1_lattices(A,B,C))))) <-> v14_lattices(A)))) # label(d14_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6521 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) -> -v3_struct_0(A) & v10_lattices(A)))) # label(cc2_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6522 $T # label(t37_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6523 (exists A (l1_lattices(A) & v6_lattices(A) & v7_lattices(A) & v1_lattices(A) & -v3_struct_0(A))) # label(rc8_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6524 (all A (v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k4_lattices(A,B,B))))) # label(t18_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6525 (all A all B all C (-v3_struct_0(A) & l2_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & v4_lattices(A) -> m1_subset_1(k3_lattices(A,B,C),u1_struct_0(A)))) # label(dt_k3_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6526 (exists A (v1_lattices(A) & l1_lattices(A))) # label(rc1_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6527 (all A (l3_lattices(A) -> (v3_lattices(A) -> A = g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A))))) # label(abstractness_v3_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6528 (exists A l2_lattices(A)) # label(existence_l2_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6529 $T # label(t8_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6530 $T # label(t35_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6531 (exists A (-v3_struct_0(A) & v6_lattices(A) & v7_lattices(A) & v10_lattices(A) & v14_lattices(A) & v15_lattices(A) & v17_lattices(A) & v16_lattices(A) & v13_lattices(A) & v11_lattices(A) & v9_lattices(A) & v8_lattices(A) & v5_lattices(A) & v4_lattices(A) & v3_lattices(A) & l3_lattices(A))) # label(rc13_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6532 (all A (v10_lattices(A) & l3_lattices(A) & v17_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k3_lattices(A,k7_lattices(A,B),B) = k6_lattices(A))))) # label(t48_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6533 $T # label(t38_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6534 (all A all B all C (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) -> (all D all E all F (g3_lattices(A,B,C) = g3_lattices(D,E,F) -> B = E & F = C & A = D)))) # label(free_g3_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6535 (all A (v4_lattices(A) & l2_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_lattices(A,C,B) & r1_lattices(A,B,C) -> B = C))))))) # label(t26_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6536 $T # label(t12_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6537 (all A (-v3_struct_0(A) & l3_lattices(A) -> (v11_lattices(A) & v16_lattices(A) & v15_lattices(A) <-> v17_lattices(A)))) # label(d20_lattices) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6538 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (C = k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) -> k4_subset_1(u1_struct_0(A),B,C) = k2_pre_topc(A)))))))) # label(t24_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6539 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> m1_subset_1(k6_pre_topc(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k6_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6540 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (D = C -> k3_xboole_0(k6_pre_topc(A,C),k2_pre_topc(B)) = k6_pre_topc(B,D)))))))))) # label(t47_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6541 $T # label(t10_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6542 (all A (l1_struct_0(A) -> k1_xboole_0 = k1_pre_topc(A))) # label(d2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6543 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (v1_pre_topc(C) & m1_pre_topc(C,A) -> (C = k3_pre_topc(A,B) <-> k2_pre_topc(C) = B))))))) # label(d10_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6544 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,C)),k5_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,C))))))))) # label(t51_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6545 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C all D (g1_pre_topc(A,B) = g1_pre_topc(C,D) -> B = D & A = C)))) # label(free_g1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6546 (all A all B all C all D (l1_struct_0(B) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) & l1_struct_0(A) -> m1_subset_1(k4_pre_topc(A,B,C,D),k1_zfmisc_1(u1_struct_0(B))))) # label(dt_k4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6547 $T # label(t29_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6548 (all A all B all C all D (l1_struct_0(A) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & l1_struct_0(B) -> m1_subset_1(k5_pre_topc(A,B,C,D),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6549 (all A (l1_pre_topc(A) -> m1_subset_1(u1_pre_topc(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))) # label(dt_u1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6550 $T # label(d4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6551 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (k6_pre_topc(A,B) = C <-> (all D (r2_hidden(D,u1_struct_0(A)) -> (r2_hidden(D,C) <-> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(E,A) & r2_hidden(D,E) & r1_xboole_0(B,E)))))))))))))) # label(d13_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6552 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(B,k2_pre_topc(A)))))) # label(t14_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6553 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> r2_hidden(k1_xboole_0,u1_pre_topc(A)))) # label(t5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6554 $T # label(t26_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6555 $T # label(t30_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6556 $T # label(t2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6557 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k6_pre_topc(A,k4_subset_1(u1_struct_0(A),B,C)) = k4_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,C)))))))) # label(t50_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6558 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> v4_pre_topc(C,A)))) -> v4_pre_topc(k6_setfam_1(u1_struct_0(A),B),A)))))) # label(t44_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6559 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> l1_pre_topc(B))))) # label(dt_m1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6560 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -((all C (m1_subset_1(C,u1_struct_0(A)) -> -r2_hidden(C,B))) & k1_pre_topc(A) != B))))) # label(t41_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6561 (all A (l1_pre_topc(A) -> (r2_hidden(u1_struct_0(A),u1_pre_topc(A)) & (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,u1_pre_topc(A)) & r2_hidden(C,u1_pre_topc(A)) -> r2_hidden(k5_subset_1(u1_struct_0(A),B,C),u1_pre_topc(A))))))) & (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(B,u1_pre_topc(A)) -> r2_hidden(k5_setfam_1(u1_struct_0(A),B),u1_pre_topc(A))))) <-> v2_pre_topc(A)))) # label(d1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6562 $T # label(t8_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6563 $T # label(t3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6564 (exists A l1_pre_topc(A)) # label(existence_l1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6565 $T # label(t38_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6566 $T # label(t40_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6567 (all A all B all C all D (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) & l1_struct_0(B) & l1_struct_0(A) -> k9_relat_1(C,D) = k4_pre_topc(A,B,C,D))) # label(redefinition_k4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6568 $T # label(t11_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6569 (all A (l1_pre_topc(A) -> (exists B (m1_pre_topc(B,A) & v1_pre_topc(B))))) # label(rc3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6570 (all A all B (-v3_struct_0(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> v1_pre_topc(k3_pre_topc(A,B)) & -v3_struct_0(k3_pre_topc(A,B)))) # label(fc3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6571 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (v1_pre_topc(B) & v2_pre_topc(B) & m1_pre_topc(B,A))))) # label(rc5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6572 $T # label(t19_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6573 $T # label(t33_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6574 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_pre_topc(A) & B = k6_pre_topc(A,B) -> v4_pre_topc(B,A)) & (v4_pre_topc(B,A) -> B = k6_pre_topc(A,B)))))) # label(t52_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6575 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k2_pre_topc(A) = k4_subset_1(u1_struct_0(A),B,k3_subset_1(u1_struct_0(A),B)))))) # label(t18_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6576 (all A (l1_struct_0(A) -> u1_struct_0(A) = k2_pre_topc(A))) # label(d3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6577 (all A (l1_pre_topc(A) -> l1_struct_0(A))) # label(dt_l1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6578 $T # label(d7_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6579 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,u1_pre_topc(A)) <-> v3_pre_topc(B,A)))))) # label(d5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6580 (all A (l1_pre_topc(A) -> (exists B m1_pre_topc(B,A)))) # label(existence_m1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6581 (all A (l1_struct_0(A) -> (all B (r1_tarski(B,k2_pre_topc(A)) -> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(t16_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6582 $T # label(t7_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6583 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> B = k5_subset_1(u1_struct_0(A),B,k2_pre_topc(A)))))) # label(t15_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6584 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_pre_topc(A) & k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) = k6_pre_topc(A,k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B)) -> v3_pre_topc(B,A)) & (v3_pre_topc(B,A) -> k6_pre_topc(A,k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B)) = k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B)))))) # label(t53_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6585 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(B = k2_pre_topc(A) & k1_xboole_0 != k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B)) & -(k2_pre_topc(A) != B & k1_xboole_0 = k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B)))))) # label(t23_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6586 $T # label(t20_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6587 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> B = k6_subset_1(u1_struct_0(A),k2_pre_topc(A),k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B)))))) # label(t22_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6588 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & l1_struct_0(B) & l1_struct_0(A) -> k5_pre_topc(A,B,C,D) = k10_relat_1(C,D))) # label(redefinition_k5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6589 (all A (l1_struct_0(A) & -v3_struct_0(A) -> -v1_xboole_0(k2_pre_topc(A)))) # label(fc2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6590 $T # label(t6_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6591 $T # label(t34_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6592 $T # label(t32_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6593 (all A (l1_struct_0(A) -> k3_subset_1(u1_struct_0(A),k1_pre_topc(A)) = k2_pre_topc(A))) # label(t27_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6594 $T # label(t31_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.15 6595 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (v4_pre_topc(C,B) <-> (exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & C = k3_xboole_0(D,k2_pre_topc(B)) & v4_pre_topc(D,A)))))))))) # label(t43_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6596 $T # label(t35_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6597 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (r2_hidden(C,u1_struct_0(A)) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,D) & v4_pre_topc(D,A) -> r2_hidden(C,D)))) <-> r2_hidden(C,k6_pre_topc(A,B))))))))) # label(t45_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6598 $T # label(t28_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6599 (all A (l1_struct_0(A) -> m1_subset_1(k1_pre_topc(A),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6600 $T # label(t1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6601 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (k4_subset_1(u1_struct_0(A),B,C) = k2_pre_topc(A) & r1_xboole_0(B,C) -> k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) = C))))))) # label(t25_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6602 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(B,k6_pre_topc(A,B)))))) # label(t48_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6603 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (m1_pre_topc(B,A) <-> r1_tarski(k2_pre_topc(B),k2_pre_topc(A)) & (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (r2_hidden(C,u1_pre_topc(B)) <-> (exists D (r2_hidden(D,u1_pre_topc(A)) & k3_xboole_0(D,k2_pre_topc(B)) = C & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))))))))))))) # label(d9_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6604 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> v4_pre_topc(k2_pre_topc(A),A))) # label(fc5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6605 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))))))))) # label(t39_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6606 $T # label(t9_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6607 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B),A) <-> v4_pre_topc(B,A)))))) # label(d6_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6608 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> v4_pre_topc(k2_pre_topc(A),A))) # label(t42_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6609 $T # label(t4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6610 (all A (l1_struct_0(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r2_hidden(B,k2_pre_topc(A)))))) # label(t13_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6611 $T # label(t37_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6612 $T # label(t36_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6613 (all A all B (v2_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> v2_pre_topc(k3_pre_topc(A,B)) & v1_pre_topc(k3_pre_topc(A,B)))) # label(fc4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6614 (exists A (l1_pre_topc(A) & v1_pre_topc(A))) # label(rc1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6615 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (exists B (-v1_xboole_0(B) & v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc7_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6616 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> v1_pre_topc(k3_pre_topc(A,B)) & m1_pre_topc(k3_pre_topc(A,B),A))) # label(dt_k3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6617 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> v2_pre_topc(B))))) # label(cc1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6618 (all A (l1_struct_0(A) -> k2_pre_topc(A) = u1_struct_0(A))) # label(t12_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6619 $T # label(d11_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6620 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (exists C ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(D,A) & r1_tarski(B,D) <-> r2_hidden(D,C)))) & k6_setfam_1(u1_struct_0(A),C) = k6_pre_topc(A,B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))))))) # label(t46_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6621 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (-v3_struct_0(A) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(D,A) & r2_hidden(C,D) & r1_xboole_0(B,D)))) <-> r2_hidden(C,k6_pre_topc(A,B))))))))) # label(t54_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6622 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (k5_setfam_1(u1_struct_0(A),B) = k2_pre_topc(A) <-> r1_pre_topc(A,B)))))) # label(d8_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6623 (all A (l1_pre_topc(A) -> (v1_pre_topc(A) -> A = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))))) # label(abstractness_v1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6624 (all A (l1_struct_0(A) -> v2_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v1_xboole_0(k1_pre_topc(A)))) # label(fc1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6625 (all A (l1_struct_0(A) -> m1_subset_1(k2_pre_topc(A),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6626 $T # label(t21_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6627 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) = k3_subset_1(u1_struct_0(A),B))))) # label(t17_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6628 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,C) -> r1_tarski(k6_pre_topc(A,B),k6_pre_topc(A,C))))))))) # label(t49_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6629 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> v1_pre_topc(g1_pre_topc(A,B)) & l1_pre_topc(g1_pre_topc(A,B)))) # label(dt_g1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6630 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (exists B (m1_pre_topc(B,A) & -v3_struct_0(B) & v1_pre_topc(B))))) # label(rc4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6631 (exists A (v2_pre_topc(A) & v1_pre_topc(A) & -v3_struct_0(A) & l1_pre_topc(A))) # label(rc2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6632 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v4_pre_topc(D,B) -> v4_pre_topc(k5_pre_topc(A,B,C,D),A)))) <-> v5_pre_topc(C,A,B)))))))) # label(d12_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6633 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(B,A))))) # label(rc6_pre_topc) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6634 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> v3_pre_topc(k2_pre_topc(A),A) & v4_pre_topc(k2_pre_topc(A),A))) # label(fc8_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6635 (all A (l1_pre_topc(A) -> k6_pre_topc(A,k2_pre_topc(A)) = k2_pre_topc(A))) # label(t27_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6636 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v5_tops_1(k3_subset_1(u1_struct_0(A),B),A) <-> v6_tops_1(B,A)))))) # label(t101_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6637 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k4_subset_1(u1_struct_0(A),k2_tops_1(A,B),k2_tops_1(A,C)) = k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),k2_tops_1(A,k4_subset_1(u1_struct_0(A),B,C)),k2_tops_1(A,k5_subset_1(u1_struct_0(A),B,C))),k5_subset_1(u1_struct_0(A),k2_tops_1(A,B),k2_tops_1(A,C))))))))) # label(t70_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6638 $T # label(t14_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6639 $T # label(t23_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6640 $T # label(t60_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6641 $T # label(t24_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6642 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k2_tops_1(A,k2_tops_1(A,B)),k2_tops_1(A,B)))))) # label(t68_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6643 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k2_tops_1(A,k1_tops_1(A,B)),k2_tops_1(A,B)))))) # label(t71_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6644 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k1_tops_1(A,B),B))))) # label(t44_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6645 (all A all B (v3_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) & v2_pre_topc(A) -> v4_pre_topc(k3_subset_1(u1_struct_0(A),B),A))) # label(fc4_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6646 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k4_subset_1(u1_struct_0(A),B,k2_tops_1(A,B)) = k6_pre_topc(A,B))))) # label(t65_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6647 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(B,A) -> v2_tops_1(B,A)))))) # label(t92_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6648 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k2_tops_1(A,k2_tops_1(A,B)) = k2_tops_1(A,k2_tops_1(A,k2_tops_1(A,B))))))) # label(t75_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6649 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> k1_tops_1(A,k2_pre_topc(A)) = k2_pre_topc(A))) # label(t43_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6650 $T # label(t17_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6651 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k2_tops_1(A,k5_subset_1(u1_struct_0(A),B,C)),k4_subset_1(u1_struct_0(A),k2_tops_1(A,B),k2_tops_1(A,C))))))))) # label(t66_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6652 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> v3_pre_topc(k1_pre_topc(A),A))) # label(t52_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6653 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k4_subset_1(u1_struct_0(A),k1_tops_1(A,B),k1_tops_1(A,C)),k1_tops_1(A,k4_subset_1(u1_struct_0(A),B,C))))))))) # label(t49_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6654 (all A (l1_pre_topc(A) -> v3_membered(k1_tops_1(A,k1_pre_topc(A))) & v5_membered(k1_tops_1(A,k1_pre_topc(A))) & v4_membered(k1_tops_1(A,k1_pre_topc(A))) & v2_membered(k1_tops_1(A,k1_pre_topc(A))) & v1_membered(k1_tops_1(A,k1_pre_topc(A))) & v1_xboole_0(k1_tops_1(A,k1_pre_topc(A))))) # label(fc5_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6655 $T # label(t15_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6656 $T # label(t28_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6657 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tops_1(B,A) <-> r1_tarski(B,k2_tops_1(A,B))))))) # label(t88_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6658 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) & v3_pre_topc(C,A) -> v3_pre_topc(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t38_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6659 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k4_subset_1(u1_struct_0(A),k5_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B)),B),k6_subset_1(u1_struct_0(A),k6_pre_topc(A,B),B)) = k2_tops_1(A,B))))) # label(t64_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6660 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_1(k3_subset_1(u1_struct_0(A),B),A) <-> v2_tops_1(B,A)))))) # label(d4_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6661 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_xboole_0(B) -> v3_tops_1(B,A)))))) # label(cc3_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6662 $T # label(t33_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6663 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,D) & v3_pre_topc(D,A) -> -r1_xboole_0(B,D) & -r1_xboole_0(k3_subset_1(u1_struct_0(A),B),D)))) <-> r2_hidden(C,k2_tops_1(A,B))))))))) # label(t61_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6664 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k1_tops_1(A,B) = k6_subset_1(u1_struct_0(A),B,k2_tops_1(A,B)))))) # label(t74_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6665 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (exists B (v3_pre_topc(B,A) & v4_pre_topc(B,A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc3_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6666 $T # label(t4_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6667 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k1_tops_1(A,k5_subset_1(u1_struct_0(A),B,C)) = k5_subset_1(u1_struct_0(A),k1_tops_1(A,B),k1_tops_1(A,C)))))))) # label(t46_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6668 $T # label(t5_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6669 $T # label(t1_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6670 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) <-> v4_pre_topc(k3_subset_1(u1_struct_0(A),B),A)))))) # label(t30_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6671 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tops_1(B,A) <-> k1_tops_1(A,B) = k1_xboole_0))))) # label(t84_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6672 $T # label(t83_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6673 (all A all B (v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v3_pre_topc(k1_tops_1(A,B),A))) # label(fc6_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6674 $T # label(t10_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6675 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k1_tops_1(A,B) = k1_tops_1(A,k1_tops_1(A,B)))))) # label(t45_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6676 $T # label(t7_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6677 $T # label(t9_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6678 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_xboole_0(k1_tops_1(A,B),k2_tops_1(A,B)))))) # label(t73_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6679 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k2_pre_topc(A) = k4_subset_1(u1_struct_0(A),B,k2_pre_topc(A)))))) # label(t2_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6680 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) & v4_pre_topc(C,A) -> k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,C)) = k5_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,C))))))))) # label(t34_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6681 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) -> (v3_tops_1(B,A) <-> k2_tops_1(A,B) = B)))))) # label(t94_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6682 $T # label(t99_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6683 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) <-> (all C (r2_hidden(C,B) <-> (exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D,A) & r2_hidden(C,D) & r1_tarski(D,B)))))))))) # label(t57_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6684 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_1(B,A) & r1_tarski(B,C) -> v1_tops_1(C,A)))))))) # label(t79_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6685 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,C) -> r1_tarski(k1_tops_1(A,B),k1_tops_1(A,C))))))))) # label(t48_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6686 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) -> r1_tarski(k2_tops_1(A,B),B)))))) # label(t69_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6687 (all A all B (l1_pre_topc(A) & v2_tops_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v1_xboole_0(k1_tops_1(A,B)) & v1_membered(k1_tops_1(A,B)) & v3_membered(k1_tops_1(A,B)) & v4_membered(k1_tops_1(A,B)) & v5_membered(k1_tops_1(A,B)) & v2_tops_1(k1_tops_1(A,B),A) & v2_membered(k1_tops_1(A,B)))) # label(fc10_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6688 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) & v2_pre_topc(A) -> v4_pre_topc(k6_pre_topc(A,B),A))) # label(fc2_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6689 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,B))) = k6_pre_topc(A,B)))))) # label(t59_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6690 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,k1_tops_1(A,C)) <-> (exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & r1_tarski(D,C) & r2_hidden(B,D) & v3_pre_topc(D,A)))))))) # label(t54_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6691 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k2_tops_1(A,k4_subset_1(u1_struct_0(A),B,C)),k4_subset_1(u1_struct_0(A),k2_tops_1(A,B),k2_tops_1(A,C))))))))) # label(t67_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6692 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(C,B) & v3_pre_topc(C,A) -> k1_xboole_0 = C))) <-> v2_tops_1(B,A)))))) # label(t86_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6693 $T # label(t12_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6694 (all A all B (v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) & v2_pre_topc(A) -> v2_tops_1(k2_tops_1(A,B),A) & v3_tops_1(k2_tops_1(A,B),A))) # label(fc13_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6695 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tops_1(B,A) & v4_pre_topc(B,A) -> v3_tops_1(B,A) & v2_tops_1(B,A)))))) # label(cc5_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6696 $T # label(t19_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6697 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(B,A) -> v1_tops_1(k3_subset_1(u1_struct_0(A),B),A)))))) # label(t91_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6698 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k2_tops_1(A,B) = k5_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B))))))) # label(d2_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6699 $T # label(t100_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6700 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) <-> k2_tops_1(A,B) = k6_subset_1(u1_struct_0(A),k6_pre_topc(A,B),B)))))) # label(t76_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6701 (all A all B (v2_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(B,A) & l1_pre_topc(A) -> v3_pre_topc(k3_subset_1(u1_struct_0(A),B),A))) # label(fc3_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6702 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> r1_tarski(k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,C)),k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,C)))))))))) # label(t40_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6703 (all A (l1_pre_topc(A) -> k1_tops_1(A,k1_pre_topc(A)) = k1_pre_topc(A))) # label(t47_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6704 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tops_1(B,A) & v4_pre_topc(B,A) -> v3_tops_1(B,A)))))) # label(t93_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6705 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(C,A) & v3_pre_topc(B,A) -> v3_pre_topc(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t37_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6706 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k1_tops_1(A,k6_subset_1(u1_struct_0(A),B,C)),k6_subset_1(u1_struct_0(A),k1_tops_1(A,B),k1_tops_1(A,C))))))))) # label(t50_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6707 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_1(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(C,A) & r1_xboole_0(B,C) & k1_xboole_0 != C)))))))) # label(t80_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6708 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v6_tops_1(C,A) -> v3_pre_topc(C,A) & v4_tops_1(C,A)) & (v4_tops_1(D,B) & v3_pre_topc(D,B) -> v6_tops_1(D,B)))))))))) # label(t107_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6709 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_1(B,A) <-> k2_pre_topc(A) = k6_pre_topc(A,B)))))) # label(d3_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6710 (all A (l1_struct_0(A) -> k1_pre_topc(A) = k3_subset_1(u1_struct_0(A),k2_pre_topc(A)))) # label(t8_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6711 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v6_tops_1(C,A) & v6_tops_1(B,A) -> v6_tops_1(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t109_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6712 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> v1_xboole_0(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v4_pre_topc(k1_pre_topc(A),A))) # label(fc1_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6713 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k2_tops_1(A,k6_pre_topc(A,B)),k2_tops_1(A,B)))))) # label(t72_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6714 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(C,A) & v3_tops_1(B,A) -> v3_tops_1(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t90_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6715 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v6_tops_1(B,A) -> k6_subset_1(u1_struct_0(A),k6_pre_topc(A,B),B) = k2_tops_1(A,k6_pre_topc(A,B)) & k2_tops_1(A,k6_pre_topc(A,B)) = k2_tops_1(A,B)))))) # label(t104_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6716 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k2_tops_1(A,B) = k2_tops_1(A,k3_subset_1(u1_struct_0(A),B)))))) # label(t62_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6717 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (k3_subset_1(u1_struct_0(A),B) = k3_subset_1(u1_struct_0(A),C) -> C = B))))))) # label(t21_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6718 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v5_tops_1(B,A) -> k2_tops_1(A,k1_tops_1(A,B)) = k2_tops_1(A,B)))))) # label(t102_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6719 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k6_pre_topc(A,k1_tops_1(A,B)) = k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,k1_tops_1(A,B)))))))) # label(t58_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6720 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_xboole_0(B,k3_subset_1(u1_struct_0(A),C)) <-> r1_tarski(B,C)))))))) # label(t20_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6721 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(B,A) & v3_pre_topc(B,A) -> v4_membered(B) & v5_membered(B) & v2_tops_1(B,A) & v3_tops_1(B,A) & v3_membered(B) & v2_membered(B) & v1_membered(B) & v4_pre_topc(B,A) & v3_pre_topc(B,A) & v1_xboole_0(B)))))) # label(cc6_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6722 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(C,A) & v4_pre_topc(B,A) -> v4_pre_topc(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t36_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6723 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_tops_1(B,A) -> v4_tops_1(k1_tops_1(A,B),A) & v4_tops_1(k6_pre_topc(A,B),A)))))) # label(t111_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6724 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v3_pre_topc(D,B) -> D = k1_tops_1(B,D)) & (C = k1_tops_1(A,C) -> v3_pre_topc(C,A)))))))))) # label(t55_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6725 (all A (l1_pre_topc(A) -> v1_tops_1(k2_pre_topc(A),A))) # label(fc9_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6726 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v5_tops_1(B,A) -> r1_tarski(k2_tops_1(A,B),k6_pre_topc(A,k1_tops_1(A,B)))))))) # label(t103_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6727 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_xboole_0(B) -> v4_pre_topc(B,A) & v3_pre_topc(B,A)))))) # label(cc1_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6728 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(B,A) -> v2_tops_1(B,A)))))) # label(cc4_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6729 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) <-> k6_subset_1(u1_struct_0(A),B,k1_tops_1(A,B)) = k2_tops_1(A,B)))))) # label(t77_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6730 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tops_1(C,A) & v4_pre_topc(C,A) & v2_tops_1(B,A) -> v2_tops_1(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t85_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6731 $T # label(t89_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6732 $T # label(t13_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6733 $T # label(t11_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6734 (all A all B (l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_tops_1(B,A) & v2_pre_topc(A) -> v1_tops_1(k3_subset_1(u1_struct_0(A),B),A))) # label(fc11_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6735 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> v1_xboole_0(k1_pre_topc(A)) & v4_pre_topc(k1_pre_topc(A),A) & v1_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v3_pre_topc(k1_pre_topc(A),A))) # label(fc7_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6736 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) -> v3_tops_1(k2_tops_1(A,B),A)))))) # label(t96_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6737 (all A all B (l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(B,A) & v2_pre_topc(A) -> v2_tops_1(k2_tops_1(A,B),A) & v3_tops_1(k2_tops_1(A,B),A))) # label(fc12_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6738 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v5_tops_1(B,A) <-> B = k6_pre_topc(A,k1_tops_1(A,B))))))) # label(d7_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6739 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B,A) & v3_membered(B) & v5_membered(B) & v3_tops_1(B,A) & v2_tops_1(B,A) & v4_membered(B) & v2_membered(B) & v1_membered(B) & v4_pre_topc(B,A))))) # label(rc5_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6740 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_hidden(C,D) & r1_xboole_0(B,D) & v3_pre_topc(D,A)))) <-> r2_hidden(C,k6_pre_topc(A,B))))))))) # label(t39_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6741 $T # label(t16_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6742 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tops_1(k6_pre_topc(A,B),A) <-> v3_tops_1(B,A)))))) # label(d5_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6743 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k1_tops_1(A,B) = k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B))))))) # label(d1_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6744 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> v4_pre_topc(k1_pre_topc(A),A))) # label(t22_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6745 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v3_pre_topc(k1_tops_1(A,B),A))))) # label(t51_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6746 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_tops_1(B,A) -> k1_xboole_0 = k1_tops_1(A,k2_tops_1(A,B))))))) # label(t110_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6747 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(C,A) -> k6_pre_topc(A,k5_subset_1(u1_struct_0(A),C,B)) = k6_pre_topc(A,C))))))))) # label(t81_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6748 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(k1_tops_1(A,k6_pre_topc(A,B)),B) & r1_tarski(B,k6_pre_topc(A,k1_tops_1(A,B))) <-> v4_tops_1(B,A)))))) # label(d6_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6749 (all A (l1_pre_topc(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v5_membered(B) & v2_tops_1(B,A) & v4_membered(B) & v1_xboole_0(B))))) # label(rc4_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6750 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_xboole_0(B) -> v2_tops_1(B,A)))))) # label(cc2_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6751 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) & v4_pre_topc(C,A) -> v4_pre_topc(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t35_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6752 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v5_tops_1(B,A) & v5_tops_1(C,A) -> v5_tops_1(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t108_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6753 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) -> (v2_tops_1(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(k1_xboole_0 != C & v3_pre_topc(C,A) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_tarski(D,C) & r1_xboole_0(B,D) & v3_pre_topc(D,A) & k1_xboole_0 != D)))))))))))) # label(t87_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6754 $T # label(t25_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6755 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k2_tops_1(A,B),k6_pre_topc(A,B)))))) # label(t63_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6756 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> m1_subset_1(k2_tops_1(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k2_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6757 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) & v4_pre_topc(B,A) -> (v6_tops_1(B,A) <-> v5_tops_1(B,A))))))) # label(t105_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6758 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> m1_subset_1(k1_tops_1(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k1_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6759 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) & r1_tarski(C,B) -> r1_tarski(k6_pre_topc(A,C),B)))))))) # label(t31_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6760 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(C,A) & v1_tops_1(C,A) & v1_tops_1(B,A) -> v1_tops_1(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t82_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6761 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> v3_tops_1(k2_tops_1(A,B),A)))))) # label(t95_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6762 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k6_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,C)),k6_pre_topc(A,k6_subset_1(u1_struct_0(A),B,C))))))))) # label(t32_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6763 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,C) & v3_pre_topc(B,A) -> r1_tarski(B,k1_tops_1(A,C))))))))) # label(t56_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6764 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k6_pre_topc(A,B) = k6_pre_topc(A,k6_pre_topc(A,B)))))) # label(t26_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6765 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (v4_pre_topc(B,A) & v3_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc2_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6766 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (v3_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc1_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6767 $T # label(t3_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6768 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) & v3_tops_1(B,A) -> k1_xboole_0 = B))))) # label(t97_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6769 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (k1_tops_1(A,k6_pre_topc(A,B)) = B <-> v6_tops_1(B,A)))))) # label(d8_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6770 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,C)) = k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,C)))))))))) # label(t41_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6771 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(k3_subset_1(u1_struct_0(A),B),A) <-> v4_pre_topc(B,A)))))) # label(t29_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6772 $T # label(t42_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6773 $T # label(t98_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6774 $T # label(t18_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6775 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v4_pre_topc(D,B) & v4_tops_1(D,B) -> v5_tops_1(D,B)) & (v5_tops_1(C,A) -> v4_tops_1(C,A) & v4_pre_topc(C,A)))))))))) # label(t106_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6776 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> v3_pre_topc(k2_pre_topc(A),A))) # label(t53_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6777 $T # label(t78_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6778 $T # label(t6_tops_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6779 $T # label(t4_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6780 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_tops_2(k7_setfam_1(u1_struct_0(A),B),A) <-> v2_tops_2(B,A)))))) # label(t16_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6781 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (l1_pre_topc(B) & -v3_struct_0(B) -> (all C (l1_pre_topc(C) & -v3_struct_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) -> (all E (v1_funct_1(E) & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C)) -> (v3_tops_2(D,A,B) & v3_tops_2(E,B,C) -> v3_tops_2(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C)))))))))))) # label(t71_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6782 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(B,C) & v2_tops_2(C,A) -> v2_tops_2(B,A)))))))) # label(t19_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6783 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_tops_2(C,A) -> v1_tops_2(k1_tops_2(A,B,C),k3_pre_topc(A,B))))))))) # label(t47_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6784 (all A (-v3_struct_0(A) & l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(r1_pre_topc(A,B) & k1_xboole_0 = B))))) # label(t5_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6785 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (v5_pre_topc(C,A,B) <-> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> r1_tarski(k6_pre_topc(A,k5_pre_topc(A,B,C,D)),k5_pre_topc(A,B,C,k6_pre_topc(B,D)))))))))))) # label(t56_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6786 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_tops_2(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> v3_pre_topc(C,A))))))))) # label(d1_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6787 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_finset_1(C) -> v1_finset_1(k1_tops_2(A,B,C))))))))) # label(t46_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6788 (all A (l1_pre_topc(A) -> (all B (-v3_struct_0(B) & l1_pre_topc(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) -> (v5_pre_topc(C,A,B) & v1_tops_2(D,B) -> (all E (m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (k9_relat_1(k3_funct_3(C),D) = E -> v1_tops_2(E,A))))))))))))) # label(t59_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6789 (all A all B all C (l1_pre_topc(A) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> m1_subset_1(k1_tops_2(A,B,C),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,B))))))) # label(dt_k1_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6790 (all A (l1_struct_0(A) -> (all B (-v3_struct_0(B) & l1_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (v2_funct_1(C) & k2_pre_topc(B) = k2_relat_1(C) -> k1_relat_1(k2_tops_2(A,B,C)) = k2_pre_topc(B) & k2_pre_topc(A) = k2_relat_1(k2_tops_2(A,B,C))))))))) # label(t62_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6791 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k1_xboole_0 != B -> k3_subset_1(A,k5_setfam_1(A,B)) = k6_setfam_1(A,k7_setfam_1(A,B))))) # label(t11_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6792 $T # label(t9_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.16 6793 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_pre_topc(C,A) -> (v2_tops_2(B,A) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(C)))) -> (B = D -> v2_tops_2(D,C))))))))))) # label(t36_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6794 $T # label(t53_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6795 $T # label(t61_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6796 (all A (l1_struct_0(A) -> (all B (-v3_struct_0(B) & l1_struct_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> k1_relat_1(C) = k2_pre_topc(A) & r1_tarski(k2_relat_1(C),k2_pre_topc(B)))))))) # label(t51_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6797 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (exists D (v1_relat_1(D) & k2_relat_1(D) = k1_tops_2(A,B,C) & (all E (r2_hidden(E,C) -> (all F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) -> (F = E -> k5_subset_1(u1_struct_0(A),F,B) = k1_funct_1(D,E)))))) & k1_relat_1(D) = C & v1_funct_1(D))))))))) # label(t50_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6798 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v2_tops_2(B,A) -> v2_tops_2(k6_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C),A)))))))) # label(t25_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6799 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_tops_2(B,A) <-> v2_tops_2(k7_setfam_1(u1_struct_0(A),B),A)))))) # label(t17_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6800 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v2_tops_2(B,A) -> v4_pre_topc(k6_setfam_1(u1_struct_0(A),B),A)))))) # label(t29_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6801 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_tops_2(C,A) & r1_tarski(B,C) -> v1_tops_2(B,A)))))))) # label(t18_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6802 $T # label(t30_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6803 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) -> -((all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(v1_tops_2(D,A) & (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (k2_pre_topc(B) = E -> k1_tops_2(A,E,D) = C)))))) & v1_tops_2(C,B)))))))) # label(t49_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6804 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (k2_relat_1(C) = k2_pre_topc(B) & v2_funct_1(C) -> k2_funct_1(C) = k2_tops_2(A,B,C)))))))) # label(d4_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6805 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v3_tops_2(C,A,B) <-> k1_relat_1(C) = k2_pre_topc(A) & k2_pre_topc(B) = k2_relat_1(C) & v5_pre_topc(k2_tops_2(A,B,C),B,A) & v5_pre_topc(C,A,B) & v2_funct_1(C)))))))) # label(d5_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6806 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_tops_2(B,A) -> v1_tops_2(k6_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C),A)))))))) # label(t22_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6807 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (k2_pre_topc(B) = k2_relat_1(C) & v2_funct_1(C) -> k5_pre_topc(B,A,k2_tops_2(A,B,C),D) = k4_pre_topc(A,B,C,D)))))))))) # label(t67_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6808 (all A (l1_struct_0(A) -> (all B (-v3_struct_0(B) & l1_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) -> m1_subset_1(k9_relat_1(k3_funct_3(C),D),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))))))))) # label(t54_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6809 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> r1_tarski(k6_subset_1(u1_struct_0(A),k5_setfam_1(u1_struct_0(A),B),k5_setfam_1(u1_struct_0(A),C)),k5_setfam_1(u1_struct_0(A),k6_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C))))))))) # label(t6_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6810 $T # label(t8_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6811 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> ((exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & C = k3_xboole_0(D,k2_pre_topc(B)) & v3_pre_topc(D,A))) <-> v3_pre_topc(C,B)))))))) # label(t32_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6812 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_pre_topc(C,A) -> (v1_tops_2(B,A) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(C)))) -> (D = B -> v1_tops_2(D,C))))))))))) # label(t35_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6813 $T # label(t2_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6814 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(B,k5_setfam_1(u1_struct_0(k3_pre_topc(A,B)),k1_tops_2(A,B,C))) -> r1_tarski(B,k5_setfam_1(u1_struct_0(A),C))))))))) # label(t45_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6815 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v2_tops_2(B,A) & v2_tops_2(C,A) -> v2_tops_2(k4_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C),A)))))))) # label(t23_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6816 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_finset_1(B) & v2_tops_2(B,A) -> v4_pre_topc(k5_setfam_1(u1_struct_0(A),B),A)))))) # label(t28_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6817 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,B))))) -> (k1_tops_2(A,B,C) = D <-> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,B)))) -> (r2_hidden(E,D) <-> (exists F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) & E = k5_subset_1(u1_struct_0(A),F,B) & r2_hidden(F,C))))))))))))))) # label(d3_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6818 $T # label(t15_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6819 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v2_tops_2(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> v4_pre_topc(C,A))))))))) # label(d2_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6820 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_tops_2(B,A) & v1_tops_2(C,A) -> v1_tops_2(k4_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C),A)))))))) # label(t20_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6821 $T # label(t69_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6822 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (k2_relat_1(C) = k2_pre_topc(B) & v2_funct_1(C) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> k6_pre_topc(B,k4_pre_topc(A,B,C,D)) = k4_pre_topc(A,B,C,k6_pre_topc(A,D)))) & k1_relat_1(C) = k2_pre_topc(A) <-> v3_tops_2(C,A,B)))))))) # label(t74_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6823 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k1_xboole_0 != B -> k5_setfam_1(A,k7_setfam_1(A,B)) = k3_subset_1(A,k6_setfam_1(A,B))))) # label(t12_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6824 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v2_funct_1(C) & k2_relat_1(C) = k2_pre_topc(B) -> k6_relat_1(k2_relat_1(C)) = k5_relat_1(k2_tops_2(A,B,C),C) & k5_relat_1(C,k2_tops_2(A,B,C)) = k6_relat_1(k1_relat_1(C))))))))) # label(t65_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6825 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_finset_1(B) <-> v1_finset_1(k7_setfam_1(u1_struct_0(A),B))))))) # label(t13_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6826 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r2_hidden(B,D) -> r2_hidden(k5_subset_1(u1_struct_0(A),B,C),k1_tops_2(A,C,D))))))))))) # label(t41_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6827 $T # label(t7_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6828 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> r1_tarski(B,k1_zfmisc_1(k2_pre_topc(A))))))) # label(t1_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6829 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(B,k5_setfam_1(u1_struct_0(A),D)) -> r1_tarski(k5_subset_1(u1_struct_0(A),B,C),k5_setfam_1(u1_struct_0(k3_pre_topc(A,C)),k1_tops_2(A,C,D)))))))))))) # label(t42_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6830 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> -(B = k1_xboole_0 & k7_setfam_1(A,B) != k1_xboole_0) & -(B != k1_xboole_0 & k1_xboole_0 = k7_setfam_1(A,B)))) # label(t10_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6831 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v2_tops_2(B,A) -> v2_tops_2(k5_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C),A)))))))) # label(t24_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6832 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> m1_subset_1(k5_subset_1(u1_struct_0(A),B,C),k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,C)))))))))) # label(t38_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6833 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) -> m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))))))) # label(t31_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6834 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v2_funct_1(C) & k2_relat_1(C) = k2_pre_topc(B) -> v2_funct_1(k2_tops_2(A,B,C))))))))) # label(t63_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6835 (all A all B all C (m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) & l1_struct_0(B) & l1_struct_0(A) -> v1_funct_2(k2_tops_2(A,B,C),u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(k2_tops_2(A,B,C),u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(k2_tops_2(A,B,C)))) # label(dt_k2_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6836 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_tops_2(B,A) -> v3_pre_topc(k5_setfam_1(u1_struct_0(A),B),A)))))) # label(t26_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6837 (all A (l1_struct_0(A) -> (all B (-v3_struct_0(B) & l1_struct_0(B) -> (all C (-v3_struct_0(C) & l1_struct_0(C) -> (all D (m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(D) -> (all E (m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C)) & v1_funct_1(E) -> (k1_relat_1(D) = k2_pre_topc(A) & k2_relat_1(D) = k2_pre_topc(B) & v2_funct_1(E) & k2_pre_topc(C) = k2_relat_1(E) & k2_pre_topc(B) = k1_relat_1(E) & v2_funct_1(D) -> k2_tops_2(A,C,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E)) = k7_funct_2(u1_struct_0(C),u1_struct_0(B),u1_struct_0(A),k2_tops_2(B,C,E),k2_tops_2(A,B,D))))))))))))) # label(t66_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6838 $T # label(t14_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6839 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(B,k5_setfam_1(u1_struct_0(A),C)) -> B = k5_setfam_1(u1_struct_0(k3_pre_topc(A,B)),k1_tops_2(A,B,C))))))))) # label(t43_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6840 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k4_pre_topc(A,B,C,k6_pre_topc(A,D)),k6_pre_topc(B,k4_pre_topc(A,B,C,D))))) <-> v5_pre_topc(C,A,B)))))))) # label(t57_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6841 $T # label(t37_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6842 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) & -v3_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (k1_relat_1(C) = k2_pre_topc(A) & k2_pre_topc(B) = k2_relat_1(C) & v2_funct_1(C) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(D,A) <-> v4_pre_topc(k4_pre_topc(A,B,C,D),B)))) <-> v3_tops_2(C,A,B)))))))) # label(t72_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6843 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (v3_tops_2(C,A,B) <-> k2_pre_topc(B) = k2_relat_1(C) & v2_funct_1(C) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> k5_pre_topc(A,B,C,k6_pre_topc(B,D)) = k6_pre_topc(A,k5_pre_topc(A,B,C,D)))) & k2_pre_topc(A) = k1_relat_1(C)))))))) # label(t73_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6844 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_pre_topc(C,A) -> (v4_pre_topc(B,A) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) -> (B = D -> v4_pre_topc(D,C))))))))))) # label(t34_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6845 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(C,D) -> r1_tarski(k1_tops_2(A,B,C),k1_tops_2(A,B,D))))))))))) # label(t40_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6846 $T # label(t39_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6847 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_tops_2(B,A) & v1_finset_1(B) -> v3_pre_topc(k6_setfam_1(u1_struct_0(A),B),A)))))) # label(t27_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6848 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) & -v3_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> k5_pre_topc(A,B,C,k2_pre_topc(B)) = k2_pre_topc(A))))))) # label(t52_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6849 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (v2_funct_1(C) & k2_relat_1(C) = k2_pre_topc(B) -> k2_tops_2(B,A,k2_tops_2(A,B,C)) = C))))))) # label(t64_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6850 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_tops_2(B,A) -> v1_tops_2(k5_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C),A)))))))) # label(t21_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6851 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (r1_tarski(C,B) -> m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))))))) # label(t3_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6852 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_pre_topc(C,A) -> (v3_pre_topc(B,A) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) -> (B = D -> v3_pre_topc(D,C))))))))))) # label(t33_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6853 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> r1_tarski(k5_setfam_1(u1_struct_0(k3_pre_topc(A,B)),k1_tops_2(A,B,C)),k5_setfam_1(u1_struct_0(A),C)))))))) # label(t44_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6854 (all A (l1_pre_topc(A) -> (all B (-v3_struct_0(B) & l1_pre_topc(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v3_pre_topc(D,B) -> v3_pre_topc(k5_pre_topc(A,B,C,D),A)))) <-> v5_pre_topc(C,A,B)))))))) # label(t55_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6855 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (v3_tops_2(C,A,B) -> v3_tops_2(k2_tops_2(A,B,C),B,A)))))))) # label(t70_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6856 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) -> (v5_pre_topc(C,A,B) & v2_tops_2(D,B) -> (all E (m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (E = k9_relat_1(k3_funct_3(C),D) -> v2_tops_2(E,A))))))))))))) # label(t60_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6857 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v2_tops_2(C,A) -> v2_tops_2(k1_tops_2(A,B,C),k3_pre_topc(A,B))))))))) # label(t48_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6858 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (k2_pre_topc(B) = k2_relat_1(C) & v2_funct_1(C) -> k4_pre_topc(B,A,k2_tops_2(A,B,C),D) = k5_pre_topc(A,B,C,D)))))))))) # label(t68_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6859 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (-v3_struct_0(C) & l1_pre_topc(C) -> (all D (m2_relset_1(D,u1_struct_0(A),u1_struct_0(C)) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(C)) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,u1_struct_0(C),u1_struct_0(B)) & m2_relset_1(E,u1_struct_0(C),u1_struct_0(B)) -> (v5_pre_topc(D,A,C) & v5_pre_topc(E,C,B) -> v5_pre_topc(k7_funct_2(u1_struct_0(A),u1_struct_0(C),u1_struct_0(B),D,E),A,B)))))))))))) # label(t58_tops_2) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6860 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_rlvect_1(A) = k2_rlvect_1(A,B,C) -> k5_rlvect_1(A,C) = B))))))) # label(t19_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6861 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k3_rlvect_1(A,B,np__3) = k9_rlvect_1(A,k8_rlvect_1(A,B,B,B)))))) # label(t93_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6862 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (-v3_struct_0(C) & v3_rlvect_1(C) & v5_rlvect_1(C) & l2_rlvect_1(C) & v7_rlvect_1(C) & v6_rlvect_1(C) & v4_rlvect_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (k3_rlvect_1(C,D,B) = k3_rlvect_1(C,D,A) -> A = B | k1_rlvect_1(C) = D))))))))) # label(t51_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6863 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k5_rlvect_1(A,k9_rlvect_1(A,k8_rlvect_1(A,B,C,D))) = k6_rlvect_1(A,k6_rlvect_1(A,k5_rlvect_1(A,B),C),D))))))))) # label(t71_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6864 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k4_rlvect_1(A,k9_rlvect_1(A,k7_rlvect_1(A,B,D)),C) = k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)))))))))) # label(t83_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6865 (all A all B all C all D (-v1_xboole_0(A) & v1_funct_1(C) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A) & m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_subset_1(B,A) -> v2_rlvect_1(g2_rlvect_1(A,B,C,D)) & -v3_struct_0(g2_rlvect_1(A,B,C,D)))) # label(fc1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6866 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k9_rlvect_1(A,k7_rlvect_1(A,B,k1_rlvect_1(A))) = B & B = k9_rlvect_1(A,k7_rlvect_1(A,k1_rlvect_1(A),B)))))) # label(t75_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6867 (all A (v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k2_rlvect_1(A,B,k1_rlvect_1(A)) & B = k2_rlvect_1(A,k1_rlvect_1(A),B))))) # label(t10_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6868 $T # label(t1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6869 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)) = k4_rlvect_1(A,k9_rlvect_1(A,k7_rlvect_1(A,C,D)),B))))))))) # label(t84_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6870 (all A (l2_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_numbers) -> k3_rlvect_1(A,B,C) = k8_funct_2(k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A),u2_rlvect_1(A),k1_domain_1(k1_numbers,u1_struct_0(A),C,B)))))))) # label(d4_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6871 $T # label(t4_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6872 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k5_rlvect_1(A,B) = C <-> k1_rlvect_1(A) = k2_rlvect_1(A,B,C))))))))) # label(d10_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6873 (all A (v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,C,B),k3_rlvect_1(A,D,B)),k3_rlvect_1(A,E,B)) = k3_rlvect_1(A,k9_rlvect_1(A,k8_rlvect_1(A,C,D,E)),B))))))))))) # label(t67_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6874 (all A all B all C (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & m1_subset_1(C,A) & v1_funct_1(B) -> (all D all E all F (g1_rlvect_1(D,E,F) = g1_rlvect_1(A,B,C) -> A = D & C = F & E = B)))) # label(free_g1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6875 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> (v2_funct_1(C) & v2_funct_1(B) & k2_relat_1(B) = k2_relat_1(C) -> k9_rlvect_1(A,B) = k9_rlvect_1(A,C)))))))) # label(t59_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6876 $T # label(t53_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6877 (all A (l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> k1_rlvect_1(A) = k9_rlvect_1(A,k8_rlvect_1(A,k1_rlvect_1(A),k1_rlvect_1(A),k1_rlvect_1(A))))) # label(t90_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6878 (all A (m1_subset_1(A,k1_numbers) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) & v6_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k6_rlvect_1(B,k3_rlvect_1(B,C,A),k3_rlvect_1(B,D,A)) = k3_rlvect_1(B,k6_rlvect_1(B,C,D),A))))))))) # label(t48_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6879 $T # label(t8_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6880 (all A (m1_subset_1(A,k1_numbers) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k3_rlvect_1(B,k5_rlvect_1(B,C),A) = k5_rlvect_1(B,k3_rlvect_1(B,C,A)))))))) # label(t39_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6881 $T # label(t13_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6882 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k6_rlvect_1(A,B,D) = k6_rlvect_1(A,B,C) -> D = C))))))))) # label(t37_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6883 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k3_finseq_1(B) = k1_nat_1(k3_finseq_1(C),np__1) & k7_relat_1(B,k4_finseq_1(C)) = C & D = k1_funct_1(B,k3_finseq_1(B)) -> k9_rlvect_1(A,B) = k2_rlvect_1(A,k9_rlvect_1(A,C),D)))))))))) # label(t55_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6884 $T # label(t52_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6885 $T # label(t6_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6886 (all A (l2_rlvect_1(A) -> (v2_rlvect_1(A) -> g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A)) = A))) # label(abstractness_v2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6887 (all A (-v3_struct_0(A) & l2_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v8_rlvect_1(B,A) <-> B != k1_rlvect_1(A)))))) # label(d13_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6888 (all A (v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (B = k5_rlvect_1(A,B) -> k1_rlvect_1(A) = B))))) # label(t33_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6889 (all A (-v3_struct_0(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (C = k2_rlvect_1(A,B,D) & m1_subset_1(D,u1_struct_0(A)))))))))) # label(t20_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6890 $T # label(t15_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6891 (exists A l1_rlvect_1(A)) # label(existence_l1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6892 (all A (l2_rlvect_1(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k3_rlvect_1(A,k3_rlvect_1(A,D,C),B) = k3_rlvect_1(A,D,k4_real_1(B,C)))))))) & (all B (m1_subset_1(B,u1_struct_0(A)) -> k3_rlvect_1(A,B,np__1) = B)) & (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,k3_rlvect_1(A,D,B),k3_rlvect_1(A,D,C)) = k3_rlvect_1(A,D,k3_real_1(B,C)))))))) & (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k3_rlvect_1(A,k2_rlvect_1(A,C,D),B) = k2_rlvect_1(A,k3_rlvect_1(A,C,B),k3_rlvect_1(A,D,B)))))))) <-> v7_rlvect_1(A)))) # label(d9_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6893 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k5_rlvect_1(A,B) = k6_rlvect_1(A,k1_rlvect_1(A),B))))) # label(t27_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6894 (all A (v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_rlvect_1(A,B,C) = k9_rlvect_1(A,k8_rlvect_1(A,k1_rlvect_1(A),B,C)) & k2_rlvect_1(A,B,C) = k9_rlvect_1(A,k8_rlvect_1(A,B,C,k1_rlvect_1(A))) & k2_rlvect_1(A,B,C) = k9_rlvect_1(A,k8_rlvect_1(A,B,k1_rlvect_1(A),C)))))))) # label(t92_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6895 (all A all B all C all D (-v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(A)) -> k11_finseq_1(B,C,D) = k8_rlvect_1(A,B,C,D))) # label(redefinition_k8_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6896 (all A (-v3_struct_0(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k2_rlvect_1(A,B,k5_rlvect_1(A,B)) = k1_rlvect_1(A) & k2_rlvect_1(A,k5_rlvect_1(A,B),B) = k1_rlvect_1(A))))) # label(t16_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6897 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_rlvect_1(A,C,k5_rlvect_1(A,B)) = k5_rlvect_1(A,k6_rlvect_1(A,B,C)))))))) # label(t47_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6898 (all A all B all C (-v3_struct_0(A) & l1_rlvect_1(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) -> m1_subset_1(k2_rlvect_1(A,B,C),u1_struct_0(A)))) # label(dt_k2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6899 (all A (-v3_struct_0(A) & l1_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_rlvect_1(A,B))))) # label(t3_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.17 6900 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (k3_finseq_1(B) = np__0 -> k1_rlvect_1(A) = k9_rlvect_1(A,B)))))) # label(t94_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6901 (all A (v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k9_rlvect_1(A,k7_rlvect_1(A,B,C)) = k2_rlvect_1(A,k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),B)),k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),C))))))))) # label(t73_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6902 (all A (l2_rlvect_1(A) -> m2_relset_1(u2_rlvect_1(A),k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A)) & v1_funct_2(u2_rlvect_1(A),k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A)) & v1_funct_1(u2_rlvect_1(A)))) # label(dt_u2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6903 $T # label(t2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6904 $T # label(t11_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6905 (exists A (l1_rlvect_1(A) & v1_rlvect_1(A))) # label(rc1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6906 (all A (m1_subset_1(A,k1_numbers) -> (all B (v4_rlvect_1(B) & l2_rlvect_1(B) & v7_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (A = np__0 | k1_rlvect_1(B) = C -> k3_rlvect_1(B,C,A) = k1_rlvect_1(B)))))))) # label(t23_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6907 (all A all B all C (-v3_struct_0(A) & v3_rlvect_1(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_rlvect_1(A) -> m1_subset_1(k4_rlvect_1(A,B,C),u1_struct_0(A)))) # label(dt_k4_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6908 (all A all B all C (-v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) -> m2_finseq_1(k7_rlvect_1(A,B,C),u1_struct_0(A)))) # label(dt_k7_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6909 (all A all B (-v3_struct_0(A) & m1_finseq_1(B,u1_struct_0(A)) & l1_rlvect_1(A) -> m1_subset_1(k9_rlvect_1(A,B),u1_struct_0(A)))) # label(dt_k9_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6910 $T # label(t18_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6911 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k9_rlvect_1(A,k8_rlvect_1(A,D,B,C)) = k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)))))))))) # label(t89_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6912 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (m1_subset_1(D,u1_struct_0(A)) & k6_rlvect_1(A,C,D) = B)))))))) # label(t36_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6913 (all A (l2_rlvect_1(A) -> l1_rlvect_1(A))) # label(dt_l2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6914 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k4_rlvect_1(A,k6_rlvect_1(A,B,C),D) = k6_rlvect_1(A,B,k6_rlvect_1(A,C,D)))))))))) # label(t43_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6915 (all A all B all C (-v3_struct_0(A) & m1_subset_1(C,k1_numbers) & m1_subset_1(B,u1_struct_0(A)) & l2_rlvect_1(A) -> m1_subset_1(k3_rlvect_1(A,B,C),u1_struct_0(A)))) # label(dt_k3_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6916 $T # label(t17_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6917 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k4_rlvect_1(A,k3_rlvect_1(A,C,B),k3_rlvect_1(A,D,B)) = k3_rlvect_1(A,k9_rlvect_1(A,k7_rlvect_1(A,C,D)),B))))))))) # label(t66_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6918 (all A (m1_subset_1(A,k1_numbers) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k3_rlvect_1(B,C,k1_real_1(A)) = k3_rlvect_1(B,k5_rlvect_1(B,C),A))))))) # label(t38_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6919 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k6_rlvect_1(A,B,C) = k9_rlvect_1(A,k7_rlvect_1(A,B,k5_rlvect_1(A,C))))))))) # label(t77_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6920 (all A (-v3_struct_0(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> k9_rlvect_1(A,k7_rlvect_1(A,k1_rlvect_1(A),k1_rlvect_1(A))) = k1_rlvect_1(A))) # label(t74_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6921 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k9_rlvect_1(A,k8_rlvect_1(A,B,D,C)) = k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)))))))))) # label(t87_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6922 (all A (l2_struct_0(A) -> u2_struct_0(A) = k1_rlvect_1(A))) # label(d2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6923 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_rlvect_1(A,B,C) = k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A),u1_rlvect_1(A),k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C)))))))) # label(d3_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6924 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k6_rlvect_1(A,k5_rlvect_1(A,C),B) = k6_rlvect_1(A,k5_rlvect_1(A,B),C))))))) # label(t46_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6925 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (k2_rlvect_1(A,D,B) = k2_rlvect_1(A,E,B) | k2_rlvect_1(A,B,D) = k2_rlvect_1(A,B,E) -> E = D))))))))))) # label(t21_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6926 (all A (l1_struct_0(A) -> (all B (r2_hidden(B,u1_struct_0(A)) <-> r1_rlvect_1(A,B))))) # label(d1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6927 (all A (v3_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> ((all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (k1_funct_1(C,D) = E & r2_hidden(D,k4_finseq_1(B)) -> k5_rlvect_1(A,E) = k1_funct_1(B,D)))))) & k3_finseq_1(C) = k3_finseq_1(B) -> k5_rlvect_1(A,k9_rlvect_1(A,C)) = k9_rlvect_1(A,B)))))))) # label(t57_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6928 (all A all B (-v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & l1_rlvect_1(A) -> m1_subset_1(k5_rlvect_1(A,B),u1_struct_0(A)))) # label(dt_k5_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6929 (all A (v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_rlvect_1(A,B,C) = k9_rlvect_1(A,k7_rlvect_1(A,B,C)))))))) # label(t62_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6930 (all A (-v3_struct_0(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (np__1 = k3_finseq_1(B) -> k9_rlvect_1(A,B) = k1_funct_1(B,np__1)))))) # label(t95_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6931 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k6_rlvect_1(A,B,C) = k1_rlvect_1(A) -> C = B))))))) # label(t35_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6932 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k9_rlvect_1(A,k8_rlvect_1(A,k1_rlvect_1(A),k1_rlvect_1(A),B)) = B & k9_rlvect_1(A,k8_rlvect_1(A,B,k1_rlvect_1(A),k1_rlvect_1(A))) = B & B = k9_rlvect_1(A,k8_rlvect_1(A,k1_rlvect_1(A),B,k1_rlvect_1(A))))))) # label(t91_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6933 (exists A (l1_rlvect_1(A) & -v3_struct_0(A) & v1_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A))) # label(rc5_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6934 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k3_rlvect_1(A,B,k1_real_1(np__1)) = k5_rlvect_1(A,B))))) # label(t29_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6935 $T # label(t65_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6936 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> ((exists D (m2_relset_1(D,k5_numbers,u1_struct_0(A)) & (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (all F (m1_subset_1(F,u1_struct_0(A)) -> (F = k1_funct_1(B,k1_nat_1(E,np__1)) -> k2_rlvect_1(A,k8_funct_2(k5_numbers,u1_struct_0(A),D,E),F) = k8_funct_2(k5_numbers,u1_struct_0(A),D,k1_nat_1(E,np__1)) | r1_xreal_0(k3_finseq_1(B),E)))))) & k1_rlvect_1(A) = k8_funct_2(k5_numbers,u1_struct_0(A),D,np__0) & C = k8_funct_2(k5_numbers,u1_struct_0(A),D,k3_finseq_1(B)) & v1_funct_2(D,k5_numbers,u1_struct_0(A)) & v1_funct_1(D))) <-> C = k9_rlvect_1(A,B)))))))) # label(d12_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6937 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) -> k5_rlvect_1(A,k1_rlvect_1(A)) = k1_rlvect_1(A))) # label(t25_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6938 (all A (l2_struct_0(A) -> m1_subset_1(k1_rlvect_1(A),u1_struct_0(A)))) # label(dt_k1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6939 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_rlvect_1(A,B,B) = k1_rlvect_1(A))))) # label(t28_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6940 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k1_rlvect_1(A) = k4_rlvect_1(A,B,B) -> k1_rlvect_1(A) = B))))) # label(t34_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6941 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_rlvect_1(A,B,k5_rlvect_1(A,C)) = k6_rlvect_1(A,B,C))))))) # label(d11_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6942 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (v5_rlvect_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k2_rlvect_1(A,B,k1_rlvect_1(A))))))) # label(d7_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6943 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k9_rlvect_1(A,k7_rlvect_1(A,k5_rlvect_1(A,B),k5_rlvect_1(A,C))) = k5_rlvect_1(A,k2_rlvect_1(A,C,B)))))))) # label(t78_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6944 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (D = k1_funct_1(B,np__2) & C = k1_funct_1(B,np__1) & np__2 = k3_finseq_1(B) -> k2_rlvect_1(A,C,D) = k9_rlvect_1(A,B)))))))))) # label(t96_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6945 (all A (m1_subset_1(A,k1_numbers) -> (all B (v3_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m2_finseq_1(C,u1_struct_0(B)) -> (all D (m2_finseq_1(D,u1_struct_0(B)) -> (k3_finseq_1(D) = k3_finseq_1(C) & (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> (k1_funct_1(D,E) = F & r2_hidden(E,k4_finseq_1(C)) -> k1_funct_1(C,E) = k3_rlvect_1(B,F,A)))))) -> k3_rlvect_1(B,k9_rlvect_1(B,D),A) = k9_rlvect_1(B,C)))))))))) # label(t56_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6946 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (v3_rlvect_1(C) & v4_rlvect_1(C) & v6_rlvect_1(C) & l2_rlvect_1(C) & v7_rlvect_1(C) & v5_rlvect_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k3_rlvect_1(C,D,k5_real_1(A,B)) = k6_rlvect_1(C,k3_rlvect_1(C,D,A),k3_rlvect_1(C,D,B)))))))))) # label(t49_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6947 (all A (v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_numbers) -> k1_rlvect_1(A) = k3_rlvect_1(A,k9_rlvect_1(A,k6_finseq_1(u1_struct_0(A))),B))))) # label(t64_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6948 (all A (l1_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,B,k6_rlvect_1(A,C,D)) = k6_rlvect_1(A,k2_rlvect_1(A,B,C),D))))))))) # label(t42_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6949 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_rlvect_1(A,k5_rlvect_1(A,C),k5_rlvect_1(A,B)) = k5_rlvect_1(A,k2_rlvect_1(A,B,C)))))))) # label(t45_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6950 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k6_rlvect_1(A,k5_rlvect_1(A,C),B) = k5_rlvect_1(A,k2_rlvect_1(A,B,C)))))))) # label(t44_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6951 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k5_rlvect_1(A,k5_rlvect_1(A,B)) = B)))) # label(t30_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6952 (all A (m1_subset_1(A,k1_numbers) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) & v6_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (k3_rlvect_1(B,C,A) = k3_rlvect_1(B,D,A) -> A = np__0 | D = C))))))))) # label(t50_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6953 (all A (l1_rlvect_1(A) -> v1_funct_2(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & m2_relset_1(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_1(u1_rlvect_1(A)))) # label(dt_u1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6954 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> k1_rlvect_1(A) = k9_rlvect_1(A,k6_finseq_1(u1_struct_0(A))))) # label(t60_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6955 (all A (v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),B)))))) # label(t61_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6956 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> k2_rlvect_1(A,k9_rlvect_1(A,B),k9_rlvect_1(A,C)) = k9_rlvect_1(A,k8_finseq_1(u1_struct_0(A),B,C)))))))) # label(t58_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6957 (all A all B all C (m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_struct_0(A) & -v3_struct_0(A) -> k7_rlvect_1(A,B,C) = k10_finseq_1(B,C))) # label(redefinition_k7_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6958 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (v4_rlvect_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,B,k2_rlvect_1(A,C,D)) = k2_rlvect_1(A,k2_rlvect_1(A,B,C),D)))))))))) # label(d6_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6959 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (k3_finseq_1(B) = np__3 & C = k1_funct_1(B,np__1) & D = k1_funct_1(B,np__2) & E = k1_funct_1(B,np__3) -> k2_rlvect_1(A,k2_rlvect_1(A,C,D),E) = k9_rlvect_1(A,B)))))))))))) # label(t97_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6960 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k9_rlvect_1(A,k7_rlvect_1(A,B,C)) = k9_rlvect_1(A,k7_rlvect_1(A,C,B)))))))) # label(t72_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6961 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k3_rlvect_1(A,B,np__2) = k9_rlvect_1(A,k7_rlvect_1(A,B,B)))))) # label(t79_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6962 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(C,k2_finseq_1(D)) & D = k3_finseq_1(B) -> m1_subset_1(k1_funct_1(B,C),u1_struct_0(A))))))))))) # label(t54_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6963 (all A (m1_subset_1(A,k1_numbers) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) & v6_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k3_rlvect_1(B,k5_rlvect_1(B,C),k1_real_1(A)) = k3_rlvect_1(B,C,A))))))) # label(t40_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6964 (exists A l2_rlvect_1(A)) # label(existence_l2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6965 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_rlvect_1(A,C,B) = k2_rlvect_1(A,B,C))))) <-> v3_rlvect_1(A)))) # label(d5_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6966 $T # label(t32_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6967 (exists A (v2_rlvect_1(A) & l2_rlvect_1(A))) # label(rc2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6968 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)) = k9_rlvect_1(A,k8_rlvect_1(A,C,D,B)))))))))) # label(t85_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6969 (all A all B all C all D (m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A) & m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A) & v1_funct_1(D) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m1_subset_1(B,A) -> l2_rlvect_1(g2_rlvect_1(A,B,C,D)) & v2_rlvect_1(g2_rlvect_1(A,B,C,D)))) # label(dt_g2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6970 (all A all B all C (v3_rlvect_1(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_rlvect_1(A) & -v3_struct_0(A) -> k4_rlvect_1(A,B,C) = k2_rlvect_1(A,B,C))) # label(redefinition_k4_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6971 $T # label(t88_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6972 (all A (v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k5_rlvect_1(A,B) = k5_rlvect_1(A,k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),B))))))) # label(t69_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6973 (all A all B all C all D (m1_subset_1(B,A) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A) & m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A) & v1_funct_1(D) -> (all E all F all G all H (g2_rlvect_1(E,F,G,H) = g2_rlvect_1(A,B,C,D) -> E = A & F = B & C = G & H = D)))) # label(free_g2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6974 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_rlvect_1(A,B,C) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_rlvect_1(A),B,C))))))) # label(t5_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6975 (exists A (l2_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & v2_rlvect_1(A) & -v3_struct_0(A))) # label(rc6_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6976 (all A (l1_rlvect_1(A) -> l2_struct_0(A))) # label(dt_l1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6977 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k3_rlvect_1(A,B,k1_real_1(np__2)) = k9_rlvect_1(A,k7_rlvect_1(A,k5_rlvect_1(A,B),k5_rlvect_1(A,B))))))) # label(t80_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6978 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (v6_rlvect_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (exists C (m1_subset_1(C,u1_struct_0(A)) & k1_rlvect_1(A) = k2_rlvect_1(A,B,C)))))))) # label(d8_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6979 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k9_rlvect_1(A,k8_rlvect_1(A,B,C,D)) = k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)))))))))) # label(t86_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6980 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k9_rlvect_1(A,k7_rlvect_1(A,k5_rlvect_1(A,B),B)) = k1_rlvect_1(A) & k9_rlvect_1(A,k7_rlvect_1(A,B,k5_rlvect_1(A,B))) = k1_rlvect_1(A))))) # label(t76_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6981 $T # label(t9_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6982 (exists A (-v3_struct_0(A) & l2_rlvect_1(A))) # label(rc3_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6983 (all A all B all C (-v3_struct_0(A) & v3_rlvect_1(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_rlvect_1(A) -> k4_rlvect_1(A,C,B) = k4_rlvect_1(A,B,C))) # label(commutativity_k4_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 17.78/17.18 6984 (all A (m1_subset_1(A,k1_numbers) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & l2_rlvect_1(B) & v7_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> -(k1_rlvect_1(B) = k3_rlvect_1(B,C,A) & np__0 != A & C != k1_rlvect_1(B)))))))) # label(t24_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 6985 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k9_rlvect_1(A,k8_rlvect_1(A,B,C,D)) = k2_rlvect_1(A,k2_rlvect_1(A,B,C),D))))))))) # label(t63_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 6986 (all A all B all C (l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & -v3_struct_0(A) -> m1_subset_1(k6_rlvect_1(A,B,C),u1_struct_0(A)))) # label(dt_k6_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 6987 (all A (v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k6_rlvect_1(A,B,k2_rlvect_1(A,C,D)) = k6_rlvect_1(A,k6_rlvect_1(A,B,D),C))))))))) # label(t41_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 6988 (all A (l2_rlvect_1(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (exists C (m1_subset_1(C,u1_struct_0(A)) & k1_rlvect_1(A) = k2_rlvect_1(A,B,C))))) & (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,k3_rlvect_1(A,C,B),k3_rlvect_1(A,D,B)) = k3_rlvect_1(A,k2_rlvect_1(A,C,D),B))))))) & (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,k3_rlvect_1(A,D,B),k3_rlvect_1(A,D,C)) = k3_rlvect_1(A,D,k3_real_1(B,C)))))))) & (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k3_rlvect_1(A,B,np__1))) & (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k3_rlvect_1(A,k3_rlvect_1(A,D,C),B) = k3_rlvect_1(A,D,k4_real_1(B,C)))))))) & (all B (m1_subset_1(B,u1_struct_0(A)) -> k2_rlvect_1(A,B,k1_rlvect_1(A)) = B)) & (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,B,k2_rlvect_1(A,C,D)) = k2_rlvect_1(A,k2_rlvect_1(A,B,C),D))))))) & (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_rlvect_1(A,C,B) = k2_rlvect_1(A,B,C))))) -> v3_rlvect_1(A) & v4_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A)))) # label(t7_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 6989 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k5_rlvect_1(A,k9_rlvect_1(A,k7_rlvect_1(A,B,C))) = k6_rlvect_1(A,k5_rlvect_1(A,B),C))))))) # label(t70_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 6990 (exists A (v1_rlvect_1(A) & -v3_struct_0(A) & l1_rlvect_1(A))) # label(rc4_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 6991 (all A all B all C all D (m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(A)) & l1_struct_0(A) & -v3_struct_0(A) -> m2_finseq_1(k8_rlvect_1(A,B,C,D),u1_struct_0(A)))) # label(dt_k8_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 6992 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k2_rlvect_1(A,B,C) = B | k2_rlvect_1(A,C,B) = B -> C = k1_rlvect_1(A)))))))) # label(t22_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 6993 (all A all B all C (v1_funct_1(B) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & m1_subset_1(C,A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> l1_rlvect_1(g1_rlvect_1(A,B,C)) & v1_rlvect_1(g1_rlvect_1(A,B,C)))) # label(dt_g1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 6994 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) -> k5_rlvect_1(A,k9_rlvect_1(A,k6_finseq_1(u1_struct_0(A)))) = k1_rlvect_1(A))) # label(t68_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 6995 $T # label(t12_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 6996 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k9_rlvect_1(A,k8_rlvect_1(A,B,C,D)) = k2_rlvect_1(A,k9_rlvect_1(A,k7_rlvect_1(A,B,C)),D))))))))) # label(t82_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 6997 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,k2_rlvect_1(A,k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),B)),k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),C))),k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),D))) = k9_rlvect_1(A,k8_rlvect_1(A,B,C,D)))))))))) # label(t81_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 6998 $T # label(t14_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 6999 (all A (-v3_struct_0(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k5_rlvect_1(A,C) = k5_rlvect_1(A,B) -> B = C))))))) # label(t31_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7000 (all A (v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_rlvect_1(A,B,k1_rlvect_1(A)) = B)))) # label(t26_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7001 (all A (l1_rlvect_1(A) -> (v1_rlvect_1(A) -> A = g1_rlvect_1(u1_struct_0(A),u1_rlvect_1(A),u2_struct_0(A))))) # label(abstractness_v1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7002 $T # label(t57_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7003 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_rlsub_1(C,A) -> (r1_rlvect_1(C,B) -> r1_rlvect_1(C,k5_rlvect_1(A,B))))))))) # label(t30_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7004 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v5_rlvect_1(B) & v6_rlvect_1(B) & l2_rlvect_1(B) & v7_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (m1_rlsub_1(B,A) <-> k1_realset1(u1_rlvect_1(A),u1_struct_0(B)) = u1_rlvect_1(B) & k8_relset_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A),u2_rlvect_1(A),k2_zfmisc_1(k1_numbers,u1_struct_0(B))) = u2_rlvect_1(B) & u2_struct_0(A) = u2_struct_0(B) & r1_tarski(u1_struct_0(B),u1_struct_0(A))))))) # label(d2_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7005 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> m2_rlsub_1(k1_struct_0(A,B),A,k1_rlsub_1(A)))))) # label(t88_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7006 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_rlsub_1(D,A) -> (all E (m1_subset_1(E,u1_struct_0(D)) -> (E = B -> k3_rlvect_1(A,B,C) = k3_rlvect_1(D,E,C)))))))))))) # label(t22_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7007 (all A (v3_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlsub_1(D,A) -> (all E (m1_subset_1(E,u1_struct_0(D)) -> (all F (m1_subset_1(F,u1_struct_0(D)) -> (B = E & F = C -> k6_rlvect_1(A,B,C) = k6_rlvect_1(D,E,F)))))))))))))) # label(t24_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7008 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_rlsub_1(C,A) -> (r1_rlvect_1(C,B) <-> k3_rlsub_1(A,k5_rlvect_1(A,B),C) = u1_struct_0(C)))))))) # label(t67_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7009 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlsub_1(D,A) -> (r1_rlvect_1(D,C) & r1_rlvect_1(D,B) -> r1_rlvect_1(D,k4_rlvect_1(A,B,C))))))))))) # label(t28_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7010 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_rlsub_1(B,A) -> r1_rlvect_1(A,k1_rlvect_1(B)))))) # label(t27_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7011 $T # label(t11_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7012 (all A (v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlsub_1(B,A) -> v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B))))) # label(dt_m1_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7013 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> v1_rlsub_1(k1_struct_0(A,k1_rlvect_1(A)),A))) # label(t7_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7014 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_rlsub_1(B,A) -> m1_rlsub_1(k1_rlsub_1(A),B))))) # label(t51_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7015 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (m2_rlsub_1(B,A,k2_rlsub_1(A)) -> B = u1_struct_0(A)))))) # label(t92_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7016 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_rlsub_1(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,B) -> r2_hidden(k5_rlvect_1(A,C),B))))))))) # label(t5_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7017 (all A (-v3_struct_0(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_rlsub_1(B,A) -> k1_rlsub_1(B) = k1_rlsub_1(A))))) # label(t48_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7018 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlsub_1(D,A) -> (r2_hidden(B,k3_rlsub_1(A,C,D)) <-> (exists E (m1_subset_1(E,u1_struct_0(A)) & k6_rlvect_1(A,C,E) = B & r1_rlvect_1(D,E)))))))))))) # label(t80_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7019 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_rlsub_1(B,A) -> k1_xboole_0 = B | r2_hidden(k1_rlvect_1(A),B)))))) # label(t4_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7020 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,C) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(C,C),C) & v1_funct_2(E,k2_zfmisc_1(C,C),C) -> (all F (v1_funct_1(F) & v1_funct_2(F,k2_zfmisc_1(k1_numbers,C),C) & m2_relset_1(F,k2_zfmisc_1(k1_numbers,C),C) -> (k1_rlvect_1(A) = D & F = k8_relset_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A),u2_rlvect_1(A),k2_zfmisc_1(k1_numbers,B)) & E = k1_realset1(u1_rlvect_1(A),B) & C = B -> m1_rlsub_1(g2_rlvect_1(C,D,E,F),A)))))))))))))) # label(t32_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7021 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlsub_1(D,A) -> (r2_hidden(B,k3_rlsub_1(A,k5_rlvect_1(A,C),D)) & r2_hidden(B,k3_rlsub_1(A,C,D)) -> r1_rlvect_1(D,C)))))))))) # label(t73_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7022 (all A all B (-v3_struct_0(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & m1_rlsub_1(B,A) & l2_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (exists C m2_rlsub_1(C,A,B)))) # label(existence_m2_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7023 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v2_rlvect_1(B) & m1_rlsub_1(B,A) -> (all C (m1_rlsub_1(C,A) & v2_rlvect_1(C) -> (all D (m2_rlsub_1(D,A,B) -> (all E (m2_rlsub_1(E,A,C) -> (D = E -> B = C))))))))))) # label(t87_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7024 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_rlsub_1(C,A) -> (all D (m2_rlsub_1(D,A,C) -> (all E (m2_rlsub_1(E,A,C) -> (r2_hidden(B,E) & r2_hidden(B,D) -> E = D))))))))))) # label(t98_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7025 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlsub_1(B,A) & v2_rlvect_1(B) -> (u1_struct_0(B) = k1_struct_0(A,k1_rlvect_1(A)) <-> B = k1_rlsub_1(A)))))) # label(d3_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7026 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v5_rlvect_1(A) -> (all B (v2_rlvect_1(B) & m1_rlsub_1(B,A) -> (all C (m1_rlsub_1(C,A) & v2_rlvect_1(C) -> (u1_struct_0(B) = u1_struct_0(C) -> B = C))))))) # label(t38_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7027 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlsub_1(D,A) & v2_rlvect_1(D) -> (all E (v2_rlvect_1(E) & m1_rlsub_1(E,A) -> (k3_rlsub_1(A,B,D) = k3_rlsub_1(A,C,E) -> E = D))))))))))) # label(t85_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7028 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_rlsub_1(C,A) -> (u1_struct_0(C) = k3_rlsub_1(A,B,C) <-> r2_hidden(k1_rlvect_1(A),k3_rlsub_1(A,B,C))))))))) # label(t63_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7029 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> u1_struct_0(A) = k3_rlsub_1(A,B,k2_rlsub_1(A)))))) # label(t62_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7030 $T # label(t45_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7031 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_rlsub_1(B,A) -> k1_rlvect_1(B) = k1_rlvect_1(A))))) # label(t19_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7032 $T # label(t56_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7033 (all A (v4_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlsub_1(D,A) -> (k3_rlsub_1(A,B,D) = k3_rlsub_1(A,C,D) <-> r2_hidden(B,k3_rlsub_1(A,C,D))))))))))) # label(t70_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7034 (all A all B all C all D (-v3_struct_0(B) & v4_rlvect_1(B) & l2_rlvect_1(B) & m1_rlsub_1(D,B) & m1_subset_1(C,u1_struct_0(B)) & v7_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (r2_hidden(A,a_3_1_rlsub_1(B,C,D)) <-> (exists E (m1_subset_1(E,u1_struct_0(B)) & k4_rlvect_1(B,C,E) = A & r1_rlvect_1(D,E)))))) # label(fraenkel_a_3_1_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7035 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_rlsub_1(E,A) -> (r2_hidden(B,k3_rlsub_1(A,C,E)) & r2_hidden(B,k3_rlsub_1(A,D,E)) -> k3_rlsub_1(A,D,E) = k3_rlsub_1(A,C,E)))))))))))) # label(t72_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7036 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlsub_1(D,A) -> (r1_rlvect_1(D,C) & r1_rlvect_1(D,B) -> r1_rlvect_1(D,k6_rlvect_1(A,B,C))))))))))) # label(t31_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7037 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlsub_1(D,A) -> (r1_rlvect_1(D,B) <-> r2_hidden(k4_rlvect_1(A,B,C),k3_rlsub_1(A,C,D))))))))))) # label(t77_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7038 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlsub_1(D,A) -> (r2_hidden(k6_rlvect_1(A,B,C),k3_rlsub_1(A,B,D)) <-> r1_rlvect_1(D,C)))))))))) # label(t78_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7039 (all A (v3_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v2_rlvect_1(A) & -v3_struct_0(A) -> (all B (v2_rlvect_1(B) & m1_rlsub_1(B,A) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_rlvect_1(B,C) <-> r1_rlvect_1(A,C)))) -> B = A))))) # label(t41_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7040 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_rlsub_1(D,A) -> (r1_rlvect_1(D,B) -> u1_struct_0(D) = k3_rlsub_1(A,k3_rlvect_1(A,B,C),D)))))))))) # label(t65_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7041 (all A (v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_rlsub_1(C,A) -> (all D (m2_rlsub_1(D,A,C) -> (r2_hidden(B,D) <-> k3_rlsub_1(A,B,C) = D))))))))) # label(t94_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7042 (all A (v3_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlsub_1(B,A) -> m1_rlsub_1(k1_rlsub_1(B),A))))) # label(t50_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7043 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(v1_rlsub_1(B,A) & (all C (m1_rlsub_1(C,A) & v2_rlvect_1(C) -> u1_struct_0(C) != B)) & k1_xboole_0 != B))))) # label(t43_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7044 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlsub_1(B,A) -> (all C (m2_rlsub_1(C,A,B) -> (C = u1_struct_0(B) <-> r2_hidden(k1_rlvect_1(A),C)))))))) # label(t93_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7045 $T # label(t47_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7046 (all A (v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,k1_numbers) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,B) -> r2_hidden(k3_rlvect_1(A,D,C),B)))))) & (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,B) & r2_hidden(C,B) -> r2_hidden(k4_rlvect_1(A,C,D),B)))))) <-> v1_rlsub_1(B,A)))))) # label(d1_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7047 (all A (v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_rlsub_1(D,A) -> (r1_rlvect_1(D,B) -> r2_hidden(k3_rlvect_1(A,B,C),k3_rlsub_1(A,B,D))))))))))) # label(t75_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7048 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_rlsub_1(B,A) -> (all C (m1_rlsub_1(C,A) -> k1_rlvect_1(C) = k1_rlvect_1(B))))))) # label(t20_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7049 (all A (-v3_struct_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> m1_rlsub_1(A,k2_rlsub_1(A)))) # label(t54_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7050 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlsub_1(B,A) -> (all C (m1_rlsub_1(C,A) -> k1_rlsub_1(C) = k1_rlsub_1(B))))))) # label(t49_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7051 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A)) = k2_rlsub_1(A))) # label(d4_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7052 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_rlsub_1(B,A) -> r1_rlvect_1(B,k1_rlvect_1(A)))))) # label(t25_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7053 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlsub_1(D,A) -> (r1_rlvect_1(D,B) <-> k3_rlsub_1(A,k6_rlvect_1(A,C,B),D) = k3_rlsub_1(A,C,D)))))))))) # label(t69_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7054 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> v2_rlvect_1(k1_rlsub_1(A)) & m1_rlsub_1(k1_rlsub_1(A),A))) # label(dt_k1_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7055 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l2_rlvect_1(B) & v7_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & v7_rlvect_1(C) & l2_rlvect_1(C) & v6_rlvect_1(C) & v5_rlvect_1(C) -> (m1_rlsub_1(A,B) & m1_rlsub_1(B,C) -> m1_rlsub_1(A,C)))))))) # label(t35_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.39 7056 (all A (v3_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_rlsub_1(D,A) -> (r2_hidden(k3_rlvect_1(A,B,C),k3_rlsub_1(A,B,D)) -> np__1 = C | r1_rlvect_1(D,B)))))))))) # label(t74_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7057 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlsub_1(B,A) -> (all C (m2_rlsub_1(C,A,B) -> (v1_rlsub_1(C,A) <-> C = u1_struct_0(B)))))))) # label(t86_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7058 (all A all B all C all D (v5_rlvect_1(B) & v7_rlvect_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & l2_rlvect_1(B) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> ((exists E exists F (A = k4_rlvect_1(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) & m1_subset_1(F,u1_struct_0(B)) & m1_subset_1(E,u1_struct_0(B)))) <-> r2_hidden(A,a_3_0_rlsub_1(B,C,D))))) # label(fraenkel_a_3_0_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7059 $T # label(t55_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7060 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v2_rlvect_1(B) & m1_rlsub_1(B,A) -> (all C (m1_rlsub_1(C,A) & v2_rlvect_1(C) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_rlvect_1(C,D) <-> r1_rlvect_1(B,D)))) -> C = B))))))) # label(t39_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7061 $T # label(t46_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7062 $T # label(t3_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7063 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_rlsub_1(B,A) -> (all C (m1_rlsub_1(C,A) -> m1_rlsub_1(k1_rlsub_1(B),C))))))) # label(t52_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7064 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_rlsub_1(D,A) -> (k3_rlsub_1(A,k3_rlvect_1(A,B,C),D) = u1_struct_0(D) -> r1_rlvect_1(D,B) | np__0 = C))))))))) # label(t66_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7065 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlsub_1(D,A) -> (all E (m2_rlsub_1(E,A,D) -> -(r2_hidden(B,E) & r2_hidden(C,E) & (all F (m1_subset_1(F,u1_struct_0(A)) -> -(k6_rlvect_1(A,B,F) = C & r1_rlvect_1(D,F))))))))))))))) # label(t96_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7066 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_rlsub_1(C,A) -> a_3_1_rlsub_1(A,B,C) = k3_rlsub_1(A,B,C))))))) # label(d5_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7067 $T # label(t13_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7068 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_rlsub_1(C,A) -> (r1_rlvect_1(C,B) <-> k3_rlsub_1(A,B,C) = u1_struct_0(C)))))))) # label(t64_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7069 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> v2_rlvect_1(k2_rlsub_1(A)) & m1_rlsub_1(k2_rlsub_1(A),A))) # label(dt_k2_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7070 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(A) = B -> v1_rlsub_1(B,A)))))) # label(t8_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7071 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k3_rlsub_1(A,B,k1_rlsub_1(A)) = k1_struct_0(A,B))))) # label(t61_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7072 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_rlsub_1(D,A) -> (r1_rlvect_1(D,B) -> r1_rlvect_1(D,k3_rlvect_1(A,B,C))))))))))) # label(t29_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7073 (all A (v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlsub_1(D,A) -> (r2_hidden(B,k3_rlsub_1(A,C,D)) <-> (exists E (B = k4_rlvect_1(A,C,E) & r1_rlvect_1(D,E) & m1_subset_1(E,u1_struct_0(A))))))))))))) # label(t79_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7074 (all A all B (-v3_struct_0(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & m1_rlsub_1(B,A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all C (m2_rlsub_1(C,A,B) -> m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))))))) # label(dt_m2_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7075 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B all C (m1_rlsub_1(C,A) -> (r1_rlvect_1(C,B) -> r1_rlvect_1(A,B)))))) # label(t17_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7076 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (v1_rlsub_1(B,A) & a_3_0_rlsub_1(A,B,C) = D & v1_rlsub_1(C,A) -> v1_rlsub_1(D,A)))))))))) # label(t9_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7077 $T # label(t1_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7078 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlsub_1(B,A) -> (all C (m1_rlsub_1(C,A) -> r1_rlvect_1(C,k1_rlvect_1(B)))))))) # label(t26_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7079 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlsub_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((exists D (m1_subset_1(D,u1_struct_0(A)) & k3_rlsub_1(A,D,B) = C)) <-> m2_rlsub_1(C,A,B)))))))) # label(d6_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7080 $T # label(t2_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7081 $T # label(t53_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7082 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlsub_1(D,A) -> (all E (m1_subset_1(E,u1_struct_0(D)) -> (all F (m1_subset_1(F,u1_struct_0(D)) -> (E = B & C = F -> k4_rlvect_1(D,E,F) = k4_rlvect_1(A,B,C)))))))))))))) # label(t21_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7083 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_rlsub_1(B,A) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> m1_subset_1(C,u1_struct_0(A)))))))) # label(t18_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7084 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_rlsub_1(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,B) & r2_hidden(C,B) -> r2_hidden(k6_rlvect_1(A,C,D),B))))))))))) # label(t6_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7085 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_rlsub_1(C,A) -> (u1_struct_0(C) = B -> v1_rlsub_1(B,A)))))))) # label(t42_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7086 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlsub_1(D,A) -> ((exists E (r2_hidden(B,E) & r2_hidden(C,E) & m2_rlsub_1(E,A,D))) <-> r1_rlvect_1(D,k6_rlvect_1(A,B,C))))))))))) # label(t97_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7087 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_rlsub_1(C,A) -> (r2_hidden(k1_rlvect_1(A),k3_rlsub_1(A,B,C)) <-> r1_rlvect_1(C,B)))))))) # label(t58_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7088 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlsub_1(D,A) -> (r1_rlvect_1(D,B) <-> k3_rlsub_1(A,k4_rlvect_1(A,C,B),D) = k3_rlsub_1(A,C,D)))))))))) # label(t68_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7089 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & -v3_struct_0(A) -> m1_rlsub_1(A,A))) # label(t33_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7090 (all A (l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlsub_1(D,A) -> -(k3_rlsub_1(A,B,D) = k3_rlsub_1(A,C,D) & (all E (m1_subset_1(E,u1_struct_0(A)) -> -(r1_rlvect_1(D,E) & k4_rlvect_1(A,B,E) = C)))))))))))) # label(t82_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7091 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> m2_rlsub_1(u1_struct_0(A),A,k2_rlsub_1(A)))) # label(t91_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7092 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_rlsub_1(C,A) -> r2_hidden(B,k3_rlsub_1(A,B,C)))))))) # label(t59_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7093 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & v2_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlsub_1(B,A) & v2_rlvect_1(B) -> (u1_struct_0(A) = u1_struct_0(B) -> B = A))))) # label(t40_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7094 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlsub_1(D,A) -> (all E (m2_rlsub_1(E,A,D) -> -((all F (m1_subset_1(F,u1_struct_0(A)) -> -(r1_rlvect_1(D,F) & C = k4_rlvect_1(A,B,F)))) & r2_hidden(C,E) & r2_hidden(B,E)))))))))))) # label(t95_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7095 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlsub_1(D,A) -> (r1_rlvect_1(D,k6_rlvect_1(A,B,C)) <-> (exists E (r2_hidden(C,k3_rlsub_1(A,E,D)) & r2_hidden(B,k3_rlsub_1(A,E,D)) & m1_subset_1(E,u1_struct_0(A))))))))))))) # label(t81_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7096 (all A (v3_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_rlsub_1(C,A) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (D = B -> k5_rlvect_1(C,D) = k5_rlvect_1(A,B)))))))))) # label(t23_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7097 (all A (v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlsub_1(D,A) -> -(k3_rlsub_1(A,C,D) = k3_rlsub_1(A,B,D) & (all E (m1_subset_1(E,u1_struct_0(A)) -> -(r1_rlvect_1(D,E) & k6_rlvect_1(A,B,E) = C)))))))))))) # label(t83_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7098 $T # label(t12_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7099 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v2_rlvect_1(A) -> (all B (v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l2_rlvect_1(B) & v7_rlvect_1(B) & -v3_struct_0(B) -> (m1_rlsub_1(B,A) & m1_rlsub_1(A,B) -> B = A))))) # label(t34_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7100 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v1_rlsub_1(B,A) & v1_rlsub_1(C,A) -> v1_rlsub_1(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t10_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7101 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_rlsub_1(C,A) -> (k3_rlsub_1(A,B,C) = k3_rlsub_1(A,k5_rlvect_1(A,B),C) <-> r1_rlvect_1(C,B)))))))) # label(t71_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7102 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B all C (m1_rlsub_1(C,A) -> (all D (m1_rlsub_1(D,A) -> (r1_rlvect_1(C,B) & m1_rlsub_1(C,D) -> r1_rlvect_1(D,B)))))))) # label(t16_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7103 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlsub_1(B,A) -> (all C (m1_rlsub_1(C,A) -> (r1_tarski(u1_struct_0(B),u1_struct_0(C)) -> m1_rlsub_1(B,C)))))))) # label(t36_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7104 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -((all C (m1_subset_1(C,u1_struct_0(A)) -> B != k1_struct_0(A,C))) & m2_rlsub_1(B,A,k1_rlsub_1(A))))))) # label(t89_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7105 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_rlsub_1(B,A) -> (all C (m1_rlsub_1(C,A) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_rlvect_1(B,D) -> r1_rlvect_1(C,D)))) -> m1_rlsub_1(B,C)))))))) # label(t37_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7106 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> (exists B m1_rlsub_1(B,A)))) # label(existence_m1_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7107 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_rlsub_1(B,A) -> m2_rlsub_1(u1_struct_0(B),A,B))))) # label(t90_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7108 (all A (v4_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (exists B (m1_rlsub_1(B,A) & -v3_struct_0(B) & v5_rlvect_1(B) & v7_rlvect_1(B) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & v2_rlvect_1(B))))) # label(rc1_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7109 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v2_rlvect_1(C) & m1_rlsub_1(C,A) -> (all D (m1_rlsub_1(D,A) & v2_rlvect_1(D) -> (k3_rlsub_1(A,B,D) = k3_rlsub_1(A,B,C) <-> C = D))))))))) # label(t84_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7110 $T # label(t15_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7111 $T # label(t14_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7112 (all A all B all C (-v3_struct_0(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & m1_rlsub_1(C,A) & m1_subset_1(B,u1_struct_0(A)) & v7_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> m1_subset_1(k3_rlsub_1(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k3_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7113 $T # label(t44_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7114 (all A (v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_rlsub_1(C,A) -> (r1_rlvect_1(C,B) <-> r2_hidden(k5_rlvect_1(A,B),k3_rlsub_1(A,B,C))))))))) # label(t76_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7115 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlsub_1(B,A) -> u1_struct_0(B) = k3_rlsub_1(A,k1_rlvect_1(A),B))))) # label(t60_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7116 $T # label(t76_group_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7117 $T # label(t38_group_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7118 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k1_group_1(A,D,k3_group_1(A,C)) = B <-> D = k1_group_1(A,B,C)))))))))) # label(t22_group_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7119 (all A (l1_group_1(A) -> l1_struct_0(A))) # label(dt_l1_group_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7120 (all A (v1_int_1(A) -> (all B (v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k3_group_1(B,k6_group_1(B,A,C)) = k6_group_1(B,k4_xcmplx_0(A),C))))))) # label(t70_group_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7121 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_group_1(A,C,B) = B | B = k1_group_1(A,B,C) -> k2_group_1(A) = C))))))) # label(t15_group_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7122 (all A (l1_group_1(A) & -v3_struct_0(A) -> ((exists B (m1_subset_1(B,u1_struct_0(A)) & (all C (m1_subset_1(C,u1_struct_0(A)) -> C = k1_group_1(A,C,B) & C = k1_group_1(A,B,C))))) <-> v2_group_1(A)))) # label(d2_group_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7123 (all A (l1_group_1(A) & -v3_struct_0(A) -> m2_relset_1(k5_group_1(A),k2_zfmisc_1(u1_struct_0(A),k5_numbers),u1_struct_0(A)) & v1_funct_2(k5_group_1(A),k2_zfmisc_1(u1_struct_0(A),k5_numbers),u1_struct_0(A)) & v1_funct_1(k5_group_1(A)))) # label(dt_k5_group_1) # label(axiom) # label(non_clause). [assumption]. 126.07/125.40 7124 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (-v3_struct_0(C) & v4_group_1(C) & l1_group_1(C) & v3_group_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k6_group_1(C,B,k6_group_1(C,A,D)) = k6_group_1(C,k2_nat_1(A,B),D))))))))) # label(t50_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7125 (all A all B (v4_group_1(A) & m1_subset_1(B,u1_struct_0(A)) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> m2_subset_1(k7_group_1(A,B),k1_numbers,k5_numbers))) # label(dt_k7_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7126 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_group_1(A,k3_group_1(A,B),k3_group_1(A,C)) = k1_group_1(A,k3_group_1(A,C),k3_group_1(A,B)) <-> k1_group_1(A,C,B) = k1_group_1(A,B,C)))))))) # label(t27_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7127 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_group_1(A,np__2,B) = k1_group_1(A,B,B))))) # label(t45_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7128 $T # label(t78_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7129 (all A all B all C (m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_group_1(A) & v7_group_1(A) & -v3_struct_0(A) -> k10_group_1(A,B,C) = k10_group_1(A,C,B))) # label(commutativity_k10_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7130 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> k1_card_1(u1_struct_0(A)) = k8_group_1(A))) # label(d13_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7131 (all A all B all C (m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_group_1(A) & v7_group_1(A) & -v3_struct_0(A) -> m1_subset_1(k10_group_1(A,B,C),u1_struct_0(A)))) # label(dt_k10_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7132 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (v6_group_1(A) -> r1_xreal_0(np__1,k9_group_1(A))))) # label(t90_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7133 (all A (v1_int_1(A) -> (all B (v3_group_1(B) & l1_group_1(B) & v4_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (k1_group_1(B,D,C) = k1_group_1(B,C,D) -> k6_group_1(B,A,k1_group_1(B,C,D)) = k1_group_1(B,k6_group_1(B,A,C),k6_group_1(B,A,D))))))))))) # label(t73_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7134 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k2_group_1(A) = k6_group_1(A,np__2,B) <-> k3_group_1(A,B) = B))))) # label(t47_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7135 $T # label(t40_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7136 $T # label(t3_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7137 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v3_struct_0(B) & l1_group_1(B) & v4_group_1(B) & v3_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k6_group_1(B,k7_binop_2(A),C) = k3_group_1(B,k6_group_1(B,A,C)))))))) # label(t71_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7138 (all A (-v3_struct_0(A) & l1_group_1(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),k5_numbers),u1_struct_0(A)) & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),k5_numbers),u1_struct_0(A)) & v1_funct_1(B) -> (B = k5_group_1(A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> k1_group_1(A,k2_binop_1(u1_struct_0(A),k5_numbers,u1_struct_0(A),B,C,D),C) = k2_binop_1(u1_struct_0(A),k5_numbers,u1_struct_0(A),B,C,k1_nat_1(D,np__1)))) & k2_group_1(A) = k2_binop_1(u1_struct_0(A),k5_numbers,u1_struct_0(A),B,C,np__0)))))))) # label(d8_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7139 $T # label(t41_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7140 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> m2_subset_1(k9_group_1(A),k1_numbers,k5_numbers))) # label(dt_k9_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7141 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,k3_group_1(A,C),k3_group_1(A,B)) = k3_group_1(A,k1_group_1(A,B,C)))))))) # label(t25_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7142 (all A (v1_int_1(A) -> (all B (v3_group_1(B) & l1_group_1(B) & v4_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k1_group_1(B,k6_group_1(B,A,C),C) = k6_group_1(B,k2_xcmplx_0(A,np__1),C) & k6_group_1(B,k2_xcmplx_0(A,np__1),C) = k1_group_1(B,C,k6_group_1(B,A,C)))))))) # label(t66_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7143 (all A (l1_group_1(A) -> (-v3_struct_0(A) & v3_group_1(A) -> v2_group_1(A) & -v3_struct_0(A)))) # label(cc1_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7144 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (np__1 = k7_group_1(A,B) -> k2_group_1(A) = B))))) # label(t85_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7145 $T # label(t89_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7146 (all A (v1_int_1(A) -> (all B (l1_group_1(B) & v4_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (np__0 = A -> k2_group_1(B) = k6_group_1(B,A,C)))))))) # label(t59_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7147 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_group_1(A,k7_group_1(A,B),B) = k2_group_1(A))))) # label(t82_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7148 (all A all B (-v3_struct_0(A) & l1_group_1(A) & m1_subset_1(B,u1_struct_0(A)) & v4_group_1(A) & v3_group_1(A) -> m1_subset_1(k3_group_1(A,B),u1_struct_0(A)))) # label(dt_k3_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7149 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (k1_group_1(A,B,D) = C & m1_subset_1(D,u1_struct_0(A)))))))))) # label(t23_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7150 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k2_group_1(A) = k1_group_1(A,B,C) & k2_group_1(A) = k1_group_1(A,C,B) -> C = k3_group_1(A,B)))))))) # label(t12_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7151 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k1_group_1(C,k6_group_1(C,A,D),k6_group_1(C,B,D)) = k6_group_1(C,k2_xcmplx_0(A,B),D))))))))) # label(t63_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7152 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k6_group_1(C,k3_xcmplx_0(A,B),D) = k6_group_1(C,B,k6_group_1(C,A,D)))))))))) # label(t67_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7153 $T # label(t57_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7154 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v7_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k3_group_1(A,k10_group_1(A,B,C)) = k10_group_1(A,k3_group_1(A,B),k3_group_1(A,C)))))))) # label(t94_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7155 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (k1_group_1(B,D,C) = k1_group_1(B,C,D) -> k1_group_1(B,k6_group_1(B,A,D),C) = k1_group_1(B,C,k6_group_1(B,A,D))))))))))) # label(t52_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7156 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> -v5_group_1(k2_group_1(A),A))) # label(t79_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7157 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v3_struct_0(B) & v4_group_1(B) & l1_group_1(B) & v3_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k1_group_1(B,C,k6_group_1(B,A,C)) = k6_group_1(B,k1_nat_1(A,np__1),C) & k1_group_1(B,k6_group_1(B,A,C),C) = k6_group_1(B,k1_nat_1(A,np__1),C))))))) # label(t49_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7158 $T # label(t93_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7159 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (v3_group_1(C) & l1_group_1(C) & v4_group_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (all E (m1_subset_1(E,u1_struct_0(C)) -> (k1_group_1(C,E,D) = k1_group_1(C,D,E) -> k1_group_1(C,k6_group_1(C,A,D),k6_group_1(C,B,E)) = k1_group_1(C,k6_group_1(C,B,E),k6_group_1(C,A,D))))))))))))) # label(t53_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7160 (all A (-v3_struct_0(A) & l1_group_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_group_1(A,k1_group_1(A,B,C),D) = k1_group_1(A,B,k1_group_1(A,C,D)))))))) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> -(all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,C,B) = C & C = k1_group_1(A,B,C) & (exists D (m1_subset_1(D,u1_struct_0(A)) & k1_group_1(A,D,C) = B & B = k1_group_1(A,C,D))))))) | v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A)))) # label(t5_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7161 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_group_1(A,B,C) = k2_group_1(A) | k1_group_1(A,C,B) = k2_group_1(A) -> k3_group_1(A,B) = C & k3_group_1(A,C) = B))))))) # label(t20_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7162 $T # label(t11_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7163 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (v1_int_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_xreal_0(np__0,B) -> k6_group_1(A,B,C) = k2_binop_1(u1_struct_0(A),k5_numbers,u1_struct_0(A),k5_group_1(A),C,k1_int_2(B))) & (-r1_xreal_0(np__0,B) -> k6_group_1(A,B,C) = k3_group_1(A,k2_binop_1(u1_struct_0(A),k5_numbers,u1_struct_0(A),k5_group_1(A),C,k1_int_2(B)))))))))) # label(d9_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7164 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (v6_group_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (B = k9_group_1(A) <-> (exists C (u1_struct_0(A) = C & B = k4_card_1(C) & v1_finset_1(C))))))))) # label(d15_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7165 (all A all B all C (-v3_struct_0(A) & v7_group_1(A) & l1_group_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> k10_group_1(A,B,C) = k1_group_1(A,B,C))) # label(redefinition_k10_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7166 (exists A (l1_group_1(A) & v1_group_1(A))) # label(rc1_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7167 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_group_1(A,k1_group_1(A,B,B),B) = k6_group_1(A,np__3,B))))) # label(t46_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7168 $T # label(t9_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7169 (all A (v1_int_1(A) -> (all B (-v3_struct_0(B) & l1_group_1(B) & v4_group_1(B) & v3_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (r1_xreal_0(np__0,A) -> k6_group_1(B,A,C) = k6_group_1(B,k1_int_2(A),C)))))))) # label(t55_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7170 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k3_group_1(A,k3_group_1(A,B)))))) # label(t19_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7171 (all A all B all C (l1_group_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & -v3_struct_0(A) -> m1_subset_1(k1_group_1(A,B,C),u1_struct_0(A)))) # label(dt_k1_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7172 (all A (l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> C = k1_group_1(A,B,C) & C = k1_group_1(A,C,B))) -> k2_group_1(A) = B))))) # label(t10_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7173 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k6_group_1(A,B,C) = k2_binop_1(u1_struct_0(A),k5_numbers,u1_struct_0(A),k5_group_1(A),C,B))))))) # label(d10_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7174 (all A (v1_int_1(A) -> (all B (-v3_struct_0(B) & l1_group_1(B) & v4_group_1(B) & v3_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (r1_xreal_0(A,np__0) -> k3_group_1(B,k6_group_1(B,k1_int_2(A),C)) = k6_group_1(B,A,C)))))))) # label(t60_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7175 (all A (-v3_struct_0(A) & l1_group_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_group_1(A,B,k1_group_1(A,C,D)) = k1_group_1(A,k1_group_1(A,B,C),D))))))) <-> v4_group_1(A)))) # label(d4_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7176 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k2_group_1(A) = k3_group_1(A,B) -> B = k2_group_1(A)))))) # label(t18_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7177 (all A (-v3_struct_0(A) & l1_group_1(A) & v2_group_1(A) -> r3_binop_1(u1_struct_0(A),k2_group_1(A),u1_group_1(A)))) # label(t32_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7178 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_group_1(A,k3_group_1(A,B),k3_group_1(A,C)) = k3_group_1(A,k1_group_1(A,B,C)) <-> k1_group_1(A,B,C) = k1_group_1(A,C,B)))))))) # label(t26_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7179 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (-v3_struct_0(C) & v4_group_1(C) & l1_group_1(C) & v3_group_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k6_group_1(C,k2_xcmplx_0(A,B),D) = k1_group_1(C,k6_group_1(C,A,D),k6_group_1(C,B,D)))))))))) # label(t64_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7180 (all A (v1_int_1(A) -> (all B (v3_group_1(B) & l1_group_1(B) & v7_group_1(B) & v4_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k10_group_1(B,k6_group_1(B,A,C),k6_group_1(B,A,D)) = k6_group_1(B,A,k10_group_1(B,C,D)))))))))) # label(t96_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7181 (all A (l1_group_1(A) & -v3_struct_0(A) -> (v7_group_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,C,B) = k1_group_1(A,B,C)))))))) # label(d16_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7182 (all A all B (-v1_xboole_0(A) & v1_funct_1(B) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> -v3_struct_0(g1_group_1(A,B)) & v1_group_1(g1_group_1(A,B)))) # label(fc1_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7183 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C) = k3_group_1(A,C))) <-> k4_group_1(A) = B))))) # label(d7_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7184 (all A (v2_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> k2_group_1(A) = k3_binop_1(u1_struct_0(A),u1_group_1(A)))) # label(t33_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7185 (all A (-v3_struct_0(A) & l1_group_1(A) -> ((exists B ((all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (k1_group_1(A,C,D) = B & k1_group_1(A,D,C) = B & m1_subset_1(D,u1_struct_0(A)))) & C = k1_group_1(A,B,C) & k1_group_1(A,C,B) = C)) & m1_subset_1(B,u1_struct_0(A)))) <-> v3_group_1(A)))) # label(d3_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7186 (exists A (v1_group_1(A) & v2_group_1(A) & v4_group_1(A) & v7_group_1(A) & v3_group_1(A) & -v3_struct_0(A) & l1_group_1(A))) # label(rc4_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7187 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> v1_funct_2(k4_group_1(A),u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(k4_group_1(A),u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(k4_group_1(A)))) # label(dt_k4_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7188 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> v1_card_1(k8_group_1(A)))) # label(dt_k8_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7189 (exists A (v1_group_1(A) & -v3_struct_0(A) & l1_group_1(A))) # label(rc2_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7190 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k3_group_1(A,C) = k3_group_1(A,B) -> C = B))))))) # label(t17_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7191 $T # label(t30_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7192 $T # label(t39_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7193 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> r1_finseqop(u1_struct_0(A),k4_group_1(A),u1_group_1(A)))) # label(t35_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7194 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (C = k1_group_1(A,k3_group_1(A,B),D) <-> k1_group_1(A,B,C) = D))))))))) # label(t21_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7195 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v3_struct_0(B) & l1_group_1(B) & v4_group_1(B) & v3_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (k1_group_1(B,D,C) = k1_group_1(B,C,D) -> k1_group_1(B,k6_group_1(B,A,C),k6_group_1(B,A,D)) = k6_group_1(B,A,k1_group_1(B,C,D))))))))))) # label(t54_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7196 (all A (-v3_struct_0(A) & v2_group_1(A) & l1_group_1(A) -> v1_setwiseo(u1_group_1(A),u1_struct_0(A)))) # label(t34_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7197 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (-v3_struct_0(C) & l1_group_1(C) & v4_group_1(C) & v3_group_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k6_group_1(C,k2_xcmplx_0(B,A),D) = k1_group_1(C,k6_group_1(C,B,D),k6_group_1(C,A,D)))))))))) # label(t65_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7198 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & v7_group_1(A) & l1_group_1(A) -> v3_rlvect_1(g1_rlvect_1(u1_struct_0(A),u1_group_1(A),k2_group_1(A))) & v4_rlvect_1(g1_rlvect_1(u1_struct_0(A),u1_group_1(A),k2_group_1(A))) & v5_rlvect_1(g1_rlvect_1(u1_struct_0(A),u1_group_1(A),k2_group_1(A))) & v6_rlvect_1(g1_rlvect_1(u1_struct_0(A),u1_group_1(A),k2_group_1(A))))) # label(t97_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7199 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (-v3_struct_0(C) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (all E (m1_subset_1(E,u1_struct_0(C)) -> (k1_group_1(C,E,D) = k1_group_1(C,D,E) -> k1_group_1(C,k6_group_1(C,A,D),k6_group_1(C,B,E)) = k1_group_1(C,k6_group_1(C,B,E),k6_group_1(C,A,D))))))))))))) # label(t74_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7200 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> v1_finseqop(u1_group_1(A),u1_struct_0(A)))) # label(t36_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7201 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> k7_group_1(A,k2_group_1(A)) = np__1)) # label(t84_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7202 $T # label(t91_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7203 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (-v3_struct_0(C) & v3_group_1(C) & l1_group_1(C) & v4_group_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k1_group_1(C,k6_group_1(C,A,D),k6_group_1(C,B,D)) = k6_group_1(C,k1_nat_1(A,B),D))))))))) # label(t48_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7204 $T # label(t87_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7205 $T # label(t4_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7206 (exists A l1_group_1(A)) # label(existence_l1_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7207 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> k6_finseqop(u1_struct_0(A),u1_group_1(A)) = k4_group_1(A))) # label(t37_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7208 $T # label(t1_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7209 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v3_group_1(B) & l1_group_1(B) & v4_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (k2_group_1(B) = k6_group_1(B,A,C) -> r1_nat_1(k7_group_1(B,C),A)))))))) # label(t86_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7210 $T # label(t80_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7211 (all A (v1_int_1(A) -> (all B (-v3_struct_0(B) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (-r1_xreal_0(np__0,A) -> k6_group_1(B,A,C) = k3_group_1(B,k6_group_1(B,k1_int_2(A),C))))))))) # label(t56_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7212 (all A (v1_int_1(A) -> (all B (v4_group_1(B) & l1_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (k1_group_1(B,C,D) = k1_group_1(B,D,C) -> k1_group_1(B,C,k6_group_1(B,A,D)) = k1_group_1(B,k6_group_1(B,A,D),C)))))))))) # label(t77_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7213 (all A (l1_group_1(A) -> m2_relset_1(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_2(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_1(u1_group_1(A)))) # label(dt_u1_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7214 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v5_group_1(B,A) <-> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (k2_group_1(A) = k6_group_1(A,C,B) -> np__0 = C)))))))) # label(d11_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7215 $T # label(t8_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7216 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> k2_group_1(A) = k3_group_1(A,k2_group_1(A)))) # label(t16_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7217 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v3_struct_0(B) & v3_group_1(B) & l1_group_1(B) & v4_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k3_group_1(B,k6_group_1(B,A,C)) = k6_group_1(B,A,k3_group_1(B,C)))))))) # label(t51_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.40 7218 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v3_struct_0(B) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) -> k6_group_1(B,A,k2_group_1(B)) = k2_group_1(B))))) # label(t42_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7219 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_group_1(A,B,C) = k1_group_1(A,C,B) <-> k1_group_1(A,B,k3_group_1(A,C)) = k1_group_1(A,k3_group_1(A,C),B)))))))) # label(t28_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7220 $T # label(t29_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7221 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (-v3_struct_0(C) & v3_group_1(C) & l1_group_1(C) & v4_group_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k6_group_1(C,k3_xcmplx_0(A,B),D) = k6_group_1(C,B,k6_group_1(C,A,D)))))))))) # label(t68_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7222 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) -> v2_binop_1(u1_group_1(A),u1_struct_0(A)))) # label(t31_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7223 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (-v3_struct_0(C) & l1_group_1(C) & v4_group_1(C) & v3_group_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k6_group_1(C,A,k6_group_1(C,B,D)) = k6_group_1(C,k3_xcmplx_0(B,A),D))))))))) # label(t69_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7224 $T # label(t83_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7225 $T # label(t81_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7226 (all A all B all C (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v1_int_1(B) & m1_subset_1(C,u1_struct_0(A)) & v4_group_1(A) -> m1_subset_1(k6_group_1(A,B,C),u1_struct_0(A)))) # label(dt_k6_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7227 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_group_1(A,B,C) = k2_group_1(A) & k1_group_1(A,C,B) = k2_group_1(A) <-> C = k3_group_1(A,B)))))))) # label(d6_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7228 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (m1_subset_1(D,u1_struct_0(A)) & k1_group_1(A,D,B) = C)))))))) # label(t24_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7229 (all A (l1_group_1(A) -> (v1_group_1(A) -> A = g1_group_1(u1_struct_0(A),u1_group_1(A))))) # label(abstractness_v1_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7230 $T # label(t13_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7231 $T # label(t88_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7232 $T # label(t2_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7233 (all A (l1_group_1(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_group_1(A,B,k1_group_1(A,C,D)) = k1_group_1(A,k1_group_1(A,B,C),D))))))) & (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (k1_group_1(A,B,D) = C & m1_subset_1(D,u1_struct_0(A)))) & (exists D (C = k1_group_1(A,D,B) & m1_subset_1(D,u1_struct_0(A)))))))) -> v4_group_1(A) & v3_group_1(A)))) # label(t6_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7234 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_group_1(A,np__1,B) = B)))) # label(t44_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7235 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k3_group_1(A,B) = k6_group_1(A,k7_binop_2(np__1),B))))) # label(t62_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7236 (all A (l1_struct_0(A) -> (v1_finset_1(u1_struct_0(A)) <-> v6_group_1(A)))) # label(d14_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7237 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k2_group_1(A) = k6_group_1(A,np__0,B))))) # label(t43_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7238 (all A (l1_group_1(A) & -v3_struct_0(A) -> (v2_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k2_group_1(A) = B <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,B,C) = C & k1_group_1(A,C,B) = C)))))))) # label(d5_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7239 (all A (v1_int_1(A) -> (all B (v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k3_group_1(B,k6_group_1(B,A,C)) = k6_group_1(B,A,k3_group_1(B,C)))))))) # label(t72_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7240 $T # label(t58_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7241 (all A all B all C (-v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_subset_1(C,A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) -> -v3_struct_0(g1_rlvect_1(A,B,C)) & v1_rlvect_1(g1_rlvect_1(A,B,C)))) # label(fc2_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7242 (exists A (l1_group_1(A) & -v3_struct_0(A) & v1_group_1(A) & v4_group_1(A) & v3_group_1(A) & v2_group_1(A))) # label(rc3_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7243 (all A all B (v1_funct_1(B) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C all D (g1_group_1(C,D) = g1_group_1(A,B) -> D = B & A = C)))) # label(free_g1_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7244 (all A (l1_group_1(A) & -v3_struct_0(A) -> m1_subset_1(k2_group_1(A),u1_struct_0(A)))) # label(dt_k2_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7245 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v3_group_1(B) & l1_group_1(B) & v7_group_1(B) & v4_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k10_group_1(B,k6_group_1(B,A,C),k6_group_1(B,A,D)) = k6_group_1(B,A,k10_group_1(B,C,D)))))))))) # label(t95_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7246 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (v5_group_1(B,A) -> (k7_group_1(A,B) = C <-> C = np__0)) & (-v5_group_1(B,A) -> (C = k7_group_1(A,B) <-> np__0 != C & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (k6_group_1(A,D,B) = k2_group_1(A) -> D = np__0 | r1_xreal_0(C,D)))) & k6_group_1(A,C,B) = k2_group_1(A))))))))) # label(d12_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7247 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (v3_group_1(C) & l1_group_1(C) & v4_group_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (all E (m1_subset_1(E,u1_struct_0(C)) -> (k1_group_1(C,D,E) = k1_group_1(C,E,D) -> k1_group_1(C,k6_group_1(C,A,D),k6_group_1(C,B,E)) = k1_group_1(C,k6_group_1(C,B,E),k6_group_1(C,A,D))))))))))))) # label(t75_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7248 (all A all B (m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> l1_group_1(g1_group_1(A,B)) & v1_group_1(g1_group_1(A,B)))) # label(dt_g1_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7249 (all A (l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_group_1(A),B,C) = k1_group_1(A,B,C))))))) # label(d1_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7250 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k1_group_1(A,B,D) = k1_group_1(A,B,C) | k1_group_1(A,C,B) = k1_group_1(A,D,B) -> D = C))))))))) # label(t14_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7251 (all A (v1_int_1(A) -> (all B (l1_group_1(B) & v4_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> k6_group_1(B,A,k2_group_1(B)) = k2_group_1(B))))) # label(t61_group_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7252 (exists A (-v3_struct_0(A) & v3_rlvect_1(A) & v7_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v9_vectsp_1(A) & -v10_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v3_vectsp_1(A) & v4_group_1(A) & v2_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & l3_vectsp_1(A))) # label(rc10_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7253 $T # label(t11_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7254 (all A (l1_struct_0(A) -> (exists B l4_vectsp_1(B,A)))) # label(existence_l4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7255 (all A (l1_vectsp_1(A) -> m1_subset_1(k2_vectsp_1(A),u1_struct_0(A)))) # label(dt_k2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7256 $T # label(t77_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7257 $T # label(d10_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7258 (exists A (l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & v1_rlvect_1(A) & -v3_struct_0(A))) # label(rc1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7259 $T # label(t62_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7260 (all A (v4_group_1(A) & v7_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v9_vectsp_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (B != k1_rlvect_1(A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (C = k4_vectsp_1(A,B) <-> k10_group_1(A,B,C) = k2_group_1(A))))))))) # label(d22_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7261 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k5_rlvect_1(A,B) = k6_rlvect_1(A,k1_rlvect_1(A),B) & B = k6_rlvect_1(A,B,k1_rlvect_1(A)))))) # label(t65_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7262 $T # label(t57_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7263 $T # label(t28_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7264 $T # label(d5_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7265 $T # label(d3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7266 (all A all B all C all D (l1_struct_0(A) & -v3_struct_0(B) & l4_vectsp_1(B,A) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(C,u1_struct_0(A)) & -v3_struct_0(A) -> m1_subset_1(k6_vectsp_1(A,B,C,D),u1_struct_0(B)))) # label(dt_k6_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7267 (exists A (l1_vectsp_1(A) & v1_vectsp_1(A))) # label(rc2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7268 $T # label(t85_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7269 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,C,B) = k2_rlvect_1(A,B,C) & k2_rlvect_1(A,k2_rlvect_1(A,B,C),D) = k2_rlvect_1(A,B,k2_rlvect_1(A,C,D)) & (exists E (m1_subset_1(E,u1_struct_0(A)) & k2_rlvect_1(A,B,E) = k1_rlvect_1(A))) & B = k2_rlvect_1(A,B,k1_rlvect_1(A))))))))))) # label(t7_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7270 (exists A (v3_vectsp_1(A) & -v3_struct_0(A) & l3_vectsp_1(A))) # label(rc7_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7271 (all A (v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v5_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> k5_rlvect_1(B,k6_vectsp_1(A,B,C,D)) = k6_vectsp_1(A,B,k5_rlvect_1(A,C),D) & k6_rlvect_1(B,E,k6_vectsp_1(A,B,C,D)) = k2_rlvect_1(B,E,k6_vectsp_1(A,B,k5_rlvect_1(A,C),D)))))))))))) # label(t68_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7272 $T # label(t83_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7273 (all A all B all C all D all E (v1_funct_1(B) & m1_subset_1(D,A) & m1_subset_1(E,A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> l3_vectsp_1(g3_vectsp_1(A,B,C,D,E)) & v3_vectsp_1(g3_vectsp_1(A,B,C,D,E)))) # label(dt_g3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7274 (all A all B all C all D (m1_relset_1(B,k2_zfmisc_1(A,A),A) & m1_subset_1(D,A) & m1_subset_1(C,A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> l2_vectsp_1(g2_vectsp_1(A,B,C,D)) & v2_vectsp_1(g2_vectsp_1(A,B,C,D)))) # label(dt_g2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7275 $T # label(d17_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7276 (exists A (v4_rlvect_1(A) & v2_group_1(A) & v4_group_1(A) & v7_group_1(A) & v4_vectsp_1(A) & -v10_vectsp_1(A) & v13_vectsp_1(A) & v9_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v5_vectsp_1(A) & v3_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) & l3_vectsp_1(A))) # label(rc15_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7277 (all A (v6_rlvect_1(A) & v5_vectsp_1(A) & l3_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_group_1(A,k6_rlvect_1(A,B,C),D) = k6_rlvect_1(A,k1_group_1(A,B,D),k1_group_1(A,C,D)))))))))) # label(t45_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7278 $T # label(d7_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7279 (all A all B (l4_vectsp_1(B,A) & l1_struct_0(A) -> v1_funct_2(u2_vectsp_1(A,B),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B)) & m2_relset_1(u2_vectsp_1(A,B),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B)) & v1_funct_1(u2_vectsp_1(A,B)))) # label(dt_u2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7280 (all A (v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_rlvect_1(A,B,C) = k5_rlvect_1(A,k2_rlvect_1(A,k5_rlvect_1(A,C),k5_rlvect_1(A,B))))))))) # label(t89_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7281 (exists A l2_vectsp_1(A)) # label(existence_l2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7282 (exists A (l1_vectsp_1(A) & v2_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & -v3_struct_0(A))) # label(rc9_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7283 $T # label(t23_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7284 (all A (l1_vectsp_1(A) -> k2_vectsp_1(A) = u1_vectsp_1(A))) # label(d9_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7285 $T # label(t25_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7286 $T # label(t17_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7287 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_rlvect_1(A,k5_rlvect_1(A,C),B) = k5_rlvect_1(A,k2_rlvect_1(A,k5_rlvect_1(A,B),C)))))))) # label(t92_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7288 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k6_vectsp_1(A,B,C,k5_rlvect_1(B,D)) = k5_rlvect_1(B,k6_vectsp_1(A,B,C,D)))))))))) # label(t69_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7289 $T # label(t58_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7290 $T # label(t38_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7291 (all A (l1_struct_0(A) -> (exists B (v11_vectsp_1(B,A) & -v3_struct_0(B) & l4_vectsp_1(B,A))))) # label(rc12_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7292 $T # label(t72_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7293 $T # label(t46_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7294 $T # label(t19_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7295 $T # label(d8_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7296 (all A (v6_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (B != k1_rlvect_1(A) -> k1_rlvect_1(A) != k4_vectsp_1(A,B) & k1_rlvect_1(A) != k5_rlvect_1(A,k4_vectsp_1(A,B))))))) # label(t74_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7297 $T # label(t52_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7298 $T # label(t75_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7299 (exists A l1_vectsp_1(A)) # label(existence_l1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7300 (all A (l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k6_rlvect_1(A,B,C) = k1_rlvect_1(A) -> C = B))))))) # label(t84_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7301 $T # label(t5_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7302 (all A (l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (B = C -> k1_rlvect_1(A) = k2_rlvect_1(A,B,k5_rlvect_1(A,C))) & (B = C -> k6_rlvect_1(A,B,C) = k1_rlvect_1(A)) & (k1_rlvect_1(A) = k6_rlvect_1(A,B,C) -> B = C) & (k1_rlvect_1(A) = k2_rlvect_1(A,B,k5_rlvect_1(A,C)) -> C = B))))))) # label(t66_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7303 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> k5_rlvect_1(A,C) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C))) <-> k7_vectsp_1(A) = B))))) # label(d25_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7304 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m1_subset_1(D,B) & v1_funct_2(E,k2_zfmisc_1(u1_struct_0(A),B),B) & m1_relset_1(E,k2_zfmisc_1(u1_struct_0(A),B),B) & v1_funct_1(E) & m1_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) & l1_struct_0(A) -> -v3_struct_0(g4_vectsp_1(A,B,C,D,E)) & v11_vectsp_1(g4_vectsp_1(A,B,C,D,E),A))) # label(fc6_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7305 (exists A (-v3_struct_0(A) & v2_vectsp_1(A) & l2_vectsp_1(A))) # label(rc5_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7306 (all A (-v3_struct_0(A) & v4_group_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v7_vectsp_1(A) & v7_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v3_struct_0(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v12_vectsp_1(C,A) & l4_vectsp_1(C,A) & v4_rlvect_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (k1_rlvect_1(C) = k6_vectsp_1(A,C,B,D) <-> k1_rlvect_1(A) = B | k1_rlvect_1(C) = D))))))))) # label(t60_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7307 (all A (l3_vectsp_1(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,k1_group_1(A,B,C),k1_group_1(A,B,D)) = k1_group_1(A,B,k2_rlvect_1(A,C,D)))))))) <-> v4_vectsp_1(A)))) # label(d11_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7308 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k6_rlvect_1(A,k5_rlvect_1(A,D),C) = k5_rlvect_1(A,k2_rlvect_1(A,C,D)) & k2_rlvect_1(A,D,C) = k5_rlvect_1(A,k6_rlvect_1(A,k5_rlvect_1(A,C),D)) & k6_rlvect_1(A,k6_rlvect_1(A,B,C),D) = k6_rlvect_1(A,B,k2_rlvect_1(A,D,C)) & k2_rlvect_1(A,D,k5_rlvect_1(A,C)) = k5_rlvect_1(A,k6_rlvect_1(A,C,D)) & k5_rlvect_1(A,k2_rlvect_1(A,D,k5_rlvect_1(A,C))) = k6_rlvect_1(A,C,D))))))))) # label(t64_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7309 $T # label(t61_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7310 (all A all B all C (m1_subset_1(C,A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> l1_vectsp_1(g1_vectsp_1(A,B,C)) & v1_vectsp_1(g1_vectsp_1(A,B,C)))) # label(dt_g1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7311 $T # label(t51_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7312 $T # label(t37_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7313 (all A (l2_vectsp_1(A) -> l2_struct_0(A) & l1_vectsp_1(A))) # label(dt_l2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7314 (all A (l3_vectsp_1(A) -> l1_rlvect_1(A) & l2_vectsp_1(A))) # label(dt_l3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7315 (all A all B all C (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_subset_1(C,A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all D all E all F (g1_vectsp_1(A,B,C) = g1_vectsp_1(D,E,F) -> E = B & F = C & D = A)))) # label(free_g1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7316 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> l1_group_1(g1_group_1(u1_struct_0(A),u1_rlvect_1(A))) & v7_group_1(g1_group_1(u1_struct_0(A),u1_rlvect_1(A))) & v4_group_1(g1_group_1(u1_struct_0(A),u1_rlvect_1(A))) & v3_group_1(g1_group_1(u1_struct_0(A),u1_rlvect_1(A))) & -v3_struct_0(g1_group_1(u1_struct_0(A),u1_rlvect_1(A))))) # label(t94_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7317 $T # label(t27_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7318 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v5_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> k6_vectsp_1(A,B,C,k6_rlvect_1(B,D,E)) = k6_rlvect_1(B,k6_vectsp_1(A,B,C,D),k6_vectsp_1(A,B,C,E)))))))))))) # label(t70_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7319 (all A (m1_subset_1(A,u1_struct_0(k3_vectsp_1)) -> (all B (m1_subset_1(B,u1_struct_0(k3_vectsp_1)) -> (all C (m1_subset_1(C,u1_struct_0(k3_vectsp_1)) -> k4_rlvect_1(k3_vectsp_1,A,k4_rlvect_1(k3_vectsp_1,B,C)) = k4_rlvect_1(k3_vectsp_1,k4_rlvect_1(k3_vectsp_1,A,B),C) & k10_group_1(k3_vectsp_1,k10_group_1(k3_vectsp_1,A,B),C) = k10_group_1(k3_vectsp_1,A,k10_group_1(k3_vectsp_1,B,C)) & k10_group_1(k3_vectsp_1,k2_group_1(k3_vectsp_1),A) = A & -(k1_rlvect_1(k3_vectsp_1) != A & (all D (m1_subset_1(D,u1_struct_0(k3_vectsp_1)) -> k2_group_1(k3_vectsp_1) != k10_group_1(k3_vectsp_1,A,D)))) & k10_group_1(k3_vectsp_1,A,k4_rlvect_1(k3_vectsp_1,B,C)) = k4_rlvect_1(k3_vectsp_1,k10_group_1(k3_vectsp_1,A,B),k10_group_1(k3_vectsp_1,A,C)) & k10_group_1(k3_vectsp_1,k4_rlvect_1(k3_vectsp_1,B,C),A) = k4_rlvect_1(k3_vectsp_1,k10_group_1(k3_vectsp_1,B,A),k10_group_1(k3_vectsp_1,C,A)) & k10_group_1(k3_vectsp_1,A,B) = k10_group_1(k3_vectsp_1,B,A) & k1_rlvect_1(k3_vectsp_1) = k4_rlvect_1(k3_vectsp_1,A,k5_rlvect_1(k3_vectsp_1,A)) & A = k4_rlvect_1(k3_vectsp_1,A,k1_rlvect_1(k3_vectsp_1)) & k4_rlvect_1(k3_vectsp_1,B,A) = k4_rlvect_1(k3_vectsp_1,A,B))))))) # label(t21_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7320 $T # label(t29_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7321 $T # label(t18_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7322 (exists A (l1_rlvect_1(A) & v13_vectsp_1(A) & -v3_struct_0(A))) # label(rc14_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7323 (exists A l3_vectsp_1(A)) # label(existence_l3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7324 $T # label(t53_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7325 (all A all B all C all D (v1_funct_1(B) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & m1_subset_1(D,A) & m1_subset_1(C,A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all E all F all G all H (g2_vectsp_1(E,F,G,H) = g2_vectsp_1(A,B,C,D) -> A = E & B = F & C = G & H = D)))) # label(free_g2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7326 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_vectsp_1(A) & l3_vectsp_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k5_rlvect_1(A,k1_group_1(A,B,C)) = k1_group_1(A,B,k5_rlvect_1(A,C)))))))) # label(t40_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7327 (all A (l3_vectsp_1(A) -> (v4_vectsp_1(A) & v5_vectsp_1(A) & -v3_struct_0(A) -> v7_vectsp_1(A) & -v3_struct_0(A)))) # label(cc2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7328 (all A (-v3_struct_0(A) & l3_vectsp_1(A) -> (all B (l4_vectsp_1(B,A) & -v3_struct_0(B) -> (v12_vectsp_1(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> k2_rlvect_1(B,k6_vectsp_1(A,B,C,E),k6_vectsp_1(A,B,D,E)) = k6_vectsp_1(A,B,k2_rlvect_1(A,C,D),E) & k6_vectsp_1(A,B,k2_group_1(A),E) = E & k6_vectsp_1(A,B,C,k6_vectsp_1(A,B,D,E)) = k6_vectsp_1(A,B,k1_group_1(A,C,D),E) & k2_rlvect_1(B,k6_vectsp_1(A,B,C,E),k6_vectsp_1(A,B,C,F)) = k6_vectsp_1(A,B,C,k2_rlvect_1(B,E,F))))))))))))))) # label(d26_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7329 (all A (l1_vectsp_1(A) & -v3_struct_0(A) -> (v6_vectsp_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k1_group_1(A,B,k2_group_1(A))))))) # label(d13_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7330 $T # label(d4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7331 $T # label(t49_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7332 $T # label(t13_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7333 $T # label(t4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7334 $T # label(t71_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7335 (all A (-v3_struct_0(A) & l3_vectsp_1(A) -> (v7_vectsp_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,k1_group_1(A,B,C),k1_group_1(A,B,D)) = k1_group_1(A,B,k2_rlvect_1(A,C,D)) & k2_rlvect_1(A,k1_group_1(A,C,B),k1_group_1(A,D,B)) = k1_group_1(A,k2_rlvect_1(A,C,D),B)))))))))) # label(d18_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7336 $T # label(t54_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7337 (all A (l1_vectsp_1(A) -> m1_subset_1(u1_vectsp_1(A),u1_struct_0(A)))) # label(dt_u1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7338 $T # label(t82_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7339 $T # label(d16_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7340 $T # label(t30_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7341 (exists A (v2_vectsp_1(A) & l2_vectsp_1(A))) # label(rc4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7342 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> v1_funct_1(k7_vectsp_1(A)) & v1_funct_2(k7_vectsp_1(A),u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(k7_vectsp_1(A),u1_struct_0(A),u1_struct_0(A)))) # label(dt_k7_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7343 (all A (-v3_struct_0(A) & l1_struct_0(A) -> (all B (l4_vectsp_1(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k6_vectsp_1(A,B,C,D) = k2_binop_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u2_vectsp_1(A,B),C,D))))))))) # label(d24_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7344 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v5_rlvect_1(C) & v6_rlvect_1(C) & v12_vectsp_1(C,A) & l4_vectsp_1(C,A) & v4_rlvect_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k1_rlvect_1(C) = k6_vectsp_1(A,C,k1_rlvect_1(A),D) & k1_rlvect_1(C) = k6_vectsp_1(A,C,B,k1_rlvect_1(C)) & k6_vectsp_1(A,C,k5_rlvect_1(A,k2_group_1(A)),D) = k5_rlvect_1(C,D))))))))) # label(t59_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7345 $T # label(t2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7346 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (B = k1_rlvect_1(A) | C = k1_rlvect_1(A) <-> k10_group_1(A,B,C) = k1_rlvect_1(A)))))))) # label(t44_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7347 $T # label(t91_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7348 (all A (-v3_struct_0(A) & v4_vectsp_1(A) & l3_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_group_1(A,B,k1_rlvect_1(A)) = k1_rlvect_1(A))))) # label(t36_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7349 $T # label(t79_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7350 $T # label(t56_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7351 $T # label(t50_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7352 $T # label(t24_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7353 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l3_vectsp_1(A) & v5_vectsp_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_rlvect_1(A) = k1_group_1(A,k1_rlvect_1(A),B))))) # label(t39_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7354 (exists A (l1_group_1(A) & -v3_struct_0(A) & v7_group_1(A) & v4_group_1(A))) # label(rc8_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7355 (all A (l1_vectsp_1(A) -> (v1_vectsp_1(A) -> g1_vectsp_1(u1_struct_0(A),u1_group_1(A),u1_vectsp_1(A)) = A))) # label(abstractness_v1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7356 $T # label(d27_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7357 (all A (v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k6_rlvect_1(A,C,B) = k5_rlvect_1(A,k6_rlvect_1(A,B,C)))))))) # label(t81_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7358 (all A (l1_vectsp_1(A) -> (v8_vectsp_1(A) & v7_group_1(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v6_vectsp_1(A)))) # label(cc5_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7359 $T # label(t1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7360 $T # label(t9_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7361 (all A (-v3_struct_0(A) & l1_vectsp_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> B = k1_group_1(A,k2_group_1(A),B))) <-> v8_vectsp_1(A)))) # label(d19_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7362 (all A (-v3_struct_0(A) & l2_vectsp_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> -((all C (m1_subset_1(C,u1_struct_0(A)) -> k2_group_1(A) != k1_group_1(A,B,C))) & B != k1_rlvect_1(A)))) <-> v9_vectsp_1(A)))) # label(d20_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7363 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & l3_vectsp_1(A) & v5_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k5_rlvect_1(A,k1_group_1(A,B,C)) = k1_group_1(A,k5_rlvect_1(A,B),C))))))) # label(t41_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7364 $T # label(d1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7365 (all A (-v3_struct_0(A) & l3_vectsp_1(A) & v4_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_group_1(A,B,k6_rlvect_1(A,C,D)) = k6_rlvect_1(A,k1_group_1(A,B,C),k1_group_1(A,B,D)))))))))) # label(t43_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7366 (all A all B all C all D all E (m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_subset_1(E,A) & m1_subset_1(D,A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all F all G all H all I all J (g3_vectsp_1(F,G,H,I,J) = g3_vectsp_1(A,B,C,D,E) -> A = F & C = H & J = E & D = I & B = G)))) # label(free_g3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7367 $T # label(d14_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7368 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v8_vectsp_1(A) & v7_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k6_rlvect_1(A,C,k10_group_1(A,D,B)) = k1_rlvect_1(A) -> k10_group_1(A,C,k4_vectsp_1(A,B)) = D | k1_rlvect_1(A) = B) & (k6_rlvect_1(A,k10_group_1(A,B,D),C) = k1_rlvect_1(A) -> k1_rlvect_1(A) = B | D = k10_group_1(A,C,k4_vectsp_1(A,B))))))))))) # label(t88_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7369 $T # label(t80_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7370 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,k5_rlvect_1(A,B),k5_rlvect_1(A,C)) = k1_group_1(A,B,C))))))) # label(t42_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7371 (exists A (v3_vectsp_1(A) & l3_vectsp_1(A))) # label(rc6_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7372 $T # label(t8_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7373 $T # label(t3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7374 $T # label(t16_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7375 (all A (-v3_struct_0(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & v7_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k5_vectsp_1(A,B,C) = k10_group_1(A,B,k4_vectsp_1(A,C)))))))) # label(d23_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7376 (all A all B all C (v7_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & v4_group_1(A) & -v3_struct_0(A) -> m1_subset_1(k5_vectsp_1(A,B,C),u1_struct_0(A)))) # label(dt_k5_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7377 $T # label(t26_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7378 $T # label(t14_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7379 (all A all B (-v3_struct_0(A) & v4_group_1(A) & v7_group_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & m1_subset_1(B,u1_struct_0(A)) & l3_vectsp_1(A) & v7_vectsp_1(A) -> m1_subset_1(k4_vectsp_1(A,B),u1_struct_0(A)))) # label(dt_k4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7380 $T # label(t31_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7381 (all A (l1_struct_0(A) -> (exists B (v11_vectsp_1(B,A) & l4_vectsp_1(B,A))))) # label(rc11_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7382 (all A (l1_vectsp_1(A) -> (v2_group_1(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v6_vectsp_1(A) & v8_vectsp_1(A)))) # label(cc3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7383 (all A (m1_subset_1(A,u1_struct_0(k1_vectsp_1)) -> (all B (m1_subset_1(B,u1_struct_0(k1_vectsp_1)) -> (all C (m1_subset_1(C,u1_struct_0(k1_vectsp_1)) -> k4_rlvect_1(k1_vectsp_1,B,A) = k4_rlvect_1(k1_vectsp_1,A,B) & A = k4_rlvect_1(k1_vectsp_1,A,k1_rlvect_1(k1_vectsp_1)) & k1_rlvect_1(k1_vectsp_1) = k4_rlvect_1(k1_vectsp_1,A,k5_rlvect_1(k1_vectsp_1,A)) & k4_rlvect_1(k1_vectsp_1,A,k4_rlvect_1(k1_vectsp_1,B,C)) = k4_rlvect_1(k1_vectsp_1,k4_rlvect_1(k1_vectsp_1,A,B),C))))))) # label(t6_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7384 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (v13_vectsp_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k2_rlvect_1(A,B,B) = k1_rlvect_1(A) -> B = k1_rlvect_1(A))))))) # label(d28_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7385 $T # label(t32_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7386 $T # label(t76_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7387 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k6_rlvect_1(A,k2_rlvect_1(A,C,B),k2_rlvect_1(A,D,B)) = k6_rlvect_1(A,C,D))))))))) # label(t90_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7388 (all A (l1_struct_0(A) -> (all B (l4_vectsp_1(B,A) -> l1_rlvect_1(B))))) # label(dt_l4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7389 (all A (v3_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (exists B (-v3_struct_0(B) & v3_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & v11_vectsp_1(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & l4_vectsp_1(B,A))))) # label(rc13_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7390 (all A (l3_vectsp_1(A) -> (v7_vectsp_1(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v4_vectsp_1(A) & v5_vectsp_1(A)))) # label(cc1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7391 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k6_rlvect_1(A,k6_rlvect_1(A,B,D),C) = k6_rlvect_1(A,k6_rlvect_1(A,B,C),D))))))))) # label(t93_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7392 $T # label(d2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7393 $T # label(t48_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7394 (all A (l3_vectsp_1(A) & -v3_struct_0(A) -> (v5_vectsp_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_group_1(A,k2_rlvect_1(A,C,D),B) = k2_rlvect_1(A,k1_group_1(A,C,B),k1_group_1(A,D,B))))))))))) # label(d12_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7395 $T # label(t47_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7396 (all A (l1_vectsp_1(A) -> (v8_vectsp_1(A) & v6_vectsp_1(A) & -v3_struct_0(A) -> v2_group_1(A) & -v3_struct_0(A)))) # label(cc4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7397 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_rlvect_1(A) = k6_rlvect_1(A,B,C) -> k6_rlvect_1(A,C,B) = k1_rlvect_1(A)))))))) # label(t87_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7398 (all A (v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v7_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (v13_vectsp_1(A) <-> k1_rlvect_1(A) != k2_rlvect_1(A,k2_group_1(A),k2_group_1(A))))) # label(d29_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7399 $T # label(t15_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7400 $T # label(t35_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7401 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v3_struct_0(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v12_vectsp_1(C,A) & l4_vectsp_1(C,A) & v4_rlvect_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (B != k1_rlvect_1(A) -> k6_vectsp_1(A,C,k4_vectsp_1(A,B),k6_vectsp_1(A,C,B,D)) = D))))))))) # label(t67_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7402 $T # label(t34_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7403 (all A (-v3_struct_0(A) & l3_vectsp_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_group_1(A,B,k2_rlvect_1(A,C,D)) = k2_rlvect_1(A,k1_group_1(A,B,C),k1_group_1(A,B,D)) & k2_rlvect_1(A,k1_group_1(A,C,B),k1_group_1(A,D,B)) = k1_group_1(A,k2_rlvect_1(A,C,D),B) & -(k1_rlvect_1(A) != B & (all E (m1_subset_1(E,u1_struct_0(A)) -> k1_group_1(A,B,E) != k2_group_1(A)))))))))) <-> v9_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & -v3_struct_0(A)))) # label(t22_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7404 (all A (v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v9_vectsp_1(A) & v7_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k10_group_1(A,B,C) = k10_group_1(A,B,D) -> D = C | k1_rlvect_1(A) = B))))))))) # label(t33_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7405 (exists A (l1_vectsp_1(A) & v1_vectsp_1(A) & -v3_struct_0(A))) # label(rc3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7406 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (B != k1_rlvect_1(A) -> B = k4_vectsp_1(A,k4_vectsp_1(A,B))))))) # label(t73_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7407 (all A (l2_vectsp_1(A) -> (v2_vectsp_1(A) -> g2_vectsp_1(u1_struct_0(A),u1_group_1(A),u1_vectsp_1(A),u2_struct_0(A)) = A))) # label(abstractness_v2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7408 (all A (-v3_struct_0(A) & l2_vectsp_1(A) -> (v10_vectsp_1(A) <-> k2_group_1(A) = k1_rlvect_1(A)))) # label(d21_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7409 $T # label(t12_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7410 (all A all B all C all D all E (l1_struct_0(A) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(u1_struct_0(A),B),B) & m1_relset_1(E,k2_zfmisc_1(u1_struct_0(A),B),B) & m1_subset_1(D,B) & m1_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all F all G all H all I all J (g4_vectsp_1(F,G,H,I,J) = g4_vectsp_1(A,B,C,D,E) -> G = B & C = H & D = I & E = J & A = F)))) # label(free_g4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7411 $T # label(t10_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7412 (all A (l1_vectsp_1(A) -> l1_group_1(A))) # label(dt_l1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.41 7413 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (C = k5_rlvect_1(A,B) <-> k2_rlvect_1(A,B,C) = k1_rlvect_1(A)))))))) # label(t63_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7414 (all A all B (l4_vectsp_1(B,A) & l1_struct_0(A) -> (v11_vectsp_1(B,A) -> B = g4_vectsp_1(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u2_vectsp_1(A,B))))) # label(abstractness_v11_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7415 (all A all B all C all D all E (v1_funct_1(C) & m1_subset_1(D,B) & v1_funct_2(E,k2_zfmisc_1(u1_struct_0(A),B),B) & m1_relset_1(E,k2_zfmisc_1(u1_struct_0(A),B),B) & v1_funct_1(E) & m1_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & l1_struct_0(A) -> v11_vectsp_1(g4_vectsp_1(A,B,C,D,E),A) & l4_vectsp_1(g4_vectsp_1(A,B,C,D,E),A))) # label(dt_g4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7416 $T # label(t55_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7417 (all A (l3_vectsp_1(A) -> (v3_vectsp_1(A) -> g3_vectsp_1(u1_struct_0(A),u1_rlvect_1(A),u1_group_1(A),u1_vectsp_1(A),u2_struct_0(A)) = A))) # label(abstractness_v3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7418 (all A (v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k5_rlvect_1(A,B) = k1_rlvect_1(A) -> k1_rlvect_1(A) = B))))) # label(t86_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7419 (all A ((all B -(v1_finset_1(B) & k1_xboole_0 = k1_setfam_1(B) & r1_tarski(B,A) & B != k1_xboole_0)) & A != k1_xboole_0 <-> v1_compts_1(A))) # label(d2_compts_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7420 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (v3_compts_1(A) & v2_compts_1(A) -> v4_compts_1(A)))) # label(t21_compts_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7421 $T # label(t2_compts_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7422 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -((all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(r1_tarski(D,C) & v1_finset_1(D) & r1_compts_1(A,D,B)))) & v1_tops_2(C,A) & r1_compts_1(A,C,B)))) <-> v6_compts_1(B,A)))))) # label(d7_compts_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7423 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) & v2_compts_1(A) -> v6_compts_1(B,A)))))) # label(t17_compts_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7424 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_pre_topc(A) -> k1_xboole_0 = B | (v2_compts_1(k3_pre_topc(A,B)) <-> v6_compts_1(B,A))) & (B = k1_xboole_0 -> (v2_compts_1(k3_pre_topc(A,B)) <-> v6_compts_1(B,A))))))) # label(t12_compts_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7425 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (v3_compts_1(A) & v2_compts_1(A) -> v5_compts_1(A)))) # label(t22_compts_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7426 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_compts_1(A,B,C) <-> r1_tarski(C,k5_setfam_1(u1_struct_0(A),B))))))))) # label(d1_compts_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7427 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_compts_1(A) & v6_compts_1(B,A) & v6_compts_1(C,A) -> v6_compts_1(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t20_compts_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7428 (all A (l1_pre_topc(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(k1_xboole_0 != B & v4_pre_topc(B,A) & v4_pre_topc(C,A) & r1_xboole_0(B,C) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_tarski(C,E) & r1_xboole_0(D,E) & r1_tarski(B,D) & v3_pre_topc(E,A) & v3_pre_topc(D,A)))))) & C != k1_xboole_0))))) <-> v5_compts_1(A)))) # label(d6_compts_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7429 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (v2_compts_1(A) & v5_pre_topc(C,A,B) & k2_relat_1(C) = k2_pre_topc(B) & v3_compts_1(B) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(D,A) -> v4_pre_topc(k4_pre_topc(A,B,C,D),B))))))))))) # label(t25_compts_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7430 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (v2_compts_1(A) <-> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(v2_tops_2(B,A) & k1_xboole_0 = k6_setfam_1(u1_struct_0(A),B) & (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(C != k1_xboole_0 & v1_finset_1(C) & k6_setfam_1(u1_struct_0(A),C) = k1_xboole_0 & r1_tarski(C,B)))) & B != k1_xboole_0)))))) # label(t14_compts_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7431 $T # label(t5_compts_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7432 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (v3_compts_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v6_compts_1(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -(r2_hidden(C,k3_subset_1(u1_struct_0(A),B)) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(E,A) & r2_hidden(C,D) & r1_xboole_0(D,E) & r1_tarski(B,E) & v3_pre_topc(D,A))))))))) | B = k1_xboole_0)))))) # label(t15_compts_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7433 (all A (l1_pre_topc(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(k1_xboole_0 != C & v4_pre_topc(C,A) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(D,A) & v3_pre_topc(E,A) & r2_hidden(B,D) & r1_xboole_0(D,E) & r1_tarski(C,E)))))) & r2_hidden(B,k3_subset_1(u1_struct_0(A),C))))))) <-> v4_compts_1(A)))) # label(d5_compts_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7434 (all A (l1_pre_topc(A) -> (v2_compts_1(A) <-> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(r1_pre_topc(A,B) & (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(r1_tarski(C,B) & v1_finset_1(C) & r1_pre_topc(A,C)))) & v1_tops_2(B,A))))))) # label(d3_compts_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7435 $T # label(t1_compts_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7436 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (v2_compts_1(A) <-> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(v1_compts_1(B) & k1_xboole_0 = k6_setfam_1(u1_struct_0(A),B) & v2_tops_2(B,A))))))) # label(t13_compts_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7437 (all A (l1_pre_topc(A) -> (v6_compts_1(k2_pre_topc(A),A) <-> v2_compts_1(A)))) # label(t10_compts_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7438 $T # label(t4_compts_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7439 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v6_compts_1(B,A) & v3_compts_1(A) -> v4_pre_topc(B,A)))))) # label(t16_compts_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7440 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v6_compts_1(B,A) & v6_compts_1(C,A) -> v6_compts_1(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t19_compts_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7441 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(C,A) & r1_tarski(C,B) & v6_compts_1(B,A) -> v6_compts_1(C,A)))))))) # label(t18_compts_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7442 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (-v3_struct_0(C) & l1_pre_topc(C) -> (all D (v1_funct_2(D,u1_struct_0(A),u1_struct_0(C)) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(C)) & v1_funct_1(D) -> (v5_pre_topc(D,A,C) & v6_compts_1(B,A) & k2_pre_topc(C) = k2_relat_1(D) -> v6_compts_1(k4_pre_topc(A,C,D,B),C)))))))))) # label(t24_compts_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7443 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(C,k2_pre_topc(B)) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (C = D -> v6_compts_1(D,B)))) <-> v6_compts_1(C,A))))))))) # label(t11_compts_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7444 (all A (l1_pre_topc(A) -> v6_compts_1(k1_pre_topc(A),A))) # label(t9_compts_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7445 $T # label(t3_compts_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7446 (all A (l1_pre_topc(A) -> (v3_compts_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(E,A) & r2_hidden(B,D) & r1_xboole_0(D,E) & r2_hidden(C,E) & v3_pre_topc(D,A)))))) & B != C)))))))) # label(d4_compts_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7447 $T # label(t7_compts_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7448 (all A (l1_pre_topc(A) -> (all B (-v3_struct_0(B) & l1_pre_topc(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v2_compts_1(A) & k2_relat_1(C) = k2_pre_topc(B) & v5_pre_topc(C,A,B) -> v2_compts_1(B)))))))) # label(t23_compts_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7449 $T # label(t8_compts_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7450 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (v2_funct_1(C) & v5_pre_topc(C,A,B) & k2_pre_topc(B) = k2_relat_1(C) & k2_pre_topc(A) = k1_relat_1(C) & v3_compts_1(B) & v2_compts_1(A) -> v3_tops_2(C,A,B)))))))) # label(t26_compts_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7451 $T # label(t6_compts_1) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7452 (all A (-v3_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_orders_1(C,k1_orders_1(u1_struct_0(A))) -> (all D (m2_orders_2(D,A,C) -> (k1_funct_1(C,u1_struct_0(A)) = B -> k1_xboole_0 = k3_orders_2(A,D,B)))))))))) # label(t81_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7453 (all A (-v3_struct_0(A) & l1_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_orders_2(A,B,B))))) # label(t24_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7454 (all A all B all C (v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & l1_orders_2(B) & -v3_struct_0(B) -> ((exists D (m1_subset_1(D,u1_struct_0(B)) & A = D & (all E (m1_subset_1(E,u1_struct_0(B)) -> (r2_hidden(E,C) -> r2_orders_2(B,D,E)))))) <-> r2_hidden(A,a_2_1_orders_2(B,C))))) # label(fraenkel_a_2_1_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7455 (all A (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_orders_2(A,B,C) <-> r2_hidden(C,k1_orders_2(A,k1_struct_0(A,B)))))))))) # label(t51_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7456 (all A (-v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (r2_orders_2(A,B,C) & m1_orders_2(E,A,D) & r2_hidden(C,E) & r2_hidden(B,D) -> r2_hidden(B,E)))))))))))) # label(t70_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7457 $T # label(t147_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7458 (all A (v2_orders_2(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -((exists D (v5_orders_2(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & r2_hidden(B,D) & r2_hidden(C,D))) & -r1_orders_2(A,C,B) & -r1_orders_2(A,B,C)) & -((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & v5_orders_2(D,A) -> -(r2_hidden(C,D) & r2_hidden(B,D)))) & (r1_orders_2(A,C,B) | r1_orders_2(A,B,C))))))))) # label(t38_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7459 $T # label(t134_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7460 $T # label(t34_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7461 (all A (-v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) -> (all B (v5_orders_2(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v3_orders_1(k2_wellord1(u1_orders_2(A),B)))))) # label(t109_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7462 (all A all B (m1_relset_1(B,A,A) & -v1_xboole_0(A) -> v1_orders_2(g1_orders_2(A,B)) & -v3_struct_0(g1_orders_2(A,B)))) # label(fc1_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7463 $T # label(d1_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7464 $T # label(t153_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7465 $T # label(t127_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7466 $T # label(t130_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7467 $T # label(t16_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7468 $T # label(t143_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7469 (all A (v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(m1_orders_2(B,A,B) & B != k1_xboole_0) & -(-m1_orders_2(B,A,B) & B = k1_xboole_0))))) # label(t68_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7470 $T # label(t100_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7471 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v5_orders_2(B,A) <-> r7_relat_2(u1_orders_2(A),B)))))) # label(d11_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7472 (all A (l1_orders_2(A) -> (r8_relat_2(u1_orders_2(A),u1_struct_0(A)) <-> v3_orders_2(A)))) # label(d5_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7473 $T # label(t8_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7474 $T # label(t94_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7475 $T # label(t123_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7476 $T # label(t77_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7477 $T # label(t2_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7478 $T # label(d3_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7479 (all A (v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_orders_1(B,k1_orders_1(u1_struct_0(A))) -> (all C (m2_orders_2(C,A,B) -> r2_hidden(k1_funct_1(B,u1_struct_0(A)),C))))))) # label(t79_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7480 $T # label(t128_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7481 $T # label(t110_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7482 (all A (v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_orders_2(A,C,D) & r2_orders_2(A,B,C) -> r2_orders_2(A,B,D)))))))))) # label(t29_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7483 $T # label(t91_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7484 $T # label(t120_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7485 $T # label(t97_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7486 $T # label(t116_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7487 (all A (v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> ((exists D (v5_orders_2(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & r2_hidden(C,D) & r2_hidden(B,D))) <-> (r2_orders_2(A,B,C) <-> -r1_orders_2(A,C,B))))))))) # label(t39_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7488 (exists A l1_orders_2(A)) # label(existence_l1_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7489 $T # label(t6_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7490 $T # label(t137_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7491 (all A (v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k3_relat_1(k2_wellord1(u1_orders_2(A),B)) = B)))) # label(t107_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7492 (all A (v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & -v3_struct_0(A) -> (all B (v5_orders_2(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r3_orders_1(u1_orders_2(A),B))))) # label(t136_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7493 (all A (l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_orders_2(C,A,B) -> r1_tarski(C,B))))))) # label(t67_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7494 $T # label(t54_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7495 $T # label(t20_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7496 (all A all B all C (m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_orders_2(A) -> -r2_orders_2(A,B,B))) # label(irreflexivity_r2_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7497 (all A all B all C (v2_orders_2(B) & v3_orders_2(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v4_orders_2(B) & -v3_struct_0(B) -> (r2_hidden(A,a_2_0_orders_2(B,C)) <-> (exists D ((all E (m1_subset_1(E,u1_struct_0(B)) -> (r2_hidden(E,C) -> r2_orders_2(B,E,D)))) & A = D & m1_subset_1(D,u1_struct_0(B))))))) # label(fraenkel_a_2_0_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7498 (all A (v2_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_orders_1(C,k1_orders_1(u1_struct_0(A))) -> (all D (m2_orders_2(D,A,C) -> (B = k3_tarski(k4_orders_2(A,C)) -> D = k3_tarski(k4_orders_2(A,C)) | m1_orders_2(D,A,B)))))))))) # label(t88_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7499 (all A all B (v4_orders_2(A) & l1_orders_2(A) & m1_orders_1(B,k1_orders_1(u1_struct_0(A))) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> -v1_xboole_0(k4_orders_2(A,B)))) # label(fc5_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7500 (all A (-v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_orders_1(D,k1_orders_1(u1_struct_0(A))) -> (all E (m2_orders_2(E,A,D) -> (r2_hidden(B,E) & C = k1_funct_1(D,u1_struct_0(A)) -> r3_orders_2(A,C,B)))))))))))) # label(t80_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7501 $T # label(t142_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7502 $T # label(t156_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7503 (all A (v2_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,k3_orders_2(A,D,C)) <-> r2_hidden(B,D) & r2_orders_2(A,B,C)))))))))) # label(t57_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7504 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,C) & m1_orders_2(C,A,D) -> k3_orders_2(A,D,B) = k3_orders_2(A,C,B)))))))))) # label(t71_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7505 $T # label(t112_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7506 (all A (l1_orders_2(A) -> l1_struct_0(A))) # label(dt_l1_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7507 (all A (v3_orders_2(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_orders_2(A,C,D) & r1_orders_2(A,B,C) -> r1_orders_2(A,B,D)))))))))) # label(t26_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7508 (all A (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r3_orders_1(u1_orders_2(A),B) -> v5_orders_2(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))))))) # label(t135_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7509 $T # label(t17_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7510 (all A (l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> a_2_0_orders_2(A,B) = k1_orders_2(A,B))))) # label(d12_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7511 (all A (l1_orders_2(A) -> (all B (v5_orders_2(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(C,B) -> v5_orders_2(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))))))))) # label(t37_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7512 (all A all B (m1_relset_1(B,A,A) -> l1_orders_2(g1_orders_2(A,B)) & v1_orders_2(g1_orders_2(A,B)))) # label(dt_g1_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7513 $T # label(t114_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7514 $T # label(t53_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7515 $T # label(t42_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7516 $T # label(t148_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7517 $T # label(t95_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7518 $T # label(t13_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7519 (all A (v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_orders_1(k2_wellord1(u1_orders_2(A),B)) -> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v5_orders_2(B,A)))))) # label(t108_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7520 $T # label(t31_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7521 (all A all B (m1_orders_1(B,k1_orders_1(u1_struct_0(A))) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (exists C m2_orders_2(C,A,B)))) # label(existence_m2_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7522 (all A (l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_orders_1(B,k1_orders_1(u1_struct_0(A))) -> (all C (m2_orders_2(C,A,B) -> (all D (m2_orders_2(D,A,B) -> (C != D -> (m1_orders_2(C,A,D) <-> -m1_orders_2(D,A,C))))))))))) # label(t83_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7523 $T # label(dt_k4_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7524 (exists A (v1_orders_2(A) & l1_orders_2(A))) # label(rc1_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7525 (all A (v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) -> v4_relat_2(u1_orders_2(A)) & v1_partfun1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)) & v8_relat_2(u1_orders_2(A)) & v1_relat_2(u1_orders_2(A)) & v1_relat_1(u1_orders_2(A)))) # label(fc2_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7526 $T # label(t76_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7527 (all A (v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (B != C -> r2_orders_2(A,B,C)))) <-> r9_orders_1(u1_orders_2(A),B)))))) # label(t161_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7528 $T # label(t21_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7529 $T # label(t141_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7530 (all A (-v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) -> k2_orders_2(A,k2_pre_topc(A)) = k1_xboole_0)) # label(t46_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7531 (all A all B (-v3_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) & v2_orders_2(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (r2_hidden(A,D) & r2_hidden(A,k2_orders_2(B,k1_struct_0(B,C))) <-> r2_hidden(A,k3_orders_2(B,D,C))))))))) # label(t56_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7532 $T # label(t132_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7533 (all A all B (m1_relset_1(B,A,A) -> (all C all D (g1_orders_2(A,B) = g1_orders_2(C,D) -> B = D & A = C)))) # label(free_g1_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7534 (all A (l1_orders_2(A) -> v5_orders_2(k1_pre_topc(A),A) & v5_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v1_xboole_0(k1_pre_topc(A)))) # label(fc4_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7535 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (B != C & r1_orders_2(A,B,C) <-> r2_orders_2(A,B,C)))))))) # label(d10_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7536 $T # label(t33_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7537 $T # label(t101_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7538 $T # label(t121_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7539 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) -> (all B (m1_orders_1(B,k1_orders_1(u1_struct_0(A))) -> (all C (v5_orders_2(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (k1_xboole_0 != C & r2_wellord1(u1_orders_2(A),C) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,C) -> k1_funct_1(B,k1_orders_2(A,k3_orders_2(A,C,D))) = D))) <-> m2_orders_2(C,A,B)))))))) # label(d16_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7540 $T # label(t27_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7541 $T # label(t129_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7542 $T # label(t146_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7543 (all A (-v3_struct_0(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (r6_orders_1(u1_orders_2(A),B) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> -r2_orders_2(A,B,C)))))))) # label(t159_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7544 $T # label(t119_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7545 (all A (v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_orders_1(B,k1_orders_1(u1_struct_0(A))) -> m2_orders_2(k3_tarski(k4_orders_2(A,B)),A,B))))) # label(t89_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7546 (all A (v2_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> -((all B (m1_subset_1(B,u1_struct_0(A)) -> (exists C (r2_orders_2(A,C,B) & m1_subset_1(C,u1_struct_0(A)))))) & (all B (v5_orders_2(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (exists C ((all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,B) -> r3_orders_2(A,C,D)))) & m1_subset_1(C,u1_struct_0(A))))))))) # label(t163_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7547 $T # label(t92_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7548 $T # label(t152_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7549 (all A (l1_orders_2(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -(r2_orders_2(A,C,B) & r2_orders_2(A,B,C)))))))) # label(t28_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7550 (all A (v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & -v3_struct_0(A) -> k2_orders_2(A,k1_pre_topc(A)) = u1_struct_0(A))) # label(t45_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7551 $T # label(t140_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7552 $T # label(t63_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7553 $T # label(t145_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7554 $T # label(t144_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7555 (all A (l1_orders_2(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v5_orders_2(B,A))))) # label(rc3_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7556 (all A (v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_orders_1(B,k1_orders_1(u1_struct_0(A))) -> (all C (k4_orders_2(A,B) = C <-> (all D (r2_hidden(D,C) <-> m2_orders_2(D,A,B))))))))) # label(d17_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7557 $T # label(t125_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7558 $T # label(t154_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7559 $T # label(t157_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7560 (all A (-v3_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(C,D) -> r1_tarski(k3_orders_2(A,C,B),k3_orders_2(A,D,B))))))))))) # label(t65_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7561 $T # label(t19_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7562 (all A all B (v3_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> m1_subset_1(k2_orders_2(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k2_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7563 $T # label(t22_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7564 (all A (-v3_struct_0(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(B,k2_orders_2(A,k1_struct_0(A,C))) <-> r2_orders_2(A,B,C)))))))) # label(t52_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7565 $T # label(t122_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7566 $T # label(t58_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7567 $T # label(t66_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7568 (all A (-v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) -> k1_orders_2(A,k2_pre_topc(A)) = k1_xboole_0)) # label(t44_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7569 $T # label(d2_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7570 (all A all B (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v3_struct_0(A) -> (exists C m1_orders_2(C,A,B)))) # label(existence_m1_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7571 $T # label(t113_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7572 (all A (v2_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k3_orders_2(A,k1_pre_topc(A),B) = k1_xboole_0)))) # label(t60_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7573 (all A (v4_orders_2(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -(r2_orders_2(A,C,B) & r1_orders_2(A,B,C)))))))) # label(t30_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7574 (exists A (l1_orders_2(A) & -v3_struct_0(A) & v1_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_orders_2(A))) # label(rc2_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7575 $T # label(t102_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7576 (all A all B (-v3_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & m1_orders_1(B,k1_orders_1(u1_struct_0(A))) & l1_orders_2(A) & v2_orders_2(A) -> (all C (m2_orders_2(C,A,B) -> v5_orders_2(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))))))) # label(dt_m2_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7577 $T # label(t103_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7578 $T # label(t74_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7579 (all A (l1_orders_2(A) -> (v2_orders_2(A) <-> r1_relat_2(u1_orders_2(A),u1_struct_0(A))))) # label(d4_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7580 $T # label(t149_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7581 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r2_wellord1(u1_orders_2(A),B) -> v5_orders_2(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))))))) # label(t40_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7582 (all A (-v3_struct_0(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k3_orders_2(A,B,C) = k5_subset_1(u1_struct_0(A),k2_orders_2(A,k1_struct_0(A,C)),B))))))) # label(d14_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7583 $T # label(t10_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7584 $T # label(t155_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7585 (all A (-v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> -r2_hidden(B,k1_orders_2(A,k1_struct_0(A,B))))))) # label(t48_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7586 $T # label(d8_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7587 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(k4_tarski(B,C),u1_orders_2(A)) <-> r1_orders_2(A,B,C)))))))) # label(d9_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7588 $T # label(t15_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7589 $T # label(t3_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7590 (all A (-v3_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> -r2_hidden(B,k2_orders_2(A,k1_struct_0(A,B))))))) # label(t50_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7591 $T # label(t124_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7592 (all A (v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> -((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v5_orders_2(B,A) -> (exists C ((all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,B) -> r3_orders_2(A,D,C)))) & m1_subset_1(C,u1_struct_0(A)))))) & (all B (m1_subset_1(B,u1_struct_0(A)) -> (exists C (r2_orders_2(A,B,C) & m1_subset_1(C,u1_struct_0(A))))))))) # label(t162_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7593 (all A (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_orders_1(B,k1_orders_1(u1_struct_0(A))) -> m2_orders_2(k1_tarski(k1_funct_1(B,u1_struct_0(A))),A,B))))) # label(t78_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7594 (all A all B (-v3_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_orders_2(A) & v2_orders_2(A) -> (all C (m1_orders_2(C,A,B) -> m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))))))) # label(dt_m1_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7595 (all A (v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k3_orders_2(A,C,B),C))))))) # label(t61_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7596 (all A (-v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (B = k1_xboole_0 -> (m1_orders_2(C,A,B) <-> C = k1_xboole_0)) & (B != k1_xboole_0 -> (m1_orders_2(C,A,B) <-> (exists D (r2_hidden(D,B) & C = k3_orders_2(A,B,D) & m1_subset_1(D,u1_struct_0(A)))))))))))) # label(d15_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7597 $T # label(t133_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7598 $T # label(t117_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7599 $T # label(t9_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7600 (all A (-v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(m1_orders_2(B,A,C) & m1_orders_2(C,A,B) & -(C = k1_xboole_0 & k1_xboole_0 = B)))))))) # label(t69_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7601 (all A (v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_orders_2(A,B,C) -> r1_tarski(k3_orders_2(A,D,B),k3_orders_2(A,D,C))))))))))) # label(t64_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7602 $T # label(t115_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7603 $T # label(t14_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7604 $T # label(t86_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7605 (all A (-v3_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_hidden(B,C) & r2_hidden(B,k2_orders_2(A,C))))))))) # label(t49_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7606 $T # label(t150_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7607 $T # label(t55_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7608 (all A all B all C (l1_orders_2(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & v2_orders_2(A) & -v3_struct_0(A) -> (r1_orders_2(A,B,C) <-> r3_orders_2(A,B,C)))) # label(redefinition_r3_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7609 $T # label(t139_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7610 $T # label(t5_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7611 (all A all B (-v3_struct_0(A) & l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> m1_subset_1(k1_orders_2(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k1_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7612 (all A (-v3_struct_0(A) & l1_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (m1_subset_1(k2_struct_0(A,B,C),k1_zfmisc_1(u1_struct_0(A))) & v5_orders_2(k2_struct_0(A,B,C),A) <-> r3_orders_2(A,B,C) | r3_orders_2(A,C,B)))))))) # label(t36_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7613 $T # label(t105_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7614 (all A (-v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_tarski(B,C) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r2_orders_2(A,D,E) & r2_hidden(E,B) -> r2_hidden(D,B)))))) & C != B & -m1_orders_2(B,A,C) & r2_wellord1(u1_orders_2(A),C)))))))) # label(t72_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7615 $T # label(t11_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7616 $T # label(t118_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7617 (all A (v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> a_2_1_orders_2(A,B) = k2_orders_2(A,B))))) # label(d13_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7618 $T # label(t41_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7619 $T # label(t111_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7620 $T # label(t59_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7621 (all A (v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> -r2_orders_2(A,C,B))) <-> r7_orders_1(u1_orders_2(A),B)))))) # label(t158_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7622 $T # label(t85_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7623 (all A (-v3_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) -> (all B (m1_orders_1(B,k1_orders_1(u1_struct_0(A))) -> (all C (m2_orders_2(C,A,B) -> (all D (m2_orders_2(D,A,B) -> (m1_orders_2(C,A,D) <-> r2_xboole_0(C,D)))))))))) # label(t84_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7624 (all A (l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -r2_hidden(B,k3_orders_2(A,C,B)))))))) # label(t62_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7625 (all A (-v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) -> u1_struct_0(A) = k1_orders_2(A,k1_pre_topc(A)))) # label(t43_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7626 (all A (v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (B != C -> r2_orders_2(A,C,B)))) <-> r8_orders_1(u1_orders_2(A),B)))))) # label(t160_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7627 $T # label(t106_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7628 (all A (v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_tarski(B,C) & r2_wellord1(u1_orders_2(A),C) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r2_hidden(E,B) & r2_hidden(D,C) & r2_orders_2(A,D,E) -> r2_hidden(D,B)))))) & -m1_orders_2(B,A,C) & C != B))))))) # label(t73_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7629 $T # label(t90_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7630 $T # label(t7_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7631 (all A all B (m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v4_relat_2(B) & v1_relat_2(B) -> v1_orders_2(g1_orders_2(A,B)) & v2_orders_2(g1_orders_2(A,B)) & v4_orders_2(g1_orders_2(A,B)) & v3_orders_2(g1_orders_2(A,B)))) # label(fc3_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7632 $T # label(t98_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7633 (all A all B all C (v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v2_orders_2(A) & -v3_struct_0(A) -> m1_subset_1(k3_orders_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k3_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7634 $T # label(t151_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.42 7635 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) -> (all B (m1_orders_1(B,k1_orders_1(u1_struct_0(A))) -> (all C (m2_orders_2(C,A,B) -> (all D (m2_orders_2(D,A,B) -> -r1_xboole_0(C,D))))))))) # label(t82_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7636 (all A (v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_orders_1(B,k1_orders_1(u1_struct_0(A))) -> k3_tarski(k4_orders_2(A,B)) != k1_xboole_0)))) # label(t87_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7637 $T # label(t93_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7638 $T # label(t4_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7639 (all A all B all C (l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & v2_orders_2(A) & -v3_struct_0(A) -> r3_orders_2(A,B,B))) # label(reflexivity_r3_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7640 (all A (-v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> v5_orders_2(k1_struct_0(A,B),A) & m1_subset_1(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))))))) # label(t35_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7641 (all A (v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_orders_2(A,B,C) & r2_orders_2(A,C,D) | r1_orders_2(A,C,D) & r2_orders_2(A,B,C) -> r2_orders_2(A,B,D)))))))))) # label(t32_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7642 $T # label(t104_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7643 $T # label(t18_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7644 $T # label(d7_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7645 $T # label(t12_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7646 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_hidden(B,k1_orders_2(A,C)) & r2_hidden(B,C)))))))) # label(t47_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7647 $T # label(t138_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7648 $T # label(t23_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7649 (all A (l1_orders_2(A) -> m2_relset_1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)))) # label(dt_u1_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7650 $T # label(t96_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7651 $T # label(t126_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7652 $T # label(t99_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7653 $T # label(t1_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7654 $T # label(t75_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7655 (all A (l1_orders_2(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_orders_2(A,B,C) & r1_orders_2(A,C,B) -> C = B))))))) # label(t25_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7656 (all A (l1_orders_2(A) -> (r4_relat_2(u1_orders_2(A),u1_struct_0(A)) <-> v4_orders_2(A)))) # label(d6_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7657 $T # label(t131_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7658 (all A (l1_orders_2(A) -> (v1_orders_2(A) -> g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = A))) # label(abstractness_v1_orders_2) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7659 (all A (-v1_xboole_0(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(k1_fraenkel(A,k1_numbers),k1_fraenkel(A,k1_numbers)),k1_fraenkel(A,k1_numbers)) & m2_relset_1(B,k2_zfmisc_1(k1_fraenkel(A,k1_numbers),k1_fraenkel(A,k1_numbers)),k1_fraenkel(A,k1_numbers)) & v1_funct_1(B) -> ((all C (m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers)) -> (all D (m2_fraenkel(D,A,k1_numbers,k1_fraenkel(A,k1_numbers)) -> k4_funcsdom(k1_numbers,A,k33_binop_2,C,D) = k1_funcsdom(A,k1_numbers,B,C,D))))) <-> B = k6_funcsdom(A)))))) # label(d2_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7660 (exists A (v5_rlvect_1(A) & (exists B ((exists C (m1_subset_1(C,u1_struct_0(A)) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (exists E (m1_subset_1(E,k1_numbers) & (exists F (m1_subset_1(F,k1_numbers) & D = k4_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,F)))))))) & (all D (m1_subset_1(D,k1_numbers) -> (all E (m1_subset_1(E,k1_numbers) -> (k4_rlvect_1(A,k3_rlvect_1(A,B,D),k3_rlvect_1(A,C,E)) = k1_rlvect_1(A) -> D = np__0 & E = np__0))))))) & m1_subset_1(B,u1_struct_0(A)))) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & v2_rlvect_1(A) & -v3_struct_0(A))) # label(t37_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7661 $T # label(t6_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7662 (all A (-v1_xboole_0(A) -> -v3_struct_0(k13_funcsdom(A)) & v1_funcsdom(k13_funcsdom(A)))) # label(fc3_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7663 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(k1_numbers,k1_fraenkel(A,k1_numbers)),k1_fraenkel(A,k1_numbers)) & v1_funct_2(B,k2_zfmisc_1(k1_numbers,k1_fraenkel(A,k1_numbers)),k1_fraenkel(A,k1_numbers)) & v1_funct_1(B) -> (B = k8_funcsdom(A) <-> (all C (m1_subset_1(C,k1_numbers) -> (all D (m2_fraenkel(D,A,k1_numbers,k1_fraenkel(A,k1_numbers)) -> (all E (m1_subset_1(E,A) -> k8_funct_2(A,k1_numbers,k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),B,k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),C,D)),E) = k4_real_1(C,k8_funct_2(A,k1_numbers,D,E))))))))))))) # label(d4_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7664 (all A all B all C (-v1_xboole_0(C) -> (all D (m2_fraenkel(D,C,k1_numbers,k1_fraenkel(C,k1_numbers)) -> (all E (m2_fraenkel(E,C,k1_numbers,k1_fraenkel(C,k1_numbers)) -> ((all F (r2_hidden(F,C) -> (A = F -> k1_funct_1(E,F) = np__0) & (F != A -> np__1 = k1_funct_1(E,F)))) & (all F (r2_hidden(F,C) -> (A = F -> k1_funct_1(D,F) = np__1) & (A != F -> np__0 = k1_funct_1(D,F)))) & k2_tarski(A,B) = C -> (all F (m2_fraenkel(F,C,k1_numbers,k1_fraenkel(C,k1_numbers)) -> (exists G (m1_subset_1(G,k1_numbers) & (exists H (m1_subset_1(H,k1_numbers) & F = k1_funcsdom(C,k1_numbers,k6_funcsdom(C),k2_funcsdom(C,k1_numbers,k1_numbers,k1_fraenkel(C,k1_numbers),k8_funcsdom(C),k1_domain_1(k1_numbers,k1_fraenkel(C,k1_numbers),G,D)),k2_funcsdom(C,k1_numbers,k1_numbers,k1_fraenkel(C,k1_numbers),k8_funcsdom(C),k1_domain_1(k1_numbers,k1_fraenkel(C,k1_numbers),H,E))))))))) | A = B))))))) # label(t31_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7665 (all A (l1_funcsdom(A) -> (v1_funcsdom(A) -> g1_funcsdom(u1_struct_0(A),u1_group_1(A),u1_rlvect_1(A),u2_rlvect_1(A),u1_vectsp_1(A),u2_struct_0(A)) = A))) # label(abstractness_v1_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7666 (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_2(D,B,A) & v1_funct_1(E) & v1_funct_2(E,B,A) & m1_relset_1(E,B,A) & m1_relset_1(D,B,A) & v1_funct_1(D) & v1_funct_1(C) & -v1_xboole_0(B) -> k3_funcop_1(C,D,E) = k4_funcsdom(A,B,C,D,E))) # label(redefinition_k4_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7667 $T # label(t1_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7668 (all A all B all C (-v1_xboole_0(C) -> (all D (m2_fraenkel(D,C,k1_numbers,k1_fraenkel(C,k1_numbers)) -> (all E (m2_fraenkel(E,C,k1_numbers,k1_fraenkel(C,k1_numbers)) -> (r2_hidden(A,C) & (all F (r2_hidden(F,C) -> (A = F -> k1_funct_1(D,F) = np__1) & (F != A -> np__0 = k1_funct_1(D,F)))) & (all F (r2_hidden(F,C) -> (F != A -> np__1 = k1_funct_1(E,F)) & (A = F -> k1_funct_1(E,F) = np__0))) & r2_hidden(B,C) -> B = A | (all F (m1_subset_1(F,k1_numbers) -> (all G (m1_subset_1(G,k1_numbers) -> (k9_funcsdom(C) = k1_funcsdom(C,k1_numbers,k6_funcsdom(C),k2_funcsdom(C,k1_numbers,k1_numbers,k1_fraenkel(C,k1_numbers),k8_funcsdom(C),k1_domain_1(k1_numbers,k1_fraenkel(C,k1_numbers),F,D)),k2_funcsdom(C,k1_numbers,k1_numbers,k1_fraenkel(C,k1_numbers),k8_funcsdom(C),k1_domain_1(k1_numbers,k1_fraenkel(C,k1_numbers),G,E))) -> np__0 = F & np__0 = G)))))))))))) # label(t29_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7669 (all A (-v1_xboole_0(A) -> g3_vectsp_1(k1_fraenkel(A,k1_numbers),k6_funcsdom(A),k7_funcsdom(A),k10_funcsdom(A),k9_funcsdom(A)) = k12_funcsdom(A))) # label(d12_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7670 (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(k1_fraenkel(A,B),k1_fraenkel(A,B)),k1_fraenkel(A,B)) & m1_subset_1(E,k1_fraenkel(A,B)) & m1_subset_1(D,k1_fraenkel(A,B)) & v1_funct_2(C,k2_zfmisc_1(k1_fraenkel(A,B),k1_fraenkel(A,B)),k1_fraenkel(A,B)) & -v1_xboole_0(A) -> m2_fraenkel(k1_funcsdom(A,B,C,D,E),A,B,k1_fraenkel(A,B)))) # label(dt_k1_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7671 (all A all B (-v1_xboole_0(B) -> (exists C ((exists D (m2_fraenkel(D,B,k1_numbers,k1_fraenkel(B,k1_numbers)) & (all E (r2_hidden(E,B) -> (E = A -> np__1 = k1_funct_1(C,E)) & (A != E -> np__0 = k1_funct_1(C,E)))) & (all E (r2_hidden(E,B) -> (E != A -> k1_funct_1(D,E) = np__1) & (A = E -> np__0 = k1_funct_1(D,E)))))) & m2_fraenkel(C,B,k1_numbers,k1_fraenkel(B,k1_numbers)))))) # label(t28_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7672 (all A (-v1_xboole_0(A) -> (all B (m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers)) -> (all C (m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers)) -> (all D (m1_subset_1(D,k1_numbers) -> k1_funcsdom(A,k1_numbers,k7_funcsdom(A),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),D,B)),C) = k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),D,k1_funcsdom(A,k1_numbers,k7_funcsdom(A),B,C))))))))))) # label(t27_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7673 (all A (-v1_xboole_0(A) -> v3_vectsp_1(k12_funcsdom(A)) & l3_vectsp_1(k12_funcsdom(A)))) # label(dt_k12_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7674 (all A (l1_funcsdom(A) -> l3_vectsp_1(A) & l2_rlvect_1(A))) # label(dt_l1_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7675 $T # label(t45_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7676 $T # label(d8_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7677 (all A (-v1_xboole_0(A) -> (all B (m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers)) -> (all C (m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers)) -> k1_funcsdom(A,k1_numbers,k6_funcsdom(A),C,B) = k1_funcsdom(A,k1_numbers,k6_funcsdom(A),B,C))))))) # label(t16_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7678 $T # label(t48_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7679 (all A (-v1_xboole_0(A) -> k11_funcsdom(A) = g2_rlvect_1(k1_fraenkel(A,k1_numbers),k9_funcsdom(A),k6_funcsdom(A),k8_funcsdom(A)))) # label(d7_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7680 (all A (-v1_xboole_0(A) -> (all B (m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers)) -> (all C (m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers)) -> (all D (m2_fraenkel(D,A,k1_numbers,k1_fraenkel(A,k1_numbers)) -> (B = k1_funcsdom(A,k1_numbers,k7_funcsdom(A),C,D) <-> (all E (m1_subset_1(E,A) -> k8_funct_2(A,k1_numbers,B,E) = k4_real_1(k8_funct_2(A,k1_numbers,C,E),k8_funct_2(A,k1_numbers,D,E))))))))))))) # label(t11_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7681 $T # label(t40_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7682 (all A (-v1_xboole_0(A) -> l1_funcsdom(k13_funcsdom(A)) & v1_funcsdom(k13_funcsdom(A)))) # label(dt_k13_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7683 $T # label(d9_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7684 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,u1_struct_0(k13_funcsdom(A))) -> (all C (m1_subset_1(C,u1_struct_0(k13_funcsdom(A))) -> (all D (m1_subset_1(D,u1_struct_0(k13_funcsdom(A))) -> (all E (m1_subset_1(E,k1_numbers) -> (all F (m1_subset_1(F,k1_numbers) -> k2_rlvect_1(k13_funcsdom(A),B,k1_rlvect_1(k13_funcsdom(A))) = B & k1_group_1(k13_funcsdom(A),k1_group_1(k13_funcsdom(A),B,C),D) = k1_group_1(k13_funcsdom(A),B,k1_group_1(k13_funcsdom(A),C,D)) & k2_rlvect_1(k13_funcsdom(A),k3_rlvect_1(k13_funcsdom(A),B,E),k3_rlvect_1(k13_funcsdom(A),C,E)) = k3_rlvect_1(k13_funcsdom(A),k2_rlvect_1(k13_funcsdom(A),B,C),E) & k3_rlvect_1(k13_funcsdom(A),B,k3_real_1(E,F)) = k2_rlvect_1(k13_funcsdom(A),k3_rlvect_1(k13_funcsdom(A),B,E),k3_rlvect_1(k13_funcsdom(A),B,F)) & k3_rlvect_1(k13_funcsdom(A),k3_rlvect_1(k13_funcsdom(A),B,F),E) = k3_rlvect_1(k13_funcsdom(A),B,k4_real_1(E,F)) & k1_group_1(k13_funcsdom(A),k3_rlvect_1(k13_funcsdom(A),B,E),C) = k3_rlvect_1(k13_funcsdom(A),k1_group_1(k13_funcsdom(A),B,C),E) & k2_rlvect_1(k13_funcsdom(A),k1_group_1(k13_funcsdom(A),B,C),k1_group_1(k13_funcsdom(A),B,D)) = k1_group_1(k13_funcsdom(A),B,k2_rlvect_1(k13_funcsdom(A),C,D)) & B = k1_group_1(k13_funcsdom(A),B,k2_group_1(k13_funcsdom(A))) & k1_group_1(k13_funcsdom(A),C,B) = k1_group_1(k13_funcsdom(A),B,C) & (exists G (m1_subset_1(G,u1_struct_0(k13_funcsdom(A))) & k1_rlvect_1(k13_funcsdom(A)) = k2_rlvect_1(k13_funcsdom(A),B,G))) & k2_rlvect_1(k13_funcsdom(A),k2_rlvect_1(k13_funcsdom(A),B,C),D) = k2_rlvect_1(k13_funcsdom(A),B,k2_rlvect_1(k13_funcsdom(A),C,D)) & k2_rlvect_1(k13_funcsdom(A),C,B) = k2_rlvect_1(k13_funcsdom(A),B,C))))))))))))) # label(t49_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7685 $T # label(t3_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7686 $T # label(d10_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7687 (all A (-v1_xboole_0(A) -> m2_fraenkel(k9_funcsdom(A),A,k1_numbers,k1_fraenkel(A,k1_numbers)))) # label(dt_k9_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7688 (all A (-v1_xboole_0(A) -> v1_funct_2(k6_funcsdom(A),k2_zfmisc_1(k1_fraenkel(A,k1_numbers),k1_fraenkel(A,k1_numbers)),k1_fraenkel(A,k1_numbers)) & m2_relset_1(k6_funcsdom(A),k2_zfmisc_1(k1_fraenkel(A,k1_numbers),k1_fraenkel(A,k1_numbers)),k1_fraenkel(A,k1_numbers)) & v1_funct_1(k6_funcsdom(A)))) # label(dt_k6_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7689 (all A (-v1_xboole_0(A) -> -v3_struct_0(k12_funcsdom(A)) & v3_rlvect_1(k12_funcsdom(A)) & v4_rlvect_1(k12_funcsdom(A)) & v6_rlvect_1(k12_funcsdom(A)) & v4_group_1(k12_funcsdom(A)) & v7_group_1(k12_funcsdom(A)) & v8_vectsp_1(k12_funcsdom(A)) & l3_vectsp_1(k12_funcsdom(A)) & v7_vectsp_1(k12_funcsdom(A)) & v6_vectsp_1(k12_funcsdom(A)) & v5_rlvect_1(k12_funcsdom(A)))) # label(t43_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7690 (exists A (v1_funcsdom(A) & l1_funcsdom(A))) # label(rc2_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7691 (all A (-v1_xboole_0(A) -> m2_relset_1(k8_funcsdom(A),k2_zfmisc_1(k1_numbers,k1_fraenkel(A,k1_numbers)),k1_fraenkel(A,k1_numbers)) & v1_funct_2(k8_funcsdom(A),k2_zfmisc_1(k1_numbers,k1_fraenkel(A,k1_numbers)),k1_fraenkel(A,k1_numbers)) & v1_funct_1(k8_funcsdom(A)))) # label(dt_k8_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7692 (all A all B all C all D all E (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & v1_funct_1(E) & m1_relset_1(E,B,A) & v1_funct_2(E,B,A) & m1_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> m2_fraenkel(k4_funcsdom(A,B,C,D,E),B,A,k1_fraenkel(B,A)))) # label(dt_k4_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7693 (all A all B all C (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> m2_fraenkel(k3_funcsdom(A,B,C),A,B,k1_fraenkel(A,B)))) # label(dt_k3_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.09/125.43 7694 (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) & v1_funct_2(E,k2_zfmisc_1(C,D),k1_fraenkel(A,B)) & m1_relset_1(E,k2_zfmisc_1(C,D),k1_fraenkel(A,B)) & m1_subset_1(F,k2_zfmisc_1(C,D)) & -v1_xboole_0(A) -> m2_fraenkel(k2_funcsdom(A,B,C,D,E,F),A,B,k1_fraenkel(A,B)))) # label(dt_k2_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7695 (all A all B all C all D all E (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(k1_fraenkel(A,B),k1_fraenkel(A,B)),k1_fraenkel(A,B)) & m1_relset_1(C,k2_zfmisc_1(k1_fraenkel(A,B),k1_fraenkel(A,B)),k1_fraenkel(A,B)) & m1_subset_1(E,k1_fraenkel(A,B)) & m1_subset_1(D,k1_fraenkel(A,B)) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k1_funcsdom(A,B,C,D,E) = k1_binop_1(C,D,E))) # label(redefinition_k1_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7696 (all A (-v1_xboole_0(A) -> (all B (m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers)) -> k1_funcsdom(A,k1_numbers,k7_funcsdom(A),k10_funcsdom(A),B) = B)))) # label(t20_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7697 (all A (-v1_xboole_0(A) -> (all B (m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers)) -> k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),np__1,B)) = B)))) # label(t23_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7698 (all A (-v1_xboole_0(A) -> (all B (m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers)) -> k9_funcsdom(A) = k1_funcsdom(A,k1_numbers,k6_funcsdom(A),B,k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),k1_real_1(np__1),B))))))) # label(t22_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7699 (all A (-v1_xboole_0(A) -> (all B (m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers)) -> (all C (m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers)) -> (all D (m2_fraenkel(D,A,k1_numbers,k1_fraenkel(A,k1_numbers)) -> k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),B,C),D) = k1_funcsdom(A,k1_numbers,k6_funcsdom(A),B,k1_funcsdom(A,k1_numbers,k6_funcsdom(A),C,D)))))))))) # label(t17_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7700 $T # label(t9_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7701 (all A (-v1_xboole_0(A) -> (all B (m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers)) -> (all C (m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers)) -> (all D (m2_fraenkel(D,A,k1_numbers,k1_fraenkel(A,k1_numbers)) -> k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k1_funcsdom(A,k1_numbers,k7_funcsdom(A),B,C),k1_funcsdom(A,k1_numbers,k7_funcsdom(A),B,D)) = k1_funcsdom(A,k1_numbers,k7_funcsdom(A),B,k1_funcsdom(A,k1_numbers,k6_funcsdom(A),C,D)))))))))) # label(t26_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7702 (all A (-v1_xboole_0(A) -> -v3_struct_0(k11_funcsdom(A)) & v2_rlvect_1(k11_funcsdom(A)) & v3_rlvect_1(k11_funcsdom(A)) & v5_rlvect_1(k11_funcsdom(A)) & l2_rlvect_1(k11_funcsdom(A)) & v7_rlvect_1(k11_funcsdom(A)) & v6_rlvect_1(k11_funcsdom(A)) & v4_rlvect_1(k11_funcsdom(A)))) # label(dt_k11_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7703 (all A all B all C all D all E all F (v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A) & m1_subset_1(F,A) & m1_subset_1(E,A) & m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all G all H all I all J all K all L (g1_funcsdom(A,B,C,D,E,F) = g1_funcsdom(G,H,I,J,K,L) -> H = B & J = D & K = E & L = F & I = C & G = A)))) # label(free_g1_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7704 (all A (l1_funcsdom(A) & -v3_struct_0(A) -> (v2_funcsdom(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,k1_numbers) -> (all F (m1_subset_1(F,k1_numbers) -> B = k1_group_1(A,B,k2_group_1(A)) & k1_group_1(A,k3_rlvect_1(A,B,E),C) = k3_rlvect_1(A,k1_group_1(A,B,C),E) & k2_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,E)) = k3_rlvect_1(A,k2_rlvect_1(A,B,C),E) & k3_rlvect_1(A,B,k4_real_1(E,F)) = k3_rlvect_1(A,k3_rlvect_1(A,B,F),E) & k2_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,B,F)) = k3_rlvect_1(A,B,k3_real_1(E,F)) & k2_rlvect_1(A,k1_group_1(A,B,C),k1_group_1(A,B,D)) = k1_group_1(A,B,k2_rlvect_1(A,C,D))))))))))))))) # label(d20_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7705 $T # label(t36_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7706 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> np__1 = k8_funct_2(A,k1_numbers,k10_funcsdom(A),B))))) # label(t12_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7707 (all A (-v1_xboole_0(A) -> (all B (m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers)) -> (all C (m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers)) -> (all D (m1_subset_1(D,k1_numbers) -> ((all E (m1_subset_1(E,A) -> k8_funct_2(A,k1_numbers,B,E) = k4_real_1(D,k8_funct_2(A,k1_numbers,C,E)))) <-> B = k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),D,C))))))))))) # label(t15_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7708 $T # label(d13_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7709 $T # label(t7_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7710 $T # label(t35_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7711 (all A (-v1_xboole_0(A) -> -v3_struct_0(g2_rlvect_1(k1_fraenkel(A,k1_numbers),k9_funcsdom(A),k6_funcsdom(A),k8_funcsdom(A))) & v4_rlvect_1(g2_rlvect_1(k1_fraenkel(A,k1_numbers),k9_funcsdom(A),k6_funcsdom(A),k8_funcsdom(A))) & v5_rlvect_1(g2_rlvect_1(k1_fraenkel(A,k1_numbers),k9_funcsdom(A),k6_funcsdom(A),k8_funcsdom(A))) & l2_rlvect_1(g2_rlvect_1(k1_fraenkel(A,k1_numbers),k9_funcsdom(A),k6_funcsdom(A),k8_funcsdom(A))) & v7_rlvect_1(g2_rlvect_1(k1_fraenkel(A,k1_numbers),k9_funcsdom(A),k6_funcsdom(A),k8_funcsdom(A))) & v6_rlvect_1(g2_rlvect_1(k1_fraenkel(A,k1_numbers),k9_funcsdom(A),k6_funcsdom(A),k8_funcsdom(A))) & v3_rlvect_1(g2_rlvect_1(k1_fraenkel(A,k1_numbers),k9_funcsdom(A),k6_funcsdom(A),k8_funcsdom(A))))) # label(t34_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7712 (all A (-v1_xboole_0(A) -> v2_group_1(k13_funcsdom(A)) & v1_funcsdom(k13_funcsdom(A)) & v8_vectsp_1(k13_funcsdom(A)) & v6_vectsp_1(k13_funcsdom(A)) & -v3_struct_0(k13_funcsdom(A)))) # label(fc4_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7713 $T # label(t8_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7714 (exists A l1_funcsdom(A)) # label(existence_l1_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7715 $T # label(t38_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7716 (exists A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v1_funcsdom(A) & v2_funcsdom(A) & v7_group_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & l1_funcsdom(A))) # label(rc4_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7717 (all A (-v1_xboole_0(A) -> v2_group_1(k12_funcsdom(A)) & v8_vectsp_1(k12_funcsdom(A)) & v6_vectsp_1(k12_funcsdom(A)) & v3_vectsp_1(k12_funcsdom(A)) & -v3_struct_0(k12_funcsdom(A)))) # label(fc2_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7718 $T # label(d14_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7719 $T # label(d11_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7720 (all A all B all C (-v1_xboole_0(C) -> -(k2_tarski(A,B) = C & B != A & (all D (m2_fraenkel(D,C,k1_numbers,k1_fraenkel(C,k1_numbers)) -> (all E (m2_fraenkel(E,C,k1_numbers,k1_fraenkel(C,k1_numbers)) -> -((all F (m2_fraenkel(F,C,k1_numbers,k1_fraenkel(C,k1_numbers)) -> (exists G (m1_subset_1(G,k1_numbers) & (exists H (m1_subset_1(H,k1_numbers) & F = k1_funcsdom(C,k1_numbers,k6_funcsdom(C),k2_funcsdom(C,k1_numbers,k1_numbers,k1_fraenkel(C,k1_numbers),k8_funcsdom(C),k1_domain_1(k1_numbers,k1_fraenkel(C,k1_numbers),G,D)),k2_funcsdom(C,k1_numbers,k1_numbers,k1_fraenkel(C,k1_numbers),k8_funcsdom(C),k1_domain_1(k1_numbers,k1_fraenkel(C,k1_numbers),H,E))))))))) & (all F (m1_subset_1(F,k1_numbers) -> (all G (m1_subset_1(G,k1_numbers) -> (k9_funcsdom(C) = k1_funcsdom(C,k1_numbers,k6_funcsdom(C),k2_funcsdom(C,k1_numbers,k1_numbers,k1_fraenkel(C,k1_numbers),k8_funcsdom(C),k1_domain_1(k1_numbers,k1_fraenkel(C,k1_numbers),F,D)),k2_funcsdom(C,k1_numbers,k1_numbers,k1_fraenkel(C,k1_numbers),k8_funcsdom(C),k1_domain_1(k1_numbers,k1_fraenkel(C,k1_numbers),G,E))) -> np__0 = F & G = np__0))))))))))))) # label(t33_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7721 (all A (-v1_xboole_0(A) -> (all B (m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers)) -> (all C (m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers)) -> (all D (m2_fraenkel(D,A,k1_numbers,k1_fraenkel(A,k1_numbers)) -> k1_funcsdom(A,k1_numbers,k7_funcsdom(A),k1_funcsdom(A,k1_numbers,k7_funcsdom(A),B,C),D) = k1_funcsdom(A,k1_numbers,k7_funcsdom(A),B,k1_funcsdom(A,k1_numbers,k7_funcsdom(A),C,D)))))))))) # label(t19_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7722 $T # label(t39_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7723 (all A all B all C all D all E all F (-v1_xboole_0(A) & -v1_xboole_0(B) & v1_funct_1(E) & m1_relset_1(E,k2_zfmisc_1(C,D),k1_fraenkel(A,B)) & m1_subset_1(F,k2_zfmisc_1(C,D)) & v1_funct_2(E,k2_zfmisc_1(C,D),k1_fraenkel(A,B)) & -v1_xboole_0(D) & -v1_xboole_0(C) -> k2_funcsdom(A,B,C,D,E,F) = k1_funct_1(E,F))) # label(redefinition_k2_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7724 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> np__0 = k8_funct_2(A,k1_numbers,k9_funcsdom(A),B))))) # label(t13_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7725 (all A all B all C all D all E (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(E) & v1_funct_2(E,B,A) & m1_relset_1(E,B,A) & m1_subset_1(D,A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & -v1_xboole_0(B) & -v1_xboole_0(A) -> m2_fraenkel(k5_funcsdom(A,B,C,D,E),B,A,k1_fraenkel(B,A)))) # label(dt_k5_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7726 $T # label(t5_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7727 (all A (-v1_xboole_0(A) -> v1_funct_1(k7_funcsdom(A)) & v1_funct_2(k7_funcsdom(A),k2_zfmisc_1(k1_fraenkel(A,k1_numbers),k1_fraenkel(A,k1_numbers)),k1_fraenkel(A,k1_numbers)) & m2_relset_1(k7_funcsdom(A),k2_zfmisc_1(k1_fraenkel(A,k1_numbers),k1_fraenkel(A,k1_numbers)),k1_fraenkel(A,k1_numbers)))) # label(dt_k7_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7728 $T # label(t2_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7729 $T # label(d17_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7730 (all A all B all C (-v1_xboole_0(C) -> -(r2_hidden(A,C) & r2_hidden(B,C) & (all D (m2_fraenkel(D,C,k1_numbers,k1_fraenkel(C,k1_numbers)) -> (all E (m2_fraenkel(E,C,k1_numbers,k1_fraenkel(C,k1_numbers)) -> (exists F (m1_subset_1(F,k1_numbers) & (exists G (m1_subset_1(G,k1_numbers) & k1_funcsdom(C,k1_numbers,k6_funcsdom(C),k2_funcsdom(C,k1_numbers,k1_numbers,k1_fraenkel(C,k1_numbers),k8_funcsdom(C),k1_domain_1(k1_numbers,k1_fraenkel(C,k1_numbers),F,D)),k2_funcsdom(C,k1_numbers,k1_numbers,k1_fraenkel(C,k1_numbers),k8_funcsdom(C),k1_domain_1(k1_numbers,k1_fraenkel(C,k1_numbers),G,E))) = k9_funcsdom(C) & -(F = np__0 & G = np__0))))))))) & A != B))) # label(t30_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7731 $T # label(d16_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7732 (all A (-v1_xboole_0(A) -> k10_funcsdom(A) = k2_funcop_1(A,np__1))) # label(d6_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7733 $T # label(t46_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7734 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(k1_fraenkel(A,k1_numbers),k1_fraenkel(A,k1_numbers)),k1_fraenkel(A,k1_numbers)) & v1_funct_2(B,k2_zfmisc_1(k1_fraenkel(A,k1_numbers),k1_fraenkel(A,k1_numbers)),k1_fraenkel(A,k1_numbers)) & v1_funct_1(B) -> (B = k7_funcsdom(A) <-> (all C (m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers)) -> (all D (m2_fraenkel(D,A,k1_numbers,k1_fraenkel(A,k1_numbers)) -> k4_funcsdom(k1_numbers,A,k35_binop_2,C,D) = k1_funcsdom(A,k1_numbers,B,C,D)))))))))) # label(d3_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7735 (all A (-v1_xboole_0(A) -> (all B (m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers)) -> (all C (m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers)) -> (all D (m2_fraenkel(D,A,k1_numbers,k1_fraenkel(A,k1_numbers)) -> (B = k1_funcsdom(A,k1_numbers,k6_funcsdom(A),C,D) <-> (all E (m1_subset_1(E,A) -> k8_funct_2(A,k1_numbers,B,E) = k3_real_1(k8_funct_2(A,k1_numbers,C,E),k8_funct_2(A,k1_numbers,D,E))))))))))))) # label(t10_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7736 (all A (-v1_xboole_0(A) -> v3_vectsp_1(k12_funcsdom(A)) & -v3_struct_0(k12_funcsdom(A)))) # label(fc1_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7737 (exists A (l1_funcsdom(A) & -v3_struct_0(A))) # label(rc3_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7738 (all A (-v1_xboole_0(A) -> (all B (m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers)) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_subset_1(D,k1_numbers) -> k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),k4_real_1(C,D),B)) = k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),C,k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),D,B)))))))))))) # label(t24_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7739 (all A (-v1_xboole_0(A) -> -v3_struct_0(k13_funcsdom(A)) & v5_rlvect_1(k13_funcsdom(A)) & v4_group_1(k13_funcsdom(A)) & v7_group_1(k13_funcsdom(A)) & l1_funcsdom(k13_funcsdom(A)) & v2_funcsdom(k13_funcsdom(A)) & v6_rlvect_1(k13_funcsdom(A)) & v4_rlvect_1(k13_funcsdom(A)) & v3_rlvect_1(k13_funcsdom(A)))) # label(t50_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7740 (all A (-v1_xboole_0(A) -> k9_funcsdom(A) != k10_funcsdom(A))) # label(t14_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7741 (all A all B all C (-v1_xboole_0(C) -> -(C = k2_tarski(A,B) & B != A & (all D (m2_fraenkel(D,C,k1_numbers,k1_fraenkel(C,k1_numbers)) -> (all E (m2_fraenkel(E,C,k1_numbers,k1_fraenkel(C,k1_numbers)) -> (exists F (m2_fraenkel(F,C,k1_numbers,k1_fraenkel(C,k1_numbers)) & (all G (m1_subset_1(G,k1_numbers) -> (all H (m1_subset_1(H,k1_numbers) -> F != k1_funcsdom(C,k1_numbers,k6_funcsdom(C),k2_funcsdom(C,k1_numbers,k1_numbers,k1_fraenkel(C,k1_numbers),k8_funcsdom(C),k1_domain_1(k1_numbers,k1_fraenkel(C,k1_numbers),G,D)),k2_funcsdom(C,k1_numbers,k1_numbers,k1_fraenkel(C,k1_numbers),k8_funcsdom(C),k1_domain_1(k1_numbers,k1_fraenkel(C,k1_numbers),H,E)))))))))))))))) # label(t32_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7742 (all A (-v1_xboole_0(A) -> (all B (m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers)) -> (all C (m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers)) -> k1_funcsdom(A,k1_numbers,k7_funcsdom(A),B,C) = k1_funcsdom(A,k1_numbers,k7_funcsdom(A),C,B))))))) # label(t18_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7743 (all A (-v1_xboole_0(A) -> k10_funcsdom(A) = k2_group_1(k12_funcsdom(A)))) # label(t41_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7744 (exists A (l3_vectsp_1(A) & -v3_struct_0(A) & v6_rlvect_1(A) & v4_group_1(A) & v3_vectsp_1(A) & v4_vectsp_1(A) & v6_vectsp_1(A) & v7_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A))) # label(rc1_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7745 (all A (-v1_xboole_0(A) -> g1_funcsdom(k1_fraenkel(A,k1_numbers),k7_funcsdom(A),k6_funcsdom(A),k8_funcsdom(A),k10_funcsdom(A),k9_funcsdom(A)) = k13_funcsdom(A))) # label(d19_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7746 (all A (-v1_xboole_0(A) -> m2_fraenkel(k10_funcsdom(A),A,k1_numbers,k1_fraenkel(A,k1_numbers)))) # label(dt_k10_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7747 $T # label(t47_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7748 (all A all B all C all D all E all F (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A) & m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A) & m1_subset_1(F,A) & m1_subset_1(E,A) & v1_funct_1(D) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> v1_funcsdom(g1_funcsdom(A,B,C,D,E,F)) & l1_funcsdom(g1_funcsdom(A,B,C,D,E,F)))) # label(dt_g1_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7749 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,u1_struct_0(k12_funcsdom(A))) -> (all C (m1_subset_1(C,u1_struct_0(k12_funcsdom(A))) -> (all D (m1_subset_1(D,u1_struct_0(k12_funcsdom(A))) -> k2_rlvect_1(k12_funcsdom(A),B,k1_rlvect_1(k12_funcsdom(A))) = B & (exists E (m1_subset_1(E,u1_struct_0(k12_funcsdom(A))) & k1_rlvect_1(k12_funcsdom(A)) = k2_rlvect_1(k12_funcsdom(A),B,E))) & k1_group_1(k12_funcsdom(A),C,B) = k1_group_1(k12_funcsdom(A),B,C) & k1_group_1(k12_funcsdom(A),k1_group_1(k12_funcsdom(A),B,C),D) = k1_group_1(k12_funcsdom(A),B,k1_group_1(k12_funcsdom(A),C,D)) & k1_group_1(k12_funcsdom(A),k2_rlvect_1(k12_funcsdom(A),C,D),B) = k2_rlvect_1(k12_funcsdom(A),k1_group_1(k12_funcsdom(A),C,B),k1_group_1(k12_funcsdom(A),D,B)) & k1_group_1(k12_funcsdom(A),B,k2_rlvect_1(k12_funcsdom(A),C,D)) = k2_rlvect_1(k12_funcsdom(A),k1_group_1(k12_funcsdom(A),B,C),k1_group_1(k12_funcsdom(A),B,D)) & k1_group_1(k12_funcsdom(A),k2_group_1(k12_funcsdom(A)),B) = B & k1_group_1(k12_funcsdom(A),B,k2_group_1(k12_funcsdom(A))) = B & k2_rlvect_1(k12_funcsdom(A),k2_rlvect_1(k12_funcsdom(A),B,C),D) = k2_rlvect_1(k12_funcsdom(A),B,k2_rlvect_1(k12_funcsdom(A),C,D)) & k2_rlvect_1(k12_funcsdom(A),C,B) = k2_rlvect_1(k12_funcsdom(A),B,C))))))))) # label(t42_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7750 (all A (-v1_xboole_0(A) -> (all B (m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers)) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_subset_1(D,k1_numbers) -> k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),C,B)),k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),D,B))) = k2_funcsdom(A,k1_numbers,k1_numbers,k1_fraenkel(A,k1_numbers),k8_funcsdom(A),k1_domain_1(k1_numbers,k1_fraenkel(A,k1_numbers),k3_real_1(C,D),B)))))))))) # label(t25_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7751 (all A (-v1_xboole_0(A) -> (all B (m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers)) -> k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k9_funcsdom(A),B) = B)))) # label(t21_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7752 (all A (-v1_xboole_0(A) -> k2_group_1(k13_funcsdom(A)) = k10_funcsdom(A))) # label(t44_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7753 $T # label(t4_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7754 (all A (-v1_xboole_0(A) -> k9_funcsdom(A) = k2_funcop_1(A,np__0))) # label(d5_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7755 $T # label(d18_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7756 (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) -> k3_funcsdom(A,B,C) = C)))))) # label(d1_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7757 (all A all B all C all D all E (-v1_xboole_0(A) & m1_subset_1(D,A) & m1_relset_1(E,B,A) & v1_funct_2(E,B,A) & v1_funct_1(E) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & -v1_xboole_0(B) -> k5_funcsdom(A,B,C,D,E) = k5_funcop_1(C,D,E))) # label(redefinition_k5_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7758 $T # label(d15_funcsdom) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7759 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,k18_rlvect_2(A)) -> k19_rlvect_2(A,B) = B)))) # label(d17_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7760 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(B) -> (v4_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (C = k6_rlvect_2(A,B) <-> (exists D (m2_finseq_1(D,u1_struct_0(A)) & B = k2_relat_1(D) & C = k9_rlvect_1(A,D) & v2_funct_1(D))))))))))) # label(d4_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7761 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlvect_2(B,A) -> (k11_rlvect_2(A) = B <-> k1_xboole_0 = k10_rlvect_2(A,B)))))) # label(d7_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7762 (all A (v3_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> k22_rlvect_2(A) = u2_rlvect_1(k23_rlvect_2(A)))) # label(t95_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7763 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v4_rlvect_1(A) -> u1_rlvect_1(k23_rlvect_2(A)) = k21_rlvect_2(A))) # label(t94_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7764 (all A all B all C (v5_rlvect_1(B) & v6_rlvect_1(B) & l2_rlvect_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v7_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (r2_hidden(A,a_2_1_rlvect_2(B,C)) <-> (exists D (D = A & m2_rlvect_2(D,B,C)))))) # label(fraenkel_a_2_1_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7765 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (all B (m1_rlvect_2(B,A) -> k10_rlvect_2(A,B) = a_2_0_rlvect_2(A,B))))) # label(d6_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7766 (all A (-v3_struct_0(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_rlvect_2(C,A) -> (all D (m1_rlvect_2(D,A) -> k5_real_1(k8_funct_2(u1_struct_0(A),k1_numbers,C,B),k8_funct_2(u1_struct_0(A),k1_numbers,D,B)) = k8_funct_2(u1_struct_0(A),k1_numbers,k17_rlvect_2(A,C,D),B))))))))) # label(t79_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7767 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_rlvect_2(C,A) -> (m2_rlvect_2(C,A,B) <-> r1_tarski(k10_rlvect_2(A,C),B)))))))) # label(d8_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7768 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k6_rlvect_2(A,k3_rlvect_2(A,C,B)) = k6_rlvect_1(A,k4_rlvect_1(A,k6_rlvect_2(A,C),k6_rlvect_2(A,B)),k6_rlvect_2(A,k2_rlvect_2(A,C,B))))))))) # label(t20_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7769 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_rlvect_2(C,A) -> (all D (m1_rlvect_2(D,A) -> (m2_rlvect_2(C,A,B) & m2_rlvect_2(D,A,B) -> m2_rlvect_2(k17_rlvect_2(A,C,D),A,B)))))))))) # label(t81_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7770 $T # label(t88_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7771 (all A all B all C (l1_struct_0(A) & v1_finset_1(B) & v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> B = k3_rlvect_2(A,B,B))) # label(idempotence_k3_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7772 (all A (-v3_struct_0(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(B) -> (all C (v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_xboole_0(C,B) -> k4_rlvect_1(A,k6_rlvect_2(A,C),k6_rlvect_2(A,B)) = k6_rlvect_2(A,k2_rlvect_2(A,C,B))))))))) # label(t18_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7773 (all A all B (-v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) -> k7_rlvect_2(A,B) = k1_tarski(B))) # label(redefinition_k7_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7774 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_rlvect_2(C,A) -> (m2_rlvect_2(C,A,B) -> m2_rlvect_2(k16_rlvect_2(A,C),A,B)))))))) # label(t76_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7775 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (B = k18_rlvect_2(A) <-> (all C (m1_rlvect_2(C,A) <-> r2_hidden(C,B))))))) # label(d16_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7776 $T # label(t39_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7777 (all A (-v3_struct_0(A) & l2_struct_0(A) -> (all B (m2_fraenkel(B,u1_struct_0(A),k1_numbers,k1_fraenkel(u1_struct_0(A),k1_numbers)) -> (m1_rlvect_2(B,A) <-> (exists C ((all D (m1_subset_1(D,u1_struct_0(A)) -> (-r2_hidden(D,C) -> np__0 = k8_funct_2(u1_struct_0(A),k1_numbers,B,D)))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(C)))))))) # label(d5_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7778 (all A all B all C (l1_struct_0(A) & v1_finset_1(B) & v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k2_rlvect_2(A,C,B) = k2_rlvect_2(A,B,C))) # label(commutativity_k2_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7779 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,u1_struct_0(A),k1_numbers) & v1_funct_2(B,u1_struct_0(A),k1_numbers) -> k12_rlvect_2(A,k6_finseq_1(u1_struct_0(A)),B) = k6_finseq_1(u1_struct_0(A)))))) # label(t41_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7780 $T # label(t29_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7781 (all A (l1_struct_0(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_funct_1(B) & v1_finset_1(B) & v1_membered(B) & v5_membered(B) & v4_membered(B) & v3_membered(B) & v2_membered(B) & v1_xboole_0(B))))) # label(rc1_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7782 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (v1_funct_1(D) & m2_relset_1(D,u1_struct_0(A),k1_numbers) & v1_funct_2(D,u1_struct_0(A),k1_numbers) -> k2_finseq_4(u1_struct_0(A),k3_rlvect_1(A,B,k8_funct_2(u1_struct_0(A),k1_numbers,D,B)),k3_rlvect_1(A,C,k8_funct_2(u1_struct_0(A),k1_numbers,D,C))) = k12_rlvect_2(A,k2_finseq_4(u1_struct_0(A),B,C),D))))))))) # label(t43_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7783 (all A (v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(C) -> k6_rlvect_1(A,k6_rlvect_2(A,k2_rlvect_2(A,C,B)),k6_rlvect_2(A,B)) = k6_rlvect_2(A,k4_rlvect_2(A,C,B)))))))) # label(t21_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7784 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),k1_numbers) & m2_relset_1(C,u1_struct_0(A),k1_numbers) -> k12_finseq_1(u1_struct_0(A),k3_rlvect_1(A,B,k8_funct_2(u1_struct_0(A),k1_numbers,C,B))) = k12_rlvect_2(A,k12_finseq_1(u1_struct_0(A),B),C))))))) # label(t42_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.43 7785 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlvect_2(B,A) -> r1_rlvect_2(A,k17_rlvect_2(A,B,B),k11_rlvect_2(A)))))) # label(t82_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7786 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) -> (all B (m1_rlvect_2(B,A) -> r1_rlvect_2(A,k16_rlvect_2(A,k16_rlvect_2(A,B)),B))))) # label(t77_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7787 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> m2_rlvect_2(k11_rlvect_2(A),A,B))))) # label(t34_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7788 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(B) -> (all C (v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k6_rlvect_1(A,k6_rlvect_2(A,C),k6_rlvect_2(A,k3_rlvect_2(A,C,B))) = k6_rlvect_2(A,k4_rlvect_2(A,C,B)))))))) # label(t22_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7789 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) -> -v1_xboole_0(k18_rlvect_2(A)))) # label(fc1_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7790 $T # label(dt_k18_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7791 $T # label(t72_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7792 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_rlvect_2(D,A) -> r1_rlvect_2(A,k15_rlvect_2(A,k3_real_1(B,C),D),k14_rlvect_2(A,k15_rlvect_2(A,B,D),k15_rlvect_2(A,C,D))))))))))) # label(t68_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7793 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_rlvect_2(C,A) -> (np__0 != B -> k10_rlvect_2(A,k15_rlvect_2(A,B,C)) = k10_rlvect_2(A,C)))))))) # label(t65_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7794 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> k1_rlvect_1(A) = k13_rlvect_2(A,k11_rlvect_2(A)))) # label(t48_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7795 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlvect_2(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> ((exists D (k9_rlvect_1(A,k12_rlvect_2(A,D,B)) = C & k2_relat_1(D) = k10_rlvect_2(A,B) & v2_funct_1(D) & m2_finseq_1(D,u1_struct_0(A)))) <-> C = k13_rlvect_2(A,B)))))))) # label(d10_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7796 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> k23_rlvect_2(A) = g2_rlvect_1(k18_rlvect_2(A),k20_rlvect_2(A,k11_rlvect_2(A)),k21_rlvect_2(A),k22_rlvect_2(A)))) # label(d21_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7797 (all A all B all C all D (m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_struct_0(A) & -v3_struct_0(A) -> k1_enumset1(B,C,D) = k9_rlvect_2(A,B,C,D))) # label(redefinition_k9_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7798 (all A all B all C (-v3_struct_0(B) & m1_rlvect_2(C,B) & l1_rlvect_1(B) -> (r2_hidden(A,a_2_0_rlvect_2(B,C)) <-> (exists D (D = A & np__0 != k8_funct_2(u1_struct_0(B),k1_numbers,C,D) & m1_subset_1(D,u1_struct_0(B))))))) # label(fraenkel_a_2_0_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7799 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (v2_rlvect_1(C) & m1_rlsub_1(C,k23_rlvect_2(A)) -> (u1_struct_0(C) = a_2_1_rlvect_2(A,B) <-> C = k24_rlvect_2(A,B)))))))) # label(d22_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7800 (all A all B (l1_rlvect_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(B) & -v3_struct_0(A) -> m1_subset_1(k6_rlvect_2(A,B),u1_struct_0(A)))) # label(dt_k6_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7801 $T # label(d2_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7802 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlvect_2(D,A) -> (k8_rlvect_2(A,B,C) = k10_rlvect_2(A,D) -> C = B | k13_rlvect_2(A,D) = k4_rlvect_1(A,k3_rlvect_1(A,B,k8_funct_2(u1_struct_0(A),k1_numbers,D,B)),k3_rlvect_1(A,C,k8_funct_2(u1_struct_0(A),k1_numbers,D,C)))))))))))) # label(t54_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7803 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (v1_funct_1(E) & m2_relset_1(E,u1_struct_0(A),k1_numbers) & v1_funct_2(E,u1_struct_0(A),k1_numbers) -> k3_finseq_4(u1_struct_0(A),k3_rlvect_1(A,B,k8_funct_2(u1_struct_0(A),k1_numbers,E,B)),k3_rlvect_1(A,C,k8_funct_2(u1_struct_0(A),k1_numbers,E,C)),k3_rlvect_1(A,D,k8_funct_2(u1_struct_0(A),k1_numbers,E,D))) = k12_rlvect_2(A,k3_finseq_4(u1_struct_0(A),B,C,D),E))))))))))) # label(t44_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7804 (all A all B all C (-v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_struct_0(A) -> k8_rlvect_2(A,B,C) = k8_rlvect_2(A,C,B))) # label(commutativity_k8_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7805 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> (all D (m2_finseq_1(D,u1_struct_0(A)) -> (k3_finseq_1(D) = k3_finseq_1(B) & (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (r2_hidden(E,k1_relat_1(B)) -> k4_rlvect_1(A,k4_finseq_4(k5_numbers,u1_struct_0(A),B,E),k4_finseq_4(k5_numbers,u1_struct_0(A),C,E)) = k1_funct_1(D,E)))) & k3_finseq_1(B) = k3_finseq_1(C) -> k9_rlvect_1(A,D) = k4_rlvect_1(A,k9_rlvect_1(A,B),k9_rlvect_1(A,C))))))))))) # label(t4_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7806 $T # label(t36_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7807 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlvect_2(B,A) -> (all C (m1_rlvect_2(C,A) -> k14_rlvect_2(A,B,k16_rlvect_2(A,C)) = k17_rlvect_2(A,B,C))))))) # label(d15_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7808 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_rlvect_2(C,A) -> (all D (m1_rlvect_2(D,A) -> r1_rlvect_2(A,k15_rlvect_2(A,B,k14_rlvect_2(A,C,D)),k14_rlvect_2(A,k15_rlvect_2(A,B,C),k15_rlvect_2(A,B,D))))))))))) # label(t69_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7809 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> u1_struct_0(k23_rlvect_2(A)) = k18_rlvect_2(A))) # label(t92_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7810 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_rlvect_2(B,A) -> (k10_rlvect_2(A,B) = k1_xboole_0 -> k13_rlvect_2(A,B) = k1_rlvect_1(A)))))) # label(t52_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7811 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m2_rlvect_2(C,A,k7_rlvect_2(A,B)) -> k13_rlvect_2(A,C) = k3_rlvect_1(A,B,k8_funct_2(u1_struct_0(A),k1_numbers,C,B)))))))) # label(t50_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7812 (all A all B all C (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & m1_subset_1(B,k1_numbers) & m1_rlvect_2(C,A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v4_rlvect_1(A) -> m1_rlvect_2(k15_rlvect_2(A,B,C),A))) # label(dt_k15_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7813 $T # label(t46_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7814 $T # label(t63_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7815 (all A (-v3_struct_0(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_rlvect_2(D,A) -> r1_rlvect_2(A,k15_rlvect_2(A,B,k15_rlvect_2(A,C,D)),k15_rlvect_2(A,k4_real_1(B,C),D)))))))))) # label(t70_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7816 (all A all B (v4_rlvect_1(A) & m1_rlvect_2(B,A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> m1_subset_1(k20_rlvect_2(A,B),k18_rlvect_2(A)))) # label(dt_k20_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7817 $T # label(t2_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7818 $T # label(d3_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7819 $T # label(t89_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7820 (all A (v3_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlvect_2(B,A) -> (all C (m1_rlvect_2(C,A) -> k14_rlvect_2(A,B,C) = k4_rlvect_1(k23_rlvect_2(A),k1_rlvect_2(k23_rlvect_2(A),B),k1_rlvect_2(k23_rlvect_2(A),C)))))))) # label(t96_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7821 (all A (l1_struct_0(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k1_rlvect_2(A,B))))) # label(t3_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7822 (all A all B (v4_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & m1_rlvect_2(B,A) & v7_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> m1_rlvect_2(k16_rlvect_2(A,B),A))) # label(dt_k16_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7823 (all A all B (-v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) -> v1_finset_1(k7_rlvect_2(A,B)) & m1_subset_1(k7_rlvect_2(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k7_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7824 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_rlvect_2(C,A) -> (all D (m1_rlvect_2(D,A) -> (m2_rlvect_2(C,A,B) & m2_rlvect_2(D,A,B) -> m2_rlvect_2(k14_rlvect_2(A,C,D),A,B)))))))))) # label(t59_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7825 (all A (v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlvect_2(B,A) -> r1_rlvect_2(A,k15_rlvect_2(A,np__0,B),k11_rlvect_2(A)))))) # label(t66_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7826 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_rlvect_1(A) & -v3_struct_0(A) -> (exists C m2_rlvect_2(C,A,B)))) # label(existence_m2_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7827 $T # label(t38_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7828 (all A all B all C (l1_struct_0(A) & v1_finset_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(C) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> m1_subset_1(k5_rlvect_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(k5_rlvect_2(A,B,C)))) # label(dt_k5_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7829 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> v2_rlvect_1(k23_rlvect_2(A)) & v4_rlvect_1(k23_rlvect_2(A)) & v5_rlvect_1(k23_rlvect_2(A)) & v7_rlvect_1(k23_rlvect_2(A)) & v6_rlvect_1(k23_rlvect_2(A)) & v3_rlvect_1(k23_rlvect_2(A)) & -v3_struct_0(k23_rlvect_2(A)))) # label(fc2_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7830 $T # label(t64_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7831 (all A (v3_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlvect_2(B,A) -> B = k20_rlvect_2(A,B))))) # label(d18_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7832 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlvect_2(B,A) -> r1_rlvect_2(A,k15_rlvect_2(A,np__1,B),B))))) # label(t71_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7833 (all A (l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> (all D (v1_funct_1(D) & v3_funct_2(D,k1_relat_1(B),k1_relat_1(B)) & m2_relset_1(D,k1_relat_1(B),k1_relat_1(B)) & v1_funct_2(D,k1_relat_1(B),k1_relat_1(B)) -> (C = k5_relat_1(D,B) -> k9_rlvect_1(A,C) = k9_rlvect_1(A,B)))))))))) # label(t9_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7834 (all A (-v3_struct_0(A) & l2_struct_0(A) -> (exists B m1_rlvect_2(B,A)))) # label(existence_m1_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7835 (all A all B all C (v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(B) & l1_struct_0(A) -> k3_xboole_0(B,C) = k3_rlvect_2(A,B,C))) # label(redefinition_k3_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7836 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_rlvect_2(B,A) -> r1_rlvect_2(A,k14_rlvect_2(A,k11_rlvect_2(A),B),B) & r1_rlvect_2(A,k14_rlvect_2(A,B,k11_rlvect_2(A)),B))))) # label(t62_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7837 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & -v3_struct_0(A) -> v1_funct_1(k21_rlvect_2(A)) & v1_funct_2(k21_rlvect_2(A),k2_zfmisc_1(k18_rlvect_2(A),k18_rlvect_2(A)),k18_rlvect_2(A)) & m2_relset_1(k21_rlvect_2(A),k2_zfmisc_1(k18_rlvect_2(A),k18_rlvect_2(A)),k18_rlvect_2(A)))) # label(dt_k21_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7838 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_rlvect_2(C,A) -> (k7_rlvect_2(A,B) = k10_rlvect_2(A,C) -> k13_rlvect_2(A,C) = k3_rlvect_1(A,B,k8_funct_2(u1_struct_0(A),k1_numbers,C,B))))))))) # label(t53_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7839 (all A all B all C (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & m1_rlvect_2(C,A) & m1_rlvect_2(B,A) & l2_rlvect_1(A) & v7_rlvect_1(A) & -v3_struct_0(A) -> m1_rlvect_2(k17_rlvect_2(A,B,C),A))) # label(dt_k17_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7840 $T # label(t45_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7841 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) -> (all B (m1_rlvect_2(B,A) -> (all C (m1_rlvect_2(C,A) -> k6_rlvect_1(k23_rlvect_2(A),k1_rlvect_2(k23_rlvect_2(A),B),k1_rlvect_2(k23_rlvect_2(A),C)) = k17_rlvect_2(A,B,C))))))) # label(t99_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7842 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k8_funct_2(u1_struct_0(A),k1_numbers,k11_rlvect_2(A),B) = np__0)))) # label(t30_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7843 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (all B (m1_rlvect_2(B,A) -> (all C (m1_rlvect_2(C,A) -> (all D (m1_rlvect_2(D,A) -> ((all E (m1_subset_1(E,u1_struct_0(A)) -> k3_real_1(k8_funct_2(u1_struct_0(A),k1_numbers,B,E),k8_funct_2(u1_struct_0(A),k1_numbers,C,E)) = k8_funct_2(u1_struct_0(A),k1_numbers,D,E))) <-> k14_rlvect_2(A,B,C) = D))))))))) # label(d12_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7844 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) -> (all B (v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(C) -> k4_rlvect_1(A,k6_rlvect_2(A,k4_rlvect_2(A,C,B)),k6_rlvect_2(A,k4_rlvect_2(A,B,C))) = k6_rlvect_2(A,k5_rlvect_2(A,C,B)))))))) # label(t24_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7845 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(C) -> k6_rlvect_2(A,k5_rlvect_2(A,C,B)) = k6_rlvect_1(A,k6_rlvect_2(A,k2_rlvect_2(A,C,B)),k6_rlvect_2(A,k3_rlvect_2(A,C,B))))))))) # label(t23_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7846 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m2_finseq_1(D,u1_struct_0(B)) -> (all E (v1_funct_1(E) & v1_funct_2(E,u1_struct_0(B),k1_numbers) & m2_relset_1(E,u1_struct_0(B),k1_numbers) -> (r2_hidden(A,k1_relat_1(D)) & k1_funct_1(D,A) = C -> k1_funct_1(k12_rlvect_2(B,D,E),A) = k3_rlvect_1(B,C,k8_funct_2(u1_struct_0(B),k1_numbers,E,C))))))))))))) # label(t40_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7847 $T # label(t90_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7848 $T # label(t13_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7849 (all A all B (v3_rlvect_1(A) & v4_rlvect_1(A) & m1_rlvect_2(B,A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> m1_subset_1(k13_rlvect_2(A,B),u1_struct_0(A)))) # label(dt_k13_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7850 $T # label(t91_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7851 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_rlvect_2(B,A) -> (all C (m1_rlvect_2(C,A) -> (r1_rlvect_2(A,k14_rlvect_2(A,B,C),k11_rlvect_2(A)) -> r1_rlvect_2(A,C,k16_rlvect_2(A,B))))))))) # label(t74_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7852 $T # label(t37_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7853 (all A all B (v4_rlvect_1(A) & m1_subset_1(B,k18_rlvect_2(A)) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> m1_rlvect_2(k19_rlvect_2(A,B),A))) # label(dt_k19_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7854 $T # label(t56_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7855 $T # label(t10_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7856 (all A (v3_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> (k3_finseq_1(B) = k3_finseq_1(C) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k1_relat_1(B)) -> k5_rlvect_1(A,k4_finseq_4(k5_numbers,u1_struct_0(A),B,D)) = k1_funct_1(C,D)))) -> k9_rlvect_1(A,C) = k5_rlvect_1(A,k9_rlvect_1(A,B))))))))) # label(t6_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7857 (all A all B (l1_struct_0(A) -> m1_subset_1(k1_rlvect_2(A,B),u1_struct_0(A)))) # label(dt_k1_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7858 $T # label(t86_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7859 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> k11_rlvect_2(A) = u2_struct_0(k23_rlvect_2(A)))) # label(t93_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7860 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m2_rlvect_2(D,A,B) -> (r1_tarski(B,C) -> m2_rlvect_2(D,A,C)))))))))) # label(t33_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7861 $T # label(t26_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7862 (all A all B all C all D (l1_struct_0(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & -v3_struct_0(A) -> v1_finset_1(k9_rlvect_2(A,B,C,D)) & m1_subset_1(k9_rlvect_2(A,B,C,D),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k9_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7863 (all A all B all C (v1_finset_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(C) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_struct_0(A) -> m1_subset_1(k3_rlvect_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(k3_rlvect_2(A,B,C)))) # label(dt_k3_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7864 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_rlvect_2(A,k7_rlvect_2(A,B)) = B)))) # label(t15_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7865 $T # label(t57_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7866 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) -> (all B (m1_rlvect_2(B,A) -> (all C (m1_rlvect_2(C,A) -> r1_tarski(k10_rlvect_2(A,k14_rlvect_2(A,B,C)),k2_rlvect_2(A,k10_rlvect_2(A,B),k10_rlvect_2(A,C))))))))) # label(t58_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7867 $T # label(t12_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7868 (all A all B all C (v1_finset_1(B) & v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_struct_0(A) -> m1_subset_1(k4_rlvect_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(k4_rlvect_2(A,B,C)))) # label(dt_k4_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7869 $T # label(t1_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7870 $T # label(t25_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7871 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m2_rlvect_2(C,A,B) -> r2_hidden(k13_rlvect_2(A,C),B))) <-> v1_rlsub_1(B,A) & B != k1_xboole_0))))) # label(t47_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7872 (all A all B all C (v1_finset_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(C) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_struct_0(A) -> k3_rlvect_2(A,B,C) = k3_rlvect_2(A,C,B))) # label(commutativity_k3_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7873 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_rlvect_2(C,A) -> k8_funct_2(u1_struct_0(A),k1_numbers,k16_rlvect_2(A,C),B) = k1_real_1(k8_funct_2(u1_struct_0(A),k1_numbers,C,B)))))))) # label(t73_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7874 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_rlvect_2(C,A) -> k3_rlvect_1(k23_rlvect_2(A),k1_rlvect_2(k23_rlvect_2(A),C),B) = k15_rlvect_2(A,B,C))))))) # label(t97_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7875 (all A all B all C (m1_rlvect_2(B,A) & m1_rlvect_2(C,A) & l1_rlvect_1(A) & -v3_struct_0(A) -> m1_rlvect_2(k14_rlvect_2(A,B,C),A))) # label(dt_k14_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7876 (all A all B (v4_rlvect_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> m1_rlsub_1(k24_rlvect_2(A,B),k23_rlvect_2(A)) & v2_rlvect_1(k24_rlvect_2(A,B)))) # label(dt_k24_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7877 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(C) & v1_finset_1(B) & l1_struct_0(A) -> k2_rlvect_2(A,B,C) = k2_xboole_0(B,C))) # label(redefinition_k2_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7878 $T # label(t85_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7879 (all A (v3_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(k1_numbers,k18_rlvect_2(A)),k18_rlvect_2(A)) & v1_funct_2(B,k2_zfmisc_1(k1_numbers,k18_rlvect_2(A)),k18_rlvect_2(A)) -> ((all C (m1_subset_1(C,k1_numbers) -> (all D (m1_subset_1(D,k18_rlvect_2(A)) -> k15_rlvect_2(A,C,k19_rlvect_2(A,D)) = k1_funct_1(B,k4_tarski(C,D)))))) <-> k22_rlvect_2(A) = B))))) # label(d20_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7880 $T # label(t87_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7881 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> k6_rlvect_2(A,k1_pre_topc(A)) = k1_rlvect_1(A))) # label(t14_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7882 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (C != B -> k4_rlvect_1(A,B,C) = k6_rlvect_2(A,k8_rlvect_2(A,B,C))))))))) # label(t16_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7883 (all A all B (m1_rlvect_2(B,A) & l1_rlvect_1(A) & -v3_struct_0(A) -> v1_finset_1(k10_rlvect_2(A,B)) & m1_subset_1(k10_rlvect_2(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k10_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7884 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> -(D != C & k6_rlvect_2(A,k9_rlvect_2(A,B,C,D)) != k4_rlvect_1(A,k4_rlvect_1(A,B,C),D) & B != D & B != C))))))))) # label(t17_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7885 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(C) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(B) & l1_struct_0(A) -> k5_rlvect_2(A,B,C) = k5_rlvect_2(A,C,B))) # label(commutativity_k5_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7886 (all A all B all C (l1_rlvect_1(A) & m1_rlvect_2(C,A) & m1_rlvect_2(B,A) & -v3_struct_0(A) -> r1_rlvect_2(A,B,B))) # label(reflexivity_r1_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7887 (all A all B all C (-v3_struct_0(A) & v6_rlvect_1(A) & m1_finseq_1(B,u1_struct_0(A)) & v1_funct_1(C) & m1_relset_1(C,u1_struct_0(A),k1_numbers) & v1_funct_2(C,u1_struct_0(A),k1_numbers) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> m2_finseq_1(k12_rlvect_2(A,B,C),u1_struct_0(A)))) # label(dt_k12_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7888 $T # label(t78_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7889 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_rlvect_2(D,A) -> (m2_rlvect_2(D,A,C) -> m2_rlvect_2(k15_rlvect_2(A,B,D),A,C)))))))))) # label(t67_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7890 (all A (-v3_struct_0(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> (all D (m2_finseq_1(D,u1_struct_0(A)) -> ((all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (r2_hidden(E,k1_relat_1(B)) -> k6_rlvect_1(A,k4_finseq_4(k5_numbers,u1_struct_0(A),B,E),k4_finseq_4(k5_numbers,u1_struct_0(A),C,E)) = k1_funct_1(D,E)))) & k3_finseq_1(D) = k3_finseq_1(B) & k3_finseq_1(B) = k3_finseq_1(C) -> k9_rlvect_1(A,D) = k6_rlvect_1(A,k9_rlvect_1(A,B),k9_rlvect_1(A,C))))))))))) # label(t7_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7891 (all A (l1_struct_0(A) -> (all B (r1_rlvect_1(A,B) -> B = k1_rlvect_2(A,B))))) # label(d1_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7892 (all A (l2_struct_0(A) & -v3_struct_0(A) -> (all B (m1_rlvect_2(B,A) -> m2_fraenkel(B,u1_struct_0(A),k1_numbers,k1_fraenkel(u1_struct_0(A),k1_numbers)))))) # label(dt_m1_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7893 (all A (v3_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> -v3_struct_0(k23_rlvect_2(A)) & v5_rlvect_1(k23_rlvect_2(A)) & v6_rlvect_1(k23_rlvect_2(A)) & l2_rlvect_1(k23_rlvect_2(A)) & v7_rlvect_1(k23_rlvect_2(A)) & v4_rlvect_1(k23_rlvect_2(A)) & v3_rlvect_1(k23_rlvect_2(A)))) # label(dt_k23_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7894 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(C) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(B) & l1_struct_0(A) -> k4_rlvect_2(A,B,C) = k4_xboole_0(B,C))) # label(redefinition_k4_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7895 (all A all B all C (-v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) -> k8_rlvect_2(A,B,C) = k2_tarski(B,C))) # label(redefinition_k8_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7896 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlvect_2(B,A) -> (all C (m1_rlvect_2(C,A) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> k8_funct_2(u1_struct_0(A),k1_numbers,C,D) = k8_funct_2(u1_struct_0(A),k1_numbers,B,D))) <-> r1_rlvect_2(A,B,C)))))))) # label(d11_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7897 $T # label(t31_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7898 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlvect_2(B,A) -> (all C (m1_rlvect_2(C,A) -> r1_tarski(k10_rlvect_2(A,k17_rlvect_2(A,B,C)),k2_rlvect_2(A,k10_rlvect_2(A,B),k10_rlvect_2(A,C))))))))) # label(t80_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7899 $T # label(t55_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7900 $T # label(t83_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7901 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m2_rlvect_2(B,A,k1_subset_1(u1_struct_0(A))) -> k13_rlvect_2(A,B) = k1_rlvect_1(A))))) # label(t49_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7902 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlvect_2(B,A) -> k10_rlvect_2(A,B) = k10_rlvect_2(A,k16_rlvect_2(A,B)))))) # label(t75_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7903 $T # label(t27_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7904 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_rlvect_2(B,A) -> k5_rlvect_1(k23_rlvect_2(A),k1_rlvect_2(k23_rlvect_2(A),B)) = k16_rlvect_2(A,B))))) # label(t98_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7905 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_rlvect_2(B,A) -> (all C (m1_rlvect_2(C,A) -> (all D (m1_rlvect_2(D,A) -> r1_rlvect_2(A,k14_rlvect_2(A,B,k14_rlvect_2(A,C,D)),k14_rlvect_2(A,k14_rlvect_2(A,B,C),D)))))))))) # label(t61_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7906 $T # label(t84_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7907 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (C != B -> (all D (m2_rlvect_2(D,A,k8_rlvect_2(A,B,C)) -> k13_rlvect_2(A,D) = k4_rlvect_1(A,k3_rlvect_1(A,B,k8_funct_2(u1_struct_0(A),k1_numbers,D,B)),k3_rlvect_1(A,C,k8_funct_2(u1_struct_0(A),k1_numbers,D,C)))))))))))) # label(t51_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7908 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> v1_funct_1(k22_rlvect_2(A)) & m2_relset_1(k22_rlvect_2(A),k2_zfmisc_1(k1_numbers,k18_rlvect_2(A)),k18_rlvect_2(A)) & v1_funct_2(k22_rlvect_2(A),k2_zfmisc_1(k1_numbers,k18_rlvect_2(A)),k18_rlvect_2(A)))) # label(dt_k22_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7909 (all A (v3_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> (all D (m2_finseq_1(D,u1_struct_0(A)) -> ((all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (r2_hidden(E,k1_relat_1(C)) -> k3_rlvect_1(A,k4_finseq_4(k5_numbers,u1_struct_0(A),C,E),B) = k1_funct_1(D,E)))) & k3_finseq_1(D) = k3_finseq_1(C) -> k9_rlvect_1(A,D) = k3_rlvect_1(A,k9_rlvect_1(A,C),B)))))))))) # label(t5_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7910 (all A all B (l1_rlvect_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v3_struct_0(A) -> (all C (m2_rlvect_2(C,A,B) -> m1_rlvect_2(C,A))))) # label(dt_m2_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7911 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (all B (m1_rlvect_2(B,A) -> (all C (m1_rlvect_2(C,A) -> r1_rlvect_2(A,k14_rlvect_2(A,B,C),k14_rlvect_2(A,C,B)))))))) # label(t60_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7912 (all A (v4_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlvect_2(B,A) -> k16_rlvect_2(A,B) = k15_rlvect_2(A,k1_real_1(np__1),B))))) # label(d14_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7913 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_rlvect_2(C,A) -> (all D (m1_rlvect_2(D,A) -> ((all E (m1_subset_1(E,u1_struct_0(A)) -> k8_funct_2(u1_struct_0(A),k1_numbers,D,E) = k4_real_1(B,k8_funct_2(u1_struct_0(A),k1_numbers,C,E)))) <-> k15_rlvect_2(A,B,C) = D))))))))) # label(d13_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7914 (all A all B all C (l1_struct_0(A) & v1_finset_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(C) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k2_rlvect_2(A,B,B) = B)) # label(idempotence_k2_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7915 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlvect_2(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (np__0 = k8_funct_2(u1_struct_0(A),k1_numbers,B,C) <-> -r2_hidden(C,k10_rlvect_2(A,B))))))))) # label(t28_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7916 (all A (v3_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(k18_rlvect_2(A),k18_rlvect_2(A)),k18_rlvect_2(A)) & v1_funct_2(B,k2_zfmisc_1(k18_rlvect_2(A),k18_rlvect_2(A)),k18_rlvect_2(A)) -> (B = k21_rlvect_2(A) <-> (all C (m1_subset_1(C,k18_rlvect_2(A)) -> (all D (m1_subset_1(D,k18_rlvect_2(A)) -> k2_binop_1(k18_rlvect_2(A),k18_rlvect_2(A),k18_rlvect_2(A),B,C,D) = k14_rlvect_2(A,k19_rlvect_2(A,C),k19_rlvect_2(A,D))))))))))) # label(d19_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7917 $T # label(t32_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7918 (all A all B all C (-v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> v1_finset_1(k8_rlvect_2(A,B,C)) & m1_subset_1(k8_rlvect_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k8_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7919 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & -v3_struct_0(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),k1_numbers) & v1_funct_2(C,u1_struct_0(A),k1_numbers) -> (all D (m2_finseq_1(D,u1_struct_0(A)) -> (D = k12_rlvect_2(A,B,C) <-> k3_finseq_1(B) = k3_finseq_1(D) & (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (r2_hidden(E,k1_relat_1(D)) -> k3_rlvect_1(A,k4_finseq_4(k5_numbers,u1_struct_0(A),B,E),k8_funct_2(u1_struct_0(A),k1_numbers,C,k4_finseq_4(k5_numbers,u1_struct_0(A),B,E))) = k1_funct_1(D,E))))))))))))) # label(d9_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7920 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(C) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(B) & l1_struct_0(A) -> v1_finset_1(k2_rlvect_2(A,B,C)) & m1_subset_1(k2_rlvect_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k2_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7921 (all A (l1_struct_0(A) & -v3_struct_0(A) -> (exists B (-v1_xboole_0(B) & v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc2_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7922 (all A all B all C (v1_finset_1(B) & v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_struct_0(A) -> k5_xboole_0(B,C) = k5_rlvect_2(A,B,C))) # label(redefinition_k5_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7923 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> m1_rlvect_2(k11_rlvect_2(A),A))) # label(dt_k11_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7924 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k6_rlvect_2(A,k2_rlvect_2(A,C,B)) = k6_rlvect_1(A,k4_rlvect_1(A,k6_rlvect_2(A,C),k6_rlvect_2(A,B)),k6_rlvect_2(A,k3_rlvect_2(A,C,B))))))))) # label(t19_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7925 (all A all B all C (l1_rlvect_1(A) & m1_rlvect_2(B,A) & m1_rlvect_2(C,A) & -v3_struct_0(A) -> (r1_rlvect_2(A,B,C) <-> B = C))) # label(redefinition_r1_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7926 $T # label(t11_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7927 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m2_rlvect_2(B,A,k1_subset_1(u1_struct_0(A))) -> k11_rlvect_2(A) = B)))) # label(t35_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7928 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> (all D (v1_funct_2(D,k1_relat_1(B),k1_relat_1(B)) & v3_funct_2(D,k1_relat_1(B),k1_relat_1(B)) & m2_relset_1(D,k1_relat_1(B),k1_relat_1(B)) & v1_funct_1(D) -> ((all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (r2_hidden(E,k1_relat_1(C)) -> k1_funct_1(B,k1_funct_1(D,E)) = k1_funct_1(C,E)))) & k3_finseq_1(C) = k3_finseq_1(B) -> k9_rlvect_1(A,C) = k9_rlvect_1(A,B)))))))))) # label(t8_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7929 (all A all B all C (-v3_struct_0(A) & m1_rlvect_2(C,A) & m1_rlvect_2(B,A) & l1_rlvect_1(A) -> (r1_rlvect_2(A,B,C) -> r1_rlvect_2(A,C,B)))) # label(symmetry_r1_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7930 (all A (v4_realset2(A) & l3_vectsp_1(A) -> (all B (m3_realset1(B,k2_realset2(A),k4_realset2(A)) -> (B = k5_realset2(A) <-> (exists C (m1_subset_1(C,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) & k1_realset2(k2_realset2(A),k3_realset2(A),B,k4_realset2(A),C) = A))))))) # label(d12_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7931 (all A (v4_realset2(A) & l3_vectsp_1(A) -> (all B (m1_subset_1(B,k2_realset2(A)) -> (all C (m1_subset_1(C,k2_realset2(A)) -> (all D (m1_subset_1(D,k2_realset2(A)) -> k1_funct_1(k5_realset2(A),k4_tarski(k1_funct_1(k3_realset2(A),k4_tarski(B,C)),D)) = k1_funct_1(k3_realset2(A),k4_tarski(k1_funct_1(k5_realset2(A),k4_tarski(B,D)),k1_funct_1(k5_realset2(A),k4_tarski(C,D)))) & k1_funct_1(k5_realset2(A),k4_tarski(B,k1_funct_1(k3_realset2(A),k4_tarski(C,D)))) = k1_funct_1(k3_realset2(A),k4_tarski(k1_funct_1(k5_realset2(A),k4_tarski(B,C)),k1_funct_1(k5_realset2(A),k4_tarski(B,D)))))))))))) # label(t3_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7932 (all A (v4_realset2(A) & l3_vectsp_1(A) -> m1_subset_1(k6_realset2(A),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))))) # label(dt_k6_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7933 (all A (l3_vectsp_1(A) & v4_realset2(A) -> (all B (m1_subset_1(B,k2_realset2(A)) -> (all C (m1_subset_1(C,k2_realset2(A)) -> k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),B,C) = k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),C,B))))))) # label(t5_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7934 (all A (v4_realset2(A) & l3_vectsp_1(A) -> (all B (m1_subset_1(B,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) -> (all C (m1_subset_1(C,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) -> m1_subset_1(k8_funct_2(k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k8_realset2(A),B),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) & m1_subset_1(k1_funct_1(k5_realset2(A),k4_tarski(B,C)),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))))))))) # label(t28_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7935 (all A (l3_vectsp_1(A) & v4_realset2(A) -> (all B (m1_subset_1(B,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) -> (all C (m1_subset_1(C,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) -> (all D (m1_subset_1(D,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) -> k1_funct_1(k5_realset2(A),k4_tarski(k1_funct_1(k5_realset2(A),k4_tarski(B,C)),D)) = k1_funct_1(k5_realset2(A),k4_tarski(B,k1_funct_1(k5_realset2(A),k4_tarski(C,D)))))))))))) # label(t8_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7936 (exists A (l3_vectsp_1(A) & -v3_realset2(A) & v3_vectsp_1(A))) # label(rc3_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7937 (exists A (l1_struct_0(A) & v3_realset2(A))) # label(rc2_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.44 7938 (all A (v4_realset2(A) & l3_vectsp_1(A) -> (all B (m1_subset_1(B,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) -> (exists C (k6_realset2(A) = k1_funct_1(k5_realset2(A),k4_tarski(B,C)) & k6_realset2(A) = k1_funct_1(k5_realset2(A),k4_tarski(C,B)) & m1_subset_1(C,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))))))))) # label(t11_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7939 (all A (l1_rlvect_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (exists C (k1_binop_1(u1_rlvect_1(A),B,C) = u2_struct_0(A) & k1_binop_1(u1_rlvect_1(A),C,B) = u2_struct_0(A) & m1_subset_1(C,u1_struct_0(A)))))) <-> v2_realset2(A)))) # label(d2_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7940 (all A (v4_realset2(A) & l3_vectsp_1(A) -> (all B (m1_subset_1(B,k2_realset2(A)) -> (all C (m1_subset_1(C,k2_realset2(A)) -> k1_funct_1(k5_realset2(A),k4_tarski(C,B)) = k1_funct_1(k5_realset2(A),k4_tarski(B,C)))))))) # label(t24_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7941 (all A (v4_realset2(A) & l3_vectsp_1(A) -> v1_funct_1(k7_realset2(A)) & m2_relset_1(k7_realset2(A),k2_realset2(A),k2_realset2(A)) & v1_funct_2(k7_realset2(A),k2_realset2(A),k2_realset2(A)))) # label(dt_k7_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7942 (all A (l3_vectsp_1(A) & v4_realset2(A) -> (all B (m1_subset_1(B,k2_realset2(A)) -> (all C (m1_subset_1(C,k2_realset2(A)) -> (all D (m1_subset_1(D,k2_realset2(A)) -> k1_funct_1(k5_realset2(A),k4_tarski(k1_funct_1(k5_realset2(A),k4_tarski(B,C)),D)) = k1_funct_1(k5_realset2(A),k4_tarski(B,k1_funct_1(k5_realset2(A),k4_tarski(C,D)))))))))))) # label(t23_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7943 (all A all B all C all D all E (-v1_realset1(A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & m1_subset_1(D,A) & m1_subset_1(E,k4_xboole_0(A,k5_realset1(A,D))) & v1_funct_1(C) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> -v3_realset2(k1_realset2(A,B,C,D,E)) & l3_vectsp_1(k1_realset2(A,B,C,D,E)) & v3_vectsp_1(k1_realset2(A,B,C,D,E)))) # label(dt_k1_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7944 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_binop_1(u1_rlvect_1(A),k1_binop_1(u1_rlvect_1(A),B,C),D) = k1_binop_1(u1_rlvect_1(A),B,k1_binop_1(u1_rlvect_1(A),C,D)))))))) <-> v4_rlvect_1(A)))) # label(d3_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7945 (all A (v4_realset2(A) & l3_vectsp_1(A) -> (all B (m1_subset_1(B,k2_realset2(A)) -> k4_realset2(A) = k1_funct_1(k5_realset2(A),k4_tarski(k4_realset2(A),B)))))) # label(t18_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7946 (all A (l3_vectsp_1(A) & v4_realset2(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 (m1_subset_1(D,B) -> (B = k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))) & D = k6_realset2(A) & C = k4_realset1(k2_realset2(A),k4_realset2(A),k5_realset2(A)) -> v4_rlvect_1(g1_rlvect_1(B,C,D)) & v1_realset2(g1_rlvect_1(B,C,D)) & v2_realset2(g1_rlvect_1(B,C,D)) & l1_rlvect_1(g1_rlvect_1(B,C,D)) & v3_rlvect_1(g1_rlvect_1(B,C,D)) & -v3_struct_0(g1_rlvect_1(B,C,D))))))))))) # label(t2_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7947 (all A (l3_vectsp_1(A) -> ((exists B (-v1_realset1(B) & (exists C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & (exists D ((exists E ((exists F ((all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,B) -> k1_funct_1(C,k4_tarski(k1_funct_1(E,k4_tarski(G,I)),k1_funct_1(E,k4_tarski(H,I)))) = k1_funct_1(E,k4_tarski(k1_funct_1(C,k4_tarski(G,H)),I)) & k1_funct_1(E,k4_tarski(G,k1_funct_1(C,k4_tarski(H,I)))) = k1_funct_1(C,k4_tarski(k1_funct_1(E,k4_tarski(G,H)),k1_funct_1(E,k4_tarski(G,I)))))))))) & (all G (-v1_xboole_0(G) -> (all H (v1_funct_1(H) & v1_funct_2(H,k2_zfmisc_1(G,G),G) & m2_relset_1(H,k2_zfmisc_1(G,G),G) -> (all I (m1_subset_1(I,G) -> (G = k4_xboole_0(B,k5_realset1(B,D)) & F = I & k4_realset1(B,D,E) = H -> v3_rlvect_1(g1_rlvect_1(G,H,I)) & v4_rlvect_1(g1_rlvect_1(G,H,I)) & v2_realset2(g1_rlvect_1(G,H,I)) & l1_rlvect_1(g1_rlvect_1(G,H,I)) & v1_realset2(g1_rlvect_1(G,H,I)) & -v3_struct_0(g1_rlvect_1(G,H,I))))))))) & l1_rlvect_1(g1_rlvect_1(B,C,D)) & v2_realset2(g1_rlvect_1(B,C,D)) & v1_realset2(g1_rlvect_1(B,C,D)) & v4_rlvect_1(g1_rlvect_1(B,C,D)) & v3_rlvect_1(g1_rlvect_1(B,C,D)) & -v3_struct_0(g1_rlvect_1(B,C,D)) & A = k1_realset2(B,C,E,D,F) & m1_subset_1(F,k4_xboole_0(B,k5_realset1(B,D))))) & m3_realset1(E,B,D))) & m1_subset_1(D,B))) & v1_funct_2(C,k2_zfmisc_1(B,B),B))))) <-> v4_realset2(A)))) # label(d8_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7948 (exists A (v4_realset2(A) & v3_vectsp_1(A) & l3_vectsp_1(A))) # label(rc4_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7949 (all A (l3_vectsp_1(A) & v4_realset2(A) -> (all B (m1_subset_1(B,k2_realset2(A)) -> (all C (m1_subset_1(C,k2_realset2(A)) -> (k4_realset2(A) = k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),B,C) -> C = k8_funct_2(k2_realset2(A),k2_realset2(A),k7_realset2(A),B)))))))) # label(t12_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7950 (all A (l3_vectsp_1(A) & v4_realset2(A) -> -v3_struct_0(g1_rlvect_1(k2_realset2(A),k3_realset2(A),k4_realset2(A))) & l1_rlvect_1(g1_rlvect_1(k2_realset2(A),k3_realset2(A),k4_realset2(A))) & v2_realset2(g1_rlvect_1(k2_realset2(A),k3_realset2(A),k4_realset2(A))) & v1_realset2(g1_rlvect_1(k2_realset2(A),k3_realset2(A),k4_realset2(A))) & v4_rlvect_1(g1_rlvect_1(k2_realset2(A),k3_realset2(A),k4_realset2(A))) & v3_rlvect_1(g1_rlvect_1(k2_realset2(A),k3_realset2(A),k4_realset2(A))))) # label(t1_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7951 (all A (v4_realset2(A) & l3_vectsp_1(A) -> (all B (m1_subset_1(B,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) -> (all C (m1_subset_1(C,k2_realset2(A)) -> (all D (m1_subset_1(D,k2_realset2(A)) -> (k1_funct_1(k5_realset2(A),k4_tarski(B,D)) = k1_funct_1(k5_realset2(A),k4_tarski(B,C)) -> D = C))))))))) # label(t30_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7952 (all A (l3_vectsp_1(A) & v4_realset2(A) -> (all B (m1_subset_1(B,k2_realset2(A)) -> (all C (m1_subset_1(C,k2_realset2(A)) -> (all D (m1_subset_1(D,k2_realset2(A)) -> k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),B,k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),C,D)) = k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),B,C),D))))))))) # label(t4_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7953 (all A (l3_vectsp_1(A) & v4_realset2(A) -> (all B (-v1_realset1(B) -> ((exists 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) & (exists D (m1_subset_1(D,B) & (exists E (m3_realset1(E,B,D) & (exists F (m1_subset_1(F,k4_xboole_0(B,k5_realset1(B,D))) & k1_realset2(B,C,E,D,F) = A)))))))) <-> k2_realset2(A) = B))))) # label(d9_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7954 (all A (v4_realset2(A) & l3_vectsp_1(A) -> (all B (m1_subset_1(B,k2_realset2(A)) -> k8_funct_2(k2_realset2(A),k2_realset2(A),k7_realset2(A),k8_funct_2(k2_realset2(A),k2_realset2(A),k7_realset2(A),B)) = B)))) # label(t13_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7955 (all A (l3_vectsp_1(A) & v4_realset2(A) -> (all B (m1_subset_1(B,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) -> (all C (m1_subset_1(C,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) -> k1_funct_1(k5_realset2(A),k4_tarski(B,C)) = k1_funct_1(k5_realset2(A),k4_tarski(C,B)))))))) # label(t9_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7956 (all A (l3_vectsp_1(A) & v4_realset2(A) -> (all B (m1_subset_1(B,k2_realset2(A)) -> (all C (m1_subset_1(C,k2_realset2(A)) -> (all D (m1_subset_1(D,k2_realset2(A)) -> (k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),B,D) = k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),B,C) -> D = C))))))))) # label(t29_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7957 (all A (l3_vectsp_1(A) & v4_realset2(A) -> k4_realset2(A) = k1_funct_1(k5_realset2(A),k4_tarski(k6_realset2(A),k4_realset2(A))))) # label(t20_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7958 (all A (v4_realset2(A) & l3_vectsp_1(A) -> v1_funct_1(k8_realset2(A)) & v1_funct_2(k8_realset2(A),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) & m2_relset_1(k8_realset2(A),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))))) # label(dt_k8_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7959 (all A (v4_realset2(A) & l3_vectsp_1(A) -> (all B (m1_subset_1(B,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) -> (all C (m1_subset_1(C,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) -> (k6_realset2(A) = k1_funct_1(k5_realset2(A),k4_tarski(B,C)) -> C = k8_funct_2(k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k8_realset2(A),B)))))))) # label(t26_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7960 (all A (v4_realset2(A) & l3_vectsp_1(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_realset2(A),k2_realset2(A)) & v1_funct_2(B,k2_realset2(A),k2_realset2(A)) -> ((all C (m1_subset_1(C,k2_realset2(A)) -> k1_funct_1(k3_realset2(A),k4_tarski(C,k8_funct_2(k2_realset2(A),k2_realset2(A),B,C))) = k4_realset2(A))) <-> B = k7_realset2(A)))))) # label(d14_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7961 (all A (v4_realset2(A) & l3_vectsp_1(A) -> v1_funct_1(k3_realset2(A)) & m2_relset_1(k3_realset2(A),k2_zfmisc_1(k2_realset2(A),k2_realset2(A)),k2_realset2(A)) & v1_funct_2(k3_realset2(A),k2_zfmisc_1(k2_realset2(A),k2_realset2(A)),k2_realset2(A)))) # label(dt_k3_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7962 (all A (v4_realset2(A) & l3_vectsp_1(A) -> (all B (m1_subset_1(B,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) -> (k1_realset2(k2_realset2(A),k3_realset2(A),k5_realset2(A),k4_realset2(A),B) = A <-> B = k6_realset2(A)))))) # label(d13_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7963 (exists A (-v3_struct_0(A) & v4_rlvect_1(A) & v2_realset2(A) & v1_realset2(A) & v3_rlvect_1(A) & v1_rlvect_1(A) & l1_rlvect_1(A))) # label(rc1_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7964 (all A (v4_realset2(A) & l3_vectsp_1(A) -> (all B (m1_subset_1(B,k2_realset2(A)) -> (all C (m1_subset_1(C,k2_realset2(A)) -> m1_subset_1(k1_funct_1(k5_realset2(A),k4_tarski(B,C)),k2_realset2(A)))))))) # label(t22_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7965 (all A (l1_rlvect_1(A) -> (v1_realset2(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k1_binop_1(u1_rlvect_1(A),B,u2_struct_0(A)) & k1_binop_1(u1_rlvect_1(A),u2_struct_0(A),B) = B))))) # label(d1_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7966 (all A (v4_realset2(A) & l3_vectsp_1(A) -> m1_subset_1(k4_realset2(A),k2_realset2(A)))) # label(dt_k4_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7967 (all A (l3_vectsp_1(A) & v4_realset2(A) -> k1_funct_1(k5_realset2(A),k4_tarski(k4_realset2(A),k6_realset2(A))) = k4_realset2(A))) # label(t21_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7968 (all A (l3_vectsp_1(A) & v4_realset2(A) -> (all B (m1_subset_1(B,k2_realset2(A)) -> (exists C (k4_realset2(A) = k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),B,C) & k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),C,B) = k4_realset2(A) & m1_subset_1(C,k2_realset2(A)))))))) # label(t7_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7969 (all A (l1_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> B = C)))) <-> v3_realset2(A)))) # label(d7_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7970 (all A (l3_vectsp_1(A) & v4_realset2(A) -> (all B (m1_subset_1(B,k2_realset2(A)) -> k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),B,k4_realset2(A)) = B & k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),k4_realset2(A),B) = B)))) # label(t6_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7971 (all A (-v1_realset1(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,k4_xboole_0(A,k5_realset1(A,D))) -> (all F (v3_vectsp_1(F) & -v3_realset2(F) & l3_vectsp_1(F) -> (u1_rlvect_1(F) = B & u1_vectsp_1(F) = E & D = u2_struct_0(F) & C = u1_group_1(F) & A = u1_struct_0(F) <-> k1_realset2(A,B,C,D,E) = F))))))))))))) # label(d6_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7972 (all A (v4_realset2(A) & l3_vectsp_1(A) -> (all B (m1_subset_1(B,k2_realset2(A)) -> (all C (m1_subset_1(C,k2_realset2(A)) -> (all D (m1_subset_1(D,k2_realset2(A)) -> k1_funct_1(k5_realset2(A),k4_tarski(B,k1_funct_1(k3_realset2(A),k4_tarski(C,k8_funct_2(k2_realset2(A),k2_realset2(A),k7_realset2(A),D))))) = k1_funct_1(k3_realset2(A),k4_tarski(k1_funct_1(k5_realset2(A),k4_tarski(B,C)),k1_funct_1(k7_realset2(A),k1_funct_1(k5_realset2(A),k4_tarski(B,D))))))))))))) # label(t15_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7973 (all A (l3_vectsp_1(A) & v4_realset2(A) -> (all B (m1_subset_1(B,k2_realset2(A)) -> k1_funct_1(k5_realset2(A),k4_tarski(B,k4_realset2(A))) = k4_realset2(A))))) # label(t17_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7974 (all A (v4_realset2(A) & l3_vectsp_1(A) -> m3_realset1(k5_realset2(A),k2_realset2(A),k4_realset2(A)))) # label(dt_k5_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7975 (all A (l3_vectsp_1(A) & v4_realset2(A) -> (all B (m1_subset_1(B,k2_realset2(A)) -> (all C (m1_subset_1(C,k2_realset2(A)) -> (all D (m1_subset_1(D,k2_realset2(A)) -> k1_funct_1(k3_realset2(A),k4_tarski(k1_funct_1(k5_realset2(A),k4_tarski(B,D)),k1_funct_1(k7_realset2(A),k1_funct_1(k5_realset2(A),k4_tarski(C,D))))) = k1_funct_1(k5_realset2(A),k4_tarski(k1_funct_1(k3_realset2(A),k4_tarski(B,k8_funct_2(k2_realset2(A),k2_realset2(A),k7_realset2(A),C))),D)))))))))) # label(t16_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7976 (all A (l3_vectsp_1(A) & v4_realset2(A) -> -v1_realset1(k2_realset2(A)))) # label(dt_k2_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7977 (all A (v4_realset2(A) & l3_vectsp_1(A) -> (all B (m1_subset_1(B,k2_realset2(A)) -> (k4_realset2(A) = B <-> (exists C (m3_realset1(C,k2_realset2(A),B) & (exists D (k1_realset2(k2_realset2(A),k3_realset2(A),C,B,D) = A & m1_subset_1(D,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),B)))))))))))) # label(d11_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7978 (all A (l3_vectsp_1(A) & v4_realset2(A) -> (all B (m1_subset_1(B,k2_realset2(A)) -> (all C (m1_subset_1(C,k2_realset2(A)) -> m1_subset_1(k1_funct_1(k3_realset2(A),k4_tarski(B,C)),k2_realset2(A)) & m1_subset_1(k8_funct_2(k2_realset2(A),k2_realset2(A),k7_realset2(A),B),k2_realset2(A)) & m1_subset_1(k1_funct_1(k5_realset2(A),k4_tarski(B,C)),k2_realset2(A)))))))) # label(t14_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7979 (all A (l3_vectsp_1(A) & v4_realset2(A) -> (all B (m1_subset_1(B,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) -> B = k1_funct_1(k5_realset2(A),k4_tarski(k6_realset2(A),B)) & k1_funct_1(k5_realset2(A),k4_tarski(B,k6_realset2(A))) = B)))) # label(t10_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7980 (all A (v4_realset2(A) & l3_vectsp_1(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(k2_realset2(A),k2_realset2(A)),k2_realset2(A)) & m2_relset_1(B,k2_zfmisc_1(k2_realset2(A),k2_realset2(A)),k2_realset2(A)) & v1_funct_1(B) -> ((exists C ((exists D (m3_realset1(D,k2_realset2(A),C) & (exists E (m1_subset_1(E,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),C))) & k1_realset2(k2_realset2(A),B,D,C,E) = A)))) & m1_subset_1(C,k2_realset2(A)))) <-> k3_realset2(A) = B))))) # label(d10_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7981 (all A (l3_vectsp_1(A) & v4_realset2(A) -> (all B (m1_subset_1(B,k2_realset2(A)) -> B = k1_funct_1(k5_realset2(A),k4_tarski(B,k6_realset2(A))) & B = k1_funct_1(k5_realset2(A),k4_tarski(k6_realset2(A),B)))))) # label(t25_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7982 (all A (v4_realset2(A) & l3_vectsp_1(A) -> (all B (m1_subset_1(B,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) -> k8_funct_2(k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k8_realset2(A),k8_funct_2(k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k8_realset2(A),B)) = B)))) # label(t27_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7983 (all A (l3_vectsp_1(A) & v4_realset2(A) -> (all B (m1_subset_1(B,k2_realset2(A)) -> (all C (m1_subset_1(C,k2_realset2(A)) -> k1_funct_1(k5_realset2(A),k4_tarski(B,k8_funct_2(k2_realset2(A),k2_realset2(A),k7_realset2(A),C))) = k1_funct_1(k7_realset2(A),k1_funct_1(k5_realset2(A),k4_tarski(B,C))))))))) # label(t19_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7984 (all A (l1_struct_0(A) -> (v1_realset1(u1_struct_0(A)) <-> v3_realset2(A)))) # label(d5_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7985 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_binop_1(u1_rlvect_1(A),C,B) = k1_binop_1(u1_rlvect_1(A),B,C))))) <-> v3_rlvect_1(A)))) # label(d4_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7986 (all A (l3_vectsp_1(A) & v4_realset2(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) & v1_funct_2(B,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) -> ((all C (m1_subset_1(C,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) -> k1_funct_1(k5_realset2(A),k4_tarski(C,k8_funct_2(k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),B,C))) = k6_realset2(A))) <-> k8_realset2(A) = B))))) # label(d15_realset2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7987 (all A all B all C (v8_metric_1(A) & l1_metric_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> k2_metric_1(A,B,C) = k4_metric_1(A,B,C))) # label(redefinition_k4_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7988 (all A all B all C (l1_metric_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> m1_subset_1(k2_metric_1(A,B,C),k1_numbers))) # label(dt_k2_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7989 (all A all B all C (v8_metric_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_metric_1(A) -> m1_subset_1(k4_metric_1(A,B,C),k1_numbers))) # label(dt_k4_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7990 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_metric_1(A,B,C) = k1_metric_1(u1_struct_0(A),u1_struct_0(A),u1_metric_1(A),B,C))))))) # label(d1_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7991 (all A all B all C all D all E (v1_funct_1(C) & m1_relset_1(C,k2_zfmisc_1(A,B),k1_numbers) & m1_subset_1(E,B) & m1_subset_1(D,A) -> k1_binop_1(C,D,E) = k1_metric_1(A,B,C,D,E))) # label(redefinition_k1_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7992 $T # label(t7_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7993 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers) & m1_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) -> l1_metric_1(g1_metric_1(A,B)) & v1_metric_1(g1_metric_1(A,B)))) # label(dt_g1_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7994 (all A (v1_xreal_0(A) -> (all B (-v3_struct_0(B) & l1_metric_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k10_metric_1(B,C,A) = a_3_1_metric_1(A,B,C))))))) # label(t19_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7995 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_1(B) -> ((all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> k1_metric_1(A,A,B,D,C) = k1_metric_1(A,A,B,C,D))))) <-> v4_metric_1(B,A)))) # label(d5_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7996 (exists A (l1_metric_1(A) & v9_metric_1(A) & v8_metric_1(A) & v7_metric_1(A) & v6_metric_1(A) & v1_metric_1(A) & -v3_struct_0(A))) # label(rc3_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7997 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v1_xreal_0(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (-v3_struct_0(A) -> ((exists E (-v3_struct_0(E) & l1_metric_1(E) & (exists F (B = F & D = a_3_1_metric_1(C,E,F) & E = A & m1_subset_1(F,u1_struct_0(E)))))) <-> D = k10_metric_1(A,B,C))) & (v3_struct_0(A) -> (D = k10_metric_1(A,B,C) <-> v1_xboole_0(D))))))))))) # label(d16_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7998 (all A (-v1_xboole_0(A) -> v1_metric_1(k6_metric_1(A)) & -v3_struct_0(k6_metric_1(A)))) # label(fc1_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 7999 (all A (l1_metric_1(A) -> (v4_metric_1(u1_metric_1(A),u1_struct_0(A)) <-> v8_metric_1(A)))) # label(d9_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8000 (all A (v1_xreal_0(A) -> (all B (l1_metric_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (-v3_struct_0(B) & -r1_xreal_0(A,k2_metric_1(B,C,D)) <-> r2_hidden(D,k9_metric_1(B,C,A))))))))))) # label(t12_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8001 (all A (v1_xreal_0(A) -> (all B (l1_metric_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> r1_tarski(k11_metric_1(B,C,A),k10_metric_1(B,C,A)))))))) # label(t16_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8002 (all A (v1_xreal_0(A) -> (all B (l1_metric_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (r1_xreal_0(k2_metric_1(B,C,D),A) & -v3_struct_0(B) <-> r2_hidden(D,k10_metric_1(B,C,A))))))))))) # label(t13_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8003 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_1(B) -> ((all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> r1_xreal_0(k1_metric_1(A,A,B,C,E),k3_real_1(k1_metric_1(A,A,B,C,D),k1_metric_1(A,A,B,D,E))))))))) <-> v5_metric_1(B,A)))) # label(d6_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8004 (exists A (l1_metric_1(A) & v1_metric_1(A))) # label(rc1_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8005 (all A (l1_metric_1(A) -> l1_struct_0(A))) # label(dt_l1_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8006 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_1(B) -> ((all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (k1_metric_1(A,A,B,C,D) = np__0 -> D = C))))) <-> v3_metric_1(B,A)))) # label(d4_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8007 (all A (v1_xreal_0(A) -> (all B (l1_metric_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> r1_tarski(k9_metric_1(B,C,A),k10_metric_1(B,C,A)))))))) # label(t15_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8008 (all A (v1_xreal_0(A) -> (all B (-v3_struct_0(B) & l1_metric_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> a_3_2_metric_1(A,B,C) = k11_metric_1(B,C,A))))))) # label(t20_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8009 (exists A (v1_metric_1(A) & -v3_struct_0(A) & l1_metric_1(A))) # label(rc2_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8010 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v1_xreal_0(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (v3_struct_0(A) -> (v1_xboole_0(D) <-> k11_metric_1(A,B,C) = D)) & (-v3_struct_0(A) -> (D = k11_metric_1(A,B,C) <-> (exists E (l1_metric_1(E) & (exists F (m1_subset_1(F,u1_struct_0(E)) & a_3_2_metric_1(C,E,F) = D & F = B & A = E)) & -v3_struct_0(E))))))))))))) # label(d17_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8011 (all A k6_metric_1(A) = g1_metric_1(A,k5_metric_1(A))) # label(d12_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8012 (all A (l1_metric_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> r1_xreal_0(k2_metric_1(A,B,D),k3_real_1(k2_metric_1(A,B,C),k2_metric_1(A,C,D))))))))) <-> v9_metric_1(A)))) # label(t4_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8013 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> k1_metric_1(k1_numbers,k1_numbers,k7_metric_1,A,B) = k1_metric_1(k1_numbers,k1_numbers,k7_metric_1,B,A))))) # label(t10_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8014 (all A (l1_metric_1(k6_metric_1(A)) & v1_metric_1(k6_metric_1(A)))) # label(dt_k6_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8015 (all A all B all C (v8_metric_1(A) & l1_metric_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> k4_metric_1(A,C,B) = k4_metric_1(A,B,C))) # label(commutativity_k4_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8016 (all A (l1_metric_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> r1_xreal_0(k2_metric_1(A,B,D),k3_real_1(k2_metric_1(A,B,C),k2_metric_1(A,C,D))) & k2_metric_1(A,C,B) = k2_metric_1(A,B,C) & (B = C -> np__0 = k2_metric_1(A,B,C)) & (np__0 = k2_metric_1(A,B,C) -> B = C))))))) -> l1_metric_1(A) & v9_metric_1(A) & v8_metric_1(A) & v7_metric_1(A) & v6_metric_1(A)))) # label(t6_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8017 (all A (l1_metric_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> k2_metric_1(A,B,B) = np__0)) <-> v6_metric_1(A)))) # label(t1_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8018 (all A (v1_xreal_0(A) -> (all B (l1_metric_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k4_subset_1(u1_struct_0(B),k11_metric_1(B,C,A),k9_metric_1(B,C,A)) = k10_metric_1(B,C,A))))))) # label(t17_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8019 (all A (l1_metric_1(A) -> v1_funct_1(u1_metric_1(A)) & m2_relset_1(u1_metric_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_numbers) & v1_funct_2(u1_metric_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_numbers))) # label(dt_u1_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8020 (all A (v6_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) & v8_metric_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r1_xreal_0(np__0,k4_metric_1(A,B,C)))))))) # label(t5_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8021 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_1(B) -> (v2_metric_1(B,A) <-> (all C (m1_subset_1(C,A) -> np__0 = k1_metric_1(A,A,B,C,C)))))) # label(d3_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8022 (all A (v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) -> (k7_metric_1 = A <-> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> k1_metric_1(k1_numbers,k1_numbers,A,B,C) = k18_complex1(k5_real_1(B,C))))))))) # label(d13_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8023 (all A all B all C all D all E (m1_relset_1(C,k2_zfmisc_1(A,B),k1_numbers) & m1_subset_1(D,A) & m1_subset_1(E,B) & v1_funct_1(C) -> m1_subset_1(k1_metric_1(A,B,C,D,E),k1_numbers))) # label(dt_k1_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8024 (all A all B all C all D (-v3_struct_0(C) & m1_subset_1(D,u1_struct_0(C)) & l1_metric_1(C) & v1_xreal_0(B) -> ((exists E (m1_subset_1(E,u1_struct_0(C)) & -r1_xreal_0(B,k2_metric_1(C,D,E)) & A = E)) <-> r2_hidden(A,a_3_0_metric_1(B,C,D))))) # label(fraenkel_a_3_0_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8025 (all A all B all C (l1_metric_1(A) & v1_xreal_0(C) & m1_subset_1(B,u1_struct_0(A)) -> m1_subset_1(k11_metric_1(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k11_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8026 (all A (l1_metric_1(A) -> (v3_metric_1(u1_metric_1(A),u1_struct_0(A)) <-> v7_metric_1(A)))) # label(d8_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8027 (exists A l1_metric_1(A)) # label(existence_l1_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8028 (all A (l1_metric_1(A) -> (v9_metric_1(A) <-> v5_metric_1(u1_metric_1(A),u1_struct_0(A))))) # label(d10_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8029 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (A = B <-> k1_metric_1(k1_numbers,k1_numbers,k7_metric_1,A,B) = np__0))))) # label(t9_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8030 (all A all B all C (v1_xreal_0(C) & m1_subset_1(B,u1_struct_0(A)) & l1_metric_1(A) -> m1_subset_1(k9_metric_1(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k9_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8031 (all A all B all C all D (m1_subset_1(D,u1_struct_0(C)) & l1_metric_1(C) & -v3_struct_0(C) & v1_xreal_0(B) -> (r2_hidden(A,a_3_1_metric_1(B,C,D)) <-> (exists E (A = E & r1_xreal_0(k2_metric_1(C,D,E),B) & m1_subset_1(E,u1_struct_0(C))))))) # label(fraenkel_a_3_1_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8032 (all A (v1_xreal_0(A) -> (all B (-v3_struct_0(B) & l1_metric_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k9_metric_1(B,C,A) = a_3_0_metric_1(A,B,C))))))) # label(t18_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8033 (all A (v6_metric_1(k6_metric_1(A)) & v7_metric_1(k6_metric_1(A)) & v8_metric_1(k6_metric_1(A)) & v9_metric_1(k6_metric_1(A)) & v1_metric_1(k6_metric_1(A)))) # label(fc2_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8034 $T # label(t8_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8035 (all A (l1_metric_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k2_metric_1(A,B,C) = np__0 -> B = C))))) <-> v7_metric_1(A)))) # label(t2_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8036 (all A (l1_metric_1(A) -> (v2_metric_1(u1_metric_1(A),u1_struct_0(A)) <-> v6_metric_1(A)))) # label(d7_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8037 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers) & m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) -> (k5_metric_1(A) = B <-> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (D != C -> k1_metric_1(A,A,B,C,D) = np__1) & np__0 = k1_metric_1(A,A,B,C,C)))))))) # label(d11_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8038 (all A (m2_relset_1(k5_metric_1(A),k2_zfmisc_1(A,A),k1_numbers) & v1_funct_2(k5_metric_1(A),k2_zfmisc_1(A,A),k1_numbers) & v1_funct_1(k5_metric_1(A)))) # label(dt_k5_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8039 (all A all B all C all D (v1_xreal_0(B) & l1_metric_1(C) & m1_subset_1(D,u1_struct_0(C)) & -v3_struct_0(C) -> ((exists E (m1_subset_1(E,u1_struct_0(C)) & E = A & k2_metric_1(C,D,E) = B)) <-> r2_hidden(A,a_3_2_metric_1(B,C,D))))) # label(fraenkel_a_3_2_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8040 (all A all B all C (l1_metric_1(A) & m1_subset_1(B,u1_struct_0(A)) & v1_xreal_0(C) -> m1_subset_1(k10_metric_1(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k10_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8041 (all A all B (v1_funct_1(B) & m1_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers) -> (all C all D (g1_metric_1(C,D) = g1_metric_1(A,B) -> B = D & A = C)))) # label(free_g1_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8042 (all A (l1_metric_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_metric_1(A,C,B) = k2_metric_1(A,B,C))))) <-> v8_metric_1(A)))) # label(t3_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8043 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> r1_xreal_0(k1_metric_1(k1_numbers,k1_numbers,k7_metric_1,A,B),k3_real_1(k1_metric_1(k1_numbers,k1_numbers,k7_metric_1,A,C),k1_metric_1(k1_numbers,k1_numbers,k7_metric_1,C,B))))))))) # label(t11_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8044 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v1_xreal_0(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (v3_struct_0(A) -> (D = k9_metric_1(A,B,C) <-> v1_xboole_0(D))) & (-v3_struct_0(A) -> (D = k9_metric_1(A,B,C) <-> (exists E (-v3_struct_0(E) & l1_metric_1(E) & (exists F (m1_subset_1(F,u1_struct_0(E)) & E = A & F = B & D = a_3_0_metric_1(C,E,F))))))))))))))) # label(d15_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8045 (all A (l1_metric_1(A) -> (v1_metric_1(A) -> A = g1_metric_1(u1_struct_0(A),u1_metric_1(A))))) # label(abstractness_v1_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8046 (all A (v1_xreal_0(A) -> (all B (l1_metric_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (-v3_struct_0(B) & A = k2_metric_1(B,C,D) <-> r2_hidden(D,k11_metric_1(B,C,A))))))))))) # label(t14_metric_1) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8047 (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]. 126.12/125.45 8048 (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]. 126.12/125.45 8049 (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]. 126.12/125.45 8050 (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]. 126.12/125.45 8051 $T # label(t9_cat_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8052 $T # label(t56_cat_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8053 (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]. 126.12/125.45 8054 $T # label(t49_cat_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8055 (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]. 126.12/125.45 8056 $T # label(t26_cat_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8057 (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]. 126.12/125.45 8058 (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]. 126.12/125.45 8059 (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]. 126.12/125.45 8060 (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]. 126.12/125.45 8061 (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]. 126.12/125.45 8062 (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]. 126.12/125.45 8063 (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]. 126.12/125.45 8064 $T # label(t46_cat_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8065 $T # label(t8_cat_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.45 8066 (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]. 126.12/125.45 8067 (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]. 126.12/125.45 8068 (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]. 126.12/125.45 8069 $T # label(t10_cat_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.46 8070 (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]. 126.12/125.46 8071 (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]. 126.12/125.46 8072 $T # label(dt_k5_cat_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.46 8073 $T # label(t32_cat_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.46 8074 (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]. 126.12/125.46 8075 (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]. 126.12/125.46 8076 (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]. 126.12/125.46 8077 (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]. 126.12/125.46 8078 (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]. 126.12/125.46 8079 (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]. 126.12/125.46 8080 (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]. 126.12/125.46 8081 $T # label(t57_cat_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.46 8082 (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]. 126.12/125.46 8083 (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]. 126.12/125.46 8084 (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]. 126.12/125.46 8085 (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]. 126.12/125.46 8086 (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]. 126.12/125.46 8087 (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]. 126.12/125.46 8088 (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]. 126.12/125.46 8089 (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]. 126.12/125.46 8090 (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]. 126.12/125.46 8091 (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]. 126.12/125.46 8092 (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]. 126.12/125.46 8093 (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]. 126.12/125.46 8094 (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]. 126.12/125.46 8095 (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]. 126.12/125.46 8096 (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]. 126.12/125.46 8097 (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]. 126.12/125.46 8098 (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]. 126.12/125.46 8099 (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]. 126.12/125.46 8100 (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]. 126.12/125.46 8101 (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]. 126.12/125.46 8102 (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]. 126.12/125.46 8103 (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]. 126.12/125.46 8104 (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]. 126.12/125.46 8105 (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]. 126.12/125.46 8106 (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]. 126.12/125.46 8107 (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]. 126.12/125.46 8108 (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]. 126.12/125.46 8109 (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]. 126.12/125.46 8110 $T # label(t20_cat_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.46 8111 (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]. 126.12/125.46 8112 (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]. 126.12/125.46 8113 (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]. 126.12/125.46 8114 (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]. 126.12/125.46 8115 (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]. 126.12/125.46 8116 (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]. 126.12/125.46 8117 (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]. 126.12/125.46 8118 (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]. 126.12/125.46 8119 (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]. 126.12/125.46 8120 (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]. 126.12/125.46 8121 $T # label(t11_cat_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.46 8122 (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]. 126.12/125.46 8123 (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]. 126.12/125.46 8124 (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]. 126.12/125.46 8125 (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]. 126.12/125.46 8126 (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]. 126.12/125.46 8127 (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]. 126.12/125.46 8128 (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]. 126.12/125.46 8129 (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]. 126.12/125.46 8130 (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]. 126.12/125.46 8131 $T # label(t5_cat_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.46 8132 (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]. 126.12/125.46 8133 (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]. 126.12/125.46 8134 (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]. 126.12/125.46 8135 (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]. 126.12/125.46 8136 (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]. 126.12/125.46 8137 (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]. 126.12/125.46 8138 (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]. 126.12/125.46 8139 (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]. 126.12/125.46 8140 (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]. 126.12/125.46 8141 (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]. 126.12/125.46 8142 (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]. 126.12/125.46 8143 (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]. 126.12/125.46 8144 (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]. 126.12/125.46 8145 (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]. 126.12/125.46 8146 (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]. 126.12/125.46 8147 (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]. 126.12/125.46 8148 (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]. 126.12/125.46 8149 (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]. 126.12/125.46 8150 (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]. 126.12/125.46 8151 (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]. 126.12/125.46 8152 (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]. 126.12/125.46 8153 (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]. 126.12/125.46 8154 (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]. 126.12/125.46 8155 (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]. 126.12/125.46 8156 (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]. 126.12/125.46 8157 (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]. 126.12/125.46 8158 (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]. 126.12/125.46 8159 (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]. 126.12/125.46 8160 (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]. 126.12/125.46 8161 (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]. 126.12/125.46 8162 (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]. 126.12/125.46 8163 (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]. 126.12/125.46 8164 (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]. 126.12/125.46 8165 $T # label(t68_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.46 8166 $T # label(t31_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.46 8167 (all A all B (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & -v3_struct_0(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v4_group_1(B) & v8_vectsp_1(B) & l3_vectsp_1(B) & v7_vectsp_1(B) & v6_vectsp_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & l3_vectsp_1(A) & v4_group_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> -v3_struct_0(k9_vectsp_2(A,B)) & v4_rlvect_1(k9_vectsp_2(A,B)) & l2_vectsp_2(k9_vectsp_2(A,B),A,B) & v4_vectsp_2(k9_vectsp_2(A,B),A,B) & v6_rlvect_1(k9_vectsp_2(A,B)) & v5_rlvect_1(k9_vectsp_2(A,B)) & v3_rlvect_1(k9_vectsp_2(A,B)))) # label(dt_k9_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.46 8168 (all A all B (l1_struct_0(B) & l1_struct_0(A) -> (all C (l2_vectsp_2(C,A,B) -> l4_vectsp_1(C,A) & l1_vectsp_2(C,B))))) # label(dt_l2_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.46 8169 (all A (m1_subset_1(A,k1_tarski(k1_xboole_0)) -> k8_vectsp_2 = A)) # label(d18_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.46 8170 (all A all B (l1_struct_0(B) & l1_struct_0(A) -> (exists C (-v3_struct_0(C) & l2_vectsp_2(C,A,B))))) # label(rc11_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.46 8171 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (k4_rlvect_1(A,C,D) = B & k4_rlvect_1(A,D,C) = B & m1_subset_1(D,u1_struct_0(A)))))))))) # label(t38_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.46 8172 (all A (l1_vectsp_1(A) -> (-v3_struct_0(A) & v7_group_1(A) & v6_vectsp_1(A) -> v2_group_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & -v3_struct_0(A)))) # label(cc3_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.46 8173 $T # label(t37_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.46 8174 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> -v3_struct_0(k4_vectsp_2(A)) & v3_rlvect_1(k4_vectsp_2(A)) & v5_rlvect_1(k4_vectsp_2(A)) & l4_vectsp_1(k4_vectsp_2(A),A) & v11_vectsp_1(k4_vectsp_2(A),A) & v6_rlvect_1(k4_vectsp_2(A)) & v4_rlvect_1(k4_vectsp_2(A)))) # label(dt_k4_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.46 8175 (exists A (l3_vectsp_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v2_group_1(A) & v4_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v5_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A))) # label(rc3_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.46 8176 $T # label(t74_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.46 8177 $T # label(t10_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.46 8178 $T # label(t12_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.46 8179 $T # label(t7_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.46 8180 (all A (v3_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (B != k1_rlvect_1(A) -> k2_group_1(A) = k2_vectsp_2(A,B,B)))))) # label(t52_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.46 8181 $T # label(t11_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.46 8182 $T # label(t21_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.46 8183 (all A (l1_vectsp_1(A) -> (-v3_struct_0(A) & v1_vectsp_2(A) -> v2_group_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & -v3_struct_0(A)))) # label(cc1_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.46 8184 $T # label(t15_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.46 8185 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> k4_vectsp_2(A) = g4_vectsp_1(A,u1_struct_0(A),u1_rlvect_1(A),u2_struct_0(A),u1_group_1(A)))) # label(d11_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.46 8186 (all A all B all C all D all E all F all G (l1_struct_0(B) & m1_subset_1(E,C) & v1_funct_1(F) & v1_funct_1(G) & m1_relset_1(G,k2_zfmisc_1(C,u1_struct_0(B)),C) & v1_funct_2(G,k2_zfmisc_1(C,u1_struct_0(B)),C) & m1_relset_1(F,k2_zfmisc_1(u1_struct_0(A),C),C) & v1_funct_2(F,k2_zfmisc_1(u1_struct_0(A),C),C) & m1_relset_1(D,k2_zfmisc_1(C,C),C) & v1_funct_2(D,k2_zfmisc_1(C,C),C) & v1_funct_1(D) & -v1_xboole_0(C) & l1_struct_0(A) -> v4_vectsp_2(g2_vectsp_2(A,B,C,D,E,F,G),A,B) & -v3_struct_0(g2_vectsp_2(A,B,C,D,E,F,G)))) # label(fc2_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.46 8187 $T # label(d10_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.46 8188 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v4_group_1(B) & v6_vectsp_1(B) & v8_vectsp_1(B) & l3_vectsp_1(B) & v7_vectsp_1(B) & v5_rlvect_1(B) -> (all C (-v3_struct_0(C) & l2_vectsp_2(C,A,B) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (m1_subset_1(F,u1_struct_0(C)) -> k6_vectsp_2(B,C,E,k6_vectsp_1(A,C,D,F)) = k6_vectsp_1(A,C,D,k6_vectsp_2(B,C,E,F)))))))) <-> v6_vectsp_2(C,A,B)))))))) # label(d24_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.46 8189 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_group_1(A) & v9_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -(k1_group_1(A,k1_vectsp_2(A,B),k1_vectsp_2(A,C)) != k1_vectsp_2(A,k1_group_1(A,C,B)) & k1_rlvect_1(A) != C & k1_rlvect_1(A) != B))))))) # label(t46_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8190 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (exists B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v3_vectsp_2(B,A) & v6_rlvect_1(B) & v3_rlvect_1(B) & l1_vectsp_2(B,A))))) # label(rc13_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8191 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v7_vectsp_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k2_group_1(A) = k1_group_1(A,B,C) -> B != k1_rlvect_1(A) & k1_rlvect_1(A) != C))))))) # label(t39_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8192 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v9_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k1_rlvect_1(A) != B -> k2_vectsp_2(A,k2_group_1(A),k1_vectsp_2(A,B)) = B & k2_vectsp_2(A,k2_group_1(A),B) = k1_vectsp_2(A,B)))))) # label(t50_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8193 (all A (v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (B != k1_rlvect_1(A) -> k2_vectsp_2(A,k6_rlvect_1(A,C,D),B) = k6_rlvect_1(A,k2_vectsp_2(A,C,B),k2_vectsp_2(A,D,B)) & k2_vectsp_2(A,k4_rlvect_1(A,C,D),B) = k4_rlvect_1(A,k2_vectsp_2(A,C,B),k2_vectsp_2(A,D,B))))))))))) # label(t55_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8194 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,B,k1_vectsp_2(A,C)) = k2_vectsp_2(A,B,C))))))) # label(d8_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8195 $T # label(t58_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8196 (all A all B (l1_vectsp_2(B,A) & l1_struct_0(A) -> v1_funct_2(u1_vectsp_2(A,B),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)),u1_struct_0(B)) & m2_relset_1(u1_vectsp_2(A,B),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)),u1_struct_0(B)) & v1_funct_1(u1_vectsp_2(A,B)))) # label(dt_u1_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8197 $T # label(t62_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8198 (all A all B (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(B) & v6_vectsp_1(B) & v7_vectsp_1(B) & v8_vectsp_1(B) & l3_vectsp_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) & l3_vectsp_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (exists C (l2_vectsp_2(C,A,B) & v3_rlvect_1(C) & v4_vectsp_2(C,A,B) & v5_vectsp_2(C,B) & v6_vectsp_2(C,A,B) & v12_vectsp_1(C,A) & v6_rlvect_1(C) & v5_rlvect_1(C) & v4_rlvect_1(C) & -v3_struct_0(C))))) # label(rc17_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8199 (all A all B all C all D all E all F all G (l1_struct_0(A) & l1_struct_0(B) & v1_funct_2(D,k2_zfmisc_1(C,C),C) & m1_relset_1(D,k2_zfmisc_1(C,C),C) & v1_funct_2(G,k2_zfmisc_1(C,u1_struct_0(B)),C) & m1_relset_1(G,k2_zfmisc_1(C,u1_struct_0(B)),C) & v1_funct_1(G) & m1_relset_1(F,k2_zfmisc_1(u1_struct_0(A),C),C) & v1_funct_2(F,k2_zfmisc_1(u1_struct_0(A),C),C) & v1_funct_1(F) & m1_subset_1(E,C) & v1_funct_1(D) -> (all H all I all J all K all L all M all N (g2_vectsp_2(A,B,C,D,E,F,G) = g2_vectsp_2(H,I,J,K,L,M,N) -> C = J & E = L & M = F & N = G & D = K & B = I & A = H)))) # label(free_g2_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8200 (all A (l1_struct_0(A) -> (exists B (v3_vectsp_2(B,A) & l1_vectsp_2(B,A))))) # label(rc8_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8201 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> -v3_struct_0(k3_vectsp_2(A)) & v1_rlvect_1(k3_vectsp_2(A)) & v6_rlvect_1(k3_vectsp_2(A)) & l1_rlvect_1(k3_vectsp_2(A)) & v5_rlvect_1(k3_vectsp_2(A)) & v4_rlvect_1(k3_vectsp_2(A)) & v3_rlvect_1(k3_vectsp_2(A)))) # label(dt_k3_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8202 $T # label(t33_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8203 $T # label(t70_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8204 $T # label(t79_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8205 (all A (-v3_struct_0(A) & l2_vectsp_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -(k1_group_1(A,B,C) = k1_rlvect_1(A) & k1_rlvect_1(A) != B & C != k1_rlvect_1(A)))))) <-> v2_vectsp_2(A)))) # label(d5_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8206 (all A (v3_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_group_1(A,B,C) = k2_group_1(A) -> k1_vectsp_2(A,B) = C & B = k1_vectsp_2(A,C)))))))) # label(t45_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8207 (all A all B (l1_struct_0(A) & l1_struct_0(B) -> (exists C l2_vectsp_2(C,A,B)))) # label(existence_l2_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8208 (all A (v6_rlvect_1(A) & v2_group_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v9_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k1_group_1(A,B,D) = k1_group_1(A,B,C) -> D = C | B = k1_rlvect_1(A)))))))))) # label(t42_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8209 (all A (v4_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> k2_group_1(A) != k1_rlvect_1(A) & -(B != k1_rlvect_1(A) & (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_group_1(A) != k1_group_1(A,B,C)))))) -> -v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A)))) # label(t16_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8210 (all A (v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (B = k6_rlvect_1(A,D,C) -> D = k4_rlvect_1(A,B,C)) & (k4_rlvect_1(A,B,C) = D -> C = k6_rlvect_1(A,D,B)) & (C = k6_rlvect_1(A,D,B) -> D = k4_rlvect_1(A,B,C)) & (k4_rlvect_1(A,B,C) = D -> B = k6_rlvect_1(A,D,C)))))))))) # label(t22_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8211 $T # label(t65_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8212 (all A all B (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & v2_group_1(A) & v4_group_1(A) & l3_vectsp_1(A) & m1_subset_1(B,u1_struct_0(A)) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v7_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> m1_subset_1(k1_vectsp_2(A,B),u1_struct_0(A)))) # label(dt_k1_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8213 (exists A (l3_vectsp_1(A) & -v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v3_vectsp_1(A) & v2_group_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A))) # label(rc4_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8214 $T # label(t4_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8215 (all A (l1_struct_0(A) -> (exists B (-v3_struct_0(B) & l1_vectsp_2(B,A))))) # label(rc9_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8216 (exists A (l3_vectsp_1(A) & -v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v2_group_1(A) & v4_group_1(A) & v5_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_vectsp_1(A) & v3_vectsp_1(A) & v6_rlvect_1(A))) # label(rc2_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8217 $T # label(d22_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8218 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v9_vectsp_1(A) & v2_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k1_rlvect_1(A) != B -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (C = k1_vectsp_2(A,B) <-> k1_group_1(A,B,C) = k2_group_1(A))))))))) # label(d7_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8219 (all A (-v3_struct_0(A) & l3_vectsp_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,B,k5_rlvect_1(A,B)) = k1_rlvect_1(A) & k1_group_1(A,k2_rlvect_1(A,C,D),B) = k2_rlvect_1(A,k1_group_1(A,C,B),k1_group_1(A,D,B)) & k2_rlvect_1(A,k1_group_1(A,B,C),k1_group_1(A,B,D)) = k1_group_1(A,B,k2_rlvect_1(A,C,D)) & k1_group_1(A,B,k1_group_1(A,C,D)) = k1_group_1(A,k1_group_1(A,B,C),D) & k1_group_1(A,k2_group_1(A),B) = B & k1_group_1(A,B,k2_group_1(A)) = B & B = k2_rlvect_1(A,B,k1_rlvect_1(A)) & k2_rlvect_1(A,k2_rlvect_1(A,B,C),D) = k2_rlvect_1(A,B,k2_rlvect_1(A,C,D)) & k2_rlvect_1(A,C,B) = k2_rlvect_1(A,B,C))))))) <-> v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & -v3_struct_0(A)))) # label(t1_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8220 $T # label(t36_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8221 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v7_group_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_group_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v2_vectsp_2(A) & -v10_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A))) # label(t13_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8222 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k5_rlvect_1(A,B) = k1_rlvect_1(A) <-> k1_rlvect_1(A) = B))))) # label(t34_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8223 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -(B != k1_rlvect_1(A) & C != k1_rlvect_1(A) & k1_group_1(A,B,C) = k1_rlvect_1(A)))))))) # label(t47_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8224 $T # label(t69_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8225 (all A all B all C (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & -v10_vectsp_1(A) & v7_vectsp_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> m1_subset_1(k2_vectsp_2(A,B,C),u1_struct_0(A)))) # label(dt_k2_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8226 $T # label(t81_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8227 $T # label(t26_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8228 (all A (m2_relset_1(A,k1_tarski(k1_xboole_0),k1_tarski(k1_xboole_0)) & v1_funct_2(A,k1_tarski(k1_xboole_0),k1_tarski(k1_xboole_0)) & v1_funct_1(A) -> A = k7_vectsp_2)) # label(d17_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8229 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> -(B != k1_rlvect_1(A) & k2_vectsp_2(A,D,k2_vectsp_2(A,B,C)) != k2_vectsp_2(A,k1_group_1(A,D,C),B) & k1_rlvect_1(A) != C))))))))) # label(t56_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8230 (all A all B all C (l1_struct_0(A) & l2_vectsp_2(C,A,B) & l1_struct_0(B) -> (v4_vectsp_2(C,A,B) -> C = g2_vectsp_2(A,B,u1_struct_0(C),u1_rlvect_1(C),u2_struct_0(C),u2_vectsp_1(B,C),u1_vectsp_2(B,C))))) # label(abstractness_v4_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8231 (all A (-v3_struct_0(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> -(k1_rlvect_1(A) != B & k2_vectsp_2(A,D,B) != k2_vectsp_2(A,k1_group_1(A,D,C),k1_group_1(A,B,C)) & k1_rlvect_1(A) != C))))))))) # label(t53_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8232 (all A (-v3_struct_0(A) & l1_vectsp_1(A) -> (v1_vectsp_2(A) -> k2_vectsp_1(A) = k2_group_1(A)))) # label(t85_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8233 (all A (-v3_struct_0(A) & l1_struct_0(A) -> (all B (l1_vectsp_2(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k2_binop_1(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),u1_vectsp_2(A,B),D,C) = k6_vectsp_2(A,B,C,D))))))))) # label(d15_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8234 $T # label(t80_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8235 $T # label(d12_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8236 (all A all B (l1_struct_0(B) & l1_struct_0(A) -> (exists C (v4_vectsp_2(C,A,B) & l2_vectsp_2(C,A,B))))) # label(rc10_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8237 $T # label(t72_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8238 (all A (l1_vectsp_1(A) -> (v8_vectsp_1(A) & v7_group_1(A) & -v3_struct_0(A) -> v2_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & -v3_struct_0(A)))) # label(cc2_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8239 $T # label(d6_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8240 (all A (l1_struct_0(A) -> (all B (l1_vectsp_2(B,A) -> l1_rlvect_1(B))))) # label(dt_l1_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8241 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & -v3_struct_0(A) -> (exists B (l4_vectsp_1(B,A) & -v3_struct_0(B) & v3_rlvect_1(B) & v6_rlvect_1(B) & v11_vectsp_1(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B))))) # label(rc12_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8242 $T # label(d4_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8243 $T # label(t25_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8244 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v8_vectsp_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> -((all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,C,B) != k2_group_1(A))) & k1_rlvect_1(A) != B))))) # label(t40_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8245 $T # label(t35_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8246 $T # label(t6_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8247 (exists A (v5_rlvect_1(A) & v4_vectsp_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v9_vectsp_1(A) & -v10_vectsp_1(A) & v8_vectsp_1(A) & v5_vectsp_1(A) & v4_group_1(A) & v2_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) & l3_vectsp_1(A))) # label(rc6_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8248 $T # label(t64_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8249 (all A all B (l1_struct_0(A) & l1_vectsp_2(B,A) -> (v3_vectsp_2(B,A) -> B = g1_vectsp_2(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u1_vectsp_2(A,B))))) # label(abstractness_v3_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8250 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(k5_vectsp_2(A))) -> (all E (m1_subset_1(E,u1_struct_0(k5_vectsp_2(A))) -> k6_vectsp_2(A,k5_vectsp_2(A),B,k4_rlvect_1(k5_vectsp_2(A),D,E)) = k4_rlvect_1(k5_vectsp_2(A),k6_vectsp_2(A,k5_vectsp_2(A),B,D),k6_vectsp_2(A,k5_vectsp_2(A),B,E)) & k6_vectsp_2(A,k5_vectsp_2(A),k1_group_1(A,C,B),D) = k6_vectsp_2(A,k5_vectsp_2(A),B,k6_vectsp_2(A,k5_vectsp_2(A),C,D)) & k6_vectsp_2(A,k5_vectsp_2(A),k2_group_1(A),D) = D & k6_vectsp_2(A,k5_vectsp_2(A),k4_rlvect_1(A,B,C),D) = k4_rlvect_1(k5_vectsp_2(A),k6_vectsp_2(A,k5_vectsp_2(A),B,D),k6_vectsp_2(A,k5_vectsp_2(A),C,D)))))))))))) # label(t77_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8251 $T # label(d16_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8252 $T # label(d20_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8253 (all A all B (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_vectsp_1(B) & v8_vectsp_1(B) & l3_vectsp_1(B) & v6_vectsp_1(B) & v4_group_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_rlvect_1(A) -> (exists C (l2_vectsp_2(C,A,B) & v3_rlvect_1(C) & v4_rlvect_1(C) & v4_vectsp_2(C,A,B) & v6_rlvect_1(C) & v5_rlvect_1(C) & -v3_struct_0(C))))) # label(rc14_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8254 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (exists B (-v3_struct_0(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & v11_vectsp_1(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & l4_vectsp_1(B,A))))) # label(rc15_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8255 $T # label(t17_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8256 (all A all B all C all D all E (l1_struct_0(A) & v1_funct_1(C) & m1_relset_1(E,k2_zfmisc_1(B,u1_struct_0(A)),B) & v1_funct_2(E,k2_zfmisc_1(B,u1_struct_0(A)),B) & v1_funct_1(E) & m1_subset_1(D,B) & m1_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & -v1_xboole_0(B) -> v3_vectsp_2(g1_vectsp_2(A,B,C,D,E),A) & -v3_struct_0(g1_vectsp_2(A,B,C,D,E)))) # label(fc1_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8257 $T # label(t27_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8258 $T # label(t76_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8259 $T # label(t8_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8260 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (B != k1_rlvect_1(A) -> k2_vectsp_2(A,k5_rlvect_1(A,C),B) = k5_rlvect_1(A,k2_vectsp_2(A,C,B)) & k2_vectsp_2(A,C,k5_rlvect_1(A,B)) = k5_rlvect_1(A,k2_vectsp_2(A,C,B))))))))) # label(t54_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8261 (all A (v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (exists B (l1_vectsp_2(B,A) & v3_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B))))) # label(rc16_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8262 $T # label(t2_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8263 $T # label(t44_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8264 $T # label(t67_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8265 $T # label(t3_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8266 (exists A (l3_vectsp_1(A) & v2_group_1(A) & v3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v5_vectsp_1(A) & v4_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A))) # label(rc1_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8267 (exists A (l3_vectsp_1(A) & v5_rlvect_1(A) & v3_vectsp_1(A) & v4_vectsp_1(A) & v8_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v5_vectsp_1(A) & v4_group_1(A) & v2_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A))) # label(rc7_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8268 $T # label(t82_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8269 $T # label(d1_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8270 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k1_rlvect_1(A) != B -> k2_group_1(A) = k1_group_1(A,k2_vectsp_2(A,k2_group_1(A),B),B) & k1_group_1(A,B,k2_vectsp_2(A,k2_group_1(A),B)) = k2_group_1(A)))))) # label(t51_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8271 (all A all B all C all D all E all F all G (l1_struct_0(A) & v1_funct_1(D) & v1_funct_1(F) & v1_funct_2(F,k2_zfmisc_1(u1_struct_0(A),C),C) & m1_relset_1(F,k2_zfmisc_1(u1_struct_0(A),C),C) & v1_funct_1(G) & v1_funct_2(G,k2_zfmisc_1(C,u1_struct_0(B)),C) & m1_relset_1(G,k2_zfmisc_1(C,u1_struct_0(B)),C) & m1_subset_1(E,C) & m1_relset_1(D,k2_zfmisc_1(C,C),C) & v1_funct_2(D,k2_zfmisc_1(C,C),C) & l1_struct_0(B) -> l2_vectsp_2(g2_vectsp_2(A,B,C,D,E,F,G),A,B) & v4_vectsp_2(g2_vectsp_2(A,B,C,D,E,F,G),A,B))) # label(dt_g2_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8272 $T # label(t23_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8273 (all A (v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> -v3_struct_0(k4_vectsp_2(A)) & v3_rlvect_1(k4_vectsp_2(A)) & v4_rlvect_1(k4_vectsp_2(A)) & v11_vectsp_1(k4_vectsp_2(A),A) & v12_vectsp_1(k4_vectsp_2(A),A) & v6_rlvect_1(k4_vectsp_2(A)) & v5_rlvect_1(k4_vectsp_2(A)))) # label(fc3_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8274 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> -(k1_vectsp_2(A,B) = k1_rlvect_1(A) & k1_rlvect_1(A) != B))))) # label(t48_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8275 $T # label(t24_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8276 $T # label(t60_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8277 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_vectsp_1(B) & l3_vectsp_1(B) & v8_vectsp_1(B) & v6_vectsp_1(B) & v4_group_1(B) & v4_rlvect_1(B) -> k9_vectsp_2(A,B) = g2_vectsp_2(A,B,k1_tarski(k1_xboole_0),k2_midsp_1,k8_vectsp_2,k10_funct_3(u1_struct_0(A),k1_tarski(k1_xboole_0)),k9_funct_3(k1_tarski(k1_xboole_0),u1_struct_0(B))))))) # label(d21_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8278 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> g1_vectsp_2(A,u1_struct_0(A),u1_rlvect_1(A),u2_struct_0(A),u1_group_1(A)) = k5_vectsp_2(A))) # label(d14_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8279 $T # label(t5_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8280 $T # label(t75_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8281 $T # label(t20_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8282 $T # label(t73_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8283 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> v3_rlvect_1(k5_vectsp_2(A)) & v4_rlvect_1(k5_vectsp_2(A)) & v5_rlvect_1(k5_vectsp_2(A)) & v6_rlvect_1(k5_vectsp_2(A)) & v5_vectsp_2(k5_vectsp_2(A),A) & v3_vectsp_2(k5_vectsp_2(A),A) & -v3_struct_0(k5_vectsp_2(A)))) # label(fc4_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8284 (all A (-v3_struct_0(A) & l1_vectsp_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> k1_group_1(A,k2_vectsp_1(A),B) = B & k1_group_1(A,B,k2_vectsp_1(A)) = B)) <-> v1_vectsp_2(A)))) # label(d2_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8285 $T # label(t18_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8286 $T # label(t28_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8287 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v6_vectsp_1(B) & v8_vectsp_1(B) & l3_vectsp_1(B) & v7_vectsp_1(B) & v4_group_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) -> -v3_struct_0(k9_vectsp_2(A,B)) & v3_rlvect_1(k9_vectsp_2(A,B)) & v4_rlvect_1(k9_vectsp_2(A,B)) & v5_rlvect_1(k9_vectsp_2(A,B)) & v12_vectsp_1(k9_vectsp_2(A,B),A) & l2_vectsp_2(k9_vectsp_2(A,B),A,B) & v6_vectsp_2(k9_vectsp_2(A,B),A,B) & v5_vectsp_2(k9_vectsp_2(A,B),B) & v6_rlvect_1(k9_vectsp_2(A,B)))))) # label(t84_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8288 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(k4_vectsp_2(A))) -> (all E (m1_subset_1(E,u1_struct_0(k4_vectsp_2(A))) -> k4_rlvect_1(k4_vectsp_2(A),k6_vectsp_1(A,k4_vectsp_2(A),B,D),k6_vectsp_1(A,k4_vectsp_2(A),B,E)) = k6_vectsp_1(A,k4_vectsp_2(A),B,k4_rlvect_1(k4_vectsp_2(A),D,E)) & k6_vectsp_1(A,k4_vectsp_2(A),k4_rlvect_1(A,B,C),D) = k4_rlvect_1(k4_vectsp_2(A),k6_vectsp_1(A,k4_vectsp_2(A),B,D),k6_vectsp_1(A,k4_vectsp_2(A),C,D)) & k6_vectsp_1(A,k4_vectsp_2(A),k1_group_1(A,B,C),D) = k6_vectsp_1(A,k4_vectsp_2(A),B,k6_vectsp_1(A,k4_vectsp_2(A),C,D)) & D = k6_vectsp_1(A,k4_vectsp_2(A),k2_group_1(A),D))))))))))) # label(t71_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.47 8289 $T # label(d3_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8290 $T # label(t19_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8291 $T # label(t14_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8292 $T # label(t61_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8293 $T # label(t63_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8294 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v6_vectsp_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k1_rlvect_1(A) != B -> k2_group_1(A) = k1_group_1(A,k1_vectsp_2(A,B),B) & k1_group_1(A,B,k1_vectsp_2(A,B)) = k2_group_1(A)))))) # label(t43_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8295 $T # label(t9_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8296 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) -> v3_rlvect_1(k5_vectsp_2(A)) & v4_rlvect_1(k5_vectsp_2(A)) & v5_rlvect_1(k5_vectsp_2(A)) & l1_vectsp_2(k5_vectsp_2(A),A) & v3_vectsp_2(k5_vectsp_2(A),A) & v6_rlvect_1(k5_vectsp_2(A)) & -v3_struct_0(k5_vectsp_2(A)))) # label(dt_k5_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8297 (all A (v4_group_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_group_1(A,B,C) = k2_group_1(A) -> k1_group_1(A,C,B) = k2_group_1(A)))))))) # label(t41_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8298 (all A all B all C all D (-v3_struct_0(A) & -v3_struct_0(B) & l1_vectsp_2(B,A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(B)) & l1_struct_0(A) -> m1_subset_1(k6_vectsp_2(A,B,C,D),u1_struct_0(B)))) # label(dt_k6_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8299 $T # label(t29_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8300 (exists A (-v3_struct_0(A) & v5_rlvect_1(A) & v2_group_1(A) & v7_group_1(A) & v4_vectsp_1(A) & v6_vectsp_1(A) & v2_vectsp_2(A) & -v10_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v5_vectsp_1(A) & v3_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & l3_vectsp_1(A))) # label(rc5_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8301 (all A (-v3_struct_0(A) & l3_vectsp_1(A) -> (all B (l1_vectsp_2(B,A) & -v3_struct_0(B) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> E = k6_vectsp_2(A,B,k2_group_1(A),E) & k6_vectsp_2(A,B,C,k6_vectsp_2(A,B,D,E)) = k6_vectsp_2(A,B,k1_group_1(A,D,C),E) & k6_vectsp_2(A,B,k2_rlvect_1(A,C,D),E) = k2_rlvect_1(B,k6_vectsp_2(A,B,C,E),k6_vectsp_2(A,B,D,E)) & k6_vectsp_2(A,B,C,k2_rlvect_1(B,E,F)) = k2_rlvect_1(B,k6_vectsp_2(A,B,C,E),k6_vectsp_2(A,B,C,F)))))))))) <-> v5_vectsp_2(B,A)))))) # label(d23_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8302 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k1_rlvect_1(A) != B -> k1_vectsp_2(A,k1_vectsp_2(A,B)) = B))))) # label(t49_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8303 $T # label(t32_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8304 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v6_vectsp_1(B) & v8_vectsp_1(B) & l3_vectsp_1(B) & v7_vectsp_1(B) & v4_group_1(B) & v3_rlvect_1(B) -> (all C (-v3_struct_0(C) & l2_vectsp_2(C,A,B) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> (all G (m1_subset_1(G,u1_struct_0(B)) -> (all H (m1_subset_1(H,u1_struct_0(C)) -> (all I (m1_subset_1(I,u1_struct_0(C)) -> H = k6_vectsp_1(A,C,k2_group_1(A),H) & k2_rlvect_1(C,k6_vectsp_2(B,C,F,H),k6_vectsp_2(B,C,F,I)) = k6_vectsp_2(B,C,F,k2_rlvect_1(C,H,I)) & k6_vectsp_2(B,C,F,k6_vectsp_1(A,C,D,H)) = k6_vectsp_1(A,C,D,k6_vectsp_2(B,C,F,H)) & H = k6_vectsp_2(B,C,k2_group_1(B),H) & k6_vectsp_2(B,C,F,k6_vectsp_2(B,C,G,H)) = k6_vectsp_2(B,C,k1_group_1(B,G,F),H) & k2_rlvect_1(C,k6_vectsp_2(B,C,F,H),k6_vectsp_2(B,C,G,H)) = k6_vectsp_2(B,C,k4_rlvect_1(B,F,G),H) & k6_vectsp_1(A,C,k1_group_1(A,D,E),H) = k6_vectsp_1(A,C,D,k6_vectsp_1(A,C,E,H)) & k2_rlvect_1(C,k6_vectsp_1(A,C,D,H),k6_vectsp_1(A,C,E,H)) = k6_vectsp_1(A,C,k4_rlvect_1(A,D,E),H) & k2_rlvect_1(C,k6_vectsp_1(A,C,D,H),k6_vectsp_1(A,C,D,I)) = k6_vectsp_1(A,C,D,k2_rlvect_1(C,H,I)))))))))))))) <-> v6_vectsp_2(C,A,B) & v12_vectsp_1(C,A) & v5_vectsp_2(C,B)))))))) # label(t83_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8305 (all A all B all C all D all E (l1_struct_0(A) & m1_relset_1(C,k2_zfmisc_1(B,B),B) & m1_subset_1(D,B) & m1_relset_1(E,k2_zfmisc_1(B,u1_struct_0(A)),B) & v1_funct_2(E,k2_zfmisc_1(B,u1_struct_0(A)),B) & v1_funct_1(E) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all F all G all H all I all J (g1_vectsp_2(A,B,C,D,E) = g1_vectsp_2(F,G,H,I,J) -> A = F & G = B & H = C & I = D & E = J)))) # label(free_g1_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8306 $T # label(d19_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8307 $T # label(t78_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8308 $T # label(t66_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8309 (all A all B all C all D all E (m1_relset_1(C,k2_zfmisc_1(B,B),B) & m1_subset_1(D,B) & m1_relset_1(E,k2_zfmisc_1(B,u1_struct_0(A)),B) & v1_funct_2(E,k2_zfmisc_1(B,u1_struct_0(A)),B) & v1_funct_1(E) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) & l1_struct_0(A) -> l1_vectsp_2(g1_vectsp_2(A,B,C,D,E),A) & v3_vectsp_2(g1_vectsp_2(A,B,C,D,E),A))) # label(dt_g1_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8310 (all A (l1_struct_0(A) -> (exists B l1_vectsp_2(B,A)))) # label(existence_l1_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8311 (all A all B (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & -v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v4_group_1(B) & v7_vectsp_1(B) & v8_vectsp_1(B) & l3_vectsp_1(B) & v6_vectsp_1(B) & v6_rlvect_1(B) & v4_rlvect_1(B) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) -> v4_rlvect_1(k9_vectsp_2(A,B)) & v5_rlvect_1(k9_vectsp_2(A,B)) & v4_vectsp_2(k9_vectsp_2(A,B),A,B) & v5_vectsp_2(k9_vectsp_2(A,B),B) & v6_vectsp_2(k9_vectsp_2(A,B),A,B) & v12_vectsp_1(k9_vectsp_2(A,B),A) & v6_rlvect_1(k9_vectsp_2(A,B)) & v3_rlvect_1(k9_vectsp_2(A,B)) & -v3_struct_0(k9_vectsp_2(A,B)))) # label(fc5_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8312 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v9_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_rlvect_1(A) != B -> k1_group_1(A,k2_vectsp_2(A,C,B),B) = C))))))) # label(t57_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8313 $T # label(d13_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8314 $T # label(t30_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8315 $T # label(t59_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8316 (all A (v3_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> g1_rlvect_1(u1_struct_0(A),u1_rlvect_1(A),u2_struct_0(A)) = k3_vectsp_2(A))) # label(d9_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8317 $T # label(t16_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8318 (all A (-v3_struct_0(A) & v17_lattices(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> (all C (v10_lattices(C) & l3_lattices(C) & v3_filter_0(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (all E (m1_filter_0(E,C) -> (all F (m1_subset_1(F,u1_struct_0(A)) -> r1_filter_0(A,B,F,F) & r1_filter_0(C,E,D,D))))))))))))) # label(t88_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8319 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_filter_0(C,A) -> r1_tarski(B,k5_filter_0(A,B,C)) & r1_tarski(C,k5_filter_0(A,B,C)))))))) # label(t49_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8320 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r3_lattices(A,B,C) -> r3_lattices(A,k4_lattices(A,D,B),C) & r3_lattices(A,k4_lattices(A,B,D),C)))))))))) # label(t2_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8321 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) -> (-v3_struct_0(A) & v3_filter_0(A) & l3_lattices(A) & v10_lattices(A) -> m2_relset_1(k10_filter_0(A,B),u1_struct_0(A),u1_struct_0(A)) & v1_partfun1(k10_filter_0(A,B),u1_struct_0(A),u1_struct_0(A)) & v8_relat_2(k10_filter_0(A,B)) & v3_relat_2(k10_filter_0(A,B))))))) # label(t84_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8322 $T # label(t8_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8323 (all A all B (-v3_struct_0(A) & v10_lattices(A) & v17_lattices(A) & m1_filter_0(B,A) & l3_lattices(A) -> v8_relat_2(k12_filter_0(A,B)) & m2_relset_1(k12_filter_0(A,B),u1_struct_0(A),u1_struct_0(A)) & v1_partfun1(k12_filter_0(A,B),u1_struct_0(A),u1_struct_0(A)) & v3_relat_2(k12_filter_0(A,B)))) # label(dt_k12_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8324 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) -> (l3_lattices(A) & r2_hidden(k5_lattices(A),B) & v13_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> k1_filter_0(A) = B & u1_struct_0(A) = B))))) # label(t32_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8325 (all A all B all C (-v3_struct_0(A) & -v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l3_lattices(A) & v10_lattices(A) -> -v1_xboole_0(k5_filter_0(A,B,C)))) # label(fc1_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8326 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) -> k3_filter_0(A,k4_subset_1(u1_struct_0(A),B,k3_filter_0(A,C))) = k3_filter_0(A,k4_subset_1(u1_struct_0(A),B,C)) & k3_filter_0(A,k4_subset_1(u1_struct_0(A),k3_filter_0(A,B),C)) = k3_filter_0(A,k4_subset_1(u1_struct_0(A),B,C)))))))) # label(t47_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8327 (all A all B (-v3_struct_0(A) & m1_filter_0(B,A) & l3_lattices(A) & v10_lattices(A) -> v3_lattices(k8_filter_0(A,B)) & v4_lattices(k8_filter_0(A,B)) & v8_lattices(k8_filter_0(A,B)) & v10_lattices(k8_filter_0(A,B)) & v9_lattices(k8_filter_0(A,B)) & v7_lattices(k8_filter_0(A,B)) & v6_lattices(k8_filter_0(A,B)) & v5_lattices(k8_filter_0(A,B)) & -v3_struct_0(k8_filter_0(A,B)))) # label(fc2_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8328 (all A (l3_lattices(A) & v17_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (v1_filter_0(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,B) <-> -r2_hidden(k7_lattices(A,C),B))))))))) # label(t59_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8329 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> a_3_0_filter_0(A,B,C) = k5_filter_0(A,B,C))))))) # label(d9_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8330 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_filter_0(D,A) -> (all E (m1_subset_1(E,u1_struct_0(k8_filter_0(A,D))) -> (all F (m1_subset_1(F,u1_struct_0(k8_filter_0(A,D))) -> (B = E & C = F -> k3_lattices(A,B,C) = k3_lattices(k8_filter_0(A,D),E,F) & k4_lattices(A,B,C) = k4_lattices(k8_filter_0(A,D),E,F)))))))))))))) # label(t64_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8331 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(B,k2_filter_0(A,C)) <-> r3_lattices(A,C,B)))))))) # label(t18_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8332 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> m1_filter_0(k1_filter_0(A),A))) # label(dt_k1_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8333 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v17_lattices(A) -> v3_filter_0(A))) # label(t40_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8334 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) -> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B))))) # label(dt_m1_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8335 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) -> (-v3_struct_0(A) & v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) -> r8_relat_2(k10_filter_0(A,B),u1_struct_0(A))))))) # label(t83_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8336 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> v13_lattices(k8_filter_0(A,k2_filter_0(A,B))))))) # label(t70_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8337 (all A (l3_lattices(A) & v3_filter_0(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_filter_0(D,A) -> (r2_hidden(k4_filter_0(A,B,C),D) & r2_hidden(B,D) -> r2_hidden(C,D)))))))))) # label(t41_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8338 (all A all B all C all D (m1_filter_0(D,B) & m1_filter_0(C,B) & l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> (r2_hidden(A,a_3_1_filter_0(B,C,D)) <-> (exists E (E = A & (exists F (m1_subset_1(F,u1_struct_0(B)) & (exists G (r2_hidden(G,D) & r2_hidden(F,C) & r3_lattices(B,k4_lattices(B,F,G),E) & m1_subset_1(G,u1_struct_0(B)))))) & m1_subset_1(E,u1_struct_0(B))))))) # label(fraenkel_a_3_1_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8339 (all A (l3_lattices(A) & -v3_struct_0(A) -> (v3_filter_0(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (r1_lattices(A,k2_lattices(A,B,D),C) & (all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_lattices(A,k2_lattices(A,B,E),C) -> r1_lattices(A,E,D)))) & m1_subset_1(D,u1_struct_0(A))))))))))) # label(d7_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8340 (all A all B all C (-v3_struct_0(A) & v10_lattices(A) & m1_filter_0(B,A) & m1_filter_0(C,A) & l3_lattices(A) & v11_lattices(A) -> k5_filter_0(A,B,C) = k6_filter_0(A,B,C))) # label(redefinition_k6_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8341 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> m1_filter_0(u1_struct_0(A),A))) # label(t15_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8342 (all A (l3_lattices(A) & v17_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (v1_filter_0(B,A) <-> u1_struct_0(A) != B & (all C (m1_subset_1(C,u1_struct_0(A)) -> r2_hidden(C,B) | r2_hidden(k7_lattices(A,C),B)))))))) # label(t57_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8343 $T # label(t79_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8344 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (l3_lattices(A) & -v3_struct_0(A) & v12_lattices(A) & l3_lattices(A) & v10_lattices(A) & v16_lattices(A) & v15_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> -v3_struct_0(k8_filter_0(A,k2_filter_0(A,B))) & v10_lattices(k8_filter_0(A,k2_filter_0(A,B))) & v15_lattices(k8_filter_0(A,k2_filter_0(A,B))) & l3_lattices(k8_filter_0(A,k2_filter_0(A,B))) & v16_lattices(k8_filter_0(A,k2_filter_0(A,B)))))))) # label(t74_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8345 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (-v3_struct_0(A) & r2_hidden(k5_lattices(A),B) & l3_lattices(A) & v13_lattices(A) & v10_lattices(A) -> u1_struct_0(A) = k3_filter_0(A,B) & k3_filter_0(A,B) = k1_filter_0(A)))))) # label(t31_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8346 $T # label(t76_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8347 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> (all C (v1_relat_1(C) -> (r1_tarski(k3_relat_1(C),u1_struct_0(A)) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r2_hidden(k9_filter_0(A,D,E),B) <-> r2_hidden(k1_domain_1(u1_struct_0(A),u1_struct_0(A),D,E),C)))))) <-> C = k10_filter_0(A,B)))))))) # label(d12_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8348 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> ((all C (m1_filter_0(C,A) -> (r1_tarski(B,C) -> C = B | u1_struct_0(A) = C))) & B != u1_struct_0(A) <-> v1_filter_0(B,A)))))) # label(d4_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8349 $T # label(t21_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8350 (all A all B (-v3_struct_0(A) & l3_lattices(A) & m1_filter_0(B,A) & v10_lattices(A) -> -v3_struct_0(k8_filter_0(A,B)) & l3_lattices(k8_filter_0(A,B)) & v10_lattices(k8_filter_0(A,B)))) # label(dt_k8_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8351 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) -> (v11_lattices(A) -> v11_lattices(k8_filter_0(A,B))))))) # label(t68_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8352 (all A (v3_filter_0(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k4_filter_0(A,B,B) = k6_lattices(A))))) # label(t38_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8353 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (-v3_struct_0(A) & l3_lattices(A) & v17_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r3_lattices(A,k4_lattices(A,B,k3_lattices(A,k7_lattices(A,B),C)),C) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r3_lattices(A,k4_lattices(A,B,D),C) -> r3_lattices(A,D,k3_lattices(A,k7_lattices(A,B),C)))))))))))) # label(t34_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8354 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k2_filter_0(A,B) = a_2_0_filter_0(A,B))))) # label(d3_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8355 (all A all B all C all D (-v3_struct_0(B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & -v1_xboole_0(D) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & -v1_xboole_0(C) & l3_lattices(B) & v10_lattices(B) -> ((exists E exists F (A = k4_lattices(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) & m1_subset_1(F,u1_struct_0(B)) & m1_subset_1(E,u1_struct_0(B)))) <-> r2_hidden(A,a_3_0_filter_0(B,C,D))))) # label(fraenkel_a_3_0_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8356 (all A (l3_lattices(A) & v17_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (all C (-v3_struct_0(C) & v10_lattices(C) & v3_filter_0(C) & l3_lattices(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (all E (m1_subset_1(E,u1_struct_0(C)) -> (all F (m1_subset_1(F,u1_struct_0(C)) -> (all G (m1_filter_0(G,C) -> (all H (m1_subset_1(H,u1_struct_0(A)) -> (all I (m1_subset_1(I,u1_struct_0(A)) -> (all J (m1_subset_1(J,u1_struct_0(A)) -> (r1_filter_0(C,G,D,E) & r1_filter_0(C,G,E,F) -> r1_filter_0(C,G,D,F)) & (r1_filter_0(A,B,H,I) & r1_filter_0(A,B,I,J) -> r1_filter_0(A,B,H,J)))))))))))))))))))))) # label(t90_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8357 $T # label(t33_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8358 (all A all B (-v3_struct_0(A) & v10_lattices(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l3_lattices(A) -> m1_filter_0(k3_filter_0(A,B),A))) # label(dt_k3_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8359 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k5_lattices(k8_filter_0(A,k2_filter_0(A,B))) = B)))) # label(t71_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8360 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (v10_lattices(A) & l3_lattices(A) & v13_lattices(A) & -v3_struct_0(A) -> k2_filter_0(A,k5_lattices(A)) = k1_filter_0(A)))) # label(t20_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8361 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v17_lattices(A) -> (all B (m1_filter_0(B,A) -> (B != k1_filter_0(A) & v2_filter_0(B,A) <-> v1_filter_0(B,A)))))) # label(t58_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8362 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v10_lattices(A) & v14_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> v15_lattices(k8_filter_0(A,k2_filter_0(A,B)))))))) # label(t73_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8363 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r3_lattices(A,D,E) & r3_lattices(A,B,C) -> r3_lattices(A,k4_lattices(A,B,D),k4_lattices(A,C,E)) & r3_lattices(A,k4_lattices(A,B,D),k4_lattices(A,E,C))))))))))))) # label(t5_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8364 (all A all B all C (v10_lattices(A) & l3_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & -v3_struct_0(A) -> m1_subset_1(k9_filter_0(A,B,C),u1_struct_0(A)))) # label(dt_k9_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8365 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (-v3_struct_0(A) & l3_lattices(A) & v3_filter_0(A) & v10_lattices(A) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k4_filter_0(A,B,C) = D <-> r3_lattices(A,k4_lattices(A,B,D),C) & (all E (m1_subset_1(E,u1_struct_0(A)) -> (r3_lattices(A,k4_lattices(A,B,E),C) -> r3_lattices(A,E,D)))))))))))))) # label(d8_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8366 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) -> r3_relat_2(k10_filter_0(A,B),u1_struct_0(A)))))) # label(t82_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8367 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k5_filter_0(A,B,C) = k5_filter_0(A,C,B))))))) # label(t46_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8368 (all A (l3_lattices(A) -> (v10_lattices(A) & v3_filter_0(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v8_lattices(A) & v9_lattices(A) & v11_lattices(A) & v12_lattices(A) & v10_lattices(A) & v7_lattices(A) & v6_lattices(A)))) # label(cc1_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8369 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (-v3_struct_0(A) & l3_lattices(A) & v14_lattices(A) & v10_lattices(A) -> m1_filter_0(k6_domain_1(u1_struct_0(A),k6_lattices(A)),A)))) # label(t13_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8370 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (v12_lattices(A) -> v12_lattices(k8_filter_0(A,B))))))) # label(t67_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8371 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r3_lattices(A,B,D) & r3_lattices(A,B,C) -> r3_lattices(A,B,k4_lattices(A,C,D))))))))))) # label(t7_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8372 (all A (v3_filter_0(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (-v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,k3_filter_0(A,k4_subset_1(u1_struct_0(A),D,k6_domain_1(u1_struct_0(A),C)))) -> r2_hidden(k4_filter_0(A,C,B),k3_filter_0(A,D))))))))))) # label(t53_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8373 (all A all B all C (-v3_struct_0(A) & v10_lattices(A) & m1_filter_0(C,A) & m1_filter_0(B,A) & l3_lattices(A) & v11_lattices(A) -> m1_filter_0(k6_filter_0(A,B,C),A))) # label(dt_k6_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8374 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_filter_0(D,A) -> (r1_filter_0(A,D,B,C) <-> r2_hidden(k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C),k10_filter_0(A,D))))))))))) # label(t87_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8375 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,C) -> r1_tarski(k2_filter_0(A,B),k3_filter_0(A,C))))))))) # label(t29_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8376 $T # label(t43_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8377 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r3_lattices(A,B,C) & r3_lattices(A,D,E) -> r3_lattices(A,k3_lattices(A,B,D),k3_lattices(A,C,E)) & r3_lattices(A,k3_lattices(A,B,D),k3_lattices(A,E,C))))))))))))) # label(t4_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8378 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) -> (-v3_struct_0(A) & l3_lattices(A) & v3_filter_0(A) & v10_lattices(A) -> v3_filter_0(k8_filter_0(A,B))))))) # label(t69_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8379 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_filter_0(D,A) -> (r1_filter_0(A,D,B,C) -> r1_filter_0(A,D,C,B)))))))))) # label(t89_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8380 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v14_lattices(A) -> k6_lattices(k8_filter_0(A,k2_filter_0(A,B))) = k6_lattices(A)))))) # label(t72_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8381 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(k3_lattices(A,C,D),B) <-> r2_hidden(D,B) | r2_hidden(C,B)))))) <-> v2_filter_0(B,A)))))) # label(d6_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8382 $T # label(t25_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8383 (all A (-v3_struct_0(A) & v17_lattices(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -(C != B & (all D (m1_filter_0(D,A) -> -((r2_hidden(C,D) & -r2_hidden(B,D) | -r2_hidden(C,D) & r2_hidden(B,D)) & v1_filter_0(D,A))))))))))) # label(t60_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8384 (all A (l3_lattices(A) & v3_filter_0(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_filter_0(E,A) -> (r2_hidden(k4_filter_0(A,B,C),E) & r2_hidden(k4_filter_0(A,C,D),E) -> r2_hidden(k4_filter_0(A,B,D),E)))))))))))) # label(t54_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8385 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (all C (m1_filter_0(C,A) -> ((all D (m1_filter_0(D,A) -> (r1_tarski(B,D) -> r1_tarski(C,D)))) & r1_tarski(B,C) <-> k3_filter_0(A,B) = C))))))) # label(d5_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8386 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_filter_0(C,A) -> k3_filter_0(A,k4_subset_1(u1_struct_0(A),B,C)) = a_3_1_filter_0(A,B,C))))))) # label(t48_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8387 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_filter_0(D,A) -> (all E (m1_subset_1(E,u1_struct_0(k8_filter_0(A,D))) -> (all F (m1_subset_1(F,u1_struct_0(k8_filter_0(A,D))) -> (B = E & F = C -> (r3_lattices(k8_filter_0(A,D),E,F) <-> r3_lattices(A,B,C))))))))))))))) # label(t65_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8388 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (m1_filter_0(k6_domain_1(u1_struct_0(A),B),A) -> v14_lattices(A)))))) # label(t14_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8389 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r3_lattices(A,B,C) -> r3_lattices(A,k3_lattices(A,B,D),k3_lattices(A,C,D)) & r3_lattices(A,k3_lattices(A,B,D),k3_lattices(A,D,C)) & r3_lattices(A,k3_lattices(A,D,B),k3_lattices(A,C,D)) & r3_lattices(A,k3_lattices(A,D,B),k3_lattices(A,D,C))))))))))) # label(t1_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8390 $T # label(t17_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8391 $T # label(t86_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8392 (all A all B (m1_filter_0(B,A) & l3_lattices(A) & v3_filter_0(A) & v10_lattices(A) & -v3_struct_0(A) -> m2_relset_1(k11_filter_0(A,B),u1_struct_0(A),u1_struct_0(A)) & v1_partfun1(k11_filter_0(A,B),u1_struct_0(A),u1_struct_0(A)) & v8_relat_2(k11_filter_0(A,B)) & v3_relat_2(k11_filter_0(A,B)))) # label(dt_k11_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8393 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v17_lattices(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> v10_lattices(k8_filter_0(A,k2_filter_0(A,B))) & v17_lattices(k8_filter_0(A,k2_filter_0(A,B))) & l3_lattices(k8_filter_0(A,k2_filter_0(A,B))) & -v3_struct_0(k8_filter_0(A,k2_filter_0(A,B)))))))) # label(t75_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8394 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (v14_lattices(A) -> v14_lattices(k8_filter_0(A,B))))))) # label(t66_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8395 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k4_lattices(A,k4_filter_0(A,B,C),k4_filter_0(A,C,B)) = k9_filter_0(A,B,C))))))) # label(d11_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8396 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> -(-(all C (m1_subset_1(C,u1_struct_0(A)) -> B = k4_lattices(A,B,C))) & u1_struct_0(A) = k2_filter_0(A,B)))))) # label(t23_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8397 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> m2_relset_1(k10_filter_0(A,B),u1_struct_0(A),u1_struct_0(A)))))) # label(t80_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8398 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (-v3_struct_0(A) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A) -> r2_hidden(k6_lattices(A),B)))))) # label(t12_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8399 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (-v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (-v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,D) & r2_hidden(C,E) -> r2_hidden(k4_lattices(A,C,B),k5_filter_0(A,D,E)) & r2_hidden(k4_lattices(A,B,C),k5_filter_0(A,D,E))))))))))))) # label(t44_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8400 (all A (-v3_struct_0(A) & l3_lattices(A) & v17_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k4_filter_0(A,B,C) = k3_lattices(A,k7_lattices(A,B),C))))))) # label(t55_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8401 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_filter_0(C,A) -> k3_filter_0(A,k5_filter_0(A,B,C)) = k3_filter_0(A,k4_subset_1(u1_struct_0(A),B,C)))))))) # label(t50_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8402 (all A (l3_lattices(A) & v10_lattices(A) & v3_lattices(A) & -v3_struct_0(A) -> A = k8_filter_0(A,k1_filter_0(A)))) # label(t62_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8403 (all A (v10_lattices(A) & l3_lattices(A) & v3_filter_0(A) & -v3_struct_0(A) -> v14_lattices(A))) # label(t37_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8404 (all A all B (l3_lattices(A) & m1_filter_0(B,A) & v3_filter_0(A) & v10_lattices(A) & -v3_struct_0(A) -> k11_filter_0(A,B) = k10_filter_0(A,B))) # label(redefinition_k11_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8405 (all A all B (l3_lattices(A) & m1_filter_0(B,A) & v10_lattices(A) & -v3_struct_0(A) -> v1_relat_1(k10_filter_0(A,B)))) # label(dt_k10_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8406 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (v10_lattices(A) & l3_lattices(A) & v3_filter_0(A) & -v3_struct_0(A) -> k3_relat_1(k10_filter_0(A,B)) = u1_struct_0(A)))))) # label(t85_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8407 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> u1_struct_0(A) = k1_filter_0(A))) # label(d2_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8408 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k9_filter_0(A,B,C) = k9_filter_0(A,C,B))))))) # label(t77_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8409 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) -> (l3_lattices(A) & v3_filter_0(A) & v10_lattices(A) & -v3_struct_0(A) -> r1_relat_2(k10_filter_0(A,B),u1_struct_0(A))))))) # label(t81_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8410 (all A all B all C (v17_lattices(A) & m1_filter_0(B,A) & m1_filter_0(C,A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> m1_filter_0(k7_filter_0(A,B,C),A))) # label(dt_k7_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8411 (all A all B (v10_lattices(A) & m1_filter_0(B,A) & l3_lattices(A) & v17_lattices(A) & -v3_struct_0(A) -> k12_filter_0(A,B) = k10_filter_0(A,B))) # label(redefinition_k12_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8412 $T # label(t28_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8413 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> (all C (-v3_struct_0(C) & v10_lattices(C) & l3_lattices(C) -> ((exists D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(B,B),B) & (exists E (C = g3_lattices(B,D,E) & k1_realset1(u1_lattices(A),B) = E & k1_realset1(u2_lattices(A),B) = D & m2_relset_1(E,k2_zfmisc_1(B,B),B) & v1_funct_2(E,k2_zfmisc_1(B,B),B) & v1_funct_1(E))) & v1_funct_2(D,k2_zfmisc_1(B,B),B))) <-> k8_filter_0(A,B) = C))))))) # label(d10_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8414 (all A (v3_filter_0(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> v11_lattices(A))) # label(t39_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8415 (exists A (l3_lattices(A) & -v3_struct_0(A) & v4_lattices(A) & v7_lattices(A) & v9_lattices(A) & v10_lattices(A) & v3_filter_0(A) & v8_lattices(A) & v6_lattices(A) & v5_lattices(A) & v3_lattices(A))) # label(rc1_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8416 (all A (l3_lattices(A) & v17_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k4_lattices(A,B,k7_lattices(A,C)) = k5_lattices(A) <-> r3_lattices(A,B,C)))))))) # label(t56_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8417 (all A all B all C (-v3_struct_0(A) & l3_lattices(A) & m1_filter_0(B,A) & m1_filter_0(C,A) & v17_lattices(A) & v10_lattices(A) -> k7_filter_0(A,B,C) = k5_filter_0(A,B,C))) # label(redefinition_k7_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8418 (all A all B all C (-v3_struct_0(B) & m1_subset_1(C,u1_struct_0(B)) & l3_lattices(B) & v10_lattices(B) -> (r2_hidden(A,a_2_0_filter_0(B,C)) <-> (exists D (m1_subset_1(D,u1_struct_0(B)) & A = D & r3_lattices(B,C,D)))))) # label(fraenkel_a_2_0_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8419 $T # label(t35_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8420 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (m1_filter_0(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(k4_lattices(A,C,D),B) <-> r2_hidden(C,B) & r2_hidden(D,B))))))))))) # label(d1_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8421 $T # label(t61_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8422 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> -(-v3_struct_0(A) & k5_lattices(A) != B & (all C (m1_filter_0(C,A) -> -(r2_hidden(B,C) & v1_filter_0(C,A)))) & l3_lattices(A) & v13_lattices(A) & v10_lattices(A)))))) # label(t24_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8423 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r3_lattices(A,B,C) -> r3_lattices(A,B,k3_lattices(A,D,C)) & r3_lattices(A,B,k3_lattices(A,C,D))))))))))) # label(t3_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8424 (all A all B all C (-v3_struct_0(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) & -v1_xboole_0(B) & l3_lattices(A) & v10_lattices(A) -> m1_subset_1(k5_filter_0(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k5_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8425 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r3_lattices(A,D,C) & r3_lattices(A,B,C) -> r3_lattices(A,k3_lattices(A,B,D),C)))))))))) # label(t6_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.48 8426 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> k1_realset1(u2_lattices(A),B) = u2_lattices(k8_filter_0(A,B)) & u1_lattices(k8_filter_0(A,B)) = k1_realset1(u1_lattices(A),B) & B = u1_struct_0(k8_filter_0(A,B)))))) # label(t63_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8427 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> k3_filter_0(A,B) = B)))) # label(t26_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8428 (all A (-v3_struct_0(A) & v17_lattices(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_filter_0(C,A) -> k3_filter_0(A,k4_subset_1(u1_struct_0(A),B,C)) = k7_filter_0(A,B,C))))))) # label(t52_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8429 (all A all B (v10_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & l3_lattices(A) & -v3_struct_0(A) -> m1_filter_0(k2_filter_0(A,B),A))) # label(dt_k2_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8430 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_filter_0(D,A) -> (r2_hidden(B,D) -> r2_hidden(k3_lattices(A,C,B),D) & r2_hidden(k3_lattices(A,B,C),D)))))))))) # label(t10_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8431 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r2_hidden(k3_lattices(A,B,C),k2_filter_0(A,B)) & r2_hidden(k3_lattices(A,C,B),k2_filter_0(A,B)) & r2_hidden(B,k2_filter_0(A,B)))))))) # label(t19_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8432 $T # label(t36_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8433 (all A (v3_filter_0(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_filter_0(C,A) -> k6_filter_0(A,B,C) = k3_filter_0(A,k4_subset_1(u1_struct_0(A),B,C)))))))) # label(t51_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8434 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(D) -> -(r2_hidden(B,k5_filter_0(A,C,D)) & (all E (m1_subset_1(E,u1_struct_0(A)) -> (all F (m1_subset_1(F,u1_struct_0(A)) -> -(r2_hidden(E,C) & r2_hidden(F,D) & k4_lattices(A,E,F) = B)))))))))))) # label(t45_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8435 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_filter_0(A,B,C,D) <-> r2_hidden(k9_filter_0(A,C,D),B)))))))))) # label(d13_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8436 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (k6_domain_1(u1_struct_0(A),B) = C -> k2_filter_0(A,B) = k3_filter_0(A,C)))))))) # label(t30_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8437 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,C) -> r1_tarski(k3_filter_0(A,B),k3_filter_0(A,C))))))))) # label(t27_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8438 (all A (-v3_struct_0(A) & v3_filter_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_filter_0(D,A) -> (r2_hidden(B,D) -> r2_hidden(k4_filter_0(A,C,B),D)))))))))) # label(t42_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8439 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (exists B m1_filter_0(B,A)))) # label(existence_m1_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8440 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (m1_filter_0(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(C,B) & r2_hidden(D,B) -> r2_hidden(k4_lattices(A,C,D),B)))))) & (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(C,B) & r3_lattices(A,C,D) -> r2_hidden(D,B))))))))))) # label(t9_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8441 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (v13_lattices(A) -> (all B (m1_filter_0(B,A) -> -((all C (m1_filter_0(C,A) -> -(r1_tarski(B,C) & v1_filter_0(C,A)))) & B != u1_struct_0(A))))))) # label(t22_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8442 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) -> (exists C (r2_hidden(C,B) & m1_subset_1(C,u1_struct_0(A)))))))) # label(t11_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8443 (all A all B all C (-v3_struct_0(A) & l3_lattices(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & v10_lattices(A) -> m1_subset_1(k4_filter_0(A,B,C),u1_struct_0(A)))) # label(dt_k4_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8444 (all A (-v3_struct_0(A) & v3_filter_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_filter_0(E,A) -> (r2_hidden(k9_filter_0(A,C,D),E) & r2_hidden(k9_filter_0(A,B,C),E) -> r2_hidden(k9_filter_0(A,B,D),E)))))))))))) # label(t78_filter_0) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8445 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (v1_group_1(B) & m1_group_2(B,A) -> (v6_group_1(A) & k17_group_2(A,B) = k9_group_1(A) -> r1_group_2(A,B,k5_group_2(A))))))) # label(t184_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8446 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_group_2(C,A) -> -(v6_group_1(C) & (all D (v1_finset_1(D) -> (all E (v1_finset_1(E) -> -(k4_card_1(E) = k9_group_1(C) & k4_card_1(D) = k9_group_1(C) & k13_group_2(A,C,B) = E & k12_group_2(A,C,B) = D)))))))))))) # label(t156_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8447 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_group_2(B,A) -> (v1_finset_1(k14_group_2(A,B)) -> (exists C (k17_group_2(A,B) = k4_card_1(C) & k14_group_2(A,B) = C & v1_finset_1(C))) & (exists C (v1_finset_1(C) & C = k15_group_2(A,B) & k4_card_1(C) = k17_group_2(A,B)))))))) # label(t176_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8448 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> k1_xboole_0 = k1_group_2(A,k1_subset_1(u1_struct_0(A))))) # label(t8_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8449 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_finset_1(B) -> -((all C -((all D (v1_finset_1(D) -> -(k4_card_1(D) = A & (all E (r2_hidden(E,B) -> r1_xboole_0(C,E) & r2_wellord2(C,E) | C = E)) & C = D))) & r2_hidden(C,B))) & (all C (v1_finset_1(C) -> -(k2_nat_1(A,k4_card_1(B)) = k4_card_1(C) & k3_tarski(B) = C)))))))) # label(t186_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8450 (all A all B all C (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & v1_group_1(B) & m1_group_2(C,A) & v1_group_1(C) & m1_group_2(B,A) & l1_group_1(A) -> (C = B <-> r1_group_2(A,B,C)))) # label(redefinition_r1_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8451 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_group_2(D,A) -> k4_group_2(A,C,k13_group_2(A,D,B)) = k13_group_2(A,D,k1_group_1(A,B,C)))))))))) # label(t129_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8452 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> g1_group_1(u1_struct_0(A),u1_group_1(A)) = k6_group_2(A))) # label(d8_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8453 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_group_2(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k13_group_2(A,B,C) = k4_group_2(A,C,k7_group_2(A,B)))))))) # label(d14_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8454 (all A all B (l1_group_1(B) & v4_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (m1_group_2(D,B) -> (r2_hidden(A,k11_group_2(B,D,C)) <-> (exists E ((exists F (m1_subset_1(F,u1_struct_0(B)) & r2_hidden(F,C) & r1_rlvect_1(D,E) & k1_group_1(B,E,F) = A)) & m1_subset_1(E,u1_struct_0(B))))))))))) # label(t115_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8455 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(D,C) <-> (exists E (k12_group_2(A,B,E) = D & m1_subset_1(E,u1_struct_0(A))))))) <-> C = k14_group_2(A,B)))))))) # label(d15_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8456 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_group_2(C,A) -> k1_card_1(k12_group_2(A,C,B)) = k8_group_1(C) & k1_card_1(k13_group_2(A,C,B)) = k8_group_1(C))))))) # label(t155_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8457 (all A all B all C (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & m1_group_2(B,A) & v4_group_1(A) -> m1_subset_1(k11_group_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k11_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8458 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> -(v4_group_1(A) & l1_group_1(A) & (all D (v1_group_1(D) & m1_group_2(D,A) -> k2_group_2(A,k7_group_2(A,B),k7_group_2(A,C)) != u1_struct_0(D))) & v7_group_1(A) & v3_group_1(A) & -v3_struct_0(A)))))))) # label(t94_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8459 (all A (v3_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_group_1(A) & v4_group_1(A) & v7_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> k4_group_2(A,B,C) = k3_group_2(A,B,C)))))))) # label(t44_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8460 $T # label(t96_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8461 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> k7_group_2(A,k8_group_2(A,B,C)) = k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k7_group_2(A,B),k7_group_2(A,C)))))))) # label(t98_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8462 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_group_2(C,A) -> r2_hidden(B,k12_group_2(A,C,B)) & r2_hidden(B,k13_group_2(A,C,B)))))))) # label(t130_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8463 (all A (-v3_struct_0(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_xboole_0 = k4_group_2(A,B,k1_subset_1(u1_struct_0(A))) & k1_xboole_0 = k3_group_2(A,B,k1_subset_1(u1_struct_0(A))))))) # label(t41_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8464 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_group_2(C,A) -> r2_wellord2(k7_group_2(A,C),k12_group_2(A,C,B)) & r2_wellord2(k7_group_2(A,C),k13_group_2(A,C,B)))))))) # label(t154_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8465 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_group_2(D,A) -> (r1_rlvect_1(D,B) & r1_rlvect_1(D,C) -> r1_rlvect_1(D,k1_group_1(A,B,C))))))))))) # label(t59_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8466 $T # label(t31_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8467 $T # label(t124_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8468 (all A all B (v4_group_1(B) & l1_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (m1_group_2(C,B) -> (all D (m1_group_2(D,B) -> (r1_rlvect_1(k8_group_2(B,C,D),A) <-> r1_rlvect_1(C,A) & r1_rlvect_1(D,A)))))))) # label(t99_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8469 (all A all B (l1_group_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> m1_subset_1(k1_group_2(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k1_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8470 (all A all B all C (v3_group_1(A) & l1_group_1(A) & m1_group_2(C,A) & m1_group_2(B,A) & v4_group_1(A) & -v3_struct_0(A) -> v1_group_1(k9_group_2(A,B,C)) & m1_group_2(k9_group_2(A,B,C),A))) # label(dt_k9_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8471 (all A (l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (v4_group_1(A) -> k4_group_2(A,D,k2_group_2(A,B,C)) = k2_group_2(A,B,k4_group_2(A,D,C))))))))))) # label(t37_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8472 $T # label(t74_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8473 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_group_2(B,A) -> (all C (v1_group_1(C) & m1_group_2(C,A) -> (m1_group_2(C,B) <-> r1_group_2(A,k9_group_2(A,C,B),C)))))))) # label(t107_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8474 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> r2_hidden(k7_group_2(A,B),k15_group_2(A,B)) & r2_hidden(k7_group_2(A,B),k14_group_2(A,B)))))) # label(t165_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8475 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (v6_group_1(A) -> v1_finset_1(k14_group_2(A,B)) & v1_finset_1(k15_group_2(A,B))))))) # label(t164_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8476 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_group_2(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k12_group_2(A,B,C) = k3_group_2(A,C,k7_group_2(A,B)))))))) # label(d13_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8477 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k1_group_2(A,B) = a_2_0_group_2(A,B))))) # label(d1_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8478 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (v6_group_1(A) -> k9_group_1(A) = k17_group_2(A,k5_group_2(A))))) # label(t183_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8479 $T # label(t163_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8480 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_group_2(B,A) -> k7_group_2(A,B) = k13_group_2(A,B,k2_group_1(A)) & k12_group_2(A,B,k2_group_1(A)) = k7_group_2(A,B))))) # label(t132_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8481 (all A all B (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B,A) -> m1_subset_1(k14_group_2(A,B),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))) # label(dt_k14_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8482 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & v1_group_1(A) & -v3_struct_0(A) -> (all B (v1_group_1(B) & m1_group_2(B,A) -> r1_group_2(A,k9_group_2(A,B,k6_group_2(A)),B) & r1_group_2(A,k9_group_2(A,k6_group_2(A),B),B))))) # label(t104_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8483 (all A all B (-v3_struct_0(B) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) -> (all C (m1_group_2(C,B) -> (r1_rlvect_1(C,A) <-> r2_hidden(A,k7_group_2(B,C))))))) # label(t88_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8484 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_group_2(C,A) -> (all D (m1_group_2(D,A) -> k11_group_2(A,C,k11_group_2(A,D,B)) = k2_group_2(A,k11_group_2(A,C,k7_group_2(A,D)),B))))))))) # label(t121_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8485 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_group_2(B,A) -> k1_card_1(k14_group_2(A,B)) = k16_group_2(A,B))))) # label(d17_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8486 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> v4_group_1(B))))) # label(cc1_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8487 $T # label(t46_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8488 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (v3_group_1(A) & v4_group_1(A) & v7_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> v7_group_1(B)))))) # label(t62_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8489 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> k17_group_2(A,k6_group_2(A)) = np__1)) # label(t180_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8490 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> k16_group_2(A,k5_group_2(A)) = k8_group_1(A))) # label(t182_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8491 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_group_2(C,A) -> (exists D (v1_group_1(D) & m1_group_2(D,A) & u1_struct_0(D) = k4_group_2(A,k3_group_1(A,B),k12_group_2(A,C,B)))))))))) # label(t150_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8492 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> (all D (v1_group_1(D) & m1_group_2(D,A) -> (k3_xboole_0(u1_struct_0(B),u1_struct_0(C)) = u1_struct_0(D) -> r1_group_2(A,D,k8_group_2(A,B,C))))) & (all D (m1_group_2(D,A) -> (D = k8_group_2(A,B,C) -> u1_struct_0(D) = k3_xboole_0(u1_struct_0(B),u1_struct_0(C))))))))))) # label(t97_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8493 (all A (-v3_struct_0(A) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> m1_group_2(A,k6_group_2(A)))) # label(t79_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8494 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_group_2(D,A) -> k11_group_2(A,D,k2_group_2(A,B,C)) = k2_group_2(A,k11_group_2(A,D,B),C))))))))) # label(t118_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8495 $T # label(t158_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8496 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) & v1_group_1(B) -> r1_group_2(A,k8_group_2(A,B,B),B))))) # label(t100_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8497 (all A (-v3_struct_0(A) & v1_group_1(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_group_2(B,A) & v1_group_1(B) -> (np__1 = k17_group_2(A,B) & v1_finset_1(k14_group_2(A,B)) -> A = B))))) # label(t181_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8498 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k2_group_2(A,k7_group_2(A,B),C) = k11_group_2(A,B,C))))))) # label(d12_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8499 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_group_2(B,A) -> k4_group_1(B) = k8_relset_1(u1_struct_0(A),u1_struct_0(A),k4_group_1(A),u1_struct_0(B)))))) # label(t58_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8500 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_group_2(C,A) -> (v3_group_1(A) & l1_group_1(A) & v7_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> k10_group_2(A,C,B) = k11_group_2(A,C,B)))))))) # label(t122_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8501 (all A (-v3_struct_0(A) & l1_group_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v7_group_1(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> k2_group_2(A,B,C) = k2_group_2(A,C,B)))))))) # label(t29_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8502 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_group_2(B,A) -> r1_rlvect_1(B,k2_group_1(A)))))) # label(t55_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8503 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> k7_group_2(A,B) = u1_struct_0(B))))) # label(d9_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8504 (all A (l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> r1_rlvect_1(A,C))))))) # label(t50_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8505 (all A (-v3_struct_0(A) & l1_group_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> a_3_0_group_2(A,B,C) = k2_group_2(A,B,C))))))) # label(d2_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8506 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> r1_group_2(A,k9_group_2(A,B,k5_group_2(A)),k5_group_2(A)) & r1_group_2(A,k9_group_2(A,k5_group_2(A),B),k5_group_2(A)))))) # label(t103_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8507 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> (all D (m1_group_2(D,A) & v1_group_1(D) -> (k8_group_2(A,B,C) = D <-> u1_struct_0(D) = k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k7_group_2(A,B),k7_group_2(A,C))))))))))) # label(d10_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8508 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) -> m1_subset_1(k18_group_2(A,B),k5_finsub_1(A)))) # label(dt_k18_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8509 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_group_2(B,A) -> m1_group_2(k5_group_2(A),B))))) # label(t77_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8510 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_rlvect_1(B,D) -> r1_rlvect_1(C,D)))) -> m1_group_2(B,C)))))))) # label(t67_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8511 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> r1_tarski(k8_group_1(B),k8_group_1(A)))))) # label(t83_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8512 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,B) & r2_hidden(C,B) -> r2_hidden(k1_group_1(A,C,D),B)))))) & (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,B) -> r2_hidden(k3_group_1(A,C),B)))) -> k2_group_2(A,B,B) = B))))) # label(t26_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8513 (all A (-v3_struct_0(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k3_group_2(A,k2_group_1(A),B) = B & B = k4_group_2(A,k2_group_1(A),B))))) # label(t43_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8514 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> u1_struct_0(A) = k3_group_2(A,B,k2_subset_1(u1_struct_0(A))) & k4_group_2(A,B,k2_subset_1(u1_struct_0(A))) = u1_struct_0(A))))) # label(t42_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8515 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_group_2(C,A) -> (r2_hidden(B,k7_group_2(A,C)) -> r2_hidden(k3_group_1(A,B),k7_group_2(A,C))))))))) # label(t90_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8516 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_group_2(B,A) -> u1_struct_0(A) = k5_setfam_1(u1_struct_0(A),k14_group_2(A,B)) & k5_setfam_1(u1_struct_0(A),k15_group_2(A,B)) = u1_struct_0(A))))) # label(t167_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8517 $T # label(t11_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8518 (all A all B (l1_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (r2_hidden(A,k4_group_2(B,D,C)) <-> (exists E (k1_group_1(B,E,D) = A & r2_hidden(E,C) & m1_subset_1(E,u1_struct_0(B))))))))))) # label(t34_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8519 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_group_2(D,A) -> k2_group_2(A,B,k11_group_2(A,D,C)) = k2_group_2(A,k10_group_2(A,D,B),C))))))))) # label(t117_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8520 $T # label(t157_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8521 (all A (l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k2_group_2(A,k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),B,C),D),k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k2_group_2(A,B,D),k2_group_2(A,C,D))))))))))) # label(t19_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8522 $T # label(t1_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8523 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_group_2(C,A) -> r1_tarski(k12_group_2(A,C,k6_group_1(A,np__2,B)),k2_group_2(A,k12_group_2(A,C,B),k12_group_2(A,C,B))))))))) # label(t141_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8524 $T # label(t4_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8525 (all A (l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (v4_group_1(A) -> k2_group_2(A,k2_group_2(A,B,C),D) = k2_group_2(A,B,k2_group_2(A,C,D))))))))))) # label(t14_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8526 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_group_2(D,A) -> r2_wellord2(k13_group_2(A,D,B),k13_group_2(A,D,C)))))))))) # label(t153_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8527 (all A all B all C (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B,A) & v1_group_1(C) & m1_group_2(C,A) & v1_group_1(B) -> r1_group_2(A,B,B))) # label(reflexivity_r1_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8528 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> (all D (m1_group_2(D,A) -> (m1_group_2(B,C) & m1_group_2(B,D) -> m1_group_2(B,k9_group_2(A,C,D))))))))))) # label(t109_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8529 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (v6_group_1(A) -> r1_xreal_0(k9_group_1(B),k9_group_1(A))))))) # label(t84_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8530 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (v1_group_1(B) & m1_group_2(B,A) -> (np__1 = k9_group_1(B) & v6_group_1(B) -> r1_group_2(A,B,k5_group_2(A))))))) # label(t82_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8531 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_rlvect_1(B,D) <-> r1_rlvect_1(C,D)))) -> g1_group_1(u1_struct_0(B),u1_group_1(B)) = g1_group_1(u1_struct_0(C),u1_group_1(C))))))))) # label(t69_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8532 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> (all D (m1_group_2(D,A) -> (m1_group_2(B,C) -> m1_group_2(k9_group_2(A,B,D),C)))))))))) # label(t108_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8533 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_group_2(C,A) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (B = D -> k3_group_1(C,D) = k3_group_1(A,B)))))))))) # label(t57_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8534 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k7_domain_1(u1_struct_0(A),k3_group_1(A,B),k3_group_1(A,C)) = k1_group_2(A,k7_domain_1(u1_struct_0(A),B,C)))))))) # label(t7_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8535 $T # label(t159_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8536 (all A all B all C (-v3_struct_0(B) & v3_group_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & l1_group_1(B) & v4_group_1(B) -> ((exists D (k3_group_1(B,D) = A & r2_hidden(D,C) & m1_subset_1(D,u1_struct_0(B)))) <-> r2_hidden(A,a_2_0_group_2(B,C))))) # label(fraenkel_a_2_0_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8537 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_group_2(D,A) -> (r1_rlvect_1(D,k1_group_1(A,C,k3_group_1(A,B))) <-> k13_group_2(A,D,B) = k13_group_2(A,D,C)))))))))) # label(t143_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8538 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> v1_group_1(k6_group_2(A)) & m1_group_2(k6_group_2(A),A))) # label(dt_k6_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8539 (all A all B (-v3_struct_0(B) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_group_2(D,B) -> ((exists E (r1_rlvect_1(D,E) & k1_group_1(B,C,E) = A & m1_subset_1(E,u1_struct_0(B)))) <-> r2_hidden(A,k12_group_2(B,D,C))))))))) # label(t125_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8540 (all A (l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r2_hidden(D,B) & r2_hidden(E,C) -> k1_group_1(A,D,E) = k1_group_1(A,E,D)))))) -> k2_group_2(A,C,B) = k2_group_2(A,B,C)))))))) # label(t28_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8541 $T # label(t86_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8542 (all A all B all C (m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & l1_group_1(A) & -v3_struct_0(A) -> m1_subset_1(k4_group_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k4_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8543 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & v1_group_1(A) -> (all B (v1_group_1(B) & m1_group_2(B,A) -> (k1_tarski(u1_struct_0(A)) = k15_group_2(A,B) -> B = A))))) # label(t174_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8544 (all A (l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k7_domain_1(u1_struct_0(A),k1_group_1(A,B,C),k1_group_1(A,B,D)) = k2_group_2(A,k6_domain_1(u1_struct_0(A),B),k7_domain_1(u1_struct_0(A),C,D)))))))))) # label(t23_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8545 $T # label(t131_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8546 (all A (-v3_struct_0(A) & l1_group_1(A) & v3_group_1(A) -> (all B (l1_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (m1_group_2(B,A) <-> u1_group_1(B) = k1_realset1(u1_group_1(A),u1_struct_0(B)) & r1_tarski(u1_struct_0(B),u1_struct_0(A))))))) # label(d5_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8547 $T # label(t47_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8548 $T # label(t72_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8549 (all A (-v3_struct_0(A) & l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v6_group_1(A) -> v1_finset_1(B)))))) # label(t3_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8550 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_group_2(B,A) & v1_group_1(B) -> (u1_struct_0(B) = k6_domain_1(u1_struct_0(A),k2_group_1(A)) <-> k5_group_2(A) = B))))) # label(d7_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8551 (all A all B (v4_group_1(A) & m1_group_2(B,A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> m1_subset_1(k7_group_2(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k7_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8552 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> (all D (m1_group_2(D,A) -> r1_group_2(A,k9_group_2(A,k9_group_2(A,B,C),D),k9_group_2(A,B,k9_group_2(A,C,D))))))))))) # label(t102_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8553 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_group_2(C,A) -> (k12_group_2(A,C,B) = k7_group_2(A,C) <-> r1_rlvect_1(C,B)))))))) # label(t136_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8554 (all A all B all C (l1_group_1(A) & v1_group_1(B) & v1_group_1(C) & m1_group_2(C,A) & m1_group_2(B,A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (r1_group_2(A,B,C) -> r1_group_2(A,C,B)))) # label(symmetry_r1_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8555 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_group_2(B,A) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> r1_rlvect_1(B,C))) -> g1_group_1(u1_struct_0(B),u1_group_1(B)) = g1_group_1(u1_struct_0(A),u1_group_1(A))))))) # label(t71_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8556 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> k16_group_2(A,B) = k1_card_1(k14_group_2(A,B)) & k1_card_1(k15_group_2(A,B)) = k16_group_2(A,B))))) # label(t175_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8557 (all A (-v3_struct_0(A) & l1_group_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> k2_group_2(A,k1_finsub_1(k1_zfmisc_1(u1_struct_0(A)),B,C),D) = k1_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k2_group_2(A,B,D),k2_group_2(A,C,D)))))))))) # label(t17_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8558 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) & v1_group_1(B) -> (a_1_0_group_2(A) = k15_group_2(A,B) -> r1_group_2(A,B,k5_group_2(A))))))) # label(t171_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8559 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> v6_group_1(k5_group_2(A)))) # label(t80_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8560 $T # label(t162_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8561 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(C,B) & r2_hidden(D,B) -> r2_hidden(k1_group_1(A,C,D),B)))))) & (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,B) -> r2_hidden(k3_group_1(A,C),B)))) & (all C (v1_group_1(C) & m1_group_2(C,A) -> u1_struct_0(C) != B)) & k1_xboole_0 != B))))) # label(t61_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8562 (all A all B all C (-v3_struct_0(A) & l1_group_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> m1_subset_1(k2_group_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k2_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8563 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (v3_group_1(B) & l1_group_1(B) & v4_group_1(B) & -v3_struct_0(B) -> (all C (v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & -v3_struct_0(C) -> (m1_group_2(B,C) & m1_group_2(A,B) -> m1_group_2(A,C)))))))) # label(t65_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8564 (all A (l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (v6_group_1(A) -> v6_group_1(B)))))) # label(t48_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8565 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & v1_group_1(A) -> (all B (v1_group_1(B) & m1_group_2(B,A) -> (k14_group_2(A,B) = k1_tarski(u1_struct_0(A)) -> A = B))))) # label(t173_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8566 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> (r1_tarski(u1_struct_0(B),u1_struct_0(C)) -> m1_group_2(B,C)))))))) # label(t66_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8567 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_domain_1(u1_struct_0(A),k3_group_1(A,B)) = k1_group_2(A,k6_domain_1(u1_struct_0(A),B)))))) # label(t6_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8568 (all A (l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> k2_group_2(A,k7_domain_1(u1_struct_0(A),B,C),k7_domain_1(u1_struct_0(A),D,E)) = k9_domain_1(u1_struct_0(A),k1_group_1(A,B,D),k1_group_1(A,B,E),k1_group_1(A,C,D),k1_group_1(A,C,E)))))))))))) # label(t25_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8569 $T # label(t95_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8570 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(B = k1_xboole_0 & k1_xboole_0 != k1_group_2(A,B)) & -(B != k1_xboole_0 & k1_xboole_0 = k1_group_2(A,B)))))) # label(t10_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8571 (all A (l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k6_domain_1(u1_struct_0(A),k1_group_1(A,B,C)) = k2_group_2(A,k6_domain_1(u1_struct_0(A),B),k6_domain_1(u1_struct_0(A),C)))))))) # label(t22_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8572 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_group_2(D,A) -> k4_group_2(A,C,k12_group_2(A,D,B)) = k3_group_2(A,B,k13_group_2(A,D,C)))))))))) # label(t128_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8573 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k1_group_2(A,k2_group_2(A,B,C)) = k2_group_2(A,k1_group_2(A,C),k1_group_2(A,B)))))))) # label(t15_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8574 $T # label(t113_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8575 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> k14_group_2(A,k6_group_2(A)) = k1_tarski(u1_struct_0(A)) & k1_tarski(u1_struct_0(A)) = k15_group_2(A,k6_group_2(A)))) # label(t172_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8576 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> m1_group_2(k9_group_2(A,B,C),C) & m1_group_2(k9_group_2(A,B,C),B))))))) # label(t106_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8577 $T # label(t73_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8578 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v7_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> v7_group_1(B) & v4_group_1(B))))) # label(cc2_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8579 (all A (-v3_struct_0(A) & l1_group_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k2_group_2(A,B,k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),C,D)),k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k2_group_2(A,B,C),k2_group_2(A,B,D))))))))))) # label(t18_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8580 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (v4_group_1(B) & l1_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (m1_group_2(B,A) & m1_group_2(A,B) -> g1_group_1(u1_struct_0(B),u1_group_1(B)) = g1_group_1(u1_struct_0(A),u1_group_1(A))))))) # label(t64_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8581 (all A (l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> k2_group_2(A,B,k1_finsub_1(k1_zfmisc_1(u1_struct_0(A)),C,D)) = k1_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k2_group_2(A,B,C),k2_group_2(A,B,D)))))))))) # label(t16_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8582 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> k7_group_2(A,B) != k1_xboole_0)))) # label(t87_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8583 (all A all B (-v3_struct_0(B) & l1_group_1(B) & v4_group_1(B) & v3_group_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (m1_group_2(D,B) -> (r2_hidden(A,k10_group_2(B,D,C)) <-> (exists E (m1_subset_1(E,u1_struct_0(B)) & (exists F (m1_subset_1(F,u1_struct_0(B)) & r2_hidden(E,C) & r1_rlvect_1(D,F) & k1_group_1(B,E,F) = A))))))))))) # label(t114_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8584 (all A all B (v3_group_1(A) & l1_group_1(A) & m1_group_2(B,A) & v4_group_1(A) & -v3_struct_0(A) -> m2_subset_1(k17_group_2(A,B),k1_numbers,k5_numbers))) # label(dt_k17_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8585 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_group_2(C,A) -> (all D (m1_group_2(D,A) -> k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k13_group_2(A,C,B),k13_group_2(A,D,B)) = k13_group_2(A,k9_group_2(A,C,D),B))))))))) # label(t149_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8586 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v7_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k1_group_2(A,k2_group_2(A,B,C)) = k2_group_2(A,k1_group_2(A,B),k1_group_2(A,C)))))))) # label(t30_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.49 8587 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> r1_rlvect_1(C,k2_group_1(B)))))))) # label(t56_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8588 (all A (-v3_struct_0(A) & l1_group_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k1_xboole_0 = k2_group_2(A,B,k1_subset_1(u1_struct_0(A))) & k1_xboole_0 = k2_group_2(A,k1_subset_1(u1_struct_0(A)),B))))) # label(t20_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8589 (all A all B all C (-v3_struct_0(A) & l1_group_1(A) & m1_group_2(B,A) & m1_subset_1(C,u1_struct_0(A)) & v4_group_1(A) & v3_group_1(A) -> m1_subset_1(k12_group_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k12_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8590 (all A (l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (v4_group_1(A) -> k4_group_2(A,D,k3_group_2(A,C,B)) = k3_group_2(A,C,k4_group_2(A,D,B))))))))))) # label(t39_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8591 (all A (l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k2_group_2(A,C,k6_domain_1(u1_struct_0(A),B)) = k4_group_2(A,B,C))))))) # label(d4_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8592 (all A all B (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B,A) -> m1_subset_1(k15_group_2(A,B),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))) # label(dt_k15_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8593 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (v1_group_1(B) & m1_group_2(B,A) -> (k14_group_2(A,B) = a_1_0_group_2(A) -> r1_group_2(A,B,k5_group_2(A))))))) # label(t170_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8594 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (v1_finset_1(k14_group_2(A,B)) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (C = k17_group_2(A,B) <-> (exists D (v1_finset_1(D) & C = k4_card_1(D) & k14_group_2(A,B) = D)))))))))) # label(d18_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8595 (all A all B (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B,A) & -v3_struct_0(A) -> v1_card_1(k16_group_2(A,B)))) # label(dt_k16_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8596 (all A all B (v3_group_1(B) & l1_group_1(B) & v4_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_group_2(D,B) -> (r2_hidden(A,k13_group_2(B,D,C)) <-> (exists E (m1_subset_1(E,u1_struct_0(B)) & k1_group_1(B,E,C) = A & r1_rlvect_1(D,E)))))))))) # label(t126_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8597 (all A all B all C (-v3_struct_0(A) & v3_group_1(A) & m1_group_2(B,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & l1_group_1(A) & v4_group_1(A) -> m1_subset_1(k10_group_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k10_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8598 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_group_2(B,A) & v1_group_1(B) -> (all C (m1_group_2(C,A) & v1_group_1(C) -> (r1_group_2(A,B,C) <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_rlvect_1(B,D) <-> r1_rlvect_1(C,D))))))))))) # label(d6_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8599 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> m1_group_2(k5_group_2(A),A) & v1_group_1(k5_group_2(A)))) # label(dt_k5_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8600 $T # label(t161_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8601 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> (u1_struct_0(B) = u1_struct_0(C) -> g1_group_1(u1_struct_0(B),u1_group_1(B)) = g1_group_1(u1_struct_0(C),u1_group_1(C))))))))) # label(t68_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8602 $T # label(t160_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8603 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_group_2(C,A) -> r1_tarski(k7_group_2(A,C),k2_group_2(A,k13_group_2(A,C,B),k13_group_2(A,C,k3_group_1(A,B)))) & r1_tarski(k7_group_2(A,C),k2_group_2(A,k13_group_2(A,C,k3_group_1(A,B)),k13_group_2(A,C,B))))))))) # label(t146_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8604 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_group_2(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(D,C) <-> (exists E (D = k13_group_2(A,B,E) & m1_subset_1(E,u1_struct_0(A))))))) <-> C = k15_group_2(A,B)))))))) # label(d16_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8605 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_group_2(C,A) -> (all D (m1_group_2(D,A) -> k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k12_group_2(A,C,B),k12_group_2(A,D,B)) = k12_group_2(A,k9_group_2(A,C,D),B))))))))) # label(t148_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8606 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_domain_1(u1_struct_0(A),B) = k12_group_2(A,k5_group_2(A),B) & k6_domain_1(u1_struct_0(A),B) = k13_group_2(A,k5_group_2(A),B))))) # label(t133_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8607 (all A all B all C (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & m1_group_2(B,A) & m1_group_2(C,A) & v4_group_1(A) -> k9_group_2(A,C,B) = k9_group_2(A,B,C))) # label(commutativity_k9_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8608 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) -> (all B (m1_group_2(B,A) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> m1_subset_1(C,u1_struct_0(A)))))))) # label(t51_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8609 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> (all D (m1_group_2(D,A) -> (m1_group_2(B,C) -> m1_group_2(k9_group_2(A,B,D),k9_group_2(A,C,D))))))))))) # label(t110_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8610 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> a_1_0_group_2(A) = k14_group_2(A,k5_group_2(A)))) # label(t168_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8611 (all A (-v3_struct_0(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k7_domain_1(u1_struct_0(A),k1_group_1(A,B,D),k1_group_1(A,C,D)) = k2_group_2(A,k7_domain_1(u1_struct_0(A),B,C),k6_domain_1(u1_struct_0(A),D)))))))))) # label(t24_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8612 (all A (l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (v4_group_1(A) -> k2_group_2(A,B,k3_group_2(A,D,C)) = k2_group_2(A,k4_group_2(A,D,B),C)))))))))) # label(t36_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8613 (all A (v3_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_group_2(D,A) -> (all E (m1_subset_1(E,u1_struct_0(D)) -> (all F (m1_subset_1(F,u1_struct_0(D)) -> (C = F & B = E -> k1_group_1(A,B,C) = k1_group_1(D,E,F)))))))))))))) # label(t52_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8614 (all A (v3_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> l1_group_1(B) & v3_group_1(B) & -v3_struct_0(B))))) # label(dt_m1_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8615 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (exists B (v3_group_1(B) & v4_group_1(B) & v2_group_1(B) & v1_group_1(B) & -v3_struct_0(B) & m1_group_2(B,A))))) # label(rc1_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8616 $T # label(t2_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8617 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> u1_struct_0(A) = k13_group_2(A,k6_group_2(A),B) & u1_struct_0(A) = k12_group_2(A,k6_group_2(A),B))))) # label(t134_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8618 (all A (-v3_struct_0(A) & l1_group_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (v4_group_1(A) -> k4_group_2(A,k1_group_1(A,C,D),B) = k4_group_2(A,D,k4_group_2(A,C,B))))))))))) # label(t40_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8619 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_group_2(B,A) -> k5_group_2(B) = k5_group_2(A))))) # label(t75_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8620 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) & v1_group_1(B) -> (k16_group_2(A,B) = k8_group_1(A) & v1_finset_1(k14_group_2(A,B)) -> v6_group_1(A) & r1_group_2(A,B,k5_group_2(A))))))) # label(t185_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8621 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> (v6_group_1(B) | v6_group_1(C) -> v6_group_1(k9_group_2(A,B,C))))))))) # label(t111_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8622 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_group_2(C,A) -> (-v3_struct_0(A) & l1_group_1(A) & v7_group_1(A) & v4_group_1(A) & v3_group_1(A) -> k12_group_2(A,C,B) = k13_group_2(A,C,B)))))))) # label(t135_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8623 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_group_2(C,A) -> (all D (m1_group_2(D,A) -> k10_group_2(A,D,k11_group_2(A,C,B)) = k11_group_2(A,C,k10_group_2(A,D,B)))))))))) # label(t120_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8624 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> u1_struct_0(A) = k1_group_2(A,k2_subset_1(u1_struct_0(A))))) # label(t9_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8625 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_group_2(D,A) -> (r2_hidden(B,k7_group_2(A,D)) & r2_hidden(C,k7_group_2(A,D)) -> r2_hidden(k1_group_1(A,B,C),k7_group_2(A,D))))))))))) # label(t89_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8626 (all A (-v3_struct_0(A) & v1_group_1(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_group_2(B,A) -> m1_group_2(B,k6_group_2(A)))))) # label(t78_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8627 (all A all B (v4_group_1(B) & l1_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> ((exists D (k3_group_1(B,D) = A & r2_hidden(D,C) & m1_subset_1(D,u1_struct_0(B)))) <-> r2_hidden(A,k1_group_2(B,C))))))) # label(t5_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8628 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> k2_group_1(C) = k2_group_1(B))))))) # label(t54_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8629 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_group_2(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k10_group_2(A,B,C) = k2_group_2(A,C,k7_group_2(A,B)))))))) # label(d11_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8630 $T # label(t32_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8631 (all A (l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k3_group_2(A,B,C) = k2_group_2(A,k6_domain_1(u1_struct_0(A),B),C))))))) # label(d3_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8632 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_group_2(D,A) -> (-r1_xboole_0(k12_group_2(A,D,B),k12_group_2(A,D,C)) <-> k12_group_2(A,D,C) = k12_group_2(A,D,B)))))))))) # label(t138_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8633 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> a_1_0_group_2(A) = k15_group_2(A,k5_group_2(A)))) # label(t169_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8634 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_group_2(B,A) -> k2_group_2(A,k7_group_2(A,B),k7_group_2(A,B)) = k7_group_2(A,B))))) # label(t91_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8635 (all A all B (m1_subset_1(B,A) & -v1_xboole_0(A) -> k18_group_2(A,B) = k1_tarski(B))) # label(redefinition_k18_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8636 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_group_2(D,A) -> r1_tarski(k4_group_2(A,C,k13_group_2(A,D,B)),k2_group_2(A,k13_group_2(A,D,B),k13_group_2(A,D,C))))))))))) # label(t145_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8637 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_group_2(D,A) -> k3_group_2(A,B,k12_group_2(A,D,C)) = k12_group_2(A,D,k1_group_1(A,B,C)))))))))) # label(t127_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8638 (all A all B (l1_group_1(B) & v4_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (r2_hidden(A,a_1_0_group_2(B)) <-> (exists C (m1_subset_1(C,u1_struct_0(B)) & k6_domain_1(u1_struct_0(B),C) = A))))) # label(fraenkel_a_1_0_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8639 (all A (l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (v4_group_1(A) -> k2_group_2(A,k3_group_2(A,D,B),C) = k3_group_2(A,D,k2_group_2(A,B,C))))))))))) # label(t35_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8640 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_group_2(C,A) -> (all D (m1_group_2(D,A) -> k10_group_2(A,D,k10_group_2(A,C,B)) = k2_group_2(A,B,k11_group_2(A,C,k7_group_2(A,D))))))))))) # label(t119_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8641 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_group_2(B,A) -> k7_group_2(A,B) = k1_group_2(A,k7_group_2(A,B)))))) # label(t92_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8642 (all A (v1_group_1(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> k9_group_2(A,k6_group_2(A),k6_group_2(A)) = A)) # label(t105_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8643 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> (all D (m1_group_2(D,C) -> (D = B & v6_group_1(A) -> k2_nat_1(k17_group_2(C,D),k17_group_2(A,C)) = k17_group_2(A,B)))))))))) # label(t179_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8644 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> k5_group_2(C) = k5_group_2(B))))))) # label(t76_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8645 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_group_2(C,A) -> (r1_rlvect_1(C,B) -> r1_rlvect_1(C,k3_group_1(A,B))))))))) # label(t60_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8646 (all A (l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (v4_group_1(A) -> k3_group_2(A,C,k3_group_2(A,D,B)) = k3_group_2(A,k1_group_1(A,C,D),B)))))))))) # label(t38_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8647 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_group_2(B,A) -> r2_wellord2(k14_group_2(A,B),k15_group_2(A,B)))))) # label(t166_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8648 (all A (-v3_struct_0(A) & v1_group_1(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_group_2(B,A) & v1_group_1(B) -> (u1_struct_0(A) = u1_struct_0(B) -> B = A))))) # label(t70_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8649 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_group_2(D,A) -> (k12_group_2(A,D,C) = k12_group_2(A,D,B) <-> r1_rlvect_1(D,k1_group_1(A,k3_group_1(A,C),B))))))))))) # label(t137_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8650 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_group_2(C,A) -> r1_tarski(k13_group_2(A,C,k6_group_1(A,np__2,B)),k2_group_2(A,k13_group_2(A,C,B),k13_group_2(A,C,B))))))))) # label(t147_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8651 $T # label(t112_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8652 (all A all B (-v3_struct_0(B) & l1_group_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> ((exists E ((exists F (m1_subset_1(F,u1_struct_0(B)) & A = k1_group_1(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D))) & m1_subset_1(E,u1_struct_0(B)))) <-> r2_hidden(A,k2_group_2(B,C,D))))))))) # label(t12_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8653 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> k9_group_1(k5_group_2(A)) = np__1)) # label(t81_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8654 (all A all B all C (-v3_struct_0(A) & v4_group_1(A) & m1_group_2(C,A) & m1_group_2(B,A) & l1_group_1(A) & v3_group_1(A) -> v1_group_1(k8_group_2(A,B,C)) & m1_group_2(k8_group_2(A,B,C),A))) # label(dt_k8_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8655 (all A all B all C all D (-v3_struct_0(B) & l1_group_1(B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (r2_hidden(A,a_3_0_group_2(B,C,D)) <-> (exists E exists F (r2_hidden(F,D) & r2_hidden(E,C) & A = k1_group_1(B,E,F) & m1_subset_1(F,u1_struct_0(B)) & m1_subset_1(E,u1_struct_0(B))))))) # label(fraenkel_a_3_0_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8656 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_group_2(C,A) -> (r1_rlvect_1(C,B) <-> k7_group_2(A,C) = k13_group_2(A,C,B)))))))) # label(t142_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8657 (all A all B all C (-v3_struct_0(A) & l1_group_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> m1_subset_1(k3_group_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k3_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8658 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> ((exists D (k2_group_2(A,k7_group_2(A,B),k7_group_2(A,C)) = u1_struct_0(D) & m1_group_2(D,A))) -> k2_group_2(A,k7_group_2(A,B),k7_group_2(A,C)) = k2_group_2(A,k7_group_2(A,C),k7_group_2(A,B))) & -(k2_group_2(A,k7_group_2(A,C),k7_group_2(A,B)) = k2_group_2(A,k7_group_2(A,B),k7_group_2(A,C)) & (all D (v1_group_1(D) & m1_group_2(D,A) -> u1_struct_0(D) != k2_group_2(A,k7_group_2(A,B),k7_group_2(A,C))))))))))) # label(t93_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8659 $T # label(t45_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8660 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_group_2(D,A) -> (-r1_xboole_0(k13_group_2(A,D,B),k13_group_2(A,D,C)) <-> k13_group_2(A,D,B) = k13_group_2(A,D,C)))))))))) # label(t144_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8661 (all A (v1_group_1(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) & v1_group_1(B) -> (k9_group_1(A) = k9_group_1(B) & v6_group_1(A) -> A = B))))) # label(t85_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8662 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,B) -> r2_hidden(k3_group_1(A,C),B)))) -> B = k1_group_2(A,B)))))) # label(t27_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8663 (all A all B (l1_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (r2_hidden(A,k3_group_2(B,D,C)) <-> (exists E (k1_group_1(B,D,E) = A & r2_hidden(E,C) & m1_subset_1(E,u1_struct_0(B))))))))))) # label(t33_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8664 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> r1_group_2(A,k8_group_2(A,B,C),k8_group_2(A,C,B)))))))) # label(t101_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8665 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_group_2(D,A) -> r2_wellord2(k12_group_2(A,D,B),k12_group_2(A,D,C)))))))))) # label(t151_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8666 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_group_2(C,A) -> r1_tarski(k7_group_2(A,C),k2_group_2(A,k12_group_2(A,C,k3_group_1(A,B)),k12_group_2(A,C,B))) & r1_tarski(k7_group_2(A,C),k2_group_2(A,k12_group_2(A,C,B),k12_group_2(A,C,k3_group_1(A,B)))))))))) # label(t140_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8667 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (k1_xboole_0 != B -> u1_struct_0(A) = k2_group_2(A,B,k2_subset_1(u1_struct_0(A))) & u1_struct_0(A) = k2_group_2(A,k2_subset_1(u1_struct_0(A)),B)))))) # label(t21_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8668 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_group_2(D,A) -> r1_tarski(k12_group_2(A,D,k1_group_1(A,B,C)),k2_group_2(A,k12_group_2(A,D,B),k12_group_2(A,D,C))))))))))) # label(t139_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8669 (all A all B (-v3_struct_0(B) & l1_group_1(B) & v3_group_1(B) -> (all C (m1_group_2(C,B) -> (r1_rlvect_1(C,A) -> r1_rlvect_1(B,A)))))) # label(t49_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8670 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> m1_group_2(A,A))) # label(t63_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8671 (all A all B all C (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & m1_group_2(B,A) & m1_group_2(C,A) & v4_group_1(A) -> k8_group_2(A,B,C) = k9_group_2(A,B,C))) # label(redefinition_k9_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8672 (all A (l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (exists B m1_group_2(B,A)))) # label(existence_m1_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8673 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_group_2(B,A) -> k2_group_1(A) = k2_group_1(B))))) # label(t53_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8674 (all A all B all C (l1_group_1(A) & m1_subset_1(C,u1_struct_0(A)) & m1_group_2(B,A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> m1_subset_1(k13_group_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k13_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8675 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_group_2(D,A) -> k2_group_2(A,B,k10_group_2(A,D,C)) = k10_group_2(A,D,k2_group_2(A,B,C)))))))))) # label(t116_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8676 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (v6_group_1(A) -> k2_nat_1(k9_group_1(B),k17_group_2(A,B)) = k9_group_1(A)))))) # label(t177_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8677 (all A (l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (k2_group_2(A,B,C) != k1_xboole_0 <-> B != k1_xboole_0 & k1_xboole_0 != C))))))) # label(t13_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8678 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_group_2(D,A) -> r2_wellord2(k12_group_2(A,D,B),k13_group_2(A,D,C)))))))))) # label(t152_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8679 $T # label(t123_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8680 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (v6_group_1(A) -> r1_nat_1(k9_group_1(B),k9_group_1(A))))))) # label(t178_group_2) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8681 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_vectsp_4(E,A,B) -> (k3_vectsp_4(A,B,k6_vectsp_1(A,B,C,D),E) = u1_struct_0(E) -> k1_rlvect_1(A) = C | r1_rlvect_1(E,D)))))))))))) # label(t66_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8682 $T # label(t98_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8683 (all A (v3_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v11_vectsp_1(B,A) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (v5_rlvect_1(C) & l4_vectsp_1(C,A) & v12_vectsp_1(C,A) & v11_vectsp_1(C,A) & v6_rlvect_1(C) & v4_rlvect_1(C) & v3_rlvect_1(C) & -v3_struct_0(C) -> (m1_vectsp_4(C,A,B) & m1_vectsp_4(B,A,C) -> C = B))))))) # label(t33_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8684 (all A all B all C (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & -v3_struct_0(B) & v4_rlvect_1(B) & v12_vectsp_1(B,A) & m1_vectsp_4(C,A,B) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) & l3_vectsp_1(A) & v8_vectsp_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all D (m2_vectsp_4(D,A,B,C) -> m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))))))) # label(dt_m2_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8685 $T # label(t14_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8686 (all A (-v3_struct_0(A) & l1_group_1(A) -> (all B (-v3_struct_0(B) & l4_vectsp_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> ((all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (r2_hidden(E,C) & r2_hidden(D,C) -> r2_hidden(k2_rlvect_1(B,D,E),C)))))) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (r2_hidden(E,C) -> r2_hidden(k6_vectsp_1(A,B,D,E),C)))))) <-> v1_vectsp_4(C,A,B)))))))) # label(d1_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8687 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v5_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) -> ((all E (m1_subset_1(E,u1_struct_0(B)) -> (r1_rlvect_1(C,E) -> r1_rlvect_1(D,E)))) -> m1_vectsp_4(C,A,D)))))))))) # label(t36_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8688 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_vectsp_4(D,A,B) -> r2_hidden(C,k3_vectsp_4(A,B,C,D)))))))))) # label(t59_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8689 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_vectsp_4(D,A,B) -> (r1_rlvect_1(D,C) -> r1_rlvect_1(D,k5_rlvect_1(B,C))))))))))) # label(t30_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8690 $T # label(t43_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8691 (all A all B (v4_rlvect_1(B) & v7_vectsp_1(B) & v8_vectsp_1(B) & l3_vectsp_1(B) & v4_group_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v12_vectsp_1(C,B) & l4_vectsp_1(C,B) -> (k1_rlvect_1(C) = A <-> r1_rlvect_1(k1_vectsp_4(B,C),A)))))) # label(t46_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8692 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_vectsp_4(D,A,B) -> (all E (m2_vectsp_4(E,A,B,D) -> (all F (m2_vectsp_4(F,A,B,D) -> (r2_hidden(C,E) & r2_hidden(C,F) -> E = F))))))))))))) # label(t97_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8693 (all A all B (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v8_vectsp_1(A) & v3_rlvect_1(B) & v5_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v3_rlvect_1(A) -> m1_vectsp_4(k1_vectsp_4(A,B),A,B) & v11_vectsp_1(k1_vectsp_4(A,B),A))) # label(dt_k1_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8694 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (v4_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m2_vectsp_4(D,A,B,C) -> (r2_hidden(k1_rlvect_1(B),D) <-> u1_struct_0(C) = D))))))))) # label(t92_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8695 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v5_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_vectsp_4(D,A,B) -> (r1_rlvect_1(D,C) <-> r2_hidden(k1_rlvect_1(B),k3_vectsp_4(A,B,C,D))))))))))) # label(t58_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8696 $T # label(t100_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8697 (all A (v3_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_vectsp_4(D,A,B) & v11_vectsp_1(D,A) -> (all E (v11_vectsp_1(E,A) & m1_vectsp_4(E,A,B) -> (k3_vectsp_4(A,B,C,D) = k3_vectsp_4(A,B,C,E) <-> D = E))))))))))) # label(t82_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8698 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) -> (r1_tarski(u1_struct_0(C),u1_struct_0(D)) -> m1_vectsp_4(C,A,D)))))))))) # label(t35_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8699 (all A all B (v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & -v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v4_rlvect_1(B) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (exists C (v4_rlvect_1(C) & v5_rlvect_1(C) & v12_vectsp_1(C,A) & v11_vectsp_1(C,A) & v6_rlvect_1(C) & v3_rlvect_1(C) & -v3_struct_0(C) & m1_vectsp_4(C,A,B))))) # label(rc1_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8700 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_vectsp_4(E,A,B) -> -(k3_vectsp_4(A,B,D,E) = k3_vectsp_4(A,B,C,E) & (all F (m1_subset_1(F,u1_struct_0(B)) -> -(k4_rlvect_1(B,C,F) = D & r1_rlvect_1(E,F))))))))))))))) # label(t80_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8701 (all A all B all C all D all E (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v4_group_1(B) & -v3_struct_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & m1_subset_1(D,u1_struct_0(C)) & m1_vectsp_4(E,B,C) & l4_vectsp_1(C,B) & v12_vectsp_1(C,B) & v6_rlvect_1(C) & v5_rlvect_1(C) & l3_vectsp_1(B) & v8_vectsp_1(B) & v7_vectsp_1(B) & -v3_struct_0(B) -> ((exists F (m1_subset_1(F,u1_struct_0(C)) & r1_rlvect_1(E,F) & A = k4_rlvect_1(C,D,F))) <-> r2_hidden(A,a_4_1_vectsp_4(B,C,D,E))))) # label(fraenkel_a_4_1_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8702 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> -(C != k1_xboole_0 & (all D (v11_vectsp_1(D,A) & m1_vectsp_4(D,A,B) -> C != u1_struct_0(D))) & v1_vectsp_4(C,A,B)))))))) # label(t42_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8703 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_vectsp_4(D,A,B) -> (exists E (m2_vectsp_4(E,A,B,D) & r2_hidden(C,E))))))))))) # label(t84_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8704 $T # label(t77_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8705 $T # label(t99_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8706 $T # label(t56_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8707 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v7_vectsp_1(A) & v9_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_vectsp_4(D,A,B) -> (u1_struct_0(D) = k3_vectsp_4(A,B,k5_rlvect_1(B,C),D) <-> r1_rlvect_1(D,C)))))))))) # label(t67_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8708 $T # label(t11_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8709 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (m1_vectsp_4(F,A,B) -> (r2_hidden(C,k3_vectsp_4(A,B,E,F)) & r2_hidden(C,k3_vectsp_4(A,B,D,F)) -> k3_vectsp_4(A,B,E,F) = k3_vectsp_4(A,B,D,F)))))))))))))) # label(t71_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8710 (all A (-v3_struct_0(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_vectsp_4(C,A,B) & v11_vectsp_1(C,A) -> (all D (v11_vectsp_1(D,A) & m1_vectsp_4(D,A,B) -> (u1_struct_0(D) = u1_struct_0(C) -> D = C))))))))) # label(t37_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8711 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_vectsp_4(E,A,B) -> (all F (m2_vectsp_4(F,A,B,E) -> -(r2_hidden(C,F) & (all G (m1_subset_1(G,u1_struct_0(B)) -> -(r1_rlvect_1(E,G) & D = k6_rlvect_1(B,C,G)))) & r2_hidden(D,F)))))))))))))) # label(t95_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8712 $T # label(t102_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8713 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v3_rlvect_1(A) -> (all B (v5_rlvect_1(B) & v11_vectsp_1(B,A) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> m1_vectsp_4(B,A,k2_vectsp_4(A,B)))))) # label(t53_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8714 (all A (v4_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v5_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_vectsp_4(C,A,B) -> m2_vectsp_4(u1_struct_0(C),A,B,C))))))) # label(t89_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8715 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & -v3_struct_0(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) -> k1_vectsp_4(A,C) = k1_vectsp_4(A,D))))))))) # label(t48_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8716 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_vectsp_4(D,A,B) -> (r2_hidden(k1_rlvect_1(B),k3_vectsp_4(A,B,C,D)) <-> u1_struct_0(D) = k3_vectsp_4(A,B,C,D)))))))))) # label(t63_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8717 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v5_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_vectsp_4(E,A,B) -> (k3_vectsp_4(A,B,D,E) = k3_vectsp_4(A,B,C,E) <-> r2_hidden(C,k3_vectsp_4(A,B,D,E))))))))))))) # label(t70_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8718 (all A (v4_rlvect_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (-v3_struct_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v12_vectsp_1(C,A) & l4_vectsp_1(C,A) -> (all D (-v3_struct_0(D) & v3_rlvect_1(D) & v4_rlvect_1(D) & v6_rlvect_1(D) & v12_vectsp_1(D,A) & l4_vectsp_1(D,A) & v5_rlvect_1(D) -> (m1_vectsp_4(B,A,C) & m1_vectsp_4(C,A,D) -> m1_vectsp_4(B,A,D)))))))))) # label(t34_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8719 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_vectsp_4(C,A,B) -> m1_vectsp_4(k1_vectsp_4(A,C),A,B))))))) # label(t49_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8720 (all A all B (-v3_struct_0(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & -v3_struct_0(B) & v3_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & l3_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> m1_vectsp_4(k2_vectsp_4(A,B),A,B) & v11_vectsp_1(k2_vectsp_4(A,B),A))) # label(dt_k2_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8721 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (v1_vectsp_4(C,A,B) -> r2_hidden(k1_rlvect_1(B),C) | C = k1_xboole_0))))))) # label(t4_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8722 $T # label(t3_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.50 8723 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_vectsp_4(E,A,B) -> (r1_rlvect_1(E,k6_rlvect_1(B,C,D)) <-> (exists F (r2_hidden(C,F) & r2_hidden(D,F) & m2_vectsp_4(F,A,B,E)))))))))))))) # label(t96_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8724 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_vectsp_4(E,A,B) -> (k3_vectsp_4(A,B,D,E) = k3_vectsp_4(A,B,k6_rlvect_1(B,D,C),E) <-> r1_rlvect_1(E,C)))))))))))) # label(t69_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8725 (all A all B all C all D (-v3_struct_0(A) & v6_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & v3_rlvect_1(B) & v5_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & m1_subset_1(C,u1_struct_0(B)) & m1_vectsp_4(D,A,B) & v6_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) & l3_vectsp_1(A) & v7_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> m1_subset_1(k3_vectsp_4(A,B,C,D),k1_zfmisc_1(u1_struct_0(B))))) # label(dt_k3_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8726 $T # label(t55_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8727 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_vectsp_4(D,A,B) -> (r1_rlvect_1(D,C) -> r2_hidden(k5_rlvect_1(B,C),k3_vectsp_4(A,B,C,D))))))))))) # label(t74_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8728 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_vectsp_4(E,A,B) -> (r1_rlvect_1(E,k6_rlvect_1(B,C,D)) <-> (exists F (m1_subset_1(F,u1_struct_0(B)) & r2_hidden(D,k3_vectsp_4(A,B,F,E)) & r2_hidden(C,k3_vectsp_4(A,B,F,E))))))))))))))) # label(t79_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8729 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_vectsp_4(E,A,B) -> (r1_rlvect_1(E,D) -> r1_rlvect_1(E,k6_vectsp_1(A,B,C,D))))))))))))) # label(t29_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8730 (all A (v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_vectsp_4(D,A,B) -> (u1_struct_0(D) = k3_vectsp_4(A,B,C,D) <-> r1_rlvect_1(D,C)))))))))) # label(t64_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8731 $T # label(t2_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8732 $T # label(t44_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8733 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_rlvect_1(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (v11_vectsp_1(C,A) & m1_vectsp_4(C,A,B) -> (all D (v11_vectsp_1(D,A) & m1_vectsp_4(D,A,B) -> ((all E (m1_subset_1(E,u1_struct_0(B)) -> (r1_rlvect_1(C,E) <-> r1_rlvect_1(D,E)))) -> C = D))))))))) # label(t38_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8734 (all A (v4_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v5_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_vectsp_4(E,A,B) -> (r1_rlvect_1(E,D) <-> r2_hidden(k6_rlvect_1(B,C,D),k3_vectsp_4(A,B,C,E))))))))))))) # label(t76_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8735 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_vectsp_4(E,A,B) -> (r1_rlvect_1(E,D) & r1_rlvect_1(E,C) -> r1_rlvect_1(E,k6_rlvect_1(B,C,D))))))))))))) # label(t31_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8736 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (u1_struct_0(C) = D -> v1_vectsp_4(D,A,B)))))))))) # label(t41_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8737 (all A (v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v5_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> m1_subset_1(D,u1_struct_0(B)))))))))) # label(t18_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8738 (all A all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v4_group_1(B) & l3_vectsp_1(B) & v8_vectsp_1(B) & v7_vectsp_1(B) & v4_rlvect_1(B) -> (all C (-v3_struct_0(C) & v3_rlvect_1(C) & v12_vectsp_1(C,B) & l4_vectsp_1(C,B) & v6_rlvect_1(C) & v5_rlvect_1(C) & v4_rlvect_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (all E (m1_vectsp_4(E,B,C) -> ((exists F (k4_rlvect_1(C,D,F) = A & r1_rlvect_1(E,F) & m1_subset_1(F,u1_struct_0(C)))) <-> r2_hidden(A,k3_vectsp_4(B,C,D,E))))))))))) # label(t57_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8739 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & v7_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_vectsp_4(E,A,B) -> (r2_hidden(k6_vectsp_1(A,B,C,D),k3_vectsp_4(A,B,D,E)) -> r1_rlvect_1(E,D) | C = k2_group_1(A)))))))))))) # label(t72_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8740 (all A all B (v3_rlvect_1(B) & v5_rlvect_1(B) & v4_group_1(B) & v7_vectsp_1(B) & v8_vectsp_1(B) & l3_vectsp_1(B) & v6_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (v3_rlvect_1(C) & v12_vectsp_1(C,B) & l4_vectsp_1(C,B) & v6_rlvect_1(C) & v5_rlvect_1(C) & v4_rlvect_1(C) & -v3_struct_0(C) -> (all D (m1_vectsp_4(D,B,C) -> (r1_rlvect_1(D,A) -> r1_rlvect_1(C,A)))))))) # label(t17_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8741 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v5_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_vectsp_4(E,A,B) -> -(k3_vectsp_4(A,B,C,E) = k3_vectsp_4(A,B,D,E) & (all F (m1_subset_1(F,u1_struct_0(B)) -> -(D = k6_rlvect_1(B,C,F) & r1_rlvect_1(E,F))))))))))))))) # label(t81_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8742 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) -> (all B (-v3_struct_0(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) -> r1_rlvect_1(D,k1_rlvect_1(C)))))))))) # label(t26_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8743 (all A all B all C all D all E (v3_rlvect_1(B) & v5_rlvect_1(B) & v4_group_1(B) & v7_vectsp_1(B) & -v3_struct_0(C) & v6_rlvect_1(C) & v12_vectsp_1(C,B) & l4_vectsp_1(C,B) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) & v5_rlvect_1(C) & v4_rlvect_1(C) & v3_rlvect_1(C) & l3_vectsp_1(B) & v8_vectsp_1(B) & v6_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (r2_hidden(A,a_4_0_vectsp_4(B,C,D,E)) <-> (exists F exists G (r2_hidden(G,E) & r2_hidden(F,D) & k4_rlvect_1(C,F,G) = A & m1_subset_1(G,u1_struct_0(C)) & m1_subset_1(F,u1_struct_0(C))))))) # label(fraenkel_a_4_0_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8744 $T # label(t52_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8745 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_vectsp_4(E,A,B) -> (k3_vectsp_4(A,B,k4_rlvect_1(B,D,C),E) = k3_vectsp_4(A,B,D,E) <-> r1_rlvect_1(E,C)))))))))))) # label(t68_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8746 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v3_rlvect_1(B) & -v3_struct_0(B) -> m2_vectsp_4(u1_struct_0(B),A,B,k2_vectsp_4(A,B)))))) # label(t90_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8747 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) -> (all B (v3_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_vectsp_4(C,A,B) & v11_vectsp_1(C,A) -> (C = k1_vectsp_4(A,B) <-> u1_struct_0(C) = k6_domain_1(u1_struct_0(B),k1_rlvect_1(B))))))))) # label(d3_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8748 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_vectsp_4(C,A,B) -> m1_vectsp_4(k1_vectsp_4(A,B),A,C))))))) # label(t50_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8749 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_vectsp_4(E,A,B) -> (r2_hidden(C,k3_vectsp_4(A,B,D,E)) <-> (exists F (r1_rlvect_1(E,F) & C = k6_rlvect_1(B,D,F) & m1_subset_1(F,u1_struct_0(B))))))))))))))) # label(t78_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8750 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v1_vectsp_4(D,A,B) & v1_vectsp_4(C,A,B) -> v1_vectsp_4(k5_subset_1(u1_struct_0(B),C,D),A,B)))))))))) # label(t10_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8751 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C (-v3_struct_0(C) & v3_rlvect_1(C) & l4_vectsp_1(C,A) & v12_vectsp_1(C,A) & v6_rlvect_1(C) & v5_rlvect_1(C) & v4_rlvect_1(C) -> (u2_struct_0(C) = u2_struct_0(B) & u2_vectsp_1(A,C) = k7_relat_1(u2_vectsp_1(A,B),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(C))) & k1_realset1(u1_rlvect_1(B),u1_struct_0(C)) = u1_rlvect_1(C) & r1_tarski(u1_struct_0(C),u1_struct_0(B)) <-> m1_vectsp_4(C,A,B)))))))) # label(d2_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8752 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) -> (v1_vectsp_4(D,A,B) & a_4_0_vectsp_4(A,B,C,D) = E & v1_vectsp_4(C,A,B) -> v1_vectsp_4(E,A,B)))))))))))) # label(t9_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8753 (all A (v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) -> (all C (m1_vectsp_4(C,A,B) -> u1_struct_0(C) = k3_vectsp_4(A,B,k1_rlvect_1(B),C))))))) # label(t60_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8754 (all A (v3_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_vectsp_4(E,A,B) -> (r1_rlvect_1(E,D) & r1_rlvect_1(E,C) -> r1_rlvect_1(E,k4_rlvect_1(B,C,D))))))))))))) # label(t28_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8755 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (v5_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_vectsp_4(D,A,B) -> (all E (m2_vectsp_4(E,A,B,D) -> (r2_hidden(C,E) <-> E = k3_vectsp_4(A,B,C,D)))))))))))) # label(t93_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8756 $T # label(t54_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8757 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_vectsp_4(C,A,B) -> k1_vectsp_4(A,B) = k1_vectsp_4(A,C))))))) # label(t47_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8758 (all A all B (-v3_struct_0(A) & v4_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & v3_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (exists C m1_vectsp_4(C,A,B)))) # label(existence_m1_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8759 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_vectsp_4(E,A,B) -> (r1_rlvect_1(E,D) -> r2_hidden(k6_vectsp_1(A,B,C,D),k3_vectsp_4(A,B,D,E))))))))))))) # label(t73_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8760 (all A (v4_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C (v11_vectsp_1(C,A) & m1_vectsp_4(C,A,B) -> (all D (v11_vectsp_1(D,A) & m1_vectsp_4(D,A,B) -> (all E (m2_vectsp_4(E,A,B,C) -> (all F (m2_vectsp_4(F,A,B,D) -> (F = E -> C = D))))))))))))) # label(t86_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8761 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & -v3_struct_0(B) -> g4_vectsp_1(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u2_vectsp_1(A,B)) = k2_vectsp_4(A,B))))) # label(d4_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8762 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) -> m1_vectsp_4(B,A,B))))) # label(t32_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8763 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_vectsp_4(E,A,B) & v11_vectsp_1(E,A) -> (all F (v11_vectsp_1(F,A) & m1_vectsp_4(F,A,B) -> (k3_vectsp_4(A,B,C,E) = k3_vectsp_4(A,B,D,F) -> F = E))))))))))))) # label(t83_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8764 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v5_rlvect_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (v1_vectsp_4(C,A,B) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (r2_hidden(D,C) -> r2_hidden(k5_rlvect_1(B,D),C))))))))))) # label(t5_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8765 (all A all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v4_group_1(B) & l3_vectsp_1(B) & v8_vectsp_1(B) & v7_vectsp_1(B) & v4_rlvect_1(B) -> (all C (-v3_struct_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & l4_vectsp_1(C,B) & v12_vectsp_1(C,B) -> (all D (m1_vectsp_4(D,B,C) -> (all E (m1_vectsp_4(E,B,C) -> (m1_vectsp_4(D,B,E) & r1_rlvect_1(D,A) -> r1_rlvect_1(E,A)))))))))) # label(t16_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8766 (all A (-v3_struct_0(A) & v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_vectsp_4(E,A,B) -> (r1_rlvect_1(E,D) -> u1_struct_0(E) = k3_vectsp_4(A,B,k6_vectsp_1(A,B,C,D),E)))))))))))) # label(t65_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8767 (all A (v4_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> k6_rlvect_1(B,k6_vectsp_1(A,B,C,E),k6_vectsp_1(A,B,D,E)) = k6_vectsp_1(A,B,k6_rlvect_1(A,C,D),E))))))))))) # label(t103_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8768 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_vectsp_4(E,A,B) -> (all F (m1_subset_1(F,u1_struct_0(E)) -> (D = F -> k6_vectsp_1(A,E,C,F) = k6_vectsp_1(A,B,C,D)))))))))))))) # label(t22_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8769 $T # label(t13_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8770 $T # label(t15_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8771 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (v1_vectsp_4(C,A,B) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (r2_hidden(D,C) & r2_hidden(E,C) -> r2_hidden(k6_rlvect_1(B,D,E),C))))))))))))) # label(t6_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8772 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v4_rlvect_1(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m2_vectsp_4(D,A,B,C) -> (v1_vectsp_4(D,A,B) <-> D = u1_struct_0(C)))))))))) # label(t85_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8773 $T # label(t1_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8774 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v11_vectsp_1(B,A) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_vectsp_4(C,A,B) & v11_vectsp_1(C,A) -> ((all D (m1_subset_1(D,u1_struct_0(B)) -> r1_rlvect_1(C,D))) -> B = C))))))) # label(t40_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8775 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v5_rlvect_1(B) -> (all C (m1_vectsp_4(C,A,B) -> r1_rlvect_1(C,k1_rlvect_1(B)))))))) # label(t25_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8776 (all A (v5_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) -> k1_rlvect_1(C) = k1_rlvect_1(D))))))))) # label(t20_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8777 (all A all B all C (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & -v3_struct_0(B) & v3_rlvect_1(B) & l4_vectsp_1(B,A) & m1_vectsp_4(C,A,B) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & l3_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (exists D m2_vectsp_4(D,A,B,C)))) # label(existence_m2_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8778 (all A (v3_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_vectsp_4(D,A,B) -> (all E (m1_subset_1(E,u1_struct_0(D)) -> (E = C -> k5_rlvect_1(D,E) = k5_rlvect_1(B,C)))))))))))) # label(t23_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8779 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_vectsp_4(E,A,B) -> (all F (m2_vectsp_4(F,A,B,E) -> -(r2_hidden(C,F) & (all G (m1_subset_1(G,u1_struct_0(B)) -> -(r1_rlvect_1(E,G) & D = k4_rlvect_1(B,C,G)))) & r2_hidden(D,F)))))))))))))) # label(t94_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8780 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> -((all D (m1_subset_1(D,u1_struct_0(B)) -> C != k6_domain_1(u1_struct_0(B),D))) & m2_vectsp_4(C,A,B,k1_vectsp_4(A,B))))))))) # label(t88_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8781 $T # label(t101_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8782 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_vectsp_4(C,A,B) -> r1_rlvect_1(B,k1_rlvect_1(C)))))))) # label(t27_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8783 (all A all B (v3_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v3_rlvect_1(B) & v5_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) & v7_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all C (m1_vectsp_4(C,A,B) -> v3_rlvect_1(C) & v12_vectsp_1(C,A) & l4_vectsp_1(C,A) & v6_rlvect_1(C) & v5_rlvect_1(C) & v4_rlvect_1(C) & -v3_struct_0(C))))) # label(dt_m1_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8784 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> v1_vectsp_4(k6_domain_1(u1_struct_0(B),k1_rlvect_1(B)),A,B))))) # label(t7_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8785 (all A (v3_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) -> (all C (m1_vectsp_4(C,A,B) -> k1_rlvect_1(C) = k1_rlvect_1(B))))))) # label(t19_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8786 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (m2_vectsp_4(C,A,B,k2_vectsp_4(A,B)) -> u1_struct_0(B) = C))))))) # label(t91_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8787 (all A (v3_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v11_vectsp_1(B,A) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (v11_vectsp_1(C,A) & m1_vectsp_4(C,A,B) -> (u1_struct_0(B) = u1_struct_0(C) -> B = C))))))) # label(t39_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8788 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v5_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_vectsp_4(E,A,B) -> (all F (m1_subset_1(F,u1_struct_0(E)) -> (all G (m1_subset_1(G,u1_struct_0(E)) -> (C = F & G = D -> k4_rlvect_1(E,F,G) = k4_rlvect_1(B,C,D)))))))))))))))) # label(t21_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8789 (all A (v6_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> m2_vectsp_4(k6_domain_1(u1_struct_0(B),C),A,B,k1_vectsp_4(A,B)))))))) # label(t87_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8790 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (v5_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (m2_vectsp_4(D,A,B,C) <-> (exists E (m1_subset_1(E,u1_struct_0(B)) & D = k3_vectsp_4(A,B,E,C)))))))))))) # label(d6_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8791 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k3_vectsp_4(A,B,C,k2_vectsp_4(A,B)) = u1_struct_0(B))))))) # label(t62_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8792 $T # label(t45_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8793 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k3_vectsp_4(A,B,C,k1_vectsp_4(A,B)) = k6_domain_1(u1_struct_0(B),C))))))) # label(t61_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8794 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_vectsp_4(E,A,B) -> (all F (m1_subset_1(F,u1_struct_0(E)) -> (all G (m1_subset_1(G,u1_struct_0(E)) -> (G = D & F = C -> k6_rlvect_1(E,F,G) = k6_rlvect_1(B,C,D)))))))))))))))) # label(t24_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8795 $T # label(t12_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8796 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (u1_struct_0(B) = C -> v1_vectsp_4(C,A,B)))))))) # label(t8_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8797 (all A (v4_rlvect_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) -> m1_vectsp_4(k1_vectsp_4(A,C),A,D))))))))) # label(t51_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8798 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (v4_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_vectsp_4(E,A,B) -> (r1_rlvect_1(E,C) <-> r2_hidden(k4_rlvect_1(B,C,D),k3_vectsp_4(A,B,D,E))))))))))))) # label(t75_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8799 (all A (v4_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_vectsp_4(D,A,B) -> k3_vectsp_4(A,B,C,D) = a_4_1_vectsp_4(A,B,C,D))))))))) # label(d5_vectsp_4) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8800 $T # label(t2_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8801 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) -> -v3_struct_0(g3_lattices(k3_vectsp_5(A,B),k5_vectsp_5(A,B),k6_vectsp_5(A,B))) & v13_lattices(g3_lattices(k3_vectsp_5(A,B),k5_vectsp_5(A,B),k6_vectsp_5(A,B))) & l3_lattices(g3_lattices(k3_vectsp_5(A,B),k5_vectsp_5(A,B),k6_vectsp_5(A,B))) & v10_lattices(g3_lattices(k3_vectsp_5(A,B),k5_vectsp_5(A,B),k6_vectsp_5(A,B))))))) # label(t76_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8802 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (v11_vectsp_1(C,A) & m1_vectsp_4(C,A,B) -> C = k1_vectsp_5(A,B,k1_vectsp_4(A,B),C) & C = k1_vectsp_5(A,B,C,k1_vectsp_4(A,B)))))))) # label(t13_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8803 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v3_rlvect_1(A) -> (all B (v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) -> (all E (m1_vectsp_4(E,A,B) -> k2_vectsp_5(A,B,k2_vectsp_5(A,B,C,D),E) = k2_vectsp_5(A,B,C,k2_vectsp_5(A,B,D,E)))))))))))) # label(t19_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8804 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) -> ((all E (m2_vectsp_4(E,A,B,C) -> (all F (m2_vectsp_4(F,A,B,D) -> (exists G (m1_subset_1(G,u1_struct_0(B)) & k6_domain_1(u1_struct_0(B),G) = k5_subset_1(u1_struct_0(B),E,F))))))) <-> r1_vectsp_5(A,B,C,D)))))))))) # label(t56_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8805 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v8_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v9_vectsp_1(A) & v7_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_5(D,A,B,C) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> k2_domain_1(u1_struct_0(B),u1_struct_0(B),k4_vectsp_5(A,B,E,D,C)) = k3_domain_1(u1_struct_0(B),u1_struct_0(B),k4_vectsp_5(A,B,E,C,D)))))))))))) # label(t70_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8806 (all A (-v3_struct_0(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (v11_vectsp_1(D,A) & m1_vectsp_4(D,A,B) -> (m1_vectsp_4(C,A,D) <-> k1_vectsp_5(A,B,C,D) = D))))))))) # label(t12_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8807 (all A all B all C (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v4_rlvect_1(B) & m1_vectsp_4(C,A,B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) & v9_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all D (m1_vectsp_5(D,A,B,C) -> m1_vectsp_4(D,A,B))))) # label(dt_m1_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8808 $T # label(t60_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8809 (all A all B all C (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & -v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & m1_vectsp_4(C,A,B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) -> (exists D m1_vectsp_5(D,A,B,C)))) # label(existence_m1_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.51 8810 (all A (v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v6_rlvect_1(B) & v11_vectsp_1(B,A) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) -> ((all E (m1_subset_1(E,u1_struct_0(B)) -> (exists F (m1_subset_1(F,u1_struct_0(B)) & (exists G (r1_rlvect_1(C,F) & E = k4_rlvect_1(B,F,G) & r1_rlvect_1(D,G) & m1_subset_1(G,u1_struct_0(B)))))))) <-> B = k1_vectsp_5(A,B,C,D)))))))))) # label(t57_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8811 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v7_group_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v5_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) -> (m1_vectsp_5(D,A,B,C) <-> r1_vectsp_5(A,B,D,C)))))))))) # label(d5_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8812 $T # label(t26_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8813 (all A (v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & -v3_struct_0(B) -> k1_vectsp_5(A,B,k2_vectsp_4(A,B),k1_vectsp_4(A,B)) = g4_vectsp_1(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u2_vectsp_1(A,B)) & k1_vectsp_5(A,B,k1_vectsp_4(A,B),k2_vectsp_4(A,B)) = g4_vectsp_1(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u2_vectsp_1(A,B)))))) # label(t14_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8814 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (k3_vectsp_5(A,B) = C <-> (all D ((exists E (m1_vectsp_4(E,A,B) & E = D & v11_vectsp_1(E,A))) <-> r2_hidden(D,C))))))))) # label(d3_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8815 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) -> (all B (-v3_struct_0(B) & v11_vectsp_1(B,A) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> r2_hidden(B,k3_vectsp_5(A,B)))))) # label(t44_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8816 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v5_rlvect_1(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(k3_vectsp_5(A,B),k3_vectsp_5(A,B)),k3_vectsp_5(A,B)) & m2_relset_1(C,k2_zfmisc_1(k3_vectsp_5(A,B),k3_vectsp_5(A,B)),k3_vectsp_5(A,B)) & v1_funct_1(C) -> ((all D (m1_subset_1(D,k3_vectsp_5(A,B)) -> (all E (m1_subset_1(E,k3_vectsp_5(A,B)) -> (all F (m1_vectsp_4(F,A,B) -> (all G (m1_vectsp_4(G,A,B) -> (F = D & G = E -> k2_binop_1(k3_vectsp_5(A,B),k3_vectsp_5(A,B),k3_vectsp_5(A,B),C,D,E) = k1_vectsp_5(A,B,F,G)))))))))) <-> C = k5_vectsp_5(A,B)))))))) # label(d7_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8817 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) -> (all E (m2_vectsp_4(E,A,B,C) -> (all F (m2_vectsp_4(F,A,B,D) -> (-r1_xboole_0(E,F) -> m2_vectsp_4(k5_subset_1(u1_struct_0(B),E,F),A,B,k2_vectsp_5(A,B,C,D))))))))))))))) # label(t55_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8818 (all A (v6_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) -> -((m1_vectsp_4(D,A,C) | m1_vectsp_4(C,A,D)) & (all E (m1_vectsp_4(E,A,B) -> k2_xboole_0(u1_struct_0(C),u1_struct_0(D)) != u1_struct_0(E)))) & -((exists E (m1_vectsp_4(E,A,B) & u1_struct_0(E) = k2_xboole_0(u1_struct_0(C),u1_struct_0(D)))) & -m1_vectsp_4(D,A,C) & -m1_vectsp_4(C,A,D)))))))))) # label(t41_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8819 (all A (v3_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v9_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_5(D,A,B,C) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> k4_rlvect_1(B,k2_domain_1(u1_struct_0(B),u1_struct_0(B),k4_vectsp_5(A,B,E,C,D)),k3_domain_1(u1_struct_0(B),u1_struct_0(B),k4_vectsp_5(A,B,E,C,D))) = E)))))))))) # label(t67_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8820 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) -> (all E (m1_vectsp_4(E,A,B) -> m1_vectsp_4(k1_vectsp_5(A,B,C,k2_vectsp_5(A,B,D,E)),A,k2_vectsp_5(A,B,k1_vectsp_5(A,B,D,C),k1_vectsp_5(A,B,C,E))))))))))))) # label(t34_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8821 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) -> (all E (m1_vectsp_4(E,A,B) -> k1_vectsp_5(A,B,k1_vectsp_5(A,B,C,D),E) = k1_vectsp_5(A,B,C,k1_vectsp_5(A,B,D,E)))))))))))) # label(t10_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8822 (all A all B all C all D all E (v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v4_group_1(B) & v7_vectsp_1(B) & v3_rlvect_1(C) & v6_rlvect_1(C) & v12_vectsp_1(C,B) & l4_vectsp_1(C,B) & m1_vectsp_4(D,B,C) & m1_vectsp_4(E,B,C) & v5_rlvect_1(C) & v4_rlvect_1(C) & -v3_struct_0(C) & l3_vectsp_1(B) & v8_vectsp_1(B) & v5_rlvect_1(B) & -v3_struct_0(B) -> ((exists F exists G (m1_subset_1(F,u1_struct_0(C)) & m1_subset_1(G,u1_struct_0(C)) & k4_rlvect_1(C,F,G) = A & r1_rlvect_1(E,G) & r1_rlvect_1(D,F))) <-> r2_hidden(A,a_4_0_vectsp_5(B,C,D,E))))) # label(fraenkel_a_4_0_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8823 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_vectsp_4(D,A,B) -> (all E (m1_vectsp_4(E,A,B) -> (r1_vectsp_5(A,B,D,E) -> (all F (m1_subset_1(F,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B))) -> (F = k4_vectsp_5(A,B,C,D,E) <-> C = k4_rlvect_1(B,k2_domain_1(u1_struct_0(B),u1_struct_0(B),F),k3_domain_1(u1_struct_0(B),u1_struct_0(B),F)) & r1_rlvect_1(E,k3_domain_1(u1_struct_0(B),u1_struct_0(B),F)) & r1_rlvect_1(D,k2_domain_1(u1_struct_0(B),u1_struct_0(B),F)))))))))))))))) # label(d6_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8824 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v9_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> v10_lattices(g3_lattices(k3_vectsp_5(A,B),k5_vectsp_5(A,B),k6_vectsp_5(A,B))) & v16_lattices(g3_lattices(k3_vectsp_5(A,B),k5_vectsp_5(A,B),k6_vectsp_5(A,B))) & l3_lattices(g3_lattices(k3_vectsp_5(A,B),k5_vectsp_5(A,B),k6_vectsp_5(A,B))) & v15_lattices(g3_lattices(k3_vectsp_5(A,B),k5_vectsp_5(A,B),k6_vectsp_5(A,B))) & -v3_struct_0(g3_lattices(k3_vectsp_5(A,B),k5_vectsp_5(A,B),k6_vectsp_5(A,B))))))) # label(t80_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8825 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) -> (all E (m1_vectsp_4(E,A,B) -> (m1_vectsp_4(C,A,D) -> m1_vectsp_4(k2_vectsp_5(A,B,C,E),A,k2_vectsp_5(A,B,D,E))))))))))))) # label(t22_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8826 $T # label(t1_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8827 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) -> (all E (m1_vectsp_4(E,A,B) -> (m1_vectsp_4(C,A,D) -> k1_vectsp_5(A,B,D,k2_vectsp_5(A,B,C,E)) = k2_vectsp_5(A,B,k1_vectsp_5(A,B,C,D),k1_vectsp_5(A,B,D,E))))))))))))) # label(t35_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8828 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) -> (all E (m1_vectsp_4(E,A,B) -> m1_vectsp_4(k1_vectsp_5(A,B,k2_vectsp_5(A,B,C,D),k2_vectsp_5(A,B,D,E)),A,k2_vectsp_5(A,B,D,k1_vectsp_5(A,B,C,E))))))))))))) # label(t32_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8829 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (v11_vectsp_1(D,A) & m1_vectsp_4(D,A,B) -> k1_vectsp_5(A,B,k2_vectsp_5(A,B,C,D),D) = D)))))))) # label(t30_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8830 $T # label(dt_k3_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8831 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (v4_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (r1_rlvect_1(D,E) | r1_rlvect_1(C,E) -> r1_rlvect_1(k1_vectsp_5(A,B,C,D),E)))))))))))) # label(t6_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8832 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v5_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (v11_vectsp_1(C,A) & m1_vectsp_4(C,A,B) -> k1_vectsp_5(A,B,C,C) = C)))))) # label(t8_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8833 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v9_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v7_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & -v3_struct_0(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_5(D,A,B,C) -> g4_vectsp_1(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u2_vectsp_1(A,B)) = k1_vectsp_5(A,B,D,C) & g4_vectsp_1(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u2_vectsp_1(A,B)) = k1_vectsp_5(A,B,C,D))))))))) # label(t49_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8834 $T # label(t74_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8835 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (v5_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_vectsp_4(C,A,B) -> k1_vectsp_5(A,B,C,k2_vectsp_4(A,B)) = g4_vectsp_1(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u2_vectsp_1(A,B)) & g4_vectsp_1(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u2_vectsp_1(A,B)) = k1_vectsp_5(A,B,k2_vectsp_4(A,B),C))))))) # label(t15_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8836 $T # label(t46_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8837 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v3_rlvect_1(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) -> k1_vectsp_5(A,B,D,C) = k1_vectsp_5(A,B,C,D))))))))) # label(t9_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8838 $T # label(t61_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8839 (all A (v3_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) -> (r1_vectsp_5(A,B,C,D) -> r1_vectsp_5(A,B,D,C)))))))))) # label(t51_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8840 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) -> m1_vectsp_4(k2_vectsp_5(A,B,C,D),A,D) & m1_vectsp_4(k2_vectsp_5(A,B,C,D),A,C))))))))) # label(t20_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8841 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (r1_vectsp_5(A,B,C,D) -> k2_domain_1(u1_struct_0(B),u1_struct_0(B),k4_vectsp_5(A,B,E,D,C)) = k3_domain_1(u1_struct_0(B),u1_struct_0(B),k4_vectsp_5(A,B,E,C,D))))))))))))) # label(t65_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8842 $T # label(t4_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8843 (all A all B all C all D (-v3_struct_0(A) & v5_rlvect_1(A) & l3_vectsp_1(A) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & m1_vectsp_4(D,A,B) & m1_vectsp_4(C,A,B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & -v3_struct_0(B) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> k2_vectsp_5(A,B,C,D) = k2_vectsp_5(A,B,D,C))) # label(commutativity_k2_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8844 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v5_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) -> (all E (m1_vectsp_4(E,A,B) -> (m1_vectsp_4(C,A,D) & m1_vectsp_4(C,A,E) -> m1_vectsp_4(C,A,k2_vectsp_5(A,B,D,E))))))))))))) # label(t24_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8845 $T # label(t72_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8846 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v7_vectsp_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) -> m1_vectsp_5(k1_vectsp_4(A,B),A,B,k2_vectsp_4(A,B)) & m1_vectsp_5(k2_vectsp_4(A,B),A,B,k1_vectsp_4(A,B)))))) # label(t54_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8847 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v5_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) -> l3_lattices(g3_lattices(k3_vectsp_5(A,B),k5_vectsp_5(A,B),k6_vectsp_5(A,B))) & v10_lattices(g3_lattices(k3_vectsp_5(A,B),k5_vectsp_5(A,B),k6_vectsp_5(A,B))) & -v3_struct_0(g3_lattices(k3_vectsp_5(A,B),k5_vectsp_5(A,B),k6_vectsp_5(A,B))))))) # label(t75_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8848 $T # label(t71_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8849 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_rlvect_1(A) -> (all B (v5_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) & v11_vectsp_1(D,A) -> (all E (m1_vectsp_4(E,A,B) & v11_vectsp_1(E,A) -> (m1_vectsp_4(C,A,D) -> m1_vectsp_4(k1_vectsp_5(A,B,C,E),A,k1_vectsp_5(A,B,D,E))))))))))))) # label(t38_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8850 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) -> (all E (m1_vectsp_4(E,A,B) & v11_vectsp_1(E,A) -> (m1_vectsp_4(E,A,C) -> k2_vectsp_5(A,B,k1_vectsp_5(A,B,E,D),C) = k1_vectsp_5(A,B,E,k2_vectsp_5(A,B,D,C))))))))))))) # label(t36_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8851 (all A all B all C all D all E (v3_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v3_rlvect_1(B) & v4_rlvect_1(B) & m1_vectsp_4(D,A,B) & m1_vectsp_4(E,A,B) & m1_subset_1(C,u1_struct_0(B)) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & -v3_struct_0(B) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> m1_subset_1(k4_vectsp_5(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B))))) # label(dt_k4_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8852 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v9_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_5(D,A,B,C) -> r1_vectsp_5(A,B,D,C) & r1_vectsp_5(A,B,C,D))))))))) # label(t48_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8853 $T # label(t62_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8854 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) -> (all E ((exists F (m1_subset_1(F,u1_struct_0(B)) & (exists G (m1_subset_1(G,u1_struct_0(B)) & k4_rlvect_1(B,F,G) = E & r1_rlvect_1(D,G) & r1_rlvect_1(C,F))))) <-> r1_rlvect_1(k1_vectsp_5(A,B,C,D),E))))))))))) # label(t5_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8855 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) -> (k1_vectsp_5(A,B,C,D) = B -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (exists F (m1_subset_1(F,u1_struct_0(B)) & (exists G ((exists H ((exists I (m1_subset_1(I,u1_struct_0(B)) & r1_rlvect_1(C,F) & -(F = H & G = I) & r1_rlvect_1(D,I) & r1_rlvect_1(D,G) & r1_rlvect_1(C,H) & k4_rlvect_1(B,H,I) = E & k4_rlvect_1(B,F,G) = E)) & m1_subset_1(H,u1_struct_0(B)))) & m1_subset_1(G,u1_struct_0(B)))))))) | r1_vectsp_5(A,B,C,D)))))))))) # label(t59_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8856 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v8_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v9_vectsp_1(A) & v7_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & v6_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) -> (r1_vectsp_5(A,B,C,D) -> m1_vectsp_5(D,A,B,C)))))))))) # label(t47_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8857 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v5_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v11_vectsp_1(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> k1_vectsp_5(A,B,k2_vectsp_4(A,B),k2_vectsp_4(A,B)) = B)))) # label(t16_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8858 $T # label(t42_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8859 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) -> (all B (v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) -> (all E (m1_vectsp_4(E,A,B) -> (m1_vectsp_4(C,A,D) -> m1_vectsp_4(C,A,k1_vectsp_5(A,B,D,E))))))))))))) # label(t39_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8860 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) -> m1_vectsp_4(C,A,k1_vectsp_5(A,B,C,D)) & m1_vectsp_4(D,A,k1_vectsp_5(A,B,C,D)))))))))) # label(t11_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8861 (all A all B all C all D (v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & -v3_struct_0(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & m1_vectsp_4(C,A,B) & m1_vectsp_4(D,A,B) & l4_vectsp_1(B,A) & v4_rlvect_1(B) & v3_rlvect_1(B) & v7_vectsp_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> v11_vectsp_1(k2_vectsp_5(A,B,C,D),A) & m1_vectsp_4(k2_vectsp_5(A,B,C,D),A,B))) # label(dt_k2_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8862 $T # label(t3_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8863 (all A (v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) -> v10_lattices(g3_lattices(k3_vectsp_5(A,B),k5_vectsp_5(A,B),k6_vectsp_5(A,B))) & l3_lattices(g3_lattices(k3_vectsp_5(A,B),k5_vectsp_5(A,B),k6_vectsp_5(A,B))) & v12_lattices(g3_lattices(k3_vectsp_5(A,B),k5_vectsp_5(A,B),k6_vectsp_5(A,B))) & -v3_struct_0(g3_lattices(k3_vectsp_5(A,B),k5_vectsp_5(A,B),k6_vectsp_5(A,B))))))) # label(t79_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8864 (all A (v3_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_5(D,A,B,C) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (m1_subset_1(F,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B))) -> (k4_rlvect_1(B,k2_domain_1(u1_struct_0(B),u1_struct_0(B),F),k3_domain_1(u1_struct_0(B),u1_struct_0(B),F)) = E & r1_rlvect_1(C,k2_domain_1(u1_struct_0(B),u1_struct_0(B),F)) & r1_rlvect_1(D,k3_domain_1(u1_struct_0(B),u1_struct_0(B),F)) -> F = k4_vectsp_5(A,B,E,C,D)))))))))))))) # label(t66_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8865 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v5_rlvect_1(B) & -v3_struct_0(B) -> v10_lattices(g3_lattices(k3_vectsp_5(A,B),k5_vectsp_5(A,B),k6_vectsp_5(A,B))) & v15_lattices(g3_lattices(k3_vectsp_5(A,B),k5_vectsp_5(A,B),k6_vectsp_5(A,B))) & l3_lattices(g3_lattices(k3_vectsp_5(A,B),k5_vectsp_5(A,B),k6_vectsp_5(A,B))) & -v3_struct_0(g3_lattices(k3_vectsp_5(A,B),k5_vectsp_5(A,B),k6_vectsp_5(A,B))))))) # label(t78_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8866 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v3_rlvect_1(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (v11_vectsp_1(D,A) & m1_vectsp_4(D,A,B) -> k2_vectsp_5(A,B,D,k1_vectsp_5(A,B,D,C)) = D)))))))) # label(t31_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8867 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v11_vectsp_1(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) -> B = k2_vectsp_5(A,B,k2_vectsp_4(A,B),k2_vectsp_4(A,B)))))) # label(t28_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8868 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (v11_vectsp_1(C,A) & m1_vectsp_4(C,A,B) -> k2_vectsp_5(A,B,C,C) = C)))))) # label(t17_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8869 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v4_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (v11_vectsp_1(C,A) & m1_vectsp_4(C,A,B) -> k2_vectsp_5(A,B,k2_vectsp_4(A,B),C) = C & k2_vectsp_5(A,B,C,k2_vectsp_4(A,B)) = C)))))) # label(t27_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8870 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) -> (all E (m1_vectsp_4(E,A,B) -> (m1_vectsp_4(C,A,D) -> m1_vectsp_4(k2_vectsp_5(A,B,C,E),A,D)))))))))))) # label(t23_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8871 $T # label(t73_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8872 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) -> (all E (m1_vectsp_4(E,A,B) -> (m1_vectsp_4(E,A,D) & m1_vectsp_4(C,A,D) -> m1_vectsp_4(k1_vectsp_5(A,B,C,E),A,D)))))))))))) # label(t40_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8873 (all A (v4_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) -> (all C (m1_vectsp_4(C,A,B) & v11_vectsp_1(C,A) -> (all D (v11_vectsp_1(D,A) & m1_vectsp_4(D,A,B) -> (D = k1_vectsp_5(A,B,C,D) <-> C = k2_vectsp_5(A,B,C,D)))))))))) # label(t37_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8874 (all A (v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) & v11_vectsp_1(D,A) -> (m1_vectsp_4(D,A,C) -> D = k2_vectsp_5(A,B,D,C)))) & (all D (m1_vectsp_4(D,A,B) -> (D = k2_vectsp_5(A,B,D,C) -> m1_vectsp_4(D,A,C)))))))))) # label(t21_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8875 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(k3_vectsp_5(A,B),k3_vectsp_5(A,B)),k3_vectsp_5(A,B)) & v1_funct_2(C,k2_zfmisc_1(k3_vectsp_5(A,B),k3_vectsp_5(A,B)),k3_vectsp_5(A,B)) -> ((all D (m1_subset_1(D,k3_vectsp_5(A,B)) -> (all E (m1_subset_1(E,k3_vectsp_5(A,B)) -> (all F (m1_vectsp_4(F,A,B) -> (all G (m1_vectsp_4(G,A,B) -> (D = F & E = G -> k2_vectsp_5(A,B,F,G) = k2_binop_1(k3_vectsp_5(A,B),k3_vectsp_5(A,B),k3_vectsp_5(A,B),C,D,E)))))))))) <-> k6_vectsp_5(A,B) = C))))))) # label(d8_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8876 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_vectsp_4(C,A,B) -> k2_vectsp_5(A,B,k1_vectsp_4(A,B),C) = k1_vectsp_4(A,B) & k1_vectsp_4(A,B) = k2_vectsp_5(A,B,C,k1_vectsp_4(A,B)))))))) # label(t25_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8877 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) -> (all E (m1_vectsp_4(E,A,B) & v11_vectsp_1(E,A) -> (k3_xboole_0(u1_struct_0(C),u1_struct_0(D)) = u1_struct_0(E) <-> E = k2_vectsp_5(A,B,C,D)))))))))))) # label(d2_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8878 $T # label(t45_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8879 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) -> (all E (v11_vectsp_1(E,A) & m1_vectsp_4(E,A,B) -> (E = k1_vectsp_5(A,B,C,D) <-> a_4_0_vectsp_5(A,B,C,D) = u1_struct_0(E)))))))))))) # label(d1_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8880 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_5(D,A,B,C) -> m1_vectsp_5(C,A,B,D))))))))) # label(t53_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8881 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v5_rlvect_1(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (r1_vectsp_5(A,B,C,D) -> k2_domain_1(u1_struct_0(B),u1_struct_0(B),k4_vectsp_5(A,B,E,C,D)) = k3_domain_1(u1_struct_0(B),u1_struct_0(B),k4_vectsp_5(A,B,E,D,C))))))))))))) # label(t64_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8882 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v8_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & v3_rlvect_1(A) -> (all B (v4_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_5(D,A,B,C) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> r1_rlvect_1(C,k2_domain_1(u1_struct_0(B),u1_struct_0(B),k4_vectsp_5(A,B,E,C,D))) & r1_rlvect_1(D,k3_domain_1(u1_struct_0(B),u1_struct_0(B),k4_vectsp_5(A,B,E,C,D))))))))))))) # label(t68_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8883 (all A (v4_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v3_rlvect_1(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) -> (all E (m1_vectsp_4(E,A,B) -> (m1_vectsp_4(C,A,D) -> k2_vectsp_5(A,B,D,k1_vectsp_5(A,B,C,E)) = k1_vectsp_5(A,B,k2_vectsp_5(A,B,C,D),k2_vectsp_5(A,B,D,E))))))))))))) # label(t33_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.12/125.52 8884 (all A all B all C all D (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & m1_vectsp_4(C,A,B) & m1_vectsp_4(D,A,B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> m1_vectsp_4(k1_vectsp_5(A,B,C,D),A,B) & v11_vectsp_1(k1_vectsp_5(A,B,C,D),A))) # label(dt_k1_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8885 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v4_rlvect_1(B) & -v3_struct_0(B) -> r1_vectsp_5(A,B,k2_vectsp_4(A,B),k1_vectsp_4(A,B)) & r1_vectsp_5(A,B,k1_vectsp_4(A,B),k2_vectsp_4(A,B)))))) # label(t52_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8886 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) -> m1_vectsp_4(k2_vectsp_5(A,B,C,D),A,k1_vectsp_5(A,B,C,D)))))))))) # label(t29_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8887 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (v5_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) -> (all E (r1_rlvect_1(k2_vectsp_5(A,B,C,D),E) <-> r1_rlvect_1(C,E) & r1_rlvect_1(D,E))))))))))) # label(t7_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8888 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> (all G (m1_subset_1(G,u1_struct_0(B)) -> (all H (m1_subset_1(H,u1_struct_0(B)) -> (all I (m1_subset_1(I,u1_struct_0(B)) -> (E = k4_rlvect_1(B,F,G) & r1_rlvect_1(C,H) & r1_rlvect_1(D,G) & r1_rlvect_1(D,I) & r1_rlvect_1(C,F) & E = k4_rlvect_1(B,H,I) & r1_vectsp_5(A,B,C,D) -> I = G & F = H))))))))))))))))))) # label(t58_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8889 (all A (v3_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v8_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v3_rlvect_1(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_5(D,A,B,C) -> k1_vectsp_4(A,B) = k2_vectsp_5(A,B,D,C) & k2_vectsp_5(A,B,C,D) = k1_vectsp_4(A,B))))))))) # label(t50_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8890 (all A all B (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) & v7_vectsp_1(A) & v4_group_1(A) & v3_rlvect_1(A) -> v1_funct_2(k5_vectsp_5(A,B),k2_zfmisc_1(k3_vectsp_5(A,B),k3_vectsp_5(A,B)),k3_vectsp_5(A,B)) & m2_relset_1(k5_vectsp_5(A,B),k2_zfmisc_1(k3_vectsp_5(A,B),k3_vectsp_5(A,B)),k3_vectsp_5(A,B)) & v1_funct_1(k5_vectsp_5(A,B)))) # label(dt_k5_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8891 $T # label(t18_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8892 (all A (v3_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v3_rlvect_1(B) -> v10_lattices(g3_lattices(k3_vectsp_5(A,B),k5_vectsp_5(A,B),k6_vectsp_5(A,B))) & v14_lattices(g3_lattices(k3_vectsp_5(A,B),k5_vectsp_5(A,B),k6_vectsp_5(A,B))) & l3_lattices(g3_lattices(k3_vectsp_5(A,B),k5_vectsp_5(A,B),k6_vectsp_5(A,B))) & -v3_struct_0(g3_lattices(k3_vectsp_5(A,B),k5_vectsp_5(A,B),k6_vectsp_5(A,B))))))) # label(t77_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8893 (all A (-v3_struct_0(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_4(D,A,B) -> (r1_vectsp_5(A,B,C,D) <-> k1_vectsp_4(A,B) = k2_vectsp_5(A,B,C,D) & g4_vectsp_1(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u2_vectsp_1(A,B)) = k1_vectsp_5(A,B,C,D)))))))))) # label(d4_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8894 $T # label(t63_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8895 (all A (v3_rlvect_1(A) & v6_rlvect_1(A) & v7_group_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_vectsp_4(C,A,B) -> (all D (m1_vectsp_5(D,A,B,C) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> k3_domain_1(u1_struct_0(B),u1_struct_0(B),k4_vectsp_5(A,B,E,D,C)) = k2_domain_1(u1_struct_0(B),u1_struct_0(B),k4_vectsp_5(A,B,E,C,D)))))))))))) # label(t69_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8896 $T # label(t43_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8897 (all A all B (v6_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v5_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) & v8_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> -v1_xboole_0(k3_vectsp_5(A,B)))) # label(fc1_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8898 (all A all B (v3_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> v1_funct_1(k6_vectsp_5(A,B)) & v1_funct_2(k6_vectsp_5(A,B),k2_zfmisc_1(k3_vectsp_5(A,B),k3_vectsp_5(A,B)),k3_vectsp_5(A,B)) & m2_relset_1(k6_vectsp_5(A,B),k2_zfmisc_1(k3_vectsp_5(A,B),k3_vectsp_5(A,B)),k3_vectsp_5(A,B)))) # label(dt_k6_vectsp_5) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8899 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_group_2(C,A) -> (all D (m1_group_2(D,A) -> r1_group_2(A,k6_group_3(A,k9_group_2(A,C,D),B),k9_group_2(A,k6_group_3(A,C,B),k6_group_3(A,D,B))))))))))) # label(t76_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8900 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_group_2(C,A) -> (all D (m1_group_2(D,A) -> (m1_group_2(C,D) -> r1_tarski(k13_group_2(A,C,B),k13_group_2(A,D,B)) & r1_tarski(k12_group_2(A,C,B),k12_group_2(A,D,B))))))))))) # label(t6_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8901 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(C,D) -> r1_tarski(k3_group_2(A,B,C),k3_group_2(A,B,D)) & r1_tarski(k4_group_2(A,B,C),k4_group_2(A,B,D))))))))))) # label(t5_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8902 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r4_group_3(A,B,C) & r4_group_3(A,C,D) -> r4_group_3(A,B,D)))))))))) # label(t107_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8903 (all A (-v3_struct_0(A) & v1_group_1(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> A = k11_group_3(A,k6_group_2(A)))) # label(t165_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8904 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> ((exists D (k6_group_3(A,C,D) = g1_group_1(u1_struct_0(B),u1_group_1(B)) & m1_subset_1(D,u1_struct_0(A)))) <-> r5_group_3(A,B,C)))))))) # label(d11_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8905 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & v1_group_1(A) & -v3_struct_0(A) -> k11_group_3(A,k5_group_2(A)) = A)) # label(t164_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8906 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,k3_group_1(A,C),k1_group_1(A,B,C)) = k2_group_3(A,B,C) & k2_group_3(A,B,C) = k1_group_1(A,k1_group_1(A,k3_group_1(A,C),B),C))))))) # label(t20_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8907 $T # label(t16_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8908 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (-v3_struct_0(A) & v3_group_1(A) & v7_group_1(A) & l1_group_1(A) & v4_group_1(A) <-> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (k1_xboole_0 != C -> k3_group_3(A,B,C) = B)))))))) # label(t65_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8909 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k2_group_2(A,k7_group_3(A,B),C) = k2_group_2(A,C,k7_group_3(A,B)))))))) # label(t102_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8910 (all A all B all C (-v3_struct_0(A) & v1_group_1(C) & m1_group_2(C,A) & m1_group_2(B,A) & v1_group_1(B) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (r5_group_3(A,B,C) <-> r6_group_3(A,B,C)))) # label(redefinition_r6_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8911 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_group_1(A,C,B) = k1_group_1(A,B,C) <-> B = k2_group_3(A,B,C)))))))) # label(t27_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8912 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> m1_subset_1(k3_group_3(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k3_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8913 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_group_2(C,A) -> (all D (m1_group_2(D,A) -> k10_group_2(A,D,k13_group_2(A,C,B)) = k11_group_2(A,C,k12_group_2(A,D,B)))))))))) # label(t15_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8914 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_group_2(C,A) & v1_group_1(C) -> (k10_group_3(A,B) = C <-> u1_struct_0(C) = a_2_3_group_3(A,B)))))))) # label(d14_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8915 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_group_2(B,A) -> (v6_group_1(A) -> v1_finset_1(k9_group_3(A,B))))))) # label(t133_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8916 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k2_group_3(A,B,k3_group_1(A,B)) & k2_group_3(A,k3_group_1(A,B),B) = k3_group_1(A,B))))) # label(t26_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8917 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k3_group_3(A,k7_domain_1(u1_struct_0(A),B,C),k6_domain_1(u1_struct_0(A),D)) = k7_domain_1(u1_struct_0(A),k2_group_3(A,B,D),k2_group_3(A,C,D)))))))))) # label(t46_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8918 (all A all B all C (l1_group_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v4_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (r2_hidden(A,a_2_1_group_3(B,C)) <-> (exists D (r4_group_3(B,C,D) & D = A & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))))))) # label(fraenkel_a_2_1_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8919 (all A all B all C (v4_group_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> m1_subset_1(k2_group_3(A,B,C),u1_struct_0(A)))) # label(dt_k2_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8920 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> -v1_xboole_0(k1_group_3(A)))) # label(fc1_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8921 (all A all B (v3_group_1(B) & l1_group_1(B) & v4_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> ((exists D (m1_subset_1(D,u1_struct_0(B)) & D = A & r2_group_3(B,C,D))) <-> r2_hidden(A,k7_group_3(B,C))))))) # label(t95_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8922 $T # label(t49_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8923 $T # label(t112_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8924 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(B,k7_group_3(A,C)) -> r2_hidden(C,k7_group_3(A,B))))))))) # label(t99_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8925 (all A all B all C (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B,A) & m1_subset_1(C,u1_struct_0(A)) -> v1_group_1(k6_group_3(A,B,C)) & m1_group_2(k6_group_3(A,B,C),A))) # label(dt_k6_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8926 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r2_hidden(B,k7_group_3(A,B)))))) # label(t98_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8927 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k2_group_3(A,k2_group_1(A),B) = k2_group_1(A))))) # label(t22_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8928 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_group_2(C,A) & v1_group_1(C) -> (A = k6_group_3(A,C,B) -> A = C))))))) # label(t83_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8929 $T # label(t64_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8930 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r2_hidden(k2_group_3(A,B,C),k7_group_3(A,B)))))))) # label(t97_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8931 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (v1_finset_1(k14_group_2(A,B)) & np__2 = k17_group_2(A,B) -> v1_group_3(B,A) & m1_group_2(B,A)))))) # label(t151_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8932 (all A all B all C (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & v4_group_1(A) -> (r2_group_3(A,B,C) -> r2_group_3(A,C,B)))) # label(symmetry_r2_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8933 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> v7_group_1(k5_group_2(A)))) # label(t3_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8934 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) & v1_group_1(C) -> (r4_group_3(A,k7_group_2(A,C),k7_group_2(A,B)) <-> r5_group_3(A,C,B)))))))) # label(t134_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8935 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_group_3(A,B,C) <-> (exists D (B = k2_group_3(A,C,D) & m1_subset_1(D,u1_struct_0(A))))))))))) # label(d7_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8936 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r3_group_3(A,B,B))))) # label(t105_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8937 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (v1_int_1(D) -> k2_group_3(A,k6_group_1(A,D,B),C) = k6_group_1(A,D,k2_group_3(A,B,C)))))))))) # label(t34_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8938 (all A all B (v4_group_1(A) & m1_group_2(B,A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> m1_subset_1(k9_group_3(A,B),k1_zfmisc_1(k1_group_3(A))))) # label(dt_k9_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8939 (all A all B (v4_group_1(B) & l1_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (r2_hidden(A,k8_group_3(B,C)) <-> (exists D (r4_group_3(B,C,D) & D = A & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))))))))) # label(t111_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8940 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_group_2(C,A) -> u1_struct_0(k6_group_3(A,C,B)) = k4_group_2(A,B,k12_group_2(A,C,k3_group_1(A,B))))))))) # label(t71_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8941 $T # label(t69_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8942 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k2_group_3(A,B,B))))) # label(t25_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8943 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_group_2(C,A) -> (v6_group_1(C) -> k9_group_1(k6_group_3(A,C,B)) = k9_group_1(C)))))))) # label(t79_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8944 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_group_2(C,A) -> k16_group_2(A,k6_group_3(A,C,B)) = k16_group_2(A,C))))))) # label(t84_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8945 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_group_2(B,A) & v1_group_1(B) -> r1_group_2(A,k6_group_3(A,B,k2_group_1(A)),B))))) # label(t73_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8946 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (v1_group_1(B) & m1_group_2(B,A) -> k1_card_1(k9_group_3(A,B)) = k16_group_2(A,k11_group_3(A,B)))))) # label(t161_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8947 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r4_group_3(A,B,C) <-> r2_hidden(B,k8_group_3(A,C))))))))) # label(t113_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8948 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_group_2(C,A) -> -((all D (m1_group_2(D,A) & v1_group_1(D) -> B != u1_struct_0(D))) & r4_group_3(A,B,k7_group_2(A,C))))))))) # label(t109_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8949 (all A all B (v4_group_1(B) & l1_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (m1_group_2(C,B) -> (r2_hidden(A,k9_group_3(B,C)) -> m1_group_2(A,B) & v1_group_1(A)))))) # label(t127_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8950 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (r2_group_3(A,B,k2_group_1(A)) | r2_group_3(A,k2_group_1(A),B) -> B = k2_group_1(A)))))) # label(t92_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8951 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k1_card_1(k8_group_3(A,B)) = k16_group_2(A,k10_group_3(A,B)))))) # label(t155_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8952 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_group_2(B,A) -> (v1_group_3(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> g1_group_1(u1_struct_0(B),u1_group_1(B)) = k6_group_3(A,B,C)))))))) # label(d13_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8953 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (B != k1_xboole_0 -> k5_group_3(A,B,k2_group_1(A)) = k6_domain_1(u1_struct_0(A),k2_group_1(A))))))) # label(t62_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8954 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_group_2(B,A) & v1_group_1(B) -> (v1_group_3(B,A) & m1_group_2(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> m1_group_2(k6_group_3(A,B,C),B)))))))) # label(t145_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8955 $T # label(t135_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8956 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k3_group_3(A,k2_group_2(A,B,C),D),k2_group_2(A,k3_group_3(A,B,D),k3_group_3(A,C,D))))))))))) # label(t41_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8957 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_group_2(D,A) -> k10_group_2(A,D,k4_group_2(A,B,C)) = k2_group_2(A,C,k12_group_2(A,D,B)))))))))) # label(t10_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8958 $T # label(t68_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8959 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> k5_group_3(A,k2_group_2(A,C,D),B) = k3_group_3(A,k5_group_3(A,C,B),D))))))))) # label(t55_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8960 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k1_group_2(A,k3_group_3(A,B,C)) = k3_group_3(A,k1_group_2(A,B),C))))))) # label(t43_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8961 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> k5_group_3(A,D,k2_group_3(A,B,C)) = k5_group_3(A,k3_group_2(A,C,D),B))))))))) # label(t58_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8962 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_group_2(B,A) -> k10_group_3(A,k7_group_2(A,B)) = k11_group_3(A,B))))) # label(d15_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8963 (all A all B (-v3_struct_0(B) & v3_group_1(B) & l1_group_1(B) & v4_group_1(B) -> (all C (m1_group_2(C,B) & v1_group_1(C) -> (r1_rlvect_1(k11_group_3(B,C),A) <-> (exists D (m1_subset_1(D,u1_struct_0(B)) & A = D & r1_group_2(B,k6_group_3(B,C,D),C)))))))) # label(t160_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8964 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_group_2(B,A) & v1_group_1(B) -> (k1_tarski(B) = k9_group_3(A,B) <-> m1_group_2(B,A) & v1_group_3(B,A)))))) # label(t146_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8965 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_group_3(A,k2_group_3(A,B,C),D) = k2_group_3(A,B,k1_group_1(A,C,D)))))))))) # label(t29_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8966 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> k3_group_3(A,C,k3_group_2(A,B,D)) = k3_group_3(A,k4_group_3(A,C,B),D))))))))) # label(t54_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8967 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) & v1_group_1(B) -> (all C (v1_group_1(C) & m1_group_2(C,A) -> (r2_hidden(B,k9_group_3(A,C)) -> r2_hidden(C,k9_group_3(A,B))))))))) # label(t131_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8968 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v7_group_1(A) & v3_group_1(A) -> B = k2_group_3(A,B,C)))))))) # label(t35_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8969 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((exists D (k4_group_3(A,B,D) = C & m1_subset_1(D,u1_struct_0(A)))) <-> r3_group_3(A,B,C)))))))) # label(t104_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8970 $T # label(t17_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8971 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_group_3(A,B,C) <-> (exists D (C = k2_group_3(A,B,D) & m1_subset_1(D,u1_struct_0(A))))))))))) # label(t88_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8972 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_group_2(C,A) -> k8_group_1(k6_group_3(A,C,B)) = k8_group_1(C))))))) # label(t77_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8973 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (v1_group_1(B) & v1_group_3(B,A) & m1_group_2(B,A) -> (all C (m1_group_2(C,A) & v1_group_3(C,A) & v1_group_1(C) -> (exists D (v1_group_3(D,A) & k2_group_2(A,k7_group_2(A,B),k7_group_2(A,C)) = u1_struct_0(D) & m1_group_2(D,A) & v1_group_1(D))))))))) # label(t149_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8974 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (v1_group_1(D) & m1_group_2(D,A) -> (D = k6_group_3(A,B,C) <-> k4_group_3(A,k7_group_2(A,B),C) = u1_struct_0(D)))))))))) # label(d6_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8975 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> a_2_0_group_3(A,B) = k5_group_3(A,k7_group_2(A,k6_group_2(A)),B))))) # label(t93_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8976 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_group_2(D,A) -> k2_group_2(A,k12_group_2(A,D,B),C) = k3_group_2(A,B,k11_group_2(A,D,C)))))))))) # label(t11_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8977 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_group_2(C,A) -> k12_group_2(A,C,B) = k10_group_2(A,C,k6_domain_1(u1_struct_0(A),B)))))))) # label(t7_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8978 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_group_1(A,k2_group_3(A,B,D),k2_group_3(A,C,D)) = k2_group_3(A,k1_group_1(A,B,C),D))))))))) # label(t28_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8979 (all A all B all C (-v3_struct_0(A) & v4_group_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C,u1_struct_0(A)) & l1_group_1(A) & v3_group_1(A) -> m1_subset_1(k5_group_3(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k5_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8980 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(D,E) & r1_tarski(B,C) -> r1_tarski(k2_group_2(A,B,D),k2_group_2(A,C,E))))))))))))) # label(t4_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8981 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> k9_domain_1(u1_struct_0(A),k2_group_3(A,B,D),k2_group_3(A,B,E),k2_group_3(A,C,D),k2_group_3(A,C,E)) = k3_group_3(A,k7_domain_1(u1_struct_0(A),B,C),k7_domain_1(u1_struct_0(A),D,E)))))))))))) # label(t47_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8982 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (v3_group_1(A) & v7_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) <-> v1_binop_1(u1_group_1(A),u1_struct_0(A))))) # label(t2_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8983 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (v6_group_1(A) -> v1_finset_1(k1_group_3(A))))) # label(t19_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8984 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k3_group_3(A,k6_domain_1(u1_struct_0(A),B),k7_domain_1(u1_struct_0(A),C,D)) = k7_domain_1(u1_struct_0(A),k2_group_3(A,B,C),k2_group_3(A,B,D)))))))))) # label(t45_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8985 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((exists D (B = k4_group_3(A,C,D) & m1_subset_1(D,u1_struct_0(A)))) <-> r3_group_3(A,B,C)))))))) # label(d9_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8986 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_group_2(A,k6_group_3(A,k5_group_2(A),B),k5_group_2(A)))))) # label(t80_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8987 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k2_group_3(A,B,C) = k2_group_3(A,D,C) -> D = B))))))))) # label(t21_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8988 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (v1_group_1(B) & m1_group_2(B,A) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_rlvect_1(B,C) -> r1_tarski(k7_group_3(A,C),k7_group_2(A,B))))) <-> v1_group_3(B,A) & m1_group_2(B,A)))))) # label(t147_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8989 (all A all B (-v3_struct_0(B) & v3_group_1(B) & l1_group_1(B) & v4_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (r2_hidden(A,k5_group_3(B,D,C)) <-> (exists E (m1_subset_1(E,u1_struct_0(B)) & k2_group_3(B,C,E) = A & r2_hidden(E,D)))))))))) # label(t51_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8990 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k8_group_3(A,k6_domain_1(u1_struct_0(A),B)) = a_2_2_group_3(A,B))))) # label(t118_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8991 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v6_group_1(A) -> v1_finset_1(k8_group_3(A,B))))))) # label(t119_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8992 $T # label(t110_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8993 $T # label(t37_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8994 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_group_2(A,k6_group_3(A,k6_group_2(A),B),k6_group_2(A)))))) # label(t82_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8995 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_group_2(D,A) -> k2_group_2(A,k13_group_2(A,D,B),C) = k11_group_2(A,D,k3_group_2(A,B,C)))))))))) # label(t13_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8996 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k4_group_3(A,k2_group_2(A,C,D),B),k2_group_2(A,k4_group_3(A,C,B),k4_group_3(A,D,B))))))))))) # label(t60_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8997 $T # label(t75_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8998 (all A all B all C (-v3_struct_0(B) & v3_group_1(B) & l1_group_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v4_group_1(B) -> (r2_hidden(A,a_2_3_group_3(B,C)) <-> (exists D (m1_subset_1(D,u1_struct_0(B)) & A = D & C = k4_group_3(B,C,D)))))) # label(fraenkel_a_2_3_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 8999 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> k3_group_3(A,k3_group_3(A,B,C),D) = k3_group_3(A,B,k2_group_2(A,C,D)))))))))) # label(t42_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 9000 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -((v1_finset_1(k8_group_3(A,B)) | v1_finset_1(k14_group_2(A,k10_group_3(A,B)))) & (all C (v1_finset_1(C) -> -(k17_group_2(A,k10_group_3(A,B)) = k4_card_1(C) & k8_group_3(A,B) = C)))))))) # label(t156_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 9001 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (v1_group_3(B,A) & m1_group_2(B,A) & v1_group_1(B) -> (all C (v1_group_1(C) & m1_group_2(C,A) & v1_group_3(C,A) -> v1_group_3(k9_group_2(A,B,C),A))))))) # label(t138_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 9002 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k2_group_3(A,B,k2_group_1(A)))))) # label(t24_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 9003 $T # label(t125_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 9004 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_group_2(D,A) -> k2_group_2(A,C,k13_group_2(A,D,B)) = k4_group_2(A,B,k10_group_2(A,D,C)))))))))) # label(t12_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 9005 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k4_group_3(A,B,C) = k3_group_3(A,B,k6_domain_1(u1_struct_0(A),C)))))))) # label(d4_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 9006 (all A all B all C all D (v4_group_1(B) & l1_group_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & v3_group_1(B) & -v3_struct_0(B) -> ((exists E exists F (m1_subset_1(E,u1_struct_0(B)) & k2_group_3(B,E,F) = A & r2_hidden(F,D) & r2_hidden(E,C) & m1_subset_1(F,u1_struct_0(B)))) <-> r2_hidden(A,a_3_0_group_3(B,C,D))))) # label(fraenkel_a_3_0_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 9007 $T # label(t126_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 9008 (all A all B all C (v3_group_1(A) & l1_group_1(A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v4_group_1(A) & -v3_struct_0(A) -> (r4_group_3(A,B,C) <-> r3_group_3(A,B,C)))) # label(redefinition_r4_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 9009 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (v1_group_1(B) & m1_group_2(B,A) -> (all C (m1_group_2(C,A) & v1_group_1(C) -> (-r1_xboole_0(k9_group_3(A,B),k9_group_3(A,C)) <-> k9_group_3(A,C) = k9_group_3(A,B)))))))) # label(t132_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 9010 (all A all B all C (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B,A) & v1_group_1(C) & m1_group_2(C,A) & v1_group_1(B) -> r6_group_3(A,B,B))) # label(reflexivity_r6_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 9011 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_group_2(C,A) -> k13_group_2(A,C,B) = k11_group_2(A,C,k6_domain_1(u1_struct_0(A),B)))))))) # label(t8_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 9012 (all A all B (-v3_struct_0(B) & v3_group_1(B) & l1_group_1(B) & v4_group_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> ((exists D (k4_group_3(B,C,D) = C & A = D & m1_subset_1(D,u1_struct_0(B)))) <-> r1_rlvect_1(k10_group_3(B,C),A)))))) # label(t154_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 9013 $T # label(t136_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 9014 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r2_hidden(B,k8_group_3(A,B)))))) # label(t115_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 9015 (all A all B all C (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v1_group_1(B) & m1_group_2(C,A) & v1_group_1(C) & m1_group_2(B,A) & v4_group_1(A) -> (r6_group_3(A,B,C) -> r6_group_3(A,C,B)))) # label(symmetry_r6_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 9016 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> k4_group_3(A,k5_group_3(A,D,B),C) = k5_group_3(A,k4_group_2(A,C,D),B))))))))) # label(t57_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 9017 (all A all B (v3_group_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> m1_subset_1(k8_group_3(A,B),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))) # label(dt_k8_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 9018 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> k6_group_1(A,D,k2_group_3(A,B,C)) = k2_group_3(A,k6_group_1(A,D,B),C))))))))) # label(t33_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 9019 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> a_2_1_group_3(A,B) = k8_group_3(A,B))))) # label(d10_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 9020 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k5_group_3(A,B,C) = k3_group_3(A,k6_domain_1(u1_struct_0(A),C),B))))))) # label(d5_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 9021 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> -((all C (v1_finset_1(C) -> -(k4_card_1(C) = k17_group_2(A,k10_group_3(A,k6_domain_1(u1_struct_0(A),B))) & k7_group_3(A,B) = C))) & (v1_finset_1(k7_group_3(A,B)) | v1_finset_1(k14_group_2(A,k10_group_3(A,k6_domain_1(u1_struct_0(A),B)))))))))) # label(t158_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 9022 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r4_group_3(A,k6_domain_1(u1_struct_0(A),B),k6_domain_1(u1_struct_0(A),C)) <-> r2_group_3(A,B,C)))))))) # label(t108_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 9023 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k2_group_1(A) = k2_group_3(A,B,C) -> B = k2_group_1(A)))))))) # label(t23_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 9024 $T # label(t94_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 9025 $T # label(dt_k1_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 9026 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> B = k4_group_3(A,B,C))))) <-> -v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v7_group_1(A) & v4_group_1(A)))) # label(t66_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 9027 $T # label(t103_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 9028 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_group_3(A,B,C) -> r1_group_3(A,C,B)))))))) # label(t90_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 9029 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> B = k4_group_3(A,B,k2_group_1(A)))))) # label(t61_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 9030 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k7_group_3(A,B) = k6_domain_1(u1_struct_0(A),k2_group_1(A)) <-> k2_group_1(A) = B))))) # label(t101_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.53 9031 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) & v1_group_1(B) -> (all C (v1_group_1(C) & m1_group_2(C,A) -> ((exists D (r1_group_2(A,C,k6_group_3(A,B,D)) & m1_subset_1(D,u1_struct_0(A)))) <-> r5_group_3(A,B,C)))))))) # label(t121_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9032 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_group_2(C,A) & v1_group_1(C) -> r1_group_2(A,k6_group_3(A,k6_group_3(A,C,k3_group_1(A,B)),B),C) & r1_group_2(A,k6_group_3(A,k6_group_3(A,C,B),k3_group_1(A,B)),C))))))) # label(t74_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9033 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_group_3(A,B,C) = B)))) -> v7_group_1(A)))) # label(t36_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9034 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,k1_group_1(A,k3_group_1(A,C),C),B) = B & B = k1_group_1(A,k1_group_1(A,C,k3_group_1(A,C)),B) & B = k1_group_1(A,B,k1_group_1(A,C,k3_group_1(A,C))) & k1_group_1(A,C,k1_group_1(A,k3_group_1(A,C),B)) = B & B = k1_group_1(A,k3_group_1(A,C),k1_group_1(A,C,B)) & B = k1_group_1(A,B,k1_group_1(A,k3_group_1(A,C),C)) & B = k1_group_1(A,k1_group_1(A,B,k3_group_1(A,C)),C) & B = k1_group_1(A,k1_group_1(A,B,C),k3_group_1(A,C)))))))) # label(t1_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9035 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (k8_group_3(A,B) = k8_group_3(A,C) <-> -r1_xboole_0(k8_group_3(A,B),k8_group_3(A,C))))))))) # label(t117_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9036 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v1_group_1(C) & m1_group_2(C,A) -> r2_hidden(k6_group_3(A,C,B),k9_group_3(A,C)))))))) # label(t129_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9037 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_group_2(C,A) -> (v6_group_1(C) <-> v6_group_1(k6_group_3(A,C,B))))))))) # label(t78_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9038 $T # label(t120_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9039 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_group_2(C,A) & v1_group_1(C) -> (r1_group_2(A,k6_group_3(A,C,B),k5_group_2(A)) -> r1_group_2(A,C,k5_group_2(A))))))))) # label(t81_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9040 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (v1_group_1(B) & v1_group_3(B,A) & m1_group_2(B,A) -> (all C (v1_group_1(C) & m1_group_2(C,A) & v1_group_3(C,A) -> k2_group_2(A,k7_group_2(A,C),k7_group_2(A,B)) = k2_group_2(A,k7_group_2(A,B),k7_group_2(A,C)))))))) # label(t148_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9041 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_group_2(B,A) & v1_group_1(B) -> (-v3_struct_0(A) & v7_group_1(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> v1_group_3(B,A)))))) # label(t139_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9042 (all A all B (m1_subset_1(B,u1_struct_0(A)) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> m1_subset_1(k7_group_3(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k7_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9043 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_group_2(B,A) -> (all C (v1_group_1(C) & m1_group_2(C,A) -> (all D (v1_group_1(D) & m1_group_2(D,A) -> (r6_group_3(A,C,D) & r5_group_3(A,D,B) -> r5_group_3(A,C,B)))))))))) # label(t124_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9044 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_group_3(A))) -> ((all D ((exists E (m1_group_2(E,A) & r5_group_3(A,B,E) & D = E & v1_group_1(E))) <-> r2_hidden(D,C))) <-> C = k9_group_3(A,B)))))))) # label(d12_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9045 (all A all B all C (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_group_1(A) -> r2_group_3(A,B,B))) # label(reflexivity_r2_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9046 (all A all B all C (-v3_struct_0(A) & l1_group_1(A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v4_group_1(A) & v3_group_1(A) -> (r4_group_3(A,B,C) -> r4_group_3(A,C,B)))) # label(symmetry_r4_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9047 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_group_2(B,A) -> (m1_group_2(B,A) & v1_group_3(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> k13_group_2(A,B,C) = k12_group_2(A,B,C)))))))) # label(t140_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9048 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) & v1_group_1(B) -> r5_group_3(A,B,B))))) # label(t122_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9049 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (v1_group_1(B) & m1_group_2(B,A) -> (all C (v1_group_1(C) & m1_group_2(C,A) -> (r5_group_3(A,B,C) -> r5_group_3(A,C,B)))))))) # label(t123_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9050 (all A all B all C (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) -> (r2_group_3(A,B,C) <-> r1_group_3(A,B,C)))) # label(redefinition_r2_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9051 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> r1_tarski(k12_group_2(A,B,C),k13_group_2(A,B,C)))) <-> v1_group_3(B,A) & m1_group_2(B,A)))))) # label(t141_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9052 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,k8_group_3(A,C)) -> r2_hidden(C,k8_group_3(A,B))))))))) # label(t116_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9053 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (v1_group_3(B,A) & m1_group_2(B,A) -> k15_group_2(A,B) = k14_group_2(A,B))))) # label(t150_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9054 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> k4_group_3(A,k3_group_3(A,C,D),B) = k3_group_3(A,C,k4_group_2(A,B,D)))))))))) # label(t53_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9055 $T # label(t31_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9056 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (exists B (m1_group_2(B,A) & v1_group_1(B) & v2_group_1(B) & v3_group_1(B) & v1_group_3(B,A) & v4_group_1(B) & -v3_struct_0(B))))) # label(rc1_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9057 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_group_2(D,A) -> k10_group_2(A,D,k3_group_2(A,B,C)) = k3_group_2(A,B,k10_group_2(A,D,C)))))))))) # label(t9_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9058 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (B = k1_group_3(A) <-> (all C (r2_hidden(C,B) <-> m1_group_2(C,A) & v1_group_1(C))))))) # label(d1_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9059 $T # label(t159_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9060 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k16_group_2(A,k10_group_3(A,k6_domain_1(u1_struct_0(A),B))) = k1_card_1(k7_group_3(A,B)))))) # label(t157_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9061 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & v1_group_1(A) & -v3_struct_0(A) -> r2_hidden(A,k1_group_3(A)))) # label(t18_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9062 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k6_domain_1(u1_struct_0(A),k2_group_3(A,B,C)) = k3_group_3(A,k6_domain_1(u1_struct_0(A),B),k6_domain_1(u1_struct_0(A),C)))))))) # label(t44_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9063 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> v1_group_3(k5_group_2(A),A) & v1_group_3(k6_group_2(A),A))) # label(t137_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9064 (all A all B (-v3_struct_0(B) & l1_group_1(B) & v4_group_1(B) & v3_group_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> ((exists E (m1_subset_1(E,u1_struct_0(B)) & (exists F (m1_subset_1(F,u1_struct_0(B)) & k2_group_3(B,E,F) = A & r2_hidden(F,D) & r2_hidden(E,C))))) <-> r2_hidden(A,k3_group_3(B,C,D))))))))) # label(t38_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9065 $T # label(t48_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9066 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k5_group_3(A,C,B),k2_group_2(A,k4_group_2(A,B,k1_group_2(A,C)),C)))))))) # label(t52_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9067 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,k1_group_1(A,k3_group_1(A,C),B),C) = k2_group_3(A,B,C))))))) # label(d2_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9068 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_group_2(C,A) -> (v1_finset_1(k14_group_2(A,C)) -> k17_group_2(A,C) = k17_group_2(A,k6_group_3(A,C,B))))))))) # label(t85_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9069 (all A all B (v3_group_1(A) & m1_group_2(B,A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> m1_group_2(k11_group_3(A,B),A) & v1_group_1(k11_group_3(A,B)))) # label(dt_k11_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9070 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r2_hidden(k4_group_3(A,C,B),k8_group_3(A,C)))))))) # label(t114_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9071 (all A all B all C (-v3_struct_0(B) & m1_subset_1(C,u1_struct_0(B)) & l1_group_1(B) & v4_group_1(B) & v3_group_1(B) -> (r2_hidden(A,a_2_2_group_3(B,C)) <-> (exists D (k6_domain_1(u1_struct_0(B),D) = A & r2_hidden(D,k7_group_3(B,C)) & m1_subset_1(D,u1_struct_0(B))))))) # label(fraenkel_a_2_2_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9072 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (-r1_xboole_0(k7_group_3(A,B),k7_group_3(A,C)) <-> k7_group_3(A,B) = k7_group_3(A,C)))))))) # label(t100_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9073 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (v1_group_1(B) & m1_group_2(B,A) -> -((all C (v1_finset_1(C) -> -(k17_group_2(A,k11_group_3(A,B)) = k4_card_1(C) & k9_group_3(A,B) = C))) & (v1_finset_1(k9_group_3(A,B)) | v1_finset_1(k14_group_2(A,k11_group_3(A,B))))))))) # label(t162_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9074 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) & v1_group_1(B) -> (v1_group_3(B,A) & m1_group_2(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> m1_group_2(B,k6_group_3(A,B,C))))))))) # label(t144_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9075 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_group_2(B,A) -> (v1_group_3(B,A) & m1_group_2(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> r1_tarski(k13_group_2(A,B,C),k12_group_2(A,B,C))))))))) # label(t142_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9076 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & v1_group_1(A) & -v3_struct_0(A) -> (all B (v1_group_1(B) & m1_group_2(B,A) -> (A = k11_group_3(A,B) <-> m1_group_2(B,A) & v1_group_3(B,A)))))) # label(t163_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9077 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(B,k7_group_3(A,C)) <-> r2_group_3(A,B,C)))))))) # label(t96_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9078 (all A all B (-v3_struct_0(A) & l1_group_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v4_group_1(A) & v3_group_1(A) -> v1_group_1(k10_group_3(A,B)) & m1_group_2(k10_group_3(A,B),A))) # label(dt_k10_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9079 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k3_group_3(A,B,C) = a_3_0_group_3(A,B,C))))))) # label(d3_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9080 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (v1_group_1(B) & m1_group_2(B,A) -> r2_hidden(B,k9_group_3(A,B)))))) # label(t130_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9081 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k4_group_3(A,C,B) = k4_group_2(A,B,k3_group_2(A,k3_group_1(A,B),C)))))))) # label(t59_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9082 (all A all B all C (-v3_struct_0(A) & l1_group_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v4_group_1(A) & v3_group_1(A) -> r4_group_3(A,B,B))) # label(reflexivity_r4_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9083 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k4_group_3(A,k4_group_3(A,C,k3_group_1(A,B)),B) = C & C = k4_group_3(A,k4_group_3(A,C,B),k3_group_1(A,B)))))))) # label(t63_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9084 (all A all B (v3_group_1(B) & l1_group_1(B) & v4_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (r2_hidden(A,k4_group_3(B,D,C)) <-> (exists E (A = k2_group_3(B,E,C) & r2_hidden(E,D) & m1_subset_1(E,u1_struct_0(B))))))))))) # label(t50_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9085 (all A all B all C (v3_group_1(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> m1_subset_1(k4_group_3(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k4_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9086 $T # label(t87_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9087 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> k4_group_3(A,k4_group_3(A,D,B),C) = k4_group_3(A,D,k1_group_1(A,B,C)))))))))) # label(t56_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9088 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (m1_group_2(B,A) & v1_group_3(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k10_group_2(A,B,C) = k11_group_2(A,B,C)))))))) # label(t143_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9089 (all A all B (-v3_struct_0(B) & l1_group_1(B) & v4_group_1(B) & v3_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_group_2(D,B) -> ((exists E (k2_group_3(B,E,C) = A & r1_rlvect_1(D,E) & m1_subset_1(E,u1_struct_0(B)))) <-> r1_rlvect_1(k6_group_3(B,D,C),A)))))))) # label(t70_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9090 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (-v3_struct_0(A) & v3_group_1(A) & v7_group_1(A) & l1_group_1(A) & v4_group_1(A) <-> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_xboole_0 != B -> k5_group_3(A,B,C) = k6_domain_1(u1_struct_0(A),C))))))))) # label(t67_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9091 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_group_3(A,B,B))))) # label(t89_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9092 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k3_group_3(A,B,C),k2_group_2(A,k2_group_2(A,k1_group_2(A,C),B),C)))))))) # label(t40_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9093 (all A all B all C (-v3_struct_0(B) & l1_group_1(B) & m1_subset_1(C,u1_struct_0(B)) & v4_group_1(B) & v3_group_1(B) -> (r2_hidden(A,a_2_0_group_3(B,C)) <-> (exists D (m1_subset_1(D,u1_struct_0(B)) & D = A & r2_group_3(B,C,D)))))) # label(fraenkel_a_2_0_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9094 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> B = k2_group_3(A,k2_group_3(A,B,C),k3_group_1(A,C)) & B = k2_group_3(A,k2_group_3(A,B,k3_group_1(A,C)),C))))))) # label(t30_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9095 $T # label(t153_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9096 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_group_3(A,k3_group_1(A,B),C) = k3_group_1(A,k2_group_3(A,B,C)))))))) # label(t32_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9097 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (k3_group_3(A,B,C) != k1_xboole_0 <-> k1_xboole_0 != B & C != k1_xboole_0))))))) # label(t39_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9098 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k5_group_3(A,k7_group_2(A,k6_group_2(A)),B) = k7_group_3(A,B))))) # label(d8_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9099 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (v3_group_1(A) & v4_group_1(A) & v7_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) & v1_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r1_group_2(A,k6_group_3(A,B,C),B)))))))) # label(t86_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9100 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_group_2(D,A) -> k4_group_2(A,B,k11_group_2(A,D,C)) = k11_group_2(A,D,k4_group_2(A,B,C)))))))))) # label(t14_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9101 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_group_2(D,A) -> r1_group_2(A,k6_group_3(A,k6_group_3(A,D,B),C),k6_group_3(A,D,k1_group_1(A,B,C))))))))))) # label(t72_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9102 $T # label(t152_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9103 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r3_group_3(A,B,C) -> r3_group_3(A,C,B)))))))) # label(t106_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9104 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (v1_group_1(B) & m1_group_2(B,A) -> (all C (m1_group_2(C,A) & v1_group_1(C) -> (r6_group_3(A,B,C) <-> r2_hidden(B,k9_group_3(A,C))))))))) # label(t128_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9105 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_group_3(A,C,D) & r2_group_3(A,B,C) -> r2_group_3(A,B,D)))))))))) # label(t91_group_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9106 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,k5_finsub_1(C)) -> (all E (m2_relset_1(E,C,u1_struct_0(A)) & v1_funct_2(E,C,u1_struct_0(A)) & v1_funct_1(E) -> (r3_lattices(A,B,k3_lattice2(C,A,D,E)) -> (all F (m1_subset_1(F,C) -> (r2_hidden(F,D) -> r3_lattices(A,B,k8_funct_2(C,u1_struct_0(A),E,F)))))))))))))))) # label(t59_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9107 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(A)) -> (all C (v10_lattices(C) & l3_lattices(C) & v14_lattices(C) & -v3_struct_0(C) -> (all D (m2_relset_1(D,A,u1_struct_0(C)) & v1_funct_2(D,A,u1_struct_0(C)) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,u1_struct_0(C)) & v1_funct_2(E,A,u1_struct_0(C)) -> (k2_partfun1(A,u1_struct_0(C),E,B) = k2_partfun1(A,u1_struct_0(C),D,B) -> k3_lattice2(A,C,B,D) = k3_lattice2(A,C,B,E)))))))))))) # label(t75_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9108 $T # label(t4_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9109 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> r1_lattice2(u1_struct_0(A),u2_lattices(A),u1_lattices(A)))) # label(t40_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9110 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (r6_binop_1(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) -> v11_lattices(A)))) # label(t36_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9111 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k5_finsub_1(B)) -> (all D (v1_funct_2(D,B,u1_struct_0(A)) & m2_relset_1(D,B,u1_struct_0(A)) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,B,u1_struct_0(A)) & v1_funct_2(E,B,u1_struct_0(A)) -> ((all F (m1_subset_1(F,B) -> (r2_hidden(F,C) -> r3_lattices(A,k8_funct_2(B,u1_struct_0(A),D,F),k8_funct_2(B,u1_struct_0(A),E,F))))) -> r3_lattices(A,k2_lattice2(B,A,C,D),k2_lattice2(B,A,C,E)) | C = k1_xboole_0))))))))))) # label(t48_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9112 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,k5_finsub_1(C)) -> (all E (m2_relset_1(E,C,u1_struct_0(A)) & v1_funct_2(E,C,u1_struct_0(A)) & v1_funct_1(E) -> ((all F (m1_subset_1(F,C) -> (r2_hidden(F,D) -> r3_lattices(A,B,k8_funct_2(C,u1_struct_0(A),E,F))))) -> D = k1_xboole_0 | r3_lattices(A,B,k3_lattice2(C,A,D,E))))))))))))) # label(t61_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9113 (all A all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> ((all F (m1_subset_1(F,A) -> (r2_hidden(F,C) -> k1_funct_1(E,F) = k1_funct_1(D,F)))) -> k1_funct_4(E,k2_partfun1(A,B,D,C)) = E))))))))) # label(t10_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9114 $T # label(t23_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9115 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (r6_binop_1(u1_struct_0(A),u1_lattices(A),u2_lattices(A)) -> v11_lattices(A)))) # label(t38_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9116 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> v3_binop_1(u2_lattices(A),u1_struct_0(A)))) # label(t26_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9117 (all A (-v3_struct_0(A) & l3_lattices(A) -> u1_struct_0(k1_lattice2(A)) = u1_struct_0(A) & u1_lattices(A) = u2_lattices(k1_lattice2(A)) & u1_lattices(k1_lattice2(A)) = u2_lattices(A))) # label(t18_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9118 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,k5_finsub_1(C)) -> (all E (v1_funct_2(E,C,u1_struct_0(A)) & m2_relset_1(E,C,u1_struct_0(A)) & v1_funct_1(E) -> ((exists F (r2_hidden(F,D) & r3_lattices(A,B,k8_funct_2(C,u1_struct_0(A),E,F)) & m1_subset_1(F,C))) -> r3_lattices(A,B,k2_lattice2(C,A,D,E))))))))))))) # label(t44_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9119 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,k5_finsub_1(C)) -> (all E (v1_funct_2(E,C,u1_struct_0(A)) & m2_relset_1(E,C,u1_struct_0(A)) & v1_funct_1(E) -> ((all F (m1_subset_1(F,C) -> (r2_hidden(F,D) -> k8_funct_2(C,u1_struct_0(A),E,F) = B))) -> k3_lattice2(C,A,D,E) = B | k1_xboole_0 = D))))))))))) # label(t57_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9120 (all A (-v3_struct_0(A) & v7_lattices(A) & l1_lattices(A) -> v1_funct_2(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_partfun1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v2_binop_1(u1_lattices(A),u1_struct_0(A)) & v1_funct_1(u1_lattices(A)) & v1_relat_1(u1_lattices(A)))) # label(fc5_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9121 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,k5_finsub_1(C)) -> (all E (m2_relset_1(E,C,u1_struct_0(A)) & v1_funct_2(E,C,u1_struct_0(A)) & v1_funct_1(E) -> (k1_xboole_0 != D -> k2_lattice2(C,A,D,k8_funcop_1(u1_struct_0(A),C,u2_lattices(A),B,E)) = k3_lattices(A,B,k2_lattice2(C,A,D,E))))))))))))) # label(t50_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9122 (all A (-v1_xboole_0(A) -> (all B (-v3_struct_0(B) & l3_lattices(B) & v10_lattices(B) -> (all C (m1_subset_1(C,k5_finsub_1(A)) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,u1_struct_0(B)) & v1_funct_2(D,A,u1_struct_0(B)) -> k3_lattice2(A,B,C,D) = k7_setwiseo(A,u1_struct_0(B),u1_lattices(B),C,D))))))))) # label(d4_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9123 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(A)) -> (all C (-v3_struct_0(C) & v10_lattices(C) & v11_lattices(C) & v13_lattices(C) & l3_lattices(C) -> (all D (m2_relset_1(D,A,u1_struct_0(C)) & v1_funct_2(D,A,u1_struct_0(C)) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,u1_struct_0(C)) & m2_relset_1(E,A,u1_struct_0(C)) -> (all F (m1_subset_1(F,u1_struct_0(C)) -> ((all G (m1_subset_1(G,A) -> (r2_hidden(G,B) -> k4_lattices(C,F,k8_funct_2(A,u1_struct_0(C),E,G)) = k8_funct_2(A,u1_struct_0(C),D,G)))) -> k2_lattice2(A,C,B,D) = k4_lattices(C,F,k2_lattice2(A,C,B,E))))))))))))))) # label(t82_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9124 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> r6_binop_1(u1_struct_0(A),u2_lattices(A),u2_lattices(A)))) # label(t34_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9125 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (r1_lattice2(A,B,C) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> k2_binop_1(A,A,A,B,D,k2_binop_1(A,A,A,C,D,E)) = D))))))))))) # label(d1_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9126 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(A)) -> (all C (v10_lattices(C) & v14_lattices(C) & l3_lattices(C) & -v3_struct_0(C) -> (all D (m2_relset_1(D,A,u1_struct_0(C)) & v1_funct_2(D,A,u1_struct_0(C)) & v1_funct_1(D) -> (all E (m1_subset_1(E,u1_struct_0(C)) -> ((all F (m1_subset_1(F,A) -> (r2_hidden(F,B) -> r3_lattices(C,E,k8_funct_2(A,u1_struct_0(C),D,F))))) -> r3_lattices(C,E,k3_lattice2(A,C,B,D))))))))))))) # label(t76_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9127 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(B,A) -> k1_funct_4(A,B) = A))))) # label(t8_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9128 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(k1_lattice2(A))) -> (all E (m1_subset_1(E,u1_struct_0(k1_lattice2(A))) -> (E = C & D = B -> k4_lattices(k1_lattice2(A),D,E) = k3_lattices(A,B,C) & k3_lattices(k1_lattice2(A),D,E) = k4_lattices(A,B,C)))))))))))) # label(t52_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9129 $T # label(t20_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9130 (all A all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> k1_funct_4(k2_partfun1(A,B,D,C),E) = E)))))))) # label(t7_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9131 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,k5_finsub_1(C)) -> (all E (v1_funct_1(E) & m2_relset_1(E,C,u1_struct_0(A)) & v1_funct_2(E,C,u1_struct_0(A)) -> ((all F (m1_subset_1(F,C) -> (r2_hidden(F,D) -> B = k8_funct_2(C,u1_struct_0(A),E,F)))) -> k1_xboole_0 = D | k2_lattice2(C,A,D,E) = B))))))))))) # label(t45_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9132 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> v3_binop_1(u1_lattices(A),u1_struct_0(A)))) # label(t30_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9133 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (l3_lattices(A) & v11_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> r6_binop_1(u1_struct_0(A),u1_lattices(A),u2_lattices(A))))) # label(t37_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9134 (all A all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (k2_partfun1(A,B,D,C) = k2_partfun1(A,B,E,C) <-> (all F (m1_subset_1(F,A) -> (r2_hidden(F,C) -> k1_funct_1(E,F) = k1_funct_1(D,F))))))))))))) # label(t5_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9135 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (-v3_struct_0(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) <-> v10_lattices(A) & l3_lattices(A) & v11_lattices(A) & -v3_struct_0(A)))) # label(t65_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9136 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(A)) -> (all C (-v3_struct_0(C) & v10_lattices(C) & l3_lattices(C) & v13_lattices(C) & v11_lattices(C) -> (all D (m2_relset_1(D,A,u1_struct_0(C)) & v1_funct_2(D,A,u1_struct_0(C)) & v1_funct_1(D) -> (all E (m1_subset_1(E,u1_struct_0(C)) -> k4_lattices(C,E,k2_lattice2(A,C,B,D)) = k2_lattice2(A,C,B,k8_funcop_1(u1_struct_0(C),A,u1_lattices(C),E,D)))))))))))) # label(t83_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9137 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k5_finsub_1(B)) -> (all D (m2_relset_1(D,B,u1_struct_0(A)) & v1_funct_2(D,B,u1_struct_0(A)) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,B,u1_struct_0(A)) & v1_funct_2(E,B,u1_struct_0(A)) -> ((all F (m1_subset_1(F,B) -> (r2_hidden(F,C) -> r3_lattices(A,k8_funct_2(B,u1_struct_0(A),D,F),k8_funct_2(B,u1_struct_0(A),E,F))))) -> C = k1_xboole_0 | r3_lattices(A,k3_lattice2(B,A,C,D),k3_lattice2(B,A,C,E))))))))))))) # label(t62_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9138 (all A all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> k1_relat_1(k2_partfun1(A,B,D,C)) = C)))))) # label(t2_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9139 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,B) -> (all D (m1_subset_1(D,k5_finsub_1(B)) -> (all E (m2_relset_1(E,B,u1_struct_0(A)) & v1_funct_2(E,B,u1_struct_0(A)) & v1_funct_1(E) -> (r2_hidden(C,D) -> r3_lattices(A,k8_funct_2(B,u1_struct_0(A),E,C),k2_lattice2(B,A,D,E))))))))))))) # label(t43_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9140 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (v1_setwiseo(u2_lattices(A),u1_struct_0(A)) -> k5_lattices(A) = k3_binop_1(u1_struct_0(A),u2_lattices(A))))) # label(t28_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9141 (all A (v10_lattices(A) & v13_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> v1_setwiseo(u2_lattices(A),u1_struct_0(A)))) # label(t67_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9142 (all A (v10_lattices(A) & l3_lattices(A) & v13_lattices(A) & -v3_struct_0(A) -> r3_binop_1(u1_struct_0(A),k5_lattices(A),u2_lattices(A)))) # label(t66_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9143 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v14_lattices(A) -> k5_lattices(k1_lattice2(A)) = k6_lattices(A))) # label(t79_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9144 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v10_lattices(A) & v1_lattice2(A) -> -v3_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v10_lattices(A) & v13_lattices(A) & v3_filter_0(A) & v9_lattices(A) & v8_lattices(A) & v7_lattices(A) & v6_lattices(A)))) # label(cc1_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9145 (all A all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (m1_subset_1(E,k5_finsub_1(A)) -> (k2_partfun1(A,B,D,E) = k2_partfun1(A,B,C,E) -> k2_funct_2(A,B,C,E) = k2_funct_2(A,B,D,E)))))))))) # label(t16_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9146 (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 (m1_subset_1(D,k5_finsub_1(A)) -> k1_relat_1(k2_partfun1(A,B,C,D)) = D)))))) # label(t13_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9147 (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_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,k5_finsub_1(A)) -> k1_funct_4(k2_partfun1(A,B,C,E),D) = D)))))))) # label(t12_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9148 (exists A (l3_lattices(A) & v5_lattices(A) & v8_lattices(A) & v9_lattices(A) & v1_lattice2(A) & v10_lattices(A) & v7_lattices(A) & v6_lattices(A) & v4_lattices(A) & -v3_struct_0(A))) # label(rc1_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9149 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,k5_finsub_1(C)) -> (all E (v1_funct_1(E) & v1_funct_2(E,C,u1_struct_0(A)) & m2_relset_1(E,C,u1_struct_0(A)) -> (k1_xboole_0 != D -> k4_lattices(A,B,k3_lattice2(C,A,D,E)) = k3_lattice2(C,A,D,k8_funcop_1(u1_struct_0(A),C,u1_lattices(A),B,E))))))))))))) # label(t58_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9150 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(A)) -> (all C (v10_lattices(C) & l3_lattices(C) & v13_lattices(C) & -v3_struct_0(C) -> (all D (m2_relset_1(D,A,u1_struct_0(C)) & v1_funct_2(D,A,u1_struct_0(C)) & v1_funct_1(D) -> (all E (m1_subset_1(E,u1_struct_0(C)) -> ((all F (m1_subset_1(F,A) -> (r2_hidden(F,B) -> r3_lattices(C,k8_funct_2(A,u1_struct_0(C),D,F),E)))) -> r3_lattices(C,k2_lattice2(A,C,B,D),E)))))))))))) # label(t70_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9151 (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) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (m1_subset_1(E,k5_finsub_1(A)) -> ((all F (m1_subset_1(F,A) -> (r2_hidden(F,E) -> k1_funct_1(D,F) = k1_funct_1(C,F)))) -> k1_funct_4(D,k2_partfun1(A,B,C,E)) = D))))))))) # label(t14_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9152 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (v14_lattices(A) <-> v13_lattices(k1_lattice2(A))))) # label(t64_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9153 $T # label(t15_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9154 $T # label(t3_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9155 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,k5_finsub_1(C)) -> (all E (v1_funct_1(E) & m2_relset_1(E,C,u1_struct_0(A)) & v1_funct_2(E,C,u1_struct_0(A)) -> ((all F (m1_subset_1(F,C) -> (r2_hidden(F,D) -> r3_lattices(A,k8_funct_2(C,u1_struct_0(A),E,F),B)))) -> k1_xboole_0 = D | r3_lattices(A,k2_lattice2(C,A,D,E),B)))))))))))) # label(t47_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9156 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v6_group_1(A) & v10_lattices(A) -> -v3_struct_0(A) & v9_lattices(A) & v10_lattices(A) & v13_lattices(A) & v8_lattices(A) & v7_lattices(A) & v6_lattices(A) & v5_lattices(A) & v4_lattices(A)))) # label(cc3_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9157 (all A (v6_lattices(A) & l1_lattices(A) & -v3_struct_0(A) -> v1_relat_1(u1_lattices(A)) & v1_funct_1(u1_lattices(A)) & v1_partfun1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_binop_1(u1_lattices(A),u1_struct_0(A)) & v1_funct_2(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)))) # label(fc4_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9158 (all A (-v1_xboole_0(A) -> (all B (l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k5_finsub_1(A)) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,u1_struct_0(B)) & m2_relset_1(D,A,u1_struct_0(B)) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,u1_struct_0(k1_lattice2(B))) & m2_relset_1(E,A,u1_struct_0(k1_lattice2(B))) -> (D = E -> k2_lattice2(A,B,C,D) = k3_lattice2(A,k1_lattice2(B),C,E) & k2_lattice2(A,k1_lattice2(B),C,E) = k3_lattice2(A,B,C,D)))))))))))) # label(t51_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9159 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(k1_lattice2(A))) -> (all E (m1_subset_1(E,u1_struct_0(k1_lattice2(A))) -> (C = E & D = B & r3_lattices(k1_lattice2(A),D,E) -> r3_lattices(A,C,B)))))))))))) # label(t54_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9160 (all A all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(k1_funct_4(C,k2_partfun1(A,B,D,E))) & m2_relset_1(k1_funct_4(C,k2_partfun1(A,B,D,E)),A,B) & v1_funct_2(k1_funct_4(C,k2_partfun1(A,B,D,E)),A,B))))))))) # label(t6_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9161 (all A (l3_lattices(A) -> (v10_lattices(A) & v3_filter_0(A) & v13_lattices(A) & -v3_struct_0(A) -> v6_lattices(A) & v8_lattices(A) & v1_lattice2(A) & v10_lattices(A) & v9_lattices(A) & v7_lattices(A) & v5_lattices(A) & v4_lattices(A) & -v3_struct_0(A)))) # label(cc2_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9162 (all A (v5_lattices(A) & l2_lattices(A) & -v3_struct_0(A) -> v1_partfun1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v2_binop_1(u2_lattices(A),u1_struct_0(A)) & v1_funct_2(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_1(u2_lattices(A)) & v1_relat_1(u2_lattices(A)))) # label(fc3_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9163 (all A (l3_lattices(A) -> (v10_lattices(A) & v6_group_1(A) & -v3_struct_0(A) -> v6_lattices(A) & v8_lattices(A) & v14_lattices(A) & v15_lattices(A) & v13_lattices(A) & v10_lattices(A) & v9_lattices(A) & v7_lattices(A) & v5_lattices(A) & v4_lattices(A) & -v3_struct_0(A)))) # label(cc5_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9164 (all A (-v1_xboole_0(A) -> (all B (-v3_struct_0(B) & l3_lattices(B) & v10_lattices(B) -> (all C (m1_subset_1(C,k5_finsub_1(A)) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,u1_struct_0(B)) & v1_funct_2(D,A,u1_struct_0(B)) -> k7_setwiseo(A,u1_struct_0(B),u2_lattices(B),C,D) = k2_lattice2(A,B,C,D))))))))) # label(d3_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9165 (all A (-v3_struct_0(A) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A) -> v1_setwiseo(u1_lattices(A),u1_struct_0(A)))) # label(t73_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9166 (all A (-v3_struct_0(A) & v5_lattices(A) & l2_lattices(A) -> v2_binop_1(u2_lattices(A),u1_struct_0(A)))) # label(t29_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9167 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_lattices(A),B,C) = C)) -> B = k6_lattices(A)))))) # label(t25_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9168 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> C = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u2_lattices(A),B,C))) -> k5_lattices(A) = B))))) # label(t22_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9169 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k5_finsub_1(B)) -> (all D (v1_funct_1(D) & v1_funct_2(D,B,u1_struct_0(A)) & m2_relset_1(D,B,u1_struct_0(A)) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,u1_struct_0(A)) & m2_relset_1(E,B,u1_struct_0(A)) -> (k2_partfun1(B,u1_struct_0(A),E,C) = k2_partfun1(B,u1_struct_0(A),D,C) -> k3_lattice2(B,A,C,E) = k3_lattice2(B,A,C,D) | k1_xboole_0 = C))))))))))) # label(t60_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9170 $T # label(t11_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9171 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,B) -> (all D (m1_subset_1(D,k5_finsub_1(B)) -> (all E (v1_funct_2(E,B,u1_struct_0(A)) & m2_relset_1(E,B,u1_struct_0(A)) & v1_funct_1(E) -> (r2_hidden(C,D) -> r3_lattices(A,k3_lattice2(B,A,D,E),k8_funct_2(B,u1_struct_0(A),E,C))))))))))))) # label(t55_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.54 9172 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> C = k4_lattices(A,B,C))) -> B = k6_lattices(A)))))) # label(t24_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9173 (all A (l3_lattices(A) & v13_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> k5_lattices(A) = k3_binop_1(u1_struct_0(A),u2_lattices(A)))) # label(t68_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9174 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (v1_setwiseo(u1_lattices(A),u1_struct_0(A)) -> k3_binop_1(u1_struct_0(A),u1_lattices(A)) = k6_lattices(A)))) # label(t33_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9175 $T # label(t42_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9176 (all A (l3_lattices(A) & v14_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> r3_binop_1(u1_struct_0(A),k6_lattices(A),u1_lattices(A)))) # label(t72_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9177 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> r1_lattice2(u1_struct_0(A),u1_lattices(A),u2_lattices(A)))) # label(t41_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9178 $T # label(t1_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9179 (all A all B all C all D (-v3_struct_0(B) & l3_lattices(B) & m1_subset_1(C,k5_finsub_1(A)) & v1_funct_1(D) & v1_funct_2(D,A,u1_struct_0(B)) & m1_relset_1(D,A,u1_struct_0(B)) & v10_lattices(B) & -v1_xboole_0(A) -> m1_subset_1(k3_lattice2(A,B,C,D),u1_struct_0(B)))) # label(dt_k3_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9180 (all A all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> k1_funct_4(D,k2_partfun1(A,B,D,C)) = D)))))) # label(t9_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9181 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,k5_finsub_1(C)) -> (all E (m2_relset_1(E,C,u1_struct_0(A)) & v1_funct_2(E,C,u1_struct_0(A)) & v1_funct_1(E) -> ((exists F (r2_hidden(F,D) & r3_lattices(A,k8_funct_2(C,u1_struct_0(A),E,F),B) & m1_subset_1(F,C))) -> r3_lattices(A,k3_lattice2(C,A,D,E),B)))))))))))) # label(t56_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9182 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(A)) -> (all C (-v3_struct_0(C) & v10_lattices(C) & v13_lattices(C) & l3_lattices(C) -> (all D (v1_funct_2(D,A,u1_struct_0(C)) & m2_relset_1(D,A,u1_struct_0(C)) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,u1_struct_0(C)) & m2_relset_1(E,A,u1_struct_0(C)) -> (k2_partfun1(A,u1_struct_0(C),E,B) = k2_partfun1(A,u1_struct_0(C),D,B) -> k2_lattice2(A,C,B,E) = k2_lattice2(A,C,B,D)))))))))))) # label(t69_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9183 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(A)) -> (all C (-v3_struct_0(C) & v14_lattices(C) & l3_lattices(C) & v10_lattices(C) -> (all D (m2_relset_1(D,A,u1_struct_0(C)) & v1_funct_2(D,A,u1_struct_0(C)) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,u1_struct_0(C)) & m2_relset_1(E,A,u1_struct_0(C)) -> ((all F (m1_subset_1(F,A) -> (r2_hidden(F,B) -> r3_lattices(C,k8_funct_2(A,u1_struct_0(C),D,F),k8_funct_2(A,u1_struct_0(C),E,F))))) -> r3_lattices(C,k3_lattice2(A,C,B,D),k3_lattice2(A,C,B,E))))))))))))) # label(t77_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9184 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r3_lattices(A,B,C) -> (all D (m1_subset_1(D,u1_struct_0(k1_lattice2(A))) -> (all E (m1_subset_1(E,u1_struct_0(k1_lattice2(A))) -> (D = B & C = E -> r3_lattices(k1_lattice2(A),E,D))))))))))))) # label(t53_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9185 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> r6_binop_1(u1_struct_0(A),u1_lattices(A),u1_lattices(A)))) # label(t39_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9186 (all A (-v3_struct_0(A) & l3_lattices(A) -> v3_lattices(k1_lattice2(A)) & -v3_struct_0(k1_lattice2(A)))) # label(fc1_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9187 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v6_group_1(A) & v10_lattices(A) -> v4_lattices(A) & v9_lattices(A) & v10_lattices(A) & v14_lattices(A) & v8_lattices(A) & v7_lattices(A) & v6_lattices(A) & v5_lattices(A) & -v3_struct_0(A)))) # label(cc4_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9188 (all A (l1_lattices(A) & v6_lattices(A) & -v3_struct_0(A) -> v1_binop_1(u1_lattices(A),u1_struct_0(A)))) # label(t31_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9189 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (v3_filter_0(A) & v13_lattices(A) <-> v1_lattice2(A)))) # label(d6_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9190 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(A)) -> (all C (v13_lattices(C) & l3_lattices(C) & v10_lattices(C) & -v3_struct_0(C) -> (all D (v1_funct_2(D,A,u1_struct_0(C)) & m2_relset_1(D,A,u1_struct_0(C)) & v1_funct_1(D) -> (all E (m2_relset_1(E,A,u1_struct_0(C)) & v1_funct_2(E,A,u1_struct_0(C)) & v1_funct_1(E) -> ((all F (m1_subset_1(F,A) -> (r2_hidden(F,B) -> r3_lattices(C,k8_funct_2(A,u1_struct_0(C),D,F),k8_funct_2(A,u1_struct_0(C),E,F))))) -> r3_lattices(C,k2_lattice2(A,C,B,D),k2_lattice2(A,C,B,E))))))))))))) # label(t71_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9191 (all A (l3_lattices(A) -> g3_lattices(u1_struct_0(A),u1_lattices(A),u2_lattices(A)) = k1_lattice2(A))) # label(d2_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9192 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (-v3_struct_0(A) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A) -> r6_binop_1(u1_struct_0(A),u2_lattices(A),u1_lattices(A))))) # label(t35_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9193 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (v6_group_1(A) <-> v6_group_1(k1_lattice2(A))))) # label(t85_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9194 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(A)) -> (all C (-v3_struct_0(C) & l3_lattices(C) & v13_lattices(C) & v11_lattices(C) & v10_lattices(C) -> (all D (v1_funct_2(D,A,u1_struct_0(C)) & m2_relset_1(D,A,u1_struct_0(C)) & v1_funct_1(D) -> (all E (m1_subset_1(E,u1_struct_0(C)) -> k2_binop_1(u1_struct_0(C),u1_struct_0(C),u1_struct_0(C),u1_lattices(C),E,k2_lattice2(A,C,B,D)) = k2_lattice2(A,C,B,k8_funcop_1(u1_struct_0(C),A,u1_lattices(C),E,D)))))))))))) # label(t81_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9195 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> v4_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v3_lattices(k1_lattice2(A)) & -v3_struct_0(k1_lattice2(A)))) # label(fc6_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9196 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (v13_lattices(A) <-> v14_lattices(k1_lattice2(A))))) # label(t63_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9197 (all A (l3_lattices(A) -> v3_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A)))) # label(dt_k1_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9198 (all A (-v3_struct_0(A) & l3_lattices(A) & v13_lattices(A) & v11_lattices(A) & v10_lattices(A) -> r6_binop_1(u1_struct_0(A),u1_lattices(A),u2_lattices(A)))) # label(t80_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9199 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,k5_finsub_1(C)) -> (all E (v1_funct_2(E,C,u1_struct_0(A)) & m2_relset_1(E,C,u1_struct_0(A)) & v1_funct_1(E) -> (r3_lattices(A,k2_lattice2(C,A,D,E),B) -> (all F (m1_subset_1(F,C) -> (r2_hidden(F,D) -> r3_lattices(A,k8_funct_2(C,u1_struct_0(A),E,F),B))))))))))))))) # label(t46_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9200 (all A (v7_lattices(A) & l1_lattices(A) & -v3_struct_0(A) -> v2_binop_1(u1_lattices(A),u1_struct_0(A)))) # label(t32_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9201 (all A all B all C all D (m1_relset_1(D,A,u1_struct_0(B)) & v1_funct_2(D,A,u1_struct_0(B)) & v1_funct_1(D) & m1_subset_1(C,k5_finsub_1(A)) & l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) & -v1_xboole_0(A) -> m1_subset_1(k2_lattice2(A,B,C,D),u1_struct_0(B)))) # label(dt_k2_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9202 (exists A (l3_lattices(A) & v7_lattices(A) & v8_lattices(A) & v3_filter_0(A) & v1_lattice2(A) & v13_lattices(A) & v10_lattices(A) & v9_lattices(A) & v6_lattices(A) & v5_lattices(A) & v4_lattices(A) & v3_lattices(A) & -v3_struct_0(A))) # label(rc2_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9203 $T # label(d5_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9204 (all A (v3_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> k1_lattice2(k1_lattice2(A)) = A)) # label(t19_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9205 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v10_lattices(A) & v11_lattices(A) & v6_group_1(A) -> -v3_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v9_lattices(A) & v13_lattices(A) & v3_filter_0(A) & v1_lattice2(A) & v10_lattices(A) & v8_lattices(A) & v7_lattices(A) & v6_lattices(A)))) # label(cc6_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9206 (all A (-v3_struct_0(A) & l3_lattices(A) -> (v1_binop_1(u2_lattices(A),u1_struct_0(A)) & v2_binop_1(u1_lattices(A),u1_struct_0(A)) & r1_lattice2(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) & r1_lattice2(u1_struct_0(A),u1_lattices(A),u2_lattices(A)) & v1_binop_1(u1_lattices(A),u1_struct_0(A)) & v2_binop_1(u2_lattices(A),u1_struct_0(A)) -> v10_lattices(A)))) # label(t17_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9207 (all A (-v3_struct_0(A) & v13_lattices(A) & l3_lattices(A) & v10_lattices(A) -> k5_lattices(A) = k6_lattices(k1_lattice2(A)))) # label(t78_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9208 (all A (-v3_struct_0(A) & l3_lattices(A) & v13_lattices(A) & v10_lattices(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (m1_subset_1(D,u1_struct_0(A)) & r3_lattices(A,k4_lattices(A,B,D),C) & (all E (m1_subset_1(E,u1_struct_0(A)) -> (r3_lattices(A,k4_lattices(A,B,E),C) -> r3_lattices(A,E,D)))))))))) <-> -v3_struct_0(A) & v10_lattices(A) & v1_lattice2(A) & l3_lattices(A)))) # label(t84_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9209 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k5_finsub_1(B)) -> (all D (v1_funct_1(D) & v1_funct_2(D,B,u1_struct_0(A)) & m2_relset_1(D,B,u1_struct_0(A)) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,u1_struct_0(A)) & m2_relset_1(E,B,u1_struct_0(A)) -> (k2_partfun1(B,u1_struct_0(A),D,C) = k2_partfun1(B,u1_struct_0(A),E,C) -> C = k1_xboole_0 | k2_lattice2(B,A,C,E) = k2_lattice2(B,A,C,D)))))))))))) # label(t49_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9210 (all A (l2_lattices(A) & v4_lattices(A) & -v3_struct_0(A) -> v1_relat_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_binop_1(u2_lattices(A),u1_struct_0(A)) & v1_partfun1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_1(u2_lattices(A)))) # label(fc2_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9211 (all A (l2_lattices(A) & v4_lattices(A) & -v3_struct_0(A) -> v1_binop_1(u2_lattices(A),u1_struct_0(A)))) # label(t27_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9212 (all A (l3_lattices(A) & v14_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> k3_binop_1(u1_struct_0(A),u1_lattices(A)) = k6_lattices(A))) # label(t74_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9213 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> C = k3_lattices(A,B,C))) -> k5_lattices(A) = B))))) # label(t21_lattice2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9214 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v3_struct_0(B) & v4_group_1(B) & l1_group_1(B) & v3_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k3_group_4(B,k1_finsop_1(u1_struct_0(B),A,C)) = k6_group_1(B,A,C))))))) # label(t15_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9215 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v3_struct_0(B) & v4_group_1(B) & l1_group_1(B) & v3_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_group_2(D,B) -> (r1_rlvect_1(D,C) -> r1_rlvect_1(D,k6_group_1(B,A,C))))))))))) # label(t5_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9216 $T # label(t36_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9217 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> (v3_group_1(A) & v4_group_1(A) & v7_group_1(A) & l1_group_1(A) & v2_funct_1(B) & k2_relat_1(B) = k2_relat_1(C) & v2_funct_1(C) & -v3_struct_0(A) -> k3_group_4(A,B) = k3_group_4(A,C)))))))) # label(t19_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9218 $T # label(t97_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9219 (all A (v1_int_1(A) -> (all B (v4_group_1(B) & l1_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_group_2(D,B) -> (r1_rlvect_1(D,C) -> r1_rlvect_1(D,k6_group_1(B,A,C))))))))))) # label(t6_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9220 $T # label(t51_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9221 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> k5_group_2(A) = k5_lattices(k11_group_4(A)))) # label(t98_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9222 (all A all B all C (m1_finseq_1(B,A) & -v1_xboole_0(A) -> k1_finseq_3(B,C) = k1_group_4(A,B,C))) # label(redefinition_k1_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9223 $T # label(t47_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9224 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> v1_funct_1(k10_group_4(A)) & m2_relset_1(k10_group_4(A),k2_zfmisc_1(k1_group_3(A),k1_group_3(A)),k1_group_3(A)) & v1_funct_2(k10_group_4(A),k2_zfmisc_1(k1_group_3(A),k1_group_3(A)),k1_group_3(A)))) # label(dt_k10_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9225 $T # label(t49_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9226 $T # label(t23_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9227 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (v2_group_4(B,A) <-> (all C (v1_group_1(C) & m1_group_2(C,A) -> (m1_group_2(B,C) -> g1_group_1(u1_struct_0(B),u1_group_1(B)) = C | g1_group_1(u1_struct_0(A),u1_group_1(A)) = C))) & g1_group_1(u1_struct_0(A),u1_group_1(A)) != g1_group_1(u1_struct_0(B),u1_group_1(B))))))) # label(d7_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9228 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> m1_group_2(k5_group_4(A,k5_subset_1(u1_struct_0(A),B,C)),k9_group_2(A,k5_group_4(A,B),k5_group_4(A,C))))))))) # label(t42_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9229 (all A (-v3_struct_0(A) & v2_group_1(A) & l1_group_1(A) -> k3_group_4(A,k6_finseq_1(u1_struct_0(A))) = k2_group_1(A))) # label(t11_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9230 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((exists D ((exists E (m2_finseq_1(E,k4_numbers) & k3_finseq_1(E) = k3_finseq_1(D) & r1_tarski(k2_relat_1(D),C) & k3_group_4(A,k4_group_4(A,E,D)) = B)) & m2_finseq_1(D,u1_struct_0(A)))) <-> r1_rlvect_1(k5_group_4(A,C),B)))))))) # label(t37_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9231 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> k1_finsop_1(u1_struct_0(A),k3_finseq_1(B),k2_group_1(A)) = k4_group_4(A,k1_finsop_1(k4_numbers,k3_finseq_1(B),k2_group_4(np__0)),B))))) # label(t32_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9232 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m1_group_2(C,A) & v1_group_1(C) -> -v2_group_4(C,A))) -> r1_rlvect_1(k6_group_4(A),B)))))) # label(t53_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9233 $T # label(t91_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9234 $T # label(t2_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9235 (all A (-v3_struct_0(A) & v2_group_1(A) & l1_group_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,k3_group_4(A,B),C) = k3_group_4(A,k8_finseq_1(u1_struct_0(A),B,k12_finseq_1(u1_struct_0(A),C))))))))) # label(t9_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9236 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (v1_group_1(B) & m1_group_2(B,A) -> r1_group_2(A,k8_group_4(A,B,B),B))))) # label(t73_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9237 (all A (-v3_struct_0(A) & v2_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k3_group_4(A,k8_finseq_1(u1_struct_0(A),k12_finseq_1(u1_struct_0(A),C),B)) = k1_group_1(A,C,k3_group_4(A,B)))))))) # label(t10_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9238 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_group_2(B,A) & v1_group_1(B) -> ((all C (m1_group_2(C,A) & v1_group_1(C) -> -v2_group_4(C,A))) -> (B = k6_group_4(A) <-> g1_group_1(u1_struct_0(A),u1_group_1(A)) = B)) & ((exists C (v2_group_4(C,A) & m1_group_2(C,A) & v1_group_1(C))) -> (k1_setfam_1(a_1_0_group_4(A)) = u1_struct_0(B) <-> B = k6_group_4(A))))))) # label(d8_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9239 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> (k7_group_4(A,C,B) = k7_group_4(A,B,C) -> k7_group_4(A,B,C) = u1_struct_0(k8_group_4(A,B,C))))))))) # label(t69_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9240 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(k1_group_3(A),k1_group_3(A)),k1_group_3(A)) & v1_funct_2(B,k2_zfmisc_1(k1_group_3(A),k1_group_3(A)),k1_group_3(A)) -> (B = k10_group_4(A) <-> (all C (m1_subset_1(C,k1_group_3(A)) -> (all D (m1_subset_1(D,k1_group_3(A)) -> (all E (m1_group_2(E,A) -> (all F (m1_group_2(F,A) -> (C = E & F = D -> k2_binop_1(k1_group_3(A),k1_group_3(A),k1_group_3(A),B,C,D) = k9_group_2(A,E,F))))))))))))))) # label(d12_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9241 (exists A (v1_group_1(A) & p1_s1_group_4(A) & m1_group_2(A,f1_s1_group_4))) -> (exists A (v1_group_1(A) & k1_setfam_1(a_0_0_group_4) = u1_struct_0(A) & m1_group_2(A,f1_s1_group_4))) # label(s1_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9242 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> k9_group_4(A) = u2_lattices(k11_group_4(A)))) # label(t93_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9243 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_group_2(B,A) & v1_group_3(B,A) & v1_group_1(B) -> (all C (m1_group_2(C,A) & v1_group_3(C,A) & v1_group_1(C) -> k7_group_4(A,B,C) = k7_group_4(A,C,B))))))) # label(t64_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9244 (all A all B (l1_group_1(B) & v4_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> ((exists C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & C = A & (exists D (v2_group_4(D,B) & C = u1_struct_0(D) & m1_group_2(D,B) & v1_group_1(D))))) <-> r2_hidden(A,a_1_0_group_4(B))))) # label(fraenkel_a_1_0_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9245 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m2_finseq_1(B,k4_numbers) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> (all D (m2_finseq_1(D,u1_struct_0(A)) -> (k4_group_4(A,B,C) = D <-> k3_finseq_1(D) = k3_finseq_1(C) & (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (r2_hidden(E,k4_finseq_1(C)) -> k6_group_1(A,k2_group_4(k4_finseq_4(k5_numbers,k4_numbers,B,E)),k4_finseq_4(k5_numbers,u1_struct_0(A),C,E)) = k1_funct_1(D,E))))))))))))) # label(d4_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9246 (all A all B all C (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B,A) & m1_group_2(C,A) & v3_group_1(A) -> m1_group_2(k8_group_4(A,B,C),A) & v1_group_1(k8_group_4(A,B,C)))) # label(dt_k8_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9247 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v3_struct_0(B) & v3_group_1(B) & l1_group_1(B) & v4_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_group_2(D,B) -> (all E (m1_subset_1(E,u1_struct_0(D)) -> (C = E -> k6_group_1(D,A,E) = k6_group_1(B,A,C)))))))))))) # label(t3_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9248 (all A (l1_group_1(A) & -v3_struct_0(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> k3_group_4(A,B) = k2_finsop_1(u1_struct_0(A),B,u1_group_1(A)))))) # label(d3_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9249 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & v7_group_1(A) & l1_group_1(A) -> k7_group_4(A,B,C) = k7_group_4(A,C,B)))))))) # label(t65_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9250 $T # label(t87_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9251 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_group_2(B,A) & v1_group_1(B) -> r1_group_2(A,k8_group_4(A,B,k5_group_2(A)),B) & r1_group_2(A,k8_group_4(A,k5_group_2(A),B),B))))) # label(t76_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9252 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (all D (-v3_struct_0(D) & v3_group_1(D) & l1_group_1(D) & v4_group_1(D) -> (all E (m1_subset_1(E,u1_struct_0(D)) -> (all F (m1_subset_1(F,u1_struct_0(D)) -> (all G (m1_subset_1(G,u1_struct_0(D)) -> k4_group_4(D,k3_finseq_4(k4_numbers,k2_group_4(A),k2_group_4(B),k2_group_4(C)),k8_rlvect_1(D,E,F,G)) = k8_rlvect_1(D,k6_group_1(D,A,E),k6_group_1(D,B,F),k6_group_1(D,C,G)))))))))))))))) # label(t30_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9253 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(k1_group_3(A),k1_group_3(A)),k1_group_3(A)) & m2_relset_1(B,k2_zfmisc_1(k1_group_3(A),k1_group_3(A)),k1_group_3(A)) -> ((all C (m1_subset_1(C,k1_group_3(A)) -> (all D (m1_subset_1(D,k1_group_3(A)) -> (all E (m1_group_2(E,A) -> (all F (m1_group_2(F,A) -> (C = E & D = F -> k2_binop_1(k1_group_3(A),k1_group_3(A),k1_group_3(A),B,C,D) = k8_group_4(A,E,F)))))))))) <-> B = k9_group_4(A)))))) # label(d11_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9254 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> (l1_group_1(A) & v7_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all D (v1_funct_2(D,k4_finseq_1(B),k4_finseq_1(B)) & m2_relset_1(D,k4_finseq_1(B),k4_finseq_1(B)) & v3_funct_2(D,k4_finseq_1(B),k4_finseq_1(B)) & v1_funct_1(D) -> (k5_relat_1(D,B) = C -> k3_group_4(A,B) = k3_group_4(A,C))))))))))) # label(t18_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9255 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> k8_group_4(A,B,C) = k5_group_4(A,k4_subset_1(u1_struct_0(A),k7_group_2(A,B),k7_group_2(A,C))))))))) # label(d10_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9256 $T # label(t7_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9257 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v3_struct_0(C) & v4_group_1(C) & l1_group_1(C) & v3_group_1(C) -> ((exists D (m1_group_2(D,C) & v2_group_4(D,C) & v1_group_1(D))) -> ((all D (m1_group_2(D,C) & v1_group_1(D) -> (v2_group_4(D,C) -> r1_rlvect_1(D,B)))) <-> r1_rlvect_1(k6_group_4(C),B))))))))) # label(t52_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9258 $T # label(t34_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9259 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> (all D (v1_group_1(D) & m1_group_2(D,A) -> (m1_group_2(C,D) & m1_group_2(B,D) -> m1_group_2(k8_group_4(A,B,C),D)))))))))) # label(t81_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9260 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> (k3_finseq_1(B) = k3_finseq_1(C) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(B)) -> k3_group_1(A,k4_finseq_4(k5_numbers,u1_struct_0(A),B,D)) = k1_funct_1(C,k2_xcmplx_0(k6_xcmplx_0(k3_finseq_1(B),D),np__1))))) -> k3_group_4(A,B) = k3_group_1(A,k3_group_4(A,C))))))))) # label(t17_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9261 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> k3_group_4(A,B) = k3_group_4(A,k1_group_4(u1_struct_0(A),B,k6_domain_1(u1_struct_0(A),k2_group_1(A)))))))) # label(t16_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9262 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> r1_group_2(A,k8_group_4(A,B,C),k8_group_4(A,C,B)))))))) # label(t74_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9263 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_group_2(C,A) -> (all D (m1_group_2(D,A) -> k10_group_2(A,D,k12_group_2(A,C,B)) = k3_group_2(A,B,k7_group_4(A,C,D)))))))))) # label(t60_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9264 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_group_2(B,A) -> (all C (v1_group_1(C) & m1_group_2(C,A) -> r1_group_2(A,k9_group_2(A,C,k8_group_4(A,C,B)),C))))))) # label(t85_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9265 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> (r1_tarski(k2_relat_1(C),k7_group_2(A,B)) -> r1_rlvect_1(B,k3_group_4(A,C))))))))) # label(t21_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9266 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (v1_group_1(B) & m1_group_2(B,A) -> (v2_group_4(B,A) -> m1_group_2(k6_group_4(A),B)))))) # label(t54_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9267 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> m1_group_2(B,k8_group_4(A,B,C)) & m1_group_2(C,k8_group_4(A,B,C)))))))) # label(t78_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9268 $T # label(t35_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9269 (exists A ((all B (m1_group_2(B,f1_s2_group_4) & v1_group_1(B) -> (r2_hidden(B,A) <-> p1_s2_group_4(B)))) & r1_tarski(A,k1_group_3(f1_s2_group_4)))) # label(s2_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9270 (all A all B all C (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B,A) & m1_group_2(C,A) -> m1_subset_1(k7_group_4(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k7_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9271 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> (all D (m1_group_2(D,A) -> k10_group_2(A,D,k7_group_4(A,B,C)) = k11_group_2(A,B,k7_group_4(A,C,D)))))))))) # label(t59_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9272 $T # label(t90_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9273 (all A (v1_int_1(A) -> k2_group_4(A) = A)) # label(d2_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9274 $T # label(t50_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9275 (all A all B (-v3_struct_0(A) & l1_group_1(A) & m1_finseq_1(B,u1_struct_0(A)) -> m1_subset_1(k3_group_4(A,B),u1_struct_0(A)))) # label(dt_k3_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9276 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) & v1_group_1(C) -> r1_group_2(A,k8_group_4(A,k9_group_2(A,B,C),C),C))))))) # label(t84_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9277 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) & v1_group_1(C) -> (m1_group_2(B,C) <-> r1_group_2(A,k8_group_4(A,B,C),C)))))))) # label(t79_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9278 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> k1_group_3(A) = u1_struct_0(k11_group_4(A)))) # label(t92_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9279 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (v1_group_1(B) & m1_group_2(B,A) & v1_group_3(B,A) -> (all C (m1_group_2(C,A) & v1_group_3(C,A) & v1_group_1(C) -> k7_group_4(A,B,C) = u1_struct_0(k8_group_4(A,B,C)))))))) # label(t71_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9280 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> v1_funct_1(k9_group_4(A)) & v1_funct_2(k9_group_4(A),k2_zfmisc_1(k1_group_3(A),k1_group_3(A)),k1_group_3(A)) & m2_relset_1(k9_group_4(A),k2_zfmisc_1(k1_group_3(A),k1_group_3(A)),k1_group_3(A)))) # label(dt_k9_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9281 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> r1_group_2(A,k8_group_4(A,B,C),k5_group_4(A,k7_group_4(A,B,C))))))))) # label(t68_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9282 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> (all D (m2_finseq_1(D,u1_struct_0(A)) -> (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & k3_finseq_1(C) = k3_finseq_1(B) & (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (r2_hidden(E,k4_finseq_1(B)) -> k1_funct_1(B,E) = k1_group_1(A,k4_finseq_4(k5_numbers,u1_struct_0(A),C,E),k4_finseq_4(k5_numbers,u1_struct_0(A),D,E))))) & k3_finseq_1(B) = k3_finseq_1(D) & v7_group_1(A) -> k1_group_1(A,k3_group_4(A,C),k3_group_4(A,D)) = k3_group_4(A,B)))))))))) # label(t20_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9283 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> (all D (m2_finseq_1(D,k4_numbers) -> (all E (m2_finseq_1(E,k4_numbers) -> (k3_finseq_1(D) = k3_finseq_1(B) & k3_finseq_1(C) = k3_finseq_1(E) -> k4_group_4(A,k8_finseq_1(k4_numbers,D,E),k8_finseq_1(u1_struct_0(A),B,C)) = k8_finseq_1(u1_struct_0(A),k4_group_4(A,D,B),k4_group_4(A,E,C))))))))))))) # label(t25_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9284 (all A (v1_int_1(A) -> (all B (-v3_struct_0(B) & v3_group_1(B) & l1_group_1(B) & v4_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_group_2(D,B) -> (all E (m1_subset_1(E,u1_struct_0(D)) -> (E = C -> k6_group_1(B,A,C) = k6_group_1(D,A,E)))))))))))) # label(t4_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9285 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v3_struct_0(B) & l1_group_1(B) & v4_group_1(B) & v3_group_1(B) -> (all C (m2_finseq_1(C,k4_numbers) -> (k3_finseq_1(C) = A -> k1_finsop_1(u1_struct_0(B),A,k2_group_1(B)) = k4_group_4(B,C,k1_finsop_1(u1_struct_0(B),A,k2_group_1(B)))))))))) # label(t33_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9286 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> B = k4_group_4(A,k1_finsop_1(k4_numbers,k3_finseq_1(B),k2_group_4(np__1)),B))))) # label(t31_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9287 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> m1_group_2(k9_group_2(A,B,C),k8_group_4(A,B,C)))))))) # label(t83_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9288 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_group_2(C,A) -> (all D (m1_group_2(D,A) -> (r1_rlvect_1(k8_group_4(A,C,D),B) <-> (exists E ((exists F (m2_finseq_1(F,k4_numbers) & k3_group_4(A,k4_group_4(A,F,E)) = B & r1_tarski(k2_relat_1(E),k4_subset_1(u1_struct_0(A),k7_group_2(A,C),k7_group_2(A,D))) & k3_finseq_1(E) = k3_finseq_1(F))) & m2_finseq_1(E,u1_struct_0(A))))))))))))) # label(t67_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9289 $T # label(t95_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9290 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_group_2(B,A) -> (all C (v1_group_1(C) & m1_group_2(C,A) -> (all D (m1_group_2(D,A) & v1_group_1(D) -> (m1_group_2(B,D) -> m1_group_2(k8_group_4(A,B,C),k8_group_4(A,D,C))))))))))) # label(t82_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9291 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_group_2(C,A) -> (all D (m1_group_2(D,A) -> k4_group_2(A,B,k7_group_4(A,C,D)) = k11_group_2(A,C,k13_group_2(A,D,B)))))))))) # label(t61_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9292 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & v1_group_1(A) & -v3_struct_0(A) -> u1_struct_0(k6_group_4(A)) = a_1_1_group_4(A))) # label(t55_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9293 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (v1_group_1(B) & m1_group_2(B,A) & v1_group_3(B,A) -> (all C (v1_group_1(C) & v1_group_3(C,A) & m1_group_2(C,A) -> v1_group_3(k8_group_4(A,B,C),A) & m1_group_2(k8_group_4(A,B,C),A))))))) # label(t72_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9294 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v7_group_1(A) & v4_group_1(A) -> k7_group_4(A,B,C) = u1_struct_0(k8_group_4(A,B,C))))))))) # label(t70_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9295 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> k2_group_2(A,k7_group_2(A,B),k7_group_2(A,C)) = k7_group_4(A,B,C))))))) # label(d9_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9296 $T # label(t22_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9297 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> l3_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & v3_lattices(k11_group_4(A)) & -v3_struct_0(k11_group_4(A)))) # label(dt_k11_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9298 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,C) -> r1_rlvect_1(k5_group_4(A,C),B)))))))) # label(t38_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9299 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> k10_group_4(A) = u1_lattices(k11_group_4(A)))) # label(t94_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9300 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> r1_group_2(A,k8_group_4(A,B,k6_group_2(A)),k6_group_2(A)) & r1_group_2(A,k8_group_4(A,k6_group_2(A),B),k6_group_2(A)))))) # label(t77_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9301 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (v1_group_1(B) & m1_group_2(B,A) -> (all C (v1_group_1(C) & m1_group_2(C,A) -> (r1_group_2(A,k8_group_4(A,B,C),C) <-> r1_group_2(A,k9_group_2(A,B,C),B)))))))) # label(t86_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9302 (all A (r2_hidden(A,a_0_0_group_4) <-> (exists B ((exists C (v1_group_1(C) & m1_group_2(C,f1_s1_group_4) & p1_s1_group_4(C) & u1_struct_0(C) = B)) & A = B & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s1_group_4))))))) # label(fraenkel_a_0_0_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9303 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> k4_group_4(A,k6_finseq_1(k4_numbers),k6_finseq_1(u1_struct_0(A))) = k1_xboole_0)) # label(t27_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9304 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> (all D (m2_finseq_1(D,k4_numbers) -> (r1_tarski(k2_relat_1(C),k7_group_2(A,B)) -> r1_rlvect_1(B,k3_group_4(A,k4_group_4(A,D,C)))))))))))) # label(t26_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9305 (all A (v1_int_1(A) -> m1_subset_1(k2_group_4(A),k4_numbers))) # label(dt_k2_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9306 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> -v3_struct_0(k11_group_4(A)) & v5_lattices(k11_group_4(A)) & v7_lattices(k11_group_4(A)) & v9_lattices(k11_group_4(A)) & v10_lattices(k11_group_4(A)) & v15_lattices(k11_group_4(A)) & v14_lattices(k11_group_4(A)) & v13_lattices(k11_group_4(A)) & v8_lattices(k11_group_4(A)) & v6_lattices(k11_group_4(A)) & v4_lattices(k11_group_4(A)) & v3_lattices(k11_group_4(A)))) # label(fc1_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9307 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,C) -> m1_group_2(k5_group_4(A,B),k5_group_4(A,C))))))))) # label(t41_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9308 $T # label(t45_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9309 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> k11_group_2(A,B,k7_group_2(A,C)) = k7_group_4(A,B,C) & k7_group_4(A,B,C) = k10_group_2(A,C,k7_group_2(A,B)) & k2_group_2(A,k7_group_2(A,B),k7_group_2(A,C)) = k7_group_4(A,B,C))))))) # label(t57_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9310 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (r1_rlvect_1(k6_group_4(A),B) <-> -v1_group_4(B,A)))))) # label(t56_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9311 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> (all D (m1_group_2(D,A) -> (m1_group_2(B,C) -> m1_group_2(B,k8_group_4(A,C,D))))))))))) # label(t80_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9312 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> r1_group_2(A,k5_group_4(A,k1_subset_1(u1_struct_0(A))),k5_group_2(A)))) # label(t39_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9313 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_group_2(C,A) -> (all D (m1_group_2(D,A) -> k10_group_2(A,D,k10_group_2(A,C,B)) = k2_group_2(A,B,k7_group_4(A,C,D)))))))))) # label(t62_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9314 $T # label(t96_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9315 (all A (v4_group_1(A) & l1_group_1(A) & v2_group_1(A) & -v3_struct_0(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> k3_group_4(A,k8_finseq_1(u1_struct_0(A),B,C)) = k1_group_1(A,k3_group_4(A,B),k3_group_4(A,C)))))))) # label(t8_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9316 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> k6_group_2(A) = k6_lattices(k11_group_4(A)))) # label(t99_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9317 (all A (l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k3_group_4(A,k12_finseq_1(u1_struct_0(A),B)))))) # label(t12_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9318 $T # label(d1_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9319 $T # label(t66_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9320 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> -v1_group_4(k2_group_1(A),A))) # label(t46_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9321 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_group_2(A,k5_group_4(A,B),k5_group_4(A,k6_subset_1(u1_struct_0(A),B,k6_domain_1(u1_struct_0(A),k2_group_1(A))))))))) # label(t44_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9322 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((exists C (g1_group_1(u1_struct_0(A),u1_group_1(A)) != k5_group_4(A,k6_subset_1(u1_struct_0(A),C,k6_domain_1(u1_struct_0(A),B))) & k5_group_4(A,C) = g1_group_1(u1_struct_0(A),u1_group_1(A)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))))) <-> v1_group_4(B,A)))))) # label(d6_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9323 (all A all B (v4_group_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> v1_group_1(k5_group_4(A,B)) & m1_group_2(k5_group_4(A,B),A))) # label(dt_k5_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9324 $T # label(t88_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9325 $T # label(t24_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9326 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (-v3_struct_0(C) & v4_group_1(C) & l1_group_1(C) & v3_group_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (all E (m1_subset_1(E,u1_struct_0(C)) -> k7_rlvect_1(C,k6_group_1(C,A,D),k6_group_1(C,B,E)) = k4_group_4(C,k2_finseq_4(k4_numbers,k2_group_4(A),k2_group_4(B)),k7_rlvect_1(C,D,E)))))))))))) # label(t29_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9327 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> m1_group_2(k6_group_4(A),A) & v1_group_1(k6_group_4(A)))) # label(dt_k6_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9328 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_group_1(A,B,k1_group_1(A,C,D)) = k3_group_4(A,k8_rlvect_1(A,B,C,D)) & k3_group_4(A,k8_rlvect_1(A,B,C,D)) = k1_group_1(A,k1_group_1(A,B,C),D))))))))) # label(t14_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9329 (all A (v1_int_1(A) -> (all B (-v3_struct_0(B) & l1_group_1(B) & v4_group_1(B) & v3_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k4_group_4(B,k12_finseq_1(k4_numbers,k2_group_4(A)),k12_finseq_1(u1_struct_0(B),C)) = k12_finseq_1(u1_struct_0(B),k6_group_1(B,A,C)))))))) # label(t28_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.55 9330 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> u1_struct_0(k5_group_4(A,B)) = k1_setfam_1(a_2_0_group_4(A,B)))))) # label(t43_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9331 $T # label(t89_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9332 (all A (-v3_struct_0(A) & v1_group_1(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_group_2(B,A) & v1_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (v2_group_4(B,A) -> k5_group_4(A,k4_subset_1(u1_struct_0(A),k7_group_2(A,B),k6_domain_1(u1_struct_0(A),C))) = A | r1_rlvect_1(B,C)))))))) # label(t48_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9333 (all A all B all C (-v1_xboole_0(A) & m1_finseq_1(B,A) -> m2_finseq_1(k1_group_4(A,B,C),A))) # label(dt_k1_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9334 (all A all B all C (-v3_struct_0(B) & v4_group_1(B) & l1_group_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v3_group_1(B) -> (r2_hidden(A,a_2_0_group_4(B,C)) <-> (exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & (exists E (m1_group_2(E,B) & r1_tarski(C,k7_group_2(B,E)) & D = u1_struct_0(E) & v1_group_1(E))) & A = D))))) # label(fraenkel_a_2_0_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9335 (all A (l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,B,C) = k3_group_4(A,k7_rlvect_1(A,B,C)))))))) # label(t13_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9336 $T # label(t1_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9337 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> k11_group_4(A) = g3_lattices(k1_group_3(A),k9_group_4(A),k10_group_4(A)))) # label(d13_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9338 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (v1_group_1(C) & m1_group_2(C,A) -> ((all D (m1_group_2(D,A) & v1_group_1(D) -> (r1_tarski(B,u1_struct_0(D)) -> m1_group_2(C,D)))) & r1_tarski(B,u1_struct_0(C)) <-> C = k5_group_4(A,B)))))))) # label(d5_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9339 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> (all D (m1_group_2(D,A) -> r1_group_2(A,k8_group_4(A,k8_group_4(A,B,C),D),k8_group_4(A,B,k8_group_4(A,C,D))))))))))) # label(t75_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9340 (all A all B (v1_group_1(B) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & -v3_struct_0(B) -> (r2_hidden(A,a_1_1_group_4(B)) <-> (exists C (C = A & -v1_group_4(C,B) & m1_subset_1(C,u1_struct_0(B))))))) # label(fraenkel_a_1_1_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9341 (all A all B all C (v3_group_1(A) & m1_finseq_1(B,k4_numbers) & m1_finseq_1(C,u1_struct_0(A)) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> m2_finseq_1(k4_group_4(A,B,C),u1_struct_0(A)))) # label(dt_k4_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9342 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_group_2(C,A) -> (all D (m1_group_2(D,A) -> k11_group_2(A,C,k11_group_2(A,D,B)) = k2_group_2(A,k7_group_4(A,C,D),B))))))))) # label(t63_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9343 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_group_2(B,A) -> k7_group_4(A,B,B) = k7_group_2(A,B))))) # label(t58_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9344 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) & v1_group_1(B) -> r1_group_2(A,k5_group_4(A,k7_group_2(A,B)),B))))) # label(t40_group_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9345 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (r1_connsp_2(A,B) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) -> -((all D (m1_subset_1(D,u1_struct_0(k3_pre_topc(A,C))) -> -(B = D & r2_hidden(B,k1_tops_1(k3_pre_topc(A,C),k1_connsp_1(k3_pre_topc(A,C),D)))))) & r2_hidden(B,C) & v3_pre_topc(C,A))))))))) # label(t20_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9346 (all A all B (v2_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> (all C (m2_connsp_2(C,A,B) -> m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))))))) # label(dt_m2_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9347 $T # label(t17_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9348 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (m1_connsp_2(D,A,B) & m1_connsp_2(C,A,B) -> m1_connsp_2(k4_subset_1(u1_struct_0(A),C,D),A,B)))))))))) # label(t3_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9349 $T # label(t16_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9350 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r2_hidden(B,k1_connsp_2(A,B)))))) # label(t30_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9351 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((exists D (v3_pre_topc(D,A) & r1_tarski(D,C) & r2_hidden(B,D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))))) <-> m1_connsp_2(C,A,B)))))))) # label(t8_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9352 (all A all B (-v3_struct_0(A) & v2_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) & l1_pre_topc(A) -> m1_subset_1(k1_connsp_2(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k1_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9353 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(k1_xboole_0 = C & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(D,C) <-> v4_pre_topc(D,A) & r2_hidden(B,D) & v3_pre_topc(D,A))))))))))) # label(t28_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9354 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (C = k1_connsp_2(A,B) <-> (exists D (k6_setfam_1(u1_struct_0(A),D) = C & (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(E,D) <-> r2_hidden(B,E) & v4_pre_topc(E,A) & v3_pre_topc(E,A)))) & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))))))))))) # label(d7_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9355 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_connsp_2(B,A) <-> v1_connsp_2(k3_pre_topc(A,B))))))) # label(d6_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9356 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (v1_connsp_2(A) & v5_compts_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(v4_pre_topc(B,A) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(v2_connsp_1(E,A) & v3_pre_topc(D,A) & r1_tarski(C,E) & r1_xboole_0(D,E) & r1_tarski(B,D) & v3_pre_topc(E,A) & v2_connsp_1(D,A)))))) & v2_connsp_1(C,A) & v2_connsp_1(B,A) & r1_xboole_0(B,C) & v4_pre_topc(C,A) & k1_xboole_0 != C & k1_xboole_0 != B)))))))) # label(t27_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9357 $T # label(t15_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9358 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,B) & v3_pre_topc(B,A) -> m1_connsp_2(B,A,C)))))))) # label(t5_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9359 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (m1_connsp_2(k5_subset_1(u1_struct_0(A),C,D),A,B) <-> m1_connsp_2(C,A,B) & m1_connsp_2(D,A,B)))))))))) # label(t4_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9360 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(m1_connsp_2(C,A,B) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(D) -> -(v3_pre_topc(D,A) & r1_tarski(D,C) & m1_connsp_2(D,A,B))))))))))) # label(t7_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9361 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (v1_connsp_2(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,B)))) & -v1_xboole_0(C) -> -(v2_connsp_1(C,k3_pre_topc(A,B)) & v3_pre_topc(C,k3_pre_topc(A,B)) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(D,A) & k5_subset_1(u1_struct_0(A),B,D) = C & v2_connsp_1(D,A)))))))))))) # label(t25_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9362 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (r1_connsp_2(A,B) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,D) & r4_connsp_1(A,C,D) & m1_connsp_2(C,A,B) -> m1_connsp_2(D,A,B))))))))))) # label(t19_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9363 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(m1_connsp_2(C,A,B) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(m1_connsp_2(D,A,B) & v2_connsp_1(D,A) & r1_tarski(D,C))))))) <-> r1_connsp_2(A,B)))))) # label(d3_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9364 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (m1_connsp_2(C,A,B) <-> m2_connsp_2(C,A,k1_struct_0(A,B))))))))) # label(t10_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9365 (all A all B (v2_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> (exists C m2_connsp_2(C,A,B)))) # label(existence_m2_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9366 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_tarski(k1_connsp_1(A,B),k1_connsp_2(A,B)))))) # label(t33_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9367 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (m1_connsp_2(B,A,C) -> r2_hidden(C,B)))))))) # label(t6_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9368 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (v1_connsp_2(A) <-> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) & r4_connsp_1(A,B,C) -> v3_pre_topc(C,A))))))))) # label(t24_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9369 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,k1_tops_1(A,C)) <-> m1_connsp_2(C,A,B)))))))) # label(d1_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9370 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(k3_pre_topc(A,B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,B)))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (all F (m1_subset_1(F,u1_struct_0(A)) -> (m1_connsp_2(D,k3_pre_topc(A,B),C) & C = F & E = D & v3_pre_topc(B,A) -> m1_connsp_2(E,A,F)))))))))))))) # label(t11_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9371 (all A all B (-v3_struct_0(A) & v2_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) & l1_pre_topc(A) -> (all C (m1_connsp_2(C,A,B) -> m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))))))) # label(dt_m1_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9372 $T # label(t29_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9373 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_connsp_2(A,B,C) <-> (all D (-v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(B = D & (all E (m1_subset_1(E,u1_struct_0(k3_pre_topc(A,D))) -> -(E = C & r1_connsp_2(k3_pre_topc(A,D),E)))))))))))))) # label(d5_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9374 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (all C (m1_subset_1(C,u1_struct_0(k3_pre_topc(A,B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,B)))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (all F (m1_subset_1(F,u1_struct_0(A)) -> (E = D & C = F & m1_connsp_2(E,A,F) -> m1_connsp_2(D,k3_pre_topc(A,B),C)))))))))))))) # label(t12_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9375 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,C) & r3_connsp_1(A,B) -> r4_connsp_1(A,C,B)))))))) # label(t13_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9376 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (m2_connsp_2(C,A,B) <-> r1_tarski(B,k1_tops_1(A,C))))))))) # label(d2_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9377 (all A all B (-v3_struct_0(A) & v2_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) & l1_pre_topc(A) -> (exists C m1_connsp_2(C,A,B)))) # label(existence_m1_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9378 $T # label(t2_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9379 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (v5_compts_1(A) <-> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(B != k1_xboole_0 & r1_tarski(B,C) & v4_pre_topc(B,A) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(D,A) & r1_tarski(B,D) & r1_tarski(k6_pre_topc(A,D),C)))) & v3_pre_topc(C,A) & C != k2_pre_topc(A))))))))) # label(t26_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9380 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> v4_pre_topc(k1_connsp_2(A,B),A))))) # label(t32_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9381 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (v1_connsp_2(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_connsp_2(A,B)))))) # label(d4_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9382 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,C) & r1_tarski(C,k1_connsp_2(A,B)) & v4_pre_topc(C,A) & v3_pre_topc(C,A) -> C = k1_connsp_2(A,B)))))))) # label(t31_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9383 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (C = D -> r1_tarski(k1_connsp_1(B,D),k1_connsp_1(A,C))))))))))) # label(t14_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9384 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (v1_connsp_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (v3_pre_topc(B,A) -> v2_connsp_2(B,A))))))) # label(t23_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9385 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> -((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(m1_connsp_2(D,A,C) & r1_tarski(D,B)))) & r2_hidden(C,B))))))))) # label(t9_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9386 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (r1_connsp_2(A,B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) -> (r2_hidden(B,C) & v3_pre_topc(C,A) -> r2_connsp_2(A,C,B))))))))) # label(t22_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9387 $T # label(t18_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9388 $T # label(t1_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9389 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (v1_connsp_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r3_connsp_1(A,B) -> v3_pre_topc(B,A))))))) # label(t21_connsp_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9390 $T # label(t33_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9391 $T # label(t1_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9392 $T # label(t27_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9393 $T # label(t15_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9394 $T # label(t22_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9395 $T # label(t32_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9396 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> k6_rlvect_1(B,E,k6_vectsp_2(A,B,C,D)) = k2_rlvect_1(B,E,k6_vectsp_2(A,B,k5_rlvect_1(A,C),D)) & k5_rlvect_1(B,k6_vectsp_2(A,B,C,D)) = k6_vectsp_2(A,B,k5_rlvect_1(A,C),D))))))))))) # label(t38_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9397 $T # label(t34_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9398 $T # label(t28_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9399 $T # label(t6_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9400 $T # label(t8_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9401 (all A (v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k5_rlvect_1(B,k6_vectsp_2(A,B,C,D)) = k6_vectsp_2(A,B,C,k5_rlvect_1(B,D)))))))))) # label(t39_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9402 $T # label(t41_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9403 $T # label(t36_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9404 $T # label(t11_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9405 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v9_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v3_struct_0(C) & v12_vectsp_1(C,A) & l4_vectsp_1(C,A) & v6_rlvect_1(C) & v5_rlvect_1(C) & v4_rlvect_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (B != k1_rlvect_1(A) -> k6_vectsp_1(A,C,k1_vectsp_2(A,B),k6_vectsp_1(A,C,B,D)) = D))))))))) # label(t26_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9406 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v3_struct_0(C) & l4_vectsp_1(C,A) & v12_vectsp_1(C,A) & v6_rlvect_1(C) & v5_rlvect_1(C) & v4_rlvect_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (k1_rlvect_1(C) = D | B = k1_rlvect_1(A) <-> k1_rlvect_1(C) = k6_vectsp_1(A,C,B,D)))))))))) # label(t25_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9407 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k1_rlvect_1(B) = k6_vectsp_2(A,B,k1_rlvect_1(A),D) & k5_rlvect_1(B,D) = k6_vectsp_2(A,B,k5_rlvect_1(A,k2_group_1(A)),D) & k1_rlvect_1(B) = k6_vectsp_2(A,B,C,k1_rlvect_1(B)))))))))) # label(t37_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9408 $T # label(t31_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9409 $T # label(t3_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9410 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v4_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_group_1(A,B,k5_rlvect_1(A,k2_group_1(A))) = k5_rlvect_1(A,B))))) # label(t13_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9411 $T # label(t23_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9412 $T # label(t4_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9413 $T # label(t7_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9414 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> k6_rlvect_1(B,k6_vectsp_2(A,B,C,D),k6_vectsp_2(A,B,C,E)) = k6_vectsp_2(A,B,C,k6_rlvect_1(B,D,E)))))))))))) # label(t40_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9415 $T # label(t24_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9416 (all A (-v3_struct_0(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v5_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k5_rlvect_1(A,B) = k1_group_1(A,k5_rlvect_1(A,k2_group_1(A)),B))))) # label(t14_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9417 $T # label(t18_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9418 $T # label(t9_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9419 $T # label(t20_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9420 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v9_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v3_struct_0(C) & v5_rlvect_1(C) & v5_vectsp_2(C,A) & l1_vectsp_2(C,A) & v6_rlvect_1(C) & v4_rlvect_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (k1_rlvect_1(C) = k6_vectsp_2(A,C,B,D) <-> D = k1_rlvect_1(C) | B = k1_rlvect_1(A)))))))))) # label(t42_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9421 $T # label(t29_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9422 $T # label(t19_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9423 $T # label(t30_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9424 $T # label(t17_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9425 $T # label(t35_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9426 $T # label(t5_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9427 $T # label(t10_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9428 $T # label(t21_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9429 (all A (v4_group_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v4_rlvect_1(C) & v6_rlvect_1(C) & v5_vectsp_2(C,A) & l1_vectsp_2(C,A) & v5_rlvect_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (k1_rlvect_1(A) != B -> k6_vectsp_2(A,C,k1_vectsp_2(A,B),k6_vectsp_2(A,C,B,D)) = D))))))))) # label(t43_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9430 $T # label(t12_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9431 $T # label(t2_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9432 $T # label(t16_mod_1) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9433 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> k1_rlvect_1(D) = k1_rlvect_1(C))))))))) # label(t20_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9434 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_rmod_2(E,A,B) -> (r1_rlvect_1(E,C) <-> r2_hidden(k4_rlvect_1(B,C,D),k3_rmod_2(A,B,D,E))))))))))))) # label(t72_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9435 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (v4_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (v3_vectsp_2(C,A) & m1_rmod_2(C,A,B) -> (all D (v3_vectsp_2(D,A) & m1_rmod_2(D,A,B) -> ((all E (m1_subset_1(E,u1_struct_0(B)) -> (r1_rlvect_1(C,E) <-> r1_rlvect_1(D,E)))) -> C = D))))))))) # label(t38_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9436 $T # label(t14_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9437 $T # label(t13_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9438 (all A all B all C (-v3_struct_0(A) & v5_vectsp_2(B,A) & m1_rmod_2(C,A,B) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all D (m2_rmod_2(D,A,B,C) -> m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))))))) # label(dt_m2_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9439 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> ((all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (r2_hidden(E,C) & r2_hidden(D,C) -> r2_hidden(k4_rlvect_1(B,D,E),C)))))) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (r2_hidden(E,C) -> r2_hidden(k6_vectsp_2(A,B,D,E),C)))))) <-> v1_rmod_2(C,A,B)))))))) # label(d1_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9440 (all A all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v4_group_1(B) & v6_vectsp_1(B) & v7_vectsp_1(B) & v8_vectsp_1(B) & l3_vectsp_1(B) -> (all C (-v3_struct_0(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v5_vectsp_2(C,B) & l1_vectsp_2(C,B) & v6_rlvect_1(C) & v3_rlvect_1(C) -> (all D (m1_rmod_2(D,B,C) -> (all E (m1_rmod_2(E,B,C) -> (r1_rlvect_1(D,A) & m1_rmod_2(D,B,E) -> r1_rlvect_1(E,A)))))))))) # label(t16_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9441 (all A (v6_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_rmod_2(D,A,B) -> r2_hidden(C,k3_rmod_2(A,B,C,D)))))))))) # label(t59_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9442 (all A all B all C all D all E (-v3_struct_0(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v4_group_1(B) & v6_vectsp_1(B) & l3_vectsp_1(B) & v3_rlvect_1(C) & v6_rlvect_1(C) & v5_vectsp_2(C,B) & l1_vectsp_2(C,B) & m1_subset_1(D,u1_struct_0(C)) & m1_rmod_2(E,B,C) & v5_rlvect_1(C) & v4_rlvect_1(C) & -v3_struct_0(C) & v8_vectsp_1(B) & v7_vectsp_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (r2_hidden(A,a_4_1_rmod_2(B,C,D,E)) <-> (exists F (m1_subset_1(F,u1_struct_0(C)) & A = k4_rlvect_1(C,D,F) & r1_rlvect_1(E,F)))))) # label(fraenkel_a_4_1_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9443 (all A (v3_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_rmod_2(D,A,B) -> (r2_hidden(k1_rlvect_1(B),k3_rmod_2(A,B,C,D)) <-> r1_rlvect_1(D,C)))))))))) # label(t58_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9444 (all A (v4_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_rmod_2(E,A,B) -> (r1_rlvect_1(E,D) & r1_rlvect_1(E,C) -> r1_rlvect_1(E,k4_rlvect_1(B,C,D))))))))))))) # label(t28_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9445 (all A (v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_rmod_2(E,A,B) -> (k3_rmod_2(A,B,k4_rlvect_1(B,D,C),E) = k3_rmod_2(A,B,D,E) <-> r1_rlvect_1(E,C)))))))))))) # label(t66_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9446 $T # label(t44_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9447 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_rmod_2(E,A,B) -> (r1_rlvect_1(E,k6_rlvect_1(B,C,D)) <-> (exists F (m1_subset_1(F,u1_struct_0(B)) & r2_hidden(C,k3_rmod_2(A,B,F,E)) & r2_hidden(D,k3_rmod_2(A,B,F,E))))))))))))))) # label(t76_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9448 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (v3_vectsp_2(C,A) & m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) & v3_vectsp_2(D,A) -> (all E (m2_rmod_2(E,A,B,C) -> (all F (m2_rmod_2(F,A,B,D) -> (E = F -> D = C))))))))))))) # label(t83_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9449 $T # label(t45_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9450 $T # label(t12_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9451 (all A (v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v5_vectsp_2(C,A) & l1_vectsp_2(C,A) & v3_rlvect_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (all E (m1_rmod_2(E,A,C) -> (r1_rlvect_1(E,D) -> k3_rmod_2(A,C,k6_vectsp_2(A,C,B,D),E) = u1_struct_0(E)))))))))))) # label(t65_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9452 (all A (-v3_struct_0(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (v1_rmod_2(C,A,B) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (r2_hidden(D,C) -> r2_hidden(k5_rlvect_1(B,D),C))))))))))) # label(t5_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9453 (all A (v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> m1_subset_1(D,u1_struct_0(B)))))))))) # label(t18_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9454 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) & v3_vectsp_2(C,A) -> (k1_rmod_2(A,B) = C <-> u1_struct_0(C) = k6_domain_1(u1_struct_0(B),k1_rlvect_1(B))))))))) # label(d3_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9455 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) -> (all B (v3_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (m1_rmod_2(F,A,B) -> (r2_hidden(C,k3_rmod_2(A,B,E,F)) & r2_hidden(C,k3_rmod_2(A,B,D,F)) -> k3_rmod_2(A,B,D,F) = k3_rmod_2(A,B,E,F)))))))))))))) # label(t69_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.56 9456 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) & v3_vectsp_2(C,A) -> (all D (v3_vectsp_2(D,A) & m1_rmod_2(D,A,B) -> (u1_struct_0(C) = u1_struct_0(D) -> D = C))))))))) # label(t37_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9457 $T # label(t43_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9458 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v3_rlvect_1(A) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v3_rlvect_1(B) & -v3_struct_0(B) -> v1_rmod_2(k6_domain_1(u1_struct_0(B),k1_rlvect_1(B)),A,B))))) # label(t7_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9459 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> u1_struct_0(C) = k3_rmod_2(A,B,k1_rlvect_1(B),C))))))) # label(t60_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9460 $T # label(t3_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9461 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v4_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> m2_rmod_2(u1_struct_0(B),A,B,k2_rmod_2(A,B)))))) # label(t87_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9462 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> m1_rmod_2(k1_rmod_2(A,B),A,C))))))) # label(t50_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9463 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (m2_rmod_2(C,A,B,k2_rmod_2(A,B)) -> u1_struct_0(B) = C))))))) # label(t88_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9464 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_rmod_2(E,A,B) -> (all F (m1_subset_1(F,u1_struct_0(E)) -> (all G (m1_subset_1(G,u1_struct_0(E)) -> (F = C & D = G -> k6_rlvect_1(E,F,G) = k6_rlvect_1(B,C,D)))))))))))))))) # label(t24_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9465 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v3_rlvect_1(A) -> (all B (v3_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> m1_rmod_2(k1_rmod_2(A,C),A,D))))))))) # label(t51_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9466 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> u1_struct_0(B) = k3_rmod_2(A,B,C,k2_rmod_2(A,B)))))))) # label(t62_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9467 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (v3_vectsp_2(C,A) & m1_rmod_2(C,A,B) -> ((all D (m1_subset_1(D,u1_struct_0(B)) -> r1_rlvect_1(C,D))) -> B = C))))))) # label(t40_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9468 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_rmod_2(E,A,B) -> (r2_hidden(k6_rlvect_1(B,C,D),k3_rmod_2(A,B,C,E)) <-> r1_rlvect_1(E,D)))))))))))) # label(t73_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9469 (all A all B (v3_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) & v7_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> m1_rmod_2(k1_rmod_2(A,B),A,B) & v3_vectsp_2(k1_rmod_2(A,B),A))) # label(dt_k1_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9470 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> -((all D (m1_subset_1(D,u1_struct_0(B)) -> C != k6_domain_1(u1_struct_0(B),D))) & m2_rmod_2(C,A,B,k1_rmod_2(A,B))))))))) # label(t85_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9471 (all A (-v3_struct_0(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) -> (v1_rmod_2(C,A,B) & a_4_0_rmod_2(A,B,C,D) = E & v1_rmod_2(D,A,B) -> v1_rmod_2(E,A,B)))))))))))) # label(t9_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9472 (all A all B all C all D (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & -v3_struct_0(B) & m1_rmod_2(D,A,B) & m1_subset_1(C,u1_struct_0(B)) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) -> m1_subset_1(k3_rmod_2(A,B,C,D),k1_zfmisc_1(u1_struct_0(B))))) # label(dt_k3_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9473 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) -> (all B (l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_rmod_2(D,A,B) -> (r2_hidden(k1_rlvect_1(B),k3_rmod_2(A,B,C,D)) <-> k3_rmod_2(A,B,C,D) = u1_struct_0(D)))))))))) # label(t63_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9474 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (v1_rmod_2(C,A,B) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (r2_hidden(E,C) & r2_hidden(D,C) -> r2_hidden(k6_rlvect_1(B,D,E),C))))))))))))) # label(t6_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9475 (all A (v3_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> k1_rlvect_1(C) = k1_rlvect_1(B))))))) # label(t19_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9476 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v3_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v5_vectsp_2(C,A) & l1_vectsp_2(C,A) & v4_rlvect_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (all E (m1_rmod_2(E,A,C) -> (r1_rlvect_1(E,D) -> r2_hidden(k6_vectsp_2(A,C,B,D),k3_rmod_2(A,C,D,E))))))))))))) # label(t70_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9477 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_rmod_2(D,A,B) -> (r1_rlvect_1(D,C) -> r1_rlvect_1(D,k5_rlvect_1(B,C))))))))))) # label(t30_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9478 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v5_rlvect_1(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> m2_rmod_2(k6_domain_1(u1_struct_0(B),C),A,B,k1_rmod_2(A,B)))))))) # label(t84_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9479 (all A (v3_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> m2_rmod_2(u1_struct_0(C),A,B,C))))))) # label(t86_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9480 (all A all B (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v3_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) -> v3_vectsp_2(k2_rmod_2(A,B),A) & m1_rmod_2(k2_rmod_2(A,B),A,B))) # label(dt_k2_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9481 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & -v3_struct_0(B) -> m1_rmod_2(B,A,B))))) # label(t32_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9482 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v3_struct_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_vectsp_2(C,A) & l1_vectsp_2(C,A) & v6_rlvect_1(C) & v5_rlvect_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (all E (m1_rmod_2(E,A,C) -> (all F (m1_subset_1(F,u1_struct_0(E)) -> (D = F -> k6_vectsp_2(A,C,B,D) = k6_vectsp_2(A,E,B,F)))))))))))))) # label(t22_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9483 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v1_rmod_2(D,A,B) & v1_rmod_2(C,A,B) -> v1_rmod_2(k5_subset_1(u1_struct_0(B),C,D),A,B)))))))))) # label(t10_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9484 (all A (v6_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> ((all E (m1_subset_1(E,u1_struct_0(B)) -> (r1_rlvect_1(C,E) -> r1_rlvect_1(D,E)))) -> m1_rmod_2(C,A,D)))))))))) # label(t36_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9485 (all A (v6_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) -> g1_vectsp_2(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u1_vectsp_2(A,B)) = k2_rmod_2(A,B))))) # label(d4_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9486 (all A all B all C all D all E (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v4_group_1(B) & v6_vectsp_1(B) & -v3_struct_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v5_vectsp_2(C,B) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) & l1_vectsp_2(C,B) & l3_vectsp_1(B) & v8_vectsp_1(B) & v7_vectsp_1(B) & v6_rlvect_1(B) & v3_rlvect_1(B) -> (r2_hidden(A,a_4_0_rmod_2(B,C,D,E)) <-> (exists F exists G (m1_subset_1(F,u1_struct_0(C)) & m1_subset_1(G,u1_struct_0(C)) & k4_rlvect_1(C,F,G) = A & r2_hidden(F,D) & r2_hidden(G,E)))))) # label(fraenkel_a_4_0_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9487 (all A all B (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & -v3_struct_0(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & l3_vectsp_1(A) & v6_vectsp_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all C (m1_rmod_2(C,A,B) -> v3_rlvect_1(C) & l1_vectsp_2(C,A) & v5_vectsp_2(C,A) & v6_rlvect_1(C) & v5_rlvect_1(C) & v4_rlvect_1(C) & -v3_struct_0(C))))) # label(dt_m1_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9488 (all A all B (-v3_struct_0(B) & v3_rlvect_1(B) & v6_rlvect_1(B) & v4_group_1(B) & v6_vectsp_1(B) & v7_vectsp_1(B) & v8_vectsp_1(B) & l3_vectsp_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (v6_rlvect_1(C) & l1_vectsp_2(C,B) & v5_vectsp_2(C,B) & v5_rlvect_1(C) & v4_rlvect_1(C) & v3_rlvect_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (all E (m1_rmod_2(E,B,C) -> (r2_hidden(A,k3_rmod_2(B,C,D,E)) <-> (exists F (r1_rlvect_1(E,F) & A = k4_rlvect_1(C,D,F) & m1_subset_1(F,u1_struct_0(C))))))))))))) # label(t57_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9489 $T # label(t74_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9490 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_rmod_2(E,A,B) -> (all F (m2_rmod_2(F,A,B,E) -> -(r2_hidden(C,F) & (all G (m1_subset_1(G,u1_struct_0(B)) -> -(D = k6_rlvect_1(B,C,G) & r1_rlvect_1(E,G)))) & r2_hidden(D,F)))))))))))))) # label(t92_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9491 (all A (v3_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> r1_rlvect_1(B,k1_rlvect_1(C)))))))) # label(t27_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9492 (all A all B (-v3_struct_0(B) & v4_group_1(B) & v6_vectsp_1(B) & l3_vectsp_1(B) & v8_vectsp_1(B) & v7_vectsp_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (-v3_struct_0(C) & v3_rlvect_1(C) & v6_rlvect_1(C) & v5_vectsp_2(C,B) & l1_vectsp_2(C,B) & v5_rlvect_1(C) & v4_rlvect_1(C) -> (r1_rlvect_1(k1_rmod_2(B,C),A) <-> k1_rlvect_1(C) = A))))) # label(t46_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9493 $T # label(t2_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9494 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k6_domain_1(u1_struct_0(B),C) = k3_rmod_2(A,B,C,k1_rmod_2(A,B)))))))) # label(t61_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9495 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m2_rmod_2(D,A,B,C) -> (r2_hidden(k1_rlvect_1(B),D) <-> u1_struct_0(C) = D))))))))) # label(t89_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9496 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_rmod_2(E,A,B) -> (r2_hidden(C,k3_rmod_2(A,B,D,E)) <-> k3_rmod_2(A,B,D,E) = k3_rmod_2(A,B,C,E)))))))))))) # label(t68_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9497 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (v1_rmod_2(C,A,B) -> r2_hidden(k1_rlvect_1(B),C) | C = k1_xboole_0))))))) # label(t4_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9498 (all A (v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> ((exists E (D = k3_rmod_2(A,B,E,C) & m1_subset_1(E,u1_struct_0(B)))) <-> m2_rmod_2(D,A,B,C)))))))))) # label(d6_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9499 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_rmod_2(D,A,B) -> (all E (m1_subset_1(E,u1_struct_0(D)) -> (E = C -> k5_rlvect_1(D,E) = k5_rlvect_1(B,C)))))))))))) # label(t23_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9500 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (v4_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_rmod_2(E,A,B) -> (all F (m1_subset_1(F,u1_struct_0(E)) -> (all G (m1_subset_1(G,u1_struct_0(E)) -> (F = C & G = D -> k4_rlvect_1(E,F,G) = k4_rlvect_1(B,C,D)))))))))))))))) # label(t21_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9501 $T # label(t55_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9502 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (m1_rmod_2(D,A,B) -> (u1_struct_0(D) = C -> v1_rmod_2(C,A,B)))))))))) # label(t41_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9503 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v3_struct_0(C) & v3_rlvect_1(C) & l1_vectsp_2(C,A) & v5_vectsp_2(C,A) & v6_rlvect_1(C) & v5_rlvect_1(C) & v4_rlvect_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (all E (m1_rmod_2(E,A,C) -> (r1_rlvect_1(E,D) -> r1_rlvect_1(E,k6_vectsp_2(A,C,B,D))))))))))))) # label(t29_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9504 (all A (v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_rmod_2(E,A,B) & v3_vectsp_2(E,A) -> (all F (v3_vectsp_2(F,A) & m1_rmod_2(F,A,B) -> (k3_rmod_2(A,B,C,E) = k3_rmod_2(A,B,D,F) -> F = E))))))))))))) # label(t80_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9505 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> r1_rlvect_1(C,k1_rlvect_1(B)))))))) # label(t25_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9506 (all A all B (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (exists C (-v3_struct_0(C) & v4_rlvect_1(C) & v5_vectsp_2(C,A) & v3_vectsp_2(C,A) & v6_rlvect_1(C) & v5_rlvect_1(C) & v3_rlvect_1(C) & m1_rmod_2(C,A,B))))) # label(rc1_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9507 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_rmod_2(D,A,B) -> (all E (m2_rmod_2(E,A,B,D) -> (all F (m2_rmod_2(F,A,B,D) -> (r2_hidden(C,E) & r2_hidden(C,F) -> E = F))))))))))))) # label(t94_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9508 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) -> (all C (v3_rlvect_1(C) & v5_vectsp_2(C,A) & l1_vectsp_2(C,A) & v6_rlvect_1(C) & v5_rlvect_1(C) & v4_rlvect_1(C) & -v3_struct_0(C) -> (all D (v3_rlvect_1(D) & v6_rlvect_1(D) & l1_vectsp_2(D,A) & v5_vectsp_2(D,A) & v5_rlvect_1(D) & v4_rlvect_1(D) & -v3_struct_0(D) -> (m1_rmod_2(B,A,C) & m1_rmod_2(C,A,D) -> m1_rmod_2(B,A,D)))))))))) # label(t34_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9509 (all A (v3_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> -(C != k1_xboole_0 & (all D (v3_vectsp_2(D,A) & m1_rmod_2(D,A,B) -> u1_struct_0(D) != C)) & v1_rmod_2(C,A,B)))))))) # label(t42_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9510 (all A all B (v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & -v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & l3_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (exists C m1_rmod_2(C,A,B)))) # label(existence_m1_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9511 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v3_vectsp_2(B,A) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) -> (all C (-v3_struct_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & v6_rlvect_1(C) & v3_vectsp_2(C,A) & l1_vectsp_2(C,A) & v5_vectsp_2(C,A) & v5_rlvect_1(C) -> (m1_rmod_2(C,A,B) & m1_rmod_2(B,A,C) -> C = B))))))) # label(t33_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9512 $T # label(t54_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9513 $T # label(t11_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9514 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_rmod_2(E,A,B) -> -((all F (m1_subset_1(F,u1_struct_0(B)) -> -(k6_rlvect_1(B,C,F) = D & r1_rlvect_1(E,F)))) & k3_rmod_2(A,B,C,E) = k3_rmod_2(A,B,D,E)))))))))))) # label(t78_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9515 $T # label(t1_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9516 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (v3_vectsp_2(D,A) & m1_rmod_2(D,A,B) -> (all E (v3_vectsp_2(E,A) & m1_rmod_2(E,A,B) -> (k3_rmod_2(A,B,C,D) = k3_rmod_2(A,B,C,E) <-> D = E))))))))))) # label(t79_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9517 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_rmod_2(E,A,B) -> (all F (m2_rmod_2(F,A,B,E) -> -(r2_hidden(D,F) & (all G (m1_subset_1(G,u1_struct_0(B)) -> -(r1_rlvect_1(E,G) & D = k4_rlvect_1(B,C,G)))) & r2_hidden(C,F)))))))))))))) # label(t91_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9518 (all A (v3_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> r1_rlvect_1(D,k1_rlvect_1(C)))))))))) # label(t26_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9519 (all A all B (-v3_struct_0(B) & v3_rlvect_1(B) & v6_vectsp_1(B) & l3_vectsp_1(B) & v8_vectsp_1(B) & v7_vectsp_1(B) & v4_group_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (-v3_struct_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l1_vectsp_2(C,B) & v5_vectsp_2(C,B) & v6_rlvect_1(C) & v5_rlvect_1(C) -> (all D (m1_rmod_2(D,B,C) -> (r1_rlvect_1(D,A) -> r1_rlvect_1(C,A)))))))) # label(t17_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9520 $T # label(t52_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9521 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (r1_tarski(u1_struct_0(C),u1_struct_0(D)) -> m1_rmod_2(C,A,D)))))))))) # label(t35_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9522 (all A (v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_rmod_2(D,A,B) -> (exists E (m2_rmod_2(E,A,B,D) & r2_hidden(C,E))))))))))) # label(t81_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9523 $T # label(t15_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9524 (all A all B all C (v3_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & m1_rmod_2(C,A,B) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & -v3_struct_0(B) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (exists D m2_rmod_2(D,A,B,C)))) # label(existence_m2_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9525 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) & v3_vectsp_2(C,A) -> (u1_struct_0(B) = u1_struct_0(C) -> C = B))))))) # label(t39_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9526 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m2_rmod_2(D,A,B,C) -> (v1_rmod_2(D,A,B) <-> u1_struct_0(C) = D))))))))) # label(t82_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9527 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v3_rlvect_1(A) -> (all B (v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> m1_rmod_2(k1_rmod_2(A,C),A,B))))))) # label(t49_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9528 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_rmod_2(E,A,B) -> -((all F (m1_subset_1(F,u1_struct_0(B)) -> -(D = k4_rlvect_1(B,C,F) & r1_rlvect_1(E,F)))) & k3_rmod_2(A,B,C,E) = k3_rmod_2(A,B,D,E)))))))))))) # label(t77_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9529 (all A (v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> k1_rmod_2(A,D) = k1_rmod_2(A,C))))))))) # label(t48_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9530 (all A (-v3_struct_0(A) & v4_group_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (u1_struct_0(B) = C -> v1_rmod_2(C,A,B)))))))) # label(t8_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9531 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_rmod_2(E,A,B) -> ((exists F (r1_rlvect_1(E,F) & C = k6_rlvect_1(B,D,F) & m1_subset_1(F,u1_struct_0(B)))) <-> r2_hidden(C,k3_rmod_2(A,B,D,E))))))))))))) # label(t75_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9532 (all A (v4_rlvect_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v3_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> m1_rmod_2(B,A,k2_rmod_2(A,B)))))) # label(t53_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9533 $T # label(t56_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9534 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_rmod_2(E,A,B) -> (r1_rlvect_1(E,D) & r1_rlvect_1(E,C) -> r1_rlvect_1(E,k6_rlvect_1(B,C,D))))))))))))) # label(t31_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9535 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_rmod_2(D,A,B) -> k3_rmod_2(A,B,C,D) = a_4_1_rmod_2(A,B,C,D))))))))) # label(d5_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9536 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (v3_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> k1_rmod_2(A,C) = k1_rmod_2(A,B))))))) # label(t47_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9537 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_rlvect_1(A) -> (all B (v4_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_rmod_2(E,A,B) -> (k3_rmod_2(A,B,D,E) = k3_rmod_2(A,B,k6_rlvect_1(B,D,C),E) <-> r1_rlvect_1(E,C)))))))))))) # label(t67_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9538 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_rmod_2(D,A,B) -> (r1_rlvect_1(D,C) -> r2_hidden(k5_rlvect_1(B,C),k3_rmod_2(A,B,C,D))))))))))) # label(t71_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9539 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_rmod_2(D,A,B) -> (r1_rlvect_1(D,C) <-> u1_struct_0(D) = k3_rmod_2(A,B,C,D)))))))))) # label(t64_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9540 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v4_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_rmod_2(E,A,B) -> (r1_rlvect_1(E,k6_rlvect_1(B,C,D)) <-> (exists F (r2_hidden(C,F) & r2_hidden(D,F) & m2_rmod_2(F,A,B,E)))))))))))))) # label(t93_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9541 (all A (-v3_struct_0(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_rmod_2(D,A,B) -> (all E (m2_rmod_2(E,A,B,D) -> (k3_rmod_2(A,B,C,D) = E <-> r2_hidden(C,E)))))))))))) # label(t90_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.57 9542 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C (v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & l1_vectsp_2(C,A) & v5_vectsp_2(C,A) & -v3_struct_0(C) -> (m1_rmod_2(C,A,B) <-> r1_tarski(u1_struct_0(C),u1_struct_0(B)) & u2_struct_0(C) = u2_struct_0(B) & k7_relat_1(u1_vectsp_2(A,B),k2_zfmisc_1(u1_struct_0(C),u1_struct_0(A))) = u1_vectsp_2(A,C) & k7_relat_1(u1_rlvect_1(B),k2_zfmisc_1(u1_struct_0(C),u1_struct_0(C))) = u1_rlvect_1(C)))))))) # label(d2_rmod_2) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9543 (all A (v3_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (m1_rmod_2(E,A,B) -> m1_rmod_2(k1_rmod_3(A,B,C,k2_rmod_3(A,B,D,E)),A,k2_rmod_3(A,B,k1_rmod_3(A,B,D,C),k1_rmod_3(A,B,C,E))))))))))))) # label(t34_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9544 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> -((exists E (u1_struct_0(E) = k2_xboole_0(u1_struct_0(C),u1_struct_0(D)) & m1_rmod_2(E,A,B))) & -m1_rmod_2(D,A,C) & -m1_rmod_2(C,A,D)) & -((m1_rmod_2(D,A,C) | m1_rmod_2(C,A,D)) & (all E (m1_rmod_2(E,A,B) -> k2_xboole_0(u1_struct_0(C),u1_struct_0(D)) != u1_struct_0(E)))))))))))) # label(t41_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9545 $T # label(t45_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9546 (all A all B (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & l3_vectsp_1(A) & v3_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> -v1_xboole_0(k3_rmod_3(A,B)))) # label(fc1_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9547 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) & v3_vectsp_2(C,A) -> (all D (v3_vectsp_2(D,A) & m1_rmod_2(D,A,B) -> (k1_rmod_3(A,B,C,D) = D <-> C = k2_rmod_3(A,B,C,D)))))))))) # label(t37_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9548 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) -> (all B (-v3_struct_0(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (m1_rmod_2(E,A,B) -> (m1_rmod_2(C,A,D) -> k2_rmod_3(A,B,D,k1_rmod_3(A,B,C,E)) = k1_rmod_3(A,B,k2_rmod_3(A,B,C,D),k2_rmod_3(A,B,D,E))))))))))))) # label(t33_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9549 $T # label(t62_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9550 $T # label(t4_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9551 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) & v3_vectsp_2(D,A) -> (all E (v3_vectsp_2(E,A) & m1_rmod_2(E,A,B) -> (m1_rmod_2(C,A,D) -> m1_rmod_2(k1_rmod_3(A,B,C,E),A,k1_rmod_3(A,B,D,E))))))))))))) # label(t38_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9552 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) -> (all C (m1_rmod_2(C,A,B) & v3_vectsp_2(C,A) -> k2_rmod_3(A,B,C,C) = C)))))) # label(t17_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9553 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (m1_rmod_2(E,A,B) -> k1_rmod_3(A,B,k1_rmod_3(A,B,C,D),E) = k1_rmod_3(A,B,C,k1_rmod_3(A,B,D,E)))))))))))) # label(t10_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9554 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) -> (all C (C = k3_rmod_3(A,B) <-> (all D ((exists E (E = D & m1_rmod_2(E,A,B) & v3_vectsp_2(E,A))) <-> r2_hidden(D,C))))))))) # label(d3_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9555 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> m1_rmod_2(k2_rmod_3(A,B,C,D),A,C) & m1_rmod_2(k2_rmod_3(A,B,C,D),A,D))))))))) # label(t20_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9556 (all A (v3_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) -> -v3_struct_0(g3_lattices(k3_rmod_3(A,B),k5_rmod_3(A,B),k6_rmod_3(A,B))) & l3_lattices(g3_lattices(k3_rmod_3(A,B),k5_rmod_3(A,B),k6_rmod_3(A,B))) & v10_lattices(g3_lattices(k3_rmod_3(A,B),k5_rmod_3(A,B),k6_rmod_3(A,B))))))) # label(t63_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9557 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) -> (all B (v4_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E ((exists F (m1_subset_1(F,u1_struct_0(B)) & (exists G (r1_rlvect_1(C,F) & r1_rlvect_1(D,G) & E = k4_rlvect_1(B,F,G) & m1_subset_1(G,u1_struct_0(B)))))) <-> r1_rlvect_1(k1_rmod_3(A,B,C,D),E))))))))))) # label(t5_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9558 $T # label(t2_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9559 $T # label(t54_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9560 (all A all B all C all D (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & m1_rmod_2(D,A,B) & m1_rmod_2(C,A,B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v3_rlvect_1(B) & -v3_struct_0(B) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> m1_rmod_2(k1_rmod_3(A,B,C,D),A,B) & v3_vectsp_2(k1_rmod_3(A,B,C,D),A))) # label(dt_k1_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9561 (all A (v4_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v3_vectsp_2(B,A) & v6_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> ((all E (m1_subset_1(E,u1_struct_0(B)) -> (exists F ((exists G (m1_subset_1(G,u1_struct_0(B)) & r1_rlvect_1(C,F) & r1_rlvect_1(D,G) & E = k4_rlvect_1(B,F,G))) & m1_subset_1(F,u1_struct_0(B)))))) <-> k1_rmod_3(A,B,C,D) = B))))))))) # label(t50_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9562 (all A all B all C all D (-v3_struct_0(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v3_rlvect_1(B) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & m1_rmod_2(D,A,B) & m1_rmod_2(C,A,B) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> v3_vectsp_2(k2_rmod_3(A,B,C,D),A) & m1_rmod_2(k2_rmod_3(A,B,C,D),A,B))) # label(dt_k2_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9563 (all A all B all C all D all E (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & -v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & m1_subset_1(C,u1_struct_0(B)) & m1_rmod_2(D,A,B) & m1_rmod_2(E,A,B) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v3_rlvect_1(B) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> m1_subset_1(k4_rmod_3(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B))))) # label(dt_k4_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9564 (all A (v3_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (v3_vectsp_2(E,A) & m1_rmod_2(E,A,B) -> (k3_xboole_0(u1_struct_0(C),u1_struct_0(D)) = u1_struct_0(E) <-> k2_rmod_3(A,B,C,D) = E))))))))))) # label(d2_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9565 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (m2_rmod_2(E,A,B,C) -> (all F (m2_rmod_2(F,A,B,D) -> (-r1_xboole_0(E,F) -> m2_rmod_2(k5_subset_1(u1_struct_0(B),E,F),A,B,k2_rmod_3(A,B,C,D))))))))))))))) # label(t48_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9566 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v3_vectsp_2(B,A) -> B = k1_rmod_3(A,B,k2_rmod_2(A,B),k1_rmod_2(A,B)) & B = k1_rmod_3(A,B,k1_rmod_2(A,B),k2_rmod_2(A,B)))))) # label(t14_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9567 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> m1_rmod_2(k2_rmod_3(A,B,C,D),A,k1_rmod_3(A,B,C,D)))))))))) # label(t29_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9568 $T # label(dt_k3_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9569 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (r1_rmod_3(A,B,C,D) -> k2_domain_1(u1_struct_0(B),u1_struct_0(B),k4_rmod_3(A,B,E,D,C)) = k3_domain_1(u1_struct_0(B),u1_struct_0(B),k4_rmod_3(A,B,E,C,D))))))))))))) # label(t58_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9570 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (v3_vectsp_2(D,A) & m1_rmod_2(D,A,B) -> (k1_rmod_3(A,B,C,D) = D <-> m1_rmod_2(C,A,D)))))))))) # label(t12_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9571 $T # label(t1_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9572 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & -v3_struct_0(B) -> r2_hidden(B,k3_rmod_3(A,B)))))) # label(t44_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9573 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & -v3_struct_0(A) -> (all B (v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> (all G (m1_subset_1(G,u1_struct_0(B)) -> (all H (m1_subset_1(H,u1_struct_0(B)) -> (all I (m1_subset_1(I,u1_struct_0(B)) -> (r1_rlvect_1(C,F) & r1_rlvect_1(C,H) & r1_rlvect_1(D,G) & r1_rlvect_1(D,I) & E = k4_rlvect_1(B,H,I) & E = k4_rlvect_1(B,F,G) & r1_rmod_3(A,B,C,D) -> I = G & H = F))))))))))))))))))) # label(t51_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9574 (all A all B (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & -v3_struct_0(B) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & l3_vectsp_1(A) & v7_vectsp_1(A) & -v3_struct_0(A) -> v1_funct_1(k5_rmod_3(A,B)) & m2_relset_1(k5_rmod_3(A,B),k2_zfmisc_1(k3_rmod_3(A,B),k3_rmod_3(A,B)),k3_rmod_3(A,B)) & v1_funct_2(k5_rmod_3(A,B),k2_zfmisc_1(k3_rmod_3(A,B),k3_rmod_3(A,B)),k3_rmod_3(A,B)))) # label(dt_k5_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9575 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) -> -v3_struct_0(g3_lattices(k3_rmod_3(A,B),k5_rmod_3(A,B),k6_rmod_3(A,B))) & v15_lattices(g3_lattices(k3_rmod_3(A,B),k5_rmod_3(A,B),k6_rmod_3(A,B))) & l3_lattices(g3_lattices(k3_rmod_3(A,B),k5_rmod_3(A,B),k6_rmod_3(A,B))) & v10_lattices(g3_lattices(k3_rmod_3(A,B),k5_rmod_3(A,B),k6_rmod_3(A,B))))))) # label(t66_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9576 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (m1_rmod_2(E,A,B) -> (m1_rmod_2(C,A,D) -> m1_rmod_2(k2_rmod_3(A,B,C,E),A,k2_rmod_3(A,B,D,E))))))))))))) # label(t22_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9577 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (r1_rlvect_1(C,E) | r1_rlvect_1(D,E) -> r1_rlvect_1(k1_rmod_3(A,B,C,D),E)))))))))))) # label(t6_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9578 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (m1_rmod_2(E,A,B) -> (m1_rmod_2(C,A,D) -> k2_rmod_3(A,B,k1_rmod_3(A,B,C,D),k1_rmod_3(A,B,D,E)) = k1_rmod_3(A,B,D,k2_rmod_3(A,B,C,E))))))))))))) # label(t35_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9579 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v4_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> k1_rmod_3(A,B,D,C) = k1_rmod_3(A,B,C,D))))))))) # label(t9_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9580 (all A (v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (v3_vectsp_2(E,A) & m1_rmod_2(E,A,B) -> (m1_rmod_2(E,A,C) -> k2_rmod_3(A,B,k1_rmod_3(A,B,E,D),C) = k1_rmod_3(A,B,E,k2_rmod_3(A,B,D,C))))))))))))) # label(t36_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9581 (all A all B (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v3_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> m2_relset_1(k6_rmod_3(A,B),k2_zfmisc_1(k3_rmod_3(A,B),k3_rmod_3(A,B)),k3_rmod_3(A,B)) & v1_funct_2(k6_rmod_3(A,B),k2_zfmisc_1(k3_rmod_3(A,B),k3_rmod_3(A,B)),k3_rmod_3(A,B)) & v1_funct_1(k6_rmod_3(A,B)))) # label(dt_k6_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9582 (all A (v6_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & -v3_struct_0(B) -> -v3_struct_0(g3_lattices(k3_rmod_3(A,B),k5_rmod_3(A,B),k6_rmod_3(A,B))) & v10_lattices(g3_lattices(k3_rmod_3(A,B),k5_rmod_3(A,B),k6_rmod_3(A,B))) & l3_lattices(g3_lattices(k3_rmod_3(A,B),k5_rmod_3(A,B),k6_rmod_3(A,B))) & v12_lattices(g3_lattices(k3_rmod_3(A,B),k5_rmod_3(A,B),k6_rmod_3(A,B))))))) # label(t67_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9583 $T # label(t43_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9584 $T # label(t55_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9585 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> k2_rmod_3(A,B,C,k1_rmod_2(A,B)) = k1_rmod_2(A,B) & k2_rmod_3(A,B,k1_rmod_2(A,B),C) = k1_rmod_2(A,B))))))) # label(t25_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9586 $T # label(t53_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9587 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (v3_vectsp_2(C,A) & m1_rmod_2(C,A,B) -> k1_rmod_3(A,B,C,C) = C)))))) # label(t8_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9588 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v3_vectsp_2(B,A) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> B = k1_rmod_3(A,B,k2_rmod_2(A,B),k2_rmod_2(A,B)))))) # label(t16_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9589 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) -> (all B (-v3_struct_0(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (v3_vectsp_2(D,A) & m1_rmod_2(D,A,B) -> (m1_rmod_2(D,A,C) -> D = k2_rmod_3(A,B,D,C)))) & (all D (m1_rmod_2(D,A,B) -> (k2_rmod_3(A,B,D,C) = D -> m1_rmod_2(D,A,C)))))))))) # label(t21_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9590 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (k1_rmod_2(A,B) = k2_rmod_3(A,B,C,D) & g1_vectsp_2(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u1_vectsp_2(A,B)) = k1_rmod_3(A,B,C,D) <-> r1_rmod_3(A,B,C,D)))))))))) # label(d4_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9591 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (r1_rmod_3(A,B,C,D) -> r1_rmod_3(A,B,D,C)))))))))) # label(t46_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9592 (all A (v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> v10_lattices(g3_lattices(k3_rmod_3(A,B),k5_rmod_3(A,B),k6_rmod_3(A,B))) & l3_lattices(g3_lattices(k3_rmod_3(A,B),k5_rmod_3(A,B),k6_rmod_3(A,B))) & v13_lattices(g3_lattices(k3_rmod_3(A,B),k5_rmod_3(A,B),k6_rmod_3(A,B))) & -v3_struct_0(g3_lattices(k3_rmod_3(A,B),k5_rmod_3(A,B),k6_rmod_3(A,B))))))) # label(t64_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9593 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (v3_vectsp_2(E,A) & m1_rmod_2(E,A,B) -> (u1_struct_0(E) = a_4_0_rmod_3(A,B,C,D) <-> E = k1_rmod_3(A,B,C,D)))))))))))) # label(d1_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9594 (all A (v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (B = k1_rmod_3(A,B,C,D) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (exists F ((exists G ((exists H ((exists I (m1_subset_1(I,u1_struct_0(B)) & k4_rlvect_1(B,H,I) = E & r1_rlvect_1(C,F) & r1_rlvect_1(D,I) & -(G = I & F = H) & r1_rlvect_1(D,G) & r1_rlvect_1(C,H) & k4_rlvect_1(B,F,G) = E)) & m1_subset_1(H,u1_struct_0(B)))) & m1_subset_1(G,u1_struct_0(B)))) & m1_subset_1(F,u1_struct_0(B)))))) | r1_rmod_3(A,B,C,D)))))))))) # label(t52_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9595 (all A all B all C all D all E (-v3_struct_0(B) & v6_rlvect_1(B) & v4_group_1(B) & v7_vectsp_1(B) & v8_vectsp_1(B) & v3_rlvect_1(C) & v5_rlvect_1(C) & v5_vectsp_2(C,B) & m1_rmod_2(D,B,C) & m1_rmod_2(E,B,C) & l1_vectsp_2(C,B) & v6_rlvect_1(C) & v4_rlvect_1(C) & -v3_struct_0(C) & l3_vectsp_1(B) & v6_vectsp_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> ((exists F exists G (A = k4_rlvect_1(C,F,G) & r1_rlvect_1(D,F) & r1_rlvect_1(E,G) & m1_subset_1(G,u1_struct_0(C)) & m1_subset_1(F,u1_struct_0(C)))) <-> r2_hidden(A,a_4_0_rmod_3(B,C,D,E))))) # label(fraenkel_a_4_0_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9596 $T # label(t61_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9597 $T # label(t42_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9598 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (m1_rmod_2(E,A,B) -> m1_rmod_2(k1_rmod_3(A,B,k2_rmod_3(A,B,C,D),k2_rmod_3(A,B,D,E)),A,k2_rmod_3(A,B,D,k1_rmod_3(A,B,C,E))))))))))))) # label(t32_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9599 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_rmod_2(D,A,B) -> (all E (m1_rmod_2(E,A,B) -> (r1_rmod_3(A,B,D,E) -> (all F (m1_subset_1(F,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B))) -> (r1_rlvect_1(D,k2_domain_1(u1_struct_0(B),u1_struct_0(B),F)) & r1_rlvect_1(E,k3_domain_1(u1_struct_0(B),u1_struct_0(B),F)) & k4_rlvect_1(B,k2_domain_1(u1_struct_0(B),u1_struct_0(B),F),k3_domain_1(u1_struct_0(B),u1_struct_0(B),F)) = C <-> k4_rmod_3(A,B,C,D,E) = F)))))))))))))) # label(d5_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9600 $T # label(t26_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9601 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> m1_rmod_2(C,A,k1_rmod_3(A,B,C,D)) & m1_rmod_2(D,A,k1_rmod_3(A,B,C,D)))))))))) # label(t11_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9602 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B,A) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) -> B = k2_rmod_3(A,B,k2_rmod_2(A,B),k2_rmod_2(A,B)))))) # label(t28_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9603 $T # label(t3_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9604 $T # label(t60_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9605 (all A (v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) -> (all C (m1_rmod_2(C,A,B) -> (all D (v3_vectsp_2(D,A) & m1_rmod_2(D,A,B) -> D = k1_rmod_3(A,B,k2_rmod_3(A,B,C,D),D))))))))) # label(t30_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9606 (all A (v6_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B,A) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) -> r1_rmod_3(A,B,k2_rmod_2(A,B),k1_rmod_2(A,B)) & r1_rmod_3(A,B,k1_rmod_2(A,B),k2_rmod_2(A,B)))))) # label(t47_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9607 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> ((all E (m2_rmod_2(E,A,B,C) -> (all F (m2_rmod_2(F,A,B,D) -> (exists G (m1_subset_1(G,u1_struct_0(B)) & k6_domain_1(u1_struct_0(B),G) = k5_subset_1(u1_struct_0(B),E,F))))))) <-> r1_rmod_3(A,B,C,D)))))))))) # label(t49_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9608 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (r1_rlvect_1(C,E) & r1_rlvect_1(D,E) <-> r1_rlvect_1(k2_rmod_3(A,B,C,D),E))))))))))) # label(t7_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9609 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(k3_rmod_3(A,B),k3_rmod_3(A,B)),k3_rmod_3(A,B)) & m2_relset_1(C,k2_zfmisc_1(k3_rmod_3(A,B),k3_rmod_3(A,B)),k3_rmod_3(A,B)) -> (k6_rmod_3(A,B) = C <-> (all D (m1_subset_1(D,k3_rmod_3(A,B)) -> (all E (m1_subset_1(E,k3_rmod_3(A,B)) -> (all F (m1_rmod_2(F,A,B) -> (all G (m1_rmod_2(G,A,B) -> (E = G & D = F -> k2_binop_1(k3_rmod_3(A,B),k3_rmod_3(A,B),k3_rmod_3(A,B),C,D,E) = k2_rmod_3(A,B,F,G))))))))))))))))) # label(d7_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9610 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> k2_rmod_3(A,B,C,D) = k2_rmod_3(A,B,D,C))))))))) # label(t18_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9611 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (m1_rmod_2(E,A,B) -> (m1_rmod_2(C,A,D) -> m1_rmod_2(C,A,k1_rmod_3(A,B,D,E))))))))))))) # label(t39_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9612 $T # label(t59_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9613 (all A (v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> -v3_struct_0(g3_lattices(k3_rmod_3(A,B),k5_rmod_3(A,B),k6_rmod_3(A,B))) & v14_lattices(g3_lattices(k3_rmod_3(A,B),k5_rmod_3(A,B),k6_rmod_3(A,B))) & l3_lattices(g3_lattices(k3_rmod_3(A,B),k5_rmod_3(A,B),k6_rmod_3(A,B))) & v10_lattices(g3_lattices(k3_rmod_3(A,B),k5_rmod_3(A,B),k6_rmod_3(A,B))))))) # label(t65_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9614 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (m1_rmod_2(E,A,B) -> k2_rmod_3(A,B,C,k2_rmod_3(A,B,D,E)) = k2_rmod_3(A,B,k2_rmod_3(A,B,C,D),E))))))))))) # label(t19_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9615 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & -v3_struct_0(B) -> (all C (v3_vectsp_2(C,A) & m1_rmod_2(C,A,B) -> k1_rmod_3(A,B,C,k1_rmod_2(A,B)) = C & k1_rmod_3(A,B,k1_rmod_2(A,B),C) = C)))))) # label(t13_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9616 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C (v3_vectsp_2(C,A) & m1_rmod_2(C,A,B) -> C = k2_rmod_3(A,B,k2_rmod_2(A,B),C) & k2_rmod_3(A,B,C,k2_rmod_2(A,B)) = C)))))) # label(t27_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9617 $T # label(t56_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9618 (all A (v3_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (v3_vectsp_2(D,A) & m1_rmod_2(D,A,B) -> k2_rmod_3(A,B,D,k1_rmod_3(A,B,D,C)) = D)))))))) # label(t31_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9619 (all A (v3_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (m1_rmod_2(E,A,B) -> (m1_rmod_2(C,A,D) & m1_rmod_2(C,A,E) -> m1_rmod_2(C,A,k2_rmod_3(A,B,D,E))))))))))))) # label(t24_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.58 9620 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(k3_rmod_3(A,B),k3_rmod_3(A,B)),k3_rmod_3(A,B)) & m2_relset_1(C,k2_zfmisc_1(k3_rmod_3(A,B),k3_rmod_3(A,B)),k3_rmod_3(A,B)) & v1_funct_1(C) -> ((all D (m1_subset_1(D,k3_rmod_3(A,B)) -> (all E (m1_subset_1(E,k3_rmod_3(A,B)) -> (all F (m1_rmod_2(F,A,B) -> (all G (m1_rmod_2(G,A,B) -> (E = G & F = D -> k2_binop_1(k3_rmod_3(A,B),k3_rmod_3(A,B),k3_rmod_3(A,B),C,D,E) = k1_rmod_3(A,B,F,G)))))))))) <-> k5_rmod_3(A,B) = C))))))) # label(d6_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9621 (all A (v3_rlvect_1(A) & v6_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v3_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (m1_rmod_2(E,A,B) -> (m1_rmod_2(C,A,D) & m1_rmod_2(E,A,D) -> m1_rmod_2(k1_rmod_3(A,B,C,E),A,D)))))))))))) # label(t40_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9622 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> k1_rmod_3(A,B,k2_rmod_2(A,B),C) = g1_vectsp_2(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u1_vectsp_2(A,B)) & k1_rmod_3(A,B,C,k2_rmod_2(A,B)) = g1_vectsp_2(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u1_vectsp_2(A,B)))))))) # label(t15_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9623 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (m1_rmod_2(E,A,B) -> (m1_rmod_2(C,A,D) -> m1_rmod_2(k2_rmod_3(A,B,C,E),A,D)))))))))))) # label(t23_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9624 (all A (-v3_struct_0(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (r1_rmod_3(A,B,C,D) -> k3_domain_1(u1_struct_0(B),u1_struct_0(B),k4_rmod_3(A,B,E,D,C)) = k2_domain_1(u1_struct_0(B),u1_struct_0(B),k4_rmod_3(A,B,E,C,D))))))))))))) # label(t57_rmod_3) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9625 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_rmod_4(D,A,B) -> (k7_rlvect_2(B,C) = k2_rmod_4(A,B,D) -> k5_rmod_4(A,B,D) = k6_vectsp_2(A,B,k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,C),C)))))))))) # label(t46_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9626 $T # label(d2_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9627 $T # label(t39_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9628 $T # label(t18_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9629 (all A (v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m2_finseq_1(C,u1_struct_0(B)) -> (all D (v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) -> (all E (m2_finseq_1(E,u1_struct_0(B)) -> ((all F (m2_subset_1(F,k1_numbers,k5_numbers) -> (r2_hidden(F,k1_relat_1(E)) -> k1_funct_1(E,F) = k6_vectsp_2(A,B,k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,k4_finseq_4(k5_numbers,u1_struct_0(B),C,F)),k4_finseq_4(k5_numbers,u1_struct_0(B),C,F))))) & k3_finseq_1(C) = k3_finseq_1(E) <-> E = k4_rmod_4(A,B,C,D)))))))))))) # label(d8_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9630 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v1_finset_1(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & v1_finset_1(D) -> k6_rlvect_1(B,k4_rlvect_1(B,k1_rmod_4(A,B,C),k1_rmod_4(A,B,D)),k1_rmod_4(A,B,k3_rlvect_2(B,C,D))) = k1_rmod_4(A,B,k2_rlvect_2(B,C,D)))))))))) # label(t10_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9631 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (v1_funct_1(F) & m2_relset_1(F,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(F,u1_struct_0(B),u1_struct_0(A)) -> k4_rmod_4(A,B,k3_finseq_4(u1_struct_0(B),C,D,E),F) = k3_finseq_4(u1_struct_0(B),k6_vectsp_2(A,B,k8_funct_2(u1_struct_0(B),u1_struct_0(A),F,C),C),k6_vectsp_2(A,B,k8_funct_2(u1_struct_0(B),u1_struct_0(A),F,D),D),k6_vectsp_2(A,B,k8_funct_2(u1_struct_0(B),u1_struct_0(A),F,E),E)))))))))))))) # label(t36_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9632 (all A (v3_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rmod_4(D,A,B) -> r1_tarski(k2_rmod_4(A,B,k7_rmod_4(A,B,C,D)),k2_rmod_4(A,B,D)))))))))) # label(t58_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9633 (all A all B all C all D (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & -v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & m1_rmod_4(C,A,B) & m1_rmod_4(D,A,B) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & l3_vectsp_1(A) & v8_vectsp_1(A) & -v3_struct_0(A) -> (D = C <-> r1_rmod_4(A,B,C,D)))) # label(redefinition_r1_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9634 $T # label(t48_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9635 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_4(C,A,B) -> r1_rmod_4(A,B,k7_rmod_4(A,B,k2_group_1(A),C),C))))))) # label(t65_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9636 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> k6_vectsp_2(A,B,C,k9_rlvect_1(B,k2_finseq_4(u1_struct_0(B),D,E))) = k4_rlvect_1(B,k6_vectsp_2(A,B,C,D),k6_vectsp_2(A,B,C,E)))))))))))) # label(t3_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9637 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v1_finset_1(C) -> (all D (v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> k1_rmod_4(A,B,k4_rlvect_2(B,C,D)) = k6_rlvect_1(B,k1_rmod_4(A,B,C),k1_rmod_4(A,B,k3_rlvect_2(B,C,D))))))))))) # label(t13_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9638 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (m1_rmod_4(D,A,B) -> (all E (m1_rmod_4(E,A,B) -> (m2_rmod_4(D,A,B,C) & m2_rmod_4(E,A,B,C) -> m2_rmod_4(k9_rmod_4(A,B,D,E),A,B,C)))))))))))) # label(t75_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9639 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & -v10_vectsp_1(A) & v2_vectsp_2(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_4(C,A,B) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (D != k1_rlvect_1(A) -> k2_rmod_4(A,B,k7_rmod_4(A,B,D,C)) = k2_rmod_4(A,B,C)))))))))) # label(t59_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9640 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (k2_group_1(A) != k1_rlvect_1(A) -> (k1_xboole_0 != C & v1_rmod_2(C,A,B) <-> (all D (m2_rmod_4(D,A,B,C) -> r2_hidden(k5_rmod_4(A,B,D),C))))))))))) # label(t40_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9641 (all A all B (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> m1_rmod_4(k3_rmod_4(A,B),A,B))) # label(dt_k3_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9642 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_rmod_4(C,A,B) -> (all D (m1_rmod_4(D,A,B) -> r1_tarski(k2_rmod_4(A,B,k9_rmod_4(A,B,C,D)),k2_rlvect_2(B,k2_rmod_4(A,B,C),k2_rmod_4(A,B,D))))))))))) # label(t74_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9643 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_rlvect_1(B) = k6_vectsp_2(A,B,C,k9_rlvect_1(B,k6_finseq_1(u1_struct_0(B)))))))))) # label(t2_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9644 (all A all B (-v3_struct_0(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & -v3_struct_0(B) & v3_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all C (m1_rmod_4(C,A,B) -> m2_fraenkel(C,u1_struct_0(B),u1_struct_0(A),k1_fraenkel(u1_struct_0(B),u1_struct_0(A))))))) # label(dt_m1_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9645 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_rmod_4(C,A,B) -> r1_rmod_4(A,B,k7_rmod_4(A,B,k1_rlvect_1(A),C),k3_rmod_4(A,B)))))))) # label(t60_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9646 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) -> (all C (m1_rmod_4(C,A,B) -> (all D (m1_rmod_4(D,A,B) -> k4_rlvect_1(B,k5_rmod_4(A,B,C),k5_rmod_4(A,B,D)) = k5_rmod_4(A,B,k6_rmod_4(A,B,C,D)))))))))) # label(t77_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9647 (all A all B all C (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v3_rlvect_1(B) & v4_rlvect_1(B) & m1_rmod_4(C,A,B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & -v3_struct_0(B) & v6_rlvect_1(A) & v4_rlvect_1(A) -> m1_rmod_4(k8_rmod_4(A,B,C),A,B))) # label(dt_k8_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9648 $T # label(t30_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9649 $T # label(t57_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9650 (all A all B all C all D (v3_rlvect_1(A) & v6_rlvect_1(A) & v8_vectsp_1(A) & -v3_struct_0(B) & v4_rlvect_1(B) & l1_vectsp_2(B,A) & m1_rmod_4(D,A,B) & m1_rmod_4(C,A,B) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> m1_rmod_4(k9_rmod_4(A,B,C,D),A,B))) # label(dt_k9_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9651 (all A all B all C (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_vectsp_2(B,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v1_finset_1(C) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & -v3_struct_0(B) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> m1_subset_1(k1_rmod_4(A,B,C),u1_struct_0(B)))) # label(dt_k1_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9652 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) -> (all C (m1_rmod_4(C,A,B) -> (k1_xboole_0 = k2_rmod_4(A,B,C) -> k1_rlvect_1(B) = k5_rmod_4(A,B,C)))))))) # label(t45_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9653 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (v1_funct_2(C,u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(C) -> k4_rmod_4(A,B,k6_finseq_1(u1_struct_0(B)),C) = k6_finseq_1(u1_struct_0(B)))))))) # label(t33_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9654 (all A (-v3_struct_0(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (m1_rmod_4(D,A,B) -> (m2_rmod_4(D,A,B,C) -> m2_rmod_4(k8_rmod_4(A,B,D),A,B,C)))))))))) # label(t70_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9655 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_4(C,A,B) -> (all D (m1_rmod_4(D,A,B) -> (r1_rmod_4(A,B,k6_rmod_4(A,B,C,D),k3_rmod_4(A,B)) -> r1_rmod_4(A,B,D,k8_rmod_4(A,B,C))))))))))) # label(t68_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9656 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_4(C,A,B) -> k2_rmod_4(A,B,C) = a_3_0_rmod_4(A,B,C))))))) # label(d5_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9657 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m2_rmod_4(D,A,B,k7_rlvect_2(B,C)) -> k6_vectsp_2(A,B,k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,C),C) = k5_rmod_4(A,B,D))))))))) # label(t43_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9658 $T # label(t56_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9659 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & v1_finset_1(D) -> k4_rlvect_1(B,k1_rmod_4(A,B,k4_rlvect_2(B,C,D)),k1_rmod_4(A,B,k4_rlvect_2(B,D,C))) = k1_rmod_4(A,B,k5_rlvect_2(B,C,D)))))))))) # label(t15_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9660 (all A all B all C (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v3_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & m1_rmod_4(C,A,B) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) & v7_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> v1_finset_1(k2_rmod_4(A,B,C)) & m1_subset_1(k2_rmod_4(A,B,C),k1_zfmisc_1(u1_struct_0(B))))) # label(dt_k2_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9661 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v4_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_rmod_4(D,A,B) -> (all E (m1_rmod_4(E,A,B) -> k6_rlvect_1(A,k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,C),k8_funct_2(u1_struct_0(B),u1_struct_0(A),E,C)) = k8_funct_2(u1_struct_0(B),u1_struct_0(A),k9_rmod_4(A,B,D,E),C))))))))))) # label(t73_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9662 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (r1_xboole_0(C,D) -> k4_rlvect_1(B,k1_rmod_4(A,B,C),k1_rmod_4(A,B,D)) = k1_rmod_4(A,B,k2_rlvect_2(B,C,D))))))))))) # label(t9_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9663 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v1_finset_1(C) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (D = k1_rmod_4(A,B,C) <-> (exists E (v2_funct_1(E) & D = k9_rlvect_1(B,E) & C = k2_relat_1(E) & m2_finseq_1(E,u1_struct_0(B))))))))))))) # label(d3_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9664 $T # label(t17_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9665 $T # label(t38_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9666 (all A all B all C all D (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & m1_rmod_4(C,A,B) & m1_rmod_4(D,A,B) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & -v3_struct_0(B) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) -> (r1_rmod_4(A,B,C,D) -> r1_rmod_4(A,B,D,C)))) # label(symmetry_r1_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9667 (all A all B all C all D (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & m1_finseq_1(C,u1_struct_0(B)) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & m1_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(D) & v3_rlvect_1(B) & -v3_struct_0(B) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> m2_finseq_1(k4_rmod_4(A,B,C,D),u1_struct_0(B)))) # label(dt_k4_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9668 (all A (v3_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & -v3_struct_0(B) -> k5_rmod_4(A,B,k3_rmod_4(A,B)) = k1_rlvect_1(B))))) # label(t41_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9669 (all A (v3_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m2_finseq_1(D,u1_struct_0(B)) -> (all E (m2_finseq_1(E,u1_struct_0(B)) -> ((all F (m2_subset_1(F,k1_numbers,k5_numbers) -> (all G (m1_subset_1(G,u1_struct_0(B)) -> (G = k1_funct_1(E,F) & r2_hidden(F,k1_relat_1(D)) -> k6_vectsp_2(A,B,C,G) = k1_funct_1(D,F)))))) & k3_finseq_1(D) = k3_finseq_1(E) -> k9_rlvect_1(B,D) = k6_vectsp_2(A,B,C,k9_rlvect_1(B,E))))))))))))) # label(t1_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9670 (all A all B all C (v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & -v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & m1_rmod_4(C,A,B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v8_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> k8_rmod_4(A,B,k8_rmod_4(A,B,C)) = C)) # label(involutiveness_k8_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9671 $T # label(t72_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9672 $T # label(t49_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9673 $T # label(t16_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9674 (all A all B all C all D (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v3_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & m1_rmod_4(D,A,B) & m1_subset_1(C,u1_struct_0(A)) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) & v8_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> m1_rmod_4(k7_rmod_4(A,B,C,D),A,B))) # label(dt_k7_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9675 (all A (v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_4(C,A,B) -> m2_rmod_4(C,A,B,k2_rmod_4(A,B,C)))))))) # label(t28_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9676 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> k1_rlvect_1(B) = k1_rmod_4(A,B,k1_pre_topc(B)))))) # label(t5_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9677 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v7_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & -v3_struct_0(B) -> (all C (m1_rmod_4(C,A,B) -> (all D (m1_rmod_4(D,A,B) -> r1_rmod_4(A,B,k6_rmod_4(A,B,C,D),k6_rmod_4(A,B,D,C)))))))))) # label(t53_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9678 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v3_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v1_finset_1(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & v1_finset_1(D) -> k1_rmod_4(A,B,k4_rlvect_2(B,C,D)) = k6_rlvect_1(B,k1_rmod_4(A,B,k2_rlvect_2(B,C,D)),k1_rmod_4(A,B,D)))))))))) # label(t12_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9679 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_4(C,A,B) -> (all D (m1_rmod_4(D,A,B) -> r1_tarski(k2_rmod_4(A,B,k6_rmod_4(A,B,C,D)),k2_rlvect_2(B,k2_rmod_4(A,B,C),k2_rmod_4(A,B,D))))))))))) # label(t51_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9680 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k1_rmod_4(A,B,k7_rlvect_2(B,C)) = C)))))) # label(t6_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.24/125.59 9681 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> k6_vectsp_2(A,B,C,k9_rlvect_1(B,k3_finseq_4(u1_struct_0(B),D,E,F))) = k4_rlvect_1(B,k4_rlvect_1(B,k6_vectsp_2(A,B,C,D),k6_vectsp_2(A,B,C,E)),k6_vectsp_2(A,B,C,F)))))))))))))) # label(t4_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.59 9682 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & -v10_vectsp_1(A) & v2_vectsp_2(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v3_rlvect_1(A) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_4(C,A,B) -> (all D (m1_rmod_4(D,A,B) -> k6_rlvect_1(B,k5_rmod_4(A,B,C),k5_rmod_4(A,B,D)) = k5_rmod_4(A,B,k9_rmod_4(A,B,C,D)))))))))) # label(t80_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.59 9683 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (all E (m2_rmod_4(E,A,B,C) -> (r1_tarski(C,D) -> m2_rmod_4(E,A,B,D)))))))))))) # label(t25_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.59 9684 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v3_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_4(C,A,B) -> r1_rmod_4(A,B,k6_rmod_4(A,B,C,k3_rmod_4(A,B)),C) & r1_rmod_4(A,B,k6_rmod_4(A,B,k3_rmod_4(A,B),C),C))))))) # label(t55_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.59 9685 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_rmod_4(C,A,B) -> r1_rmod_4(A,B,k9_rmod_4(A,B,C,C),k3_rmod_4(A,B)))))))) # label(t76_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.59 9686 (all A (v5_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_4(C,A,B) -> (all D (m1_rmod_4(D,A,B) -> (all E (m1_rmod_4(E,A,B) -> ((all F (m1_subset_1(F,u1_struct_0(B)) -> k4_rlvect_1(A,k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,F),k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,F)) = k8_funct_2(u1_struct_0(B),u1_struct_0(A),E,F))) <-> k6_rmod_4(A,B,C,D) = E))))))))))) # label(d11_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.59 9687 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v3_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_rmod_4(E,A,B) -> r1_rmod_4(A,B,k7_rmod_4(A,B,k4_rlvect_1(A,C,D),E),k6_rmod_4(A,B,k7_rmod_4(A,B,C,E),k7_rmod_4(A,B,D,E))))))))))))) # label(t62_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.59 9688 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rmod_4(D,A,B) -> (all E (m1_rmod_4(E,A,B) -> ((all F (m1_subset_1(F,u1_struct_0(B)) -> k8_funct_2(u1_struct_0(B),u1_struct_0(A),E,F) = k1_group_1(A,k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,F),C))) <-> E = k7_rmod_4(A,B,C,D)))))))))))) # label(d12_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.59 9689 $T # label(d1_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.59 9690 $T # label(t31_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.59 9691 (all A all B all C all D (-v3_struct_0(A) & v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & -v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & m1_rmod_4(C,A,B) & m1_rmod_4(D,A,B) & v4_rlvect_1(B) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> m1_rmod_4(k6_rmod_4(A,B,C,D),A,B))) # label(dt_k6_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.59 9692 (all A (v3_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (C != D -> (all E (m2_rmod_4(E,A,B,k8_rlvect_2(B,C,D)) -> k5_rmod_4(A,B,E) = k4_rlvect_1(B,k6_vectsp_2(A,B,k8_funct_2(u1_struct_0(B),u1_struct_0(A),E,C),C),k6_vectsp_2(A,B,k8_funct_2(u1_struct_0(B),u1_struct_0(A),E,D),D))))))))))))) # label(t44_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.59 9693 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_rmod_4(D,A,B) -> (-r2_hidden(C,k2_rmod_4(A,B,D)) <-> k1_rlvect_1(A) = k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,C)))))))))) # label(t20_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.59 9694 (all A (v3_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_4(C,A,B) -> (all D (m1_rmod_4(D,A,B) -> (all E (m1_rmod_4(E,A,B) -> r1_rmod_4(A,B,k6_rmod_4(A,B,C,k6_rmod_4(A,B,D,E)),k6_rmod_4(A,B,k6_rmod_4(A,B,C,D),E)))))))))))) # label(t54_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.59 9695 $T # label(t71_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.59 9696 $T # label(t29_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.59 9697 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (v1_funct_1(E) & m2_relset_1(E,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(A)) -> k2_finseq_4(u1_struct_0(B),k6_vectsp_2(A,B,k8_funct_2(u1_struct_0(B),u1_struct_0(A),E,C),C),k6_vectsp_2(A,B,k8_funct_2(u1_struct_0(B),u1_struct_0(A),E,D),D)) = k4_rmod_4(A,B,k2_finseq_4(u1_struct_0(B),C,D),E))))))))))) # label(t35_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.59 9698 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v2_vectsp_2(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & -v3_struct_0(B) -> (all C (m1_rmod_4(C,A,B) -> k5_rmod_4(A,B,k8_rmod_4(A,B,C)) = k5_rlvect_1(B,k5_rmod_4(A,B,C)))))))) # label(t79_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.59 9699 (all A (v3_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_4(C,A,B) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (D = k5_rmod_4(A,B,C) <-> (exists E (k2_relat_1(E) = k2_rmod_4(A,B,C) & k9_rlvect_1(B,k4_rmod_4(A,B,E,C)) = D & v2_funct_1(E) & m2_finseq_1(E,u1_struct_0(B))))))))))))) # label(d9_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.59 9700 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rmod_4(D,A,B) -> (all E (m1_rmod_4(E,A,B) -> r1_rmod_4(A,B,k7_rmod_4(A,B,C,k6_rmod_4(A,B,D,E)),k6_rmod_4(A,B,k7_rmod_4(A,B,C,D),k7_rmod_4(A,B,C,E))))))))))))) # label(t63_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.59 9701 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) -> (all C (m1_rmod_4(C,A,B) -> (all D (m1_rmod_4(D,A,B) -> k9_rmod_4(A,B,C,D) = k6_rmod_4(A,B,C,k8_rmod_4(A,B,D)))))))))) # label(d14_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.59 9702 (all A all B all C all D (v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v4_group_1(B) & v6_vectsp_1(B) & v5_vectsp_2(C,B) & m1_rmod_4(D,B,C) & l1_vectsp_2(C,B) & v6_rlvect_1(C) & v5_rlvect_1(C) & v4_rlvect_1(C) & v3_rlvect_1(C) & -v3_struct_0(C) & l3_vectsp_1(B) & v8_vectsp_1(B) & v7_vectsp_1(B) & v5_rlvect_1(B) & -v3_struct_0(B) -> ((exists E (m1_subset_1(E,u1_struct_0(C)) & A = E & k8_funct_2(u1_struct_0(C),u1_struct_0(B),D,E) != k1_rlvect_1(B))) <-> r2_hidden(A,a_3_0_rmod_4(B,C,D))))) # label(fraenkel_a_3_0_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.59 9703 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_rmod_4(C,A,B) -> (all D (m1_rmod_4(D,A,B) -> (r1_rmod_4(A,B,C,D) <-> (all E (m1_subset_1(E,u1_struct_0(B)) -> k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,E) = k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,E)))))))))))) # label(d10_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.59 9704 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m2_finseq_1(C,u1_struct_0(B)) -> (all D (m2_finseq_1(D,u1_struct_0(B)) -> (all E (v1_funct_1(E) & m2_relset_1(E,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(A)) -> k4_rmod_4(A,B,k8_finseq_1(u1_struct_0(B),C,D),E) = k8_finseq_1(u1_struct_0(B),k4_rmod_4(A,B,C,E),k4_rmod_4(A,B,D,E)))))))))))) # label(t37_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.59 9705 (all A (v4_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> -(C != D & D != E & C != E & k4_rlvect_1(B,k4_rlvect_1(B,C,D),E) != k1_rmod_4(A,B,k9_rlvect_2(B,C,D,E))))))))))))) # label(t8_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.59 9706 $T # label(t66_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.59 9707 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v3_rlvect_1(B) -> (all C (m2_rmod_4(C,A,B,k1_subset_1(u1_struct_0(B))) -> C = k3_rmod_4(A,B))))))) # label(t27_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.59 9708 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) -> (all B (v4_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_4(C,A,B) -> (k1_xboole_0 = k2_rmod_4(A,B,C) <-> k3_rmod_4(A,B) = C))))))) # label(d6_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.59 9709 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v2_vectsp_2(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_4(C,A,B) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k6_vectsp_2(A,B,D,k5_rmod_4(A,B,C)) = k5_rmod_4(A,B,k7_rmod_4(A,B,D,C)))))))))) # label(t78_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.59 9710 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v3_rlvect_1(B) -> (all C all D (m1_rmod_4(D,A,B) -> ((exists E (C = E & k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,E) != k1_rlvect_1(A) & m1_subset_1(E,u1_struct_0(B)))) <-> r2_hidden(C,k2_rmod_4(A,B,D))))))))) # label(t19_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.59 9711 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m2_finseq_1(E,u1_struct_0(B)) -> (all F (v1_funct_1(F) & v1_funct_2(F,u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(F,u1_struct_0(B),u1_struct_0(A)) -> (k1_funct_1(E,C) = D & r2_hidden(C,k1_relat_1(E)) -> k1_funct_1(k4_rmod_4(A,B,E,F),C) = k6_vectsp_2(A,B,k8_funct_2(u1_struct_0(B),u1_struct_0(A),F,D),D)))))))))))))) # label(t32_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.59 9712 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (all E (m1_rmod_4(E,A,B) -> (m2_rmod_4(E,A,B,D) -> m2_rmod_4(k7_rmod_4(A,B,C,E),A,B,D)))))))))))) # label(t61_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9713 $T # label(t21_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9714 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v1_finset_1(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & v1_finset_1(D) -> k6_rlvect_1(B,k4_rlvect_1(B,k1_rmod_4(A,B,C),k1_rmod_4(A,B,D)),k1_rmod_4(A,B,k2_rlvect_2(B,C,D))) = k1_rmod_4(A,B,k3_rlvect_2(B,C,D)))))))))) # label(t11_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9715 $T # label(t23_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9716 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> m2_rmod_4(k3_rmod_4(A,B),A,B,C))))))) # label(t26_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9717 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) -> k4_rmod_4(A,B,k12_finseq_1(u1_struct_0(B),C),D) = k12_finseq_1(u1_struct_0(B),k6_vectsp_2(A,B,k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,C),C)))))))))) # label(t34_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9718 (all A all B all C (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & -v3_struct_0(B) & v4_rlvect_1(B) & v5_vectsp_2(B,A) & m1_rmod_4(C,A,B) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) & l3_vectsp_1(A) & v7_vectsp_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> m1_subset_1(k5_rmod_4(A,B,C),u1_struct_0(B)))) # label(dt_k5_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9719 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v1_finset_1(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & v1_finset_1(D) -> k1_rmod_4(A,B,k5_rlvect_2(B,C,D)) = k6_rlvect_1(B,k1_rmod_4(A,B,k2_rlvect_2(B,C,D)),k1_rmod_4(A,B,k3_rlvect_2(B,C,D))))))))))) # label(t14_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9720 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_rmod_4(E,A,B) -> (k2_rmod_4(A,B,E) = k8_rlvect_2(B,C,D) -> k5_rmod_4(A,B,E) = k4_rlvect_1(B,k6_vectsp_2(A,B,k8_funct_2(u1_struct_0(B),u1_struct_0(A),E,C),C),k6_vectsp_2(A,B,k8_funct_2(u1_struct_0(B),u1_struct_0(A),E,D),D)) | C = D))))))))))) # label(t47_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9721 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_rmod_4(D,A,B) -> k8_funct_2(u1_struct_0(B),u1_struct_0(A),k8_rmod_4(A,B,D),C) = k5_rlvect_1(A,k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,C)))))))))) # label(t67_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9722 (all A all B all C (v3_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & -v3_struct_0(B) & v5_vectsp_2(B,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & v8_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all D (m2_rmod_4(D,A,B,C) -> m1_rmod_4(D,A,B))))) # label(dt_m2_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9723 (all A all B all C all D (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & -v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & m1_rmod_4(C,A,B) & m1_rmod_4(D,A,B) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v3_rlvect_1(B) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> r1_rmod_4(A,B,C,C))) # label(reflexivity_r1_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9724 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_rmod_4(C,A,B) -> k2_rmod_4(A,B,k8_rmod_4(A,B,C)) = k2_rmod_4(A,B,C))))))) # label(t69_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9725 $T # label(t24_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9726 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (m1_rmod_4(D,A,B) -> (m2_rmod_4(D,A,B,C) <-> r1_tarski(k2_rmod_4(A,B,D),C)))))))))) # label(d7_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9727 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v3_rlvect_1(B) -> (all C (m2_rmod_4(C,A,B,k1_subset_1(u1_struct_0(B))) -> k5_rmod_4(A,B,C) = k1_rlvect_1(B))))))) # label(t42_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9728 (all A all B (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & -v3_struct_0(B) & v3_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & l3_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (exists C m1_rmod_4(C,A,B)))) # label(existence_m1_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9729 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (D != C -> k4_rlvect_1(B,C,D) = k1_rmod_4(A,B,k8_rlvect_2(B,C,D))))))))))) # label(t7_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9730 (all A (v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) -> (all C (m1_rmod_4(C,A,B) -> k7_rmod_4(A,B,k5_rlvect_1(A,k2_group_1(A)),C) = k8_rmod_4(A,B,C))))))) # label(d13_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9731 $T # label(t50_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9732 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_rmod_4(E,A,B) -> r1_rmod_4(A,B,k7_rmod_4(A,B,D,k7_rmod_4(A,B,C,E)),k7_rmod_4(A,B,k1_group_1(A,C,D),E)))))))))))) # label(t64_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9733 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (m1_rmod_4(D,A,B) -> (all E (m1_rmod_4(E,A,B) -> (m2_rmod_4(E,A,B,C) & m2_rmod_4(D,A,B,C) -> m2_rmod_4(k6_rmod_4(A,B,D,E),A,B,C)))))))))))) # label(t52_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9734 (all A all B all C (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & -v3_struct_0(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (exists D m2_rmod_4(D,A,B,C)))) # label(existence_m2_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9735 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m2_fraenkel(C,u1_struct_0(B),u1_struct_0(A),k1_fraenkel(u1_struct_0(B),u1_struct_0(A))) -> ((exists D ((all E (m1_subset_1(E,u1_struct_0(B)) -> (-r2_hidden(E,D) -> k1_rlvect_1(A) = k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,E)))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & v1_finset_1(D))) <-> m1_rmod_4(C,A,B)))))))) # label(d4_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9736 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v4_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k8_funct_2(u1_struct_0(B),u1_struct_0(A),k3_rmod_4(A,B),C) = k1_rlvect_1(A))))))) # label(t22_rmod_4) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9737 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> ((all D (m2_rmod_4(D,A,B,C) -> (k1_rlvect_1(B) = k5_rmod_4(A,B,D) -> k1_xboole_0 = k2_rmod_4(A,B,D)))) <-> v1_rmod_5(C,A,B)))))))) # label(d1_rmod_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9738 (all A all B all C all D (v4_rlvect_1(B) & v6_vectsp_1(B) & v2_vectsp_2(B) & -v3_struct_0(C) & v5_rlvect_1(C) & l1_vectsp_2(C,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) & v5_vectsp_2(C,B) & v6_rlvect_1(C) & v4_rlvect_1(C) & v3_rlvect_1(C) & l3_vectsp_1(B) & -v10_vectsp_1(B) & v8_vectsp_1(B) & v7_vectsp_1(B) & v7_group_1(B) & v4_group_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> ((exists E (m2_rmod_4(E,B,C,D) & k5_rmod_4(B,C,E) = A)) <-> r2_hidden(A,a_3_0_rmod_5(B,C,D))))) # label(fraenkel_a_3_0_rmod_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9739 $T # label(t8_rmod_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9740 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v7_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v2_vectsp_2(A) & -v10_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> k1_rmod_3(A,B,k1_rmod_5(A,B,C),k1_rmod_5(A,B,D)) = k1_rmod_5(A,B,k4_subset_1(u1_struct_0(B),C,D)))))))))) # label(t17_rmod_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9741 (all A all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v4_group_1(B) & v6_vectsp_1(B) & -v10_vectsp_1(B) & v2_vectsp_2(B) & l3_vectsp_1(B) & v8_vectsp_1(B) & v7_vectsp_1(B) & v7_group_1(B) & v6_rlvect_1(B) -> (all C (v3_rlvect_1(C) & v4_rlvect_1(C) & v6_rlvect_1(C) & l1_vectsp_2(C,B) & v5_vectsp_2(C,B) & v5_rlvect_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) -> (r2_hidden(A,D) -> r1_rlvect_1(k1_rmod_5(B,C,D),A)))))))) # label(t10_rmod_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9742 (all A (-v3_struct_0(A) & v7_group_1(A) & v6_vectsp_1(A) & v2_vectsp_2(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v3_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> -(C != k1_xboole_0 & k7_rlvect_2(B,k1_rlvect_1(B)) != C & k1_rmod_2(A,B) = k1_rmod_5(A,B,C)))))))) # label(t12_rmod_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9743 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & -v3_struct_0(B) -> v1_rmod_5(k1_subset_1(u1_struct_0(B)),A,B))))) # label(t4_rmod_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9744 (all A all B (v4_rlvect_1(B) & v6_rlvect_1(B) & v6_vectsp_1(B) & v7_vectsp_1(B) & v8_vectsp_1(B) & v2_vectsp_2(B) & l3_vectsp_1(B) & -v10_vectsp_1(B) & v7_group_1(B) & v4_group_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (v3_rlvect_1(C) & v4_rlvect_1(C) & v6_rlvect_1(C) & v5_vectsp_2(C,B) & l1_vectsp_2(C,B) & v5_rlvect_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) -> (r1_rlvect_1(k1_rmod_5(B,C,D),A) <-> (exists E (k5_rmod_4(B,C,E) = A & m2_rmod_4(E,B,C,D)))))))))) # label(t9_rmod_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9745 (all A (v3_rlvect_1(A) & v6_rlvect_1(A) & v7_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & -v10_vectsp_1(A) & v2_vectsp_2(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v3_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (C = u1_struct_0(B) -> k1_rlvect_1(A) = k2_group_1(A) | k1_rmod_5(A,B,C) = B))))))) # label(t14_rmod_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9746 (all A (v3_rlvect_1(A) & v6_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v2_vectsp_2(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v3_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (B = k1_rmod_5(A,B,C) & r1_tarski(C,D) -> B = k1_rmod_5(A,B,D)))))))))) # label(t16_rmod_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9747 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v8_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v2_vectsp_2(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v3_rlvect_1(B) & -v3_struct_0(B) -> k1_rmod_2(A,B) = k1_rmod_5(A,B,k1_subset_1(u1_struct_0(B))))))) # label(t11_rmod_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9748 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v2_vectsp_2(A) & -v10_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (v3_vectsp_2(D,A) & m1_rmod_2(D,A,B) -> (k1_rmod_5(A,B,C) = D <-> a_3_0_rmod_5(A,B,C) = u1_struct_0(D)))))))))) # label(d2_rmod_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9749 (all A all B all C (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v7_group_1(A) & v8_vectsp_1(A) & v2_vectsp_2(A) & v3_rlvect_1(B) & v5_rlvect_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> m1_rmod_2(k1_rmod_5(A,B,C),A,B) & v3_vectsp_2(k1_rmod_5(A,B,C),A))) # label(dt_k1_rmod_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9750 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v2_vectsp_2(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (m1_rmod_2(D,A,B) & v3_vectsp_2(D,A) -> (u1_struct_0(D) = C -> k1_rmod_5(A,B,C) = D | k1_rlvect_1(A) = k2_group_1(A)))))))))) # label(t13_rmod_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9751 $T # label(t7_rmod_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9752 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (r1_tarski(C,D) & v1_rmod_5(D,A,B) -> v1_rmod_5(C,A,B)))))))))) # label(t2_rmod_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9753 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v2_vectsp_2(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v7_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (r1_tarski(C,D) -> m1_rmod_2(k1_rmod_5(A,B,C),A,k1_rmod_5(A,B,D))))))))))) # label(t15_rmod_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9754 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v2_vectsp_2(A) & -v10_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> m1_rmod_2(k1_rmod_5(A,B,k5_subset_1(u1_struct_0(B),C,D)),A,k2_rmod_3(A,B,k1_rmod_5(A,B,C),k1_rmod_5(A,B,D))))))))))) # label(t18_rmod_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9755 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (k1_rlvect_1(A) != k2_group_1(A) -> -v1_rmod_5(k8_rlvect_2(B,C,k1_rlvect_1(B)),A,B) & -v1_rmod_5(k8_rlvect_2(B,k1_rlvect_1(B),C),A,B)))))))) # label(t6_rmod_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9756 (all A (v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (v1_rmod_5(k8_rlvect_2(B,C,D),A,B) -> D != k1_rlvect_1(B) & C != k1_rlvect_1(B) | k1_rlvect_1(A) = k2_group_1(A)))))))))) # label(t5_rmod_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9757 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> -(k2_group_1(A) != k1_rlvect_1(A) & v1_rmod_5(C,A,B) & r2_hidden(k1_rlvect_1(B),C)))))))) # label(t3_rmod_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9758 $T # label(t1_rmod_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9759 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(k2_oppcat_1(A))) -> k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(A),k12_cat_1(k2_oppcat_1(A),A,k11_oppcat_1(A)),B) = k4_oppcat_1(A,B))))) # label(t69_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9760 (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) -> m1_oppcat_1(k8_oppcat_1(A,B,C),k2_oppcat_1(A),B))))))) # label(t58_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9761 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_oppcat_1(C,k2_oppcat_1(A),B) -> (all D (m1_subset_1(D,u1_cat_1(k2_oppcat_1(A))) -> k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(B),k12_cat_1(k2_oppcat_1(A),B,C),D) = k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,k7_oppcat_1(A,B,C)),k4_oppcat_1(A,D)))))))))) # label(t38_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9762 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (v1_funct_2(D,u2_cat_1(A),u2_cat_1(B)) & m2_relset_1(D,u2_cat_1(A),u2_cat_1(B)) & v1_funct_1(D) -> (all E (m2_relset_1(E,u2_cat_1(B),u2_cat_1(C)) & v1_funct_2(E,u2_cat_1(B),u2_cat_1(C)) & v1_funct_1(E) -> k8_oppcat_1(A,C,k7_funct_2(u2_cat_1(A),u2_cat_1(B),u2_cat_1(C),D,E)) = k7_funct_2(u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B),u2_cat_1(C),k8_oppcat_1(A,B,D),E))))))))))) # label(t53_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9763 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> k10_cat_1(k2_oppcat_1(A),k3_oppcat_1(A,B)) = k5_oppcat_1(A,k10_cat_1(A,B)))))) # label(t21_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9764 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_oppcat_1(C,k2_oppcat_1(A),B) -> m2_cat_1(k7_oppcat_1(A,B,C),A,B))))))) # label(t39_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9765 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) & v1_cat_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) -> k9_oppcat_1(A,k2_oppcat_1(B),k9_oppcat_1(A,B,C)) = C)))))) # label(t51_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9766 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_oppcat_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),k3_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),k2_cat_1(A,D)) = k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)))))))))) # label(t33_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9767 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (v6_cat_1(k3_oppcat_1(A,B),k2_oppcat_1(A)) <-> v7_cat_1(B,A)))))) # label(t26_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9768 (all A (v2_cat_1(A) & l1_cat_1(A) -> k10_oppcat_1(A) = k9_oppcat_1(A,A,k15_cat_1(A)))) # label(d10_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9769 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_oppcat_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(t32_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9770 (all A (l1_cat_1(A) & v2_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)) = k2_oppcat_1(k2_oppcat_1(A)))) # label(t2_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9771 (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)) -> k3_oppcat_1(B,k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D)) = k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(k2_oppcat_1(B)),k12_cat_1(k2_oppcat_1(A),k2_oppcat_1(B),k9_oppcat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C))),k3_oppcat_1(A,D)))))))))) # label(t62_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9772 (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 (k10_cat_1(B,E) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) & m1_subset_1(E,u1_cat_1(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,k2_cat_1(A,D))) & k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k3_cat_1(A,D))) = k10_cat_1(B,k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))))) & (all D (m1_subset_1(D,u2_cat_1(A)) -> (all E (m1_subset_1(E,u2_cat_1(A)) -> (k2_cat_1(A,E) = k3_cat_1(A,D) -> k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k4_cat_1(A,D,E)) = k4_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))))))) <-> m1_oppcat_1(C,A,B)))))))) # label(d7_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9773 (all A all B all C (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) & v2_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> v1_funct_1(k8_oppcat_1(A,B,C)) & m2_relset_1(k8_oppcat_1(A,B,C),u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B)) & v1_funct_2(k8_oppcat_1(A,B,C),u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B)))) # label(dt_k8_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9774 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (v3_cat_1(k5_oppcat_1(A,B),k2_oppcat_1(A)) <-> v4_cat_1(B,A)))))) # label(t23_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9775 (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,C) = k3_cat_1(A,B) -> k4_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,C),k5_oppcat_1(A,B)) = k5_oppcat_1(A,k4_cat_1(A,B,C))))))))) # label(t17_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9776 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_oppcat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D) = k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(B),k12_cat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C)),k3_oppcat_1(A,D)))))))))) # label(t45_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9777 (all A all B (v2_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & l1_cat_1(A) -> (all C (m1_oppcat_1(C,A,B) -> 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))))) # label(dt_m1_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9778 (all A all B (v2_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) & l1_cat_1(A) -> m1_subset_1(k3_oppcat_1(A,B),u1_cat_1(k2_oppcat_1(A))))) # label(dt_k3_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9779 (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(k2_oppcat_1(A),k5_oppcat_1(A,C)) = k2_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,B)) -> k4_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,C),k5_oppcat_1(A,B)) = k5_oppcat_1(A,k4_cat_1(A,B,C))))))))) # label(t18_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9780 (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,u2_cat_1(A)) -> (r2_hidden(k5_oppcat_1(A,D),k6_cat_1(k2_oppcat_1(A),k3_oppcat_1(A,C),k3_oppcat_1(A,B))) <-> r2_hidden(D,k6_cat_1(A,B,C))))))))))) # label(t13_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9781 (all A (v2_cat_1(A) & l1_cat_1(A) -> m1_oppcat_1(k10_oppcat_1(A),A,k2_oppcat_1(A)))) # label(dt_k10_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9782 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (v7_cat_1(k3_oppcat_1(A,B),k2_oppcat_1(A)) <-> v6_cat_1(B,A)))))) # label(t27_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9783 (all A (l1_cat_1(A) & v2_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 (v1_funct_2(D,u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B)) & m2_relset_1(D,u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B)) & v1_funct_1(D) -> ((all E (m1_subset_1(E,u2_cat_1(k2_oppcat_1(A))) -> k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k6_oppcat_1(A,E)) = k8_funct_2(u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B),D,E))) <-> D = k8_oppcat_1(A,B,C)))))))))) # label(d8_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9784 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> k5_oppcat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)) = k8_funct_2(u2_cat_1(k2_oppcat_1(A)),u2_cat_1(k2_oppcat_1(B)),k9_oppcat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C)),k5_oppcat_1(A,D)))))))))) # label(t47_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9785 (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 (m1_oppcat_1(D,A,B) -> (all E (m2_cat_1(E,B,C) -> m1_oppcat_1(k7_funct_2(u2_cat_1(A),u2_cat_1(B),u2_cat_1(C),D,E),A,C))))))))))) # label(t60_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9786 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (v5_cat_1(k5_oppcat_1(A,B),k2_oppcat_1(A)) <-> v5_cat_1(B,A)))))) # label(t25_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9787 (all A all B (v2_cat_1(A) & l1_cat_1(A) & m1_subset_1(B,u2_cat_1(k2_oppcat_1(A))) -> m1_subset_1(k6_oppcat_1(A,B),u2_cat_1(A)))) # label(dt_k6_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9788 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) -> k8_oppcat_1(A,B,C) = k7_funct_2(u2_cat_1(k2_oppcat_1(A)),u2_cat_1(A),u2_cat_1(B),k11_oppcat_1(A),C) & k7_funct_2(u2_cat_1(A),u2_cat_1(B),u2_cat_1(k2_oppcat_1(B)),C,k10_oppcat_1(B)) = k9_oppcat_1(A,B,C))))))) # label(t70_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9789 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_oppcat_1(C,A,B) -> m2_cat_1(k9_oppcat_1(A,B,C),A,k2_oppcat_1(B)))))))) # label(t57_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9790 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(k2_oppcat_1(A))) -> k6_oppcat_1(A,k10_cat_1(k2_oppcat_1(A),B)) = k10_cat_1(A,k4_oppcat_1(A,B)))))) # label(t22_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9791 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> k2_cat_1(A,B) = k3_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,B)) & k2_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,B)) = k3_cat_1(A,B))))) # label(t9_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9792 (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) -> m1_oppcat_1(k9_oppcat_1(A,B,C),A,k2_oppcat_1(B)))))))) # label(t59_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9793 (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) -> k9_oppcat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C)) = k8_oppcat_1(A,k2_oppcat_1(B),k9_oppcat_1(A,B,C)))))))) # label(t50_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9794 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_oppcat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> k8_funct_2(u1_cat_1(A),u1_cat_1(k2_oppcat_1(B)),k12_cat_1(A,k2_oppcat_1(B),k9_oppcat_1(A,B,C)),D) = k3_oppcat_1(B,k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D)))))))))) # label(t46_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9795 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(k2_oppcat_1(A))) -> k6_oppcat_1(A,B) = k5_oppcat_1(k2_oppcat_1(A),B))))) # label(d5_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9796 (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) -> -(k4_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,F),k5_oppcat_1(A,E)) != k5_oppcat_1(A,k9_cat_1(A,B,C,D,E,F)) & k6_cat_1(A,C,D) != k1_xboole_0 & k1_xboole_0 != k6_cat_1(A,B,C)))))))))))))) # label(t20_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9797 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D) = k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(B),k12_cat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C)),k3_oppcat_1(A,D)))))))))) # label(t42_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9798 (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,k2_oppcat_1(A),B) -> m1_oppcat_1(k7_oppcat_1(A,B,C),A,B))))))) # label(t35_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9799 (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(k2_oppcat_1(A)),k12_cat_1(A,k2_oppcat_1(A),k10_oppcat_1(A)),B) = k3_oppcat_1(A,B))))) # label(t67_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9800 (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(k2_oppcat_1(A)),u2_cat_1(B)) & v1_funct_2(C,u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B)) -> k8_oppcat_1(A,B,k7_oppcat_1(A,B,C)) = C)))))) # label(t49_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9801 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(k2_oppcat_1(A))) -> k8_funct_2(u2_cat_1(k2_oppcat_1(A)),u2_cat_1(A),k11_oppcat_1(A),B) = k6_oppcat_1(A,B))))) # label(t68_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9802 (all A all B all C all D (-v1_xboole_0(C) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) & -v1_xboole_0(B) & -v1_xboole_0(A) -> v1_funct_1(k1_oppcat_1(A,B,C,D)) & m2_relset_1(k1_oppcat_1(A,B,C,D),k2_zfmisc_1(B,A),C))) # label(dt_k1_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9803 (all A all B (m1_subset_1(B,u2_cat_1(A)) & l1_cat_1(A) & v2_cat_1(A) -> m1_subset_1(k5_oppcat_1(A,B),u2_cat_1(k2_oppcat_1(A))))) # label(dt_k5_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9804 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(k2_oppcat_1(A))) -> (all C (m1_subset_1(C,u2_cat_1(k2_oppcat_1(A))) -> (k2_cat_1(k2_oppcat_1(A),C) = k3_cat_1(k2_oppcat_1(A),B) -> k4_cat_1(A,k6_oppcat_1(A,C),k6_oppcat_1(A,B)) = k6_oppcat_1(A,k4_cat_1(k2_oppcat_1(A),B,C))))))))) # label(t19_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9805 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_oppcat_1(C,k2_oppcat_1(A),B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(B),k12_cat_1(k2_oppcat_1(A),B,C),k3_oppcat_1(A,D)) = k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,k7_oppcat_1(A,B,C)),D))))))))) # label(t37_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9806 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> k8_funct_2(u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B),k8_oppcat_1(A,B,C),k5_oppcat_1(A,D)) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))))))))) # label(t40_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9807 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> B = k4_oppcat_1(A,k3_oppcat_1(A,B)))))) # label(t4_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9808 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(k2_oppcat_1(A))) -> k4_oppcat_1(A,B) = k3_oppcat_1(k2_oppcat_1(A),B))))) # label(d3_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9809 (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) -> m2_cat_1(k9_oppcat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C)),k2_oppcat_1(A),k2_oppcat_1(B)))))))) # label(t64_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9810 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v1_funct_2(C,u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B)) & m2_relset_1(C,u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,u2_cat_1(k2_oppcat_1(A))) -> k8_funct_2(u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B),C,D) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),k7_oppcat_1(A,B,C),k6_oppcat_1(A,D)))))))))) # label(t28_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9811 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(k2_oppcat_1(A))) -> B = k3_oppcat_1(A,k4_oppcat_1(A,B)))))) # label(t5_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9812 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(k2_oppcat_1(A))) -> k2_cat_1(k2_oppcat_1(A),B) = k3_cat_1(A,k6_oppcat_1(A,B)) & k2_cat_1(A,k6_oppcat_1(A,B)) = k3_cat_1(k2_oppcat_1(A),B))))) # label(t10_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.60 9813 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(k2_oppcat_1(A))) -> (all C (m1_subset_1(C,u1_cat_1(k2_oppcat_1(A))) -> (all D (m1_subset_1(D,u2_cat_1(k2_oppcat_1(A))) -> (r2_hidden(k6_oppcat_1(A,D),k6_cat_1(A,k4_oppcat_1(A,C),k4_oppcat_1(A,B))) <-> r2_hidden(D,k6_cat_1(k2_oppcat_1(A),B,C))))))))))) # label(t14_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9814 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> k5_oppcat_1(k2_oppcat_1(A),k5_oppcat_1(A,B)) = B)))) # label(t6_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9815 (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,k2_oppcat_1(A),B) -> (all D (m1_subset_1(D,u1_cat_1(k2_oppcat_1(A))) -> k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(B),k12_cat_1(k2_oppcat_1(A),B,C),D) = k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,k7_oppcat_1(A,B,C)),k4_oppcat_1(A,D)))))))))) # label(t30_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9816 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> k6_oppcat_1(A,k5_oppcat_1(A,B)) = B)))) # label(t7_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9817 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_oppcat_1(C,A,B) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (all E (m1_subset_1(E,u2_cat_1(A)) -> (k2_cat_1(A,E) = k3_cat_1(A,D) -> k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)) = k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))))))))))))) # label(t34_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9818 (all A (l1_cat_1(A) & v2_cat_1(A) -> k11_oppcat_1(A) = k8_oppcat_1(A,A,k15_cat_1(A)))) # label(d11_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9819 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> B = k3_oppcat_1(k2_oppcat_1(A),k3_oppcat_1(A,B)))))) # label(t3_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9820 (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 (v1_funct_1(D) & m2_relset_1(D,u2_cat_1(A),u2_cat_1(B)) & v1_funct_2(D,u2_cat_1(A),u2_cat_1(B)) -> (all E (v1_funct_1(E) & m2_relset_1(E,u2_cat_1(B),u2_cat_1(C)) & v1_funct_2(E,u2_cat_1(B),u2_cat_1(C)) -> k7_funct_2(u2_cat_1(k2_oppcat_1(A)),u2_cat_1(k2_oppcat_1(B)),u2_cat_1(k2_oppcat_1(C)),k9_oppcat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,D)),k9_oppcat_1(k2_oppcat_1(B),C,k8_oppcat_1(B,C,E))) = k9_oppcat_1(k2_oppcat_1(A),C,k8_oppcat_1(A,C,k7_funct_2(u2_cat_1(A),u2_cat_1(B),u2_cat_1(C),D,E))))))))))))) # label(t55_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9821 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_oppcat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(k2_oppcat_1(B)),k12_cat_1(k2_oppcat_1(A),k2_oppcat_1(B),k9_oppcat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C))),k3_oppcat_1(A,D)) = k3_oppcat_1(B,k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D)))))))))) # label(t63_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9822 (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,k2_oppcat_1(A),B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(B),k12_cat_1(k2_oppcat_1(A),B,C),k3_oppcat_1(A,D)) = k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,k7_oppcat_1(A,B,C)),D))))))))) # label(t29_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9823 (all A (l1_cat_1(A) & v2_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(k2_oppcat_1(A)),u2_cat_1(B)) & v1_funct_2(C,u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B)) -> (all D (v1_funct_2(D,u2_cat_1(A),u2_cat_1(B)) & m2_relset_1(D,u2_cat_1(A),u2_cat_1(B)) & v1_funct_1(D) -> (D = k7_oppcat_1(A,B,C) <-> (all E (m1_subset_1(E,u2_cat_1(A)) -> k8_funct_2(u2_cat_1(A),u2_cat_1(B),D,E) = k8_funct_2(u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B),C,k5_oppcat_1(A,E))))))))))))) # label(d6_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9824 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> k5_oppcat_1(A,B) = B)))) # label(d4_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9825 (all A all B all C (v2_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v1_funct_2(C,u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B)) & m1_relset_1(C,u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B)) & v1_funct_1(C) & l1_cat_1(A) -> v1_funct_1(k7_oppcat_1(A,B,C)) & m2_relset_1(k7_oppcat_1(A,B,C),u2_cat_1(A),u2_cat_1(B)) & v1_funct_2(k7_oppcat_1(A,B,C),u2_cat_1(A),u2_cat_1(B)))) # label(dt_k7_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9826 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_oppcat_1(C,A,B) -> m2_cat_1(k8_oppcat_1(A,B,C),k2_oppcat_1(A),B))))))) # label(t56_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9827 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(k2_oppcat_1(A))) -> (all C (m1_subset_1(C,u1_cat_1(k2_oppcat_1(A))) -> (all D (m1_cat_1(D,k2_oppcat_1(A),B,C) -> (k1_xboole_0 != k6_cat_1(k2_oppcat_1(A),B,C) -> m1_cat_1(k6_oppcat_1(A,D),A,k4_oppcat_1(A,C),k4_oppcat_1(A,B))))))))))) # label(t16_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9828 (all A (v2_cat_1(A) & l1_cat_1(A) -> v1_cat_1(k2_oppcat_1(A)) & l1_cat_1(k2_oppcat_1(A)) & v2_cat_1(k2_oppcat_1(A)))) # label(dt_k2_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9829 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_1(C) -> k7_oppcat_1(A,B,k8_oppcat_1(A,B,C)) = C)))))) # label(t48_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9830 (all A (v2_cat_1(A) & l1_cat_1(A) -> k2_oppcat_1(A) = g1_cat_1(u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),k1_oppcat_1(u2_cat_1(A),u2_cat_1(A),u2_cat_1(A),u5_cat_1(A)),u6_cat_1(A)))) # label(d1_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9831 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> k5_oppcat_1(A,B) = k8_funct_2(u2_cat_1(A),u2_cat_1(k2_oppcat_1(A)),k10_oppcat_1(A),B))))) # label(t66_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9832 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_oppcat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(k2_oppcat_1(A))) -> k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),k4_oppcat_1(A,D)) = k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(B),k12_cat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C)),D))))))))) # label(t44_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9833 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_oppcat_1(C,A,B) -> m1_oppcat_1(k9_oppcat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C)),k2_oppcat_1(A),k2_oppcat_1(B)))))))) # label(t65_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9834 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> k2_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,B)) = k3_oppcat_1(A,k3_cat_1(A,B)) & k3_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,B)) = k3_oppcat_1(A,k2_cat_1(A,B)))))) # label(t11_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9835 (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 (m1_oppcat_1(E,B,C) -> m1_oppcat_1(k7_funct_2(u2_cat_1(A),u2_cat_1(B),u2_cat_1(C),D,E),A,C))))))))))) # label(t61_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9836 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(k2_oppcat_1(A))) -> B = k5_oppcat_1(A,k6_oppcat_1(A,B)))))) # label(t8_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9837 (all A all B all C all D (-v1_xboole_0(B) & v1_funct_1(D) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & -v1_xboole_0(C) & -v1_xboole_0(A) -> k2_funct_4(D) = k1_oppcat_1(A,B,C,D))) # label(redefinition_k1_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9838 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(k2_oppcat_1(A))) -> k4_oppcat_1(A,k2_cat_1(k2_oppcat_1(A),B)) = k3_cat_1(A,k6_oppcat_1(A,B)) & k4_oppcat_1(A,k3_cat_1(k2_oppcat_1(A),B)) = k2_cat_1(A,k6_oppcat_1(A,B)))))) # label(t12_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9839 (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 (m1_oppcat_1(D,A,B) -> (all E (m1_oppcat_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(t36_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9840 (all A all B all C (l1_cat_1(A) & v2_cat_1(B) & v1_funct_1(C) & m1_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & l1_cat_1(B) & v2_cat_1(A) -> v1_funct_1(k9_oppcat_1(A,B,C)) & v1_funct_2(k9_oppcat_1(A,B,C),u2_cat_1(A),u2_cat_1(k2_oppcat_1(B))) & m2_relset_1(k9_oppcat_1(A,B,C),u2_cat_1(A),u2_cat_1(k2_oppcat_1(B))))) # label(dt_k9_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9841 (all A all B (l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(A) -> (exists C m1_oppcat_1(C,A,B)))) # label(existence_m1_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9842 (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) & m2_relset_1(D,u2_cat_1(A),u2_cat_1(k2_oppcat_1(B))) & v1_funct_2(D,u2_cat_1(A),u2_cat_1(k2_oppcat_1(B))) -> (k9_oppcat_1(A,B,C) = D <-> (all E (m1_subset_1(E,u2_cat_1(A)) -> k5_oppcat_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(k2_oppcat_1(B)),D,E)))))))))))) # label(d9_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9843 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> k3_oppcat_1(A,B) = B)))) # label(d2_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9844 (all A all B (v2_cat_1(A) & m1_subset_1(B,u1_cat_1(k2_oppcat_1(A))) & l1_cat_1(A) -> m1_subset_1(k4_oppcat_1(A,B),u1_cat_1(A)))) # label(dt_k4_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9845 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_oppcat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> (k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,E) -> E = k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D)))))))))))) # label(t31_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9846 (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(k2_oppcat_1(A))) -> k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(B),k12_cat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C)),D) = k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),k4_oppcat_1(A,D)))))))))) # label(t41_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9847 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> k8_funct_2(u1_cat_1(A),u1_cat_1(k2_oppcat_1(B)),k12_cat_1(A,k2_oppcat_1(B),k9_oppcat_1(A,B,C)),D) = k3_oppcat_1(B,k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D)))))))))) # label(t43_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9848 (all A (v2_cat_1(A) & l1_cat_1(A) -> m1_oppcat_1(k11_oppcat_1(A),k2_oppcat_1(A),A))) # label(dt_k11_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9849 (all A (l1_cat_1(A) & v2_cat_1(A) -> v2_cat_1(g1_cat_1(u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),k1_oppcat_1(u2_cat_1(A),u2_cat_1(A),u2_cat_1(A),u5_cat_1(A)),u6_cat_1(A))) & l1_cat_1(g1_cat_1(u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),k1_oppcat_1(u2_cat_1(A),u2_cat_1(A),u2_cat_1(A),u5_cat_1(A)),u6_cat_1(A))))) # label(t1_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9850 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (v4_cat_1(k5_oppcat_1(A,B),k2_oppcat_1(A)) <-> v3_cat_1(B,A)))))) # label(t24_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9851 (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_relset_1(D,u2_cat_1(A),u2_cat_1(B)) & v1_funct_2(D,u2_cat_1(A),u2_cat_1(B)) & v1_funct_1(D) -> (all E (v1_funct_2(E,u2_cat_1(B),u2_cat_1(C)) & m2_relset_1(E,u2_cat_1(B),u2_cat_1(C)) & v1_funct_1(E) -> k9_oppcat_1(A,C,k7_funct_2(u2_cat_1(A),u2_cat_1(B),u2_cat_1(C),D,E)) = k7_funct_2(u2_cat_1(A),u2_cat_1(B),u2_cat_1(k2_oppcat_1(C)),D,k9_oppcat_1(B,C,E)))))))))))) # label(t54_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9852 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (k6_cat_1(A,B,C) != k1_xboole_0 -> m1_cat_1(k5_oppcat_1(A,D),k2_oppcat_1(A),k3_oppcat_1(A,C),k3_oppcat_1(A,B))))))))))) # label(t15_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9853 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v1_cat_1(B) & l1_cat_1(B) & v2_cat_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u2_cat_1(B),u2_cat_1(A)) & m2_relset_1(C,u2_cat_1(B),u2_cat_1(A)) -> k8_oppcat_1(k2_oppcat_1(B),A,k8_oppcat_1(B,A,C)) = C)))))) # label(t52_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9854 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k2_filter_0(A,C) = k2_filter_0(A,B) -> C = B))))))) # label(t2_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9855 (all A all B all C (-v3_struct_0(A) & m1_subset_1(C,u1_struct_0(A)) & m1_filter_0(B,A) & l3_lattices(A) & v10_lattices(A) -> m1_subset_1(k6_filter_1(A,B,C),u1_struct_0(k5_filter_1(A,B))))) # label(dt_k6_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9856 (all A all B all C (-v3_struct_0(A) & m1_filter_0(B,A) & m1_filter_0(C,A) & l3_lattices(A) & v10_lattices(A) -> m1_filter_0(k1_filter_1(A,B,C),A))) # label(dt_k1_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9857 (all A (v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> r3_lattices(A,k4_lattices(A,k4_filter_0(A,B,C),k4_filter_0(A,D,C)),k4_filter_0(A,k3_lattices(A,B,D),C)))))))))) # label(t57_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9858 (all A (-v3_struct_0(A) & l3_lattices(A) & v3_filter_0(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (all F (m1_subset_1(F,u1_struct_0(A)) -> (r2_hidden(k9_filter_0(A,E,F),B) & r2_hidden(k9_filter_0(A,C,D),B) -> r2_hidden(k9_filter_0(A,k4_lattices(A,C,E),k4_lattices(A,D,F)),B) & r2_hidden(k9_filter_0(A,k3_lattices(A,C,E),k3_lattices(A,D,F)),B)))))))))))))) # label(t59_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9859 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (v10_lattices(B) & l3_lattices(B) & -v3_struct_0(B) -> (l3_lattices(A) & -v3_struct_0(B) & v10_lattices(B) & v13_lattices(B) & l3_lattices(B) & v13_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> k10_filter_1(A,B,k5_lattices(A),k5_lattices(B)) = k5_lattices(k8_filter_1(A,B))))))) # label(t43_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9860 (all A (v10_lattices(A) & l3_lattices(A) & v3_filter_0(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> m2_filter_1(u1_lattices(A),u1_struct_0(A),k11_filter_0(A,B)))))) # label(t14_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9861 (all A (-v3_struct_0(A) & l3_lattices(A) & v3_filter_0(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> m2_filter_1(u2_lattices(A),u1_struct_0(A),k11_filter_0(A,B)))))) # label(t13_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9862 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> u1_struct_0(A) = k1_relat_1(k9_filter_1(A)) & k2_relat_1(k9_filter_1(A)) = u1_struct_0(A) & u1_struct_0(A) = k3_relat_1(k9_filter_1(A)))) # label(t33_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9863 (all A all B (-v3_struct_0(A) & l3_lattices(A) & -v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) & v10_lattices(A) -> (r1_filter_1(A,B) -> r1_filter_1(B,A)))) # label(symmetry_r1_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9864 (all A all B (-v1_xboole_0(A) & v1_relat_1(B) -> (exists C m1_filter_1(C,A,B)))) # label(existence_m1_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9865 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (m2_relset_1(D,k2_zfmisc_1(B,B),B) & v1_funct_2(D,k2_zfmisc_1(B,B),B) & v1_funct_1(D) -> (v1_binop_1(D,B) & v1_binop_1(C,A) <-> v1_binop_1(k7_filter_1(A,B,C,D),k2_zfmisc_1(A,B))))))))))) # label(t23_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9866 (all A (-v3_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k4_lattices(A,B,k7_lattices(A,C)) = k7_lattices(A,k4_filter_0(A,B,C)) & k7_lattices(A,k9_filter_0(A,B,C)) = k3_lattices(A,k4_lattices(A,B,k7_lattices(A,C)),k4_lattices(A,k7_lattices(A,B),C)) & k9_filter_0(A,B,k7_lattices(A,C)) = k7_lattices(A,k9_filter_0(A,B,C)) & k7_lattices(A,k9_filter_0(A,B,C)) = k9_filter_0(A,k7_lattices(A,B),C))))))) # label(t52_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9867 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> k2_filter_1(A,B,C) = k6_eqrel_1(A,B,C))) # label(redefinition_k2_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9868 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) -> (l3_lattices(A) & v3_filter_0(A) & v10_lattices(A) & -v3_struct_0(A) -> (all C (v10_lattices(C) & l3_lattices(C) & v3_lattices(C) & -v3_struct_0(C) -> (C = k5_filter_1(A,B) <-> (all D (v3_relat_2(D) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) & v1_partfun1(D,u1_struct_0(A),u1_struct_0(A)) & v8_relat_2(D) -> (k10_filter_0(A,B) = D -> g3_lattices(k8_eqrel_1(u1_struct_0(A),D),k4_filter_1(u1_struct_0(A),D,u2_lattices(A)),k4_filter_1(u1_struct_0(A),D,u1_lattices(A))) = C))))))))))) # label(d5_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9869 (all A (-v1_xboole_0(A) -> (all B (v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v8_relat_2(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) -> (m1_filter_1(C,A,B) -> (all D (m2_relset_1(D,k8_eqrel_1(A,B),k8_eqrel_1(A,B)) & v1_funct_2(D,k8_eqrel_1(A,B),k8_eqrel_1(A,B)) & v1_funct_1(D) -> ((all E all F (r2_hidden(F,E) & r2_hidden(E,k8_eqrel_1(A,B)) -> k1_funct_1(D,E) = k6_eqrel_1(A,B,k1_funct_1(C,F)))) <-> D = k3_filter_1(A,B,C))))))))))) # label(d3_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9870 (all A all B (-v1_xboole_0(A) & v1_relat_1(B) -> (all C (m2_filter_1(C,A,B) -> v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A))))) # label(dt_m2_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9871 (all A (m1_subset_1(A,f1_s3_filter_1) -> (all B (m1_subset_1(B,f1_s3_filter_1) -> (all C (m1_subset_1(C,f1_s3_filter_1) -> p1_s3_filter_1(k2_filter_1(f1_s3_filter_1,f2_s3_filter_1,A),k2_filter_1(f1_s3_filter_1,f2_s3_filter_1,B),k2_filter_1(f1_s3_filter_1,f2_s3_filter_1,C)))))))) -> (all A (m2_subset_1(A,k1_zfmisc_1(f1_s3_filter_1),k8_eqrel_1(f1_s3_filter_1,f2_s3_filter_1)) -> (all B (m2_subset_1(B,k1_zfmisc_1(f1_s3_filter_1),k8_eqrel_1(f1_s3_filter_1,f2_s3_filter_1)) -> (all C (m2_subset_1(C,k1_zfmisc_1(f1_s3_filter_1),k8_eqrel_1(f1_s3_filter_1,f2_s3_filter_1)) -> p1_s3_filter_1(A,B,C))))))) # label(s3_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9872 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (v10_lattices(B) & l3_lattices(B) & -v3_struct_0(B) -> (r4_wellord1(k9_filter_1(A),k9_filter_1(B)) <-> r1_filter_1(A,B)))))) # label(d9_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9873 (all A (m1_subset_1(A,f1_s2_filter_1) -> (all B (m1_subset_1(B,f1_s2_filter_1) -> p1_s2_filter_1(k2_filter_1(f1_s2_filter_1,f2_s2_filter_1,A),k2_filter_1(f1_s2_filter_1,f2_s2_filter_1,B)))))) -> (all A (m2_subset_1(A,k1_zfmisc_1(f1_s2_filter_1),k8_eqrel_1(f1_s2_filter_1,f2_s2_filter_1)) -> (all B (m2_subset_1(B,k1_zfmisc_1(f1_s2_filter_1),k8_eqrel_1(f1_s2_filter_1,f2_s2_filter_1)) -> p1_s2_filter_1(A,B))))) # label(s2_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9874 (all A (-v1_xboole_0(A) -> (all B (v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v3_relat_2(B) -> (all C (m2_filter_1(C,A,B) -> (all D (m2_filter_1(D,A,B) -> (r5_binop_1(A,C,D) -> r5_binop_1(k8_eqrel_1(A,B),k4_filter_1(A,B,C),k4_filter_1(A,B,D))))))))))) # label(t10_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9875 (all A all B (-v3_struct_0(A) & -v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) & l3_lattices(A) & v10_lattices(A) -> v4_lattices(k8_filter_1(A,B)) & v5_lattices(k8_filter_1(A,B)) & v6_lattices(k8_filter_1(A,B)) & v7_lattices(k8_filter_1(A,B)) & v8_lattices(k8_filter_1(A,B)) & v10_lattices(k8_filter_1(A,B)) & v9_lattices(k8_filter_1(A,B)) & v3_lattices(k8_filter_1(A,B)) & -v3_struct_0(k8_filter_1(A,B)))) # label(fc3_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9876 (all A (m1_subset_1(A,f1_s6_filter_1) -> (all B (m1_subset_1(B,f1_s6_filter_1) -> (all C (m1_subset_1(C,f1_s6_filter_1) -> (all D (m1_subset_1(D,f2_s6_filter_1) -> (all E (m1_subset_1(E,f2_s6_filter_1) -> (all F (m1_subset_1(F,f2_s6_filter_1) -> p1_s6_filter_1(k1_domain_1(f1_s6_filter_1,f2_s6_filter_1,A,D),k1_domain_1(f1_s6_filter_1,f2_s6_filter_1,B,E),k1_domain_1(f1_s6_filter_1,f2_s6_filter_1,C,F)))))))))))))) -> (all A (m1_subset_1(A,k2_zfmisc_1(f1_s6_filter_1,f2_s6_filter_1)) -> (all B (m1_subset_1(B,k2_zfmisc_1(f1_s6_filter_1,f2_s6_filter_1)) -> (all C (m1_subset_1(C,k2_zfmisc_1(f1_s6_filter_1,f2_s6_filter_1)) -> p1_s6_filter_1(A,B,C))))))) # label(s6_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9877 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) -> (all E (m2_relset_1(E,k2_zfmisc_1(B,B),B) & v1_funct_2(E,k2_zfmisc_1(B,B),B) & v1_funct_1(E) -> (all F (m2_relset_1(F,k2_zfmisc_1(B,B),B) & v1_funct_2(F,k2_zfmisc_1(B,B),B) & v1_funct_1(F) -> (r1_lattice2(k2_zfmisc_1(A,B),k7_filter_1(A,B,C,E),k7_filter_1(A,B,D,F)) <-> r1_lattice2(B,E,F) & r1_lattice2(A,C,D)))))))))))))) # label(t31_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9878 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> (r3_lattices(k8_filter_1(A,B),k10_filter_1(A,B,C,E),k10_filter_1(A,B,D,F)) <-> r3_lattices(B,E,F) & r3_lattices(A,C,D)))))))))))))) # label(t37_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9879 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (-v3_struct_0(B) & l3_lattices(B) & v10_lattices(B) -> (v12_lattices(B) & v12_lattices(A) <-> v12_lattices(k8_filter_1(A,B))))))) # label(t38_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9880 (all A all B all C (-v3_struct_0(A) & m1_filter_0(C,A) & m1_filter_0(B,A) & l3_lattices(A) & v10_lattices(A) -> k1_filter_1(A,B,C) = k3_xboole_0(B,C))) # label(redefinition_k1_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9881 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(A,A),A) & m2_relset_1(E,k2_zfmisc_1(A,A),A) -> (all F (v1_funct_1(F) & m2_relset_1(F,k2_zfmisc_1(B,B),B) & v1_funct_2(F,k2_zfmisc_1(B,B),B) -> (r3_binop_1(B,D,F) & r3_binop_1(A,C,E) <-> r3_binop_1(k2_zfmisc_1(A,B),k1_domain_1(A,B,C,D),k7_filter_1(A,B,E,F))))))))))))))) # label(t27_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9882 (all A all B (-v3_struct_0(A) & l3_lattices(A) & -v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) & v10_lattices(A) -> r1_filter_1(A,A))) # label(reflexivity_r1_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9883 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> (l3_lattices(A) & -v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) & v15_lattices(B) & v15_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (r2_lattices(B,E,F) & r2_lattices(A,C,D) <-> r2_lattices(k8_filter_1(A,B),k10_filter_1(A,B,C,E),k10_filter_1(A,B,D,F)))))))))))))))) # label(t45_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9884 (all A (l3_lattices(A) & v3_filter_0(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k6_filter_1(A,B,k3_lattices(A,C,D)) = k3_lattices(k5_filter_1(A,B),k6_filter_1(A,B,C),k6_filter_1(A,B,D)) & k6_filter_1(A,B,k4_lattices(A,C,D)) = k4_lattices(k5_filter_1(A,B),k6_filter_1(A,B,C),k6_filter_1(A,B,D)))))))))) # label(t15_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9885 (all A all B all C all D (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & m1_relset_1(D,k2_zfmisc_1(B,B),B) & v1_funct_2(D,k2_zfmisc_1(B,B),B) & m1_relset_1(C,k2_zfmisc_1(A,A),A) -> v1_funct_1(k7_filter_1(A,B,C,D)) & v1_funct_2(k7_filter_1(A,B,C,D),k2_zfmisc_1(k2_zfmisc_1(A,B),k2_zfmisc_1(A,B)),k2_zfmisc_1(A,B)) & m2_relset_1(k7_filter_1(A,B,C,D),k2_zfmisc_1(k2_zfmisc_1(A,B),k2_zfmisc_1(A,B)),k2_zfmisc_1(A,B)))) # label(dt_k7_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9886 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l3_lattices(B) & v10_lattices(B) -> (-v3_struct_0(k8_filter_1(A,B)) & v15_lattices(k8_filter_1(A,B)) & l3_lattices(k8_filter_1(A,B)) & v16_lattices(k8_filter_1(A,B)) & v10_lattices(k8_filter_1(A,B)) <-> v15_lattices(A) & v16_lattices(A) & v16_lattices(B) & l3_lattices(B) & v15_lattices(B) & v10_lattices(B) & -v3_struct_0(B) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A)))))) # label(t46_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9887 (all A (l3_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l3_lattices(B) -> (-v3_struct_0(k8_filter_1(A,B)) & l3_lattices(k8_filter_1(A,B)) & v10_lattices(k8_filter_1(A,B)) -> -v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & -v3_struct_0(B) & v10_lattices(B) & l3_lattices(B)))))) # label(t35_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9888 (all A (l3_lattices(A) & v3_filter_0(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k4_filter_0(A,C,B) = k4_filter_0(A,k3_lattices(A,B,C),B) & k4_filter_0(A,B,C) = k4_filter_0(A,B,k4_lattices(A,B,C)))))))) # label(t55_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9889 (all A (-v3_struct_0(A) & l3_lattices(A) & v17_lattices(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> v17_lattices(k5_filter_1(A,B)) & l3_lattices(k5_filter_1(A,B)) & v10_lattices(k5_filter_1(A,B)) & -v3_struct_0(k5_filter_1(A,B)))))) # label(t21_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9890 (all A (v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r3_lattices(k5_filter_1(A,B),k6_filter_1(A,B,C),k6_filter_1(A,B,D)) <-> r2_hidden(k4_filter_0(A,C,D),B)))))))))) # label(t16_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9891 (all A all B (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & -v1_xboole_0(A) -> -v1_xboole_0(k7_eqrel_1(A,B)))) # label(fc1_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9892 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & v10_lattices(C) & l3_lattices(C) -> (r1_filter_1(B,C) & r1_filter_1(A,B) -> r1_filter_1(A,C)))))))) # label(t34_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9893 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v3_filter_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> r3_lattices(A,k4_lattices(A,k4_filter_0(A,B,C),k4_filter_0(A,B,D)),k4_filter_0(A,B,k4_lattices(A,C,D))))))))))) # label(t58_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9894 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (v10_lattices(B) & l3_lattices(B) & -v3_struct_0(B) -> (v3_filter_0(B) & v3_filter_0(A) <-> v3_filter_0(k8_filter_1(A,B))))))) # label(t48_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9895 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (v10_lattices(A) & l3_lattices(A) & v3_filter_0(A) & -v3_struct_0(A) -> (all D (m1_subset_1(D,u1_struct_0(k5_filter_1(A,B))) -> ((all E (v8_relat_2(E) & v1_partfun1(E,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(E,u1_struct_0(A),u1_struct_0(A)) & v3_relat_2(E) -> (E = k10_filter_0(A,B) -> k2_filter_1(u1_struct_0(A),E,C) = D))) <-> D = k6_filter_1(A,B,C))))))))))) # label(d6_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9896 (all A (m1_subset_1(A,f1_s5_filter_1) -> (all B (m1_subset_1(B,f1_s5_filter_1) -> (all C (m1_subset_1(C,f2_s5_filter_1) -> (all D (m1_subset_1(D,f2_s5_filter_1) -> p1_s5_filter_1(k1_domain_1(f1_s5_filter_1,f2_s5_filter_1,A,C),k1_domain_1(f1_s5_filter_1,f2_s5_filter_1,B,D)))))))))) -> (all A (m1_subset_1(A,k2_zfmisc_1(f1_s5_filter_1,f2_s5_filter_1)) -> (all B (m1_subset_1(B,k2_zfmisc_1(f1_s5_filter_1,f2_s5_filter_1)) -> p1_s5_filter_1(A,B))))) # label(s5_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9897 (all A (-v1_xboole_0(A) -> (all B (v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> (all C (m2_filter_1(C,A,B) -> (all D (m2_filter_1(D,A,B) -> (r6_binop_1(A,C,D) -> r6_binop_1(k8_eqrel_1(A,B),k4_filter_1(A,B,C),k4_filter_1(A,B,D))))))))))) # label(t11_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9898 (all A (v3_filter_0(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k4_filter_0(A,B,k4_filter_0(A,C,D)) = k4_filter_0(A,k4_lattices(A,B,C),D))))))))) # label(t17_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9899 (all A (-v1_xboole_0(A) -> (all B (v1_relat_1(B) -> (all C (v1_funct_2(C,A,A) & m2_relset_1(C,A,A) & v1_funct_1(C) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (r2_hidden(k1_domain_1(A,A,D,E),B) -> r2_hidden(k1_domain_1(A,A,k8_funct_2(A,A,C,D),k8_funct_2(A,A,C,E)),B)))))) <-> m1_filter_1(C,A,B)))))))) # label(d1_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9900 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> (v15_lattices(B) & v15_lattices(A) <-> v15_lattices(k8_filter_1(A,B))))))) # label(t42_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9901 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C),k9_filter_1(A)) <-> r3_lattices(A,B,C)))))))) # label(t32_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9902 (all A all B all C all D (v10_lattices(A) & l3_lattices(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(B)) & l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) & -v3_struct_0(A) -> k4_tarski(C,D) = k10_filter_1(A,B,C,D))) # label(redefinition_k10_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9903 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l3_lattices(B) & v10_lattices(B) -> k1_lattice2(k8_filter_1(A,B)) = k8_filter_1(k1_lattice2(A),k1_lattice2(B)))))) # label(t49_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9904 (all A all B (-v1_xboole_0(A) & v1_relat_1(B) -> (all C (m1_filter_1(C,A,B) -> m2_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C))))) # label(dt_m1_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9905 (all A all B all C all D (m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(B)) & l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> m1_subset_1(k10_filter_1(A,B,C,D),u1_struct_0(k8_filter_1(A,B))))) # label(dt_k10_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9906 (all A all B (l3_lattices(B) & -v3_struct_0(B) & l3_lattices(A) & -v3_struct_0(A) -> v3_lattices(k8_filter_1(A,B)) & l3_lattices(k8_filter_1(A,B)))) # label(dt_k8_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9907 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> k10_filter_1(A,B,k3_lattices(A,C,D),k3_lattices(B,E,F)) = k3_lattices(k8_filter_1(A,B),k10_filter_1(A,B,C,E),k10_filter_1(A,B,D,F)) & k4_lattices(k8_filter_1(A,B),k10_filter_1(A,B,C,E),k10_filter_1(A,B,D,F)) = k10_filter_1(A,B,k4_lattices(A,C,D),k4_lattices(B,E,F)))))))))))))) # label(t36_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9908 (all A all B all C all D (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & m1_relset_1(D,k2_zfmisc_1(B,B),B) & v1_funct_2(D,k2_zfmisc_1(B,B),B) & v1_funct_1(D) & v1_funct_1(C) -> k3_funct_4(C,D) = k7_filter_1(A,B,C,D))) # label(redefinition_k7_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9909 (all A (v10_lattices(A) & v17_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_filter_1(A,k8_filter_1(k5_filter_1(A,k2_filter_0(A,B)),k8_filter_0(A,k2_filter_0(A,B)))))))) # label(t62_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9910 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_2(D,k2_zfmisc_1(B,B),B) & m2_relset_1(D,k2_zfmisc_1(B,B),B) & v1_funct_1(D) -> (v2_binop_1(C,A) & v2_binop_1(D,B) <-> v2_binop_1(k7_filter_1(A,B,C,D),k2_zfmisc_1(A,B))))))))))) # label(t24_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9911 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_filter_0(C,A) -> m1_filter_0(k5_subset_1(u1_struct_0(A),B,C),A))))))) # label(t1_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9912 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> (all C (m1_subset_1(C,A) -> (all D (m2_filter_1(D,A,B) -> (r3_binop_1(A,C,D) -> r3_binop_1(k8_eqrel_1(A,B),k2_filter_1(A,B,C),k4_filter_1(A,B,D))))))))))) # label(t8_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9913 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,B) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(A,A),A) & v1_funct_2(E,k2_zfmisc_1(A,A),A) -> (all F (v1_funct_2(F,k2_zfmisc_1(B,B),B) & m2_relset_1(F,k2_zfmisc_1(B,B),B) & v1_funct_1(F) -> (r1_binop_1(k2_zfmisc_1(A,B),k1_domain_1(A,B,C,D),k7_filter_1(A,B,E,F)) <-> r1_binop_1(A,C,E) & r1_binop_1(B,D,F)))))))))))))) # label(t25_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9914 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> v1_relat_1(k9_filter_1(A)))) # label(dt_k9_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9915 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (v10_lattices(B) & l3_lattices(B) & -v3_struct_0(B) -> r1_filter_1(k8_filter_1(A,B),k8_filter_1(B,A)))))) # label(t50_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9916 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (m2_filter_1(C,A,B) -> (all D (v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(k8_eqrel_1(A,B),k8_eqrel_1(A,B)),k8_eqrel_1(A,B)) & m2_relset_1(D,k2_zfmisc_1(k8_eqrel_1(A,B),k8_eqrel_1(A,B)),k8_eqrel_1(A,B)) -> (k4_filter_1(A,B,C) = D <-> (all E all F all G all H (r2_hidden(E,k8_eqrel_1(A,B)) & r2_hidden(H,F) & r2_hidden(G,E) & r2_hidden(F,k8_eqrel_1(A,B)) -> k6_eqrel_1(A,B,k1_binop_1(C,G,H)) = k1_binop_1(D,E,F))))))))))))) # label(d4_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9917 (all A (-v1_xboole_0(A) -> (all B (v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) -> (all C (m2_filter_1(C,A,B) -> (v1_binop_1(C,A) -> v1_binop_1(k4_filter_1(A,B,C),k8_eqrel_1(A,B))))))))) # label(t4_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9918 (all A (v17_lattices(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k9_filter_0(A,B,D) = k9_filter_0(A,B,C) -> D = C))))))))) # label(t53_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9919 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) -> (v13_lattices(B) & v13_lattices(A) <-> v13_lattices(k8_filter_1(A,B))))))) # label(t40_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9920 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> (v14_lattices(A) & v14_lattices(B) <-> v14_lattices(k8_filter_1(A,B))))))) # label(t41_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9921 (all A all B (-v3_struct_0(A) & m1_filter_0(B,A) & l3_lattices(A) & v10_lattices(A) -> -v3_struct_0(k5_filter_1(A,B)) & v3_lattices(k5_filter_1(A,B)) & v10_lattices(k5_filter_1(A,B)) & l3_lattices(k5_filter_1(A,B)))) # label(dt_k5_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9922 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) -> (all E (v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(B,B),B) & m2_relset_1(E,k2_zfmisc_1(B,B),B) -> (all F (v1_funct_2(F,k2_zfmisc_1(B,B),B) & m2_relset_1(F,k2_zfmisc_1(B,B),B) & v1_funct_1(F) -> (r5_binop_1(B,E,F) & r5_binop_1(A,C,D) <-> r5_binop_1(k2_zfmisc_1(A,B),k7_filter_1(A,B,C,E),k7_filter_1(A,B,D,F))))))))))))))) # label(t29_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9923 (all A (-v1_xboole_0(A) -> (all B (v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (m2_filter_1(C,A,B) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,A) -> (r2_hidden(k1_domain_1(A,A,F,G),B) & r2_hidden(k1_domain_1(A,A,D,E),B) -> r2_hidden(k1_domain_1(A,A,k2_binop_1(A,A,A,C,D,F),k2_binop_1(A,A,A,C,E,G)),B))))))))))))))))) # label(d2_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.61 9924 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) -> (v10_lattices(k8_filter_1(A,B)) & v17_lattices(k8_filter_1(A,B)) & l3_lattices(k8_filter_1(A,B)) & -v3_struct_0(k8_filter_1(A,B)) <-> -v3_struct_0(A) & v10_lattices(A) & -v3_struct_0(B) & l3_lattices(B) & v17_lattices(B) & v10_lattices(B) & l3_lattices(A) & v17_lattices(A)))))) # label(t47_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9925 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> k9_filter_1(A) = a_1_0_filter_1(A))) # label(d8_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9926 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (v10_lattices(B) & l3_lattices(B) & -v3_struct_0(B) -> (v11_lattices(k8_filter_1(A,B)) & l3_lattices(k8_filter_1(A,B)) & v10_lattices(k8_filter_1(A,B)) & -v3_struct_0(k8_filter_1(A,B)) <-> v10_lattices(A) & v11_lattices(B) & l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) & l3_lattices(A) & v11_lattices(A) & -v3_struct_0(A)))))) # label(t39_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9927 (all A all B all C (-v1_xboole_0(A) & v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & m1_subset_1(C,A) -> m2_subset_1(k2_filter_1(A,B,C),k1_zfmisc_1(A),k8_eqrel_1(A,B)))) # label(dt_k2_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9928 (all A all B (-v3_struct_0(B) & l3_lattices(B) & v10_lattices(B) -> (r2_hidden(A,a_1_0_filter_1(B)) <-> (exists C exists D (A = k1_domain_1(u1_struct_0(B),u1_struct_0(B),C,D) & r3_lattices(B,C,D) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(C,u1_struct_0(B))))))) # label(fraenkel_a_1_0_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9929 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) -> (all E (v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(B,B),B) & m2_relset_1(E,k2_zfmisc_1(B,B),B) -> (all F (v1_funct_2(F,k2_zfmisc_1(B,B),B) & m2_relset_1(F,k2_zfmisc_1(B,B),B) & v1_funct_1(F) -> (r6_binop_1(B,E,F) & r6_binop_1(A,C,D) <-> r6_binop_1(k2_zfmisc_1(A,B),k7_filter_1(A,B,C,E),k7_filter_1(A,B,D,F))))))))))))))) # label(t30_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9930 (all A all B all C (-v1_xboole_0(A) & v3_relat_2(B) & v8_relat_2(B) & m1_relset_1(B,A,A) & v1_funct_1(C) & v1_funct_2(C,A,A) & m1_relset_1(C,A,A) & v1_partfun1(B,A,A) -> v1_funct_1(k3_filter_1(A,B,C)) & v1_funct_2(k3_filter_1(A,B,C),k8_eqrel_1(A,B),k8_eqrel_1(A,B)) & m2_relset_1(k3_filter_1(A,B,C),k8_eqrel_1(A,B),k8_eqrel_1(A,B)))) # label(dt_k3_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9931 (all A (-v1_xboole_0(A) -> (all B (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m2_filter_1(E,A,B) -> k2_binop_1(k8_eqrel_1(A,B),k8_eqrel_1(A,B),k8_eqrel_1(A,B),k4_filter_1(A,B,E),k2_filter_1(A,B,C),k2_filter_1(A,B,D)) = k2_filter_1(A,B,k2_binop_1(A,A,A,E,C,D)))))))))))) # label(t3_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9932 (all A (m1_subset_1(A,f1_s1_filter_1) -> p1_s1_filter_1(k2_filter_1(f1_s1_filter_1,f2_s1_filter_1,A)))) -> (all A (m2_subset_1(A,k1_zfmisc_1(f1_s1_filter_1),k8_eqrel_1(f1_s1_filter_1,f2_s1_filter_1)) -> p1_s1_filter_1(A))) # label(s1_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9933 (all A (-v3_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k3_lattices(A,k4_lattices(A,B,C),k4_lattices(A,k7_lattices(A,B),k7_lattices(A,C))) = k9_filter_0(A,B,C))))))) # label(t51_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9934 (all A all B all C (v10_lattices(A) & l3_lattices(A) & m1_filter_0(C,A) & m1_filter_0(B,A) & -v3_struct_0(A) -> k1_filter_1(A,B,C) = k1_filter_1(A,C,B))) # label(commutativity_k1_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9935 (all A (-v1_xboole_0(A) -> (all B (v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v3_relat_2(B) -> (all C (m2_filter_1(C,A,B) -> (all D (m2_filter_1(D,A,B) -> (r1_lattice2(A,C,D) -> r1_lattice2(k8_eqrel_1(A,B),k4_filter_1(A,B,C),k4_filter_1(A,B,D))))))))))) # label(t12_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9936 (all A (-v3_struct_0(A) & v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> r3_lattices(A,k4_filter_0(A,B,C),k4_filter_0(A,B,k3_lattices(A,C,D))) & r3_lattices(A,k4_filter_0(A,B,C),k4_filter_0(A,k4_lattices(A,D,B),C)) & r3_lattices(A,k4_filter_0(A,B,C),k4_filter_0(A,B,k3_lattices(A,D,C))) & r3_lattices(A,k4_filter_0(A,B,C),k4_filter_0(A,k4_lattices(A,B,D),C)))))))))) # label(t56_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9937 (all A (-v3_struct_0(A) & v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) -> (v13_lattices(A) -> -v3_struct_0(k5_filter_1(A,B)) & v10_lattices(k5_filter_1(A,B)) & v13_lattices(k5_filter_1(A,B)) & l3_lattices(k5_filter_1(A,B)) & k5_lattices(k5_filter_1(A,B)) = k6_filter_1(A,B,k5_lattices(A))))))) # label(t18_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9938 (all A (-v1_xboole_0(A) -> (all B (v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v3_relat_2(B) -> (all C (m2_filter_1(C,A,B) -> (v2_binop_1(C,A) -> v2_binop_1(k4_filter_1(A,B,C),k8_eqrel_1(A,B))))))))) # label(t5_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9939 (all A (-v3_struct_0(A) & l3_lattices(A) & v17_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> C = k9_filter_0(A,B,k9_filter_0(A,B,C)))))))) # label(t54_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9940 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v17_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r2_hidden(k3_lattices(A,B,k9_filter_0(A,B,C)),k2_filter_1(u1_struct_0(A),k12_filter_0(A,k2_filter_0(A,C)),B)) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,k2_filter_1(u1_struct_0(A),k12_filter_0(A,k2_filter_0(A,C)),B)) -> r3_lattices(A,D,k3_lattices(A,B,k9_filter_0(A,B,C)))))))))))) # label(t61_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9941 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v3_filter_0(A) -> (all B (m1_filter_0(B,A) -> v10_lattices(k5_filter_1(A,B)) & v14_lattices(k5_filter_1(A,B)) & l3_lattices(k5_filter_1(A,B)) & k6_filter_1(A,B,k6_lattices(A)) = k6_lattices(k5_filter_1(A,B)) & -v3_struct_0(k5_filter_1(A,B)))))) # label(t19_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9942 (all A all B all C (-v3_struct_0(A) & l3_lattices(A) & m1_filter_0(C,A) & m1_filter_0(B,A) & v10_lattices(A) -> k1_filter_1(A,B,B) = B)) # label(idempotence_k1_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9943 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(A,A),A) & m2_relset_1(E,k2_zfmisc_1(A,A),A) -> (all F (v1_funct_1(F) & v1_funct_2(F,k2_zfmisc_1(B,B),B) & m2_relset_1(F,k2_zfmisc_1(B,B),B) -> (r2_binop_1(k2_zfmisc_1(A,B),k1_domain_1(A,B,C,D),k7_filter_1(A,B,E,F)) <-> r2_binop_1(B,D,F) & r2_binop_1(A,C,E)))))))))))))) # label(t26_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9944 (all A (-v1_xboole_0(A) -> (all B (v3_relat_2(B) & v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) -> (all C (m1_subset_1(C,A) -> (all D (m2_filter_1(D,A,B) -> (r2_binop_1(A,C,D) -> r2_binop_1(k8_eqrel_1(A,B),k2_filter_1(A,B,C),k4_filter_1(A,B,D))))))))))) # label(t7_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9945 (all A (-v1_xboole_0(A) -> (all B (v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v3_relat_2(B) -> (all C (m1_subset_1(C,A) -> (all D (m2_filter_1(D,A,B) -> (r1_binop_1(A,C,D) -> r1_binop_1(k8_eqrel_1(A,B),k2_filter_1(A,B,C),k4_filter_1(A,B,D))))))))))) # label(t6_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9946 (all A all B (v1_relat_1(B) & -v1_xboole_0(A) -> (exists C m2_filter_1(C,A,B)))) # label(existence_m2_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9947 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (all G (m2_relset_1(G,k2_zfmisc_1(A,A),A) & v1_funct_2(G,k2_zfmisc_1(A,A),A) & v1_funct_1(G) -> (all H (m2_relset_1(H,k2_zfmisc_1(B,B),B) & v1_funct_2(H,k2_zfmisc_1(B,B),B) & v1_funct_1(H) -> k1_domain_1(A,B,k2_binop_1(A,A,A,G,C,D),k2_binop_1(B,B,B,H,E,F)) = k2_binop_1(k2_zfmisc_1(A,B),k2_zfmisc_1(A,B),k2_zfmisc_1(A,B),k7_filter_1(A,B,G,H),k1_domain_1(A,B,C,E),k1_domain_1(A,B,D,F)))))))))))))))))) # label(t22_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9948 (all A (l3_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l3_lattices(B) -> g3_lattices(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k7_filter_1(u1_struct_0(A),u1_struct_0(B),u2_lattices(A),u2_lattices(B)),k7_filter_1(u1_struct_0(A),u1_struct_0(B),u1_lattices(A),u1_lattices(B))) = k8_filter_1(A,B))))) # label(d7_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9949 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (v10_lattices(B) & l3_lattices(B) & -v3_struct_0(B) -> (-v3_struct_0(A) & v14_lattices(A) & l3_lattices(A) & l3_lattices(B) & v14_lattices(B) & v10_lattices(B) & -v3_struct_0(B) & v10_lattices(A) -> k10_filter_1(A,B,k6_lattices(A),k6_lattices(B)) = k6_lattices(k8_filter_1(A,B))))))) # label(t44_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9950 (all A (m1_subset_1(A,f1_s4_filter_1) -> (all B (m1_subset_1(B,f2_s4_filter_1) -> p1_s4_filter_1(k1_domain_1(f1_s4_filter_1,f2_s4_filter_1,A,B)))))) -> (all A (m1_subset_1(A,k2_zfmisc_1(f1_s4_filter_1,f2_s4_filter_1)) -> p1_s4_filter_1(A))) # label(s4_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9951 (all A (-v3_struct_0(A) & l3_lattices(A) & v3_filter_0(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> v3_filter_0(k5_filter_1(A,B)))))) # label(t20_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9952 (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,k2_zfmisc_1(A,A),A) & m2_relset_1(D,k2_zfmisc_1(A,A),A) -> (all E (v1_funct_2(E,k2_zfmisc_1(B,B),B) & m2_relset_1(E,k2_zfmisc_1(B,B),B) & v1_funct_1(E) -> (all F (v1_funct_2(F,k2_zfmisc_1(B,B),B) & m2_relset_1(F,k2_zfmisc_1(B,B),B) & v1_funct_1(F) -> (r4_binop_1(A,C,D) & r4_binop_1(B,E,F) <-> r4_binop_1(k2_zfmisc_1(A,B),k7_filter_1(A,B,C,E),k7_filter_1(A,B,D,F))))))))))))))) # label(t28_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9953 (all A (l3_lattices(A) & v3_filter_0(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r2_hidden(E,k2_filter_1(u1_struct_0(A),k11_filter_0(A,B),D)) & r2_hidden(C,k2_filter_1(u1_struct_0(A),k11_filter_0(A,B),D)) -> r2_hidden(k3_lattices(A,C,E),k2_filter_1(u1_struct_0(A),k11_filter_0(A,B),D)) & r2_hidden(k4_lattices(A,C,E),k2_filter_1(u1_struct_0(A),k11_filter_0(A,B),D))))))))))))) # label(t60_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9954 (all A all B all C (-v1_xboole_0(A) & v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m1_relset_1(B,A,A) -> v1_funct_2(k4_filter_1(A,B,C),k2_zfmisc_1(k8_eqrel_1(A,B),k8_eqrel_1(A,B)),k8_eqrel_1(A,B)) & m2_relset_1(k4_filter_1(A,B,C),k2_zfmisc_1(k8_eqrel_1(A,B),k8_eqrel_1(A,B)),k8_eqrel_1(A,B)) & v1_funct_1(k4_filter_1(A,B,C)))) # label(dt_k4_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9955 (all A (-v1_xboole_0(A) -> (all B (v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) -> (all C (m2_filter_1(C,A,B) -> (all D (m2_filter_1(D,A,B) -> (r4_binop_1(A,C,D) -> r4_binop_1(k8_eqrel_1(A,B),k4_filter_1(A,B,C),k4_filter_1(A,B,D))))))))))) # label(t9_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9956 (all A all B (-v3_struct_0(B) & l3_lattices(B) & l3_lattices(A) & -v3_struct_0(A) -> -v3_struct_0(k8_filter_1(A,B)) & v3_lattices(k8_filter_1(A,B)))) # label(fc2_filter_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9957 $T # label(t51_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9958 (all A (v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(k7_nat_lat,k7_nat_lat),k7_nat_lat) & v1_funct_2(A,k2_zfmisc_1(k7_nat_lat,k7_nat_lat),k7_nat_lat) -> ((all B (m1_nat_lat(B,k1_numbers,k5_numbers,k7_nat_lat) -> (all C (m1_nat_lat(C,k1_numbers,k5_numbers,k7_nat_lat) -> k5_nat_1(B,C) = k2_binop_1(k7_nat_lat,k7_nat_lat,k7_nat_lat,A,B,C))))) <-> A = k11_nat_lat))) # label(d13_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9959 $T # label(t40_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9960 (all A (m1_subset_1(A,u1_struct_0(k6_nat_lat)) -> (all B (m1_subset_1(B,u1_struct_0(k6_nat_lat)) -> (all C (m1_subset_1(C,u1_struct_0(k6_nat_lat)) -> k1_binop_1(k1_nat_lat,k1_binop_1(k1_nat_lat,A,C),B) = k1_binop_1(k1_nat_lat,A,k1_binop_1(k1_nat_lat,B,C)) & k1_binop_1(k1_nat_lat,k1_binop_1(k1_nat_lat,C,A),B) = k1_binop_1(k1_nat_lat,A,k1_binop_1(k1_nat_lat,B,C)) & k1_binop_1(k1_nat_lat,k1_binop_1(k1_nat_lat,C,B),A) = k1_binop_1(k1_nat_lat,A,k1_binop_1(k1_nat_lat,B,C)) & k1_binop_1(k1_nat_lat,k1_binop_1(k1_nat_lat,B,A),C) = k1_binop_1(k1_nat_lat,A,k1_binop_1(k1_nat_lat,B,C)))))))) # label(t66_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9961 $T # label(t6_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9962 $T # label(t37_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9963 $T # label(t26_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9964 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m2_nat_lat(B,A) -> -v3_struct_0(B) & v10_lattices(B) & l3_lattices(B))))) # label(dt_m2_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9965 $T # label(t24_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9966 $T # label(t54_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9967 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> (all B (m1_subset_1(B,A) -> v1_xcmplx_0(B) & v1_xreal_0(B))))) # label(cc1_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9968 $T # label(t7_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9969 $T # label(t8_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9970 $T # label(t44_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9971 $T # label(t58_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9972 $T # label(t11_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9973 $T # label(t47_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9974 $T # label(t9_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9975 $T # label(t14_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9976 $T # label(t57_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9977 (all A (m1_subset_1(A,u1_struct_0(k6_nat_lat)) -> (all B (m1_subset_1(B,u1_struct_0(k6_nat_lat)) -> (all C (m1_subset_1(C,u1_struct_0(k6_nat_lat)) -> k1_binop_1(k2_nat_lat,A,k1_binop_1(k2_nat_lat,B,C)) = k1_binop_1(k2_nat_lat,k1_binop_1(k2_nat_lat,A,B),C))))))) # label(t63_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9978 (all A (m1_subset_1(A,u1_struct_0(g3_lattices(k5_numbers,k2_nat_lat,k1_nat_lat))) -> k2_lattices(g3_lattices(k5_numbers,k2_nat_lat,k1_nat_lat),k4_nat_lat,A) = k4_nat_lat & k2_lattices(g3_lattices(k5_numbers,k2_nat_lat,k1_nat_lat),A,k4_nat_lat) = k4_nat_lat)) # label(t56_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9979 $T # label(t30_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9980 $T # label(d2_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9981 $T # label(t50_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9982 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (-r1_xreal_0(A,np__0) -> k8_nat_lat(A) = A))) # label(d10_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9983 $T # label(t15_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9984 (all A (m1_subset_1(A,k5_numbers) -> m1_nat_lat(k8_nat_lat(A),k1_numbers,k5_numbers,k7_nat_lat))) # label(dt_k8_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9985 (all A (m2_relset_1(A,k2_zfmisc_1(k7_nat_lat,k7_nat_lat),k7_nat_lat) & v1_funct_2(A,k2_zfmisc_1(k7_nat_lat,k7_nat_lat),k7_nat_lat) & v1_funct_1(A) -> ((all B (m1_nat_lat(B,k1_numbers,k5_numbers,k7_nat_lat) -> (all C (m1_nat_lat(C,k1_numbers,k5_numbers,k7_nat_lat) -> k6_nat_1(B,C) = k2_binop_1(k7_nat_lat,k7_nat_lat,k7_nat_lat,A,B,C))))) <-> k10_nat_lat = A))) # label(d12_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9986 (all A (m1_subset_1(A,u1_struct_0(k6_nat_lat)) -> (all B (m1_subset_1(B,u1_struct_0(k6_nat_lat)) -> k1_binop_1(k1_nat_lat,A,B) = k1_binop_1(k1_nat_lat,B,A))))) # label(t62_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9987 $T # label(t29_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9988 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (exists B (m2_nat_lat(B,A) & -v3_struct_0(B) & v3_lattices(B) & v4_lattices(B) & v5_lattices(B) & v8_lattices(B) & v9_lattices(B) & v10_lattices(B) & v7_lattices(B) & v6_lattices(B))))) # label(rc1_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9989 $T # label(t12_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9990 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(B)) & -v1_xboole_0(C) & -v1_xboole_0(B) -> (all D (m1_subset_1(D,C) <-> m1_nat_lat(D,A,B,C))))) # label(redefinition_m1_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9991 $T # label(t22_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9992 $T # label(t27_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9993 (all A (m1_subset_1(A,u1_struct_0(g3_lattices(k7_nat_lat,k11_nat_lat,k10_nat_lat))) -> (all B (m1_subset_1(B,u1_struct_0(g3_lattices(k7_nat_lat,k11_nat_lat,k10_nat_lat))) -> k1_lattices(g3_lattices(k7_nat_lat,k11_nat_lat,k10_nat_lat),A,B) = k5_nat_1(k12_nat_lat(A),k12_nat_lat(B)))))) # label(t69_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9994 (all A (m1_subset_1(A,u1_struct_0(k6_nat_lat)) -> (all B (m1_subset_1(B,u1_struct_0(k6_nat_lat)) -> k1_binop_1(k1_nat_lat,A,k1_binop_1(k2_nat_lat,B,A)) = A & k1_binop_1(k1_nat_lat,k1_binop_1(k2_nat_lat,A,B),A) = A & k1_binop_1(k1_nat_lat,k1_binop_1(k2_nat_lat,B,A),A) = A & k1_binop_1(k1_nat_lat,A,k1_binop_1(k2_nat_lat,A,B)) = A)))) # label(t67_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9995 $T # label(t21_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9996 $T # label(t10_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9997 $T # label(t17_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9998 $T # label(t53_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 9999 (all A (m1_subset_1(A,u1_struct_0(k6_nat_lat)) -> (all B (m1_subset_1(B,u1_struct_0(k6_nat_lat)) -> (all C (m1_subset_1(C,u1_struct_0(k6_nat_lat)) -> k1_binop_1(k1_nat_lat,k1_binop_1(k1_nat_lat,A,B),C) = k1_binop_1(k1_nat_lat,A,k1_binop_1(k1_nat_lat,B,C)))))))) # label(t65_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10000 $T # label(t46_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10001 $T # label(t36_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10002 $T # label(t35_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10003 (all A (m1_subset_1(A,u1_struct_0(g3_lattices(k7_nat_lat,k11_nat_lat,k10_nat_lat))) -> (all B (m1_subset_1(B,u1_struct_0(g3_lattices(k7_nat_lat,k11_nat_lat,k10_nat_lat))) -> k2_lattices(g3_lattices(k7_nat_lat,k11_nat_lat,k10_nat_lat),A,B) = k6_nat_1(k12_nat_lat(A),k12_nat_lat(B)))))) # label(t70_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10004 $T # label(t74_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10005 (all A (m1_subset_1(A,u1_struct_0(g3_lattices(k5_numbers,k2_nat_lat,k1_nat_lat))) -> (all B (m1_subset_1(B,u1_struct_0(g3_lattices(k5_numbers,k2_nat_lat,k1_nat_lat))) -> k2_lattices(g3_lattices(k5_numbers,k2_nat_lat,k1_nat_lat),A,B) = k6_nat_1(k3_nat_lat(A),k3_nat_lat(B)))))) # label(t49_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10006 $T # label(t16_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10007 (all A (m1_subset_1(A,u1_struct_0(g3_lattices(k5_numbers,k2_nat_lat,k1_nat_lat))) -> (all B (m1_subset_1(B,u1_struct_0(g3_lattices(k5_numbers,k2_nat_lat,k1_nat_lat))) -> (r1_lattices(g3_lattices(k5_numbers,k2_nat_lat,k1_nat_lat),A,B) -> r1_nat_1(k3_nat_lat(A),k3_nat_lat(B))))))) # label(t52_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10008 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> (m2_nat_lat(B,A) <-> k1_realset1(u2_lattices(A),u1_struct_0(B)) = u2_lattices(B) & u1_lattices(B) = k1_realset1(u1_lattices(A),u1_struct_0(B)) & r1_tarski(u1_struct_0(B),u1_struct_0(A))))))) # label(d16_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10009 (all A (m1_subset_1(A,u1_struct_0(g3_lattices(k5_numbers,k2_nat_lat,k1_nat_lat))) -> m2_subset_1(k3_nat_lat(A),k1_numbers,k5_numbers))) # label(dt_k3_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10010 (all A all B all C (-v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(A) -> (all D (m1_nat_lat(D,A,B,C) -> m2_subset_1(D,A,B))))) # label(dt_m1_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10011 $T # label(t72_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10012 (all A (m1_subset_1(A,u1_struct_0(g3_lattices(k7_nat_lat,k11_nat_lat,k10_nat_lat))) -> A = k12_nat_lat(A))) # label(d14_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10013 $T # label(t71_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10014 $T # label(t23_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10015 $T # label(t39_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10016 (all A (m1_subset_1(A,u1_struct_0(g3_lattices(k7_nat_lat,k11_nat_lat,k10_nat_lat))) -> m1_nat_lat(k12_nat_lat(A),k1_numbers,k5_numbers,k7_nat_lat))) # label(dt_k12_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10017 $T # label(t25_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10018 $T # label(d1_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10019 $T # label(t33_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10020 (all A (m1_subset_1(A,u1_struct_0(k6_nat_lat)) -> (all B (m1_subset_1(B,u1_struct_0(k6_nat_lat)) -> k1_binop_1(k2_nat_lat,A,B) = k1_binop_1(k2_nat_lat,B,A))))) # label(t61_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10021 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (exists B m2_nat_lat(B,A)))) # label(existence_m2_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10022 $T # label(t19_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10023 $T # label(t42_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10024 $T # label(t5_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10025 $T # label(t32_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10026 $T # label(t13_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10027 $T # label(t18_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10028 (all A (m1_nat_lat(A,k1_numbers,k5_numbers,k7_nat_lat) -> A = k9_nat_lat(A))) # label(d11_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10029 $T # label(t59_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10030 (all A (m1_subset_1(A,k7_nat_lat) -> m1_nat_lat(k9_nat_lat(A),k1_numbers,k5_numbers,k7_nat_lat))) # label(dt_k9_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10031 (all A (m1_subset_1(A,u1_struct_0(k6_nat_lat)) -> (all B (m1_subset_1(B,u1_struct_0(k6_nat_lat)) -> (all C (m1_subset_1(C,u1_struct_0(k6_nat_lat)) -> k1_binop_1(k2_nat_lat,k1_binop_1(k2_nat_lat,B,A),C) = k1_binop_1(k2_nat_lat,A,k1_binop_1(k2_nat_lat,B,C)) & k1_binop_1(k2_nat_lat,k1_binop_1(k2_nat_lat,A,C),B) = k1_binop_1(k2_nat_lat,A,k1_binop_1(k2_nat_lat,B,C)) & k1_binop_1(k2_nat_lat,k1_binop_1(k2_nat_lat,C,B),A) = k1_binop_1(k2_nat_lat,A,k1_binop_1(k2_nat_lat,B,C)) & k1_binop_1(k2_nat_lat,A,k1_binop_1(k2_nat_lat,B,C)) = k1_binop_1(k2_nat_lat,k1_binop_1(k2_nat_lat,C,A),B))))))) # label(t64_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10032 $T # label(t1_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10033 $T # label(t73_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10034 $T # label(t28_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10035 (all A (v1_funct_2(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) & m2_relset_1(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) & v1_funct_1(A) -> ((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k6_nat_1(B,C) = k2_binop_1(k5_numbers,k5_numbers,k5_numbers,A,B,C))))) <-> A = k1_nat_lat))) # label(d3_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10036 $T # label(t31_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10037 $T # label(t2_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10038 (all A (m1_subset_1(A,u1_struct_0(g3_lattices(k5_numbers,k2_nat_lat,k1_nat_lat))) -> (all B (m1_subset_1(B,u1_struct_0(g3_lattices(k5_numbers,k2_nat_lat,k1_nat_lat))) -> k1_lattices(g3_lattices(k5_numbers,k2_nat_lat,k1_nat_lat),A,B) = k5_nat_1(k3_nat_lat(A),k3_nat_lat(B)))))) # label(t48_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10039 $T # label(t38_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10040 (all A (m1_subset_1(A,k1_zfmisc_1(k5_numbers)) -> (all B (m1_subset_1(B,A) -> v1_xcmplx_0(B) & v1_xreal_0(B))))) # label(cc2_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10041 $T # label(t34_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10042 $T # label(t4_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10043 $T # label(t41_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10044 $T # label(t3_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10045 (all A (m1_subset_1(A,u1_struct_0(g3_lattices(k5_numbers,k2_nat_lat,k1_nat_lat))) -> k3_nat_lat(A) = A)) # label(d5_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10046 $T # label(t20_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10047 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(B)) & -v1_xboole_0(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> (exists D m1_nat_lat(D,A,B,C)))) # label(existence_m1_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10048 $T # label(t43_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10049 (all A (v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) & m2_relset_1(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) -> ((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k2_binop_1(k5_numbers,k5_numbers,k5_numbers,A,B,C) = k5_nat_1(B,C))))) <-> k2_nat_lat = A))) # label(d4_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10050 $T # label(t45_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10051 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> m2_nat_lat(A,A))) # label(t75_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10052 (all A (m1_subset_1(A,u1_struct_0(k6_nat_lat)) -> (all B (m1_subset_1(B,u1_struct_0(k6_nat_lat)) -> k1_binop_1(k2_nat_lat,A,k1_binop_1(k1_nat_lat,B,A)) = A & k1_binop_1(k2_nat_lat,k1_binop_1(k1_nat_lat,A,B),A) = A & A = k1_binop_1(k2_nat_lat,k1_binop_1(k1_nat_lat,B,A),A) & A = k1_binop_1(k2_nat_lat,A,k1_binop_1(k1_nat_lat,A,B)))))) # label(t68_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10053 (all A (m1_subset_1(A,k1_zfmisc_1(k5_numbers)) -> ((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (-r1_xreal_0(B,np__0) <-> r2_hidden(B,A)))) <-> k7_nat_lat = A))) # label(d9_nat_lat) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10054 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,B,C) = k1_group_1(A,C,B))) <-> r1_rlvect_1(k10_group_5(A),B)))))) # label(t89_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10055 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (v1_group_1(B) & m1_group_2(B,A) -> (k17_group_2(A,B) = np__2 & v1_finset_1(k14_group_2(A,B)) -> m1_group_2(k9_group_5(A),B)))))) # label(t86_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10056 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_group_2(D,A) -> (r1_rlvect_1(D,C) & r1_rlvect_1(D,B) -> r1_rlvect_1(D,k2_group_3(A,B,C))))))))))) # label(t2_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10057 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_group_5(A,B,C) = k1_group_1(A,k3_group_1(A,B),k2_group_3(A,B,C)) & k2_group_5(A,B,C) = k1_group_1(A,k2_group_3(A,k3_group_1(A,C),B),C))))))) # label(t21_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10058 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> v7_group_1(k10_group_5(A)))) # label(t92_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10059 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_group_2(D,A) -> (all E (m1_group_2(E,A) -> (r1_rlvect_1(D,B) & r1_rlvect_1(E,C) -> r1_rlvect_1(k8_group_5(A,D,E),k2_group_5(A,B,C))))))))))))) # label(t74_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10060 $T # label(t11_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10061 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_group_1(A) = k1_group_1(A,k1_group_1(A,k2_group_3(A,k3_group_5(A,B,k3_group_1(A,C),D),C),k2_group_3(A,k3_group_5(A,C,k3_group_1(A,D),B),D)),k2_group_3(A,k3_group_5(A,D,k3_group_1(A,B),C),B)))))))))) # label(t50_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10062 $T # label(t88_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10063 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_group_1(A,C,B) = k1_group_1(A,B,C) <-> k2_group_5(A,B,C) = k2_group_1(A)))))))) # label(t39_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10064 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> a_3_0_group_5(A,B,C) = k4_group_5(A,B,C))))))) # label(d4_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10065 (all A all B (v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & -v3_struct_0(B) -> (r2_hidden(A,a_1_0_group_5(B)) <-> (exists C (m1_subset_1(C,u1_struct_0(B)) & A = C & (all D (m1_subset_1(D,u1_struct_0(B)) -> k1_group_1(B,C,D) = k1_group_1(B,D,C)))))))) # label(fraenkel_a_1_0_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10066 (all A (v1_int_1(A) -> (all B (-v3_struct_0(B) & v3_group_1(B) & l1_group_1(B) & v4_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k2_group_5(B,k6_group_1(B,A,C),D) = k1_group_1(B,k6_group_1(B,k4_xcmplx_0(A),C),k6_group_1(B,A,k2_group_3(B,C,D))))))))))) # label(t37_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10067 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (r1_rlvect_1(k10_group_5(A),B) <-> k7_group_3(A,B) = k6_domain_1(u1_struct_0(A),B)))))) # label(t93_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10068 (all A (-v3_struct_0(A) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (-v3_struct_0(A) & v3_group_1(A) & v7_group_1(A) & l1_group_1(A) & v4_group_1(A) <-> r1_group_2(A,k9_group_5(A),k5_group_2(A))))) # label(t85_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10069 (all A all B all C (m1_subset_1(C,u1_struct_0(A)) & m1_finseq_1(B,u1_struct_0(A)) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> m2_finseq_1(k1_group_5(A,B,C),u1_struct_0(A)))) # label(dt_k1_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10070 $T # label(t81_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10071 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> r2_hidden(k2_group_1(A),k5_group_5(A,B,C)))))))) # label(t59_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10072 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_group_2(B,A) & v1_group_3(B,A) & v1_group_1(B) -> (all C (v1_group_1(C) & v1_group_3(C,A) & m1_group_2(C,A) -> m1_group_2(k8_group_5(A,B,C),A) & v1_group_3(k8_group_5(A,B,C),A))))))) # label(t77_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10073 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> (all D (m2_finseq_1(D,u1_struct_0(A)) -> k1_group_5(A,k8_finseq_1(u1_struct_0(A),C,D),B) = k8_finseq_1(u1_struct_0(A),k1_group_5(A,C,B),k1_group_5(A,D,B)))))))))) # label(t12_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10074 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_group_5(A,B,k1_group_1(A,C,D)) = k1_group_1(A,k2_group_5(A,B,D),k2_group_3(A,k2_group_5(A,B,C),D)))))))))) # label(t29_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10075 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (m1_group_2(B,k10_group_5(A)) -> m1_group_2(B,A) & v1_group_3(B,A)))))) # label(t91_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10076 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v7_group_1(A) & -v3_struct_0(A) <-> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(k6_domain_1(u1_struct_0(A),k2_group_1(A)) != k4_group_5(A,B,C) & C != k1_xboole_0 & k1_xboole_0 != B)))))))) # label(t56_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10077 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (v1_group_1(B) & m1_group_2(B,A) -> (B = k10_group_5(A) <-> a_1_0_group_5(A) = u1_struct_0(B)))))) # label(d10_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10078 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_group_5(A,B,k3_group_1(A,C)) = k2_group_3(A,k2_group_5(A,C,B),k3_group_1(A,C)))))))) # label(t31_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10079 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,C) & r1_tarski(D,E) -> m1_group_2(k7_group_5(A,B,D),k7_group_5(A,C,E))))))))))))) # label(t70_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10080 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_group_3(A,k2_group_5(A,B,C),D) = k2_group_5(A,k2_group_3(A,B,D),k2_group_3(A,C,D)))))))))) # label(t26_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10081 (all A all B (l1_group_1(B) & v4_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (r2_hidden(A,k6_group_5(B)) <-> (exists C ((exists D (m1_subset_1(D,u1_struct_0(B)) & k2_group_5(B,C,D) = A)) & m1_subset_1(C,u1_struct_0(B))))))) # label(t65_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10082 $T # label(t9_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10083 $T # label(t67_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10084 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> k8_group_5(A,k6_group_2(A),k6_group_2(A)) = k9_group_5(A))) # label(d9_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10085 (all A ((exists B exists C exists D (m1_subset_1(B,f1_s1_group_5) & m1_subset_1(C,f2_s1_group_5) & m1_subset_1(D,f3_s1_group_5) & A = f4_s1_group_5(B,C,D) & p1_s1_group_5(B,C,D))) <-> r2_hidden(A,a_0_0_group_5))) # label(fraenkel_a_0_0_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10086 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> k1_group_5(A,k8_rlvect_1(A,B,C,D),E) = k8_rlvect_1(A,k2_group_3(A,B,E),k2_group_3(A,C,E),k2_group_3(A,D,E)))))))))))) # label(t16_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10087 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> m1_group_2(k10_group_5(A),A) & v1_group_1(k10_group_5(A)))) # label(dt_k10_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10088 (all A all B all C (-v3_struct_0(A) & l1_group_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & v4_group_1(A) & v3_group_1(A) -> m1_subset_1(k2_group_5(A,B,C),u1_struct_0(A)))) # label(dt_k2_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10089 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k1_xboole_0 = k4_group_5(A,B,k1_subset_1(u1_struct_0(A))) & k4_group_5(A,k1_subset_1(u1_struct_0(A)),B) = k1_xboole_0)))) # label(t53_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10090 (all A all B all C (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> m1_subset_1(k4_group_5(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k4_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10091 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k2_group_5(A,k2_group_1(A),B) = k2_group_1(A) & k2_group_5(A,B,k2_group_1(A)) = k2_group_1(A))))) # label(t22_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10092 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k3_group_5(A,B,C,D) = k2_group_5(A,k2_group_5(A,B,C),D))))))))) # label(d3_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10093 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,k1_group_1(A,k1_group_1(A,k3_group_1(A,B),k3_group_1(A,C)),B),C) = k2_group_5(A,B,C))))))) # label(d2_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10094 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_group_5(A,k3_group_1(A,C),B) = k2_group_5(A,k2_group_3(A,B,k3_group_1(A,C)),C))))))) # label(t34_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10095 $T # label(t42_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10096 (all A all B (v4_group_1(B) & l1_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (m1_group_2(C,B) -> (all D (m1_group_2(D,B) -> (r2_hidden(A,k7_group_4(B,C,D)) <-> (exists E (m1_subset_1(E,u1_struct_0(B)) & (exists F (m1_subset_1(F,u1_struct_0(B)) & A = k1_group_1(B,E,F) & r1_rlvect_1(C,E) & r1_rlvect_1(D,F)))))))))))) # label(t4_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10097 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (all C (v1_group_1(C) & m1_group_2(C,A) & v1_group_3(C,A) -> m1_group_2(k8_group_5(A,B,C),C) & m1_group_2(k8_group_5(A,C,B),C))))))) # label(t76_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10098 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) & v1_group_3(C,A) -> k7_group_4(A,B,C) = k7_group_4(A,C,B))))))) # label(t8_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10099 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> (all D (m1_group_2(D,A) -> (all E (m1_group_2(E,A) -> (m1_group_2(D,E) & m1_group_2(B,C) -> r1_tarski(k5_group_5(A,B,D),k5_group_5(A,C,E))))))))))))) # label(t62_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10100 (all A (-v3_struct_0(A) & v1_group_1(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r1_rlvect_1(k9_group_5(A),k2_group_5(A,B,C)))))))) # label(t84_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10101 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> m1_group_2(k9_group_5(A),A) & v1_group_3(k9_group_5(A),A) & v1_group_1(k9_group_5(A)))) # label(dt_k9_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10102 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,D) & r2_hidden(C,E) -> r1_rlvect_1(k7_group_5(A,D,E),k2_group_5(A,B,C))))))))))))) # label(t68_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10103 (all A all B all C (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B,A) & m1_group_2(C,A) -> m1_group_2(k8_group_5(A,B,C),A) & v1_group_1(k8_group_5(A,B,C)))) # label(dt_k8_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10104 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> k3_group_4(A,k1_group_5(A,C,B)) = k2_group_3(A,k3_group_4(A,C),B))))))) # label(t17_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10105 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k3_group_5(A,B,C,k2_group_3(A,C,B)) = k2_group_5(A,C,k2_group_5(A,C,B)))))))) # label(t47_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10106 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (l1_group_1(A) & v7_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) <-> k6_domain_1(u1_struct_0(A),k2_group_1(A)) = k6_group_5(A)))) # label(t66_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10107 $T # label(t10_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10108 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (v1_group_1(B) & m1_group_2(B,A) & v1_group_3(B,A) -> (all C (m1_group_2(C,A) & v1_group_3(C,A) & v1_group_1(C) -> (all D (v1_group_1(D) & v1_group_3(D,A) & m1_group_2(D,A) -> r1_group_2(A,k8_group_5(A,B,k8_group_4(A,C,D)),k8_group_4(A,k8_group_5(A,B,C),k8_group_5(A,B,D))))))))))) # label(t80_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10109 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> m1_subset_1(k6_group_5(A),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k6_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10110 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (all C (v1_group_1(C) & m1_group_2(C,A) & v1_group_3(C,A) -> r1_tarski(k5_group_5(A,C,B),k7_group_2(A,C)) & r1_tarski(k5_group_5(A,B,C),k7_group_2(A,C)))))))) # label(t61_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10111 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (v1_group_1(D) & v1_group_3(D,A) & m1_group_2(D,A) -> (r1_rlvect_1(D,B) -> r1_rlvect_1(D,k2_group_3(A,B,C))))))))))) # label(t3_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10112 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> (all D (m2_finseq_1(D,k4_numbers) -> k4_group_4(A,D,k1_group_5(A,C,B)) = k1_group_5(A,k4_group_4(A,D,C),B))))))))) # label(t18_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10113 (all A all B (-v3_struct_0(B) & v4_group_1(B) & l1_group_1(B) & v3_group_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> ((exists E ((exists F (m1_subset_1(F,u1_struct_0(B)) & r2_hidden(E,C) & r2_hidden(F,D) & k2_group_5(B,E,F) = A)) & m1_subset_1(E,u1_struct_0(B)))) <-> r2_hidden(A,k4_group_5(B,C,D))))))))) # label(t52_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10114 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_group_5(A,C,B) = k3_group_1(A,k2_group_5(A,B,C)))))))) # label(t25_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10115 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_group_5(A,k7_rlvect_1(A,B,C),D) = k7_rlvect_1(A,k2_group_3(A,B,D),k2_group_3(A,C,D)))))))))) # label(t15_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10116 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v3_struct_0(B) & v3_group_1(B) & l1_group_1(B) & v4_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k2_group_5(B,k6_group_1(B,A,C),D) = k1_group_1(B,k6_group_1(B,k4_xcmplx_0(A),C),k6_group_1(B,A,k2_group_3(B,C,D))))))))))) # label(t35_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10117 (all A (v1_int_1(A) -> (all B (-v3_struct_0(B) & v4_group_1(B) & l1_group_1(B) & v3_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k2_group_5(B,C,k6_group_1(B,A,D)) = k1_group_1(B,k6_group_1(B,k4_xcmplx_0(A),k2_group_3(B,D,C)),k6_group_1(B,A,D)))))))))) # label(t38_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10118 (all A all B (-v3_struct_0(B) & l1_group_1(B) & v4_group_1(B) & v3_group_1(B) -> (all C (v1_group_3(C,B) & m1_group_2(C,B) & v1_group_1(C) -> (all D (v1_group_1(D) & m1_group_2(D,B) & v1_group_3(D,B) -> (r1_rlvect_1(k8_group_4(B,C,D),A) <-> (exists E (m1_subset_1(E,u1_struct_0(B)) & (exists F (m1_subset_1(F,u1_struct_0(B)) & A = k1_group_1(B,E,F) & r1_rlvect_1(D,F) & r1_rlvect_1(C,E)))))))))))) # label(t7_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10119 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> r1_group_2(A,k9_group_5(A),k5_group_4(A,k6_group_5(A))))) # label(t82_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.62 10120 (all A all B (l1_group_1(B) & v4_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (m1_group_2(C,B) -> (all D (m1_group_2(D,B) -> (k7_group_4(B,D,C) = k7_group_4(B,C,D) -> (r1_rlvect_1(k8_group_4(B,C,D),A) <-> (exists E ((exists F (m1_subset_1(F,u1_struct_0(B)) & r1_rlvect_1(D,F) & r1_rlvect_1(C,E) & A = k1_group_1(B,E,F))) & m1_subset_1(E,u1_struct_0(B)))))))))))) # label(t5_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10121 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_group_5(A,B,C) = k1_group_1(A,k1_group_1(A,k6_group_1(A,np__2,k3_group_1(A,B)),k6_group_1(A,np__2,k1_group_1(A,B,k3_group_1(A,C)))),k6_group_1(A,np__2,C)))))))) # label(t27_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10122 $T # label(t57_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10123 $T # label(t64_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10124 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k2_group_1(A) = k2_group_5(A,B,B))))) # label(t23_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10125 $T # label(t87_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10126 (all A all B (-v3_struct_0(B) & v4_group_1(B) & l1_group_1(B) & v3_group_1(B) -> (r1_rlvect_1(k5_group_2(B),A) <-> A = k2_group_1(B)))) # label(t1_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10127 (all A all B (l1_group_1(B) & v4_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> ((exists E ((exists F (k3_group_4(B,k4_group_4(B,F,E)) = A & r1_tarski(k2_relat_1(E),k4_group_5(B,C,D)) & k3_finseq_1(E) = k3_finseq_1(F) & m2_finseq_1(F,k4_numbers))) & m2_finseq_1(E,u1_struct_0(B)))) <-> r1_rlvect_1(k7_group_5(B,C,D),A)))))))) # label(t69_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10128 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m2_finseq_1(D,u1_struct_0(A)) -> (k1_group_5(A,B,C) = D <-> k3_finseq_1(B) = k3_finseq_1(D) & (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (r2_hidden(E,k4_finseq_1(B)) -> k1_funct_1(D,E) = k2_group_3(A,k4_finseq_4(k5_numbers,u1_struct_0(A),B,E),C))))))))))))) # label(d1_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10129 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k3_group_5(A,B,C,C) = k2_group_3(A,k1_group_1(A,k2_group_5(A,B,k3_group_1(A,C)),k2_group_5(A,B,C)),C))))))) # label(t46_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10130 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> r1_group_2(A,k8_group_5(A,B,C),k5_group_4(A,k5_group_5(A,B,C))))))))) # label(t72_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10131 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_group_5(A,B,C) = k1_group_1(A,k3_group_1(A,k1_group_1(A,C,B)),k1_group_1(A,B,C)))))))) # label(t20_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10132 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k3_group_5(A,B,B,C) = k2_group_1(A))))))) # label(t44_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10133 (all A all B (-v3_struct_0(B) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) -> (r1_rlvect_1(k9_group_5(B),A) <-> (exists C (m2_finseq_1(C,u1_struct_0(B)) & (exists D (k3_group_4(B,k4_group_4(B,D,C)) = A & r1_tarski(k2_relat_1(C),k6_group_5(B)) & k3_finseq_1(C) = k3_finseq_1(D) & m2_finseq_1(D,k4_numbers)))))))) # label(t83_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10134 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_5(A,k12_finseq_1(u1_struct_0(A),B),C) = k12_finseq_1(u1_struct_0(A),k2_group_3(A,B,C)))))))) # label(t14_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10135 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (v1_group_3(B,A) & m1_group_2(B,A) & v1_group_1(B) -> (all C (v1_group_3(C,A) & m1_group_2(C,A) & v1_group_1(C) -> (all D (v1_group_1(D) & v1_group_3(D,A) & m1_group_2(D,A) -> r1_group_2(A,k8_group_5(A,k8_group_4(A,B,C),D),k8_group_4(A,k8_group_5(A,B,D),k8_group_5(A,C,D))))))))))) # label(t79_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10136 (all A all B (l1_group_1(B) & v4_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (m1_group_2(C,B) -> (all D (m1_group_2(D,B) -> ((exists E ((exists F (k3_finseq_1(F) = k3_finseq_1(E) & r1_tarski(k2_relat_1(E),k5_group_5(B,C,D)) & A = k3_group_4(B,k4_group_4(B,F,E)) & m2_finseq_1(F,k4_numbers))) & m2_finseq_1(E,u1_struct_0(B)))) <-> r1_rlvect_1(k8_group_5(B,C,D),A)))))))) # label(t73_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10137 (all A all B all C (m1_group_2(C,A) & m1_group_2(B,A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> m1_subset_1(k5_group_5(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k5_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10138 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k5_group_4(A,k4_group_5(A,B,C)) = k7_group_5(A,B,C))))))) # label(d7_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10139 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> v1_group_3(k10_group_5(A),A) & m1_group_2(k10_group_5(A),A))) # label(t90_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10140 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> ((all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> k6_domain_1(u1_struct_0(A),k2_group_1(A)) = k5_group_5(A,B,C))))) <-> -v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & v7_group_1(A) & l1_group_1(A)))) # label(t63_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10141 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_group_5(A,k3_group_1(A,B),C) = k2_group_3(A,k2_group_5(A,C,B),k3_group_1(A,B)))))))) # label(t30_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10142 (all A all B (v4_group_1(B) & l1_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (m1_group_2(C,B) -> (all D (m1_group_2(D,B) -> ((exists E ((exists F (r1_rlvect_1(C,E) & r1_rlvect_1(D,F) & k2_group_5(B,E,F) = A & m1_subset_1(F,u1_struct_0(B)))) & m1_subset_1(E,u1_struct_0(B)))) <-> r2_hidden(A,k5_group_5(B,C,D))))))))) # label(t58_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10143 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_group_5(A,B,C) = k1_group_1(A,k1_group_1(A,k1_group_1(A,k3_group_1(A,B),k3_group_1(A,C)),B),C) & k2_group_5(A,B,C) = k1_group_1(A,k3_group_1(A,B),k1_group_1(A,k1_group_1(A,k3_group_1(A,C),B),C)) & k2_group_5(A,B,C) = k1_group_1(A,k1_group_1(A,k3_group_1(A,B),k3_group_1(A,C)),k1_group_1(A,B,C)) & k2_group_5(A,B,C) = k1_group_1(A,k3_group_1(A,B),k1_group_1(A,k3_group_1(A,C),k1_group_1(A,B,C))) & k2_group_5(A,B,C) = k1_group_1(A,k1_group_1(A,k3_group_1(A,B),k1_group_1(A,k3_group_1(A,C),B)),C))))))) # label(t19_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10144 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (v7_group_1(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_group_1(A) = k2_group_5(A,B,C)))))))) # label(t40_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10145 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & v1_group_1(A) & -v3_struct_0(A) -> (k10_group_5(A) = A <-> l1_group_1(A) & v7_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A)))) # label(t94_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10146 (all A all B all C (-v3_struct_0(A) & l1_group_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v4_group_1(A) & v3_group_1(A) -> v1_group_1(k7_group_5(A,B,C)) & m1_group_2(k7_group_5(A,B,C),A))) # label(dt_k7_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10147 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_group_5(A,B,k1_group_1(A,C,D)) = k1_group_1(A,k1_group_1(A,k2_group_5(A,B,D),k2_group_5(A,B,C)),k3_group_5(A,B,C,D)))))))))) # label(t49_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10148 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> k5_group_5(A,k6_group_2(A),k6_group_2(A)) = k6_group_5(A))) # label(d6_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10149 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> k5_group_5(A,k5_group_2(A),B) = k6_domain_1(u1_struct_0(A),k2_group_1(A)) & k6_domain_1(u1_struct_0(A),k2_group_1(A)) = k5_group_5(A,B,k5_group_2(A)))))) # label(t60_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10150 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> k5_group_5(A,B,C) = k4_group_5(A,k7_group_2(A,B),k7_group_2(A,C)))))))) # label(d5_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10151 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_group_1(A) = k3_group_5(A,k2_group_1(A),B,C) & k2_group_1(A) = k3_group_5(A,B,k2_group_1(A),C) & k2_group_1(A) = k3_group_5(A,B,C,k2_group_1(A)))))))) # label(t43_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10152 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v3_group_1(B) & l1_group_1(B) & v4_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k2_group_5(B,C,k6_group_1(B,A,D)) = k1_group_1(B,k6_group_1(B,k4_xcmplx_0(A),k2_group_3(B,D,C)),k6_group_1(B,A,D)))))))))) # label(t36_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10153 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_group_1(A,k2_group_3(A,k2_group_5(A,B,D),C),k2_group_5(A,C,D)) = k2_group_5(A,k1_group_1(A,B,C),D))))))))) # label(t28_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10154 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_group_5(A,C,k3_group_1(A,B)) = k2_group_5(A,B,k2_group_3(A,C,k3_group_1(A,B))))))))) # label(t33_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10155 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k6_domain_1(u1_struct_0(A),k2_group_5(A,B,C)) = k4_group_5(A,k6_domain_1(u1_struct_0(A),B),k6_domain_1(u1_struct_0(A),C)))))))) # label(t54_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10156 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> k8_group_5(A,B,C) = k7_group_5(A,k7_group_2(A,B),k7_group_2(A,C)))))))) # label(d8_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10157 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) -> (all D (m1_group_2(D,A) -> (all E (m1_group_2(E,A) -> (m1_group_2(B,C) & m1_group_2(D,E) -> m1_group_2(k8_group_5(A,B,D),k8_group_5(A,C,E))))))))))))) # label(t75_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10158 (all A all B all C all D (v3_group_1(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> m1_subset_1(k3_group_5(A,B,C,D),u1_struct_0(A)))) # label(dt_k3_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10159 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_group_2(B,A) & v1_group_3(B,A) -> (all C (m1_group_2(C,A) & v1_group_3(C,A) -> r1_group_2(A,k8_group_5(A,B,C),k8_group_5(A,C,B)))))))) # label(t78_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10160 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k2_group_1(A) = k2_group_5(A,k3_group_1(A,B),B) & k2_group_1(A) = k2_group_5(A,B,k3_group_1(A,B)))))) # label(t24_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10161 $T # label(t51_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10162 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,C) & r1_tarski(D,E) -> r1_tarski(k4_group_5(A,B,D),k4_group_5(A,C,E))))))))))))) # label(t55_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10163 $T # label(t71_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10164 (all A all B (-v3_struct_0(B) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) -> (all C (m1_group_2(C,B) -> (all D (m1_group_2(D,B) -> (v3_group_1(B) & v4_group_1(B) & v7_group_1(B) & l1_group_1(B) & -v3_struct_0(B) -> (r1_rlvect_1(k8_group_4(B,C,D),A) <-> (exists E ((exists F (A = k1_group_1(B,E,F) & r1_rlvect_1(D,F) & r1_rlvect_1(C,E) & m1_subset_1(F,u1_struct_0(B)))) & m1_subset_1(E,u1_struct_0(B)))))))))))) # label(t6_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10165 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_group_5(A,k2_group_3(A,B,C),B) = k3_group_5(A,B,C,B))))))) # label(t45_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10166 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_group_3(A,k2_group_5(A,B,C),k3_group_1(A,k1_group_1(A,C,B))) = k2_group_5(A,k3_group_1(A,B),k3_group_1(A,C)) & k2_group_3(A,k2_group_5(A,B,C),k3_group_1(A,k1_group_1(A,B,C))) = k2_group_5(A,k3_group_1(A,B),k3_group_1(A,C)))))))) # label(t32_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10167 (all A all B all C all D (l1_group_1(B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v4_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (r2_hidden(A,a_3_0_group_5(B,C,D)) <-> (exists E exists F (m1_subset_1(E,u1_struct_0(B)) & k2_group_5(B,E,F) = A & r2_hidden(F,D) & r2_hidden(E,C) & m1_subset_1(F,u1_struct_0(B))))))) # label(fraenkel_a_3_0_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10168 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_group_1(A,k1_group_1(A,k2_group_5(A,B,D),k3_group_5(A,B,D,C)),k2_group_5(A,C,D)) = k2_group_5(A,k1_group_1(A,B,C),D))))))))) # label(t48_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10169 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_xboole_0 = k1_group_5(A,k6_finseq_1(u1_struct_0(A)),B))))) # label(t13_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.63 10170 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_group_2(D,A) -> (r1_rlvect_1(D,C) & r1_rlvect_1(D,B) -> r1_rlvect_1(D,k2_group_5(A,B,C))))))))))) # label(t41_group_5) # label(axiom) # label(non_clause). [assumption]. 126.30/125.65 10171 (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]. 126.30/125.65 10172 (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]. 126.30/125.65 10173 (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]. 126.30/125.65 10174 (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]. 126.30/125.65 10175 $T # label(t29_nattra_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.65 10176 (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]. 126.30/125.65 10177 (exists A (v2_nattra_1(A) & v2_cat_1(A) & l1_cat_1(A))) # label(rc1_nattra_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.65 10178 (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]. 126.30/125.65 10179 (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]. 126.30/125.65 10180 $T # label(t38_nattra_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.65 10181 (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]. 126.30/125.65 10182 (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]. 126.30/125.65 10183 (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]. 126.30/125.65 10184 (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]. 126.30/125.65 10185 (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]. 126.30/125.65 10186 (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]. 126.30/125.65 10187 (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]. 126.30/125.65 10188 (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]. 126.30/125.65 10189 (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]. 126.30/125.65 10190 (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]. 126.30/125.65 10191 (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]. 126.30/125.65 10192 (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]. 126.30/125.65 10193 (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]. 126.30/125.65 10194 (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]. 126.30/125.65 10195 (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]. 126.30/125.65 10196 (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]. 126.30/125.65 10197 (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]. 126.30/125.65 10198 (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]. 126.30/125.65 10199 (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]. 126.30/125.65 10200 (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]. 126.30/125.65 10201 (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]. 126.30/125.65 10202 (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]. 126.30/125.65 10203 (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]. 126.30/125.65 10204 (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]. 126.30/125.65 10205 (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]. 126.30/125.65 10206 (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]. 126.30/125.65 10207 (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]. 126.30/125.65 10208 (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]. 126.30/125.65 10209 (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]. 126.30/125.65 10210 (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]. 126.30/125.65 10211 (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]. 126.30/125.65 10212 (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]. 126.30/125.65 10213 (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]. 126.30/125.65 10214 (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]. 126.30/125.65 10215 $T # label(t43_nattra_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.65 10216 (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]. 126.30/125.65 10217 (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]. 126.30/125.65 10218 (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]. 126.30/125.65 10219 (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]. 126.30/125.65 10220 (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]. 126.30/125.65 10221 (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]. 126.30/125.65 10222 (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]. 126.30/125.65 10223 (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]. 126.30/125.65 10224 (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]. 126.30/125.65 10225 (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]. 126.30/125.65 10226 (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]. 126.30/125.65 10227 (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]. 126.30/125.65 10228 $T # label(t24_nattra_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.65 10229 (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]. 126.30/125.65 10230 (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]. 126.30/125.65 10231 (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]. 126.30/125.65 10232 (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]. 126.30/125.65 10233 (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]. 126.30/125.65 10234 (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]. 126.30/125.65 10235 (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]. 126.30/125.65 10236 (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]. 126.30/125.65 10237 (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]. 126.30/125.65 10238 (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]. 126.30/125.65 10239 (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]. 126.30/125.65 10240 (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]. 126.30/125.65 10241 (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]. 126.30/125.65 10242 (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]. 126.30/125.65 10243 (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]. 126.30/125.65 10244 (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]. 126.30/125.65 10245 (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]. 126.30/125.65 10246 (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]. 126.30/125.65 10247 (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]. 126.30/125.65 10248 $T # label(t37_nattra_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.65 10249 (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]. 126.30/125.65 10250 (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]. 126.30/125.65 10251 (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]. 126.30/125.65 10252 (all A all B v2_nattra_1(k8_cat_1(A,B))) # label(t46_nattra_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.65 10253 (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]. 126.30/125.65 10254 (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]. 126.30/125.65 10255 (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]. 126.30/125.65 10256 (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]. 126.30/125.65 10257 (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]. 126.30/125.65 10258 (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]. 126.30/125.65 10259 (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]. 126.30/125.65 10260 (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]. 126.30/125.65 10261 (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]. 126.30/125.65 10262 (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]. 126.30/125.65 10263 (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]. 126.30/125.65 10264 (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]. 126.30/125.65 10265 (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]. 126.30/125.65 10266 (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]. 126.30/125.65 10267 (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]. 126.30/125.65 10268 (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]. 126.30/125.65 10269 (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]. 126.30/125.65 10270 (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]. 126.30/125.65 10271 $T # label(t36_nattra_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.65 10272 (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]. 126.30/125.65 10273 (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]. 126.30/125.65 10274 (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]. 126.30/125.65 10275 $T # label(t18_nattra_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.65 10276 (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]. 126.30/125.65 10277 (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]. 126.30/125.65 10278 (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]. 126.30/125.65 10279 (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]. 126.30/125.65 10280 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> -((all E (m1_subset_1(E,k1_numbers) -> -(-r1_xreal_0(E,np__0) & r1_tarski(k9_metric_1(A,D,E),C)))) & r2_hidden(D,C)))) <-> r2_hidden(C,B)))) <-> k4_pcomps_1(A) = B))))) # label(d5_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.65 10281 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (v3_compts_1(A) & v2_pcomps_1(A) -> v4_compts_1(A)))) # label(t27_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.65 10282 (exists A (-v3_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & v3_pcomps_1(A) & l1_pre_topc(A))) # label(rc3_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.65 10283 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (v1_xreal_0(D) -> -((all E (m1_subset_1(E,k1_numbers) -> -(-r1_xreal_0(E,np__0) & r1_tarski(k9_metric_1(A,B,E),k9_metric_1(A,C,D))))) & r2_hidden(B,k9_metric_1(A,C,D)) & v9_metric_1(A)))))))))) # label(t30_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.65 10284 (all A v2_compts_1(k2_pcomps_1(k1_tarski(A)))) # label(t9_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.65 10285 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(a_3_1_pcomps_1(A,B,C),B))))))) # label(t11_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.65 10286 (all A all B (v1_funct_1(B) & m1_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers) & -v1_xboole_0(A) -> v6_metric_1(k6_pcomps_1(A,B)) & v8_metric_1(k6_pcomps_1(A,B)) & l1_metric_1(k6_pcomps_1(A,B)) & v9_metric_1(k6_pcomps_1(A,B)) & v7_metric_1(k6_pcomps_1(A,B)) & v1_metric_1(k6_pcomps_1(A,B)) & -v3_struct_0(k6_pcomps_1(A,B)))) # label(dt_k6_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.65 10287 (all A (-v3_struct_0(A) & l1_metric_1(A) -> -v3_struct_0(k5_pcomps_1(A)) & v2_pre_topc(k5_pcomps_1(A)) & v1_pre_topc(k5_pcomps_1(A)))) # label(fc4_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.65 10288 (all A all B all C all D (l1_pre_topc(B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) -> (r2_hidden(A,a_3_0_pcomps_1(B,C,D)) <-> (exists E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & E = A & -r1_xboole_0(E,D) & r2_hidden(E,C)))))) # label(fraenkel_a_3_0_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.65 10289 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (C = k3_pcomps_1(A,B) <-> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(D,C) <-> (exists E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & r2_hidden(E,B) & D = k6_pre_topc(A,E))))))))))))) # label(d3_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.65 10290 $T # label(t32_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.65 10291 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(v2_pcomps_1(A) & v4_pre_topc(B,A) & r1_xboole_0(B,C) & (all D (m1_subset_1(D,u1_struct_0(A)) -> -((all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (all F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(F,A) & r1_tarski(B,E) & r2_hidden(D,F) & r1_xboole_0(E,F) & v3_pre_topc(E,A)))))) & r2_hidden(D,C)))) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(E,A) & r1_tarski(C,E) & r1_xboole_0(D,E) & r1_tarski(B,D) & v3_pre_topc(D,A)))))) & v4_pre_topc(C,A)))))))) # label(t26_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.65 10292 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_1(B) -> (v7_metric_1(g1_metric_1(A,B)) & v9_metric_1(g1_metric_1(A,B)) & l1_metric_1(g1_metric_1(A,B)) & v8_metric_1(g1_metric_1(A,B)) & v6_metric_1(g1_metric_1(A,B)) <-> r1_pcomps_1(A,B)))) # label(t39_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10293 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_pcomps_1(B,A) -> k6_pre_topc(A,k5_setfam_1(u1_struct_0(A),B)) = k5_setfam_1(u1_struct_0(A),k3_pcomps_1(A,B))))))) # label(t23_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10294 (all A (v6_metric_1(A) & v7_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) & v8_metric_1(A) & -v3_struct_0(A) -> v3_compts_1(k5_pcomps_1(A)))) # label(t38_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10295 (all A (l1_pre_topc(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(r1_pre_topc(A,B) & (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(r1_setfam_1(C,B) & v1_pcomps_1(C,A) & r1_pre_topc(A,C) & v1_tops_2(C,A)))) & v1_tops_2(B,A)))) <-> v2_pcomps_1(A)))) # label(d4_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10296 (all A (m1_subset_1(A,k1_zfmisc_1(u1_struct_0(f1_s1_pcomps_1))) -> (r2_hidden(A,f2_s1_pcomps_1) -> r2_hidden(f4_s1_pcomps_1(A),f3_s1_pcomps_1)))) -> (exists A (v1_funct_1(A) & m2_relset_1(A,f2_s1_pcomps_1,f3_s1_pcomps_1) & (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s1_pcomps_1))) -> (r2_hidden(B,f2_s1_pcomps_1) -> k1_funct_1(A,B) = f4_s1_pcomps_1(B)))) & v1_funct_2(A,f2_s1_pcomps_1,f3_s1_pcomps_1))) # label(s1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10297 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (exists C (-r1_xreal_0(C,np__0) & r1_tarski(k9_metric_1(A,B,C),u1_struct_0(A)) & m1_subset_1(C,k1_numbers))))))) # label(t29_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10298 (all A (l1_metric_1(A) -> l1_pre_topc(g1_pre_topc(u1_struct_0(A),k4_pcomps_1(A))) & v2_pre_topc(g1_pre_topc(u1_struct_0(A),k4_pcomps_1(A))))) # label(t37_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10299 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(B,C) & v1_pcomps_1(C,A) -> v1_pcomps_1(B,A)))))))) # label(t12_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10300 $T # label(t6_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10301 (all A k2_pcomps_1(A) = g1_pre_topc(A,k1_pcomps_1(A))) # label(d1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10302 $T # label(t3_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10303 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(k6_pre_topc(A,B) != k1_xboole_0 & B = k1_xboole_0) & -(k1_xboole_0 = k6_pre_topc(A,B) & k1_xboole_0 != B))))) # label(t2_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10304 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,k4_pcomps_1(A)) & r2_hidden(B,k4_pcomps_1(A)) -> r2_hidden(k5_subset_1(u1_struct_0(A),B,C),k4_pcomps_1(A))))))))) # label(t35_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10305 (exists A (l1_pre_topc(A) & -v3_struct_0(A) & v2_pcomps_1(A) & v2_pre_topc(A))) # label(rc1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10306 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (v3_compts_1(A) & v2_pcomps_1(A) -> v5_compts_1(A)))) # label(t28_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10307 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> r1_tarski(k5_setfam_1(u1_struct_0(A),B),k5_setfam_1(u1_struct_0(A),k3_pcomps_1(A,B))))))) # label(t22_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10308 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_pre_topc(A,B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (r2_hidden(C,D) & r2_hidden(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))))))))))) # label(t5_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10309 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (v2_compts_1(A) -> v2_pcomps_1(A)))) # label(t25_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10310 (all A all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers) -> (r1_pcomps_1(A,B) <-> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (np__0 = k1_metric_1(A,A,B,C,D) -> D = C) & (C = D -> np__0 = k1_metric_1(A,A,B,C,D)) & r1_xreal_0(k1_metric_1(A,A,B,C,E),k3_real_1(k1_metric_1(A,A,B,C,D),k1_metric_1(A,A,B,D,E))) & k1_metric_1(A,A,B,C,D) = k1_metric_1(A,A,B,D,C)))))))))) # label(d7_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10311 (all A (-v1_xboole_0(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers) & m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_1(B) -> (r1_pcomps_1(A,B) -> g1_metric_1(A,B) = k6_pcomps_1(A,B)))))) # label(d8_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10312 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_finset_1(B) -> v1_pcomps_1(B,A)))))) # label(t13_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10313 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> v2_tops_2(k3_pcomps_1(A,B),A))))) # label(t14_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10314 (all A (l1_metric_1(A) -> r2_hidden(u1_struct_0(A),k4_pcomps_1(A)))) # label(t34_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10315 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (B = k1_xboole_0 -> k3_pcomps_1(A,B) = k1_xboole_0))))) # label(t15_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10316 (all A (l1_metric_1(A) -> m1_subset_1(k4_pcomps_1(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))) # label(dt_k4_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10317 (all A (l1_metric_1(A) -> l1_pre_topc(k5_pcomps_1(A)))) # label(dt_k5_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10318 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v3_compts_1(A) -> v4_pre_topc(k1_struct_0(A,B),A)))))) # label(t10_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10319 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & l1_pre_topc(A) -> m1_subset_1(k3_pcomps_1(A,B),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))) # label(dt_k3_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10320 (all A m1_subset_1(k1_pcomps_1(A),k1_zfmisc_1(k1_zfmisc_1(A)))) # label(dt_k1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10321 (all A l1_pre_topc(k2_pcomps_1(A))) # label(dt_k2_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10322 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> k4_subset_1(k1_zfmisc_1(u1_struct_0(A)),k3_pcomps_1(A,B),k3_pcomps_1(A,C)) = k3_pcomps_1(A,k4_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C)))))))) # label(t18_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10323 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> ((exists B (v1_funct_1(B) & k4_pcomps_1(k6_pcomps_1(u1_struct_0(A),B)) = u1_pre_topc(A) & r1_pcomps_1(u1_struct_0(A),B) & m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_numbers) & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_numbers))) <-> v3_pcomps_1(A)))) # label(d9_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10324 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v2_tops_2(B,A) & v1_pcomps_1(B,A) -> v4_pre_topc(k5_setfam_1(u1_struct_0(A),B),A)))))) # label(t24_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10325 (all A (v2_pre_topc(k2_pcomps_1(A)) & v1_pre_topc(k2_pcomps_1(A)))) # label(fc1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10326 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_pcomps_1(B,A) -> v1_pcomps_1(k3_pcomps_1(A,B),A)))))) # label(t21_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10327 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_finset_1(B) -> k6_pre_topc(A,k5_setfam_1(u1_struct_0(A),B)) = k5_setfam_1(u1_struct_0(A),k3_pcomps_1(A,B))))))) # label(t19_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10328 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (all F (m1_subset_1(F,u1_struct_0(A)) -> -((all G (m1_subset_1(G,k1_numbers) -> -(r1_tarski(k9_metric_1(A,D,G),k9_metric_1(A,E,B)) & r1_tarski(k9_metric_1(A,D,G),k9_metric_1(A,F,C))))) & r2_hidden(D,k5_subset_1(u1_struct_0(A),k9_metric_1(A,E,B),k9_metric_1(A,F,C))) & v9_metric_1(A)))))))))))))) # label(t31_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10329 (all A A = u1_struct_0(k2_pcomps_1(A))) # label(t8_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10330 (all A (l1_metric_1(A) -> k5_pcomps_1(A) = g1_pre_topc(u1_struct_0(A),k4_pcomps_1(A)))) # label(d6_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10331 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> r1_setfam_1(B,k3_pcomps_1(A,B)))))) # label(t20_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10332 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v1_xreal_0(C) -> (v9_metric_1(A) -> r2_hidden(k9_metric_1(A,B,C),k4_pcomps_1(A))))))))) # label(t33_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10333 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(B,C) -> r1_tarski(k3_pcomps_1(A,B),k3_pcomps_1(A,C))))))))) # label(t17_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10334 $T # label(t4_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10335 (all A (l1_metric_1(A) -> v2_pre_topc(k5_pcomps_1(A)) & v1_pre_topc(k5_pcomps_1(A)))) # label(fc3_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10336 (all A u1_pre_topc(k2_pcomps_1(A)) = k1_pcomps_1(A)) # label(t7_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10337 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (k1_tarski(B) = C -> k3_pcomps_1(A,C) = k1_tarski(k6_pre_topc(A,B))))))))) # label(t16_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10338 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(C,D) -> r1_tarski(k9_metric_1(A,B,C),k9_metric_1(A,B,D))))))))))) # label(t1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10339 (all A all B all C all D (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & l1_pre_topc(B) & v2_pre_topc(B) & -v3_struct_0(B) -> ((exists E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & r2_hidden(E,C) & -r1_xboole_0(E,D) & E = A)) <-> r2_hidden(A,a_3_1_pcomps_1(B,C,D))))) # label(fraenkel_a_3_1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10340 (exists A (-v3_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & v3_compts_1(A) & l1_pre_topc(A))) # label(rc2_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10341 (all A (-v1_xboole_0(A) -> -v3_struct_0(k2_pcomps_1(A)) & v1_pre_topc(k2_pcomps_1(A)) & v2_pre_topc(k2_pcomps_1(A)))) # label(fc2_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10342 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (v3_pre_topc(D,A) & v1_finset_1(a_3_0_pcomps_1(A,B,D)) & r2_hidden(C,D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))))))) <-> v1_pcomps_1(B,A)))))) # label(d2_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10343 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(B,k4_pcomps_1(A)) -> r2_hidden(k5_setfam_1(u1_struct_0(A),B),k4_pcomps_1(A))))))) # label(t36_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10344 (all A k1_zfmisc_1(A) = k1_pcomps_1(A)) # label(redefinition_k1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10345 (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)) & v2_cat_1(A) -> v1_funct_1(k22_ens_1(A,B,C)) & v1_funct_2(k22_ens_1(A,B,C),k6_cat_1(A,k3_cat_1(A,B),k2_cat_1(A,C)),k6_cat_1(A,k2_cat_1(A,B),k3_cat_1(A,C))) & m2_relset_1(k22_ens_1(A,B,C),k6_cat_1(A,k3_cat_1(A,B),k2_cat_1(A,C)),k6_cat_1(A,k2_cat_1(A,B),k3_cat_1(A,C))))) # label(dt_k22_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10346 (all A all B (l1_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) & v2_cat_1(A) -> v1_funct_2(k21_ens_1(A,B),u2_cat_1(A),k2_ens_1(k17_ens_1(A))) & m2_relset_1(k21_ens_1(A,B),u2_cat_1(A),k2_ens_1(k17_ens_1(A))) & v1_funct_1(k21_ens_1(A,B)))) # label(dt_k21_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10347 (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_partfun1(k6_cat_1(A,B,C)) = k19_ens_1(A,C,k10_cat_1(A,B)))))))) # label(t44_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10348 (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)) -> (k1_xboole_0 = k6_cat_1(A,k2_cat_1(A,B),k3_cat_1(A,C)) -> k1_xboole_0 = k6_cat_1(A,k3_cat_1(A,B),k2_cat_1(A,C))))))))) # label(t51_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10349 (all A all B (m1_subset_1(B,k2_ens_1(A)) & -v1_xboole_0(A) -> m1_subset_1(k4_ens_1(A,B),A))) # label(dt_k4_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10350 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> r1_tarski(k7_ens_1(A,B,C),k2_ens_1(A)))))))) # label(t17_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10351 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) -> m1_subset_1(k5_ens_1(A,B),k2_ens_1(A)))) # label(dt_k5_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10352 (all A all B all C all D (m1_subset_1(C,B) & m1_subset_1(D,B) & -v1_xboole_0(B) -> ((exists E (k1_domain_1(k2_zfmisc_1(B,B),k1_ens_1(B),k1_domain_1(B,B,C,D),E) = A & r2_hidden(k1_domain_1(k2_zfmisc_1(B,B),k1_ens_1(B),k1_domain_1(B,B,C,D),E),k2_ens_1(B)) & m1_subset_1(E,k1_ens_1(B)))) <-> r2_hidden(A,a_3_0_ens_1(B,C,D))))) # label(fraenkel_a_3_0_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10353 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> k1_funct_1(k3_funct_5(k23_ens_1(A)),k10_cat_1(A,B)) = k20_ens_1(A,B) & k1_funct_1(k5_funct_5(k23_ens_1(A)),k10_cat_1(A,B)) = k21_ens_1(A,B))))) # label(t57_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10354 (all A (-v1_xboole_0(A) -> m2_relset_1(k10_ens_1(A),k2_zfmisc_1(k2_ens_1(A),k2_ens_1(A)),k2_ens_1(A)) & v1_funct_1(k10_ens_1(A)))) # label(dt_k10_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10355 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k2_ens_1(A)) -> (v1_ens_1(B,A) <-> k2_relat_1(k2_mcart_1(B)) = k4_ens_1(A,B)))))) # label(d9_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10356 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,u2_cat_1(k11_cat_2(A,A)),k2_ens_1(k17_ens_1(A))) & v1_funct_2(B,u2_cat_1(k11_cat_2(A,A)),k2_ens_1(k17_ens_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(k11_cat_2(A,A)),k2_ens_1(k17_ens_1(A)),B,k13_cat_2(A,A,C,D)) = k1_domain_1(k2_zfmisc_1(k1_zfmisc_1(u2_cat_1(A)),k1_zfmisc_1(u2_cat_1(A))),k1_zfmisc_1(k2_zfmisc_1(k6_cat_1(A,k3_cat_1(A,C),k2_cat_1(A,D)),k6_cat_1(A,k2_cat_1(A,C),k3_cat_1(A,D)))),k1_domain_1(k1_zfmisc_1(u2_cat_1(A)),k1_zfmisc_1(u2_cat_1(A)),k6_cat_1(A,k3_cat_1(A,C),k2_cat_1(A,D)),k6_cat_1(A,k2_cat_1(A,C),k3_cat_1(A,D))),k22_ens_1(A,C,D)))))) <-> k23_ens_1(A) = B))))) # label(d25_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10357 (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)) -> (all D (m2_relset_1(D,k6_cat_1(A,B,k2_cat_1(A,C)),k6_cat_1(A,B,k3_cat_1(A,C))) & v1_funct_2(D,k6_cat_1(A,B,k2_cat_1(A,C)),k6_cat_1(A,B,k3_cat_1(A,C))) & v1_funct_1(D) -> ((all E (m1_subset_1(E,u2_cat_1(A)) -> (r2_hidden(E,k6_cat_1(A,B,k2_cat_1(A,C))) -> k1_funct_1(D,E) = k4_cat_1(A,E,C)))) <-> k18_ens_1(A,B,C) = D))))))))) # label(d20_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10358 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,u1_cat_1(k12_ens_1(A))) -> -(k1_tarski(k1_xboole_0) != A & v6_cat_1(B,k12_ens_1(A)) & (all C B != k1_tarski(C))))))) # label(t34_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10359 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k2_ens_1(A)) -> -(k4_ens_1(A,B) = k1_xboole_0 & k1_xboole_0 != k3_ens_1(A,B)) & v1_funct_1(k2_mcart_1(B)) & m2_relset_1(k2_mcart_1(B),k3_ens_1(A,B),k4_ens_1(A,B)) & v1_funct_2(k2_mcart_1(B),k3_ens_1(A,B),k4_ens_1(A,B)))))) # label(t9_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10360 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k2_ens_1(A)) -> k6_ens_1(A,k5_ens_1(A,k3_ens_1(A,B)),B) = B & B = k6_ens_1(A,B,k5_ens_1(A,k4_ens_1(A,B))))))) # label(t14_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10361 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k2_ens_1(A)) -> k4_ens_1(A,B) = k2_mcart_1(k1_mcart_1(B)))))) # label(d5_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10362 (all A all B (l1_cat_1(B) & v2_cat_1(B) & -v1_xboole_0(A) -> m2_cat_1(k26_ens_1(A,B),k11_cat_2(k2_oppcat_1(B),B),k12_ens_1(A)))) # label(dt_k26_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10363 (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)) -> m1_subset_1(k1_domain_1(k2_zfmisc_1(k1_zfmisc_1(u2_cat_1(A)),k1_zfmisc_1(u2_cat_1(A))),k1_zfmisc_1(k2_zfmisc_1(k6_cat_1(A,k3_cat_1(A,B),k2_cat_1(A,C)),k6_cat_1(A,k2_cat_1(A,B),k3_cat_1(A,C)))),k1_domain_1(k1_zfmisc_1(u2_cat_1(A)),k1_zfmisc_1(u2_cat_1(A)),k6_cat_1(A,k3_cat_1(A,B),k2_cat_1(A,C)),k6_cat_1(A,k2_cat_1(A,B),k3_cat_1(A,C))),k22_ens_1(A,B,C)),k2_ens_1(k17_ens_1(A))))))))) # label(t52_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10364 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,u2_cat_1(k12_ens_1(A))) -> m1_subset_1(B,k2_ens_1(A)))))) # label(t25_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10365 (all A (-v1_xboole_0(A) -> k2_ens_1(A) = a_1_1_ens_1(A))) # label(d2_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10366 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,u2_cat_1(k12_ens_1(A))) -> k16_ens_1(A,B) = B)))) # label(d18_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10367 (all A (-v1_xboole_0(A) -> -v1_xboole_0(k2_ens_1(A)))) # label(fc2_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10368 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,u2_cat_1(k12_ens_1(A))) -> k4_ens_1(A,k16_ens_1(A,B)) = k3_cat_1(k12_ens_1(A),B) & k3_ens_1(A,k16_ens_1(A,B)) = k2_cat_1(k12_ens_1(A),B))))) # label(t26_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10369 (all A (-v1_xboole_0(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C all D (r2_hidden(k4_tarski(k4_tarski(C,D),B),k2_ens_1(A)) -> (k1_xboole_0 = D -> C = k1_xboole_0) & v1_funct_1(B) & v1_funct_2(B,C,D) & m2_relset_1(B,C,D))))))) # label(t10_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10370 (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)) -> (k6_cat_1(A,k2_cat_1(A,C),B) = k1_xboole_0 -> k6_cat_1(A,k3_cat_1(A,C),B) = k1_xboole_0) & (k1_xboole_0 = k6_cat_1(A,B,k3_cat_1(A,C)) -> k6_cat_1(A,B,k2_cat_1(A,C)) = k1_xboole_0))))))) # label(t42_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10371 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,u1_cat_1(k12_ens_1(A))) -> m1_subset_1(B,A))))) # label(t23_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10372 (all A (l1_cat_1(A) & v2_cat_1(A) -> -v1_xboole_0(k17_ens_1(A)))) # label(fc5_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10373 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (m1_subset_1(B,u1_cat_1(k12_ens_1(A))) -> -((all C B != k1_tarski(C)) & v6_cat_1(B,k12_ens_1(A))))))) # label(t35_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10374 (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,k2_ens_1(A)) -> (r2_hidden(D,k7_ens_1(A,B,C)) -> D = k4_tarski(k1_domain_1(A,A,B,C),k2_mcart_1(D))))))))))) # label(t16_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10375 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> k3_ens_1(A,k5_ens_1(A,B)) = B & B = k4_ens_1(A,k5_ens_1(A,B)) & k2_mcart_1(k5_ens_1(A,B)) = k6_partfun1(B))))) # label(t11_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10376 (all A all B (m1_subset_1(B,u1_cat_1(k12_ens_1(A))) & -v1_xboole_0(A) -> m1_subset_1(k14_ens_1(A,B),A))) # label(dt_k14_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10377 (all A (v2_cat_1(A) & l1_cat_1(A) -> k17_ens_1(A) = a_1_3_ens_1(A))) # label(d19_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10378 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_ens_1(A),A) & v1_funct_2(B,k2_ens_1(A),A) & v1_funct_1(B) -> ((all C (m1_subset_1(C,k2_ens_1(A)) -> k8_funct_2(k2_ens_1(A),A,B,C) = k4_ens_1(A,C))) <-> k9_ens_1(A) = B))))) # label(d11_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10379 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_ens_1(A),A) & m2_relset_1(B,k2_ens_1(A),A) -> ((all C (m1_subset_1(C,k2_ens_1(A)) -> k3_ens_1(A,C) = k8_funct_2(k2_ens_1(A),A,B,C))) <-> k8_ens_1(A) = B))))) # label(d10_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10380 (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)) -> m1_subset_1(k1_domain_1(k2_zfmisc_1(k1_zfmisc_1(u2_cat_1(A)),k1_zfmisc_1(u2_cat_1(A))),k1_zfmisc_1(k2_zfmisc_1(k6_cat_1(A,k3_cat_1(A,C),B),k6_cat_1(A,k2_cat_1(A,C),B))),k1_domain_1(k1_zfmisc_1(u2_cat_1(A)),k1_zfmisc_1(u2_cat_1(A)),k6_cat_1(A,k3_cat_1(A,C),B),k6_cat_1(A,k2_cat_1(A,C),B)),k19_ens_1(A,B,C)),k2_ens_1(k17_ens_1(A))))))))) # label(t48_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10381 (all A (-v1_xboole_0(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (r1_tarski(k17_ens_1(B),A) -> k26_ens_1(A,B) = k23_ens_1(B)))))) # label(d28_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10382 (all A all B (m1_subset_1(B,k2_ens_1(A)) & -v1_xboole_0(A) -> m1_subset_1(k15_ens_1(A,B),u2_cat_1(k12_ens_1(A))))) # label(dt_k15_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10383 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_0_ens_1(B)) <-> (exists C exists D (k1_funct_2(C,D) = A & m1_subset_1(D,B) & m1_subset_1(C,B)))))) # label(fraenkel_a_1_0_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10384 (all A (-v1_xboole_0(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> (r1_tarski(k17_ens_1(B),A) -> k8_funct_2(u1_cat_1(B),u1_cat_1(k12_ens_1(A)),k12_cat_1(B,k12_ens_1(A),k24_ens_1(A,B,C)),D) = k6_cat_1(B,C,D)))))))))) # label(t60_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10385 (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)) -> (all E (m1_subset_1(E,u2_cat_1(A)) -> (k2_cat_1(A,D) = k3_cat_1(A,E) & k2_cat_1(A,C) = k3_cat_1(A,B) -> k22_ens_1(A,k4_cat_1(A,B,C),k4_cat_1(A,E,D)) = k1_partfun1(k6_cat_1(A,k3_cat_1(A,C),k2_cat_1(A,E)),k6_cat_1(A,k2_cat_1(A,C),k3_cat_1(A,E)),k6_cat_1(A,k3_cat_1(A,B),k2_cat_1(A,D)),k6_cat_1(A,k2_cat_1(A,B),k3_cat_1(A,D)),k22_ens_1(A,C,E),k22_ens_1(A,B,D))))))))))))) # label(t56_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10386 (all A all B (l1_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) & v2_cat_1(A) -> m2_relset_1(k20_ens_1(A,B),u2_cat_1(A),k2_ens_1(k17_ens_1(A))) & v1_funct_2(k20_ens_1(A,B),u2_cat_1(A),k2_ens_1(k17_ens_1(A))) & v1_funct_1(k20_ens_1(A,B)))) # label(dt_k20_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10387 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,k2_ens_1(A)) & m1_subset_1(B,k2_ens_1(A)) -> m1_subset_1(k6_ens_1(A,B,C),k2_ens_1(A)))) # label(dt_k6_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10388 (all A (-v1_xboole_0(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> (r1_tarski(k17_ens_1(B),A) -> k25_ens_1(A,B,C) = k15_cat_2(k2_oppcat_1(B),B,k12_ens_1(A),k26_ens_1(A,B),C)))))))) # label(t66_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10389 (all A (-v1_xboole_0(A) -> (all B (r2_hidden(B,k1_ens_1(A)) <-> (exists C (m1_subset_1(C,A) & (exists D (m1_subset_1(D,A) & (D = k1_xboole_0 -> k1_xboole_0 = C) & v1_funct_2(B,C,D) & m2_relset_1(B,C,D) & v1_funct_1(B))))))))) # label(t1_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10390 (all A all B (m1_subset_1(B,u2_cat_1(k12_ens_1(A))) & -v1_xboole_0(A) -> m1_subset_1(k16_ens_1(A,B),k2_ens_1(A)))) # label(dt_k16_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10391 (all A (-v1_xboole_0(A) -> g1_cat_1(A,k2_ens_1(A),k8_ens_1(A),k9_ens_1(A),k10_ens_1(A),k11_ens_1(A)) = k12_ens_1(A))) # label(d14_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10392 (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,k2_ens_1(A)) -> (k4_ens_1(A,D) = C & k3_ens_1(A,D) = B <-> r2_hidden(D,k7_ens_1(A,B,C))))))))))) # label(t19_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10393 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,u2_cat_1(k12_ens_1(A))) -> (v4_cat_1(B,k12_ens_1(A)) -> (all C (m1_subset_1(C,A) -> (all D all E -(r2_hidden(D,C) & E != D & r2_hidden(E,C))))) | v1_ens_1(k16_ens_1(A,B),A)))))) # label(t37_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10394 (all A (-v1_xboole_0(A) -> k3_tarski(a_1_2_ens_1(A)) = k2_ens_1(A))) # label(t18_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10395 $T # label(dt_k2_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10396 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,C) & v1_funct_2(D,B,C) -> ((C = k1_xboole_0 -> B = k1_xboole_0) -> r2_hidden(k1_domain_1(k2_zfmisc_1(A,A),k1_zfmisc_1(k2_zfmisc_1(B,C)),k1_domain_1(A,A,B,C),D),k2_ens_1(A))))))))))) # label(t5_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10397 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,u1_cat_1(k12_ens_1(A))) -> ((exists C k1_tarski(C) = B) -> v6_cat_1(B,k12_ens_1(A))))))) # label(t33_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10398 (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)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (k3_cat_1(A,D) = k2_cat_1(A,C) -> k19_ens_1(A,B,k4_cat_1(A,D,C)) = k1_partfun1(k6_cat_1(A,k3_cat_1(A,C),B),k6_cat_1(A,k2_cat_1(A,C),B),k6_cat_1(A,k3_cat_1(A,D),B),k6_cat_1(A,k2_cat_1(A,D),B),k19_ens_1(A,B,C),k19_ens_1(A,B,D))))))))))) # label(t46_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10399 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> m1_subset_1(B,u1_cat_1(k12_ens_1(A))))))) # label(t22_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10400 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> r1_tarski(k1_funct_2(B,C),k1_ens_1(A)))))))) # label(t2_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10401 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (v1_funct_1(C) & v1_funct_2(C,u2_cat_1(A),k2_ens_1(k17_ens_1(A))) & m2_relset_1(C,u2_cat_1(A),k2_ens_1(k17_ens_1(A))) -> ((all D (m1_subset_1(D,u2_cat_1(A)) -> k8_funct_2(u2_cat_1(A),k2_ens_1(k17_ens_1(A)),C,D) = k1_domain_1(k2_zfmisc_1(k1_zfmisc_1(u2_cat_1(A)),k1_zfmisc_1(u2_cat_1(A))),k1_zfmisc_1(k2_zfmisc_1(k6_cat_1(A,B,k2_cat_1(A,D)),k6_cat_1(A,B,k3_cat_1(A,D)))),k1_domain_1(k1_zfmisc_1(u2_cat_1(A)),k1_zfmisc_1(u2_cat_1(A)),k6_cat_1(A,B,k2_cat_1(A,D)),k6_cat_1(A,B,k3_cat_1(A,D))),k18_ens_1(A,B,D)))) <-> k20_ens_1(A,B) = C))))))) # label(d22_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10402 (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)) -> r2_hidden(k6_cat_1(A,B,C),k17_ens_1(A)))))))) # label(t41_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10403 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,A,k2_ens_1(A)) & v1_funct_2(B,A,k2_ens_1(A)) -> ((all C (m1_subset_1(C,A) -> k5_ens_1(A,C) = k8_funct_2(A,k2_ens_1(A),B,C))) <-> B = k11_ens_1(A)))))) # label(d13_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10404 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,u2_cat_1(k12_ens_1(A))) -> (v2_funct_1(k2_mcart_1(k16_ens_1(A,B))) <-> v3_cat_1(B,k12_ens_1(A))))))) # label(t36_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10405 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k2_ens_1(A)) -> (all C (m1_subset_1(C,k2_ens_1(A)) -> (k3_ens_1(A,C) = k4_ens_1(A,B) -> k6_ens_1(A,B,C) = k4_tarski(k1_domain_1(A,A,k3_ens_1(A,B),k4_ens_1(A,C)),k5_relat_1(k2_mcart_1(B),k2_mcart_1(C)))))))))) # label(d7_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10406 (all A all B all C (-v1_xboole_0(A) & l1_cat_1(B) & m1_subset_1(C,u1_cat_1(B)) & v2_cat_1(B) -> m2_cat_1(k24_ens_1(A,B,C),B,k12_ens_1(A)))) # label(dt_k24_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10407 (all A (-v1_xboole_0(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> (all D (m1_subset_1(D,u2_cat_1(B)) -> (r1_tarski(k17_ens_1(B),A) -> k8_funct_2(u2_cat_1(B),u2_cat_1(k12_ens_1(A)),k24_ens_1(A,B,C),D) = k1_domain_1(k2_zfmisc_1(k1_zfmisc_1(u2_cat_1(B)),k1_zfmisc_1(u2_cat_1(B))),k1_zfmisc_1(k2_zfmisc_1(k6_cat_1(B,C,k2_cat_1(B,D)),k6_cat_1(B,C,k3_cat_1(B,D)))),k1_domain_1(k1_zfmisc_1(u2_cat_1(B)),k1_zfmisc_1(u2_cat_1(B)),k6_cat_1(B,C,k2_cat_1(B,D)),k6_cat_1(B,C,k3_cat_1(B,D))),k18_ens_1(B,C,D))))))))))) # label(t59_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10408 (all A (-v1_xboole_0(A) -> k3_tarski(a_1_0_ens_1(A)) = k1_ens_1(A))) # label(d1_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10409 $T # label(dt_k1_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10410 (all A all B (l1_cat_1(B) & v2_cat_1(B) -> ((exists C exists D (A = k6_cat_1(B,C,D) & m1_subset_1(D,u1_cat_1(B)) & m1_subset_1(C,u1_cat_1(B)))) <-> r2_hidden(A,a_1_3_ens_1(B))))) # label(fraenkel_a_1_3_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10411 (all A (-v1_xboole_0(A) -> v2_cat_1(g1_cat_1(A,k2_ens_1(A),k8_ens_1(A),k9_ens_1(A),k10_ens_1(A),k11_ens_1(A))) & l1_cat_1(g1_cat_1(A,k2_ens_1(A),k8_ens_1(A),k9_ens_1(A),k10_ens_1(A),k11_ens_1(A))))) # label(t21_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10412 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k2_ens_1(A)) -> B = k15_ens_1(A,B))))) # label(d17_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10413 (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_partfun1(k6_cat_1(A,B,C)) = k22_ens_1(A,k10_cat_1(A,B),k10_cat_1(A,C)))))))) # label(t54_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10414 $T # label(dt_k7_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10415 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> k18_ens_1(A,B,C) = k22_ens_1(A,k10_cat_1(A,B),C) & k22_ens_1(A,C,k10_cat_1(A,B)) = k19_ens_1(A,B,C))))))) # label(t53_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10416 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k2_ens_1(A)) -> B = k4_tarski(k1_domain_1(A,A,k3_ens_1(A,B),k4_ens_1(A,B)),k2_mcart_1(B)))))) # label(t8_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10417 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> a_3_0_ens_1(A,B,C) = k7_ens_1(A,B,C))))))) # label(d8_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10418 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,u1_cat_1(k12_ens_1(A))) -> (k1_xboole_0 = B -> v7_cat_1(B,k12_ens_1(A))))))) # label(t30_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10419 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k2_ens_1(A)) -> (exists C (m1_subset_1(C,k1_ens_1(A)) & (exists D (m1_subset_1(D,A) & (exists E (k1_domain_1(k2_zfmisc_1(A,A),k1_ens_1(A),k1_domain_1(A,A,D,E),C) = B & v1_funct_1(C) & m2_relset_1(C,D,E) & v1_funct_2(C,D,E) & (E = k1_xboole_0 -> k1_xboole_0 = D) & m1_subset_1(E,A))))))))))) # label(t4_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10420 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m2_relset_1(D,B,C) & v1_funct_2(D,B,C) & v1_funct_1(D) -> ((C = k1_xboole_0 -> B = k1_xboole_0) -> r2_hidden(k1_domain_1(k2_zfmisc_1(A,A),k1_zfmisc_1(k2_zfmisc_1(B,C)),k1_domain_1(A,A,B,C),D),k7_ens_1(A,B,C))))))))))) # label(t15_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10421 (all A all B (m1_subset_1(B,k2_ens_1(A)) & -v1_xboole_0(A) -> m1_subset_1(k3_ens_1(A,B),A))) # label(dt_k3_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10422 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k2_ens_1(A)) -> k1_mcart_1(k1_mcart_1(B)) = k3_ens_1(A,B))))) # label(d4_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10423 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(k2_ens_1(A),k2_ens_1(A)),k2_ens_1(A)) -> ((all C (m1_subset_1(C,k2_ens_1(A)) -> (all D (m1_subset_1(D,k2_ens_1(A)) -> (k3_ens_1(A,C) = k4_ens_1(A,D) <-> r2_hidden(k1_domain_1(k2_ens_1(A),k2_ens_1(A),C,D),k1_relat_1(B))))))) & (all C (m1_subset_1(C,k2_ens_1(A)) -> (all D (m1_subset_1(D,k2_ens_1(A)) -> (k4_ens_1(A,D) = k3_ens_1(A,C) -> k1_funct_1(B,k1_domain_1(k2_ens_1(A),k2_ens_1(A),C,D)) = k6_ens_1(A,D,C)))))) <-> k10_ens_1(A) = B))))) # label(d12_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10424 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,u2_cat_1(k12_ens_1(A))) -> (v1_ens_1(k16_ens_1(A,B),A) -> v4_cat_1(B,k12_ens_1(A))))))) # label(t38_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10425 (all A (-v1_xboole_0(A) -> v1_funct_2(k8_ens_1(A),k2_ens_1(A),A) & m2_relset_1(k8_ens_1(A),k2_ens_1(A),A) & v1_funct_1(k8_ens_1(A)))) # label(dt_k8_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10426 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,u1_cat_1(k12_ens_1(A))) -> k14_ens_1(A,B) = B)))) # label(d16_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10427 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k2_ens_1(A)) -> (all C (m1_subset_1(C,k2_ens_1(A)) -> (k3_ens_1(A,B) = k4_ens_1(A,C) -> k3_ens_1(A,k6_ens_1(A,C,B)) = k3_ens_1(A,C) & k4_ens_1(A,B) = k4_ens_1(A,k6_ens_1(A,C,B)) & k5_relat_1(k2_mcart_1(C),k2_mcart_1(B)) = k2_mcart_1(k6_ens_1(A,C,B))))))))) # label(t12_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10428 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,u1_cat_1(k12_ens_1(A))) -> (all C (m1_subset_1(C,u1_cat_1(k12_ens_1(A))) -> k6_cat_1(k12_ens_1(A),B,C) = k7_ens_1(A,k14_ens_1(A,B),k14_ens_1(A,C)))))))) # label(t27_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10429 (all A (-v1_xboole_0(A) -> -v1_xboole_0(k1_ens_1(A)) & v1_fraenkel(k1_ens_1(A)))) # label(fc1_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.30/125.66 10430 (all A all B all C (v2_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) & m1_subset_1(C,u2_cat_1(A)) & l1_cat_1(A) -> v1_funct_2(k18_ens_1(A,B,C),k6_cat_1(A,B,k2_cat_1(A,C)),k6_cat_1(A,B,k3_cat_1(A,C))) & m2_relset_1(k18_ens_1(A,B,C),k6_cat_1(A,B,k2_cat_1(A,C)),k6_cat_1(A,B,k3_cat_1(A,C))) & v1_funct_1(k18_ens_1(A,B,C)))) # label(dt_k18_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.66 10431 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> k13_ens_1(A,B) = B)))) # label(d15_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.66 10432 (all A (-v1_xboole_0(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> (r1_tarski(k17_ens_1(B),A) -> k6_cat_1(B,D,C) = k8_funct_2(u1_cat_1(B),u1_cat_1(k12_ens_1(A)),k12_cat_1(B,k12_ens_1(A),k25_ens_1(A,B,C)),D)))))))))) # label(t62_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.66 10433 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (m1_subset_1(B,u1_cat_1(k12_ens_1(A))) -> (v7_cat_1(B,k12_ens_1(A)) -> B = k1_xboole_0))))) # label(t32_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.66 10434 (all A (-v1_xboole_0(A) -> r1_tarski(k2_ens_1(A),k2_zfmisc_1(k2_zfmisc_1(A,A),k1_ens_1(A))))) # label(t6_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.66 10435 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,u2_cat_1(k12_ens_1(A))) -> (all C (m1_subset_1(C,u2_cat_1(k12_ens_1(A))) -> (k2_cat_1(k12_ens_1(A),B) = k3_cat_1(k12_ens_1(A),C) -> k6_ens_1(A,k16_ens_1(A,C),k16_ens_1(A,B)) = k4_cat_1(k12_ens_1(A),C,B)))))))) # label(t28_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.66 10436 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) -> r1_tarski(k1_ens_1(B),k1_ens_1(A)))))) # label(t3_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.66 10437 (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)) -> k1_partfun1(k6_cat_1(A,k3_cat_1(A,B),k2_cat_1(A,C)),k6_cat_1(A,k2_cat_1(A,B),k2_cat_1(A,C)),k6_cat_1(A,k2_cat_1(A,B),k2_cat_1(A,C)),k6_cat_1(A,k2_cat_1(A,B),k3_cat_1(A,C)),k19_ens_1(A,k2_cat_1(A,C),B),k18_ens_1(A,k2_cat_1(A,B),C)) = k22_ens_1(A,B,C))))))) # label(t55_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.66 10438 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,k2_ens_1(A)) -> v1_relat_1(k2_mcart_1(B)) & v1_funct_1(k2_mcart_1(B)))) # label(fc3_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.66 10439 (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)) -> k18_ens_1(A,B,k10_cat_1(A,C)) = k6_partfun1(k6_cat_1(A,B,C)))))))) # label(t43_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.66 10440 $T # label(d3_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.66 10441 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (v1_funct_1(D) & m2_relset_1(D,k6_cat_1(A,k3_cat_1(A,C),B),k6_cat_1(A,k2_cat_1(A,C),B)) & v1_funct_2(D,k6_cat_1(A,k3_cat_1(A,C),B),k6_cat_1(A,k2_cat_1(A,C),B)) -> (D = k19_ens_1(A,B,C) <-> (all E (m1_subset_1(E,u2_cat_1(A)) -> (r2_hidden(E,k6_cat_1(A,k3_cat_1(A,C),B)) -> k4_cat_1(A,C,E) = k1_funct_1(D,E))))))))))))) # label(d21_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.66 10442 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) -> r1_tarski(k2_ens_1(B),k2_ens_1(A)))))) # label(t7_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.66 10443 (all A all B (-v1_xboole_0(B) -> ((exists C exists D (k7_ens_1(B,C,D) = A & m1_subset_1(D,B) & m1_subset_1(C,B))) <-> r2_hidden(A,a_1_2_ens_1(B))))) # label(fraenkel_a_1_2_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.66 10444 (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)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (k3_cat_1(A,D) = k2_cat_1(A,C) -> k1_partfun1(k6_cat_1(A,B,k2_cat_1(A,D)),k6_cat_1(A,B,k3_cat_1(A,D)),k6_cat_1(A,B,k2_cat_1(A,C)),k6_cat_1(A,B,k3_cat_1(A,C)),k18_ens_1(A,B,D),k18_ens_1(A,B,C)) = k18_ens_1(A,B,k4_cat_1(A,D,C))))))))))) # label(t45_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.66 10445 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> k1_domain_1(k2_zfmisc_1(A,A),k1_zfmisc_1(k2_zfmisc_1(B,B)),k1_domain_1(A,A,B,B),k6_partfun1(B)) = k5_ens_1(A,B))))) # label(d6_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.66 10446 (all A (v2_cat_1(A) & l1_cat_1(A) -> v1_funct_2(k23_ens_1(A),u2_cat_1(k11_cat_2(A,A)),k2_ens_1(k17_ens_1(A))) & m2_relset_1(k23_ens_1(A),u2_cat_1(k11_cat_2(A,A)),k2_ens_1(k17_ens_1(A))) & v1_funct_1(k23_ens_1(A)))) # label(dt_k23_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.66 10447 (all A all B (m1_subset_1(B,A) & -v1_xboole_0(A) -> m1_subset_1(k13_ens_1(A,B),u1_cat_1(k12_ens_1(A))))) # label(dt_k13_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.66 10448 (all A (-v1_xboole_0(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> (r1_tarski(k17_ens_1(B),A) -> m1_oppcat_1(k21_ens_1(B,C),B,k12_ens_1(A))))))))) # label(t50_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.66 10449 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> m1_subset_1(k1_domain_1(k2_zfmisc_1(k1_zfmisc_1(u2_cat_1(A)),k1_zfmisc_1(u2_cat_1(A))),k1_zfmisc_1(k2_zfmisc_1(k6_cat_1(A,B,k2_cat_1(A,C)),k6_cat_1(A,B,k3_cat_1(A,C)))),k1_domain_1(k1_zfmisc_1(u2_cat_1(A)),k1_zfmisc_1(u2_cat_1(A)),k6_cat_1(A,B,k2_cat_1(A,C)),k6_cat_1(A,B,k3_cat_1(A,C))),k18_ens_1(A,B,C)),k2_ens_1(k17_ens_1(A))))))))) # label(t47_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.66 10450 (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 (v1_funct_1(D) & m2_relset_1(D,k6_cat_1(A,k3_cat_1(A,B),k2_cat_1(A,C)),k6_cat_1(A,k2_cat_1(A,B),k3_cat_1(A,C))) & v1_funct_2(D,k6_cat_1(A,k3_cat_1(A,B),k2_cat_1(A,C)),k6_cat_1(A,k2_cat_1(A,B),k3_cat_1(A,C))) -> (D = k22_ens_1(A,B,C) <-> (all E (m1_subset_1(E,u2_cat_1(A)) -> (r2_hidden(E,k6_cat_1(A,k3_cat_1(A,B),k2_cat_1(A,C))) -> k4_cat_1(A,B,k4_cat_1(A,E,C)) = k1_funct_1(D,E))))))))))))) # label(d24_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.66 10451 (all A all B all C (m1_subset_1(C,u1_cat_1(B)) & l1_cat_1(B) & v2_cat_1(B) & -v1_xboole_0(A) -> m1_oppcat_1(k25_ens_1(A,B,C),B,k12_ens_1(A)))) # label(dt_k25_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.66 10452 (all A (-v1_xboole_0(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> (r1_tarski(k17_ens_1(B),A) -> k21_ens_1(B,C) = k25_ens_1(A,B,C)))))))) # label(d27_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.66 10453 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (v1_funct_2(C,u2_cat_1(A),k2_ens_1(k17_ens_1(A))) & m2_relset_1(C,u2_cat_1(A),k2_ens_1(k17_ens_1(A))) & v1_funct_1(C) -> ((all D (m1_subset_1(D,u2_cat_1(A)) -> k1_domain_1(k2_zfmisc_1(k1_zfmisc_1(u2_cat_1(A)),k1_zfmisc_1(u2_cat_1(A))),k1_zfmisc_1(k2_zfmisc_1(k6_cat_1(A,k3_cat_1(A,D),B),k6_cat_1(A,k2_cat_1(A,D),B))),k1_domain_1(k1_zfmisc_1(u2_cat_1(A)),k1_zfmisc_1(u2_cat_1(A)),k6_cat_1(A,k3_cat_1(A,D),B),k6_cat_1(A,k2_cat_1(A,D),B)),k19_ens_1(A,B,D)) = k8_funct_2(u2_cat_1(A),k2_ens_1(k17_ens_1(A)),C,D))) <-> C = k21_ens_1(A,B)))))))) # label(d23_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.66 10454 (all A all B all C (v2_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) & m1_subset_1(C,u2_cat_1(A)) & l1_cat_1(A) -> v1_funct_1(k19_ens_1(A,B,C)) & v1_funct_2(k19_ens_1(A,B,C),k6_cat_1(A,k3_cat_1(A,C),B),k6_cat_1(A,k2_cat_1(A,C),B)) & m2_relset_1(k19_ens_1(A,B,C),k6_cat_1(A,k3_cat_1(A,C),B),k6_cat_1(A,k2_cat_1(A,C),B)))) # label(dt_k19_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.66 10455 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k2_ens_1(A)) -> (all C (m1_subset_1(C,k2_ens_1(A)) -> (all D (m1_subset_1(D,k2_ens_1(A)) -> (k3_ens_1(A,B) = k4_ens_1(A,C) & k4_ens_1(A,B) = k3_ens_1(A,D) -> k6_ens_1(A,k6_ens_1(A,C,B),D) = k6_ens_1(A,C,k6_ens_1(A,B,D))))))))))) # label(t13_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.66 10456 (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,k2_ens_1(A)) -> (r2_hidden(D,k7_ens_1(A,B,C)) -> r2_hidden(k2_mcart_1(D),k1_funct_2(B,C))))))))))) # label(t20_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.66 10457 (all A (-v1_xboole_0(A) -> v1_funct_2(k9_ens_1(A),k2_ens_1(A),A) & m2_relset_1(k9_ens_1(A),k2_ens_1(A),A) & v1_funct_1(k9_ens_1(A)))) # label(dt_k9_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.66 10458 (all A (-v1_xboole_0(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> (all D (m1_subset_1(D,u2_cat_1(B)) -> (r1_tarski(k17_ens_1(B),A) -> k1_domain_1(k2_zfmisc_1(k1_zfmisc_1(u2_cat_1(B)),k1_zfmisc_1(u2_cat_1(B))),k1_zfmisc_1(k2_zfmisc_1(k6_cat_1(B,k3_cat_1(B,D),C),k6_cat_1(B,k2_cat_1(B,D),C))),k1_domain_1(k1_zfmisc_1(u2_cat_1(B)),k1_zfmisc_1(u2_cat_1(B)),k6_cat_1(B,k3_cat_1(B,D),C),k6_cat_1(B,k2_cat_1(B,D),C)),k19_ens_1(B,C,D)) = k8_funct_2(u2_cat_1(B),u2_cat_1(k12_ens_1(A)),k25_ens_1(A,B,C),D)))))))))) # label(t61_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.66 10459 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,u1_cat_1(k12_ens_1(A))) -> k5_ens_1(A,k14_ens_1(A,B)) = k10_cat_1(k12_ens_1(A),B))))) # label(t29_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.66 10460 (all A (-v1_xboole_0(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> (r1_tarski(k17_ens_1(B),A) -> k24_ens_1(A,B,C) = k20_ens_1(B,C)))))))) # label(d26_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.66 10461 (all A all B (-v1_xboole_0(B) -> ((exists C exists D exists E (m1_subset_1(D,B) & (k1_xboole_0 = D -> k1_xboole_0 = C) & v1_funct_1(E) & v1_funct_2(E,C,D) & m2_relset_1(E,C,D) & k1_domain_1(k2_zfmisc_1(B,B),k1_ens_1(B),k1_domain_1(B,B,C,D),E) = A & m1_subset_1(E,k1_ens_1(B)) & m1_subset_1(C,B))) <-> r2_hidden(A,a_1_1_ens_1(B))))) # label(fraenkel_a_1_1_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.66 10462 (all A (-v1_xboole_0(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> (r1_tarski(k17_ens_1(B),A) -> k14_cat_2(k2_oppcat_1(B),B,k12_ens_1(A),k26_ens_1(A,B),k3_oppcat_1(B,C)) = k24_ens_1(A,B,C)))))))) # label(t65_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.66 10463 (all A (-v1_xboole_0(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u2_cat_1(B)) -> (all D (m1_subset_1(D,u2_cat_1(B)) -> (r1_tarski(k17_ens_1(B),A) -> k1_domain_1(k2_zfmisc_1(k1_zfmisc_1(u2_cat_1(B)),k1_zfmisc_1(u2_cat_1(B))),k1_zfmisc_1(k2_zfmisc_1(k6_cat_1(B,k3_cat_1(B,C),k2_cat_1(B,D)),k6_cat_1(B,k2_cat_1(B,C),k3_cat_1(B,D)))),k1_domain_1(k1_zfmisc_1(u2_cat_1(B)),k1_zfmisc_1(u2_cat_1(B)),k6_cat_1(B,k3_cat_1(B,C),k2_cat_1(B,D)),k6_cat_1(B,k2_cat_1(B,C),k3_cat_1(B,D))),k22_ens_1(B,C,D)) = k8_funct_2(u2_cat_1(k11_cat_2(k2_oppcat_1(B),B)),u2_cat_1(k12_ens_1(A)),k26_ens_1(A,B),k13_cat_2(k2_oppcat_1(B),B,k5_oppcat_1(B,C),D))))))))))) # label(t63_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.66 10464 (all A (-v1_xboole_0(A) -> v2_cat_1(k12_ens_1(A)) & v1_cat_1(k12_ens_1(A)))) # label(fc4_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.66 10465 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) -> r1_cat_2(k12_ens_1(B),k12_ens_1(A)))))) # label(t40_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.66 10466 (all A (-v1_xboole_0(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> (r1_tarski(k17_ens_1(B),A) -> m2_cat_1(k20_ens_1(B,C),B,k12_ens_1(A))))))))) # label(t49_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.66 10467 (all A (-v1_xboole_0(A) -> l1_cat_1(k12_ens_1(A)))) # label(dt_k12_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.66 10468 (all A (-v1_xboole_0(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> (r1_tarski(k17_ens_1(B),A) -> k6_cat_1(B,C,D) = k8_funct_2(u1_cat_1(k11_cat_2(k2_oppcat_1(B),B)),u1_cat_1(k12_ens_1(A)),k12_cat_1(k11_cat_2(k2_oppcat_1(B),B),k12_ens_1(A),k26_ens_1(A,B)),k12_cat_2(k2_oppcat_1(B),B,k3_oppcat_1(B,C),D))))))))))) # label(t64_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10469 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (m1_subset_1(B,u2_cat_1(k12_ens_1(A))) -> (v4_cat_1(B,k12_ens_1(A)) -> v1_ens_1(k16_ens_1(A,B),A)))))) # label(t39_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10470 (all A (-v1_xboole_0(A) -> v1_funct_1(k11_ens_1(A)) & m2_relset_1(k11_ens_1(A),A,k2_ens_1(A)) & v1_funct_2(k11_ens_1(A),A,k2_ens_1(A)))) # label(dt_k11_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10471 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,u1_cat_1(k12_ens_1(A))) -> (v7_cat_1(B,k12_ens_1(A)) & r2_hidden(k1_xboole_0,A) -> B = k1_xboole_0))))) # label(t31_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10472 $T # label(dt_k17_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10473 (all A (-v1_xboole_0(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (r1_tarski(k17_ens_1(B),A) -> m2_cat_1(k23_ens_1(B),k11_cat_2(k2_oppcat_1(B),B),k12_ens_1(A))))))) # label(t58_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10474 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k2_ens_1(A)) -> m1_subset_1(B,u2_cat_1(k12_ens_1(A))))))) # label(t24_ens_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10475 (all A all B all C (-v3_struct_0(A) & v2_pre_topc(A) & m1_pre_topc(B,A) & -v1_xboole_0(C) & m1_eqrel_1(C,u1_struct_0(B)) & -v3_struct_0(B) & l1_pre_topc(A) -> m1_eqrel_1(k18_borsuk_1(A,B,C),u1_struct_0(A)) & -v1_xboole_0(k18_borsuk_1(A,B,C)))) # label(dt_k18_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10476 (all A all B all C all D (l1_pre_topc(A) & v2_pre_topc(B) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(C,u1_struct_0(A)) & l1_pre_topc(B) & -v3_struct_0(B) & v2_pre_topc(A) & -v3_struct_0(A) -> m1_subset_1(k8_borsuk_1(A,B,C,D),u1_struct_0(k6_borsuk_1(A,B))))) # label(dt_k8_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10477 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) -> (v1_tops_2(C,k6_borsuk_1(A,B)) -> v1_tops_2(k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(B),k13_borsuk_1(A,B),C),B) & v1_tops_2(k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(A),k12_borsuk_1(A,B),C),A)))))))) # label(t60_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10478 (all A all B all C all D all E all F (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(B) & m1_subset_1(D,u1_struct_0(B)) & m1_connsp_2(F,B,D) & m2_connsp_2(E,A,C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(B) & v2_pre_topc(B) & -v3_struct_0(A) -> m2_connsp_2(k10_borsuk_1(A,B,C,D,E,F),k6_borsuk_1(A,B),k7_borsuk_1(A,B,C,k1_struct_0(B,D))))) # label(dt_k10_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10479 (all A all B all C (l1_struct_0(B) & m1_subset_1(C,u1_struct_0(B)) & -v3_struct_0(B) & l1_struct_0(A) -> v1_funct_1(k3_borsuk_1(A,B,C)) & v1_funct_2(k3_borsuk_1(A,B,C),u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(k3_borsuk_1(A,B,C),u1_struct_0(A),u1_struct_0(B)))) # label(dt_k3_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10480 (all A (-v1_xboole_0(A) -> (all B (m1_eqrel_1(B,A) & -v1_xboole_0(B) -> (all C (m1_subset_1(C,A) -> (all D (m2_subset_1(D,k1_zfmisc_1(A),B) -> (r2_hidden(C,D) -> k8_funct_2(A,B,k2_borsuk_1(A,B),C) = D))))))))) # label(t29_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10481 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> k1_tops_1(k6_borsuk_1(A,B),C) = k5_setfam_1(u1_struct_0(k6_borsuk_1(A,B)),k11_borsuk_1(A,B,C)))))))) # label(t55_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10482 (all A all B all C (-v3_struct_0(A) & v2_pre_topc(A) & v1_borsuk_1(B,A) & m1_pre_topc(B,A) & m1_borsuk_1(C,B) & v2_borsuk_1(C,B) & -v3_struct_0(B) & l1_pre_topc(A) -> k16_borsuk_1(B,C) = k21_borsuk_1(A,B,C))) # label(redefinition_k21_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10483 (all A all B all C all D all E (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(B) & -v3_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C)) & v5_pre_topc(E,B,C) & m1_relset_1(E,u1_struct_0(B),u1_struct_0(C)) & v1_funct_1(E) & v5_pre_topc(D,A,B) & v1_funct_1(D) & l1_pre_topc(B) & v2_pre_topc(B) -> v1_funct_1(k4_borsuk_1(A,B,C,D,E)) & v1_funct_2(k4_borsuk_1(A,B,C,D,E),u1_struct_0(A),u1_struct_0(C)) & v5_pre_topc(k4_borsuk_1(A,B,C,D,E),A,C) & m2_relset_1(k4_borsuk_1(A,B,C,D,E),u1_struct_0(A),u1_struct_0(C)))) # label(dt_k4_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10484 (all A (-v3_struct_0(A) & l1_struct_0(A) -> v1_setfam_1(k15_borsuk_1(A)) & -v1_xboole_0(k15_borsuk_1(A)))) # label(fc3_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10485 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) -> (all D -(r2_hidden(D,k2_funct_2(k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(B)),k13_borsuk_1(A,B),C)) & (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> -(D = k2_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B),k10_funct_3(u1_struct_0(A),u1_struct_0(B)),E) & r2_hidden(E,C)))))))))))) # label(t58_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10486 (all A all B (v2_pre_topc(A) & l1_pre_topc(A) & v2_pre_topc(B) & l1_pre_topc(B) -> v1_pre_topc(k6_borsuk_1(A,B)) & l1_pre_topc(k6_borsuk_1(A,B)) & v2_pre_topc(k6_borsuk_1(A,B)))) # label(dt_k6_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10487 (all A all B all C (-v3_struct_0(A) & v2_pre_topc(A) & m1_subset_1(C,u1_struct_0(B)) & l1_pre_topc(B) & v2_pre_topc(B) & -v3_struct_0(B) & l1_pre_topc(A) -> -v1_xboole_0(k3_borsuk_1(A,B,C)) & v1_relat_1(k3_borsuk_1(A,B,C)) & v1_funct_1(k3_borsuk_1(A,B,C)) & v1_funct_2(k3_borsuk_1(A,B,C),u1_struct_0(A),u1_struct_0(B)) & v1_partfun1(k3_borsuk_1(A,B,C),u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(k3_borsuk_1(A,B,C),A,B))) # label(fc1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10488 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> k3_tarski(a_2_0_borsuk_1(A,B)) = k3_tarski(k5_setfam_1(A,B)))) # label(t17_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10489 (all A (-v1_xboole_0(A) -> (all B (m1_eqrel_1(B,A) & -v1_xboole_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(B)) -> k3_tarski(C) = k3_funct_2(A,B,k2_borsuk_1(A,B),C))))))) # label(t31_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10490 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_eqrel_1(C,u1_struct_0(B)) & -v1_xboole_0(C) -> r1_tarski(C,k18_borsuk_1(A,B,C)))))))) # label(t73_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10491 (all A all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) -> k5_setfam_1(B,k2_funct_2(k1_zfmisc_1(A),k1_zfmisc_1(B),k2_funct_3(A,B,C),D)) = k2_funct_2(A,B,C,k5_setfam_1(A,D)))))))) # label(t16_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10492 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (v5_pre_topc(C,A,B) <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_connsp_2(E,B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D)) -> (exists F (r1_tarski(k4_pre_topc(A,B,C,F),E) & m1_connsp_2(F,A,D)))))))))))))) # label(d2_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10493 (all A all B all C (v2_pre_topc(B) & -v3_struct_0(C) & m1_pre_topc(C,B) & l1_pre_topc(B) & -v3_struct_0(B) -> (r2_hidden(A,a_2_3_borsuk_1(B,C)) <-> (exists D (m1_subset_1(D,u1_struct_0(B)) & A = k1_struct_0(B,D) & -r2_hidden(D,u1_struct_0(C))))))) # label(fraenkel_a_2_3_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10494 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & m1_eqrel_1(B,A) -> (all C (m2_subset_1(C,k1_zfmisc_1(A),B) -> (exists D (m1_subset_1(D,A) & C = k8_funct_2(A,B,k2_borsuk_1(A,B),D))))))))) # label(t32_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10495 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> ((exists C (v5_pre_topc(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v3_borsuk_1(C,A,B) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C))) <-> r1_borsuk_1(A,B)))))) # label(d20_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10496 (all A (-v1_xboole_0(A) -> (all B (m1_eqrel_1(B,A) & -v1_xboole_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(D,B) -> r1_tarski(D,C) | r1_xboole_0(D,C)))) -> k3_funct_2(A,B,k2_borsuk_1(A,B),k2_funct_2(A,B,k2_borsuk_1(A,B),C)) = C))))))) # label(t33_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10497 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v1_xboole_0(C) & m1_eqrel_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(k8_funct_2(u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,k18_borsuk_1(A,B,C))),k17_borsuk_1(A,k18_borsuk_1(A,B,C)),D),u1_struct_0(k16_borsuk_1(B,C))) -> r2_hidden(D,u1_struct_0(B))))))))))) # label(t79_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10498 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & v1_borsuk_1(B,A) & -v3_struct_0(B) -> (all C (v2_borsuk_1(C,B) & m1_borsuk_1(C,B) -> (r2_borsuk_1(A,B) -> r2_borsuk_1(k16_borsuk_1(A,k20_borsuk_1(A,B,C)),k21_borsuk_1(A,B,C))))))))) # label(t85_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10499 (all A all B all C all D (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(C,u1_struct_0(A)) & l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> k4_tarski(C,D) = k8_borsuk_1(A,B,C,D))) # label(redefinition_k8_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10500 (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_1(E) & m2_relset_1(E,A,C) & v1_funct_2(E,A,C) -> -((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,A) -> (k8_funct_2(A,B,D,F) = k8_funct_2(A,B,D,G) -> k8_funct_2(A,C,E,F) = k8_funct_2(A,C,E,G)))))) & (all F (v1_funct_1(F) & m2_relset_1(F,B,C) & v1_funct_2(F,B,C) -> E != k7_funct_2(A,B,C,D,F)))))))))))))) # label(t19_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10501 (all A all B all C (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(B) & v1_borsuk_1(B,A) & m1_borsuk_1(C,B) & m1_pre_topc(B,A) -> m1_borsuk_1(k19_borsuk_1(A,B,C),A))) # label(dt_k19_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10502 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) -> -((all E (m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) -> -(r1_tarski(E,D) & C = k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(A),k12_borsuk_1(A,B),E) & v1_finset_1(E)))) & r1_tarski(C,k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(A),k12_borsuk_1(A,B),D)) & v1_finset_1(C)))))))))) # label(t64_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10503 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(B)) -> m1_subset_1(k3_tarski(C),k1_zfmisc_1(A)))))))) # label(t25_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10504 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,B) -> (all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (all F (v1_funct_2(F,B,C) & m2_relset_1(F,B,C) & v1_funct_1(F) -> r1_tarski(k3_funct_2(A,B,E,k6_domain_1(B,D)),k3_funct_2(A,C,k7_funct_2(A,B,C,E,F),k6_domain_1(C,k8_funct_2(B,C,F,D)))))))))))))))) # label(t20_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10505 (all A all B (m1_eqrel_1(B,u1_struct_0(A)) & l1_pre_topc(A) & v2_pre_topc(A) -> v2_pre_topc(k16_borsuk_1(A,B)) & l1_pre_topc(k16_borsuk_1(A,B)) & v1_pre_topc(k16_borsuk_1(A,B)))) # label(dt_k16_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10506 (all A all B all C (v2_pre_topc(B) & l1_pre_topc(B) & m1_eqrel_1(C,u1_struct_0(B)) -> (r2_hidden(A,a_2_2_borsuk_1(B,C)) <-> (exists D (m1_subset_1(D,k1_zfmisc_1(C)) & A = D & r2_hidden(k3_tarski(D),u1_pre_topc(B))))))) # label(fraenkel_a_2_2_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10507 (all A all B (-v3_struct_0(A) & l1_pre_topc(A) & l1_pre_topc(B) & v2_pre_topc(B) & -v3_struct_0(B) & v2_pre_topc(A) -> v1_funct_1(k12_borsuk_1(A,B)) & v1_funct_2(k12_borsuk_1(A,B),k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(A))) & m2_relset_1(k12_borsuk_1(A,B),k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(A))))) # label(dt_k12_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10508 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_borsuk_1(B,A) -> (all C (m1_subset_1(C,u1_struct_0(k16_borsuk_1(A,B))) -> (all D (m2_connsp_2(D,A,k5_pre_topc(A,k16_borsuk_1(A,B),k17_borsuk_1(A,B),k1_struct_0(k16_borsuk_1(A,B),C))) -> m1_connsp_2(k4_pre_topc(A,k16_borsuk_1(A,B),k17_borsuk_1(A,B),D),k16_borsuk_1(A,B),C))))))))) # label(t81_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10509 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> r1_tarski(k5_setfam_1(u1_struct_0(k6_borsuk_1(A,B)),k11_borsuk_1(A,B,C)),C))))))) # label(t53_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10510 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (m1_pre_topc(B,A) & v1_pre_topc(B) & v2_pre_topc(B) & v1_borsuk_1(B,A))))) # label(rc3_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10511 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_eqrel_1(B,u1_struct_0(A)) -> (all C (v2_pre_topc(C) & l1_pre_topc(C) & v1_pre_topc(C) -> (k16_borsuk_1(A,B) = C <-> u1_pre_topc(C) = a_2_2_borsuk_1(A,B) & u1_struct_0(C) = B))))))) # label(d10_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10512 (all A all B all C all D all E (-v3_struct_0(A) & v2_pre_topc(A) & v2_pre_topc(B) & m1_subset_1(C,u1_struct_0(B)) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(D,A,B) & m1_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & m1_connsp_2(E,B,C) & v1_funct_1(D) & l1_pre_topc(B) & -v3_struct_0(B) & l1_pre_topc(A) -> m2_connsp_2(k5_borsuk_1(A,B,C,D,E),A,k5_pre_topc(A,B,D,k1_struct_0(B,C))))) # label(dt_k5_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10513 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) -> ((exists D (k3_tarski(D) = A & r2_hidden(D,C) & m1_subset_1(D,k1_zfmisc_1(B)))) <-> r2_hidden(A,a_2_0_borsuk_1(B,C))))) # label(fraenkel_a_2_0_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10514 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (C = D -> (v6_compts_1(D,B) <-> v6_compts_1(C,A))))))))))) # label(t42_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10515 (all A all B all C (-v3_struct_0(A) & -v3_struct_0(B) & v2_borsuk_1(C,B) & m1_borsuk_1(C,B) & m1_pre_topc(B,A) & v1_borsuk_1(B,A) & l1_pre_topc(A) & v2_pre_topc(A) -> m1_borsuk_1(k20_borsuk_1(A,B,C),A) & v2_borsuk_1(k20_borsuk_1(A,B,C),A))) # label(dt_k20_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10516 (all A all B all C all D (l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & v2_pre_topc(B) & l1_pre_topc(A) & v2_pre_topc(A) -> k2_zfmisc_1(C,D) = k7_borsuk_1(A,B,C,D))) # label(redefinition_k7_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10517 (all A (-v1_xboole_0(A) -> (all B (m1_eqrel_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (k3_tarski(C) = D -> k3_tarski(k3_subset_1(B,C)) = k3_subset_1(A,D)))))))))) # label(t27_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10518 $T # label(t7_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10519 $T # label(t22_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10520 (all A all B all C all D all E all F (v2_pre_topc(B) & l1_pre_topc(B) & m1_connsp_2(E,A,C) & m1_connsp_2(F,B,D) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(C,u1_struct_0(A)) & -v3_struct_0(B) & l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> m1_connsp_2(k9_borsuk_1(A,B,C,D,E,F),k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D)))) # label(dt_k9_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10521 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> v6_compts_1(k1_struct_0(A,B),A))))) # label(t41_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10522 (all A all B all C (v2_pre_topc(A) & -v3_struct_0(B) & v1_borsuk_1(B,A) & v2_borsuk_1(C,B) & m1_borsuk_1(C,B) & m1_pre_topc(B,A) & l1_pre_topc(A) & -v3_struct_0(A) -> v1_borsuk_1(k21_borsuk_1(A,B,C),k16_borsuk_1(A,k20_borsuk_1(A,B,C))) & m1_pre_topc(k21_borsuk_1(A,B,C),k16_borsuk_1(A,k20_borsuk_1(A,B,C))) & v1_pre_topc(k21_borsuk_1(A,B,C)))) # label(dt_k21_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10523 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> v1_tops_2(k11_borsuk_1(A,B,C),k6_borsuk_1(A,B)))))))) # label(t51_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10524 (all A all B all C all D (v1_funct_1(C) & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) & m1_relset_1(C,k1_pcomps_1(A),k1_pcomps_1(B)) & v1_funct_2(C,k1_pcomps_1(A),k1_pcomps_1(B)) -> m1_subset_1(k14_borsuk_1(A,B,C,D),k1_zfmisc_1(k1_zfmisc_1(B))))) # label(dt_k14_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10525 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) -> (all D -(r2_hidden(D,k2_funct_2(k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(A)),k12_borsuk_1(A,B),C)) & (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> -(r2_hidden(E,C) & k2_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(A),k9_funct_3(u1_struct_0(A),u1_struct_0(B)),E) = D))))))))))) # label(t57_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10526 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v1_borsuk_1(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (C = u1_struct_0(B) -> v4_pre_topc(C,A))))))))) # label(d14_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10527 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (A = k5_setfam_1(A,B) -> (all C (m1_subset_1(C,k1_zfmisc_1(B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (k3_tarski(C) = D -> r1_tarski(k3_subset_1(A,D),k3_tarski(k3_subset_1(B,C))))))))))) # label(t18_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10528 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_eqrel_1(B,u1_struct_0(A)) & -v1_xboole_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(B)) -> (r2_hidden(C,u1_pre_topc(k16_borsuk_1(A,B))) <-> r2_hidden(k3_tarski(C),u1_pre_topc(A))))))))) # label(t69_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10529 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,u1_struct_0(B)) -> D = k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D)))) <-> v3_borsuk_1(C,A,B)))))))) # label(d19_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10530 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) -> (r1_compts_1(k6_borsuk_1(A,B),C,k7_borsuk_1(A,B,D,E)) -> (D != k1_xboole_0 -> r1_compts_1(B,k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(B),k13_borsuk_1(A,B),C),E)) & (E != k1_xboole_0 -> r1_compts_1(A,k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(A),k12_borsuk_1(A,B),C),D))))))))))))) # label(t62_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10531 $T # label(t8_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10532 (all A (l1_struct_0(A) -> m1_eqrel_1(k15_borsuk_1(A),u1_struct_0(A)))) # label(dt_k15_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10533 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(k6_borsuk_1(A,B))) -> (exists D ((exists E (k8_borsuk_1(A,B,D,E) = C & m1_subset_1(E,u1_struct_0(B)))) & m1_subset_1(D,u1_struct_0(A)))))))))) # label(t50_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10534 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_eqrel_1(B,u1_struct_0(A)) & -v1_xboole_0(B) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> (all D (m2_connsp_2(D,A,C) -> (exists E (v3_pre_topc(E,A) & r1_tarski(C,E) & (all F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(F,B) -> r1_xboole_0(F,E) | r1_tarski(F,E)))) & r1_tarski(E,D) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))))))))) <-> m1_borsuk_1(B,A)))))) # label(d13_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10535 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,k10_relat_1(C,B)) -> r1_tarski(k9_relat_1(C,A),B)))) # label(t5_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10536 (all A all B (l1_pre_topc(A) & -v1_xboole_0(B) & m1_eqrel_1(B,u1_struct_0(A)) & v2_pre_topc(A) & -v3_struct_0(A) -> v2_pre_topc(k16_borsuk_1(A,B)) & v1_pre_topc(k16_borsuk_1(A,B)) & -v3_struct_0(k16_borsuk_1(A,B)))) # label(fc4_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10537 (all A all B (l1_pre_topc(A) & -v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & v2_pre_topc(A) & -v3_struct_0(A) -> v2_pre_topc(k6_borsuk_1(A,B)) & v1_pre_topc(k6_borsuk_1(A,B)) & -v3_struct_0(k6_borsuk_1(A,B)))) # label(fc2_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10538 (all A all B all C all D all E (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & m1_connsp_2(E,B,C) & m1_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(D,A,B) & v1_funct_1(D) & m1_subset_1(C,u1_struct_0(B)) & l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> k5_borsuk_1(A,B,C,D,E) = k10_relat_1(D,E))) # label(redefinition_k5_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10539 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> (v3_pre_topc(C,k6_borsuk_1(A,B)) <-> (exists D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) & C = k5_setfam_1(u1_struct_0(k6_borsuk_1(A,B)),D) & (all E -(r2_hidden(E,D) & (all F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) -> (all G (m1_subset_1(G,k1_zfmisc_1(u1_struct_0(B))) -> -(v3_pre_topc(F,A) & v3_pre_topc(G,B) & E = k12_mcart_1(u1_struct_0(A),u1_struct_0(B),F,G))))))))))))))))) # label(t45_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10540 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,C) -> k3_funct_2(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C),k16_funct_3(A,C,B,C,D,k6_partfun1(C)),k6_domain_1(k2_zfmisc_1(B,C),k1_domain_1(B,C,E,F))) = k12_mcart_1(A,C,k3_funct_2(A,B,D,k6_domain_1(B,E)),k6_domain_1(C,F)))))))))))))) # label(t24_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10541 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v1_xboole_0(C) & m1_eqrel_1(C,u1_struct_0(B)) -> k18_borsuk_1(A,B,C) = k2_xboole_0(C,a_2_3_borsuk_1(A,B)))))))) # label(d12_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10542 $T # label(t1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10543 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> r1_tarski(u1_struct_0(B),u1_struct_0(A)))))) # label(t35_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10544 (all A all B all C (r1_tarski(A,k2_zfmisc_1(B,C)) -> k2_funct_2(k2_zfmisc_1(B,C),B,k9_funct_3(B,C),A) = k1_funct_1(k1_funct_3(k9_funct_3(B,C)),A))) # label(t9_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10545 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> (r1_tarski(C,D) -> r1_tarski(k11_borsuk_1(A,B,C),k11_borsuk_1(A,B,D))))))))))) # label(t52_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10546 $T # label(t11_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10547 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(B)) -> (k1_xboole_0 != k12_mcart_1(A,B,C,D) -> k2_funct_2(k2_zfmisc_1(A,B),B,k10_funct_3(A,B),k12_mcart_1(A,B,C,D)) = D & C = k2_funct_2(k2_zfmisc_1(A,B),A,k9_funct_3(A,B),k12_mcart_1(A,B,C,D))))))) # label(t12_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10548 (all A all B (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (exists C (v1_relat_1(C) & v5_pre_topc(C,A,B) & v1_partfun1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) & -v1_xboole_0(C) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)))))) # label(rc2_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10549 (all A (-v1_xboole_0(A) -> (exists B (-v1_xboole_0(B) & v1_setfam_1(B) & m1_eqrel_1(B,A))))) # label(rc1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10550 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> v5_pre_topc(k3_borsuk_1(B,A,C),B,A))))))) # label(t36_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10551 (all A (-v1_xboole_0(A) -> (all B (m1_eqrel_1(B,A) & -v1_xboole_0(B) -> (all C (m2_subset_1(C,k1_zfmisc_1(A),B) -> k3_funct_2(A,B,k2_borsuk_1(A,B),k6_domain_1(B,C)) = C)))))) # label(t30_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10552 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_eqrel_1(B,A) -> v1_funct_1(k2_borsuk_1(A,B)) & v1_funct_2(k2_borsuk_1(A,B),A,B) & m2_relset_1(k2_borsuk_1(A,B),A,B))) # label(dt_k2_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10553 (all A all B all C r1_tarski(k9_relat_1(k2_funcop_1(A,B),C),k1_tarski(B))) # label(t6_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10554 (all A all B all C all D all E all F (v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & m2_connsp_2(E,A,C) & m1_connsp_2(F,B,D) & m1_subset_1(D,u1_struct_0(B)) & l1_pre_topc(B) & v2_pre_topc(B) & -v3_struct_0(B) & -v3_struct_0(A) -> k2_zfmisc_1(E,F) = k10_borsuk_1(A,B,C,D,E,F))) # label(redefinition_k10_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10555 (all A all B all C all D (v2_pre_topc(B) & v2_pre_topc(C) & l1_pre_topc(C) & l1_pre_topc(D) & v2_pre_topc(D) & v1_pre_topc(D) & l1_pre_topc(B) -> ((exists E (m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(D)))) & k5_setfam_1(u1_struct_0(D),E) = A & r1_tarski(E,a_2_1_borsuk_1(B,C)))) <-> r2_hidden(A,a_3_0_borsuk_1(B,C,D))))) # label(fraenkel_a_3_0_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10556 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m2_connsp_2(D,A,C) -> (r1_tarski(B,C) -> m2_connsp_2(D,A,B)))))))))) # label(t39_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10557 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(A,B)))) -> ((all E (r2_hidden(E,D) -> r1_tarski(E,C) & (exists F (m1_subset_1(F,k1_zfmisc_1(A)) & (exists G (E = k12_mcart_1(A,B,F,G) & m1_subset_1(G,k1_zfmisc_1(B)))))))) -> r1_tarski(k2_zfmisc_1(k1_setfam_1(k9_relat_1(k1_funct_3(k9_funct_3(A,B)),D)),k3_tarski(k9_relat_1(k1_funct_3(k10_funct_3(A,B)),D))),C)))))) # label(t15_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10558 $T # label(t40_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10559 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> m1_borsuk_1(k15_borsuk_1(A),A))) # label(t82_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10560 (all A all B all C (m1_subset_1(C,A) & -v1_xboole_0(A) -> k1_borsuk_1(A,B,C) = k2_funcop_1(B,C))) # label(redefinition_k1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10561 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,C) -> k1_domain_1(B,C,k8_funct_2(A,B,D,E),F) = k8_funct_2(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C),k16_funct_3(A,C,B,C,D,k6_partfun1(C)),k1_domain_1(A,C,E,F)))))))))))))) # label(t21_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10562 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) & m1_eqrel_1(B,u1_struct_0(A)) -> u1_struct_0(k16_borsuk_1(A,B)) = k2_relat_1(k17_borsuk_1(A,B)))))) # label(t72_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10563 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) -> (all C (v1_pre_topc(C) & v2_pre_topc(C) & l1_pre_topc(C) -> (a_3_0_borsuk_1(A,B,C) = u1_pre_topc(C) & k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)) = u1_struct_0(C) <-> k6_borsuk_1(A,B) = C))))))) # label(d5_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10564 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> r1_tarski(k5_pre_topc(A,B,C,k1_tops_1(B,D)),k1_tops_1(A,k5_pre_topc(A,B,C,D))))))))))) # label(t37_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10565 (all A all B all C (v2_pre_topc(A) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) & l1_pre_topc(A) -> m1_subset_1(k11_borsuk_1(A,B,C),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))))) # label(dt_k11_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10566 (all A all B (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(A) -> v1_funct_1(k13_borsuk_1(A,B)) & m2_relset_1(k13_borsuk_1(A,B),k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(B))) & v1_funct_2(k13_borsuk_1(A,B),k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(B))))) # label(dt_k13_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10567 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(B)) -> (k12_mcart_1(A,B,C,D) != k1_xboole_0 -> k1_funct_1(k1_funct_3(k10_funct_3(A,B)),k12_mcart_1(A,B,C,D)) = D & C = k1_funct_1(k1_funct_3(k9_funct_3(A,B)),k12_mcart_1(A,B,C,D))))))) # label(t13_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10568 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> a_3_1_borsuk_1(A,B,C) = k11_borsuk_1(A,B,C))))))) # label(d6_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10569 (all A all B all C (r1_tarski(A,k2_zfmisc_1(B,C)) -> k2_funct_2(k2_zfmisc_1(B,C),C,k10_funct_3(B,C),A) = k1_funct_1(k1_funct_3(k10_funct_3(B,C)),A))) # label(t10_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10570 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> k1_tops_1(k6_borsuk_1(A,B),k7_borsuk_1(A,B,C,D)) = k7_borsuk_1(A,B,k1_tops_1(A,C),k1_tops_1(B,D)))))))))) # label(t47_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10571 (all A (l1_pre_topc(A) -> (A = k22_borsuk_1 <-> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(k8_metric_1)))) -> (B = k1_rcomp_1(np__0,np__1) -> k3_pre_topc(k5_pcomps_1(k8_metric_1),B) = A)))))) # label(d16_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10572 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_compts_1(A,C,D) & (all E (m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(r1_tarski(E,C) & r1_compts_1(A,E,D) & (all F -(r1_xboole_0(F,D) & r2_hidden(F,E))))))))))))))) # label(t63_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10573 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) -> ((all E (r2_hidden(E,D) -> r1_tarski(E,C) & (exists F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) & (exists G (k7_borsuk_1(A,B,F,G) = E & m1_subset_1(G,k1_zfmisc_1(u1_struct_0(B))))))))) -> r1_tarski(k7_borsuk_1(A,B,k5_setfam_1(u1_struct_0(A),k2_funct_2(k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(A)),k12_borsuk_1(A,B),D)),k6_setfam_1(u1_struct_0(B),k2_funct_2(k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(B)),k13_borsuk_1(A,B),D))),C)))))))))) # label(t56_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10574 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> k2_funct_3(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B),k10_funct_3(u1_struct_0(A),u1_struct_0(B))) = k13_borsuk_1(A,B))))) # label(d8_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10575 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (exists B m1_borsuk_1(B,A)))) # label(existence_m1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10576 (all A all B (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & -v1_xboole_0(B) & m1_eqrel_1(B,u1_struct_0(A)) -> v1_funct_1(k17_borsuk_1(A,B)) & v1_funct_2(k17_borsuk_1(A,B),u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,B))) & m2_relset_1(k17_borsuk_1(A,B),u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,B))) & v5_pre_topc(k17_borsuk_1(A,B),A,k16_borsuk_1(A,B)))) # label(dt_k17_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10577 (all A all B all C (v1_borsuk_1(B,A) & m1_pre_topc(B,A) & m1_borsuk_1(C,B) & -v3_struct_0(B) & l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> k19_borsuk_1(A,B,C) = k18_borsuk_1(A,B,C))) # label(redefinition_k19_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10578 (all A (l1_struct_0(A) -> (all B (-v3_struct_0(B) & l1_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k3_borsuk_1(A,B,C) = k1_borsuk_1(u1_struct_0(B),u1_struct_0(A),C))))))) # label(d3_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10579 (all A (-v1_xboole_0(A) -> (all B (m1_eqrel_1(B,A) & -v1_xboole_0(B) -> (all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> ((all D (m1_subset_1(D,A) -> r2_hidden(D,k8_funct_2(A,B,C,D)))) <-> C = k2_borsuk_1(A,B)))))))) # label(d1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10580 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_connsp_2(E,A,C) -> (all F (m1_connsp_2(F,B,D) -> m1_connsp_2(k7_borsuk_1(A,B,E,F),k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D)))))))))))))) # label(t48_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10581 (all A all B all C (m1_subset_1(C,A) & -v1_xboole_0(A) -> v1_funct_2(k1_borsuk_1(A,B,C),B,A) & m2_relset_1(k1_borsuk_1(A,B,C),B,A) & v1_funct_1(k1_borsuk_1(A,B,C)))) # label(dt_k1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10582 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k3_funct_2(A,A,k6_partfun1(A),B) = B)) # label(t4_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10583 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (exists B (m1_borsuk_1(B,A) & v1_setfam_1(B) & v2_borsuk_1(B,A) & -v1_xboole_0(B))))) # label(rc5_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10584 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(B,C)))) & l1_pre_topc(C) & v2_pre_topc(C) & l1_pre_topc(B) & v2_pre_topc(B) -> ((exists E exists F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(C))) & v3_pre_topc(E,B) & v3_pre_topc(F,C) & r1_tarski(k7_borsuk_1(B,C,E,F),D) & k7_borsuk_1(B,C,E,F) = A & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))))) <-> r2_hidden(A,a_3_1_borsuk_1(B,C,D))))) # label(fraenkel_a_3_1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10585 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v6_compts_1(D,B) -> (all E (m2_connsp_2(E,k6_borsuk_1(B,A),k7_borsuk_1(B,A,D,k1_struct_0(A,C))) -> (exists F ((exists G (m1_connsp_2(G,A,C) & r1_tarski(k10_borsuk_1(B,A,D,C,F,G),E))) & m2_connsp_2(F,B,D)))))))))))))) # label(t67_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10586 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v1_xboole_0(C) & m1_eqrel_1(C,u1_struct_0(B)) -> (all D (r2_hidden(D,u1_struct_0(B)) -> r2_hidden(k1_funct_1(k17_borsuk_1(A,k18_borsuk_1(A,B,C)),D),u1_struct_0(k16_borsuk_1(B,C))))))))))) # label(t80_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10587 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (k1_xboole_0 != k7_borsuk_1(A,B,C,D) -> D = k8_funct_2(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(B)),k13_borsuk_1(A,B),k7_borsuk_1(A,B,C,D)) & k8_funct_2(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(A)),k12_borsuk_1(A,B),k7_borsuk_1(A,B,C,D)) = C))))))))) # label(t65_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.67 10588 (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) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,k1_zfmisc_1(A)) -> (all F (m1_subset_1(F,k1_zfmisc_1(C)) -> k2_funct_2(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C),k16_funct_3(A,C,B,C,D,k6_partfun1(C)),k12_mcart_1(A,C,E,F)) = k12_mcart_1(B,C,k2_funct_2(A,B,D,E),F))))))))))))) # label(t23_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10589 (all A all B (m1_eqrel_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(B)) -> k3_xboole_0(k3_tarski(C),k3_tarski(D)) = k3_tarski(k5_subset_1(B,C,D)))))))) # label(t26_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10590 $T # label(d4_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10591 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,k1_pcomps_1(A),k1_pcomps_1(B)) & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) & v1_funct_2(C,k1_pcomps_1(A),k1_pcomps_1(B)) -> k9_relat_1(C,D) = k14_borsuk_1(A,B,C,D))) # label(redefinition_k14_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10592 (all A all B all C (v2_pre_topc(B) & v2_pre_topc(C) & l1_pre_topc(C) & l1_pre_topc(B) -> (r2_hidden(A,a_2_1_borsuk_1(B,C)) <-> (exists D exists E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C))) & A = k12_mcart_1(u1_struct_0(B),u1_struct_0(C),D,E) & r2_hidden(D,u1_pre_topc(B)) & r2_hidden(E,u1_pre_topc(C)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))))))) # label(fraenkel_a_2_1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10593 $T # label(t43_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10594 $T # label(t3_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10595 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(A,B)))) -> ((all E (r2_hidden(E,D) -> r1_tarski(E,C) & (exists F ((exists G (m1_subset_1(G,k1_zfmisc_1(B)) & E = k12_mcart_1(A,B,F,G))) & m1_subset_1(F,k1_zfmisc_1(A)))))) -> r1_tarski(k2_zfmisc_1(k3_tarski(k9_relat_1(k1_funct_3(k9_funct_3(A,B)),D)),k1_setfam_1(k9_relat_1(k1_funct_3(k10_funct_3(A,B)),D))),C)))))) # label(t14_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10596 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & v1_borsuk_1(B,A) & -v3_struct_0(B) -> (all C (m1_borsuk_1(C,B) & v2_borsuk_1(C,B) -> (r1_borsuk_1(A,B) -> r1_borsuk_1(k16_borsuk_1(A,k20_borsuk_1(A,B,C)),k21_borsuk_1(A,B,C))))))))) # label(t84_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10597 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_eqrel_1(C,u1_struct_0(B)) & -v1_xboole_0(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -((all E (m1_subset_1(E,u1_struct_0(A)) -> -(D = k1_struct_0(A,E) & -r2_hidden(E,k2_pre_topc(B))))) & -r2_hidden(D,C) & r2_hidden(D,k18_borsuk_1(A,B,C))))))))))) # label(t74_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10598 (all A all B all C all D (v2_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & l1_pre_topc(B) & l1_pre_topc(A) & v2_pre_topc(A) -> m1_subset_1(k7_borsuk_1(A,B,C,D),k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))))) # label(dt_k7_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10599 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v1_xboole_0(B) & m1_eqrel_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r2_hidden(C,k8_funct_2(u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,B)),k17_borsuk_1(A,B),C)))))))) # label(t70_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10600 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) -> (k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(A),k12_borsuk_1(A,B),C) = k1_xboole_0 | k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(B),k13_borsuk_1(A,B),C) = k1_xboole_0 -> C = k1_xboole_0))))))) # label(t61_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10601 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_borsuk_1(B,A) -> -v1_xboole_0(B) & m1_eqrel_1(B,u1_struct_0(A)))))) # label(dt_m1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10602 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_eqrel_1(C,u1_struct_0(B)) & -v1_xboole_0(C) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,u1_struct_0(B)) -> k1_funct_1(k17_borsuk_1(B,C),D) = k8_funct_2(u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,k18_borsuk_1(A,B,C))),k17_borsuk_1(A,k18_borsuk_1(A,B,C)),D)))))))))) # label(t76_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10603 $T # label(t2_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10604 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v3_pre_topc(D,B) & v3_pre_topc(C,A) -> v3_pre_topc(k7_borsuk_1(A,B,C,D),k6_borsuk_1(A,B))))))))))) # label(t46_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10605 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_eqrel_1(C,u1_struct_0(B)) & -v1_xboole_0(C) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (-r2_hidden(D,u1_struct_0(B)) -> r2_hidden(k1_struct_0(A,D),k18_borsuk_1(A,B,C))))))))))) # label(t75_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10606 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) -> k1_funct_1(k12_borsuk_1(A,B),k1_xboole_0) = k1_xboole_0 & k1_xboole_0 = k1_funct_1(k13_borsuk_1(A,B),k1_xboole_0))))) # label(t66_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10607 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (exists B (m1_pre_topc(B,A) & -v3_struct_0(B) & v1_pre_topc(B) & v1_borsuk_1(B,A) & v2_pre_topc(B))))) # label(rc4_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10608 (all A all B all C all D all E all F (-v3_struct_0(A) & v2_pre_topc(A) & m1_connsp_2(E,A,C) & m1_connsp_2(F,B,D) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(C,u1_struct_0(A)) & l1_pre_topc(B) & v2_pre_topc(B) & -v3_struct_0(B) & l1_pre_topc(A) -> k9_borsuk_1(A,B,C,D,E,F) = k2_zfmisc_1(E,F))) # label(redefinition_k9_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10609 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_eqrel_1(B,u1_struct_0(A)) & -v1_xboole_0(B) -> k2_borsuk_1(u1_struct_0(A),B) = k17_borsuk_1(A,B))))) # label(d11_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10610 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_eqrel_1(C,u1_struct_0(B)) & -v1_xboole_0(C) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (k8_funct_2(u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,k18_borsuk_1(A,B,C))),k17_borsuk_1(A,k18_borsuk_1(A,B,C)),D) = k8_funct_2(u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,k18_borsuk_1(A,B,C))),k17_borsuk_1(A,k18_borsuk_1(A,B,C)),E) -> r2_hidden(D,u1_struct_0(B)) | E = D))))))))))) # label(t78_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10611 (all A all B all C (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(B) & v2_borsuk_1(C,B) & m1_borsuk_1(C,B) & m1_pre_topc(B,A) & v1_borsuk_1(B,A) & -v3_struct_0(A) -> k18_borsuk_1(A,B,C) = k20_borsuk_1(A,B,C))) # label(redefinition_k20_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10612 $T # label(t34_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10613 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> (v3_pre_topc(C,k6_borsuk_1(A,B)) -> C = k5_setfam_1(u1_struct_0(k6_borsuk_1(A,B)),k11_borsuk_1(A,B,C))))))))) # label(t54_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10614 (all A (-v1_xboole_0(A) -> (all B (v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v3_relat_2(B) -> -v1_xboole_0(k8_eqrel_1(A,B)))))) # label(t28_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10615 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_eqrel_1(B,u1_struct_0(A)) & -v1_xboole_0(B) -> (all C (m1_subset_1(C,u1_struct_0(k16_borsuk_1(A,B))) -> (exists D (k8_funct_2(u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,B)),k17_borsuk_1(A,B),D) = C & m1_subset_1(D,u1_struct_0(A)))))))))) # label(t71_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10616 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> (v3_pre_topc(C,k6_borsuk_1(A,B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) -> (E = k2_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B),k10_funct_3(u1_struct_0(A),u1_struct_0(B)),C) -> v3_pre_topc(E,B)) & (k2_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(A),k9_funct_3(u1_struct_0(A),u1_struct_0(B)),C) = D -> v3_pre_topc(D,A))))))))))))) # label(t59_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10617 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -((all C (m1_subset_1(C,u1_struct_0(A)) -> k1_struct_0(A,C) != B)) & r2_hidden(B,k15_borsuk_1(A))))))) # label(t68_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10618 $T # label(t44_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10619 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (all E (m2_connsp_2(E,A,C) -> (all F (m2_connsp_2(F,B,D) -> m2_connsp_2(k7_borsuk_1(A,B,E,F),k6_borsuk_1(A,B),k7_borsuk_1(A,B,C,D)))))))))))))) # label(t49_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10620 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_eqrel_1(C,u1_struct_0(B)) & -v1_xboole_0(C) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (-r2_hidden(D,u1_struct_0(B)) -> k8_funct_2(u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,k18_borsuk_1(A,B,C))),k17_borsuk_1(A,k18_borsuk_1(A,B,C)),D) = k1_struct_0(A,D)))))))))) # label(t77_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10621 (all A all B all C all D all E (-v3_struct_0(A) & l1_pre_topc(A) & -v3_struct_0(B) & l1_pre_topc(B) & v2_pre_topc(C) & v1_funct_1(D) & v5_pre_topc(D,A,B) & m1_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C)) & m1_relset_1(E,u1_struct_0(B),u1_struct_0(C)) & v5_pre_topc(E,B,C) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & l1_pre_topc(C) & -v3_struct_0(C) & v2_pre_topc(B) & v2_pre_topc(A) -> k5_relat_1(D,E) = k4_borsuk_1(A,B,C,D,E))) # label(redefinition_k4_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10622 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_borsuk_1(B,A) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> v6_compts_1(C,A)))) <-> v2_borsuk_1(B,A)))))) # label(d15_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10623 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> k12_borsuk_1(A,B) = k2_funct_3(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(A),k9_funct_3(u1_struct_0(A),u1_struct_0(B))))))) # label(d7_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10624 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> ((exists C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k6_borsuk_1(A,k22_borsuk_1)),u1_struct_0(A)) & v5_pre_topc(C,k6_borsuk_1(A,k22_borsuk_1),A) & (all D (m1_subset_1(D,u1_struct_0(A)) -> D = k8_funct_2(u1_struct_0(k6_borsuk_1(A,k22_borsuk_1)),u1_struct_0(A),C,k8_borsuk_1(A,k22_borsuk_1,D,k23_borsuk_1)) & r2_hidden(k8_funct_2(u1_struct_0(k6_borsuk_1(A,k22_borsuk_1)),u1_struct_0(A),C,k8_borsuk_1(A,k22_borsuk_1,D,k24_borsuk_1)),u1_struct_0(B)) & (r2_hidden(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(k22_borsuk_1)) -> k8_funct_2(u1_struct_0(k6_borsuk_1(A,k22_borsuk_1)),u1_struct_0(A),C,k8_borsuk_1(A,k22_borsuk_1,D,E)) = D))))) & m2_relset_1(C,u1_struct_0(k6_borsuk_1(A,k22_borsuk_1)),u1_struct_0(A)))) <-> r2_borsuk_1(A,B)))))) # label(d21_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10625 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (v5_pre_topc(D,B,A) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(D) -> (all E (m1_connsp_2(E,A,C) -> m2_connsp_2(k5_pre_topc(B,A,D,E),B,k5_pre_topc(B,A,D,k1_struct_0(A,C))))))))))))) # label(t38_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10626 (all A (l1_struct_0(A) -> k15_borsuk_1(A) = k8_eqrel_1(u1_struct_0(A),k6_partfun1(u1_struct_0(A))))) # label(d9_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10627 (all A (v1_classes2(A) & -v1_xboole_0(A) -> v1_cat_1(k28_grcat_1(A)))) # label(fc10_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10628 (all A (l1_grcat_1(A) -> l1_rlvect_1(k9_grcat_1(A)) & v6_rlvect_1(k9_grcat_1(A)) & v5_rlvect_1(k9_grcat_1(A)) & v4_rlvect_1(k9_grcat_1(A)) & -v3_struct_0(k9_grcat_1(A)))) # label(dt_k9_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10629 (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) -> k3_grcat_1(A,B) = k2_partfun1(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k1_grcat_1(A,B)))))) # label(d7_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10630 $T # label(t35_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10631 (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) -> k2_partfun1(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k1_grcat_1(A,B)) = k2_grcat_1(A,B))))) # label(d6_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10632 (all A (-v1_xboole_0(A) & v4_grcat_1(A) -> (exists B (m1_subset_1(B,A) & -v3_struct_0(B) & v5_rlvect_1(B) & v1_algstr_1(B) & v2_algstr_1(B) & v4_algstr_1(B) & v5_algstr_1(B) & v6_algstr_1(B) & v3_algstr_1(B) & v6_rlvect_1(B) & v4_rlvect_1(B) & v1_rlvect_1(B))))) # label(rc5_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10633 (all A (l1_grcat_1(A) -> (v2_grcat_1(A) -> A = g1_grcat_1(u1_grcat_1(A),u2_grcat_1(A),u3_grcat_1(A))))) # label(abstractness_v2_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10634 (all A all B (v6_rlvect_1(A) & v6_rlvect_1(B) & l1_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all C (m4_grcat_1(C,A,B) -> v5_grcat_1(C) & -v1_xboole_0(C))))) # label(dt_m4_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10635 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(B) -> (all C (v2_grcat_1(C) & m1_grcat_1(C,A,B) -> m4_grcat_1(k1_tarski(C),A,B))))))) # label(t39_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10636 (all A (-v1_xboole_0(A) & v4_grcat_1(A) -> (exists B m2_grcat_1(B,A)))) # label(existence_m2_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10637 (all A (v3_grcat_1(A) & l1_grcat_1(A) -> v1_grcat_1(u3_grcat_1(A),u1_grcat_1(A),u2_grcat_1(A)))) # label(t18_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10638 $T # label(d2_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10639 (all A (v4_grcat_1(A) & -v1_xboole_0(A) -> (all B (m3_grcat_1(B,k20_grcat_1(A)) -> (all C (m3_grcat_1(C,k20_grcat_1(A)) -> -(k21_grcat_1(A,B) = k22_grcat_1(A,C) & (all D (m2_grcat_1(D,A) & v1_rlvect_1(D) -> (all E (m2_grcat_1(E,A) & v1_rlvect_1(E) -> (all F (v1_rlvect_1(F) & m2_grcat_1(F,A) -> -(m1_grcat_1(B,E,F) & m1_grcat_1(C,D,E))))))))))))))) # label(t44_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10640 (all A all B (l1_struct_0(A) & l1_struct_0(B) & -v3_struct_0(B) -> -v1_xboole_0(k17_grcat_1(A,B)))) # label(fc7_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10641 (all A all B all C all D all E (v4_rlvect_1(A) & -v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(B) & v4_rlvect_1(C) & l1_rlvect_1(C) & m1_grcat_1(E,A,B) & m1_grcat_1(D,B,C) & v6_rlvect_1(C) & v5_rlvect_1(C) & -v3_struct_0(C) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> k15_grcat_1(D,E) = k16_grcat_1(A,B,C,D,E))) # label(redefinition_k16_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10642 (all A (l1_grcat_1(A) -> v6_rlvect_1(u1_grcat_1(A)) & l1_rlvect_1(u1_grcat_1(A)) & v5_rlvect_1(u1_grcat_1(A)) & v4_rlvect_1(u1_grcat_1(A)) & -v3_struct_0(u1_grcat_1(A)))) # label(dt_u1_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10643 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (m1_subset_1(B,u1_cat_1(k28_grcat_1(A))) -> (all C (m2_grcat_1(C,k19_grcat_1(A)) -> (C = B -> k5_cat_1(k28_grcat_1(A),B) = k23_grcat_1(k19_grcat_1(A),C)))))))) # label(t48_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10644 $T # label(t27_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10645 (all A all B (v2_cat_1(A) & l1_cat_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) & -v1_xboole_0(B) -> m3_cat_2(k6_grcat_1(A,B),A))) # label(dt_k6_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10646 (all A (-v1_xboole_0(A) & v4_grcat_1(A) -> (all B (v1_funct_2(B,k20_grcat_1(A),A) & m2_relset_1(B,k20_grcat_1(A),A) & v1_funct_1(B) -> (B = k25_grcat_1(A) <-> (all C (m3_grcat_1(C,k20_grcat_1(A)) -> k22_grcat_1(A,C) = k8_funct_2(k20_grcat_1(A),A,B,C)))))))) # label(d33_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10647 (all A (-v1_xboole_0(A) & v1_classes2(A) -> r2_hidden(k2_algstr_1,k31_grcat_1(A)))) # label(t54_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10648 (all A all B all C (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(B) & v5_rlvect_1(B) & m4_grcat_1(C,A,B) & l1_rlvect_1(B) & v6_rlvect_1(B) & -v3_struct_0(B) & l1_rlvect_1(A) & v5_rlvect_1(A) -> (exists D m7_grcat_1(D,A,B,C)))) # label(existence_m7_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10649 (all A all B (-v1_xboole_0(A) & v4_grcat_1(A) & m1_subset_1(B,k20_grcat_1(A)) -> m2_grcat_1(k22_grcat_1(A,B),A) & v1_rlvect_1(k22_grcat_1(A,B)))) # label(dt_k22_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10650 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (l1_grcat_1(B) & v3_grcat_1(B) & v2_grcat_1(B) -> (k10_grcat_1(B) = A -> k15_grcat_1(k13_grcat_1(A),B) = B))) & (all B (v3_grcat_1(B) & l1_grcat_1(B) & v2_grcat_1(B) -> (A = k9_grcat_1(B) -> k15_grcat_1(B,k13_grcat_1(A)) = B))) & k10_grcat_1(k13_grcat_1(A)) = A & k9_grcat_1(k13_grcat_1(A)) = A)) # label(t34_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10651 $T # label(d3_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10652 (all A (v1_classes2(A) & -v1_xboole_0(A) -> -v1_xboole_0(k29_grcat_1(A)))) # label(fc12_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10653 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> m1_grcat_1(k13_grcat_1(A),A,A))) # label(dt_k13_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10654 (all A all B all C (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & l1_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & -v3_struct_0(B) & l1_rlvect_1(A) & v5_rlvect_1(A) -> v2_grcat_1(g1_grcat_1(A,B,C)) & l1_grcat_1(g1_grcat_1(A,B,C)))) # label(dt_g1_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10655 (all A (-v1_xboole_0(A) & v1_classes2(A) -> k31_grcat_1(A) = u1_cat_1(k32_grcat_1(A)))) # label(t53_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10656 (all A (l1_grcat_1(A) -> u1_grcat_1(A) = k9_grcat_1(A))) # label(d14_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10657 (all A (-v1_xboole_0(A) & v1_classes2(A) -> l1_cat_1(k28_grcat_1(A)))) # label(dt_k28_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10658 (all A (l1_grcat_1(A) & v3_grcat_1(A) -> (all B (l1_grcat_1(B) & v3_grcat_1(B) -> -((all C (v5_rlvect_1(C) & v6_rlvect_1(C) & l1_rlvect_1(C) & v4_rlvect_1(C) & -v3_struct_0(C) -> (all D (v4_rlvect_1(D) & v5_rlvect_1(D) & l1_rlvect_1(D) & v6_rlvect_1(D) & -v3_struct_0(D) -> (all E (v4_rlvect_1(E) & v6_rlvect_1(E) & l1_rlvect_1(E) & v5_rlvect_1(E) & -v3_struct_0(E) -> -(m1_grcat_1(A,D,E) & m1_grcat_1(B,C,D)))))))) & k10_grcat_1(B) = k9_grcat_1(A)))))) # label(t26_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10659 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(B) -> (all C (m4_grcat_1(C,A,B) -> ((all D (m1_grcat_1(D,A,B) & v2_grcat_1(D) <-> r2_hidden(D,C))) <-> k18_grcat_1(A,B) = C))))))) # label(d27_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10660 (all A (-v1_xboole_0(A) & v1_classes2(A) -> r2_hidden(k2_algstr_1,k19_grcat_1(A)))) # label(t42_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10661 (all A all B all C (-v3_struct_0(B) & l1_struct_0(B) & -v1_xboole_0(C) & m5_grcat_1(C,A,B) & l1_struct_0(A) -> (all D (m6_grcat_1(D,A,B,C) -> v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)))))) # label(dt_m6_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10662 (all A (-v1_xboole_0(A) & v4_grcat_1(A) -> v5_grcat_1(k20_grcat_1(A)) & -v1_xboole_0(k20_grcat_1(A)))) # label(dt_k20_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10663 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (m1_subset_1(B,k19_grcat_1(A)) -> v1_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(B) & -v3_struct_0(B))))) # label(t43_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10664 (all A (v1_classes2(A) & -v1_xboole_0(A) -> -v1_xboole_0(k19_grcat_1(A)))) # label(fc8_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10665 $T # label(dt_m5_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10666 $T # label(t1_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10667 (all A (-v1_xboole_0(A) & v1_classes2(A) -> m1_subset_1(k29_grcat_1(A),k1_zfmisc_1(u1_cat_1(k28_grcat_1(A)))))) # label(dt_k29_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10668 (all A all B (r1_grcat_1(A,B) <-> (exists C exists D exists E exists F ((exists G (v1_rlvect_1(G) & v4_rlvect_1(G) & v6_rlvect_1(G) & l1_rlvect_1(G) & D = u1_rlvect_1(G) & F = u2_struct_0(G) & k7_vectsp_1(G) = E & C = u1_struct_0(G) & B = G & v5_rlvect_1(G) & -v3_struct_0(G))) & k4_mcart_1(C,D,E,F) = A)))) # label(d28_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10669 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) -> (all B (-v3_struct_0(B) & l1_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v1_grcat_1(C,A,B) -> m1_grcat_1(g1_grcat_1(A,B,C),A,B) & v2_grcat_1(g1_grcat_1(A,B,C))))))))) # label(t20_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10670 (all A (-v1_xboole_0(A) & v5_grcat_1(A) -> (all B (m1_subset_1(B,A) <-> m3_grcat_1(B,A))))) # label(redefinition_m3_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10671 (all A (v2_grcat_1(A) & v3_grcat_1(A) & l1_grcat_1(A) -> v5_grcat_1(k1_tarski(A)) & -v1_xboole_0(k1_tarski(A)))) # label(t37_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10672 (all A (v4_grcat_1(A) & -v1_xboole_0(A) -> (all B (m1_subset_1(B,A) <-> m2_grcat_1(B,A))))) # label(redefinition_m2_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10673 (all A all B (l1_struct_0(A) & l1_struct_0(B) & -v3_struct_0(B) -> (exists C (m5_grcat_1(C,A,B) & -v1_xboole_0(C))))) # label(rc8_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10674 (all A (l1_grcat_1(A) -> v1_funct_1(u3_grcat_1(A)) & m2_relset_1(u3_grcat_1(A),u1_struct_0(u1_grcat_1(A)),u1_struct_0(u2_grcat_1(A))) & v1_funct_2(u3_grcat_1(A),u1_struct_0(u1_grcat_1(A)),u1_struct_0(u2_grcat_1(A))))) # label(dt_u3_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10675 (all A all B (-v3_struct_0(A) & v5_rlvect_1(A) & -v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & l1_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> v2_grcat_1(k12_grcat_1(A,B)) & v3_grcat_1(k12_grcat_1(A,B)))) # label(fc5_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10676 (exists A (l1_grcat_1(A) & v2_grcat_1(A))) # label(rc1_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10677 (all A all B (v2_cat_1(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) & l1_cat_1(A) -> v2_cat_1(k6_grcat_1(A,B)) & v1_cat_1(k6_grcat_1(A,B)))) # label(fc3_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10678 (exists A (v4_grcat_1(A) & -v1_xboole_0(A))) # label(rc4_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10679 (all A (l1_grcat_1(A) -> u2_grcat_1(A) = k10_grcat_1(A))) # label(d15_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10680 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (m1_subset_1(B,u2_cat_1(k28_grcat_1(A))) -> (all C (m3_grcat_1(C,k20_grcat_1(k19_grcat_1(A))) -> (all D (m1_subset_1(D,u1_cat_1(k28_grcat_1(A))) -> (all E (m2_grcat_1(E,k19_grcat_1(A)) -> m3_grcat_1(B,k20_grcat_1(k19_grcat_1(A))) & m1_subset_1(C,u2_cat_1(k28_grcat_1(A))) & m1_subset_1(E,u1_cat_1(k28_grcat_1(A))) & m2_grcat_1(D,k19_grcat_1(A)) & v1_rlvect_1(D) & v2_grcat_1(B))))))))))) # label(t47_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10681 (all A all B (v2_cat_1(A) & l1_cat_1(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) -> -v1_xboole_0(k1_grcat_1(A,B)))) # label(fc2_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10682 (all A (-v3_struct_0(A) & l1_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k8_funct_2(u1_struct_0(A),u1_struct_0(A),k7_grcat_1(A),B) = B)))) # label(t11_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10683 (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) -> k1_grcat_1(A,B) = k3_tarski(a_2_0_grcat_1(A,B)))))) # label(d5_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10684 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) & -v1_xboole_0(B) & l1_cat_1(A) & v2_cat_1(A) -> v1_funct_1(k5_grcat_1(A,B)) & m2_relset_1(k5_grcat_1(A,B),B,k1_grcat_1(A,B)) & v1_funct_2(k5_grcat_1(A,B),B,k1_grcat_1(A,B)))) # label(dt_k5_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10685 (all A (v4_grcat_1(A) & -v1_xboole_0(A) -> (all B (m2_relset_1(B,k20_grcat_1(A),A) & v1_funct_2(B,k20_grcat_1(A),A) & v1_funct_1(B) -> (k24_grcat_1(A) = B <-> (all C (m3_grcat_1(C,k20_grcat_1(A)) -> k21_grcat_1(A,C) = k8_funct_2(k20_grcat_1(A),A,B,C)))))))) # label(d32_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10686 (all A (v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (l1_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (v4_rlvect_1(C) & v5_rlvect_1(C) & l1_rlvect_1(C) & v6_rlvect_1(C) & -v3_struct_0(C) -> (all D (m1_grcat_1(D,B,C) -> (all E (m1_grcat_1(E,A,B) -> (all F (v1_funct_1(F) & m2_relset_1(F,u1_struct_0(B),u1_struct_0(C)) & v1_funct_2(F,u1_struct_0(B),u1_struct_0(C)) -> (all G (v1_funct_2(G,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(G,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(G) -> (g1_grcat_1(B,C,F) = D & E = g1_grcat_1(A,B,G) -> g1_grcat_1(A,C,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),G,F)) = k16_grcat_1(A,B,C,D,E)))))))))))))))) # label(t29_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10687 (all A (v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(B) -> (all C (v5_grcat_1(C) & -v1_xboole_0(C) -> (m4_grcat_1(C,A,B) <-> (all D (m3_grcat_1(D,C) -> m1_grcat_1(D,A,B) & v2_grcat_1(D)))))))))) # label(d24_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10688 (all A (v4_grcat_1(A) & -v1_xboole_0(A) -> v1_funct_1(k25_grcat_1(A)) & v1_funct_2(k25_grcat_1(A),k20_grcat_1(A),A) & m2_relset_1(k25_grcat_1(A),k20_grcat_1(A),A))) # label(dt_k25_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10689 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & l1_rlvect_1(B) -> v1_grcat_1(k8_grcat_1(A,B),A,B))))) # label(t16_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10690 (all A (l1_grcat_1(A) & v3_grcat_1(A) & v2_grcat_1(A) -> (exists B (-v3_struct_0(B) & v6_rlvect_1(B) & l1_rlvect_1(B) & (exists C (-v3_struct_0(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & l1_rlvect_1(C) & (exists D (v1_funct_2(D,u1_struct_0(B),u1_struct_0(C)) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) & v1_grcat_1(D,B,C) & A = g1_grcat_1(B,C,D) & m1_grcat_1(A,B,C) & v1_funct_1(D))))) & v5_rlvect_1(B) & v4_rlvect_1(B))))) # label(t25_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10691 (all A (-v1_xboole_0(A) & v1_classes2(A) -> m1_subset_1(k31_grcat_1(A),k1_zfmisc_1(u1_cat_1(k30_grcat_1(A)))))) # label(dt_k31_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10692 (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))) -> k5_grcat_1(A,B) = k2_partfun1(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B))))) # label(d9_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10693 (all A (-v1_xboole_0(A) & v4_grcat_1(A) -> (all B (-v1_xboole_0(B) & v5_grcat_1(B) -> ((all C (r2_hidden(C,B) <-> (exists D (v1_rlvect_1(D) & (exists E (m1_grcat_1(C,D,E) & v2_grcat_1(C) & m2_grcat_1(E,A) & v1_rlvect_1(E))) & m2_grcat_1(D,A))))) <-> k20_grcat_1(A) = B))))) # label(d30_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10694 (all A (l1_grcat_1(A) -> -v3_struct_0(k10_grcat_1(A)) & v5_rlvect_1(k10_grcat_1(A)) & l1_rlvect_1(k10_grcat_1(A)) & v6_rlvect_1(k10_grcat_1(A)) & v4_rlvect_1(k10_grcat_1(A)))) # label(dt_k10_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10695 (all A all B all C (l1_struct_0(A) & l1_struct_0(B) & m5_grcat_1(C,A,B) & -v1_xboole_0(C) & -v3_struct_0(B) -> (all D (m6_grcat_1(D,A,B,C) <-> m1_subset_1(D,C))))) # label(redefinition_m6_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10696 (all A (l1_struct_0(A) -> v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)))) # label(dt_k7_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10697 (all A all B (v5_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(B) & l1_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & l1_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all C (m1_grcat_1(C,A,B) -> l1_grcat_1(C) & v3_grcat_1(C))))) # label(dt_m1_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10698 (all A (v4_grcat_1(A) <-> (all B (r2_hidden(B,A) -> v1_rlvect_1(B) & v5_rlvect_1(B) & l1_rlvect_1(B) & v6_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B))))) # label(d22_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10699 (all A all B (v3_grcat_1(B) & l1_grcat_1(B) & l1_grcat_1(A) & v3_grcat_1(A) -> l1_grcat_1(k15_grcat_1(A,B)) & v3_grcat_1(k15_grcat_1(A,B)) & v2_grcat_1(k15_grcat_1(A,B)))) # label(dt_k15_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10700 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) -> k1_realset1(u5_cat_1(A),k1_grcat_1(A,B)) = k4_grcat_1(A,B))))) # label(d8_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10701 (all A all B all C (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(B) & l1_rlvect_1(B) & m4_grcat_1(C,A,B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all D (m7_grcat_1(D,A,B,C) -> m1_grcat_1(D,A,B))))) # label(dt_m7_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10702 (all A (-v1_xboole_0(A) & v1_classes2(A) -> k30_grcat_1(A) = k6_grcat_1(k28_grcat_1(A),k29_grcat_1(A)))) # label(d38_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10703 $T # label(d4_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10704 (all A all B (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) & l1_rlvect_1(A) & v6_rlvect_1(A) -> v2_grcat_1(k12_grcat_1(A,B)))) # label(fc4_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10705 (all A (-v1_xboole_0(A) & v4_grcat_1(A) -> (all B (m2_grcat_1(B,A) -> l1_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B))))) # label(dt_m2_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10706 $T # label(dt_k19_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10707 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (m1_subset_1(B,u2_cat_1(k28_grcat_1(A))) -> (all C (m3_grcat_1(C,k20_grcat_1(k19_grcat_1(A))) -> (C = B -> k21_grcat_1(k19_grcat_1(A),C) = k2_cat_1(k28_grcat_1(A),B) & k3_cat_1(k28_grcat_1(A),B) = k22_grcat_1(k19_grcat_1(A),C)))))))) # label(t49_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10708 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) & v4_grcat_1(A) -> m3_grcat_1(k23_grcat_1(A,B),k20_grcat_1(A)) & v2_grcat_1(k23_grcat_1(A,B)))) # label(dt_k23_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10709 (exists A (-v1_xboole_0(A) & v5_grcat_1(A))) # label(rc6_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10710 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) -> g1_cat_1(B,k1_grcat_1(A,B),k2_grcat_1(A,B),k3_grcat_1(A,B),k4_grcat_1(A,B),k5_grcat_1(A,B)) = k6_grcat_1(A,B))))) # label(d10_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10711 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> v1_grcat_1(k7_grcat_1(A),A,A))) # label(t21_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10712 (all A (v4_grcat_1(A) & -v1_xboole_0(A) -> v1_funct_1(k27_grcat_1(A)) & m2_relset_1(k27_grcat_1(A),k2_zfmisc_1(k20_grcat_1(A),k20_grcat_1(A)),k20_grcat_1(A)))) # label(dt_k27_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10713 (all A (v4_grcat_1(A) & -v1_xboole_0(A) -> v1_funct_2(k24_grcat_1(A),k20_grcat_1(A),A) & m2_relset_1(k24_grcat_1(A),k20_grcat_1(A),A) & v1_funct_1(k24_grcat_1(A)))) # label(dt_k24_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10714 (all A (l1_grcat_1(A) -> u3_grcat_1(A) = k11_grcat_1(A))) # label(d16_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10715 (all A all B all C all D -((all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> D != k4_tarski(E,F))))) & r1_tarski(C,k2_zfmisc_1(A,B)) & r2_hidden(D,C))) # label(t2_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10716 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,k20_grcat_1(A)) & v4_grcat_1(A) -> k9_grcat_1(B) = k21_grcat_1(A,B))) # label(redefinition_k21_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10717 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) -> (all B (v4_rlvect_1(B) & l1_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & l1_rlvect_1(C) & -v3_struct_0(C) -> (all D (l1_rlvect_1(D) & v6_rlvect_1(D) & v5_rlvect_1(D) & v4_rlvect_1(D) & -v3_struct_0(D) -> (all E (m1_grcat_1(E,A,B) & v2_grcat_1(E) -> (all F (m1_grcat_1(F,B,C) & v2_grcat_1(F) -> (all G (v2_grcat_1(G) & m1_grcat_1(G,C,D) -> k16_grcat_1(A,C,D,G,k16_grcat_1(A,B,C,F,E)) = k16_grcat_1(A,B,D,k16_grcat_1(B,C,D,G,F),E))))))))))))))) # label(t32_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10718 (all A (-v3_struct_0(A) & l2_struct_0(A) -> (all B (-v3_struct_0(B) & l2_struct_0(B) -> k2_funcop_1(u1_struct_0(A),k1_rlvect_1(B)) = k8_grcat_1(A,B))))) # label(d12_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10719 (all A all B (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(B) & l1_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(A) -> (exists C m4_grcat_1(C,A,B)))) # label(existence_m4_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10720 (all A (v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> v2_grcat_1(k13_grcat_1(A)) & v3_grcat_1(k13_grcat_1(A)))) # label(fc6_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10721 (all A all B (-v1_xboole_0(B) & v1_classes2(B) -> ((exists C (A = C & (exists D (-v3_struct_0(D) & v5_rlvect_1(D) & v1_midsp_2(D) & D = C & l1_rlvect_1(D) & v6_rlvect_1(D) & v4_rlvect_1(D) & v3_rlvect_1(D))) & m1_subset_1(C,u1_cat_1(k30_grcat_1(B))))) <-> r2_hidden(A,a_1_1_grcat_1(B))))) # label(fraenkel_a_1_1_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10722 (all A (v5_grcat_1(A) <-> (all B (r2_hidden(B,A) -> v2_grcat_1(B) & v3_grcat_1(B) & l1_grcat_1(B))))) # label(d23_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10723 (all A (-v1_xboole_0(A) & v5_grcat_1(A) -> (all B (m3_grcat_1(B,A) -> l1_grcat_1(B) & v3_grcat_1(B))))) # label(dt_m3_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10724 $T # label(d1_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10725 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) -> (all C ((all D (r2_hidden(D,C) -> v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(D))) <-> m5_grcat_1(C,A,B))))))) # label(d25_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10726 (all A (-v1_xboole_0(A) & v1_classes2(A) -> r2_hidden(k2_algstr_1,k29_grcat_1(A)))) # label(t51_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10727 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (m1_subset_1(B,u2_cat_1(k28_grcat_1(A))) -> (all C (m1_subset_1(C,u2_cat_1(k28_grcat_1(A))) -> (k3_cat_1(k28_grcat_1(A),B) = k2_cat_1(k28_grcat_1(A),C) <-> r2_hidden(k4_tarski(C,B),k1_relat_1(u5_cat_1(k28_grcat_1(A))))))))))) # label(t46_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10728 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) -> k13_grcat_1(A) = g1_grcat_1(A,A,k7_grcat_1(A)))) # label(d20_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10729 (all A all B (l1_struct_0(B) & l1_struct_0(A) -> m5_grcat_1(k17_grcat_1(A,B),A,B))) # label(dt_k17_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10730 (all A (v2_grcat_1(A) & l1_grcat_1(A) & v3_grcat_1(A) -> (all B (l1_grcat_1(B) & v3_grcat_1(B) & v2_grcat_1(B) -> (k9_grcat_1(B) = k10_grcat_1(A) -> k10_grcat_1(k15_grcat_1(B,A)) = k10_grcat_1(B) & k9_grcat_1(A) = k9_grcat_1(k15_grcat_1(B,A))))))) # label(t31_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10731 (all A all B (v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(B) & v5_rlvect_1(B) & l1_rlvect_1(B) & v6_rlvect_1(B) & v4_rlvect_1(B) & v4_rlvect_1(A) & -v3_struct_0(A) -> m1_grcat_1(k14_grcat_1(A,B),A,B) & v2_grcat_1(k14_grcat_1(A,B)))) # label(dt_k14_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10732 (all A (-v1_xboole_0(A) & v4_grcat_1(A) -> (all B (m2_grcat_1(B,A) -> k13_grcat_1(B) = k23_grcat_1(A,B))))) # label(d31_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10733 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) -> k1_funct_2(u1_struct_0(A),u1_struct_0(B)) = k17_grcat_1(A,B))))) # label(d26_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10734 (all A all B all C (r1_grcat_1(A,C) & r1_grcat_1(A,B) -> B = C)) # label(t40_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10735 (all A (v1_classes2(A) & -v1_xboole_0(A) -> a_1_0_grcat_1(A) = k29_grcat_1(A))) # label(d37_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10736 (all A all B (m1_subset_1(B,k20_grcat_1(A)) & v4_grcat_1(A) & -v1_xboole_0(A) -> m2_grcat_1(k21_grcat_1(A,B),A) & v1_rlvect_1(k21_grcat_1(A,B)))) # label(dt_k21_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10737 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,k20_grcat_1(A)) & v4_grcat_1(A) -> k10_grcat_1(B) = k22_grcat_1(A,B))) # label(redefinition_k22_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10738 (all A (l1_grcat_1(A) -> v1_funct_2(k11_grcat_1(A),u1_struct_0(k9_grcat_1(A)),u1_struct_0(k10_grcat_1(A))) & m2_relset_1(k11_grcat_1(A),u1_struct_0(k9_grcat_1(A)),u1_struct_0(k10_grcat_1(A))) & v1_funct_1(k11_grcat_1(A)))) # label(dt_k11_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.68 10739 (all A all B all C all D all E (v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & m1_grcat_1(D,B,C) & m1_grcat_1(E,A,B) & l1_rlvect_1(C) & -v3_struct_0(C) & l1_rlvect_1(B) & v4_rlvect_1(B) & v4_rlvect_1(A) & -v3_struct_0(A) -> v2_grcat_1(k16_grcat_1(A,B,C,D,E)) & m1_grcat_1(k16_grcat_1(A,B,C,D,E),A,C))) # label(dt_k16_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10740 (all A all B (v5_rlvect_1(A) & v6_rlvect_1(B) & l1_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> k14_grcat_1(A,B) = k12_grcat_1(A,B))) # label(redefinition_k14_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10741 (all A all B (l1_cat_1(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) & v2_cat_1(A) -> m2_relset_1(k4_grcat_1(A,B),k12_mcart_1(u2_cat_1(A),u2_cat_1(A),k1_grcat_1(A,B),k1_grcat_1(A,B)),k1_grcat_1(A,B)) & v1_funct_1(k4_grcat_1(A,B)))) # label(dt_k4_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10742 (all A (l2_struct_0(A) & -v3_struct_0(A) -> (all B (l1_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_rlvect_1(B) = k8_funct_2(u1_struct_0(A),u1_struct_0(B),k8_grcat_1(A,B),C))))))) # label(t15_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10743 (all A (v3_grcat_1(A) & l1_grcat_1(A) & v2_grcat_1(A) -> (all B (v2_grcat_1(B) & v3_grcat_1(B) & l1_grcat_1(B) -> -((all C (v4_rlvect_1(C) & l1_rlvect_1(C) & v6_rlvect_1(C) & v5_rlvect_1(C) & -v3_struct_0(C) -> (all D (v4_rlvect_1(D) & v5_rlvect_1(D) & v6_rlvect_1(D) & l1_rlvect_1(D) & -v3_struct_0(D) -> (all E (-v3_struct_0(E) & v4_rlvect_1(E) & l1_rlvect_1(E) & v6_rlvect_1(E) & v5_rlvect_1(E) -> (all F (v1_funct_1(F) & v1_funct_2(F,u1_struct_0(C),u1_struct_0(D)) & m2_relset_1(F,u1_struct_0(C),u1_struct_0(D)) -> (all G (v1_funct_1(G) & m2_relset_1(G,u1_struct_0(D),u1_struct_0(E)) & v1_funct_2(G,u1_struct_0(D),u1_struct_0(E)) -> -(g1_grcat_1(C,D,F) = A & g1_grcat_1(C,E,k7_funct_2(u1_struct_0(C),u1_struct_0(D),u1_struct_0(E),F,G)) = k15_grcat_1(B,A) & B = g1_grcat_1(D,E,G)))))))))))) & k9_grcat_1(B) = k10_grcat_1(A)))))) # label(t30_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10744 (all A all B (-v3_struct_0(A) & l2_struct_0(B) & -v3_struct_0(B) & l2_struct_0(A) -> v1_funct_1(k8_grcat_1(A,B)) & m2_relset_1(k8_grcat_1(A,B),u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(k8_grcat_1(A,B),u1_struct_0(A),u1_struct_0(B)))) # label(dt_k8_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10745 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & l1_rlvect_1(B) & v6_rlvect_1(B) & -v3_struct_0(B) -> (all C (l1_grcat_1(C) & v3_grcat_1(C) -> (m1_grcat_1(C,A,B) <-> k10_grcat_1(C) = B & A = k9_grcat_1(C)))))))) # label(d19_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10746 (all A (-v1_xboole_0(A) & v1_classes2(A) -> r2_hidden(k2_zfmisc_1(k1_tarski(k1_xboole_0),k1_tarski(k1_xboole_0)),A) & r2_hidden(k7_vectsp_2,A) & r2_hidden(k2_midsp_1,A) & r2_hidden(k4_tarski(k1_tarski(k1_xboole_0),k1_tarski(k1_xboole_0)),A) & r2_hidden(k1_tarski(k1_xboole_0),A))) # label(t6_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10747 (all A (-v1_xboole_0(A) & v1_classes2(A) -> v4_grcat_1(k19_grcat_1(A)) & -v1_xboole_0(k19_grcat_1(A)))) # label(fc9_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10748 (all A all B all C (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(B) & m4_grcat_1(C,A,B) & v4_rlvect_1(B) & l1_rlvect_1(A) -> (all D (m1_subset_1(D,C) <-> m7_grcat_1(D,A,B,C))))) # label(redefinition_m7_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10749 (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) -> (r2_hidden(A,a_2_0_grcat_1(B,C)) <-> (exists D exists E (m1_subset_1(E,u1_cat_1(B)) & r2_hidden(D,C) & r2_hidden(E,C) & A = k6_cat_1(B,D,E) & m1_subset_1(D,u1_cat_1(B))))))) # label(fraenkel_a_2_0_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10750 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> C = k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),C,k7_grcat_1(B)) & C = k1_partfun1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),k7_grcat_1(A),C))))))) # label(t12_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10751 (all A all B (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(B) & v4_rlvect_1(B) & l1_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & l1_rlvect_1(A) -> (exists C m1_grcat_1(C,A,B)))) # label(existence_m1_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10752 (all A (m1_subset_1(A,f1_s2_grcat_1) -> (all B (m1_subset_1(B,f2_s2_grcat_1) -> (p1_s2_grcat_1(A,B) -> r2_hidden(f4_s2_grcat_1(A,B),f3_s2_grcat_1)))))) -> (exists A ((all B (m1_subset_1(B,f1_s2_grcat_1) -> (all C (m1_subset_1(C,f2_s2_grcat_1) -> (r2_hidden(k4_tarski(B,C),k1_relat_1(A)) -> k1_funct_1(A,k4_tarski(B,C)) = f4_s2_grcat_1(B,C)))))) & (all B (m1_subset_1(B,f1_s2_grcat_1) -> (all C (m1_subset_1(C,f2_s2_grcat_1) -> (r2_hidden(k4_tarski(B,C),k1_relat_1(A)) <-> p1_s2_grcat_1(B,C)))))) & m2_relset_1(A,k2_zfmisc_1(f1_s2_grcat_1,f2_s2_grcat_1),f3_s2_grcat_1) & v1_funct_1(A))) # label(s2_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10753 (all A all B all C (v4_rlvect_1(A) & v6_rlvect_1(B) & m4_grcat_1(C,A,B) & l1_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (exists D (m1_subset_1(D,C) & v3_grcat_1(D) & v2_grcat_1(D))))) # label(rc9_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10754 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (l1_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_grcat_1(C,A,B) -> (exists D (v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v1_grcat_1(D,A,B) & g1_grcat_1(A,B,D) = g1_grcat_1(u1_grcat_1(C),u2_grcat_1(C),u3_grcat_1(C)) & v1_funct_1(D))))))))) # label(t22_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10755 (all A (-v1_xboole_0(A) & v4_grcat_1(A) -> (all B (m3_grcat_1(B,k20_grcat_1(A)) -> (all C (m3_grcat_1(C,k20_grcat_1(A)) -> (k22_grcat_1(A,C) = k21_grcat_1(A,B) -> r2_hidden(k15_grcat_1(B,C),k20_grcat_1(A))))))))) # label(t45_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10756 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (all B (l1_rlvect_1(B) & -v3_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v1_grcat_1(C,A,B) <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k2_rlvect_1(A,D,E)) = k2_rlvect_1(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E))))))))))))) # label(d13_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10757 (all A (v5_grcat_1(A) & -v1_xboole_0(A) -> (exists B m3_grcat_1(B,A)))) # label(existence_m3_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10758 (all A (-v1_xboole_0(A) & v1_classes2(A) -> v2_cat_1(k28_grcat_1(A)) & v1_cat_1(k28_grcat_1(A)))) # label(fc11_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10759 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (exists B (r2_hidden(B,A) & r1_grcat_1(B,k2_algstr_1))))) # label(t41_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10760 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l1_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (l1_rlvect_1(C) & v6_rlvect_1(C) & v5_rlvect_1(C) & v4_rlvect_1(C) & -v3_struct_0(C) -> (all D (m1_grcat_1(D,B,C) -> (all E (m1_grcat_1(E,A,B) -> m1_grcat_1(k15_grcat_1(D,E),A,C))))))))))) # label(t28_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10761 (all A (v4_grcat_1(A) & -v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(k20_grcat_1(A),k20_grcat_1(A)),k20_grcat_1(A)) & v1_funct_1(B) -> ((all C (m3_grcat_1(C,k20_grcat_1(A)) -> (all D (m3_grcat_1(D,k20_grcat_1(A)) -> (k22_grcat_1(A,D) = k21_grcat_1(A,C) <-> r2_hidden(k4_tarski(C,D),k1_relat_1(B))))))) & (all C (m3_grcat_1(C,k20_grcat_1(A)) -> (all D (m3_grcat_1(D,k20_grcat_1(A)) -> (r2_hidden(k4_tarski(C,D),k1_relat_1(B)) -> k1_funct_1(B,k4_tarski(C,D)) = k15_grcat_1(C,D)))))) <-> k27_grcat_1(A) = B))))) # label(d35_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10762 (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))) -> r1_cat_2(g1_cat_1(B,k1_grcat_1(A,B),k2_grcat_1(A,B),k3_grcat_1(A,B),k4_grcat_1(A,B),k5_grcat_1(A,B)),A))))) # label(t9_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10763 (all A (l1_grcat_1(A) -> -v3_struct_0(u2_grcat_1(A)) & v5_rlvect_1(u2_grcat_1(A)) & l1_rlvect_1(u2_grcat_1(A)) & v6_rlvect_1(u2_grcat_1(A)) & v4_rlvect_1(u2_grcat_1(A)))) # label(dt_u2_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10764 (all A (-v1_xboole_0(A) -> (all B (l1_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & v4_rlvect_1(C) & l1_rlvect_1(C) & v6_rlvect_1(C) & v5_rlvect_1(C) -> ((all D (m1_subset_1(D,A) -> v2_grcat_1(D) & m1_grcat_1(D,B,C))) <-> m4_grcat_1(A,B,C)))))))) # label(t38_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10765 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> m1_subset_1(k4_mcart_1(B,C,D,E),A) & m1_subset_1(k3_mcart_1(B,C,D),A))))))))))) # label(t3_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10766 (all A all B (v5_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(B) & v5_rlvect_1(B) & l1_rlvect_1(B) & v6_rlvect_1(B) & v4_rlvect_1(B) & l1_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> l1_grcat_1(k12_grcat_1(A,B)))) # label(dt_k12_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10767 (all A (-v1_xboole_0(A) & v1_classes2(A) -> m3_cat_2(k30_grcat_1(A),k28_grcat_1(A)))) # label(dt_k30_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10768 (all A (v5_grcat_1(A) & -v1_xboole_0(A) -> (exists B (v3_grcat_1(B) & v2_grcat_1(B) & m1_subset_1(B,A))))) # label(rc7_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10769 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (m1_subset_1(B,u2_cat_1(k28_grcat_1(A))) -> (all C (m1_subset_1(C,u2_cat_1(k28_grcat_1(A))) -> (all D (m3_grcat_1(D,k20_grcat_1(k19_grcat_1(A))) -> (all E (m3_grcat_1(E,k20_grcat_1(k19_grcat_1(A))) -> (C = E & D = B -> (k3_cat_1(k28_grcat_1(A),B) = k2_cat_1(k28_grcat_1(A),C) -> k21_grcat_1(k19_grcat_1(A),E) = k22_grcat_1(k19_grcat_1(A),D)) & (k2_cat_1(k28_grcat_1(A),C) = k3_cat_1(k28_grcat_1(A),B) -> r2_hidden(k4_tarski(E,D),k1_relat_1(k27_grcat_1(k19_grcat_1(A))))) & (r2_hidden(k4_tarski(E,D),k1_relat_1(k27_grcat_1(k19_grcat_1(A)))) -> k3_cat_1(k28_grcat_1(A),B) = k2_cat_1(k28_grcat_1(A),C)) & (k3_cat_1(k28_grcat_1(A),B) = k2_cat_1(k28_grcat_1(A),C) -> k4_cat_1(k28_grcat_1(A),B,C) = k15_grcat_1(E,D)) & (k3_cat_1(k28_grcat_1(A),B) = k3_cat_1(k28_grcat_1(A),C) -> k22_grcat_1(k19_grcat_1(A),E) = k22_grcat_1(k19_grcat_1(A),D)) & (k22_grcat_1(k19_grcat_1(A),E) = k22_grcat_1(k19_grcat_1(A),D) -> k3_cat_1(k28_grcat_1(A),C) = k3_cat_1(k28_grcat_1(A),B)) & (k21_grcat_1(k19_grcat_1(A),E) = k21_grcat_1(k19_grcat_1(A),D) -> k2_cat_1(k28_grcat_1(A),C) = k2_cat_1(k28_grcat_1(A),B)) & (k2_cat_1(k28_grcat_1(A),C) = k2_cat_1(k28_grcat_1(A),B) -> k21_grcat_1(k19_grcat_1(A),D) = k21_grcat_1(k19_grcat_1(A),E)) & (k22_grcat_1(k19_grcat_1(A),D) = k21_grcat_1(k19_grcat_1(A),E) -> k2_cat_1(k28_grcat_1(A),C) = k3_cat_1(k28_grcat_1(A),B))))))))))))) # label(t50_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10770 (all A (l1_struct_0(A) -> k7_grcat_1(A) = k6_partfun1(u1_struct_0(A)))) # label(d11_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10771 (all A (l1_grcat_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & l1_rlvect_1(B) & v6_rlvect_1(B) -> (all C (-v3_struct_0(C) & v4_rlvect_1(C) & l1_rlvect_1(C) & v6_rlvect_1(C) & v5_rlvect_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C)) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) -> (g1_grcat_1(B,C,D) = A -> k9_grcat_1(A) = B & C = k10_grcat_1(A) & k11_grcat_1(A) = D))))))))) # label(t17_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10772 (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))) -> B = u1_cat_1(k6_grcat_1(A,B)))))) # label(t10_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10773 (all A all B (v2_cat_1(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) & l1_cat_1(A) -> v1_funct_2(k2_grcat_1(A,B),k1_grcat_1(A,B),B) & m2_relset_1(k2_grcat_1(A,B),k1_grcat_1(A,B),B) & v1_funct_1(k2_grcat_1(A,B)))) # label(dt_k2_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10774 (all A (-v1_xboole_0(A) & v1_classes2(A) -> g1_cat_1(k19_grcat_1(A),k20_grcat_1(k19_grcat_1(A)),k24_grcat_1(k19_grcat_1(A)),k25_grcat_1(k19_grcat_1(A)),k27_grcat_1(k19_grcat_1(A)),k26_grcat_1(k19_grcat_1(A))) = k28_grcat_1(A))) # label(d36_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10775 (all A all B (-v3_struct_0(A) & v6_rlvect_1(A) & v4_rlvect_1(B) & l1_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & -v3_struct_0(B) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> m4_grcat_1(k18_grcat_1(A,B),A,B))) # label(dt_k18_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10776 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (v6_rlvect_1(B) & l1_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> g1_grcat_1(A,B,k8_grcat_1(A,B)) = k12_grcat_1(A,B))))) # label(d17_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10777 (all A (l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (l1_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (v2_grcat_1(C) & l1_grcat_1(C) -> (v1_grcat_1(k11_grcat_1(C),k9_grcat_1(C),k10_grcat_1(C)) & B = k10_grcat_1(C) & A = k9_grcat_1(C) -> v2_grcat_1(C) & m1_grcat_1(C,A,B)))))))) # label(t19_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10778 (all A all B (r2_hidden(B,f2_s1_grcat_1) & p1_s1_grcat_1(A,B) & r2_hidden(A,f1_s1_grcat_1) -> r2_hidden(f4_s1_grcat_1(A,B),f3_s1_grcat_1))) -> (exists A (v1_funct_1(A) & (all B all C (r2_hidden(k4_tarski(B,C),k1_relat_1(A)) -> k1_funct_1(A,k4_tarski(B,C)) = f4_s1_grcat_1(B,C))) & (all B all C (r2_hidden(B,f1_s1_grcat_1) & p1_s1_grcat_1(B,C) & r2_hidden(C,f2_s1_grcat_1) <-> r2_hidden(k4_tarski(B,C),k1_relat_1(A)))) & m2_relset_1(A,k2_zfmisc_1(f1_s1_grcat_1,f2_s1_grcat_1),f3_s1_grcat_1))) # label(s1_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10779 (all A all B (-v1_xboole_0(B) & v1_classes2(B) -> ((exists C ((exists D (v5_rlvect_1(D) & l1_rlvect_1(D) & D = C & v6_rlvect_1(D) & v4_rlvect_1(D) & v3_rlvect_1(D) & -v3_struct_0(D))) & C = A & m1_subset_1(C,u1_cat_1(k28_grcat_1(B))))) <-> r2_hidden(A,a_1_0_grcat_1(B))))) # label(fraenkel_a_1_0_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10780 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (B = k19_grcat_1(A) <-> (all C ((exists D (r2_hidden(D,A) & r1_grcat_1(D,C))) <-> r2_hidden(C,B))))))) # label(d29_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10781 (all A (v1_classes2(A) & -v1_xboole_0(A) -> a_1_1_grcat_1(A) = k31_grcat_1(A))) # label(d39_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10782 (all A (-v1_xboole_0(A) & v4_grcat_1(A) -> v1_funct_1(k26_grcat_1(A)) & v1_funct_2(k26_grcat_1(A),A,k20_grcat_1(A)) & m2_relset_1(k26_grcat_1(A),A,k20_grcat_1(A)))) # label(dt_k26_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10783 (all A (-v1_xboole_0(A) & v1_classes2(A) -> m3_cat_2(k32_grcat_1(A),k30_grcat_1(A)))) # label(dt_k32_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10784 (all A (v3_grcat_1(A) & l1_grcat_1(A) -> (all B (v3_grcat_1(B) & l1_grcat_1(B) -> (k10_grcat_1(B) = k9_grcat_1(A) -> (all C (l1_grcat_1(C) & v3_grcat_1(C) & v2_grcat_1(C) -> ((all D (-v3_struct_0(D) & l1_rlvect_1(D) & v6_rlvect_1(D) & v5_rlvect_1(D) & v4_rlvect_1(D) -> (all E (v6_rlvect_1(E) & l1_rlvect_1(E) & v5_rlvect_1(E) & v4_rlvect_1(E) & -v3_struct_0(E) -> (all F (-v3_struct_0(F) & v5_rlvect_1(F) & v6_rlvect_1(F) & l1_rlvect_1(F) & v4_rlvect_1(F) -> (all G (v1_funct_1(G) & v1_funct_2(G,u1_struct_0(E),u1_struct_0(F)) & m2_relset_1(G,u1_struct_0(E),u1_struct_0(F)) -> (all H (v1_funct_2(H,u1_struct_0(D),u1_struct_0(E)) & m2_relset_1(H,u1_struct_0(D),u1_struct_0(E)) & v1_funct_1(H) -> (g1_grcat_1(u1_grcat_1(B),u2_grcat_1(B),u3_grcat_1(B)) = g1_grcat_1(D,E,H) & g1_grcat_1(E,F,G) = g1_grcat_1(u1_grcat_1(A),u2_grcat_1(A),u3_grcat_1(A)) -> g1_grcat_1(D,F,k7_funct_2(u1_struct_0(D),u1_struct_0(E),u1_struct_0(F),H,G)) = C))))))))))) <-> k15_grcat_1(A,B) = C)))))))) # label(d21_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10785 $T # label(t36_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10786 (all A (v1_classes2(A) & -v1_xboole_0(A) -> k29_grcat_1(A) = u1_cat_1(k30_grcat_1(A)))) # label(t52_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10787 (exists A (v3_grcat_1(A) & v2_grcat_1(A) & l1_grcat_1(A))) # label(rc2_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10788 (exists A l1_grcat_1(A)) # label(existence_l1_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10789 (all A (m1_subset_1(A,u1_struct_0(k2_algstr_1)) -> k1_xboole_0 = A)) # label(t8_grcat_1_AndLHS) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10790 (all A (m1_subset_1(A,u1_struct_0(k2_algstr_1)) -> (all B (m1_subset_1(B,u1_struct_0(k2_algstr_1)) -> k1_xboole_0 = k4_rlvect_1(k2_algstr_1,A,B))))) # label(t8_grcat_1_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10791 (all A (m1_subset_1(A,u1_struct_0(k2_algstr_1)) -> k5_rlvect_1(k2_algstr_1,A) = k1_xboole_0)) # label(t8_grcat_1_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10792 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B all C (r2_hidden(B,C) & r2_hidden(C,A) -> r2_hidden(B,A))))) # label(t4_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10793 (all A (-v1_xboole_0(A) & v1_classes2(A) -> v2_cat_1(k30_grcat_1(A)) & v1_cat_1(k30_grcat_1(A)))) # label(fc13_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10794 (all A all B all C (l1_struct_0(A) & -v3_struct_0(B) & l1_struct_0(B) & m5_grcat_1(C,A,B) & -v1_xboole_0(C) -> (exists D m6_grcat_1(D,A,B,C)))) # label(existence_m6_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10795 $T # label(dt_l1_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10796 (all A (-v1_xboole_0(A) & v1_classes2(A) -> v1_cat_1(k32_grcat_1(A)) & v2_cat_1(k32_grcat_1(A)))) # label(fc15_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10797 (all A (l1_grcat_1(A) & v3_grcat_1(A) -> (exists B (-v3_struct_0(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(B) & (exists C (v5_rlvect_1(C) & l1_rlvect_1(C) & m1_grcat_1(A,B,C) & v6_rlvect_1(C) & v4_rlvect_1(C) & -v3_struct_0(C))) & v4_rlvect_1(B))))) # label(t24_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10798 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l1_rlvect_1(B) -> (all C (l1_rlvect_1(C) & -v3_struct_0(C) -> (all D (m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(D) -> (all E (m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C)) & v1_funct_1(E) -> (v1_grcat_1(D,A,B) & v1_grcat_1(E,B,C) -> v1_grcat_1(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C)))))))))))) # label(t14_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10799 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) & -v1_xboole_0(B) & l1_cat_1(A) & v2_cat_1(A) -> v1_funct_1(k3_grcat_1(A,B)) & m2_relset_1(k3_grcat_1(A,B),k1_grcat_1(A,B),B) & v1_funct_2(k3_grcat_1(A,B),k1_grcat_1(A,B),B))) # label(dt_k3_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10800 (all A (v4_grcat_1(A) & -v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,A,k20_grcat_1(A)) & v1_funct_2(B,A,k20_grcat_1(A)) -> ((all C (m2_grcat_1(C,A) -> k8_funct_2(A,k20_grcat_1(A),B,C) = k23_grcat_1(A,C))) <-> k26_grcat_1(A) = B))))) # label(d34_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10801 (all A (l1_grcat_1(A) -> (v3_grcat_1(A) <-> v1_grcat_1(k11_grcat_1(A),k9_grcat_1(A),k10_grcat_1(A))))) # label(d18_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10802 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(B) -> (all C (v2_grcat_1(C) & m1_grcat_1(C,A,B) -> (exists D (v1_funct_1(D) & g1_grcat_1(A,B,D) = C & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)))))))))) # label(t23_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10803 (all A (v1_classes2(A) & -v1_xboole_0(A) -> -v1_xboole_0(k31_grcat_1(A)))) # label(fc14_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10804 (all A (v1_classes2(A) & -v1_xboole_0(A) -> k6_grcat_1(k30_grcat_1(A),k31_grcat_1(A)) = k32_grcat_1(A))) # label(d40_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10805 (all A all B (v5_rlvect_1(A) & v4_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(B) & v5_rlvect_1(B) & -v3_struct_0(B) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (exists C (m1_grcat_1(C,A,B) & v3_grcat_1(C) & v2_grcat_1(C))))) # label(rc3_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10806 (all A all B all C (v4_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(B) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) & v5_rlvect_1(B) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all D all E all F (g1_grcat_1(D,E,F) = g1_grcat_1(A,B,C) -> B = E & C = F & D = A)))) # label(free_g1_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10807 (all A (v3_grcat_1(A) & l1_grcat_1(A) & v2_grcat_1(A) -> (all B (l1_grcat_1(B) & v3_grcat_1(B) & v2_grcat_1(B) -> (all C (l1_grcat_1(C) & v3_grcat_1(C) & v2_grcat_1(C) -> (k9_grcat_1(B) = k10_grcat_1(A) & k10_grcat_1(B) = k9_grcat_1(C) -> k15_grcat_1(k15_grcat_1(C,B),A) = k15_grcat_1(C,k15_grcat_1(B,A))))))))) # label(t33_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10808 (all A all B (l1_struct_0(B) & l1_struct_0(A) -> (exists C m5_grcat_1(C,A,B)))) # label(existence_m5_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10809 (all A all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) & l1_cat_1(A) & v2_cat_1(A) -> m1_subset_1(k1_grcat_1(A,B),k1_zfmisc_1(u2_cat_1(A))))) # label(dt_k1_grcat_1) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10810 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (v4_group_1(B) & l1_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_group_6(C,A,B) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v4_group_6(C,A,B) <-> v3_group_6(C,A,B) & v2_group_6(C,A,B)))))))) # label(d14_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10811 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_group_2(C,A) & v1_group_3(C,A) -> (all D (m1_subset_1(D,u1_struct_0(k6_group_6(A,C))) -> (D = k12_group_2(A,C,B) -> k3_group_1(k6_group_6(A,C),D) = k12_group_2(A,C,k3_group_1(A,B))))))))))) # label(t30_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10812 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (-v3_struct_0(B) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (v1_funct_1(E) & v1_group_6(E,A,B) & m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(E,u1_struct_0(A),u1_struct_0(B)) -> k8_funct_2(u1_struct_0(A),u1_struct_0(B),E,k2_group_5(A,C,D)) = k2_group_5(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),E,C),k8_funct_2(u1_struct_0(A),u1_struct_0(B),E,D)))))))))))) # label(t43_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10813 $T # label(t76_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10814 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) -> (all C (v1_funct_2(C,u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) & v1_group_6(C,B,A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v1_group_6(D,A,B) -> (D = k2_funct_1(C) & v4_group_6(C,B,A) -> v4_group_6(D,A,B)))))))))) # label(t73_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10815 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (-v3_struct_0(B) & l1_group_1(B) & v4_group_1(B) & v3_group_1(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) & v1_group_6(C,B,A) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A)) -> (v6_group_1(B) -> r1_xreal_0(k9_group_1(k13_group_6(B,A,C)),k9_group_1(B))))))))) # label(t62_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10816 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (v1_group_3(B,A) & m1_group_2(B,A) -> u1_struct_0(k6_group_6(A,B)) = k4_group_6(A,B))))) # label(t22_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10817 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) & v1_group_3(B,A) -> (all C (m1_subset_1(C,u1_struct_0(k6_group_6(A,B))) -> (all D (m1_subset_1(D,u1_struct_0(k6_group_6(A,B))) -> k2_group_2(A,k7_group_6(A,B,C),k7_group_6(A,B,D)) = k1_group_1(k6_group_6(A,B),C,D))))))))) # label(t24_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10818 (all A all B all C (v3_group_1(A) & m1_group_2(B,A) & v1_group_3(C,A) & m1_group_2(C,A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> v1_group_1(k2_group_6(A,B,C)) & v1_group_3(k2_group_6(A,B,C),B) & m1_group_6(k2_group_6(A,B,C),A,B))) # label(dt_k2_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10819 (all A all B all C (-v3_struct_0(A) & m1_group_2(B,A) & v1_group_3(C,A) & m1_group_2(C,A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> k8_group_2(A,B,C) = k2_group_6(A,B,C))) # label(redefinition_k2_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10820 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (-v3_struct_0(B) & l1_group_1(B) & v4_group_1(B) & v3_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v1_group_6(D,A,B) & v1_funct_1(D) -> (r1_rlvect_1(k13_group_6(A,B,D),C) & v2_group_6(D,A,B) -> C = k1_funct_1(D,k1_funct_1(k2_funct_1(D),C))))))))))) # label(t63_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10821 (all A all B all C (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & m1_group_2(B,A) & m1_group_2(C,A) & v1_group_3(C,A) & l1_group_1(A) -> v1_group_1(k1_group_6(A,B,C)) & v1_group_3(k1_group_6(A,B,C),B) & m1_group_6(k1_group_6(A,B,C),A,B))) # label(dt_k1_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10822 (all A (-v3_struct_0(A) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> r2_group_6(A,k6_group_6(A,k5_group_2(A))))) # label(t82_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10823 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & v1_group_1(A) -> (v3_realset2(A) -> k5_group_2(A) = A))) # label(t13_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10824 (all A (v1_group_1(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & v1_group_1(B) -> (v6_group_1(A) & r2_group_6(A,B) -> k9_group_1(A) = k9_group_1(B)))))) # label(t86_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10825 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> -v3_struct_0(k5_group_2(A)) & v2_group_1(k5_group_2(A)) & v3_group_1(k5_group_2(A)) & v1_group_3(k5_group_2(A),A) & v4_group_1(k5_group_2(A)) & v1_group_1(k5_group_2(A)))) # label(fc1_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10826 (all A all B (l1_group_1(A) & -v3_struct_0(B) & l1_group_1(B) & v4_group_1(B) & v3_group_1(B) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> m2_relset_1(k10_group_6(A,B),u1_struct_0(A),u1_struct_0(B)) & v1_group_6(k10_group_6(A,B),A,B) & v1_funct_2(k10_group_6(A,B),u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(k10_group_6(A,B)))) # label(dt_k10_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10827 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (B = a_1_0_group_6(A) -> r1_group_2(A,k9_group_5(A),k5_group_4(A,B))))))) # label(t7_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10828 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (v1_group_3(B,A) & m1_group_2(B,A) -> v3_group_6(k11_group_6(A,B),A,k6_group_6(A,B)))))) # label(t69_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10829 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & -v3_struct_0(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_group_6(C,A,B) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (all D (m1_group_2(D,A) & v1_group_1(D) -> (D = k12_group_6(A,B,C) <-> u1_struct_0(D) = a_3_0_group_6(A,B,C)))))))))) # label(d10_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10830 (all A all B all C (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(B) & v3_group_1(B) & v1_funct_1(C) & v1_group_6(C,A,B) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & l1_group_1(B) & v4_group_1(B) -> m1_subset_1(k9_group_6(A,B,C),k1_zfmisc_1(u1_struct_0(B))))) # label(dt_k9_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10831 (exists A (v2_group_1(A) & v3_group_1(A) & v3_realset2(A) & v4_group_1(A) & -v3_struct_0(A) & l1_group_1(A))) # label(rc1_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10832 $T # label(t20_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10833 (all A all B (v1_group_3(B,A) & m1_group_2(B,A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> v1_group_6(k11_group_6(A,B),A,k6_group_6(A,B)) & m2_relset_1(k11_group_6(A,B),u1_struct_0(A),u1_struct_0(k6_group_6(A,B))) & v1_funct_2(k11_group_6(A,B),u1_struct_0(A),u1_struct_0(k6_group_6(A,B))) & v1_funct_1(k11_group_6(A,B)))) # label(dt_k11_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10834 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (v3_group_1(B) & l1_group_1(B) & v4_group_1(B) & -v3_struct_0(B) -> (v6_group_1(A) & r1_group_6(A,B) -> v6_group_1(B)))))) # label(t85_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10835 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_1(A) -> (all B (v1_group_1(B) & m1_group_2(B,A) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> r1_rlvect_1(B,k2_group_5(A,C,D)))))) <-> m1_group_6(k9_group_5(A),A,B)))))) # label(t8_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10836 (all A all B all C (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_group_6(C,A,B) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) & -v3_struct_0(B) & v4_group_1(A) -> k2_relat_1(C) = k9_group_6(A,B,C))) # label(redefinition_k9_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10837 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (l1_group_1(B) & v4_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (all F (v1_funct_2(F,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(F,u1_struct_0(A),u1_struct_0(B)) & v1_group_6(F,A,B) & v1_funct_1(F) -> k8_funct_2(u1_struct_0(A),u1_struct_0(B),F,k3_group_5(A,C,D,E)) = k3_group_5(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),F,C),k8_funct_2(u1_struct_0(A),u1_struct_0(B),F,D),k8_funct_2(u1_struct_0(A),u1_struct_0(B),F,E)))))))))))))) # label(t44_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10838 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> -v3_struct_0(k6_group_2(A)) & v3_group_1(k6_group_2(A)) & v1_group_3(k6_group_2(A),A) & v4_group_1(k6_group_2(A)) & v2_group_1(k6_group_2(A)) & v1_group_1(k6_group_2(A)))) # label(fc2_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10839 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l1_group_1(B) & v4_group_1(B) & v3_group_1(B) -> (all C (v1_funct_1(C) & v1_group_6(C,B,A) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A)) -> (r1_group_2(B,k12_group_6(B,A,C),k5_group_2(B)) <-> v2_group_6(C,B,A)))))))) # label(t66_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10840 (all A all B all C (-v3_struct_0(A) & v3_group_1(A) & -v3_struct_0(B) & l1_group_1(B) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_group_6(C,A,B) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) & v4_group_1(B) & v3_group_1(B) & l1_group_1(A) & v4_group_1(A) -> -v3_struct_0(k12_group_6(A,B,C)) & v1_group_1(k12_group_6(A,B,C)) & v2_group_1(k12_group_6(A,B,C)) & v4_group_1(k12_group_6(A,B,C)) & v1_group_3(k12_group_6(A,B,C),A) & v3_group_1(k12_group_6(A,B,C)))) # label(fc6_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10841 (all A all B (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(B) & l1_group_1(B) & v4_group_1(B) & v3_group_1(B) & v1_group_1(B) & v1_group_1(A) & -v3_struct_0(A) -> r2_group_6(A,A))) # label(reflexivity_r2_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10842 (all A all B (v4_group_1(A) & l1_group_1(A) & v1_group_3(B,A) & m1_group_2(B,A) & v3_group_1(A) & -v3_struct_0(A) -> -v3_struct_0(k6_group_6(A,B)) & v2_group_1(k6_group_6(A,B)) & v4_group_1(k6_group_6(A,B)) & v3_group_1(k6_group_6(A,B)) & v1_group_1(k6_group_6(A,B)))) # label(fc5_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10843 (all A all B (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(B) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & v1_group_1(B) & v1_group_1(A) -> (r2_group_6(A,B) -> r2_group_6(B,A)))) # label(symmetry_r2_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10844 (all A all B (v4_group_1(A) & m1_group_2(B,A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (exists C m1_group_6(C,A,B)))) # label(existence_m1_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10845 (all A all B (v3_group_1(A) & l1_group_1(A) & m1_group_2(B,A) & v1_group_3(B,A) & v4_group_1(A) & -v3_struct_0(A) -> -v3_struct_0(k6_group_6(A,B)) & v1_group_1(k6_group_6(A,B)))) # label(fc4_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10846 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (-v3_struct_0(B) & v3_group_1(B) & l1_group_1(B) & v4_group_1(B) -> r2_group_6(k5_group_2(A),k5_group_2(B)))))) # label(t81_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10847 $T # label(t88_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10848 (all A all B (-v3_struct_0(A) & l1_group_1(A) & m1_group_2(B,A) & v4_group_1(A) & v3_group_1(A) -> (all C (m1_group_6(C,A,B) -> m1_group_2(C,A))))) # label(dt_m1_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10849 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> v3_realset2(k5_group_2(A)))) # label(t11_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10850 (all A all B all C (v3_group_1(A) & v4_group_1(A) & v1_group_3(B,A) & m1_subset_1(C,u1_struct_0(k6_group_6(A,B))) & m1_group_2(B,A) & l1_group_1(A) & -v3_struct_0(A) -> m1_subset_1(k7_group_6(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k7_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10851 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & v1_group_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v1_group_1(B) & v3_group_1(B) & l1_group_1(B) & v4_group_1(B) -> (v3_realset2(B) & v3_realset2(A) -> r2_group_6(A,B)))))) # label(t80_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10852 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (v1_group_3(B,A) & m1_group_2(B,A) -> (all C (m1_subset_1(C,u1_struct_0(k6_group_6(A,B))) -> (all D (m1_subset_1(D,u1_struct_0(k6_group_6(A,B))) -> k7_group_6(A,B,k1_group_1(k6_group_6(A,B),C,D)) = k2_group_2(A,k7_group_6(A,B,C),k7_group_6(A,B,D)))))))))) # label(t25_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10853 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (v1_group_3(B,A) & m1_group_2(B,A) -> (v1_finset_1(k14_group_2(A,B)) -> k17_group_2(A,B) = k9_group_1(k6_group_6(A,B))))))) # label(t33_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10854 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & v1_group_1(A) -> (all B (v3_group_1(B) & l1_group_1(B) & v4_group_1(B) & v1_group_1(B) & -v3_struct_0(B) -> (r2_group_6(A,B) -> k8_group_1(B) = k8_group_1(A)))))) # label(t84_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10855 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_group_1(B) & l1_group_1(B) & v4_group_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_group_6(C,A,B) -> (v4_group_6(C,A,B) <-> k9_group_6(A,B,C) = u1_struct_0(B) & v2_funct_1(C)))))))) # label(t70_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10856 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (v1_group_6(D,A,B) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(D) -> (r1_rlvect_1(k12_group_6(A,B,D),C) <-> k8_funct_2(u1_struct_0(A),u1_struct_0(B),D,C) = k2_group_1(B)))))))))) # label(t50_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10857 (all A all B (l1_group_1(A) & m1_group_2(B,A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all C (m1_group_6(C,A,B) <-> m1_group_2(C,B))))) # label(redefinition_m1_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10858 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v1_group_3(C,A) & m1_group_2(C,A) -> r2_hidden(k13_group_2(A,C,B),k4_group_6(A,C)) & r2_hidden(k12_group_2(A,C,B),k4_group_6(A,C)))))))) # label(t16_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10859 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (-v3_struct_0(B) & v1_group_1(B) & l1_group_1(B) & v4_group_1(B) & v3_group_1(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_group_6(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v3_group_6(C,A,B) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (exists E (D = k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E) & m1_subset_1(E,u1_struct_0(A))))))))))))) # label(t68_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10860 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (v3_realset2(A) <-> v6_group_1(A) & k9_group_1(A) = np__1))) # label(t12_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10861 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (l1_group_1(B) & v4_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A)) & v1_group_6(C,B,A) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) -> r2_group_6(k6_group_6(B,k12_group_6(B,A,C)),k13_group_6(B,A,C)))))))) # label(t90_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10862 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (v3_group_1(B) & l1_group_1(B) & v4_group_1(B) & -v3_struct_0(B) -> (all C (v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & -v3_struct_0(C) -> (all D (v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v1_group_6(D,B,A) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) & v1_group_6(E,A,C) & v1_funct_2(E,u1_struct_0(A),u1_struct_0(C)) -> v1_funct_2(k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(C),D,E),u1_struct_0(B),u1_struct_0(C)) & m2_relset_1(k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(C),D,E),u1_struct_0(B),u1_struct_0(C)) & v1_group_6(k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(C),D,E),B,C) & v1_funct_1(k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(C),D,E)))))))))))) # label(t48_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10863 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (-v3_struct_0(B) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (v1_group_6(D,A,B) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(D) -> (v2_group_6(D,A,B) -> C = k1_funct_1(k2_funct_1(D),k8_funct_2(u1_struct_0(A),u1_struct_0(B),D,C))))))))))) # label(t64_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10864 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (v1_group_3(B,A) & m1_group_2(B,A) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(k6_group_6(A,B))) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(k6_group_6(A,B))) & v1_group_6(C,A,k6_group_6(A,B)) & v1_funct_1(C) -> (k11_group_6(A,B) = C <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> k12_group_2(A,B,D) = k8_funct_2(u1_struct_0(A),u1_struct_0(k6_group_6(A,B)),C,D)))))))))) # label(d9_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10865 (all A all B all C (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & v3_group_1(B) & v4_group_1(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_group_6(C,A,B) & l1_group_1(B) & -v3_struct_0(B) & l1_group_1(A) -> v1_group_1(k12_group_6(A,B,C)) & m1_group_2(k12_group_6(A,B,C),A))) # label(dt_k12_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.69 10866 (all A all B all C (v3_group_1(A) & v1_group_3(B,A) & m1_group_2(C,A) & m1_group_2(B,A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> k8_group_2(A,B,C) = k3_group_6(A,B,C))) # label(redefinition_k3_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10867 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B all C (m1_group_2(C,A) & v1_group_3(C,A) -> ((exists D (k12_group_2(A,C,D) = B & B = k13_group_2(A,C,D) & m1_subset_1(D,u1_struct_0(A)))) <-> r1_rlvect_1(k6_group_6(A,C),B)))))) # label(t28_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10868 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) -> r1_group_2(B,k13_group_6(A,B,k10_group_6(A,B)),k5_group_2(B)))))) # label(t56_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10869 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v1_group_3(C,A) & m1_group_2(C,A) -> m1_subset_1(k13_group_2(A,C,B),u1_struct_0(k6_group_6(A,C))) & m1_subset_1(k7_group_2(A,C),u1_struct_0(k6_group_6(A,C))) & m1_subset_1(k12_group_2(A,C,B),u1_struct_0(k6_group_6(A,C))))))))) # label(t27_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10870 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_group_2(B,A) & v1_group_3(B,A) -> (all C (m1_group_2(C,A) & v1_group_3(C,A) & v1_group_1(C) -> (all D (v1_group_1(D) & v1_group_3(D,k6_group_6(A,C)) & m1_group_2(D,k6_group_6(A,C)) -> (k6_group_6(B,k1_group_6(A,B,C)) = D & m1_group_6(C,A,B) -> r2_group_6(k6_group_6(k6_group_6(A,C),D),k6_group_6(A,B))))))))))) # label(t92_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10871 $T # label(t39_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10872 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (v3_group_1(B) & l1_group_1(B) & v4_group_1(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_group_6(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> r1_group_2(B,k13_group_6(A,B,C),k5_group_4(B,k9_group_6(A,B,C))))))))) # label(t55_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10873 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (v3_group_1(B) & l1_group_1(B) & v4_group_1(B) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & v4_group_1(C) & l1_group_1(C) & v3_group_1(C) -> (r1_group_6(B,C) & r1_group_6(A,B) -> r1_group_6(A,C)))))))) # label(t78_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10874 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (-v3_struct_0(B) & l1_group_1(B) & v4_group_1(B) & v3_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v1_group_6(D,A,B) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(D) -> k3_group_1(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),D,C)) = k8_funct_2(u1_struct_0(A),u1_struct_0(B),D,k3_group_1(A,C)))))))))) # label(t41_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10875 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (-v3_struct_0(B) & l1_group_1(B) & v4_group_1(B) & v3_group_1(B) -> (all C (v1_group_6(C,B,A) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(C) -> v1_group_6(C,B,k13_group_6(B,A,C)) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(k13_group_6(B,A,C))) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(k13_group_6(B,A,C))) & v1_funct_1(C))))))) # label(t58_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10876 (all A all B all C all D (l1_group_1(B) & -v3_struct_0(C) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) & v1_group_6(D,B,C) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C)) & v4_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> ((exists E (m1_subset_1(E,u1_struct_0(B)) & k8_funct_2(u1_struct_0(B),u1_struct_0(C),D,E) = k2_group_1(C) & A = E)) <-> r2_hidden(A,a_3_0_group_6(B,C,D))))) # label(fraenkel_a_3_0_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10877 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (v1_group_3(B,A) & m1_group_2(B,A) -> k14_group_2(A,B) = k4_group_6(A,B) & k4_group_6(A,B) = k15_group_2(A,B))))) # label(t14_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10878 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (v1_group_1(B) & v1_group_3(B,A) & m1_group_2(B,A) -> r1_group_2(A,k12_group_6(A,k6_group_6(A,B),k11_group_6(A,B)),B))))) # label(t52_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10879 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (v3_group_1(B) & l1_group_1(B) & v4_group_1(B) & -v3_struct_0(B) -> (r1_group_6(A,B) <-> (exists C (v1_funct_1(C) & v1_group_6(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v4_group_6(C,A,B) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))))))))) # label(d15_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10880 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (v1_group_3(B,A) & m1_group_2(B,A) -> k16_group_2(A,B) = k8_group_1(k6_group_6(A,B)))))) # label(t32_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10881 (all A (v1_int_1(A) -> (all B (-v3_struct_0(B) & v3_group_1(B) & l1_group_1(B) & v4_group_1(B) -> (all C (-v3_struct_0(C) & v4_group_1(C) & l1_group_1(C) & v3_group_1(C) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (v1_funct_1(E) & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) & v1_group_6(E,B,C) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C)) -> k6_group_1(C,A,k8_funct_2(u1_struct_0(B),u1_struct_0(C),E,D)) = k8_funct_2(u1_struct_0(B),u1_struct_0(C),E,k6_group_1(B,A,D)))))))))))) # label(t46_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10882 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (v1_group_3(B,A) & m1_group_2(B,A) -> k6_group_6(A,B) = g1_group_1(k4_group_6(A,B),k5_group_6(A,B)))))) # label(d5_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10883 (all A all B (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & -v3_struct_0(B) & l1_group_1(A) -> r1_group_6(A,A))) # label(reflexivity_r1_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10884 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_group_2(B,A) -> (all C (v1_group_3(C,A) & m1_group_2(C,A) -> (m1_group_6(g1_group_1(u1_struct_0(C),u1_group_1(C)),A,B) -> k1_group_6(A,B,C) = g1_group_1(u1_struct_0(C),u1_group_1(C))))))))) # label(d1_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10885 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (v1_group_1(B) & v4_group_1(B) & l1_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (r1_group_6(A,B) & -v3_struct_0(A) & v4_group_1(A) & v7_group_1(A) & l1_group_1(A) & v3_group_1(A) -> -v3_struct_0(B) & v7_group_1(B) & l1_group_1(B) & v4_group_1(B) & v3_group_1(B)))))) # label(t89_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10886 (all A all B (v3_group_1(A) & v4_group_1(A) & v1_group_3(B,A) & m1_group_2(B,A) & l1_group_1(A) & -v3_struct_0(A) -> -v1_xboole_0(k4_group_6(A,B)))) # label(fc3_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10887 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_group_3(A,C,k3_group_1(A,B)) = k1_group_1(A,B,k1_group_1(A,C,k3_group_1(A,B))) & k2_group_3(A,C,k3_group_1(A,B)) = k1_group_1(A,k1_group_1(A,B,C),k3_group_1(A,B)))))))) # label(t4_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10888 (all A all B all C all D all E (l1_group_1(A) & -v3_struct_0(B) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & -v3_struct_0(C) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & v1_group_6(D,A,B) & m1_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C)) & m1_relset_1(E,u1_struct_0(B),u1_struct_0(C)) & v1_group_6(E,B,C) & v1_funct_1(D) & l1_group_1(C) & v4_group_1(C) & v3_group_1(C) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> k5_relat_1(D,E) = k8_group_6(A,B,C,D,E))) # label(redefinition_k8_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10889 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (v3_group_1(B) & l1_group_1(B) & v4_group_1(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A)) & v1_group_6(C,B,A) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) -> r1_tarski(k8_group_1(k13_group_6(B,A,C)),k8_group_1(B)))))))) # label(t61_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10890 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l1_group_1(B) & v4_group_1(B) & v3_group_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_group_6(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k2_group_1(A)) = k2_group_1(B))))))) # label(t40_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10891 (all A all B (l1_group_1(A) & -v3_struct_0(B) & v3_group_1(B) & l1_group_1(B) & v4_group_1(B) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (exists C (-v1_xboole_0(C) & v1_relat_1(C) & v1_funct_1(C) & v1_partfun1(C,u1_struct_0(A),u1_struct_0(B)) & v1_group_6(C,A,B) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)))))) # label(rc2_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10892 (all A all B (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & m1_group_2(B,A) & v1_group_3(B,A) & l1_group_1(A) -> l1_group_1(k6_group_6(A,B)))) # label(dt_k6_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10893 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & -v3_struct_0(B) -> (all C (v1_group_6(C,B,A) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(C) -> (v2_group_6(C,B,A) -> v1_funct_1(k2_funct_1(C)) & v1_funct_2(k2_funct_1(C),u1_struct_0(k13_group_6(B,A,C)),u1_struct_0(B)) & m2_relset_1(k2_funct_1(C),u1_struct_0(k13_group_6(B,A,C)),u1_struct_0(B)) & v1_group_6(k2_funct_1(C),k13_group_6(B,A,C),B)))))))) # label(t65_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10894 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (v1_group_3(B,A) & m1_group_2(B,A) -> k2_group_1(k6_group_6(A,B)) = k7_group_2(A,B))))) # label(t29_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10895 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (-v3_struct_0(B) & l1_group_1(B) & v4_group_1(B) & v3_group_1(B) -> (all C (m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) & v1_group_6(C,B,A) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(C) -> (v6_group_1(B) -> v6_group_1(k13_group_6(B,A,C))))))))) # label(t59_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10896 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (v4_group_1(B) & l1_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (v1_group_6(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (all D (m1_group_2(D,B) & v1_group_1(D) -> (k2_funct_2(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(A)) = u1_struct_0(D) <-> D = k13_group_6(A,B,C)))))))))) # label(d11_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10897 (all A (-v3_struct_0(A) & l1_struct_0(A) -> ((exists B k1_tarski(B) = u1_struct_0(A)) <-> v3_realset2(A)))) # label(d2_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10898 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B all C (m1_group_2(C,A) & v1_group_3(C,A) -> (r2_hidden(B,k4_group_6(A,C)) -> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))))))) # label(t17_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10899 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> v4_group_6(k11_group_6(A,k5_group_2(A)),A,k6_group_6(A,k5_group_2(A))))) # label(t75_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10900 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (-v3_struct_0(B) & l1_group_1(B) & v4_group_1(B) & v3_group_1(B) -> (all C (v1_funct_2(C,u1_struct_0(B),u1_struct_0(A)) & v1_group_6(C,B,A) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(C) -> (v2_group_6(C,B,A) -> r1_group_6(B,k13_group_6(B,A,C))))))))) # label(t79_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10901 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l1_group_1(B) & v4_group_1(B) & v3_group_1(B) -> (all C (v1_group_6(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v4_group_6(C,A,B) -> k9_group_6(A,B,C) = u1_struct_0(B) & k1_relat_1(C) = u1_struct_0(A)))))))) # label(t71_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10902 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> v3_realset2(k6_group_6(A,k6_group_2(A))))) # label(t83_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10903 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) & v1_group_3(B,A) -> k4_group_6(A,B) = k14_group_2(A,B))))) # label(d3_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10904 (all A all B all C (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(B) & v4_group_1(B) & v1_group_6(C,A,B) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) & l1_group_1(B) & v3_group_1(B) & v3_group_1(A) -> m1_group_2(k13_group_6(A,B,C),B) & v1_group_1(k13_group_6(A,B,C)))) # label(dt_k13_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10905 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (l1_group_1(B) & v4_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & v3_group_1(C) & l1_group_1(C) & v4_group_1(C) -> (all D (v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & v1_group_6(D,A,B) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C)) & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) & v1_group_6(E,B,C) -> (v4_group_6(E,B,C) & v4_group_6(D,A,B) -> v4_group_6(k8_group_6(A,B,C,D,E),A,C)))))))))))) # label(t74_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10906 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (v4_group_1(B) & l1_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(B),u1_struct_0(A)) & v1_group_6(C,B,A) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(C) -> (exists D (v1_funct_1(D) & v1_funct_2(D,u1_struct_0(k6_group_6(B,k12_group_6(B,A,C))),u1_struct_0(k13_group_6(B,A,C))) & v4_group_6(D,k6_group_6(B,k12_group_6(B,A,C)),k13_group_6(B,A,C)) & C = k8_group_6(B,k6_group_6(B,k12_group_6(B,A,C)),k13_group_6(B,A,C),k11_group_6(B,k12_group_6(B,A,C)),D) & m2_relset_1(D,u1_struct_0(k6_group_6(B,k12_group_6(B,A,C))),u1_struct_0(k13_group_6(B,A,C))) & v1_group_6(D,k6_group_6(B,k12_group_6(B,A,C)),k13_group_6(B,A,C)))))))))) # label(t91_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10907 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & v1_group_1(A) -> (all B (-v3_struct_0(B) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & v1_group_1(B) -> A = k12_group_6(A,B,k10_group_6(A,B)))))) # label(t51_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10908 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_group_2(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_group_6(D,A,B) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (C = E -> k12_group_2(A,D,C) = k12_group_2(B,D,E) & k13_group_2(B,D,E) = k13_group_2(A,D,C)))))))))))) # label(t2_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10909 (all A all B (v3_group_1(A) & l1_group_1(A) & v3_group_1(B) & l1_group_1(B) & v4_group_1(B) & v1_group_1(B) & -v3_struct_0(B) & v4_group_1(A) & v1_group_1(A) & -v3_struct_0(A) -> (r1_group_6(A,B) <-> r2_group_6(A,B)))) # label(redefinition_r2_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10910 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> v1_funct_1(k6_partfun1(u1_struct_0(A))) & v1_group_6(k6_partfun1(u1_struct_0(A)),A,A) & m2_relset_1(k6_partfun1(u1_struct_0(A)),u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(k6_partfun1(u1_struct_0(A)),u1_struct_0(A),u1_struct_0(A)))) # label(t47_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10911 (all A (l1_group_1(A) & -v3_struct_0(A) -> (all B (l1_group_1(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (v1_group_6(C,A,B) <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k1_group_1(A,D,E)) = k1_group_1(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E))))))))))))) # label(d7_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10912 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k12_group_2(A,B,C) = k3_group_2(A,C,k7_group_4(A,B,B)) & k4_group_2(A,C,k7_group_4(A,B,B)) = k13_group_2(A,B,C) & k13_group_2(A,B,C) = k11_group_2(A,B,k13_group_2(A,B,C)) & k12_group_2(A,B,C) = k10_group_2(A,B,k12_group_2(A,B,C)))))))) # label(t6_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10913 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (v1_group_3(B,A) & m1_group_2(B,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(k4_group_6(A,B),k4_group_6(A,B)),k4_group_6(A,B)) & m2_relset_1(C,k2_zfmisc_1(k4_group_6(A,B),k4_group_6(A,B)),k4_group_6(A,B)) -> (C = k5_group_6(A,B) <-> (all D (m1_subset_1(D,k4_group_6(A,B)) -> (all E (m1_subset_1(E,k4_group_6(A,B)) -> (all F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) -> (all G (m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A))) -> (G = E & D = F -> k2_binop_1(k4_group_6(A,B),k4_group_6(A,B),k4_group_6(A,B),C,D,E) = k2_group_2(A,F,G))))))))))))))))) # label(d4_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10914 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (v1_group_3(D,A) & m1_group_2(D,A) -> (r2_hidden(C,k4_group_6(A,D)) & r2_hidden(B,k4_group_6(A,D)) -> r2_hidden(k2_group_2(A,B,C),k4_group_6(A,D))))))))))) # label(t18_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10915 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B all C (v1_group_3(C,A) & m1_group_2(C,A) -> -(r2_hidden(B,k4_group_6(A,C)) & (all D (m1_subset_1(D,u1_struct_0(A)) -> -(B = k12_group_2(A,C,D) & B = k13_group_2(A,C,D))))))))) # label(t15_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10916 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (all C (v1_group_3(C,A) & m1_group_2(C,A) -> (m1_group_6(C,A,B) -> v1_group_3(C,B) & m1_group_6(C,A,B)))))))) # label(t9_group_6) # label(axiom) # label(non_clause). [assumption]. 126.39/125.70 10917 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v3_struct_0(B) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) -> (all C (v3_group_1(C) & l1_group_1(C) & v4_group_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (v1_funct_1(E) & v1_group_6(E,B,C) & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C)) -> k8_funct_2(u1_struct_0(B),u1_struct_0(C),E,k6_group_1(B,A,D)) = k6_group_1(C,A,k8_funct_2(u1_struct_0(B),u1_struct_0(C),E,D)))))))))))) # label(t45_group_6) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10918 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_group_2(B,A) & v1_group_3(B,A) -> (all C (m1_subset_1(C,u1_struct_0(k6_group_6(A,B))) -> k7_group_6(A,B,C) = C)))))) # label(d6_group_6) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10919 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_6(C,A,B) -> (all D (m1_group_6(D,A,B) -> k9_group_2(A,C,D) = k9_group_2(B,C,D))))))))) # label(t3_group_6) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10920 (all A all B all C (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_3(B,A) & m1_group_2(C,A) & m1_group_2(B,A) -> v1_group_3(k3_group_6(A,B,C),C) & m1_group_6(k3_group_6(A,B,C),A,C) & v1_group_1(k3_group_6(A,B,C)))) # label(dt_k3_group_6) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10921 $T # label(t19_group_6) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10922 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_group_1(B) & l1_group_1(B) & v4_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (v1_funct_1(E) & v1_funct_2(E,u1_struct_0(A),u1_struct_0(B)) & v1_group_6(E,A,B) & m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) -> k2_group_3(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),E,C),k8_funct_2(u1_struct_0(A),u1_struct_0(B),E,D)) = k8_funct_2(u1_struct_0(A),u1_struct_0(B),E,k2_group_3(A,C,D)))))))))))) # label(t42_group_6) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10923 $T # label(dt_k4_group_6) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10924 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l1_group_1(B) & v4_group_1(B) & v3_group_1(B) -> (all C (v1_funct_1(C) & v1_group_6(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (v2_group_6(C,A,B) <-> v2_funct_1(C)))))))) # label(d12_group_6) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10925 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (l1_group_1(B) & v4_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_group_6(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (v3_group_6(C,A,B) <-> k9_group_6(A,B,C) = u1_struct_0(B)))))))) # label(d13_group_6) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10926 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (-v3_struct_0(B) & v3_group_1(B) & l1_group_1(B) & v4_group_1(B) -> (all C all D (v1_group_6(D,B,A) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(D) -> (r1_rlvect_1(k13_group_6(B,A,D),C) <-> (exists E (k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,E) = C & m1_subset_1(E,u1_struct_0(B))))))))))) # label(t54_group_6) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10927 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_group_2(B,A) & v1_group_3(B,A) -> (v1_finset_1(k14_group_2(A,B)) -> v6_group_1(k6_group_6(A,B))))))) # label(t31_group_6) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10928 (all A all B (-v3_struct_0(B) & v4_group_1(B) & l1_group_1(B) & v3_group_1(B) -> ((exists C exists D (m1_subset_1(D,u1_struct_0(B)) & A = k2_group_5(B,C,D) & m1_subset_1(C,u1_struct_0(B)))) <-> r2_hidden(A,a_1_0_group_6(B))))) # label(fraenkel_a_1_0_group_6) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10929 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_group_2(B,A) -> (all C (v1_group_3(C,A) & m1_group_2(C,A) & v1_group_1(C) -> r2_group_6(k6_group_6(k8_group_4(A,B,C),k1_group_6(A,k8_group_4(A,B,C),C)),k6_group_6(B,k2_group_6(A,B,C))))))))) # label(t93_group_6) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10930 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_group_1(B) & l1_group_1(B) & v4_group_1(B) -> (all C (v3_group_1(C) & l1_group_1(C) & v4_group_1(C) & -v3_struct_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & v1_group_6(D,A,B) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) -> (all E (v1_funct_1(E) & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) & v1_group_6(E,B,C) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C)) -> k10_group_6(A,C) = k8_group_6(A,B,C,D,k10_group_6(B,C)) & k10_group_6(A,C) = k8_group_6(A,B,C,k10_group_6(A,B),E))))))))))) # label(t49_group_6) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10931 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (v3_group_1(B) & l1_group_1(B) & v4_group_1(B) & -v3_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_group_6(C,A,B) & v1_funct_1(C) -> u1_struct_0(k13_group_6(A,B,C)) = k9_group_6(A,B,C))))))) # label(t53_group_6) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10932 (all A (v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (v4_group_1(B) & l1_group_1(B) & v3_group_1(B) & v1_group_1(B) & -v3_struct_0(B) -> (r2_group_6(A,B) & v3_realset2(A) -> v3_realset2(B)))))) # label(t87_group_6) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10933 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_group_2(B,A) -> (all C (v1_group_1(C) & v1_group_3(C,A) & m1_group_2(C,A) -> (m1_group_6(C,A,B) -> m1_group_2(k6_group_6(B,k1_group_6(A,B,C)),k6_group_6(A,C))))))))) # label(t34_group_6) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10934 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (v1_group_1(B) & m1_group_2(B,A) & v1_group_3(B,A) -> (all C (m1_group_2(C,A) & v1_group_3(C,A) & v1_group_1(C) -> (m1_group_6(C,A,B) -> m1_group_2(k6_group_6(B,k1_group_6(A,B,C)),k6_group_6(A,C)) & v1_group_3(k6_group_6(B,k1_group_6(A,B,C)),k6_group_6(A,C))))))))) # label(t35_group_6) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10935 (all A all B (v3_group_1(A) & l1_group_1(A) & m1_group_2(B,A) & v1_group_3(B,A) & v4_group_1(A) & -v3_struct_0(A) -> v1_funct_2(k5_group_6(A,B),k2_zfmisc_1(k4_group_6(A,B),k4_group_6(A,B)),k4_group_6(A,B)) & m2_relset_1(k5_group_6(A,B),k2_zfmisc_1(k4_group_6(A,B),k4_group_6(A,B)),k4_group_6(A,B)) & v1_funct_1(k5_group_6(A,B)))) # label(dt_k5_group_6) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10936 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (v1_group_3(B,A) & m1_group_2(B,A) -> k5_group_6(A,B) = u1_group_1(k6_group_6(A,B)))))) # label(t23_group_6) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10937 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (v2_funct_1(C) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (k8_funct_2(A,B,C,E) = k8_funct_2(A,B,C,D) -> D = E)))))))))))) # label(t1_group_6) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10938 (all A all B all C all D all E (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(B) & v3_group_1(B) & -v3_struct_0(C) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C)) & v1_group_6(E,B,C) & m1_relset_1(E,u1_struct_0(B),u1_struct_0(C)) & v1_group_6(D,A,B) & l1_group_1(B) & v4_group_1(B) & v3_group_1(A) -> m2_relset_1(k8_group_6(A,B,C,D,E),u1_struct_0(A),u1_struct_0(C)) & v1_group_6(k8_group_6(A,B,C,D,E),A,C) & v1_funct_2(k8_group_6(A,B,C,D,E),u1_struct_0(A),u1_struct_0(C)) & v1_funct_1(k8_group_6(A,B,C,D,E)))) # label(dt_k8_group_6) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10939 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (v1_group_1(B) & v4_group_1(B) & l1_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (v1_group_6(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v4_group_6(C,A,B) -> v1_funct_1(k2_funct_1(C)) & m2_relset_1(k2_funct_1(C),u1_struct_0(B),u1_struct_0(A)) & v1_group_6(k2_funct_1(C),B,A) & v1_funct_2(k2_funct_1(C),u1_struct_0(B),u1_struct_0(A))))))))) # label(t72_group_6) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10940 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & v1_group_1(A) -> (all B (m1_group_2(B,A) & v1_group_3(B,A) & v1_group_1(B) -> (v3_group_1(k6_group_6(A,B)) & l1_group_1(k6_group_6(A,B)) & v7_group_1(k6_group_6(A,B)) & v4_group_1(k6_group_6(A,B)) & -v3_struct_0(k6_group_6(A,B)) <-> m1_group_6(k9_group_5(A),A,B)))))) # label(t36_group_6) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10941 $T # label(t21_group_6) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10942 $T # label(t37_group_6) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10943 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (v1_group_3(B,A) & m1_group_2(B,A) -> (all C (m1_subset_1(C,u1_struct_0(k6_group_6(A,B))) -> (exists D (C = k13_group_2(A,B,D) & C = k12_group_2(A,B,D) & m1_subset_1(D,u1_struct_0(A)))))))))) # label(t26_group_6) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10944 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v1_group_1(B) & v3_group_1(B) & l1_group_1(B) & v4_group_1(B) -> (all C (v1_group_6(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v3_group_6(C,A,B) <-> k13_group_6(A,B,C) = B))))))) # label(t67_group_6) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10945 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (v3_group_1(B) & l1_group_1(B) & v4_group_1(B) & -v3_struct_0(B) -> (all C (m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) & v1_group_6(C,B,A) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(C) -> (v3_group_1(B) & v4_group_1(B) & v7_group_1(B) & l1_group_1(B) & -v3_struct_0(B) -> v7_group_1(k13_group_6(B,A,C))))))))) # label(t60_group_6) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10946 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (v1_group_3(B,A) & m1_group_2(B,A) -> k13_group_6(A,k6_group_6(A,B),k11_group_6(A,B)) = k6_group_6(A,B))))) # label(t57_group_6) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10947 (all A (v1_group_1(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (v1_group_1(B) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & -v3_struct_0(B) -> (r1_group_6(A,B) -> r1_group_6(B,A)))))) # label(t77_group_6) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10948 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (-v3_struct_0(B) & v4_group_1(B) & l1_group_1(B) & v3_group_1(B) -> (all C (v1_group_6(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (k10_group_6(A,B) = C <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D) = k2_group_1(B)))))))))) # label(d8_group_6) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10949 $T # label(t5_group_6) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10950 $T # label(t38_group_6) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10951 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (all C (m1_group_2(C,A) & v1_group_3(C,A) -> v1_group_3(k9_group_2(A,B,C),B) & m1_group_6(k9_group_2(A,C,B),A,B) & v1_group_3(k9_group_2(A,C,B),B) & m1_group_6(k9_group_2(A,B,C),A,B))))))) # label(t10_group_6) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10952 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,C) -> (all D (m1_connsp_2(D,A,B) -> (all E (m1_subset_1(E,u1_struct_0(k3_pre_topc(A,C))) -> (all F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,C)))) -> (F = k5_subset_1(u1_struct_0(A),D,C) & B = E -> m1_connsp_2(F,k3_pre_topc(A,C),E))))))))))))))) # label(t6_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10953 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> k5_pcomps_1(k2_topmetr(A,B)) = k4_topmetr(A,B))))) # label(d8_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10954 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_topmetr))) -> (C = k1_rcomp_1(A,B) -> k3_pre_topc(k3_topmetr,C) = k4_topmetr(A,B))))))))) # label(t26_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10955 (all A (v7_metric_1(A) & l1_metric_1(A) & v9_metric_1(A) & v8_metric_1(A) & v6_metric_1(A) -> (exists B m1_topmetr(B,A)))) # label(existence_m1_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10956 (all A all B all C (m1_relset_1(B,A,u1_struct_0(k3_topmetr)) & v1_funct_1(B) -> v1_xreal_0(k1_funct_1(B,C)) & v1_xcmplx_0(k1_funct_1(B,C)))) # label(fc3_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10957 (all A (m1_subset_1(A,u1_struct_0(k8_metric_1)) -> (all B (m1_subset_1(B,u1_struct_0(k8_metric_1)) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (D = B & A = C -> k4_metric_1(k8_metric_1,A,B) = k18_complex1(k6_xcmplx_0(C,D))))))))))) # label(t15_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10958 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (m1_pre_topc(D,B) -> (v5_pre_topc(C,A,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,u1_struct_0(A),u1_struct_0(D)) & m2_relset_1(E,u1_struct_0(A),u1_struct_0(D)) -> (E = C -> v5_pre_topc(E,A,D))))))))))))) # label(t8_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10959 (all A (v1_xreal_0(A) -> (all B (v6_metric_1(B) & v8_metric_1(B) & l1_metric_1(B) & v9_metric_1(B) & v7_metric_1(B) -> (all C (m1_topmetr(C,B) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(C)) -> (E = D -> k9_metric_1(C,E,A) = k3_xboole_0(k9_metric_1(B,D,A),u1_struct_0(C))))))))))))) # label(t13_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10960 (all A all B (-v3_struct_0(A) & v8_metric_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & l1_metric_1(A) & v9_metric_1(A) & v7_metric_1(A) & v6_metric_1(A) -> v1_metric_1(k1_topmetr(A,B)) & m1_topmetr(k1_topmetr(A,B),A))) # label(dt_k1_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10961 (all A (v1_funct_1(A) & v1_funct_2(A,u1_struct_0(k3_topmetr),u1_struct_0(k3_topmetr)) & m2_relset_1(A,u1_struct_0(k3_topmetr),u1_struct_0(k3_topmetr)) -> ((exists B (m1_subset_1(B,k1_numbers) & (exists C ((all D (m1_subset_1(D,k1_numbers) -> k3_real_1(k4_real_1(B,D),C) = k1_funct_1(A,D))) & m1_subset_1(C,k1_numbers))))) -> v5_pre_topc(A,k3_topmetr,k3_topmetr)))) # label(t28_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10962 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> m1_pre_topc(k4_topmetr(A,B),k3_topmetr) & v1_pre_topc(k4_topmetr(A,B)) & -v3_struct_0(k4_topmetr(A,B)))) # label(dt_k4_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10963 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> m1_subset_1(C,u1_struct_0(A)))))))) # label(t2_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10964 (all A (l1_metric_1(A) -> (v2_topmetr(A) <-> v2_compts_1(k5_pcomps_1(A))))) # label(d6_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10965 (all A (-v3_struct_0(A) & v9_metric_1(A) & l1_metric_1(A) & v8_metric_1(A) & v7_metric_1(A) & v6_metric_1(A) -> (all B (m1_topmetr(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> m1_subset_1(C,u1_struct_0(A)))))))) # label(t12_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10966 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> m1_pre_topc(k3_pre_topc(A,B),k3_pre_topc(A,k4_subset_1(u1_struct_0(A),B,C))) & m1_pre_topc(k3_pre_topc(A,C),k3_pre_topc(A,k4_subset_1(u1_struct_0(A),B,C))))))))) # label(t5_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10967 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) -> k1_rcomp_1(A,B) = u1_struct_0(k2_topmetr(A,B))))))) # label(t14_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10968 (all A (v6_metric_1(A) & v7_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A)))) -> (v3_pre_topc(B,k5_pcomps_1(A)) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> -(r2_hidden(C,B) & (all D (v1_xreal_0(D) -> -(r1_tarski(k9_metric_1(A,C,D),B) & -r1_xreal_0(D,np__0)))))))))))) # label(t22_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10969 (all A (-v3_struct_0(A) & v6_metric_1(A) & v7_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -((all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(r1_tarski(C,B) & v1_finset_1(C) & r1_topmetr(A,C)))) & r1_topmetr(A,B) & v1_topmetr(B,A)))) <-> v2_topmetr(A)))) # label(t23_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10970 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(u1_struct_0(A),k5_setfam_1(u1_struct_0(A),B)) <-> r1_topmetr(A,B)))))) # label(d5_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10971 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v5_pre_topc(C,A,B) -> (all E (v1_funct_1(E) & m2_relset_1(E,u1_struct_0(A),u1_struct_0(k3_pre_topc(B,D))) & v1_funct_2(E,u1_struct_0(A),u1_struct_0(k3_pre_topc(B,D))) -> (C = E -> v5_pre_topc(E,A,k3_pre_topc(B,D)))))))))))))) # label(t9_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10972 (all A (l1_pre_topc(A) -> (all B (-v3_struct_0(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(D) -> (all E (v1_funct_2(E,u1_struct_0(k3_pre_topc(A,C)),u1_struct_0(B)) & m2_relset_1(E,u1_struct_0(k3_pre_topc(A,C)),u1_struct_0(B)) & v1_funct_1(E) -> (k2_partfun1(u1_struct_0(A),u1_struct_0(B),D,C) = E & v5_pre_topc(D,A,B) -> v5_pre_topc(E,k3_pre_topc(A,C),B)))))))))))) # label(t10_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10973 (all A (v1_xreal_0(A) -> (all B (v9_metric_1(B) & l1_metric_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(B)))) -> (k9_metric_1(B,C,A) = D -> v3_pre_topc(D,k5_pcomps_1(B))))))))))) # label(t21_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10974 $T # label(t18_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10975 (all A (-v3_struct_0(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) & v7_metric_1(A) & v6_metric_1(A) -> (exists B (v1_metric_1(B) & v6_metric_1(B) & v7_metric_1(B) & v9_metric_1(B) & v8_metric_1(B) & -v3_struct_0(B) & m1_topmetr(B,A))))) # label(rc2_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10976 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) -> (r1_tarski(u1_struct_0(B),u1_struct_0(C)) -> m1_pre_topc(B,C)))))))) # label(t4_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10977 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) -> k1_rcomp_1(A,B) = u1_struct_0(k4_topmetr(A,B))))))) # label(t25_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10978 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(u1_struct_0(A),k5_setfam_1(u1_struct_0(A),B)) <-> r1_pre_topc(A,B)))))) # label(t1_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10979 (all A all B (-v3_struct_0(A) & v6_metric_1(A) & v7_metric_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & l1_metric_1(A) & v9_metric_1(A) & v8_metric_1(A) -> -v3_struct_0(k1_topmetr(A,B)) & v6_metric_1(k1_topmetr(A,B)) & v7_metric_1(k1_topmetr(A,B)) & v8_metric_1(k1_topmetr(A,B)) & v9_metric_1(k1_topmetr(A,B)) & v1_metric_1(k1_topmetr(A,B)))) # label(fc1_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10980 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> m1_topmetr(k2_topmetr(A,B),k8_metric_1) & v1_metric_1(k2_topmetr(A,B)) & -v3_struct_0(k2_topmetr(A,B)))) # label(dt_k2_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10981 $T # label(t11_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10982 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) -> (all C (l1_pre_topc(C) & v2_pre_topc(C) -> (all D (m2_relset_1(D,u1_struct_0(A),u1_struct_0(C)) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(C)) & v1_funct_1(D) -> (m1_pre_topc(C,B) & v5_pre_topc(D,A,C) -> (all E (v1_funct_1(E) & m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(E,u1_struct_0(A),u1_struct_0(B)) -> (D = E -> v5_pre_topc(E,A,B))))))))))))) # label(t7_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10983 $T # label(t17_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10984 (all A (v7_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) & v6_metric_1(A) -> (all B (m1_topmetr(B,A) -> v6_metric_1(B) & v8_metric_1(B) & l1_metric_1(B) & v9_metric_1(B) & v7_metric_1(B))))) # label(dt_m1_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10985 (all A (-v3_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) & v7_metric_1(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_topmetr(C,A) & v1_metric_1(C) -> (k1_topmetr(A,B) = C <-> B = u1_struct_0(C)))))))) # label(d2_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10986 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_topmetr(B,A) <-> (all C -(r2_hidden(C,B) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,k1_numbers) -> k9_metric_1(A,D,E) != C))))))))))) # label(d4_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10987 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (v3_compts_1(A) -> v3_compts_1(B)))))) # label(t3_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10988 (all A (l1_metric_1(A) -> u1_pre_topc(k5_pcomps_1(A)) = k4_pcomps_1(A) & u1_struct_0(k5_pcomps_1(A)) = u1_struct_0(A))) # label(t16_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10989 (all A (v7_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) & v8_metric_1(A) & v6_metric_1(A) -> (exists B (v6_metric_1(B) & v7_metric_1(B) & v9_metric_1(B) & v8_metric_1(B) & v1_metric_1(B) & m1_topmetr(B,A))))) # label(rc1_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10990 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) -> (all C (m1_topmetr(C,k8_metric_1) & v1_metric_1(C) & -v3_struct_0(C) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k8_metric_1))) & -v1_xboole_0(D) -> (k1_rcomp_1(A,B) = D -> C = k1_topmetr(k8_metric_1,D)))) <-> C = k2_topmetr(A,B))))))))) # label(d3_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10991 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k14_euclid(A)))) -> (C = B -> k5_pcomps_1(k1_topmetr(k14_euclid(A),C)) = k3_pre_topc(k15_euclid(A),B)))))))) # label(t20_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.70 10992 (all A (v6_metric_1(A) & v7_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) -> (all B (l1_metric_1(B) & v9_metric_1(B) & v8_metric_1(B) & v7_metric_1(B) & v6_metric_1(B) -> (r1_tarski(u1_struct_0(B),u1_struct_0(A)) & (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k1_metric_1(u1_struct_0(B),u1_struct_0(B),u1_metric_1(B),C,D) = k1_binop_1(u1_metric_1(A),C,D))))) <-> m1_topmetr(B,A)))))) # label(d1_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 10993 (all A (-v3_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & l1_metric_1(A) & v9_metric_1(A) & v7_metric_1(A) -> (all B (-v3_struct_0(B) & m1_topmetr(B,A) -> m1_pre_topc(k5_pcomps_1(B),k5_pcomps_1(A)))))) # label(t19_topmetr) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 10994 (all A (m1_finseq_1(A,k4_numbers) -> v1_int_1(k2_gr_cy_1(A)))) # label(dt_k2_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 10995 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> k1_binop_1(k44_binop_2,A,B) = k2_xcmplx_0(A,B))))) # label(t14_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 10996 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v6_group_1(A) -> k6_group_1(A,k9_group_1(A),B) = k2_group_1(A)))))) # label(t29_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 10997 (all A (v1_funct_2(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) & m2_relset_1(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) & v1_funct_1(A) -> ((all B (m1_subset_1(B,k4_numbers) -> (all C (m1_subset_1(C,k4_numbers) -> k2_binop_1(k4_numbers,k4_numbers,k4_numbers,A,B,C) = k1_binop_1(k33_binop_2,B,C))))) <-> k44_binop_2 = A))) # label(d2_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 10998 $T # label(t6_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 10999 $T # label(t19_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11000 (all A (m1_subset_1(A,k4_numbers) -> A = k2_gr_cy_1(k12_finseq_1(k4_numbers,A)))) # label(t21_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11001 (all A (v4_ordinal2(A) -> (-r1_xreal_0(A,np__0) -> (all B (v1_funct_2(B,k2_zfmisc_1(k1_gr_cy_1(A),k1_gr_cy_1(A)),k1_gr_cy_1(A)) & m2_relset_1(B,k2_zfmisc_1(k1_gr_cy_1(A),k1_gr_cy_1(A)),k1_gr_cy_1(A)) & v1_funct_1(B) -> ((all C (m2_subset_1(C,k5_numbers,k1_gr_cy_1(A)) -> (all D (m2_subset_1(D,k5_numbers,k1_gr_cy_1(A)) -> k2_binop_1(k1_gr_cy_1(A),k1_gr_cy_1(A),k1_gr_cy_1(A),B,C,D) = k4_nat_1(k1_nat_1(C,D),A))))) <-> k4_gr_cy_1(A) = B)))))) # label(d5_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11002 $T # label(t7_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11003 (all A (m1_subset_1(A,k4_numbers) -> (A = np__0 -> r3_binop_1(k4_numbers,A,k44_binop_2)))) # label(t15_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11004 (all A (v4_ordinal2(A) -> (-r1_xreal_0(A,np__0) -> g1_group_1(k1_gr_cy_1(A),k4_gr_cy_1(A)) = k5_gr_cy_1(A)))) # label(d6_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11005 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_group_2(B,A) & v1_group_1(B) -> (-v3_struct_0(A) & v1_gr_cy_1(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & v6_group_1(A) -> v3_group_1(B) & l1_group_1(B) & v1_gr_cy_1(B) & v4_group_1(B) & -v3_struct_0(B)))))) # label(t44_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11006 (all A (v4_ordinal2(A) -> v1_group_1(k5_gr_cy_1(A)) & l1_group_1(k5_gr_cy_1(A)) & v4_group_1(k5_gr_cy_1(A)) & v3_group_1(k5_gr_cy_1(A)) & -v3_struct_0(k5_gr_cy_1(A)))) # label(dt_k5_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11007 (all A (m1_subset_1(A,k4_numbers) -> (all B (m2_finseq_1(B,k4_numbers) -> k2_gr_cy_1(k8_finseq_1(k4_numbers,B,k12_finseq_1(k4_numbers,A))) = k2_xcmplx_0(k2_gr_cy_1(B),k2_group_4(A)))))) # label(t20_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11008 $T # label(t4_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11009 $T # label(t1_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11010 (exists A (l1_group_1(A) & -v3_struct_0(A) & v1_group_1(A) & v2_group_1(A) & v4_group_1(A) & v1_gr_cy_1(A) & v3_group_1(A))) # label(rc1_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11011 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (-r1_xreal_0(A,np__0) -> -v3_struct_0(k5_gr_cy_1(A)) & v4_group_1(k5_gr_cy_1(A)) & v1_gr_cy_1(k5_gr_cy_1(A)) & l1_group_1(k5_gr_cy_1(A)) & v3_group_1(k5_gr_cy_1(A))))) # label(t49_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11012 $T # label(t9_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11013 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> ((exists D (v1_int_1(D) & k6_group_1(A,D,C) = B)) <-> r1_rlvect_1(k5_group_4(A,k1_struct_0(A,C)),B)))))))) # label(t25_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11014 (all A (m1_subset_1(A,u1_struct_0(k3_gr_cy_1)) -> k6_gr_cy_1(A) = A)) # label(d7_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11015 (all A (m1_subset_1(A,u1_struct_0(k3_gr_cy_1)) -> (all B (v1_int_1(B) -> (A = np__1 -> k6_group_1(k3_gr_cy_1,B,A) = B))))) # label(t39_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11016 $T # label(t11_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11017 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (-v3_struct_0(A) & v1_gr_cy_1(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) <-> (exists B ((all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (k6_group_1(A,D,B) = C & v1_int_1(D))))) & m1_subset_1(B,u1_struct_0(A))))))) # label(t41_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11018 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> -(v6_group_1(A) & v5_group_1(B,A)))))) # label(t26_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11019 $T # label(t18_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11020 $T # label(t2_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11021 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> v1_gr_cy_1(k5_group_2(A)))) # label(t40_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11022 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (v6_group_1(A) -> (v3_group_1(A) & v1_gr_cy_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) <-> (exists B ((all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (m2_subset_1(D,k1_numbers,k5_numbers) & C = k6_group_1(A,D,B))))) & m1_subset_1(B,u1_struct_0(A)))))))) # label(t42_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11023 (all A (l1_group_1(A) -> (-v3_struct_0(A) & v4_group_1(A) & v1_gr_cy_1(A) & v3_group_1(A) -> v2_group_1(A) & v4_group_1(A) & v7_group_1(A) & v3_group_1(A) & -v3_struct_0(A)))) # label(cc1_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11024 $T # label(t47_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11025 (all A (v4_ordinal2(A) -> (-r1_xreal_0(A,np__0) -> v3_group_1(g1_group_1(k1_gr_cy_1(A),k4_gr_cy_1(A))) & v4_group_1(g1_group_1(k1_gr_cy_1(A),k4_gr_cy_1(A)))))) # label(t34_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11026 $T # label(t8_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11027 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v3_group_1(B) & l1_group_1(B) & v4_group_1(B) & v1_group_1(B) & -v3_struct_0(B) -> (v1_int_2(A) & A = k9_group_1(B) & v6_group_1(B) -> -v3_struct_0(B) & v4_group_1(B) & l1_group_1(B) & v1_gr_cy_1(B) & v3_group_1(B)))))) # label(t45_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11028 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,k4_numbers) -> k6_group_1(A,k2_gr_cy_1(C),B) = k3_group_4(A,k4_group_4(A,C,k1_finsop_1(u1_struct_0(A),k3_finseq_1(C),B))))))))) # label(t24_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11029 (all A (v4_ordinal2(A) -> (-r1_xreal_0(A,np__0) -> np__0 = k2_group_1(k5_gr_cy_1(A))))) # label(t36_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11030 (all A (v1_int_1(A) -> m1_subset_1(k7_gr_cy_1(A),u1_struct_0(k3_gr_cy_1)))) # label(dt_k7_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11031 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v3_struct_0(B) & v3_group_1(B) & l1_group_1(B) & v4_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (v6_group_1(B) -> k3_group_1(B,k6_group_1(B,A,C)) = k6_group_1(B,k10_binop_2(k9_group_1(B),k4_nat_1(A,k9_group_1(B))),C)))))))) # label(t30_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11032 $T # label(t16_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11033 (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_xreal_0(A,np__0) | r1_tarski(k1_gr_cy_1(A),k1_gr_cy_1(B))))))) # label(t51_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11034 (all A (v4_ordinal2(A) -> (-r1_xreal_0(A,np__0) -> a_1_0_gr_cy_1(A) = k1_gr_cy_1(A)))) # label(d1_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11035 (all A (m1_subset_1(A,u1_struct_0(k3_gr_cy_1)) -> v1_int_1(k6_gr_cy_1(A)))) # label(dt_k6_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11036 (all A (v4_ordinal2(A) -> -v1_xboole_0(k1_gr_cy_1(A)) & m1_subset_1(k1_gr_cy_1(A),k1_zfmisc_1(k5_numbers)))) # label(dt_k1_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11037 (all A (v1_int_1(A) -> A = k7_gr_cy_1(A))) # label(d8_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11038 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & v1_group_1(A) & -v3_struct_0(A) -> (v6_group_1(A) -> (-v3_struct_0(A) & v3_group_1(A) & v1_gr_cy_1(A) & l1_group_1(A) & v4_group_1(A) <-> (exists B (k9_group_1(A) = k7_group_1(A,B) & m1_subset_1(B,u1_struct_0(A)))))))) # label(t43_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11039 $T # label(t17_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11040 $T # label(t23_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11041 $T # label(t3_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11042 (all A (v1_group_1(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> -(-r1_xreal_0(k9_group_1(A),np__1) & (all B (m1_subset_1(B,u1_struct_0(A)) -> k2_group_1(A) = B))))) # label(t31_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11043 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> ((exists B (m1_subset_1(B,u1_struct_0(A)) & k5_group_4(A,k1_struct_0(A,B)) = g1_group_1(u1_struct_0(A),u1_group_1(A)))) <-> v1_gr_cy_1(A)))) # label(d9_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11044 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> -(-r1_xreal_0(A,np__0) & (all B (m1_subset_1(B,u1_struct_0(k5_gr_cy_1(A))) -> (exists C (m1_subset_1(C,u1_struct_0(k5_gr_cy_1(A))) & (all D (v1_int_1(D) -> C != k6_group_1(k5_gr_cy_1(A),D,B)))))))))) # label(t46_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11045 (all A (m2_finseq_1(A,k4_numbers) -> k2_finsop_1(k4_numbers,A,k44_binop_2) = k2_gr_cy_1(A))) # label(d3_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11046 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (-r1_xreal_0(A,np__0) -> (r2_hidden(B,k1_gr_cy_1(A)) <-> -r1_xreal_0(A,B))))))) # label(t10_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11047 (all A (m1_subset_1(A,u1_struct_0(k3_gr_cy_1)) -> k3_group_1(k3_gr_cy_1,A) = k4_xcmplx_0(k6_gr_cy_1(A)))) # label(t37_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11048 (all A (m1_subset_1(A,u1_struct_0(k3_gr_cy_1)) -> (np__1 = A -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k6_group_1(k3_gr_cy_1,B,A) = B))))) # label(t38_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11049 (all A (v4_ordinal2(A) -> (-r1_xreal_0(A,np__0) -> r2_hidden(np__0,k1_gr_cy_1(A))))) # label(t12_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11050 (all A all B (v4_ordinal2(B) -> (r2_hidden(A,a_1_0_gr_cy_1(B)) <-> (exists C (-r1_xreal_0(B,C) & A = C & m2_subset_1(C,k1_numbers,k5_numbers)))))) # label(fraenkel_a_1_0_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11051 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v6_group_1(A) -> r1_nat_1(k7_group_1(A,B),k9_group_1(A))))))) # label(t28_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11052 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v6_group_1(A) -> k7_group_1(A,B) = k9_group_1(k5_group_4(A,k1_struct_0(A,B)))))))) # label(t27_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11053 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v4_group_1(B) & l1_group_1(B) & v3_group_1(B) & v1_group_1(B) & -v3_struct_0(B) -> (v6_group_1(B) & v1_int_2(A) & k9_group_1(B) = A -> (all C (m1_group_2(C,B) & v1_group_1(C) -> B = C | r1_group_2(B,C,k5_group_2(B))))))))) # label(t32_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11054 (all A (v4_ordinal2(A) -> m2_relset_1(k4_gr_cy_1(A),k2_zfmisc_1(k1_gr_cy_1(A),k1_gr_cy_1(A)),k1_gr_cy_1(A)) & v1_funct_2(k4_gr_cy_1(A),k2_zfmisc_1(k1_gr_cy_1(A),k1_gr_cy_1(A)),k1_gr_cy_1(A)) & v1_funct_1(k4_gr_cy_1(A)))) # label(dt_k4_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11055 $T # label(t5_gr_cy_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11056 (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]. 126.42/125.71 11057 (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]. 126.42/125.71 11058 $T # label(t51_isocat_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11059 (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]. 126.42/125.71 11060 (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]. 126.42/125.71 11061 (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]. 126.42/125.71 11062 (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]. 126.42/125.71 11063 (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]. 126.42/125.71 11064 (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]. 126.42/125.71 11065 (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]. 126.42/125.71 11066 (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]. 126.42/125.71 11067 (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]. 126.42/125.71 11068 (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]. 126.42/125.71 11069 (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]. 126.42/125.71 11070 (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]. 126.42/125.71 11071 (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]. 126.42/125.71 11072 (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]. 126.42/125.71 11073 (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]. 126.42/125.71 11074 (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]. 126.42/125.71 11075 (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]. 126.42/125.71 11076 (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]. 126.42/125.71 11077 (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]. 126.42/125.71 11078 (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]. 126.42/125.71 11079 (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]. 126.42/125.71 11080 $T # label(t5_isocat_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11081 (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]. 126.42/125.71 11082 (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]. 126.42/125.71 11083 (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]. 126.42/125.71 11084 (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]. 126.42/125.71 11085 (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]. 126.42/125.71 11086 (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]. 126.42/125.71 11087 (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]. 126.42/125.71 11088 (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]. 126.42/125.71 11089 (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]. 126.42/125.71 11090 (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]. 126.42/125.71 11091 (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]. 126.42/125.71 11092 (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]. 126.42/125.71 11093 (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]. 126.42/125.71 11094 (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]. 126.42/125.71 11095 (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]. 126.42/125.71 11096 $T # label(t18_isocat_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11097 (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]. 126.42/125.71 11098 (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]. 126.42/125.71 11099 (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]. 126.42/125.71 11100 (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]. 126.42/125.71 11101 (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]. 126.42/125.71 11102 (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]. 126.42/125.71 11103 (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]. 126.42/125.71 11104 (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]. 126.42/125.71 11105 (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]. 126.42/125.71 11106 (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]. 126.42/125.71 11107 (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]. 126.42/125.71 11108 (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]. 126.42/125.71 11109 (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]. 126.42/125.71 11110 $T # label(t19_isocat_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11111 (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]. 126.42/125.71 11112 (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]. 126.42/125.71 11113 (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]. 126.42/125.71 11114 (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]. 126.42/125.71 11115 (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]. 126.42/125.71 11116 (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]. 126.42/125.71 11117 (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]. 126.42/125.71 11118 $T # label(t6_isocat_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11119 (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]. 126.42/125.71 11120 (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]. 126.42/125.71 11121 (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]. 126.42/125.71 11122 (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]. 126.42/125.71 11123 (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]. 126.42/125.71 11124 (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]. 126.42/125.71 11125 (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]. 126.42/125.71 11126 $T # label(t52_isocat_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11127 (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]. 126.42/125.71 11128 (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]. 126.42/125.71 11129 (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]. 126.42/125.71 11130 (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]. 126.42/125.71 11131 (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]. 126.42/125.71 11132 (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]. 126.42/125.71 11133 (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]. 126.42/125.71 11134 (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]. 126.42/125.71 11135 (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]. 126.42/125.71 11136 (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]. 126.42/125.71 11137 (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]. 126.42/125.71 11138 (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]. 126.42/125.71 11139 (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]. 126.42/125.71 11140 (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]. 126.42/125.71 11141 (all A all B all C (m1_pre_topc(B,A) & m1_pre_topc(C,A) & l1_pre_topc(A) -> (r1_tsep_1(A,B,C) -> r1_tsep_1(A,C,B)))) # label(symmetry_r1_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11142 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (-r1_tsep_1(A,B,C) -> (m1_pre_topc(B,C) -> k2_tsep_1(A,B,C) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))) & (k2_tsep_1(A,B,C) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) -> m1_pre_topc(B,C)) & (g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) = k2_tsep_1(A,B,C) -> m1_pre_topc(C,B)) & (m1_pre_topc(C,B) -> g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) = k2_tsep_1(A,B,C))))))))) # label(t31_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11143 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) & v4_pre_topc(C,A) -> r2_tsep_1(A,B,C)))))))) # label(t53_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11144 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (v1_borsuk_1(B,A) & m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (r1_tarski(u1_struct_0(B),u1_struct_0(C)) -> m1_pre_topc(B,C) & v1_borsuk_1(B,C) & -v3_struct_0(B)))))))) # label(t14_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11145 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_tsep_1(A,B,C) -> r2_tsep_1(A,k4_subset_1(u1_struct_0(A),B,D),k4_subset_1(u1_struct_0(A),C,D))))))))))) # label(t55_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11146 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> m1_subset_1(u1_struct_0(B),k1_zfmisc_1(u1_struct_0(A))))))) # label(t1_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11147 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r1_connsp_1(A,C,D) | r1_connsp_1(A,B,D) -> r1_connsp_1(A,k5_subset_1(u1_struct_0(A),B,C),D)))))))))) # label(t44_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11148 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (v1_tsep_1(B,A) & v2_pre_topc(B) & v1_pre_topc(B) & m1_pre_topc(B,A))))) # label(rc1_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11149 $T # label(t50_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11150 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) -> (v3_pre_topc(C,A) & r1_tarski(D,C) & D = E & r1_tarski(C,u1_struct_0(B)) -> (v3_pre_topc(D,A) <-> v3_pre_topc(E,B))))))))))))) # label(t9_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11151 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> ((exists D (-v3_struct_0(D) & (exists E (m1_pre_topc(E,A) & m1_pre_topc(B,D) & m1_pre_topc(C,E) & r1_tsep_1(A,D,C) & r1_tsep_1(A,E,B) & v1_tsep_1(E,A) & -v3_struct_0(E))) & m1_pre_topc(D,A) & v1_tsep_1(D,A))) <-> r3_tsep_1(A,B,C)))))))) # label(t82_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11152 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r1_connsp_1(A,C,D) & r1_connsp_1(A,B,D) <-> r1_connsp_1(A,k4_subset_1(u1_struct_0(A),B,C),D)))))))))) # label(t45_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11153 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(C) = E & D = u1_struct_0(B) -> r1_connsp_1(A,D,E)))))) <-> r3_tsep_1(A,B,C)))))))) # label(d8_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11154 $T # label(t28_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.71 11155 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (all D (-v3_struct_0(D) & m1_pre_topc(D,A) -> (r3_tsep_1(A,k1_tsep_1(A,B,C),D) <-> r3_tsep_1(A,C,D) & r3_tsep_1(A,B,D)))))))))) # label(t79_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11156 $T # label(t69_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11157 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (k4_subset_1(u1_struct_0(A),B,C) = u1_struct_0(A) -> ((exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & (exists E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & (exists F (k4_subset_1(u1_struct_0(A),B,C) = k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),D,E),F) & v4_pre_topc(D,A) & v4_pre_topc(E,A) & v3_pre_topc(F,A) & r1_tarski(F,k5_subset_1(u1_struct_0(A),B,C)) & r1_tarski(E,C) & r1_tarski(D,B) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))))))))) <-> r2_tsep_1(A,B,C))))))))) # label(t61_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11158 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (all D (m1_pre_topc(D,A) & -v3_struct_0(D) -> -(-r1_tsep_1(A,D,C) & -(k1_tsep_1(A,k2_tsep_1(A,B,D),k2_tsep_1(A,C,D)) = k2_tsep_1(A,k1_tsep_1(A,B,C),D) & k2_tsep_1(A,D,k1_tsep_1(A,B,C)) = k1_tsep_1(A,k2_tsep_1(A,D,B),k2_tsep_1(A,D,C))) & -r1_tsep_1(A,B,D)))))))))) # label(t35_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11159 $T # label(d4_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11160 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & v1_tsep_1(B,A) -> (all C (m1_pre_topc(C,B) & v1_tsep_1(C,B) -> m1_pre_topc(C,A) & v1_tsep_1(C,A))))))) # label(t18_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11161 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(C,A) & v3_pre_topc(B,A) -> (r1_connsp_1(A,B,C) <-> r1_xboole_0(B,C))))))))) # label(t41_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11162 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (all D (m1_pre_topc(D,A) & -v3_struct_0(D) -> (r3_tsep_1(A,B,D) -> r3_tsep_1(A,k2_tsep_1(A,B,C),D) | r1_tsep_1(A,B,C)))))))))) # label(t78_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11163 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & v1_tsep_1(B,A) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & v1_tsep_1(C,A) & -v3_struct_0(C) -> (-r1_tsep_1(A,B,C) -> m1_pre_topc(k2_tsep_1(A,B,C),A) & v1_tsep_1(k2_tsep_1(A,B,C),A)))))))) # label(t33_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11164 $T # label(t27_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11165 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & (exists E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & r1_tarski(B,D) & r1_xboole_0(k5_subset_1(u1_struct_0(A),D,E),k4_subset_1(u1_struct_0(A),B,C)) & v4_pre_topc(D,A) & v4_pre_topc(E,A) & r1_tarski(C,E))))) <-> r1_connsp_1(A,B,C)))))))) # label(t47_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11166 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(B) = C -> (m1_pre_topc(B,A) & v1_tsep_1(B,A) <-> v3_pre_topc(C,A))))))))) # label(t16_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11167 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (m1_pre_topc(B,C) <-> g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) = k1_tsep_1(A,B,C)))))))) # label(t23_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11168 (all A (l1_pre_topc(A) & v1_pre_topc(A) -> A = k3_pre_topc(A,k2_pre_topc(A)))) # label(t3_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11169 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) & v3_pre_topc(C,A) -> r2_tsep_1(A,B,C)))))))) # label(t54_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11170 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (all D (m1_pre_topc(D,A) & -v3_struct_0(D) -> (r4_tsep_1(A,B,C) -> r4_tsep_1(A,k1_tsep_1(A,B,D),k1_tsep_1(A,C,D))))))))))) # label(t89_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11171 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (-r1_tsep_1(A,B,C) -> m1_pre_topc(k2_tsep_1(A,B,C),B) & m1_pre_topc(k2_tsep_1(A,B,C),C)))))))) # label(t30_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11172 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_tsep_1(A,C,D) & r2_tsep_1(A,B,D) -> r2_tsep_1(A,k4_subset_1(u1_struct_0(A),B,C),D)))))))))) # label(t58_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11173 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) -> (v4_pre_topc(C,A) & r1_tarski(C,u1_struct_0(B)) & r1_tarski(D,C) & E = D -> (v4_pre_topc(E,B) <-> v4_pre_topc(D,A))))))))))))) # label(t8_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11174 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (r1_tsep_1(A,B,C) & A = k1_tsep_1(A,B,C) -> (r4_tsep_1(A,B,C) <-> v1_borsuk_1(B,A) & v1_borsuk_1(C,A) & m1_pre_topc(C,A) & m1_pre_topc(B,A))))))))) # label(t95_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11175 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (all D (m1_pre_topc(D,A) & -v3_struct_0(D) -> (-r1_tsep_1(A,B,C) -> k2_tsep_1(A,k1_tsep_1(A,D,B),k1_tsep_1(A,D,C)) = k1_tsep_1(A,D,k2_tsep_1(A,B,C)) & k2_tsep_1(A,k1_tsep_1(A,B,D),k1_tsep_1(A,C,D)) = k1_tsep_1(A,k2_tsep_1(A,B,C),D)))))))))) # label(t36_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11176 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (all D (-v3_struct_0(D) & m1_pre_topc(D,A) -> (all E (-v3_struct_0(E) & m1_pre_topc(E,A) -> (m1_pre_topc(D,B) & m1_pre_topc(E,C) & r4_tsep_1(A,C,B) -> r4_tsep_1(A,k1_tsep_1(A,C,D),k1_tsep_1(A,B,E)) & r4_tsep_1(A,k1_tsep_1(A,D,C),k1_tsep_1(A,E,B))))))))))))) # label(t90_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11177 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_tsep_1(A,B,C) & r1_xboole_0(B,C) <-> r1_connsp_1(A,B,C)))))))) # label(t51_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11178 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> ((exists D (-v3_struct_0(D) & v1_tsep_1(D,A) & (exists E (v1_tsep_1(E,A) & m1_pre_topc(E,A) & m1_pre_topc(B,D) & (r1_tsep_1(A,k2_tsep_1(A,D,E),k1_tsep_1(A,B,C)) | r1_tsep_1(A,D,E)) & m1_pre_topc(C,E) & -v3_struct_0(E))) & m1_pre_topc(D,A))) <-> r3_tsep_1(A,B,C)))))))) # label(t83_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11179 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,B) -> m1_pre_topc(C,A))))))) # label(t7_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11180 (all A all B all C (m1_pre_topc(B,A) & m1_pre_topc(C,A) & l1_pre_topc(A) -> (r4_tsep_1(A,B,C) -> r4_tsep_1(A,C,B)))) # label(symmetry_r4_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11181 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (v1_borsuk_1(k1_tsep_1(A,B,C),A) & r3_tsep_1(A,B,C) & m1_pre_topc(k1_tsep_1(A,B,C),A) -> m1_pre_topc(B,A) & v1_borsuk_1(B,A)))))))) # label(t72_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11182 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(k4_subset_1(u1_struct_0(A),B,C) = u1_struct_0(A) & r2_tsep_1(A,B,C) & -r1_tarski(B,C) & -r1_tarski(C,B) & (all D (-v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (-v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(D,A) & r1_tarski(D,B) & r1_tarski(E,C) & -((all F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(F) -> -(r1_tarski(F,k5_subset_1(u1_struct_0(A),B,C)) & v4_pre_topc(F,A) & k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),D,E),F) = k4_subset_1(u1_struct_0(A),B,C)))) & k4_subset_1(u1_struct_0(A),D,E) != k4_subset_1(u1_struct_0(A),B,C)) & v3_pre_topc(E,A))))))))))))) # label(t66_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11183 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(C,A) & v4_pre_topc(B,A) -> (r1_xboole_0(B,C) <-> r1_connsp_1(A,B,C))))))))) # label(t38_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11184 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (v1_tsep_1(k1_tsep_1(A,B,C),A) & r3_tsep_1(A,B,C) & m1_pre_topc(k1_tsep_1(A,B,C),A) -> v1_tsep_1(B,A) & m1_pre_topc(B,A)))))))) # label(t75_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11185 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (r1_tsep_1(A,B,C) & k1_tsep_1(A,B,C) = A -> (v1_tsep_1(B,A) & v1_tsep_1(C,A) & m1_pre_topc(C,A) & m1_pre_topc(B,A) <-> r4_tsep_1(A,B,C))))))))) # label(t98_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11186 (all A all B all C (l1_pre_topc(A) & m1_pre_topc(C,A) & m1_pre_topc(B,A) -> (r3_tsep_1(A,B,C) -> r3_tsep_1(A,C,B)))) # label(symmetry_r3_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11187 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (all D (m1_pre_topc(D,A) & -v3_struct_0(D) -> (r4_tsep_1(A,B,D) & r4_tsep_1(A,C,D) -> r4_tsep_1(A,k1_tsep_1(A,B,C),D)) & (r4_tsep_1(A,D,C) & r4_tsep_1(A,D,B) -> r4_tsep_1(A,D,k1_tsep_1(A,B,C))))))))))) # label(t92_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11188 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_connsp_1(A,B,C) <-> (exists D ((exists E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & r1_xboole_0(D,C) & v4_pre_topc(E,A) & v4_pre_topc(D,A) & r1_xboole_0(E,B) & r1_tarski(C,E) & r1_tarski(B,D))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))))))))))) # label(t46_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11189 $T # label(t37_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11190 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(A) = k4_subset_1(u1_struct_0(A),B,C) -> ((exists D ((exists E ((exists F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) & k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),D,E),F) = k4_subset_1(u1_struct_0(A),B,C) & r1_tarski(E,C) & v3_pre_topc(E,A) & v4_pre_topc(F,A) & v3_pre_topc(D,A) & r1_tarski(F,k5_subset_1(u1_struct_0(A),B,C)) & r1_tarski(D,B))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))))) <-> r2_tsep_1(A,B,C))))))))) # label(t65_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11191 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (r3_tsep_1(A,B,C) <-> (exists D (-v3_struct_0(D) & m1_pre_topc(D,A) & (exists E (v1_borsuk_1(E,A) & (r1_tsep_1(A,k2_tsep_1(A,D,E),k1_tsep_1(A,B,C)) | r1_tsep_1(A,D,E)) & m1_pre_topc(C,E) & m1_pre_topc(B,D) & m1_pre_topc(E,A) & -v3_struct_0(E))) & v1_borsuk_1(D,A)))))))))) # label(t81_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11192 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(B) = C -> (m1_pre_topc(B,A) & v1_borsuk_1(B,A) <-> v4_pre_topc(C,A))))))))) # label(t11_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11193 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & v1_tsep_1(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (r1_tarski(u1_struct_0(B),u1_struct_0(C)) -> m1_pre_topc(B,C) & v1_tsep_1(B,C)))))))) # label(t19_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11194 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (-r1_tsep_1(A,B,C) -> m1_pre_topc(k2_tsep_1(A,B,C),k1_tsep_1(A,B,C))))))))) # label(t34_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11195 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) -> (m1_pre_topc(B,C) & m1_pre_topc(C,B) -> g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))))))))) # label(t6_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11196 (all A all B all C (l1_pre_topc(A) & m1_pre_topc(B,A) & m1_pre_topc(C,A) & -v3_struct_0(C) & -v3_struct_0(B) & -v3_struct_0(A) -> k1_tsep_1(A,C,B) = k1_tsep_1(A,B,C))) # label(commutativity_k1_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11197 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> -((all C (v1_pre_topc(C) & m1_pre_topc(C,A) & v1_borsuk_1(C,A) & -v3_struct_0(C) -> u1_struct_0(C) != B)) & v4_pre_topc(B,A)))))) # label(t15_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11198 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & v1_tsep_1(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & v1_tsep_1(C,A) & -v3_struct_0(C) -> m1_pre_topc(k1_tsep_1(A,B,C),A) & v1_tsep_1(k1_tsep_1(A,B,C),A))))))) # label(t25_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11199 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> (r2_tsep_1(A,B,C) -> r2_tsep_1(A,C,B)))) # label(symmetry_r2_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11200 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) -> (r1_xboole_0(u1_struct_0(B),u1_struct_0(C)) <-> r1_tsep_1(A,B,C)))))))) # label(d3_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11201 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & v1_borsuk_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (D = C -> (v4_pre_topc(C,A) <-> v4_pre_topc(D,B))))))))))) # label(t12_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11202 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (v1_borsuk_1(B,A) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & v1_borsuk_1(C,A) -> r4_tsep_1(A,B,C))))))) # label(t87_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11203 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (r3_tsep_1(A,B,C) -> r1_tsep_1(A,B,C)))))))) # label(t68_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11204 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_xboole_0(B,C) & v3_pre_topc(B,A) -> r1_xboole_0(B,k6_pre_topc(A,C))))))))) # label(t40_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11205 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & v1_tsep_1(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) & v1_tsep_1(C,A) -> (r1_tsep_1(A,B,C) <-> r3_tsep_1(A,B,C)))))))) # label(t73_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11206 (all A all B all C (l1_pre_topc(A) & -v3_struct_0(B) & m1_pre_topc(C,A) & -v3_struct_0(C) & m1_pre_topc(B,A) & -v3_struct_0(A) -> v1_pre_topc(k2_tsep_1(A,B,C)) & m1_pre_topc(k2_tsep_1(A,B,C),A) & -v3_struct_0(k2_tsep_1(A,B,C)))) # label(dt_k2_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11207 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(k4_subset_1(u1_struct_0(A),B,C),A) & r1_connsp_1(A,B,C) -> v4_pre_topc(B,A) & v4_pre_topc(C,A)))))))) # label(t39_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11208 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & v1_tsep_1(B,A) -> (all C (m1_pre_topc(C,A) & v1_tsep_1(C,A) -> r4_tsep_1(A,B,C))))))) # label(t88_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11209 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,C) -> r2_tsep_1(A,B,C)))))))) # label(t52_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11210 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r1_connsp_1(A,B,C) -> r1_connsp_1(A,k5_subset_1(u1_struct_0(A),B,D),k5_subset_1(u1_struct_0(A),C,D))))))))))) # label(t43_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11211 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(k4_subset_1(u1_struct_0(A),B,C),A) & r1_connsp_1(A,B,C) -> v3_pre_topc(B,A) & v3_pre_topc(C,A)))))))) # label(t42_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11212 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) -> (m1_pre_topc(B,C) <-> r1_tarski(u1_struct_0(B),u1_struct_0(C))))))))) # label(t4_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11213 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (r4_tsep_1(A,B,C) & r1_tsep_1(A,B,C) <-> r3_tsep_1(A,B,C)))))))) # label(t85_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11214 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> ((exists D ((exists E (m1_pre_topc(B,D) & m1_pre_topc(C,E) & (r1_tsep_1(A,k2_tsep_1(A,D,E),k1_tsep_1(A,B,C)) | r1_tsep_1(A,D,E)) & r4_tsep_1(A,D,E) & m1_pre_topc(E,A) & -v3_struct_0(E))) & m1_pre_topc(D,A) & -v3_struct_0(D))) <-> r3_tsep_1(A,B,C)))))))) # label(t99_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11215 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((exists D ((exists E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & (exists F (r1_tarski(k5_subset_1(u1_struct_0(A),D,k4_subset_1(u1_struct_0(A),B,C)),B) & r1_tarski(k5_subset_1(u1_struct_0(A),E,k4_subset_1(u1_struct_0(A),B,C)),C) & r1_tarski(k5_subset_1(u1_struct_0(A),F,k4_subset_1(u1_struct_0(A),B,C)),k5_subset_1(u1_struct_0(A),B,C)) & u1_struct_0(A) = k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),D,E),F) & v3_pre_topc(F,A) & v4_pre_topc(E,A) & v4_pre_topc(D,A) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))))))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))))) <-> r2_tsep_1(A,B,C)))))))) # label(t59_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11216 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (-r1_tsep_1(A,B,C) -> (all D (v1_pre_topc(D) & m1_pre_topc(D,A) & -v3_struct_0(D) -> (k2_tsep_1(A,B,C) = D <-> u1_struct_0(D) = k3_xboole_0(u1_struct_0(B),u1_struct_0(C)))))))))))) # label(d5_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11217 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -((all D (-v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (-v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(v4_pre_topc(D,A) & r1_tarski(k5_subset_1(u1_struct_0(A),D,k4_subset_1(u1_struct_0(A),B,C)),B) & -(-r1_tarski(k4_subset_1(u1_struct_0(A),B,C),k4_subset_1(u1_struct_0(A),D,E)) & (all F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(F) -> -(r1_tarski(k5_subset_1(u1_struct_0(A),F,k4_subset_1(u1_struct_0(A),B,C)),k5_subset_1(u1_struct_0(A),B,C)) & k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),D,E),F) = u1_struct_0(A) & v3_pre_topc(F,A))))) & r1_tarski(k5_subset_1(u1_struct_0(A),E,k4_subset_1(u1_struct_0(A),B,C)),C) & v4_pre_topc(E,A)))))) & -r1_tarski(C,B) & -r1_tarski(B,C) & r2_tsep_1(A,B,C)))))))) # label(t60_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11218 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) -> (u1_struct_0(C) = u1_struct_0(B) -> g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(C),u1_pre_topc(C))))))))) # label(t5_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11219 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (v1_borsuk_1(B,A) & m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & v1_borsuk_1(C,A) & m1_pre_topc(C,A) -> (r3_tsep_1(A,B,C) <-> r1_tsep_1(A,B,C)))))))) # label(t70_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11220 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (all D (-v3_struct_0(D) & m1_pre_topc(D,A) & v1_pre_topc(D) -> (k2_xboole_0(u1_struct_0(B),u1_struct_0(C)) = u1_struct_0(D) <-> k1_tsep_1(A,B,C) = D))))))))) # label(d2_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11221 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & v1_borsuk_1(B,A) -> (all C (m1_pre_topc(C,B) & v1_borsuk_1(C,B) -> v1_borsuk_1(C,A) & m1_pre_topc(C,A))))))) # label(t13_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11222 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (-v3_struct_0(B) & v2_pre_topc(B) & v1_tsep_1(B,A) & v1_pre_topc(B) & m1_pre_topc(B,A))))) # label(rc2_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11223 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (-r1_tsep_1(A,B,C) -> (-(-m1_pre_topc(B,C) & (all D (-v3_struct_0(D) & v1_tsep_1(D,A) & m1_pre_topc(D,A) -> (all E (-v3_struct_0(E) & v1_tsep_1(E,A) & m1_pre_topc(E,A) -> -(m1_pre_topc(k2_tsep_1(A,D,k1_tsep_1(A,B,C)),B) & -((all F (-v3_struct_0(F) & m1_pre_topc(F,A) & v1_borsuk_1(F,A) -> -(m1_pre_topc(k2_tsep_1(A,F,k1_tsep_1(A,B,C)),k2_tsep_1(A,B,C)) & k1_tsep_1(A,k1_tsep_1(A,D,E),F) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))))) & -m1_pre_topc(k1_tsep_1(A,B,C),k1_tsep_1(A,D,E))) & m1_pre_topc(k2_tsep_1(A,E,k1_tsep_1(A,B,C)),C)))))) & -m1_pre_topc(C,B)) <-> r4_tsep_1(A,B,C))))))))) # label(t96_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11224 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (all D (m1_pre_topc(D,A) & -v3_struct_0(D) -> (r3_tsep_1(A,C,D) -> r1_tsep_1(A,C,B) | r3_tsep_1(A,k2_tsep_1(A,C,B),k2_tsep_1(A,D,B)) & r3_tsep_1(A,k2_tsep_1(A,B,C),k2_tsep_1(A,B,D)) | r1_tsep_1(A,D,B)))))))))) # label(t76_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11225 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((exists D ((exists E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & (exists F (r1_tarski(k5_subset_1(u1_struct_0(A),F,k4_subset_1(u1_struct_0(A),B,C)),k5_subset_1(u1_struct_0(A),B,C)) & v3_pre_topc(D,A) & v3_pre_topc(E,A) & v4_pre_topc(F,A) & k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),D,E),F) = u1_struct_0(A) & r1_tarski(k5_subset_1(u1_struct_0(A),E,k4_subset_1(u1_struct_0(A),B,C)),C) & r1_tarski(k5_subset_1(u1_struct_0(A),D,k4_subset_1(u1_struct_0(A),B,C)),B) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))))))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))))) <-> r2_tsep_1(A,B,C)))))))) # label(t63_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11226 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_tsep_1(A,B,D) & r2_tsep_1(A,C,D) -> r2_tsep_1(A,k5_subset_1(u1_struct_0(A),B,C),D)))))))))) # label(t57_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11227 (all A (l1_pre_topc(A) -> m1_pre_topc(A,A))) # label(t2_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11228 $T # label(t26_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11229 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (-r1_tsep_1(A,B,C) -> (r4_tsep_1(A,B,C) <-> -(-m1_pre_topc(B,C) & (all D (m1_pre_topc(D,A) & v1_borsuk_1(D,A) & -v3_struct_0(D) -> (all E (-v3_struct_0(E) & m1_pre_topc(E,A) & v1_borsuk_1(E,A) -> -(m1_pre_topc(k2_tsep_1(A,D,k1_tsep_1(A,B,C)),B) & -(-m1_pre_topc(k1_tsep_1(A,B,C),k1_tsep_1(A,D,E)) & (all F (-v3_struct_0(F) & v1_tsep_1(F,A) & m1_pre_topc(F,A) -> -(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = k1_tsep_1(A,k1_tsep_1(A,D,E),F) & m1_pre_topc(k2_tsep_1(A,F,k1_tsep_1(A,B,C)),k2_tsep_1(A,B,C)))))) & m1_pre_topc(k2_tsep_1(A,E,k1_tsep_1(A,B,C)),C)))))) & -m1_pre_topc(C,B)))))))))) # label(t93_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11230 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> m1_pre_topc(B,k1_tsep_1(A,B,C)))))))) # label(t22_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11231 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (r3_tsep_1(A,B,C) & k1_tsep_1(A,B,C) = A -> v1_tsep_1(B,A) & m1_pre_topc(B,A)))))))) # label(t74_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11232 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> -((all C (-v3_struct_0(C) & v1_pre_topc(C) & m1_pre_topc(C,A) & v1_tsep_1(C,A) -> B != u1_struct_0(C))) & v3_pre_topc(B,A)))))) # label(t20_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11233 $T # label(d6_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11234 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) -> (r4_tsep_1(A,B,C) <-> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (E = u1_struct_0(C) & u1_struct_0(B) = D -> r2_tsep_1(A,D,E))))))))))))) # label(d9_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11235 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (k1_tsep_1(A,B,C) = A -> (r4_tsep_1(A,B,C) <-> -((all D (-v3_struct_0(D) & m1_pre_topc(D,A) & v1_tsep_1(D,A) -> (all E (v1_tsep_1(E,A) & m1_pre_topc(E,A) & -v3_struct_0(E) -> -(m1_pre_topc(D,B) & m1_pre_topc(E,C) & -((all F (-v3_struct_0(F) & m1_pre_topc(F,A) & v1_borsuk_1(F,A) -> -(A = k1_tsep_1(A,k1_tsep_1(A,D,E),F) & m1_pre_topc(F,k2_tsep_1(A,B,C))))) & k1_tsep_1(A,D,E) != A)))))) & -m1_pre_topc(C,B) & -m1_pre_topc(B,C))) | r1_tsep_1(A,B,C)))))))) # label(t97_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11236 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (r3_tsep_1(A,B,C) & A = k1_tsep_1(A,B,C) -> v1_borsuk_1(B,A) & m1_pre_topc(B,A)))))))) # label(t71_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11237 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (r2_tsep_1(A,C,B) & r1_tarski(E,C) & r1_tarski(D,B) -> r2_tsep_1(A,k4_subset_1(u1_struct_0(A),C,D),k4_subset_1(u1_struct_0(A),B,E))))))))))))) # label(t56_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11238 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (r3_tsep_1(A,B,C) <-> (exists D (-v3_struct_0(D) & v1_borsuk_1(D,A) & m1_pre_topc(D,A) & (exists E (v1_borsuk_1(E,A) & m1_pre_topc(C,E) & r1_tsep_1(A,D,C) & r1_tsep_1(A,E,B) & m1_pre_topc(B,D) & m1_pre_topc(E,A) & -v3_struct_0(E)))))))))))) # label(t80_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11239 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (all D (-v3_struct_0(D) & m1_pre_topc(D,A) -> (-r1_tsep_1(A,B,C) -> k2_tsep_1(A,C,B) = k2_tsep_1(A,B,C)) & (-r1_tsep_1(A,B,k2_tsep_1(A,C,D)) & -r1_tsep_1(A,C,D) | -r1_tsep_1(A,k2_tsep_1(A,B,C),D) & -r1_tsep_1(A,B,C) -> k2_tsep_1(A,k2_tsep_1(A,B,C),D) = k2_tsep_1(A,B,k2_tsep_1(A,C,D))))))))))) # label(t29_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11240 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_connsp_1(A,k6_subset_1(u1_struct_0(A),B,C),k6_subset_1(u1_struct_0(A),C,B)) <-> r2_tsep_1(A,B,C)))))))) # label(d7_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11241 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(-r1_tarski(B,C) & (all D (-v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (-v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(D,A) & r1_tarski(k5_subset_1(u1_struct_0(A),D,k4_subset_1(u1_struct_0(A),B,C)),B) & r1_tarski(k5_subset_1(u1_struct_0(A),E,k4_subset_1(u1_struct_0(A),B,C)),C) & -(-r1_tarski(k4_subset_1(u1_struct_0(A),B,C),k4_subset_1(u1_struct_0(A),D,E)) & (all F (-v1_xboole_0(F) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) -> -(v4_pre_topc(F,A) & r1_tarski(k5_subset_1(u1_struct_0(A),F,k4_subset_1(u1_struct_0(A),B,C)),k5_subset_1(u1_struct_0(A),B,C)) & k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),D,E),F) = u1_struct_0(A))))) & v3_pre_topc(E,A)))))) & -r1_tarski(C,B) & r2_tsep_1(A,B,C)))))))) # label(t64_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11242 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & (exists E (r1_tarski(B,D) & r1_tarski(C,E) & r1_xboole_0(E,B) & v3_pre_topc(E,A) & v3_pre_topc(D,A) & r1_xboole_0(D,C) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))))))) <-> r1_connsp_1(A,B,C)))))))) # label(t48_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11243 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (all D (m1_pre_topc(D,A) -> (all E (m1_pre_topc(E,A) -> (m1_pre_topc(D,B) & r3_tsep_1(A,B,C) & m1_pre_topc(E,C) -> r3_tsep_1(A,D,E)))))))))))) # label(t77_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11244 (all A all B all C (-v3_struct_0(A) & l1_pre_topc(A) & -v3_struct_0(B) & m1_pre_topc(C,A) & -v3_struct_0(C) & m1_pre_topc(B,A) -> -v3_struct_0(k1_tsep_1(A,B,C)) & m1_pre_topc(k1_tsep_1(A,B,C),A) & v1_pre_topc(k1_tsep_1(A,B,C)))) # label(dt_k1_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11245 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (C = u1_struct_0(B) -> v3_pre_topc(C,A)))) <-> v1_tsep_1(B,A)))))) # label(d1_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11246 $T # label(t84_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11247 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & (exists E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & r1_tarski(C,E) & r1_xboole_0(k5_subset_1(u1_struct_0(A),D,E),k4_subset_1(u1_struct_0(A),B,C)) & v3_pre_topc(E,A) & v3_pre_topc(D,A) & r1_tarski(B,D))))) <-> r1_connsp_1(A,B,C)))))))) # label(t49_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11248 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & v1_borsuk_1(B,A) & -v3_struct_0(B) -> (all C (v1_borsuk_1(C,A) & m1_pre_topc(C,A) & -v3_struct_0(C) -> (-r1_tsep_1(A,B,C) -> v1_borsuk_1(k2_tsep_1(A,B,C),A) & m1_pre_topc(k2_tsep_1(A,B,C),A)))))))) # label(t32_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11249 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (m1_pre_topc(B,C) -> r4_tsep_1(A,B,C)))))))) # label(t86_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11250 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & v1_tsep_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (D = C -> (v3_pre_topc(C,A) <-> v3_pre_topc(D,B))))))))))) # label(t17_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11251 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (all D (-v3_struct_0(D) & m1_pre_topc(D,A) -> (-r1_tsep_1(A,C,D) -> (r4_tsep_1(A,C,B) & r4_tsep_1(A,D,B) -> r4_tsep_1(A,k2_tsep_1(A,C,D),B)) & (r4_tsep_1(A,B,D) & r4_tsep_1(A,B,C) -> r4_tsep_1(A,B,k2_tsep_1(A,C,D)))))))))))) # label(t91_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.72 11252 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(u1_struct_0(A) = k4_subset_1(u1_struct_0(A),B,C) & -r1_tarski(B,C) & -r1_tarski(C,B) & (all D (-v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (-v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(v4_pre_topc(D,A) & r1_tarski(D,B) & -((all F (-v1_xboole_0(F) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(F,A) & r1_tarski(F,k5_subset_1(u1_struct_0(A),B,C)) & k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),D,E),F) = k4_subset_1(u1_struct_0(A),B,C)))) & k4_subset_1(u1_struct_0(A),B,C) != k4_subset_1(u1_struct_0(A),D,E)) & r1_tarski(E,C) & v4_pre_topc(E,A)))))) & r2_tsep_1(A,B,C)))))))) # label(t62_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11253 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (k1_tsep_1(A,B,C) = A -> r1_tsep_1(A,B,C) | (-((all D (-v3_struct_0(D) & m1_pre_topc(D,A) & v1_borsuk_1(D,A) -> (all E (-v3_struct_0(E) & v1_borsuk_1(E,A) & m1_pre_topc(E,A) -> -(m1_pre_topc(E,C) & -((all F (-v3_struct_0(F) & v1_tsep_1(F,A) & m1_pre_topc(F,A) -> -(A = k1_tsep_1(A,k1_tsep_1(A,D,E),F) & m1_pre_topc(F,k2_tsep_1(A,B,C))))) & A != k1_tsep_1(A,D,E)) & m1_pre_topc(D,B)))))) & -m1_pre_topc(C,B) & -m1_pre_topc(B,C)) <-> r4_tsep_1(A,B,C))))))))) # label(t94_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11254 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_connsp_1(A,B,C) <-> (exists D ((exists E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & r1_tarski(B,D) & r1_xboole_0(k5_subset_1(u1_struct_0(A),D,E),k4_subset_1(u1_struct_0(A),B,C)) & r1_tarski(C,E) & r2_tsep_1(A,D,E))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))))))))))) # label(t67_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11255 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (exists C (-v3_struct_0(C) & v1_pre_topc(C) & m1_pre_topc(C,A) & B = u1_struct_0(C))))))) # label(t10_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11256 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (all D (m1_pre_topc(D,A) & -v3_struct_0(D) -> k1_tsep_1(A,B,k1_tsep_1(A,C,D)) = k1_tsep_1(A,k1_tsep_1(A,B,C),D))))))))) # label(t21_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11257 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v1_borsuk_1(B,A) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) & v1_borsuk_1(C,A) -> m1_pre_topc(k1_tsep_1(A,B,C),A) & v1_borsuk_1(k1_tsep_1(A,B,C),A))))))) # label(t24_tsep_1) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11258 (all A (v4_lattice3(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k15_lattice3(A,k1_struct_0(A,B)) & k16_lattice3(A,k1_struct_0(A,B)) = B)))) # label(t43_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11259 (all A (-v3_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) -> (v6_lattice3(A) <-> (all B all C (m1_subset_1(C,u1_struct_0(A)) -> r3_lattices(A,k16_lattice3(A,a_3_5_lattice3(A,B,C)),k3_lattices(A,C,k16_lattice3(A,B)))))))) # label(t36_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11260 (exists A (v3_orders_2(A) & v1_lattice3(A) & v3_lattice3(A) & v2_lattice3(A) & v4_orders_2(A) & v2_orders_2(A) & v1_orders_2(A) & -v3_struct_0(A) & l1_orders_2(A))) # label(rc2_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11261 (all A v6_lattice3(k1_lattice3(A))) # label(t27_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11262 (all A all B (v10_lattices(B) & v17_lattices(B) & l3_lattices(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (r4_lattice3(B,k7_lattices(B,C),a_2_0_lattice3(A,B)) <-> r3_lattice3(B,C,A)))))) # label(t24_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11263 (all A all B (l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(k3_lattice3(B))) -> (r1_lattice3(k3_lattice3(B),A,C) <-> r3_lattice3(B,k5_lattice3(B,C),A)))))) # label(t29_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11264 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(k3_lattice3(A))) -> k5_lattice3(A,B) = B)))) # label(d4_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11265 (all A (v2_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & v1_lattice3(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k12_lattice3(A,B,k13_lattice3(A,B,C)) = B)))))) # label(t18_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11266 (all A (l1_orders_2(A) -> g1_orders_2(u1_struct_0(A),k6_relset_1(u1_struct_0(A),u1_struct_0(A),u1_orders_2(A))) = k7_lattice3(A))) # label(d5_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11267 (all A all B all C (l3_lattices(B) & -v3_struct_0(B) -> ((exists D (m1_subset_1(D,u1_struct_0(B)) & r3_lattice3(B,D,C) & A = D)) <-> r2_hidden(A,a_2_1_lattice3(B,C))))) # label(fraenkel_a_2_1_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11268 (all A (l1_orders_2(A) -> l3_lattices(k14_lattice3(A)) & v10_lattices(k14_lattice3(A)) & v3_lattices(k14_lattice3(A)) & -v3_struct_0(k14_lattice3(A)))) # label(dt_k14_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11269 (all A all B all C (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) & v4_lattice3(B) -> ((exists D (D = A & (exists E (r2_hidden(E,C) & r3_lattices(B,E,D) & m1_subset_1(E,u1_struct_0(B)))) & m1_subset_1(D,u1_struct_0(B)))) <-> r2_hidden(A,a_2_6_lattice3(B,C))))) # label(fraenkel_a_2_6_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11270 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r3_orders_2(k3_lattice3(A),k4_lattice3(A,B),k4_lattice3(A,C)) <-> r3_lattices(A,B,C)))))))) # label(t7_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11271 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> v3_orders_2(k3_lattice3(A)) & v4_orders_2(k3_lattice3(A)) & v2_orders_2(k3_lattice3(A)) & v1_orders_2(k3_lattice3(A)) & -v3_struct_0(k3_lattice3(A)))) # label(fc4_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11272 (all A all B (-v3_struct_0(B) & v4_lattice3(B) & v6_lattice3(B) & l3_lattices(B) & v10_lattices(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k3_lattices(B,k16_lattice3(B,A),C) = k16_lattice3(B,a_3_10_lattice3(A,B,C)) & k16_lattice3(B,a_3_9_lattice3(A,B,C)) = k3_lattices(B,C,k16_lattice3(B,A)))))) # label(t55_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11273 (all A (l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (r4_lattice3(A,B,C) <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,C) -> r1_lattices(A,D,B)))))))))) # label(d17_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11274 (all A (l1_orders_2(A) & -v3_struct_0(A) -> v1_orders_2(k7_lattice3(A)) & -v3_struct_0(k7_lattice3(A)))) # label(fc6_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11275 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> k7_lattice3(k3_lattice3(A)) = k3_lattice3(k1_lattice2(A)) & k6_lattice3(u1_struct_0(A),k2_lattice3(A)) = k2_lattice3(k1_lattice2(A)))) # label(t20_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11276 (all A all B all C all D (-v3_struct_0(B) & v10_lattices(B) & m1_subset_1(C,u1_struct_0(B)) & l3_lattices(B) & v4_lattice3(B) -> ((exists E (m1_subset_1(E,u1_struct_0(B)) & r2_hidden(E,D) & A = k4_lattices(B,C,E))) <-> r2_hidden(A,a_3_2_lattice3(B,C,D))))) # label(fraenkel_a_3_2_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11277 (all A (-v3_struct_0(A) & l3_lattices(A) & v4_lattice3(A) & v10_lattices(A) -> (all B k16_lattice3(A,a_2_2_lattice3(A,B)) = k15_lattice3(A,B)))) # label(t37_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11278 (all A all B (m1_subset_1(B,u1_struct_0(k7_lattice3(A))) & l1_orders_2(A) -> m1_subset_1(k9_lattice3(A,B),u1_struct_0(A)))) # label(dt_k9_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11279 (all A (v13_lattices(k1_lattice3(A)) & k1_xboole_0 = k5_lattices(k1_lattice3(A)))) # label(t3_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11280 (all A (l1_orders_2(A) -> (v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> ((exists D (r1_orders_2(A,B,D) & r1_orders_2(A,C,D) & (all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_orders_2(A,B,E) & r1_orders_2(A,C,E) -> r1_orders_2(A,D,E)))) & m1_subset_1(D,u1_struct_0(A)))) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k10_lattice3(A,B,C) = D <-> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_orders_2(A,B,E) & r1_orders_2(A,C,E) -> r1_orders_2(A,D,E)))) & r1_orders_2(A,C,D) & r1_orders_2(A,B,D)))))))))))) # label(d13_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11281 (all A (l1_orders_2(A) -> (v2_lattice3(A) -> -v3_struct_0(A)))) # label(cc2_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11282 (all A all B all C all D (m1_subset_1(D,u1_struct_0(B)) & l3_lattices(B) & -v3_struct_0(B) -> ((exists E (m1_subset_1(E,u1_struct_0(B)) & k2_lattices(B,D,E) = A & r2_hidden(E,C))) <-> r2_hidden(A,a_3_0_lattice3(B,C,D))))) # label(fraenkel_a_3_0_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11283 (all A (v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k16_lattice3(A,k2_struct_0(A,B,C)) = k4_lattices(A,B,C) & k3_lattices(A,B,C) = k15_lattice3(A,k2_struct_0(A,B,C)))))))) # label(t44_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11284 (all A all B all C (v17_lattices(C) & l3_lattices(C) & v10_lattices(C) & -v3_struct_0(C) -> ((exists D (m1_subset_1(D,u1_struct_0(C)) & k7_lattices(C,D) = A & r2_hidden(D,B))) <-> r2_hidden(A,a_2_0_lattice3(B,C))))) # label(fraenkel_a_2_0_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11285 (exists A (p1_s1_lattice3(A) & m1_subset_1(A,f2_s1_lattice3))) -> a_0_0_lattice3 = k1_tarski(f1_s1_lattice3) # label(s1_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11286 (all A (v3_lattices(k1_lattice3(A)) & l3_lattices(k1_lattice3(A)))) # label(dt_k1_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11287 (all A all B all C (v10_lattices(B) & l3_lattices(B) & m1_subset_1(C,u1_struct_0(B)) & v4_lattice3(B) & -v3_struct_0(B) -> ((exists D (r3_lattices(B,C,D) & D = A & m1_subset_1(D,u1_struct_0(B)))) <-> r2_hidden(A,a_2_4_lattice3(B,C))))) # label(fraenkel_a_2_4_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11288 (all A (v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k11_lattice3(A,B,C) = k11_lattice3(A,C,B))))))) # label(t15_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11289 (all A all B (m1_subset_1(B,u1_struct_0(k1_lattice3(A))) -> (all C (m1_subset_1(C,u1_struct_0(k1_lattice3(A))) -> k1_lattices(k1_lattice3(A),B,C) = k2_xboole_0(B,C) & k3_xboole_0(B,C) = k2_lattices(k1_lattice3(A),B,C))))) # label(t1_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11290 (all A all B all C (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) & v4_lattice3(B) -> (r2_hidden(A,a_2_2_lattice3(B,C)) <-> (exists D (m1_subset_1(D,u1_struct_0(B)) & A = D & r4_lattice3(B,D,C)))))) # label(fraenkel_a_2_2_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11291 (all A (r2_hidden(A,a_0_1_lattice3) <-> (exists B (p1_s2_lattice3(B) & A = f3_s2_lattice3(B) & m1_subset_1(B,f1_s2_lattice3))))) # label(fraenkel_a_0_1_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11292 (all A all B (l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(k3_lattice3(B))) -> (r4_lattice3(B,k5_lattice3(B,C),A) <-> r2_lattice3(k3_lattice3(B),A,C)))))) # label(t31_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11293 (all A all B all C (m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_orders_2(A) -> m1_subset_1(k10_lattice3(A,B,C),u1_struct_0(A)))) # label(dt_k10_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.42/125.73 11294 (all A (-v3_struct_0(A) & l3_lattices(A) & v4_lattice3(A) & v10_lattices(A) -> (v10_lattices(A) & l3_lattices(A) & v3_filter_0(A) & -v3_struct_0(A) -> v5_lattice3(A)))) # label(t53_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11295 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> k9_filter_1(A) = k2_lattice3(A))) # label(redefinition_k2_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11296 (all A all B all C all D (l3_lattices(B) & m1_subset_1(C,u1_struct_0(B)) & v4_lattice3(B) & v10_lattices(B) & -v3_struct_0(B) -> ((exists E (m1_subset_1(E,u1_struct_0(B)) & r2_hidden(E,D) & k3_lattices(B,C,E) = A)) <-> r2_hidden(A,a_3_4_lattice3(B,C,D))))) # label(fraenkel_a_3_4_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11297 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k8_lattice3(A,B) = B)))) # label(d6_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11298 (all A (l1_orders_2(A) -> (v3_lattice3(A) <-> (all B exists C (m1_subset_1(C,u1_struct_0(A)) & r2_lattice3(A,B,C) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_lattice3(A,B,D) -> r1_orders_2(A,C,D))))))))) # label(d12_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11299 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> g1_orders_2(u1_struct_0(A),k2_lattice3(A)) = k3_lattice3(A))) # label(d2_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11300 (all A (-v3_struct_0(A) & v4_lattice3(A) & l3_lattices(A) & v10_lattices(A) -> (all B all C ((all D (m1_subset_1(D,u1_struct_0(A)) -> -(r2_hidden(D,B) & (all E (m1_subset_1(E,u1_struct_0(A)) -> -(r3_lattices(A,D,E) & r2_hidden(E,C))))))) -> r3_lattices(A,k15_lattice3(A,B),k15_lattice3(A,C)))))) # label(t48_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11301 (all A all B all C (v4_orders_2(A) & v2_lattice3(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_orders_2(A) -> k12_lattice3(A,B,C) = k11_lattice3(A,B,C))) # label(redefinition_k12_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11302 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(k7_lattice3(A))) -> k9_lattice3(A,B) = B)))) # label(d7_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11303 (all A all B (m1_subset_1(B,u1_struct_0(k1_lattice3(A))) -> (all C (m1_subset_1(C,u1_struct_0(k1_lattice3(A))) -> (r1_lattices(k1_lattice3(A),B,C) <-> r1_tarski(B,C)))))) # label(t2_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11304 (all A all B (-v3_struct_0(B) & v10_lattices(B) & v17_lattices(B) & l3_lattices(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (r4_lattice3(B,C,A) <-> r3_lattice3(B,k7_lattices(B,C),a_2_0_lattice3(A,B))))))) # label(t23_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11305 (all A all B all C all D (-v3_struct_0(C) & v6_lattice3(C) & l3_lattices(C) & m1_subset_1(D,u1_struct_0(C)) & v4_lattice3(C) & v10_lattices(C) -> (r2_hidden(A,a_3_10_lattice3(B,C,D)) <-> (exists E (m1_subset_1(E,u1_struct_0(C)) & A = k3_lattices(C,E,D) & r2_hidden(E,B)))))) # label(fraenkel_a_3_10_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11306 (all A (v10_lattices(A) & l3_lattices(A) & v4_lattice3(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C r3_lattices(A,k15_lattice3(A,a_3_2_lattice3(A,B,C)),k4_lattices(A,B,k15_lattice3(A,C)))))))) # label(t32_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11307 (all A all B all C all D (-v3_struct_0(B) & v4_lattice3(B) & m1_subset_1(D,u1_struct_0(B)) & l3_lattices(B) & v10_lattices(B) -> ((exists E (r2_hidden(E,C) & A = k3_lattices(B,D,E) & m1_subset_1(E,u1_struct_0(B)))) <-> r2_hidden(A,a_3_5_lattice3(B,C,D))))) # label(fraenkel_a_3_5_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11308 (exists A (l3_lattices(A) & v4_lattices(A) & v6_lattices(A) & v7_lattices(A) & v9_lattices(A) & v6_lattice3(A) & v5_lattice3(A) & v4_lattice3(A) & v10_lattices(A) & v8_lattices(A) & v5_lattices(A) & v3_lattices(A) & -v3_struct_0(A))) # label(rc3_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11309 (all A (l1_orders_2(A) & v2_lattice3(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (v3_orders_2(A) -> k11_lattice3(A,B,k11_lattice3(A,C,D)) = k11_lattice3(A,k11_lattice3(A,B,C),D)))))))))) # label(t16_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11310 (all A (-v3_struct_0(A) & l3_lattices(A) -> (v5_lattice3(A) <-> (all B all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> ((all F (m1_subset_1(F,u1_struct_0(A)) -> (r4_lattice3(A,F,B) -> r1_lattices(A,C,F)))) & (all F (m1_subset_1(F,u1_struct_0(A)) -> (r4_lattice3(A,F,a_3_0_lattice3(A,B,D)) -> r1_lattices(A,E,F)))) & r4_lattice3(A,E,a_3_0_lattice3(A,B,D)) & r4_lattice3(A,C,B) -> r1_lattices(A,k2_lattices(A,D,C),E))))))))))) # label(d19_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11311 (all A (-v3_struct_0(A) & v4_lattice3(A) & l3_lattices(A) & v10_lattices(A) -> -v3_struct_0(A) & v13_lattices(A) & k5_lattices(A) = k15_lattice3(A,k1_xboole_0) & l3_lattices(A) & v10_lattices(A))) # label(t50_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11312 (all A (l1_orders_2(A) -> (v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> ((exists D (r1_orders_2(A,D,B) & (all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_orders_2(A,E,B) & r1_orders_2(A,E,C) -> r1_orders_2(A,E,D)))) & r1_orders_2(A,D,C) & m1_subset_1(D,u1_struct_0(A)))) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> ((all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_orders_2(A,E,B) & r1_orders_2(A,E,C) -> r1_orders_2(A,E,D)))) & r1_orders_2(A,D,C) & r1_orders_2(A,D,B) <-> k11_lattice3(A,B,C) = D))))))))))) # label(d14_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11313 (all A (v4_lattices(k1_lattice3(A)) & v5_lattices(k1_lattice3(A)) & v6_lattices(k1_lattice3(A)) & v7_lattices(k1_lattice3(A)) & v9_lattices(k1_lattice3(A)) & v15_lattices(k1_lattice3(A)) & v17_lattices(k1_lattice3(A)) & v16_lattices(k1_lattice3(A)) & v14_lattices(k1_lattice3(A)) & v13_lattices(k1_lattice3(A)) & v12_lattices(k1_lattice3(A)) & v11_lattices(k1_lattice3(A)) & v10_lattices(k1_lattice3(A)) & v8_lattices(k1_lattice3(A)) & v3_lattices(k1_lattice3(A)) & -v3_struct_0(k1_lattice3(A)))) # label(fc3_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11314 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> v1_orders_2(k3_lattice3(A)) & v3_orders_2(k3_lattice3(A)) & l1_orders_2(k3_lattice3(A)) & v4_orders_2(k3_lattice3(A)) & v2_orders_2(k3_lattice3(A)))) # label(dt_k3_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11315 (all A (v14_lattices(k1_lattice3(A)) & k6_lattices(k1_lattice3(A)) = A)) # label(t4_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11316 (all A all B all C (m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_orders_2(A) -> m1_subset_1(k11_lattice3(A,B,C),u1_struct_0(A)))) # label(dt_k11_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11317 (all A all B (v1_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v4_relat_2(B) -> B = k6_lattice3(A,k6_lattice3(A,B)))) # label(involutiveness_k6_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11318 (all A (l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C ((all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,C) -> r1_lattices(A,B,D)))) <-> r3_lattice3(A,B,C))))))) # label(d16_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11319 (all A (-v3_struct_0(A) & v4_lattice3(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (r3_lattice3(A,B,C) -> r3_lattices(A,B,k16_lattice3(A,C)))))))) # label(t40_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11320 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> v2_lattice3(k3_lattice3(A)) & v1_lattice3(k3_lattice3(A)))) # label(t11_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11321 (all A all B (m1_subset_1(B,u1_struct_0(A)) & l1_orders_2(A) -> m1_subset_1(k8_lattice3(A,B),u1_struct_0(k7_lattice3(A))))) # label(dt_k8_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11322 (all A (l3_lattices(A) & -v3_struct_0(A) -> (all B k15_lattice3(A,a_2_1_lattice3(A,B)) = k16_lattice3(A,B)))) # label(d22_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11323 (all A (v3_lattices(k1_lattice3(A)) & -v3_struct_0(k1_lattice3(A)))) # label(fc1_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11324 (all A (l1_orders_2(A) -> k7_lattice3(k7_lattice3(A)) = g1_orders_2(u1_struct_0(A),u1_orders_2(A)))) # label(t8_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11325 (all A all B (l3_lattices(B) & v3_lattices(B) -> ((all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> k5_subset_1(A,C,D) = k1_binop_1(u1_lattices(B),C,D) & k4_subset_1(A,C,D) = k1_binop_1(u2_lattices(B),C,D))))) & u1_struct_0(B) = k1_zfmisc_1(A) <-> k1_lattice3(A) = B))) # label(d1_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11326 (all A (-v3_struct_0(A) & v4_lattice3(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (r4_lattice3(A,B,C) & r2_hidden(B,C) -> B = k15_lattice3(A,C))))))) # label(t41_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11327 (all A (v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (k16_lattice3(A,C) = B <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r3_lattice3(A,D,C) -> r3_lattices(A,D,B)))) & r3_lattice3(A,B,C))))))) # label(t34_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11328 (all A all B all C (-v3_struct_0(B) & l3_lattices(B) & v4_lattice3(B) & v10_lattices(B) -> ((exists D (m1_subset_1(D,u1_struct_0(B)) & (exists E (r2_hidden(E,C) & r3_lattices(B,D,E) & m1_subset_1(E,u1_struct_0(B)))) & A = D)) <-> r2_hidden(A,a_2_5_lattice3(B,C))))) # label(fraenkel_a_2_5_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11329 (all A all B (m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v4_relat_2(B) & v1_relat_2(B) -> v4_relat_2(k6_lattice3(A,B)) & v1_partfun1(k6_lattice3(A,B),A,A) & m2_relset_1(k6_lattice3(A,B),A,A) & v8_relat_2(k6_lattice3(A,B)) & v1_relat_2(k6_lattice3(A,B)))) # label(dt_k6_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11330 (all A (l1_orders_2(A) -> (v1_lattice3(A) -> -v3_struct_0(A)))) # label(cc1_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11331 (all A v5_lattice3(k1_lattice3(A))) # label(t26_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11332 (all A (l1_orders_2(A) -> (v2_lattice3(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (r1_orders_2(A,D,B) & (all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_orders_2(A,E,B) & r1_orders_2(A,E,C) -> r1_orders_2(A,E,D)))) & r1_orders_2(A,D,C) & m1_subset_1(D,u1_struct_0(A))))))))))) # label(d11_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11333 (all A (l3_lattices(A) & v4_lattice3(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v3_filter_0(A) -> k4_filter_0(A,B,C) = k15_lattice3(A,a_3_6_lattice3(A,B,C))))))))) # label(t52_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11334 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) -> (k3_lattice3(A) = k3_lattice3(B) -> g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B))))))) # label(t6_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11335 (all A (l1_orders_2(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (m1_subset_1(D,u1_struct_0(A)) & r1_orders_2(A,C,D) & (all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_orders_2(A,C,E) & r1_orders_2(A,B,E) -> r1_orders_2(A,D,E)))) & r1_orders_2(A,B,D))))))) <-> v1_lattice3(A)))) # label(d10_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11336 (all A (-v3_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k15_lattice3(A,a_2_3_lattice3(A,B)) = B & B = k16_lattice3(A,a_2_4_lattice3(A,B)))))) # label(t45_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11337 (all A all B (v10_lattices(B) & v5_lattice3(B) & l3_lattices(B) & v4_lattice3(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k15_lattice3(B,a_3_8_lattice3(A,B,C)) = k4_lattices(B,k15_lattice3(B,A),C) & k15_lattice3(B,a_3_7_lattice3(A,B,C)) = k4_lattices(B,C,k15_lattice3(B,A)))))) # label(t54_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11338 (all A all B all C all D (-v3_struct_0(B) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(C,u1_struct_0(B)) & l3_lattices(B) & v4_lattice3(B) & v10_lattices(B) -> ((exists E (m1_subset_1(E,u1_struct_0(B)) & r3_lattices(B,k4_lattices(B,C,E),D) & A = E)) <-> r2_hidden(A,a_3_6_lattice3(B,C,D))))) # label(fraenkel_a_3_6_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11339 (all A (l1_orders_2(A) -> l1_orders_2(k7_lattice3(A)) & v1_orders_2(k7_lattice3(A)))) # label(dt_k7_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11340 (all A (v10_lattices(A) & l3_lattices(A) & v4_lattice3(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C r3_lattices(A,k3_lattices(A,B,k16_lattice3(A,C)),k16_lattice3(A,a_3_4_lattice3(A,B,C)))))))) # label(t35_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11341 (all A (l1_orders_2(A) -> (all B all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_lattice3(A,B,C) <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,B) -> r1_orders_2(A,D,C))))))))) # label(d9_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11342 (all A (-v3_struct_0(A) & v4_lattice3(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (r2_hidden(B,C) -> r3_lattices(A,k16_lattice3(A,C),B) & r3_lattices(A,B,k15_lattice3(A,C)))))))) # label(t38_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11343 (all A (l3_lattices(A) & v4_lattice3(A) & v10_lattices(A) & -v3_struct_0(A) -> v14_lattices(A) & l3_lattices(A) & k6_lattices(A) = k15_lattice3(A,u1_struct_0(A)) & v10_lattices(A) & -v3_struct_0(A))) # label(t51_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11344 (all A all B (-v3_struct_0(A) & v10_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & l3_lattices(A) -> m1_subset_1(k4_lattice3(A,B),u1_struct_0(k3_lattice3(A))))) # label(dt_k4_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11345 (all A (l3_lattices(A) & -v3_struct_0(A) -> (l3_lattices(A) & v4_lattice3(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B all C (m1_subset_1(C,u1_struct_0(A)) -> (C = k15_lattice3(A,B) <-> r4_lattice3(A,C,B) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r4_lattice3(A,D,B) -> r1_lattices(A,C,D)))))))))) # label(d21_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11346 (all A all B (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B,u1_struct_0(k3_lattice3(A))) -> m1_subset_1(k5_lattice3(A,B),u1_struct_0(A)))) # label(dt_k5_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11347 (all A (-v3_struct_0(A) & v4_lattice3(A) & l3_lattices(A) & v10_lattices(A) -> (all B (k15_lattice3(A,B) = k15_lattice3(A,a_2_5_lattice3(A,B)) & k16_lattice3(A,B) = k16_lattice3(A,a_2_6_lattice3(A,B)))))) # label(t47_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11348 (all A (l1_orders_2(A) -> (all B all C (m1_subset_1(C,u1_struct_0(A)) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,B) -> r1_orders_2(A,C,D)))) <-> r1_lattice3(A,B,C)))))) # label(d8_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11349 (all A ((exists B (m1_subset_1(B,f2_s1_lattice3) & p1_s1_lattice3(B) & A = f1_s1_lattice3)) <-> r2_hidden(A,a_0_0_lattice3))) # label(fraenkel_a_0_0_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11350 (all A (-v3_struct_0(A) & v4_lattice3(A) & l3_lattices(A) & v10_lattices(A) -> (all B all C (r1_tarski(B,C) -> r3_lattices(A,k15_lattice3(A,B),k15_lattice3(A,C)) & r3_lattices(A,k16_lattice3(A,C),k16_lattice3(A,B)))))) # label(t46_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11351 (all A all B all C (v4_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & v2_lattice3(A) -> k12_lattice3(A,C,B) = k12_lattice3(A,B,C))) # label(commutativity_k12_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11352 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> v1_relat_2(k2_lattice3(A)) & v4_relat_2(k2_lattice3(A)) & v1_partfun1(k2_lattice3(A),u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(k2_lattice3(A),u1_struct_0(A),u1_struct_0(A)) & v8_relat_2(k2_lattice3(A)))) # label(dt_k2_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11353 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k1_zfmisc_1(A),A) & v1_funct_2(B,k1_zfmisc_1(A),A) -> -((all C (m1_subset_1(C,A) -> k8_funct_2(k1_zfmisc_1(A),A,B,k6_domain_1(A,C)) = C)) & (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> k8_funct_2(k1_zfmisc_1(A),A,B,k10_relset_1(k1_zfmisc_1(A),A,B,C)) = k1_funct_1(B,k3_tarski(C)))) & (all C (-v3_struct_0(C) & l3_lattices(C) & v4_lattice3(C) & v10_lattices(C) & v3_lattices(C) -> -(A = u1_struct_0(C) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) -> k1_funct_1(B,D) = k15_lattice3(C,D))))))))))) # label(t56_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11354 (all A all B all C all D (l3_lattices(B) & m1_subset_1(D,u1_struct_0(B)) & v4_lattice3(B) & v10_lattices(B) & -v3_struct_0(B) -> (r2_hidden(A,a_3_3_lattice3(B,C,D)) <-> (exists E (m1_subset_1(E,u1_struct_0(B)) & A = k4_lattices(B,D,E) & r2_hidden(E,C)))))) # label(fraenkel_a_3_3_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11355 (all A (v10_lattices(A) & l3_lattices(A) & v4_lattice3(A) & -v3_struct_0(A) -> (v5_lattice3(A) <-> (all B all C (m1_subset_1(C,u1_struct_0(A)) -> r3_lattices(A,k4_lattices(A,C,k15_lattice3(A,B)),k15_lattice3(A,a_3_3_lattice3(A,B,C)))))))) # label(t33_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11356 (all A (v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> C = k13_lattice3(A,k12_lattice3(A,B,C),C))))))) # label(t17_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11357 (all A (l1_orders_2(A) & v3_lattice3(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> -v3_struct_0(k14_lattice3(A)) & v3_lattices(k14_lattice3(A)) & v4_lattices(k14_lattice3(A)) & v5_lattices(k14_lattice3(A)) & v6_lattices(k14_lattice3(A)) & v8_lattices(k14_lattice3(A)) & v4_lattice3(k14_lattice3(A)) & v10_lattices(k14_lattice3(A)) & v9_lattices(k14_lattice3(A)) & v7_lattices(k14_lattice3(A)))) # label(fc7_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11358 (all A (v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (r2_hidden(B,C) & r3_lattice3(A,B,C) -> k16_lattice3(A,C) = B)))))) # label(t42_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11359 (all A (l1_orders_2(A) & v1_lattice3(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k10_lattice3(A,B,C) = k10_lattice3(A,C,B))))))) # label(t13_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11360 (all A (l3_lattices(A) & -v3_struct_0(A) -> ((all B exists C (m1_subset_1(C,u1_struct_0(A)) & r4_lattice3(A,C,B) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r4_lattice3(A,D,B) -> r1_lattices(A,C,D)))))) <-> v4_lattice3(A)))) # label(d18_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11361 (all A all B (v1_relat_2(B) & v4_relat_2(B) & v8_relat_2(B) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) -> k6_lattice3(A,B) = k4_relat_1(B))) # label(redefinition_k6_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.73 11362 (all A all B all C (v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) & -v3_struct_0(B) -> (r2_hidden(A,a_2_7_lattice3(B,C)) <-> (exists D (A = k15_lattice3(B,D) & r2_hidden(D,C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))))))) # label(fraenkel_a_2_7_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11363 (all A all B (m1_subset_1(B,u1_struct_0(k1_lattice3(A))) -> k4_xboole_0(A,B) = k7_lattices(k1_lattice3(A),B))) # label(t5_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11364 (exists A (v1_orders_2(A) & v3_lattice3(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) & l1_orders_2(A))) # label(rc1_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11365 (all A v4_lattice3(k1_lattice3(A))) # label(t25_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11366 (all A all B all C (l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & v1_lattice3(A) & v4_orders_2(A) -> k13_lattice3(A,C,B) = k13_lattice3(A,B,C))) # label(commutativity_k13_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11367 (all A (l1_orders_2(A) -> (v3_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & v2_lattice3(A) & v4_orders_2(A) & v2_orders_2(A) -> (all B (v3_lattices(B) & v10_lattices(B) & l3_lattices(B) & -v3_struct_0(B) -> (B = k14_lattice3(A) <-> g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = k3_lattice3(B))))))) # label(d15_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11368 (all A (r2_hidden(A,a_0_2_lattice3) <-> (exists B (p1_s2_lattice3(B) & k1_funct_1(f4_s2_lattice3,f3_s2_lattice3(B)) = A & m1_subset_1(B,f1_s2_lattice3))))) # label(fraenkel_a_0_2_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11369 (all A all B all C all D (-v3_struct_0(C) & v5_lattice3(C) & l3_lattices(C) & m1_subset_1(D,u1_struct_0(C)) & v4_lattice3(C) & v10_lattices(C) -> ((exists E (m1_subset_1(E,u1_struct_0(C)) & r2_hidden(E,B) & k4_lattices(C,E,D) = A)) <-> r2_hidden(A,a_3_8_lattice3(B,C,D))))) # label(fraenkel_a_3_8_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11370 (all A (v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) -> v4_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v1_orders_2(k7_lattice3(A)))) # label(fc5_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11371 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (v3_lattice3(A) -> v2_lattice3(A) & v1_lattice3(A)))) # label(t12_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11372 (all A (l3_lattices(A) & v4_lattice3(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (r1_tarski(B,k1_zfmisc_1(u1_struct_0(A))) -> k15_lattice3(A,a_2_7_lattice3(A,B)) = k15_lattice3(A,k3_tarski(B)))))) # label(t49_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11373 (all A all B all C (v4_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_orders_2(A) & v1_lattice3(A) -> k10_lattice3(A,B,C) = k13_lattice3(A,B,C))) # label(redefinition_k13_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11374 (all A all B (v10_lattices(B) & l3_lattices(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (r1_lattice3(k3_lattice3(B),A,k4_lattice3(B,C)) <-> r3_lattice3(B,C,A)))))) # label(t28_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11375 (all A all B (-v3_struct_0(B) & l3_lattices(B) & v10_lattices(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (r4_lattice3(B,C,A) <-> r2_lattice3(k3_lattice3(B),A,k4_lattice3(B,C))))))) # label(t30_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11376 (all A all B all C (-v3_struct_0(B) & v10_lattices(B) & m1_subset_1(C,u1_struct_0(B)) & l3_lattices(B) & v4_lattice3(B) -> ((exists D (D = A & r3_lattices(B,D,C) & m1_subset_1(D,u1_struct_0(B)))) <-> r2_hidden(A,a_2_3_lattice3(B,C))))) # label(fraenkel_a_2_3_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11377 (all A (v4_orders_2(A) & l1_orders_2(A) & v1_lattice3(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (v3_orders_2(A) -> k10_lattice3(A,B,k10_lattice3(A,C,D)) = k10_lattice3(A,k10_lattice3(A,B,C),D)))))))))) # label(t14_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11378 (all A (v2_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) -> (exists B (v3_lattices(B) & l3_lattices(B) & g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = k3_lattice3(B) & v10_lattices(B) & -v3_struct_0(B))))) # label(t19_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11379 (all A all B all C all D (-v3_struct_0(C) & l3_lattices(C) & m1_subset_1(D,u1_struct_0(C)) & v6_lattice3(C) & v4_lattice3(C) & v10_lattices(C) -> ((exists E (k3_lattices(C,D,E) = A & r2_hidden(E,B) & m1_subset_1(E,u1_struct_0(C)))) <-> r2_hidden(A,a_3_9_lattice3(B,C,D))))) # label(fraenkel_a_3_9_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11380 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r3_lattice3(A,B,k2_struct_0(A,C,D)) <-> r3_lattices(A,B,k4_lattices(A,C,D))))))))))) # label(t21_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11381 (all A all B all C all D (-v3_struct_0(B) & l3_lattices(B) & m1_subset_1(D,u1_struct_0(B)) -> (r2_hidden(A,a_3_1_lattice3(B,C,D)) <-> (exists E (k1_lattices(B,D,E) = A & r2_hidden(E,C) & m1_subset_1(E,u1_struct_0(B))))))) # label(fraenkel_a_3_1_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11382 (all A all B all C (l1_orders_2(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & v1_lattice3(A) & v4_orders_2(A) -> m1_subset_1(k13_lattice3(A,B,C),u1_struct_0(A)))) # label(dt_k13_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11383 $T # label(t39_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11384 (all A all B all C all D (-v3_struct_0(C) & v10_lattices(C) & v4_lattice3(C) & m1_subset_1(D,u1_struct_0(C)) & l3_lattices(C) & v5_lattice3(C) -> ((exists E (k4_lattices(C,D,E) = A & r2_hidden(E,B) & m1_subset_1(E,u1_struct_0(C)))) <-> r2_hidden(A,a_3_7_lattice3(B,C,D))))) # label(fraenkel_a_3_7_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11385 (all A all B all C (v4_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_orders_2(A) & v2_lattice3(A) -> m1_subset_1(k12_lattice3(A,B,C),u1_struct_0(A)))) # label(dt_k12_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11386 (all A (v4_lattices(k1_lattice3(A)) & v5_lattices(k1_lattice3(A)) & v6_lattices(k1_lattice3(A)) & v7_lattices(k1_lattice3(A)) & v8_lattices(k1_lattice3(A)) & v9_lattices(k1_lattice3(A)) & v10_lattices(k1_lattice3(A)) & v3_lattices(k1_lattice3(A)) & -v3_struct_0(k1_lattice3(A)))) # label(fc2_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11387 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k4_lattice3(A,B) = B)))) # label(d3_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11388 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r3_lattices(A,k3_lattices(A,C,D),B) <-> r4_lattice3(A,B,k2_struct_0(A,C,D))))))))))) # label(t22_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11389 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_orders_2(k7_lattice3(A),k8_lattice3(A,C),k8_lattice3(A,B)) <-> r1_orders_2(A,B,C)))))))) # label(t9_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11390 (all A all B (-v3_struct_0(A) & l3_lattices(A) -> m1_subset_1(k15_lattice3(A,B),u1_struct_0(A)))) # label(dt_k15_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11391 (all A (-v3_struct_0(A) & l3_lattices(A) -> (v6_lattice3(A) <-> (all B all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r3_lattice3(A,C,B) & (all F (m1_subset_1(F,u1_struct_0(A)) -> (r3_lattice3(A,F,B) -> r1_lattices(A,F,C)))) & r3_lattice3(A,E,a_3_1_lattice3(A,B,D)) & (all F (m1_subset_1(F,u1_struct_0(A)) -> (r3_lattice3(A,F,a_3_1_lattice3(A,B,D)) -> r1_lattices(A,F,E)))) -> r1_lattices(A,E,k1_lattices(A,D,C)))))))))))) # label(d20_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11392 (all A all B (-v3_struct_0(A) & l3_lattices(A) -> m1_subset_1(k16_lattice3(A,B),u1_struct_0(A)))) # label(dt_k16_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11393 r1_tarski(f2_s2_lattice3,k1_relat_1(f4_s2_lattice3)) -> a_0_2_lattice3 = k9_relat_1(f4_s2_lattice3,a_0_1_lattice3) # label(s2_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11394 (all A (l1_orders_2(A) -> (v1_lattice3(A) <-> v2_lattice3(k7_lattice3(A))))) # label(t10_lattice3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11395 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (-v3_struct_0(C) & l1_group_1(C) & v4_group_1(C) & v3_group_1(C) & v1_group_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (k5_group_4(C,k1_struct_0(C,D)) = C & k9_group_1(C) = A & v6_group_1(C) -> (C = k5_group_4(C,k1_struct_0(C,k6_group_1(C,B,D))) <-> np__1 = k6_nat_1(B,A))))))))))) # label(t18_gr_cy_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11396 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k5_group_4(A,k1_struct_0(A,B)) = A & v6_group_1(A) -> (all C (m1_group_2(C,A) & v1_group_1(C) -> (exists D (r1_group_2(A,C,k5_group_4(A,k1_struct_0(A,k6_group_1(A,D,B)))) & m2_subset_1(D,k1_numbers,k5_numbers)))))))))) # label(t13_gr_cy_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11397 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v6_group_1(A) -> (A = k5_group_4(A,k1_struct_0(A,B)) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (k6_group_1(A,D,B) = C & m2_subset_1(D,k1_numbers,k5_numbers))))))))))) # label(t12_gr_cy_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11398 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_group_1(B) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & v1_gr_cy_1(B) & -v3_struct_0(B) -> -((all C (m1_group_2(C,B) -> -(np__2 = k9_group_1(C) & v3_group_1(C) & l1_group_1(C) & v1_gr_cy_1(C) & v4_group_1(C) & -v3_struct_0(C)))) & (exists C (A = k2_nat_1(np__2,C) & m2_subset_1(C,k1_numbers,k5_numbers))) & A = k9_group_1(B) & v6_group_1(B)))))) # label(t31_gr_cy_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11399 (all A (-v3_struct_0(A) & v1_group_1(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (A = k5_group_4(A,k1_struct_0(A,B)) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (k6_group_1(A,D,B) = C & v1_int_1(D)))))))))) # label(t11_gr_cy_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11400 (all A (-v3_struct_0(A) & v1_gr_cy_1(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (A = k5_group_4(A,k1_struct_0(A,B)) -> ((exists C ((exists D (v1_int_1(D) & k6_group_1(A,C,B) = k6_group_1(A,D,B) & C != D)) & v1_int_1(C))) <-> v6_group_1(A))))))) # label(t20_gr_cy_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11401 (all A (v1_group_1(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (k9_group_1(A) = np__2 & v6_group_1(A) -> (all B (m1_group_2(B,A) & v1_group_1(B) -> B = A | r1_group_2(A,B,k5_group_2(A))))))) # label(t26_gr_cy_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11402 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> -(-r1_xreal_0(k7_group_1(A,B),np__1) & k6_group_1(A,D,C) = B & D = np__0))))))))) # label(t6_gr_cy_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11403 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r1_nat_1(C,D) -> r1_rlvect_1(k5_group_4(A,k1_struct_0(A,k6_group_1(A,C,B))),k6_group_1(A,D,B))))))))))) # label(t15_gr_cy_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11404 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_rlvect_1(k5_group_4(A,k1_struct_0(A,B)),B))))) # label(t8_gr_cy_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11405 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (C = D -> k5_group_4(A,k1_struct_0(A,C)) = k5_group_4(B,k1_struct_0(B,D))))))))))) # label(t9_gr_cy_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11406 $T # label(t7_gr_cy_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11407 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & v1_group_1(A) & -v3_struct_0(A) -> (all B (l1_group_1(B) & v4_group_1(B) & v3_group_1(B) & v1_group_1(B) & -v3_struct_0(B) -> (r2_group_6(A,B) -> v3_group_1(A) & l1_group_1(A) & v3_group_1(B) & v4_group_1(B) & v1_gr_cy_1(B) & l1_group_1(B) & -v3_struct_0(B) & v1_gr_cy_1(A) & v4_group_1(A) & -v3_struct_0(A) | -(-v3_struct_0(A) & l1_group_1(A) & v1_gr_cy_1(A) & v4_group_1(A) & v3_group_1(A)) & -(v3_group_1(B) & v1_gr_cy_1(B) & l1_group_1(B) & v4_group_1(B) & -v3_struct_0(B))))))) # label(t33_gr_cy_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11408 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_group_1(B) & v4_group_1(B) & l1_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (v3_group_1(B) & v1_gr_cy_1(B) & k9_group_1(B) = A & l1_group_1(B) & v4_group_1(B) & -v3_struct_0(B) & v6_group_1(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(r1_nat_1(C,A) & (all D (m1_group_2(D,B) & v1_group_1(D) -> -((all E (m1_group_2(E,B) & v1_group_1(E) -> (C = k9_group_1(E) -> r1_group_2(B,E,D)))) & k9_group_1(D) = C))))))))))) # label(t28_gr_cy_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11409 $T # label(t5_gr_cy_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11410 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (C = k2_nat_1(D,E) & C = k9_group_1(A) & A = k5_group_4(A,k1_struct_0(A,B)) & v6_group_1(A) -> k7_group_1(A,k6_group_1(A,D,B)) = E))))))))))) # label(t14_gr_cy_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11411 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & v1_group_1(A) & -v3_struct_0(A) -> (all B (v3_group_1(B) & l1_group_1(B) & v4_group_1(B) & v1_group_1(B) & -v3_struct_0(B) -> (v6_group_1(A) & v6_group_1(B) & np__2 = k9_group_1(A) & k9_group_1(B) = np__2 -> r2_group_6(A,B)))))) # label(t25_gr_cy_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11412 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (k9_group_1(k5_group_4(A,k1_struct_0(A,k6_group_1(A,D,B)))) = k9_group_1(k5_group_4(A,k1_struct_0(A,k6_group_1(A,C,B)))) & r1_rlvect_1(k5_group_4(A,k1_struct_0(A,k6_group_1(A,C,B))),k6_group_1(A,D,B)) & v6_group_1(A) -> r1_group_2(A,k5_group_4(A,k1_struct_0(A,k6_group_1(A,C,B))),k5_group_4(A,k1_struct_0(A,k6_group_1(A,D,B))))))))))))) # label(t16_gr_cy_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11413 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v3_struct_0(B) & v1_group_1(B) & v3_group_1(B) & v1_gr_cy_1(B) & l1_group_1(B) & v4_group_1(B) -> (v6_group_1(B) & k9_group_1(B) = A -> r2_group_6(k5_gr_cy_1(A),B)))))) # label(t21_gr_cy_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11414 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_gr_cy_1(A) & v1_group_1(A) -> (-v6_group_1(A) -> r2_group_6(k3_gr_cy_1,A)))) # label(t22_gr_cy_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11415 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (v4_group_1(B) & l1_group_1(B) & v3_group_1(B) & v1_group_1(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) & v1_group_6(C,B,A) -> (-v3_struct_0(B) & v3_group_1(B) & v1_gr_cy_1(B) & l1_group_1(B) & v4_group_1(B) -> -v3_struct_0(k13_group_6(B,A,C)) & v3_group_1(k13_group_6(B,A,C)) & v4_group_1(k13_group_6(B,A,C)) & v1_gr_cy_1(k13_group_6(B,A,C)) & l1_group_1(k13_group_6(B,A,C))))))))) # label(t32_gr_cy_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11416 (all A (v1_group_1(A) & l1_group_1(A) & v1_gr_cy_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_group_1(B) & v1_gr_cy_1(B) & l1_group_1(B) & v3_group_1(B) & v1_group_1(B) -> (v6_group_1(B) & k9_group_1(B) = k9_group_1(A) & v6_group_1(A) -> r2_group_6(B,A)))))) # label(t23_gr_cy_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11417 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> -v3_struct_0(k10_group_5(A)) & v1_group_1(k10_group_5(A)) & v2_group_1(k10_group_5(A)) & v3_group_1(k10_group_5(A)) & v4_group_1(k10_group_5(A)) & v1_group_3(k10_group_5(A),A))) # label(fc1_gr_cy_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11418 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (all F (m2_subset_1(F,k1_numbers,k5_numbers) -> (k5_group_4(A,k1_struct_0(A,C)) = A & E = k9_group_1(B) & k5_group_4(A,k1_struct_0(A,k6_group_1(A,F,C))) = B & D = k9_group_1(A) & v6_group_1(A) -> r1_nat_1(D,k2_nat_1(F,E))))))))))))))) # label(t17_gr_cy_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11419 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_group_1(B) & l1_group_1(B) & v4_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & l1_group_1(C) & v4_group_1(C) & v3_group_1(C) & v1_group_1(C) -> (v6_group_1(C) & k9_group_1(B) = A & A = k9_group_1(C) & v1_int_2(A) & v6_group_1(B) -> r2_group_6(B,C)))))))) # label(t24_gr_cy_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11420 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (-r1_xreal_0(A,np__0) -> (all B (m1_subset_1(B,u1_struct_0(k5_gr_cy_1(A))) -> k1_gr_cy_2(A,B) = B))))) # label(d1_gr_cy_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11421 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> -v3_struct_0(k5_group_4(A,k1_struct_0(A,B))) & v4_group_1(k5_group_4(A,k1_struct_0(A,B))) & v1_gr_cy_1(k5_group_4(A,k1_struct_0(A,B))) & l1_group_1(k5_group_4(A,k1_struct_0(A,B))) & v3_group_1(k5_group_4(A,k1_struct_0(A,B))))))) # label(t10_gr_cy_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11422 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v1_gr_cy_1(A) & v3_group_1(A) -> (all B (m1_group_2(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_rlvect_1(B,C) & A = k5_group_4(A,k1_struct_0(A,C)) -> g1_group_1(u1_struct_0(B),u1_group_1(B)) = g1_group_1(u1_struct_0(A),u1_group_1(A))))))))) # label(t19_gr_cy_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11423 $T # label(t4_gr_cy_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11424 (all A all B (m1_subset_1(B,u1_struct_0(k5_gr_cy_1(A))) & m1_subset_1(A,k5_numbers) -> m2_subset_1(k1_gr_cy_2(A,B),k1_numbers,k5_numbers))) # label(dt_k1_gr_cy_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11425 $T # label(t1_gr_cy_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11426 (all A (v3_group_1(A) & v1_gr_cy_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (A = k5_group_4(A,k1_struct_0(A,B)) -> (all C (v4_group_1(C) & l1_group_1(C) & v3_group_1(C) & -v3_struct_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,u1_struct_0(C),u1_struct_0(A)) & v1_group_6(D,C,A) & m2_relset_1(D,u1_struct_0(C),u1_struct_0(A)) -> (r1_rlvect_1(k13_group_6(C,A,D),B) -> v3_group_6(D,C,A))))))))))) # label(t29_gr_cy_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11427 $T # label(t3_gr_cy_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11428 $T # label(t2_gr_cy_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11429 (all A (v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (v6_group_1(A) & k9_group_1(A) = np__2 -> v3_group_1(A) & v4_group_1(A) & v1_gr_cy_1(A) & l1_group_1(A) & -v3_struct_0(A)))) # label(t27_gr_cy_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11430 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v3_struct_0(B) & v1_group_1(B) & v4_group_1(B) & l1_group_1(B) & v1_gr_cy_1(B) & v3_group_1(B) -> -(v6_group_1(B) & (exists C (m2_subset_1(C,k1_numbers,k5_numbers) & A = k2_nat_1(np__2,C))) & (all C (m1_subset_1(C,u1_struct_0(B)) -> -(np__2 = k7_group_1(B,C) & (all D (m1_subset_1(D,u1_struct_0(B)) -> (np__2 = k7_group_1(B,D) -> C = D)))))) & k9_group_1(B) = A))))) # label(t30_gr_cy_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11431 (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,k12_nattra_1(A,k11_cat_2(B,C)),k11_cat_2(k12_nattra_1(A,B),k12_nattra_1(A,C))) -> ((all E (m2_cat_1(E,A,k11_cat_2(B,C)) -> (all F (m2_cat_1(F,A,k11_cat_2(B,C)) -> (r2_nattra_1(A,k11_cat_2(B,C),E,F) -> (all G (m2_nattra_1(G,A,k11_cat_2(B,C),E,F) -> k1_funct_1(D,k4_tarski(k4_tarski(E,F),G)) = k4_tarski(k4_tarski(k4_tarski(k11_isocat_2(A,B,C,E),k11_isocat_2(A,B,C,F)),k13_isocat_2(A,B,C,E,F,G)),k4_tarski(k4_tarski(k12_isocat_2(A,B,C,E),k12_isocat_2(A,B,C,F)),k14_isocat_2(A,B,C,E,F,G)))))))))) <-> k17_isocat_2(A,B,C) = D))))))))) # label(d13_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11432 (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)) -> r4_nattra_1(u1_cat_1(A),u2_cat_1(B),u1_cat_1(A),u2_cat_1(B),k7_nattra_1(A,B,k11_isocat_2(A,B,C,D)),k13_isocat_2(A,B,C,D,D,k7_nattra_1(A,k11_cat_2(B,C),D))) & r4_nattra_1(u1_cat_1(A),u2_cat_1(C),u1_cat_1(A),u2_cat_1(C),k7_nattra_1(A,C,k12_isocat_2(A,B,C,D)),k14_isocat_2(A,B,C,D,D,k7_nattra_1(A,k11_cat_2(B,C),D))))))))))) # label(t40_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11433 (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,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]. 126.45/125.74 11434 (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) -> (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]. 126.45/125.74 11435 (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) -> r1_isocat_1(k12_nattra_1(A,k11_cat_2(B,C)),k11_cat_2(k12_nattra_1(A,B),k12_nattra_1(A,C))))))))) # label(t49_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11436 (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)) -> k2_isocat_1(A,k11_cat_2(B,C),B,D,k8_isocat_2(B,C)) = k11_isocat_2(A,B,C,D))))))))) # label(d7_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11437 (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(k11_cat_2(A,B),C,D,k12_cat_2(A,B,E,F)) = k13_cat_1(B,C,k14_cat_2(A,B,C,D,E),F))))))))))))) # label(t12_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11438 $T # label(t10_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11439 (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,k1_fraenkel(B,C)) & m2_relset_1(D,A,k1_fraenkel(B,C)) -> 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]. 126.45/125.74 11440 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,A) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> r2_hidden(k8_funct_2(A,B,D,C),k2_relat_1(D)))))))))) # label(t4_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11441 (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)) -> k12_isocat_2(A,B,C,D) = k2_isocat_1(A,k11_cat_2(B,C),C,D,k9_isocat_2(B,C)))))))))) # label(d8_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11442 (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))) <-> m2_cat_1(C,A,B))))))) # label(t8_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11443 (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(B),u2_cat_1(A),u2_cat_1(B),k11_isocat_2(A,B,C,k10_isocat_2(A,B,C,D,E)),D) & 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))))))))))) # label(t36_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11444 (all A all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k1_tarski(A),B) & m2_relset_1(C,k1_tarski(A),B) -> (all D (v1_funct_2(D,k1_tarski(A),B) & m2_relset_1(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]. 126.45/125.74 11445 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,C) -> (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) -> k3_nattra_1(A,k11_cat_2(B,C),k10_isocat_2(A,B,C,D,E),F,G,H) = k13_cat_2(B,C,k3_nattra_1(A,B,D,F,G,H),k3_nattra_1(A,C,E,F,G,H))))))))))))))))))) # label(t42_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11446 (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 <-> 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))))))))))))) # label(t13_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11447 (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(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]. 126.45/125.74 11448 (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) -> 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]. 126.45/125.74 11449 (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(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(t48_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11450 (all A all B all C all D all E all F (v2_cat_1(A) & l1_cat_1(C) & m2_cat_1(D,A,k11_cat_2(B,C)) & m2_nattra_1(F,A,k11_cat_2(B,C),D,E) & m2_cat_1(E,A,k11_cat_2(B,C)) & v2_cat_1(C) & l1_cat_1(B) & v2_cat_1(B) & l1_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]. 126.45/125.74 11451 (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) -> (all F (m2_cat_1(F,A,C) -> (all G (m2_cat_1(G,A,C) -> (r2_nattra_1(A,B,D,E) & r2_nattra_1(A,C,F,G) -> r2_nattra_1(A,k11_cat_2(B,C),k10_isocat_2(A,B,C,D,F),k10_isocat_2(A,B,C,E,G))))))))))))))))) # label(t46_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11452 (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,k12_nattra_1(k11_cat_2(A,B),C),k12_nattra_1(A,k12_nattra_1(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) -> 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)) = k1_funct_1(D,k4_tarski(k4_tarski(E,F),G))))))))) <-> k7_isocat_2(A,B,C) = D))))))))) # label(d6_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11453 (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,A,C) -> (all G (m2_cat_1(G,A,C) -> (r1_nattra_1(A,C,F,G) & r1_nattra_1(A,B,D,E) -> r1_nattra_1(A,k11_cat_2(B,C),k10_isocat_2(A,B,C,D,F),k10_isocat_2(A,B,C,E,G))))))))))))))))) # label(t44_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11454 (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) -> (all F (m2_cat_1(F,A,C) -> (all G (m2_cat_1(G,A,C) -> (r2_nattra_1(A,C,F,G) & r2_nattra_1(A,B,D,E) -> (all H (m2_nattra_1(H,A,B,D,E) -> (all I (m2_nattra_1(I,A,C,F,G) -> r4_nattra_1(u1_cat_1(A),u2_cat_1(B),u1_cat_1(A),u2_cat_1(B),k13_isocat_2(A,B,C,k10_isocat_2(A,B,C,D,F),k10_isocat_2(A,B,C,E,G),k16_isocat_2(A,B,C,D,E,F,G,H,I)),H) & r4_nattra_1(u1_cat_1(A),u2_cat_1(C),u1_cat_1(A),u2_cat_1(C),k14_isocat_2(A,B,C,k10_isocat_2(A,B,C,D,F),k10_isocat_2(A,B,C,E,G),k16_isocat_2(A,B,C,D,E,F,G,H,I)),I)))))))))))))))))))) # label(t47_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11455 (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,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]. 126.45/125.74 11456 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & -v1_xboole_0(C) & v1_funct_2(D,A,k1_fraenkel(B,C)) & m1_relset_1(D,A,k1_fraenkel(B,C)) & v1_funct_1(D) -> k1_isocat_2(A,B,C,D) = k4_funct_5(D))) # label(redefinition_k1_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11457 (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)) -> k3_isocat_2(A,B,C,D,E) = k1_funct_1(k3_funct_5(D),E))))))))))) # label(d2_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11458 (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(D,k11_cat_2(A,B),C) & m1_subset_1(E,u2_cat_1(A)) & v2_cat_1(C) & l1_cat_1(B) -> 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]. 126.45/125.74 11459 (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,A,C) -> (all G (m2_cat_1(G,A,C) -> (r1_nattra_1(A,B,D,E) & r1_nattra_1(A,C,F,G) -> (all H (m1_nattra_1(H,A,B,D,E) -> (all I (m1_nattra_1(I,A,C,F,G) -> (all J (m1_subset_1(J,u1_cat_1(A)) -> k13_cat_2(B,C,k5_nattra_1(A,B,D,E,H,J),k5_nattra_1(A,C,F,G,I,J)) = k5_nattra_1(A,k11_cat_2(B,C),k10_isocat_2(A,B,C,D,F),k10_isocat_2(A,B,C,E,G),k15_isocat_2(A,B,C,D,E,F,G,H,I),J)))))))))))))))))))))) # label(t45_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11460 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (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]. 126.45/125.74 11461 (all A all B (l1_cat_1(B) & v2_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> k9_isocat_2(A,B) = k17_cat_2(A,B))) # label(redefinition_k9_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11462 (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]. 126.45/125.74 11463 (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 (m2_cat_1(D,k12_nattra_1(A,B),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) -> (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)))))))) <-> k2_isocat_2(A,B,C) = D))))))))) # label(d1_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11464 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u2_cat_1(A)) -> (all F (m1_subset_1(F,u2_cat_1(A)) -> (k2_cat_1(A,E) = k3_cat_1(A,F) -> (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]. 126.45/125.74 11465 (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)) -> (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]. 126.45/125.74 11466 (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(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)) -> (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))) & r2_nattra_1(k11_cat_2(A,B),C,D,E)))))))))))))) # label(t32_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11467 (all A all B all C all D all E all F (v2_cat_1(A) & v2_cat_1(B) & l1_cat_1(C) & m2_cat_1(D,k11_cat_2(A,B),C) & m2_cat_1(E,k11_cat_2(A,B),C) & m2_nattra_1(F,k11_cat_2(A,B),C,D,E) & v2_cat_1(C) & l1_cat_1(B) & l1_cat_1(A) -> 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]. 126.45/125.74 11468 (all A all B (v2_cat_1(B) & l1_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> 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]. 126.45/125.74 11469 (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,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) -> k6_isocat_1(A,k11_cat_2(B,C),B,D,E,F,k8_isocat_2(B,C)) = k13_isocat_2(A,B,C,D,E,F))))))))))))) # label(d9_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11470 (all A all B all C (v2_cat_1(A) & v2_cat_1(B) & m1_subset_1(C,u1_cat_1(A)) & l1_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]. 126.45/125.74 11471 (all A all B all C all D all E all F all G all H all I (v2_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(C) & l1_cat_1(C) & m2_cat_1(D,A,B) & m2_cat_1(F,A,C) & m2_cat_1(G,A,C) & m2_nattra_1(I,A,C,F,G) & m2_nattra_1(H,A,B,D,E) & m2_cat_1(E,A,B) & l1_cat_1(A) -> 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]. 126.45/125.74 11472 (all A all B (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) -> k16_cat_2(A,B) = k8_isocat_2(A,B))) # label(redefinition_k8_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11473 (all A all B all C all D (v2_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(C) & m2_cat_1(D,A,k11_cat_2(B,C)) & l1_cat_1(C) & l1_cat_1(A) -> m2_cat_1(k11_isocat_2(A,B,C,D),A,B))) # label(dt_k11_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11474 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (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]. 126.45/125.74 11475 (all A (l1_cat_1(A) & v2_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]. 126.45/125.74 11476 (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(k12_isocat_2(A,B,C,D),A,C))) # label(dt_k12_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11477 (all A all B (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) -> 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]. 126.45/125.74 11478 (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_cat_1(F,A,k11_cat_2(B,C)) -> (all G (m2_cat_1(G,A,k11_cat_2(B,C)) -> (r2_nattra_1(A,k11_cat_2(B,C),D,E) & r2_nattra_1(A,k11_cat_2(B,C),F,G) -> (all H (m2_nattra_1(H,A,k11_cat_2(B,C),D,E) -> (all I (m2_nattra_1(I,A,k11_cat_2(B,C),F,G) -> (r4_nattra_1(u1_cat_1(A),u2_cat_1(B),u1_cat_1(A),u2_cat_1(B),k13_isocat_2(A,B,C,D,E,H),k13_isocat_2(A,B,C,F,G,I)) & r4_nattra_1(u1_cat_1(A),u2_cat_1(C),u1_cat_1(A),u2_cat_1(C),k14_isocat_2(A,B,C,D,E,H),k14_isocat_2(A,B,C,F,G,I)) -> r4_nattra_1(u1_cat_1(A),u2_cat_1(k11_cat_2(B,C)),u1_cat_1(A),u2_cat_1(k11_cat_2(B,C)),H,I))))))))))))))))))))) # label(t39_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11479 (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)) -> k14_cat_2(A,B,C,D,E) = k13_cat_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),E))))))))))) # label(t24_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11480 (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) -> 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]. 126.45/125.74 11481 $T # label(t22_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11482 (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(H,B,E,F) & m1_cat_1(G,A,C,D))))))))))))))))))) # label(t14_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11483 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,k2_zfmisc_1(B,C)) & m2_relset_1(E,A,k2_zfmisc_1(B,C)) -> (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]. 126.45/125.74 11484 (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) -> k5_relat_1(G,F) = k6_isocat_1(A,B,C,D,E,G,F)))))))))))))))) # label(t35_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11485 (all A all B all C (l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(C) & v2_cat_1(C) & l1_cat_1(B) & v2_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]. 126.45/125.74 11486 (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,A,C) -> (all G (m2_cat_1(G,A,C) -> (r2_nattra_1(A,B,D,E) & r2_nattra_1(A,C,F,G) -> (all H (m2_nattra_1(H,A,B,D,E) -> (all I (m2_nattra_1(I,A,C,F,G) -> k15_isocat_2(A,B,C,D,E,F,G,H,I) = k16_isocat_2(A,B,C,D,E,F,G,H,I)))))))))))))))))))) # label(d12_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.74 11487 (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) -> 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]. 126.45/125.74 11488 (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) -> (all F (m2_cat_1(F,k11_cat_2(A,B),C) -> (r2_nattra_1(k11_cat_2(A,B),C,D,E) & r2_nattra_1(k11_cat_2(A,B),C,E,F) -> (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]. 126.45/125.75 11489 (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)) -> 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))) = 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))))))))))))) # label(t19_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11490 (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(D,A,B) & m2_cat_1(E,A,C) & v2_cat_1(C) -> 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]. 126.45/125.75 11491 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> k4_cat_1(A,B,k10_cat_1(A,k3_cat_1(A,B))) = B)))) # label(t6_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11492 (all A all B all C (v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(C) & l1_cat_1(C) & l1_cat_1(A) & v2_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]. 126.45/125.75 11493 $T # label(t23_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11494 (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,k12_nattra_1(B,C)) -> (exists 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)),D,k5_isocat_2(A,B,C,E)))))))))))) # label(t31_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11495 (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 (m2_nattra_1(F,A,B,D,E) & E = k3_cat_1(k12_nattra_1(A,B),C) & C = k4_tarski(k4_tarski(D,E),F) & D = k2_cat_1(k12_nattra_1(A,B),C) & r2_nattra_1(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]. 126.45/125.75 11496 (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,A,k12_nattra_1(B,C)) -> (k5_isocat_2(A,B,C,D) = E <-> (all F (m1_subset_1(F,u2_cat_1(A)) -> k8_funct_2(u2_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),E,F) = 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))))))))))))))) # label(d4_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11497 (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(k11_cat_2(A,B),C,D,E) -> (all F (m2_nattra_1(F,k11_cat_2(A,B),C,D,E) -> (exists G ((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)))))) & m2_nattra_1(G,A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E)))) & 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]. 126.45/125.75 11498 (all A all B all C all D all E (l1_cat_1(B) & l1_cat_1(C) & m2_cat_1(D,A,B) & m2_cat_1(E,A,C) & v2_cat_1(C) & v2_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> k10_isocat_2(A,B,C,D,E) = k13_funct_3(D,E))) # label(redefinition_k10_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11499 (all A all B all C all D (v1_funct_2(D,A,k1_fraenkel(B,C)) & m1_relset_1(D,A,k1_fraenkel(B,C)) & v1_funct_1(D) & -v1_xboole_0(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> 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) & v1_funct_1(k1_isocat_2(A,B,C,D)))) # label(dt_k1_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11500 (all A all B all C all D (v2_cat_1(B) & m2_cat_1(D,k11_cat_2(A,B),C) & l1_cat_1(C) & v2_cat_1(C) & l1_cat_1(B) & l1_cat_1(A) & 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]. 126.45/125.75 11501 (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,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]. 126.45/125.75 11502 (all A all B all C all D all E (v2_cat_1(B) & m1_subset_1(E,u2_cat_1(A)) & m2_cat_1(D,k11_cat_2(A,B),C) & l1_cat_1(C) & v2_cat_1(C) & l1_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> v1_funct_2(k3_isocat_2(A,B,C,D,E),u2_cat_1(B),u2_cat_1(C)) & m2_relset_1(k3_isocat_2(A,B,C,D,E),u2_cat_1(B),u2_cat_1(C)) & v1_funct_1(k3_isocat_2(A,B,C,D,E)))) # label(dt_k3_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11503 (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) -> (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]. 126.45/125.75 11504 (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,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(axiom) # label(non_clause). [assumption]. 126.45/125.75 11505 (all A all B all C all D all E all F (l1_cat_1(A) & l1_cat_1(B) & l1_cat_1(C) & 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)) & v2_cat_1(C) & v2_cat_1(B) & v2_cat_1(A) -> 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]. 126.45/125.75 11506 (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,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]. 126.45/125.75 11507 (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,u2_cat_1(A)) -> 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)) = k4_isocat_2(A,B,C,D,E))))))))))) # label(d3_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11508 (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 (m2_nattra_1(G,A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E)) -> (k6_isocat_2(A,B,C,D,E,F) = G <-> (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)) -> 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) = 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))))))))))))))))))))))) # label(d5_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11509 (all A all B all C all D all E all F all G all H all I (v2_cat_1(C) & l1_cat_1(C) & m2_cat_1(D,A,B) & m2_cat_1(E,A,B) & m2_cat_1(F,A,C) & m1_nattra_1(I,A,C,F,G) & m1_nattra_1(H,A,B,D,E) & m2_cat_1(G,A,C) & l1_cat_1(B) & v2_cat_1(B) & l1_cat_1(A) & 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]. 126.45/125.75 11510 (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,A,C) -> (all G (m2_cat_1(G,A,C) -> (r1_nattra_1(A,C,F,G) & r1_nattra_1(A,B,D,E) -> (all H (m1_nattra_1(H,A,B,D,E) -> (all I (m1_nattra_1(I,A,C,F,G) -> k15_isocat_2(A,B,C,D,E,F,G,H,I) = k14_funct_3(u1_cat_1(A),u2_cat_1(B),u2_cat_1(C),H,I)))))))))))))))))))) # label(d11_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11511 (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,C) -> (all F (m1_subset_1(F,u1_cat_1(A)) -> k13_cat_1(A,k11_cat_2(B,C),k10_isocat_2(A,B,C,D,E),F) = k12_cat_2(B,C,k13_cat_1(A,B,D,F),k13_cat_1(A,C,E,F)))))))))))))) # label(t43_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11512 (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)) -> (all F (m2_cat_1(F,A,k11_cat_2(B,C)) -> (r2_nattra_1(A,k11_cat_2(B,C),D,E) & r2_nattra_1(A,k11_cat_2(B,C),E,F) -> (all G (m2_nattra_1(G,A,k11_cat_2(B,C),D,E) -> (all H (m2_nattra_1(H,A,k11_cat_2(B,C),E,F) -> r4_nattra_1(u1_cat_1(A),u2_cat_1(C),u1_cat_1(A),u2_cat_1(C),k14_isocat_2(A,B,C,D,F,k8_nattra_1(A,k11_cat_2(B,C),D,E,F,G,H)),k8_nattra_1(A,C,k12_isocat_2(A,B,C,D),k12_isocat_2(A,B,C,E),k12_isocat_2(A,B,C,F),k14_isocat_2(A,B,C,D,E,G),k14_isocat_2(A,B,C,E,F,H))) & r4_nattra_1(u1_cat_1(A),u2_cat_1(B),u1_cat_1(A),u2_cat_1(B),k13_isocat_2(A,B,C,D,F,k8_nattra_1(A,k11_cat_2(B,C),D,E,F,G,H)),k8_nattra_1(A,B,k11_isocat_2(A,B,C,D),k11_isocat_2(A,B,C,E),k11_isocat_2(A,B,C,F),k13_isocat_2(A,B,C,D,E,G),k13_isocat_2(A,B,C,E,F,H)))))))))))))))))))) # label(t41_isocat_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11513 (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)) -> (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]. 126.45/125.75 11514 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v4_tdlat_3(A) -> (exists B (-v3_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & v4_tdlat_3(B) & m1_pre_topc(B,A))))) # label(rc10_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11515 (all A (l1_pre_topc(A) -> (v1_tdlat_3(A) & v2_tdlat_3(A) -> k2_tarski(k1_xboole_0,u1_struct_0(A)) = k1_pcomps_1(u1_struct_0(A))))) # label(t12_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11516 (exists A (v2_tdlat_3(A) & v1_tdlat_3(A) & v1_pre_topc(A) & -v3_struct_0(A) & l1_pre_topc(A))) # label(rc1_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11517 $T # label(t1_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11518 (all A (v2_pre_topc(A) & v4_tdlat_3(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(k4_tdlat_1(A))) -> (all C (m1_subset_1(C,u1_struct_0(k4_tdlat_1(A))) -> (all D (m1_subset_1(D,k1_tdlat_1(A)) -> (all E (m1_subset_1(E,k1_tdlat_1(A)) -> (E = C & D = B -> k4_lattices(k4_tdlat_1(A),B,C) = k3_xboole_0(D,E) & k3_lattices(k4_tdlat_1(A),B,C) = k2_xboole_0(D,E)))))))))))) # label(t48_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11519 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k6_pre_topc(A,B) = k3_subset_1(u1_struct_0(A),k1_tops_1(A,k3_subset_1(u1_struct_0(A),B))))))) # label(t2_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11520 (exists A (l1_pre_topc(A) & v3_tdlat_3(A) & v1_pre_topc(A))) # label(rc2_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11521 (exists A (l1_pre_topc(A) & -v3_struct_0(A) & v1_pre_topc(A) & v4_tdlat_3(A) & v2_pre_topc(A))) # label(rc8_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11522 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (v2_tdlat_3(A) <-> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(B != k1_xboole_0 & B != u1_struct_0(A) & v4_pre_topc(B,A))))))) # label(t21_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11523 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> v4_pre_topc(B,A)))) <-> v3_tdlat_3(A)))) # label(t23_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11524 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (-v3_struct_0(k4_tdlat_1(A)) & l3_lattices(k4_tdlat_1(A)) & v12_lattices(k4_tdlat_1(A)) & v10_lattices(k4_tdlat_1(A)) <-> v4_tdlat_3(A)))) # label(t51_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11525 (all A (-v3_struct_0(A) & v4_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_1(C,A) & C = u1_struct_0(B) -> v4_tdlat_3(B)))))))) # label(t39_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11526 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> ((all B (-v3_struct_0(B) & v1_borsuk_1(B,A) & m1_pre_topc(B,A) -> v4_tdlat_3(B))) -> v5_tdlat_3(A)))) # label(t40_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11527 (all A (-v3_struct_0(A) & v1_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (exists B (m1_pre_topc(B,A) & v1_tsep_1(B,A) & v1_tdlat_3(B) & v3_tdlat_3(B) & v1_borsuk_1(B,A) & v2_pre_topc(B) & v1_pre_topc(B))))) # label(rc4_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11528 (all A (l1_pre_topc(A) -> (v2_tdlat_3(A) -> v3_tdlat_3(A)))) # label(cc4_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11529 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) & v4_pre_topc(B,A) -> k6_pre_topc(A,k1_tops_1(A,B)) = k1_tops_1(A,k6_pre_topc(A,B))))))) # label(t8_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11530 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v4_tdlat_3(A) & v2_pre_topc(A) -> k4_tdlat_1(A) = k8_tdlat_1(A))) # label(t43_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11531 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (v4_tdlat_3(A) <-> -v3_struct_0(k4_tdlat_1(A)) & v17_lattices(k4_tdlat_1(A)) & l3_lattices(k4_tdlat_1(A)) & v10_lattices(k4_tdlat_1(A))))) # label(t55_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11532 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (v3_tdlat_3(A) <-> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) -> v3_pre_topc(B,A))))))) # label(t24_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11533 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (v4_tdlat_3(A) <-> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) -> v4_pre_topc(k1_tops_1(A,B),A))))))) # label(t29_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11534 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_tarski(C) = B -> k6_pre_topc(A,B) = u1_struct_0(A)))))) -> v2_tdlat_3(A)))) # label(t22_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11535 (exists A (l1_pre_topc(A) & v1_pre_topc(A) & v2_pre_topc(A) & v1_tdlat_3(A) & v2_tdlat_3(A) & v3_tdlat_3(A) & -v3_struct_0(A))) # label(rc3_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11536 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (v4_tdlat_3(A) <-> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_tops_1(B,A) -> k6_pre_topc(A,B) = k1_tops_1(A,B))))))) # label(t37_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11537 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (v3_tdlat_3(A) <-> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) -> k1_tops_1(A,B) = B)))))) # label(t26_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11538 (all A (l1_pre_topc(A) & v3_tdlat_3(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) -> v3_tdlat_3(B) & v2_pre_topc(B) & -v3_struct_0(B)))))) # label(cc9_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11539 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (B = k1_tarski(C) -> v3_pre_topc(k6_pre_topc(A,B),A)))))) -> v3_tdlat_3(A)))) # label(t27_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11540 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_tops_1(B,A) -> k1_tops_1(A,B) = k1_tops_1(A,k6_pre_topc(A,B)) & k6_pre_topc(A,k1_tops_1(A,B)) = k6_pre_topc(A,B)))))) # label(t11_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11541 (all A (l1_pre_topc(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,u1_pre_topc(A)) -> r2_hidden(k4_xboole_0(u1_struct_0(A),B),u1_pre_topc(A))))) <-> v3_tdlat_3(A)))) # label(d3_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11542 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v5_tdlat_3(A) -> (exists B (m1_pre_topc(B,A) & v4_tdlat_3(B) & v5_tdlat_3(B) & v2_pre_topc(B) & v1_pre_topc(B) & -v3_struct_0(B))))) # label(rc11_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11543 (all A (-v3_struct_0(A) & v2_pre_topc(A) & v4_tdlat_3(A) & l1_pre_topc(A) -> k3_tdlat_1(A) = k11_tdlat_1(A) & k10_tdlat_1(A) = k2_tdlat_1(A))) # label(t45_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11544 (all A (l1_pre_topc(A) -> (v3_tdlat_3(A) & v2_pre_topc(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v5_tdlat_3(A) & v2_pre_topc(A)))) # label(cc13_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11545 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (v4_tdlat_3(A) <-> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v6_tops_1(B,A) -> v5_tops_1(B,A)) & (v5_tops_1(B,A) -> v6_tops_1(B,A))))))) # label(t38_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11546 (all A (v2_pre_topc(A) & l1_pre_topc(A) & v2_tdlat_3(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> v2_pre_topc(B) & v3_tdlat_3(B) & v2_tdlat_3(B))))) # label(cc6_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11547 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (v1_tdlat_3(A) <-> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v3_pre_topc(B,A)))))) # label(t17_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11548 (all A (l1_pre_topc(A) -> (-v3_struct_0(A) & v2_pre_topc(A) & v5_tdlat_3(A) -> -v3_struct_0(A) & v4_tdlat_3(A) & v2_pre_topc(A)))) # label(cc12_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11549 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (v4_tdlat_3(A) <-> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_tops_1(B,A) -> k6_pre_topc(A,k1_tops_1(A,B)) = k1_tops_1(A,k6_pre_topc(A,B)))))))) # label(t36_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11550 (exists A (l1_pre_topc(A) & -v3_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & v5_tdlat_3(A))) # label(rc9_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11551 (all A (l1_pre_topc(A) -> (r2_hidden(u1_struct_0(A),u1_pre_topc(A)) & k2_tarski(k1_xboole_0,u1_struct_0(A)) = k1_pcomps_1(u1_struct_0(A)) & r2_hidden(k1_xboole_0,u1_pre_topc(A)) -> v1_tdlat_3(A) & v2_tdlat_3(A)))) # label(t13_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11552 (all A (v2_tdlat_3(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,u1_pre_topc(A)) -> r2_hidden(k4_xboole_0(u1_struct_0(A),B),u1_pre_topc(A))))))) # label(t15_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11553 (all A (v3_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v1_borsuk_1(B,A) -> v2_pre_topc(B) & v1_tsep_1(B,A)))))) # label(cc11_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11554 (all A (l1_pre_topc(A) -> (k1_pcomps_1(u1_struct_0(A)) = u1_pre_topc(A) <-> v1_tdlat_3(A)))) # label(d1_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11555 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> k6_pre_topc(A,B) = k1_tops_1(A,k6_pre_topc(A,B))))) <-> v4_tdlat_3(A)))) # label(t32_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11556 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_tops_1(B,A) -> v6_tops_1(B,A) & v5_tops_1(B,A)))) <-> v4_tdlat_3(A)))) # label(t35_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11557 (all A (v2_pre_topc(A) & l1_pre_topc(A) & v1_tdlat_3(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> v2_pre_topc(B) & v1_borsuk_1(B,A) & v1_tsep_1(B,A) & v3_tdlat_3(B) & v1_tdlat_3(B))))) # label(cc5_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11558 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (k4_tdlat_1(A) = k8_tdlat_1(A) -> v4_tdlat_3(A)))) # label(t52_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11559 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (B = k1_tarski(C) -> v3_pre_topc(B,A)))))) -> v1_tdlat_3(A)))) # label(t19_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11560 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (k1_pcomps_1(u1_struct_0(A)) = k2_tarski(k1_xboole_0,u1_struct_0(A)) -> v1_tdlat_3(A) & v2_tdlat_3(A)))) # label(t16_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11561 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v3_tdlat_3(A) -> (all B (m1_pre_topc(B,A) -> (v1_tsep_1(B,A) -> v1_borsuk_1(B,A) & v2_pre_topc(B)))))) # label(cc10_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11562 $T # label(t5_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11563 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (v4_tdlat_3(A) <-> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) & v4_pre_topc(C,A) & u1_struct_0(A) = k4_subset_1(u1_struct_0(A),B,C) -> k4_subset_1(u1_struct_0(A),k1_tops_1(A,B),k1_tops_1(A,C)) = u1_struct_0(A))))))))) # label(t31_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11564 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> v3_pre_topc(k6_pre_topc(A,B),A)))) <-> v4_tdlat_3(A)))) # label(d4_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11565 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v4_tdlat_3(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_tdlat_2(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k4_tdlat_1(A)))) -> (B = C -> k6_pre_topc(A,k5_setfam_1(u1_struct_0(A),B)) = k15_lattice3(k4_tdlat_1(A),C))))))))) # label(t49_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11566 (all A (l1_pre_topc(A) -> (v2_tdlat_3(A) <-> u1_pre_topc(A) = k2_tarski(k1_xboole_0,u1_struct_0(A))))) # label(d2_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11567 (all A (l1_pre_topc(A) -> (v1_tdlat_3(A) -> v2_pre_topc(A)))) # label(cc1_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11568 (all A (v2_pre_topc(A) & l1_pre_topc(A) & v4_tdlat_3(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_tdlat_2(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k4_tdlat_1(A)))) -> (B = C -> (k1_xboole_0 = C -> k2_pre_topc(A) = k16_lattice3(k4_tdlat_1(A),C)) & (C != k1_xboole_0 -> k1_tops_1(A,k6_setfam_1(u1_struct_0(A),B)) = k16_lattice3(k4_tdlat_1(A),C)))))))))) # label(t50_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11569 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v4_tdlat_3(A) -> (all B (m1_subset_1(B,k1_tdlat_1(A)) -> (all C (m1_subset_1(C,k1_tdlat_1(A)) -> k1_binop_1(k3_tdlat_1(A),B,C) = k3_xboole_0(B,C) & k1_binop_1(k2_tdlat_1(A),B,C) = k2_xboole_0(B,C))))))) # label(t47_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11570 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v4_pre_topc(B,A))) <-> v1_tdlat_3(A)))) # label(t18_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11571 (exists A (v2_pre_topc(A) & v3_tdlat_3(A) & v1_pre_topc(A) & l1_pre_topc(A))) # label(rc6_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11572 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (v2_tdlat_3(A) <-> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(B != u1_struct_0(A) & B != k1_xboole_0 & v3_pre_topc(B,A))))))) # label(t20_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11573 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (k12_tdlat_1(A) = k8_tdlat_1(A) -> v4_tdlat_3(A)))) # label(t54_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11574 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> B = k6_pre_topc(A,B)))) <-> v3_tdlat_3(A)))) # label(t25_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11575 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_tops_1(B,A) & r1_tarski(k6_pre_topc(A,k1_tops_1(A,B)),k1_tops_1(A,k6_pre_topc(A,B))) -> v5_tops_1(B,A) & v6_tops_1(B,A)))))) # label(t9_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11576 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> ((all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> v4_tdlat_3(B))) <-> v5_tdlat_3(A)))) # label(d5_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11577 (all A (v2_pre_topc(A) & l1_pre_topc(A) & v5_tdlat_3(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) -> -v3_struct_0(B) & v4_tdlat_3(B) & v5_tdlat_3(B) & v2_pre_topc(B)))))) # label(cc15_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11578 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) & v3_pre_topc(B,A) <-> k1_tops_1(A,B) = k6_pre_topc(A,B)))))) # label(t7_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11579 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v4_tdlat_3(A) & v2_pre_topc(A) -> k9_tdlat_1(A) = k1_tdlat_1(A))) # label(t44_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11580 (all A (l1_pre_topc(A) -> (v2_tdlat_3(A) & v2_pre_topc(A) -> v3_tdlat_3(A) & v2_pre_topc(A)))) # label(cc8_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11581 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v4_tdlat_3(A) & v2_pre_topc(A) -> k3_tdlat_1(A) = k7_tdlat_1(A) & k2_tdlat_1(A) = k6_tdlat_1(A))) # label(t42_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11582 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(k6_pre_topc(A,k1_tops_1(A,B)),k1_tops_1(A,k6_pre_topc(A,B))) & v4_tops_1(B,A) -> v3_pre_topc(B,A) & v4_pre_topc(B,A)))))) # label(t10_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11583 (all A (-v3_struct_0(A) & v2_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (exists B (v2_tdlat_3(B) & v3_tdlat_3(B) & v2_pre_topc(B) & m1_pre_topc(B,A))))) # label(rc5_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11584 (all A (l1_pre_topc(A) -> (v1_tdlat_3(A) & v2_pre_topc(A) -> v2_pre_topc(A) & v3_tdlat_3(A)))) # label(cc7_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11585 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v3_tdlat_3(A) & v2_pre_topc(A) -> (exists B (m1_pre_topc(B,A) & -v3_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & v3_tdlat_3(B))))) # label(rc7_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11586 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B)) = k3_subset_1(u1_struct_0(A),k1_tops_1(A,B)))))) # label(t3_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11587 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(A) = k4_subset_1(u1_struct_0(A),B,C) -> (v4_pre_topc(B,A) -> k4_subset_1(u1_struct_0(A),B,k1_tops_1(A,C)) = u1_struct_0(A)) & (v4_pre_topc(C,A) -> u1_struct_0(A) = k4_subset_1(u1_struct_0(A),k1_tops_1(A,B),C))))))))) # label(t6_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11588 (all A (l1_pre_topc(A) -> (v2_tdlat_3(A) -> v2_pre_topc(A)))) # label(cc2_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11589 (all A (v4_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> k12_tdlat_1(A) = k4_tdlat_1(A))) # label(t46_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11590 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) -> k6_pre_topc(A,k1_tops_1(A,B)) = k1_tops_1(A,B)))) <-> v4_tdlat_3(A)))) # label(t33_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11591 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B)) = k1_tops_1(A,k3_subset_1(u1_struct_0(A),B)))))) # label(t4_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11592 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (v3_tdlat_3(A) & (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_tarski(C) = B -> v4_pre_topc(B,A)))))) <-> v1_tdlat_3(A)))) # label(t28_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11593 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) & r1_xboole_0(B,C) & v3_pre_topc(C,A) -> r1_xboole_0(k6_pre_topc(A,B),k6_pre_topc(A,C))))))) <-> v4_tdlat_3(A)))) # label(t30_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11594 (all A (v1_tdlat_3(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r2_hidden(k4_xboole_0(u1_struct_0(A),B),u1_pre_topc(A)))))) # label(t14_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11595 (all A (v2_pre_topc(A) & l1_pre_topc(A) & v4_tdlat_3(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v1_tsep_1(B,A) & -v3_struct_0(B) -> v2_pre_topc(B) & v4_tdlat_3(B) & -v3_struct_0(B)))))) # label(cc14_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11596 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (k12_tdlat_1(A) = k4_tdlat_1(A) -> v4_tdlat_3(A)))) # label(t53_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11597 (all A (l1_pre_topc(A) -> (v1_tdlat_3(A) -> v3_tdlat_3(A)))) # label(cc3_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11598 (all A (v2_pre_topc(A) & v4_tdlat_3(A) & l1_pre_topc(A) & -v3_struct_0(A) -> k5_tdlat_1(A) = k1_tdlat_1(A))) # label(t41_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11599 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (v4_tdlat_3(A) <-> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_tops_1(B,A) -> v3_pre_topc(B,A) & v4_pre_topc(B,A))))))) # label(t34_tdlat_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11600 (all A (l1_unialg_1(A) -> m2_finseq_1(u1_unialg_1(A),k4_partfun1(k13_finseq_1(u1_struct_0(A)),u1_struct_0(A))))) # label(dt_u1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11601 (all A all B (m1_finseq_1(B,k4_partfun1(k13_finseq_1(A),A)) -> (all C all D (g1_unialg_1(A,B) = g1_unialg_1(C,D) -> B = D & A = C)))) # label(free_g1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11602 (exists A l1_unialg_1(A)) # label(existence_l1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11603 (all A (-v1_xboole_0(A) -> (exists B (v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v5_unialg_1(B,A) & v4_unialg_1(B,A) & m1_finseq_1(B,k4_partfun1(k13_finseq_1(A),A)))))) # label(rc4_unialg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11604 (exists A (v3_unialg_1(A) & -v3_struct_0(A) & l1_unialg_1(A))) # label(rc3_unialg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11605 $T # label(d6_unialg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11606 (all A (l1_unialg_1(A) -> (v3_unialg_1(A) -> g1_unialg_1(u1_struct_0(A),u1_unialg_1(A)) = A))) # label(abstractness_v3_unialg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11607 (all A (l1_unialg_1(A) & v8_unialg_1(A) -> v1_relat_1(u1_unialg_1(A)) & v1_funct_1(u1_unialg_1(A)) & v1_finseq_1(u1_unialg_1(A)) & v2_relat_1(u1_unialg_1(A)) & -v1_xboole_0(u1_unialg_1(A)))) # label(fc4_unialg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11608 (all A all B (m2_relset_1(B,k13_finseq_1(A),A) & v1_funct_1(B) -> ((all C (m2_finseq_1(C,A) -> (all D (m2_finseq_1(D,A) -> (k3_finseq_1(D) = k3_finseq_1(C) & r2_hidden(C,k1_relat_1(B)) -> r2_hidden(D,k1_relat_1(B))))))) <-> v2_unialg_1(B,A)))) # label(d2_unialg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11609 (all A (-v1_xboole_0(A) -> (exists B (v1_relat_1(B) & v1_funct_1(B) & v2_unialg_1(B,A) & v1_unialg_1(B,A) & -v1_xboole_0(B) & m1_relset_1(B,k13_finseq_1(A),A))))) # label(rc1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11610 (all A (v6_unialg_1(A) & l1_unialg_1(A) -> v1_relat_1(u1_unialg_1(A)) & v1_funct_1(u1_unialg_1(A)) & v1_finseq_1(u1_unialg_1(A)) & v4_unialg_1(u1_unialg_1(A),u1_struct_0(A)))) # label(fc2_unialg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11611 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> m1_subset_1(k2_funcop_1(k1_tarski(k6_finseq_1(A)),B),k4_partfun1(k13_finseq_1(A),A)))))) # label(t3_unialg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11612 (all A (l1_unialg_1(A) -> (v4_unialg_1(u1_unialg_1(A),u1_struct_0(A)) <-> v6_unialg_1(A)))) # label(d7_unialg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11613 (all A all B (v1_funct_1(B) & m2_relset_1(B,k13_finseq_1(A),A) -> -(k1_relat_1(B) != k1_xboole_0 & v1_xboole_0(B)) & -(k1_xboole_0 = k1_relat_1(B) & -v1_xboole_0(B)))) # label(t1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11614 (all A all B (m2_finseq_1(B,k4_partfun1(k13_finseq_1(A),A)) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_relset_1(D,k13_finseq_1(A),A) & v1_funct_1(D) -> (D = k1_funct_1(B,C) & r2_hidden(C,k4_finseq_1(B)) -> v2_unialg_1(D,A)))))) <-> v5_unialg_1(B,A)))) # label(d5_unialg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11615 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & v1_funct_1(B) & v1_unialg_1(B,A) & m2_relset_1(B,k13_finseq_1(A),A) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (C = k2_unialg_1(A,B) <-> (all D (m2_finseq_1(D,A) -> (r2_hidden(D,k1_relat_1(B)) -> C = k3_finseq_1(D))))))))))) # label(d10_unialg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11616 (exists A (v3_unialg_1(A) & l1_unialg_1(A))) # label(rc2_unialg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11617 (all A (-v3_struct_0(A) & v6_unialg_1(A) & v8_unialg_1(A) & l1_unialg_1(A) -> m2_finseq_1(k3_unialg_1(A),k5_numbers))) # label(dt_k3_unialg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11618 (all A all B (m1_finseq_1(B,k4_partfun1(k13_finseq_1(A),A)) -> v3_unialg_1(g1_unialg_1(A,B)) & l1_unialg_1(g1_unialg_1(A,B)))) # label(dt_g1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11619 (all A (l1_unialg_1(A) -> (k1_xboole_0 != u1_unialg_1(A) & v2_relat_1(u1_unialg_1(A)) <-> v8_unialg_1(A)))) # label(d9_unialg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11620 $T # label(d3_unialg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11621 (all A all B (-v1_xboole_0(A) & m1_finseq_1(B,k4_partfun1(k13_finseq_1(A),A)) -> -v3_struct_0(g1_unialg_1(A,B)) & v3_unialg_1(g1_unialg_1(A,B)))) # label(fc1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11622 (all A all B (m2_relset_1(B,k13_finseq_1(A),A) & v1_funct_1(B) -> ((all C (m2_finseq_1(C,A) -> (all D (m2_finseq_1(D,A) -> (r2_hidden(D,k1_relat_1(B)) & r2_hidden(C,k1_relat_1(B)) -> k3_finseq_1(C) = k3_finseq_1(D)))))) <-> v1_unialg_1(B,A)))) # label(d1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11623 (all A (v8_unialg_1(A) & l1_unialg_1(A) & v6_unialg_1(A) & -v3_struct_0(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(B,k4_finseq_1(u1_unialg_1(A))) -> m2_relset_1(k1_funct_1(u1_unialg_1(A),B),k13_finseq_1(u1_struct_0(A)),u1_struct_0(A)) & v1_funct_1(k1_funct_1(u1_unialg_1(A),B))))))) # label(t5_unialg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11624 (all A (l1_unialg_1(A) -> l1_struct_0(A))) # label(dt_l1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11625 (all A (-v3_struct_0(A) & v6_unialg_1(A) & l1_unialg_1(A) & v8_unialg_1(A) -> (all B (m2_finseq_1(B,k5_numbers) -> (k3_unialg_1(A) = B <-> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(C,k4_finseq_1(B)) -> (all D (m2_relset_1(D,k13_finseq_1(u1_struct_0(A)),u1_struct_0(A)) & v1_unialg_1(D,u1_struct_0(A)) & v1_funct_1(D) & -v1_xboole_0(D) -> (D = k1_funct_1(u1_unialg_1(A),C) -> k1_funct_1(B,C) = k2_unialg_1(u1_struct_0(A),D))))))) & k3_finseq_1(B) = k3_finseq_1(u1_unialg_1(A))))))) # label(d11_unialg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11626 (all A (l1_unialg_1(A) -> (v5_unialg_1(u1_unialg_1(A),u1_struct_0(A)) <-> v7_unialg_1(A)))) # label(d8_unialg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11627 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> v1_unialg_1(k2_funcop_1(k1_tarski(k6_finseq_1(A)),B),A) & m2_relset_1(k2_funcop_1(k1_tarski(k6_finseq_1(A)),B),k13_finseq_1(A),A) & v2_unialg_1(k2_funcop_1(k1_tarski(k6_finseq_1(A)),B),A) & v1_funct_1(k2_funcop_1(k1_tarski(k6_finseq_1(A)),B)) & -v1_xboole_0(k2_funcop_1(k1_tarski(k6_finseq_1(A)),B)))))) # label(t2_unialg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11628 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,k4_partfun1(k13_finseq_1(A),A)) -> (C = k2_funcop_1(k1_tarski(k6_finseq_1(A)),B) -> v2_relat_1(k1_unialg_1(A,C)) & v5_unialg_1(k1_unialg_1(A,C),A) & v4_unialg_1(k1_unialg_1(A,C),A)))))))) # label(t4_unialg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11629 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,k4_partfun1(k13_finseq_1(A),A)) -> k1_unialg_1(A,B) = k5_finseq_1(B))) # label(redefinition_k1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11630 (all A all B (-v1_xboole_0(B) & m1_relset_1(B,k13_finseq_1(A),A) & v1_unialg_1(B,A) & v1_funct_1(B) & -v1_xboole_0(A) -> m2_subset_1(k2_unialg_1(A,B),k1_numbers,k5_numbers))) # label(dt_k2_unialg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11631 (all A (v7_unialg_1(A) & l1_unialg_1(A) -> v1_relat_1(u1_unialg_1(A)) & v1_funct_1(u1_unialg_1(A)) & v5_unialg_1(u1_unialg_1(A),u1_struct_0(A)) & v1_finseq_1(u1_unialg_1(A)))) # label(fc3_unialg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11632 (all A all B (m2_finseq_1(B,k4_partfun1(k13_finseq_1(A),A)) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (v1_funct_1(D) & m2_relset_1(D,k13_finseq_1(A),A) -> (D = k1_funct_1(B,C) & r2_hidden(C,k4_finseq_1(B)) -> v1_unialg_1(D,A)))))) <-> v4_unialg_1(B,A)))) # label(d4_unialg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11633 (exists A (v6_unialg_1(A) & v8_unialg_1(A) & v7_unialg_1(A) & v3_unialg_1(A) & -v3_struct_0(A) & l1_unialg_1(A))) # label(rc5_unialg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11634 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,k4_partfun1(k13_finseq_1(A),A)) -> m2_finseq_1(k1_unialg_1(A,B),k4_partfun1(k13_finseq_1(A),A)))) # label(dt_k1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11635 (exists A (l1_vectsp_1(A) & -v3_struct_0(A) & v7_group_1(A) & v6_vectsp_1(A) & v13_monoid_0(A) & v16_monoid_0(A) & v17_monoid_0(A) & v15_monoid_0(A) & v14_monoid_0(A) & v12_monoid_0(A) & v11_monoid_0(A) & v10_monoid_0(A) & v2_monoid_0(A) & v1_monoid_0(A) & v1_vectsp_2(A) & v8_vectsp_1(A) & v1_vectsp_1(A) & v4_group_1(A) & v3_group_1(A) & v2_group_1(A))) # label(rc4_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11636 (all A all B (m1_monoid_0(B,k15_monoid_0(A)) & v1_vectsp_2(B) & v1_vectsp_1(B) & -v3_struct_0(B) -> k16_monoid_0(A) = B)) # label(d38_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11637 (all A (m1_subset_1(A,u1_struct_0(k5_monoid_0)) <-> m1_subset_1(A,k1_numbers))) # label(t41_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11638 (all A (l1_group_1(A) & v16_monoid_0(A) & -v3_struct_0(A) -> (all B (m1_monoid_0(B,A) -> v15_monoid_0(B) & v16_monoid_0(B) & v14_monoid_0(B) & -v3_struct_0(B))))) # label(cc20_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11639 (all A (m1_subset_1(A,u1_struct_0(k5_monoid_0)) -> (all B (m1_subset_1(B,u1_struct_0(k5_monoid_0)) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_subset_1(D,k1_numbers) -> (D = B & A = C -> k9_binop_2(C,D) = k10_group_1(k5_monoid_0,A,B)))))))))) # label(t40_monoid_0_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11640 (all A (-v3_struct_0(A) & l1_group_1(A) -> (all B (m2_monoid_0(B,A) & -v3_struct_0(B) -> (v17_monoid_0(A) & r2_hidden(k3_binop_1(u1_struct_0(A),u1_group_1(A)),u1_struct_0(B)) -> v17_monoid_0(B)))))) # label(t38_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11641 (all A (m2_monoid_0(A,k9_monoid_0) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,k1_numbers) -> (all E (m1_subset_1(E,k1_numbers) -> (E = C & B = D -> k10_group_1(A,B,C) = k11_binop_2(D,E)))))))))))) # label(t58_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11642 (all A (v1_vectsp_2(A) & m1_monoid_0(A,k10_monoid_0) & v1_vectsp_1(A) & -v3_struct_0(A) -> k11_monoid_0 = A)) # label(d32_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11643 (all A (v1_monoid_0(A) & l1_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> v1_relat_1(B) & v1_funct_1(B))))) # label(cc1_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11644 (all A (-v1_xboole_0(A) -> k1_xboole_0 = k3_binop_1(u1_struct_0(k12_monoid_0(A)),u1_group_1(k12_monoid_0(A))))) # label(t69_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11645 (all A (u1_struct_0(k19_monoid_0(A)) = k1_funct_2(A,A) & k1_realset1(k17_monoid_0(A),k1_funct_2(A,A)) = u1_group_1(k19_monoid_0(A)) & k6_partfun1(A) = u1_vectsp_1(k19_monoid_0(A)))) # label(t85_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11646 (all A (-v1_xboole_0(A) -> u1_struct_0(k13_monoid_0(A)) = k3_finseq_2(A) & k14_monoid_0(A) = u1_group_1(k13_monoid_0(A)) & k1_xboole_0 = u1_vectsp_1(k13_monoid_0(A)))) # label(t70_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11647 (all A (l1_group_1(A) -> (-v3_struct_0(A) & v13_monoid_0(A) -> -v3_struct_0(A) & v12_monoid_0(A) & v11_monoid_0(A)))) # label(cc7_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11648 (all A (m1_struct_0(A,f1_s3_monoid_0,f2_s3_monoid_0) -> (all B (m1_struct_0(B,f1_s3_monoid_0,f2_s3_monoid_0) -> r2_hidden(k1_group_1(f1_s3_monoid_0,A,B),f2_s3_monoid_0))))) & r2_hidden(u1_vectsp_1(f1_s3_monoid_0),f2_s3_monoid_0) -> (exists A (v1_vectsp_1(A) & m3_monoid_0(A,f1_s3_monoid_0) & u1_struct_0(A) = f2_s3_monoid_0 & -v3_struct_0(A))) # label(s3_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11649 (all A (l1_group_1(A) & -v3_struct_0(A) -> (v1_binop_1(u1_group_1(A),u1_struct_0(A)) <-> v7_group_1(A)))) # label(d11_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11650 (all A (v2_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (exists B (m1_monoid_0(B,A) & -v3_struct_0(B) & v2_group_1(B) & v1_vectsp_2(B) & v8_vectsp_1(B) & v6_vectsp_1(B) & v1_vectsp_1(B))))) # label(rc6_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11651 (all A (-v1_xboole_0(A) -> -v3_struct_0(k13_monoid_0(A)) & v1_vectsp_2(k13_monoid_0(A)) & m1_monoid_0(k13_monoid_0(A),k12_monoid_0(A)) & v1_vectsp_1(k13_monoid_0(A)))) # label(dt_k13_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11652 (all A (-v3_struct_0(A) & l1_group_1(A) -> (v11_monoid_0(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (C = k1_group_1(A,D,B) & m1_subset_1(D,u1_struct_0(A))))))))))) # label(t10_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11653 (all A (-v3_struct_0(A) & m2_monoid_0(A,k5_monoid_0) & v2_group_1(A) -> np__0 = k3_binop_1(u1_struct_0(A),u1_group_1(A)))) # label(t44_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11654 (all A (l1_group_1(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k1_group_1(A,B,C) = k1_group_1(A,B,D) -> C = D))))))) <-> v14_monoid_0(A)))) # label(t13_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11655 (all A (m1_struct_0(A,f1_s1_monoid_0,f2_s1_monoid_0) -> (all B (m1_struct_0(B,f1_s1_monoid_0,f2_s1_monoid_0) -> r2_hidden(k1_group_1(f1_s1_monoid_0,A,B),f2_s1_monoid_0))))) -> (exists A (v1_group_1(A) & m2_monoid_0(A,f1_s1_monoid_0) & u1_struct_0(A) = f2_s1_monoid_0 & -v3_struct_0(A))) # label(s1_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11656 (all A (-v1_xboole_0(A) -> (all B (m2_monoid_0(B,k12_monoid_0(A)) & -v3_struct_0(B) -> (m1_subset_1(k1_xboole_0,u1_struct_0(B)) -> k3_binop_1(u1_struct_0(B),u1_group_1(B)) = k1_xboole_0 & v2_group_1(B)))))) # label(t74_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11657 (all A (-v1_xboole_0(A) -> v1_funct_2(k14_monoid_0(A),k2_zfmisc_1(k3_finseq_2(A),k3_finseq_2(A)),k3_finseq_2(A)) & m2_relset_1(k14_monoid_0(A),k2_zfmisc_1(k3_finseq_2(A),k3_finseq_2(A)),k3_finseq_2(A)) & v1_funct_1(k14_monoid_0(A)))) # label(dt_k14_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.75 11658 (all A all B all C (m1_finseq_1(B,A) & m1_finseq_1(C,A) -> m2_finseq_2(k1_monoid_0(A,B,C),A,k3_finseq_2(A)))) # label(dt_k1_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11659 (all A (l1_vectsp_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m3_monoid_0(B,A) -> (all C (-v3_struct_0(C) & m3_monoid_0(C,A) -> (u1_struct_0(C) = u1_struct_0(B) -> g1_vectsp_1(u1_struct_0(B),u1_group_1(B),u1_vectsp_1(B)) = g1_vectsp_1(u1_struct_0(C),u1_group_1(C),u1_vectsp_1(C))))))))) # label(t29_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11660 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (v7_monoid_0(B,A) <-> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (k2_binop_1(A,A,A,B,E,C) = k2_binop_1(A,A,A,B,D,C) -> E = D)))))))))))) # label(d7_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11661 (all A (l1_group_1(A) -> (-v3_struct_0(A) & v15_monoid_0(A) & v14_monoid_0(A) -> -v3_struct_0(A) & v16_monoid_0(A)))) # label(cc10_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11662 (all A (l1_group_1(A) -> (v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v13_monoid_0(A)))) # label(cc5_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11663 (all A all B (-v3_struct_0(B) & m2_monoid_0(B,k15_monoid_0(A)) -> (m1_subset_1(k6_partfun1(A),u1_struct_0(B)) -> k6_partfun1(A) = k3_binop_1(u1_struct_0(B),u1_group_1(B)) & v2_group_1(B)))) # label(t80_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11664 (all A all B (l1_group_1(A) & m1_monoid_0(B,A) -> (all C (m4_monoid_0(C,A,B) -> m2_monoid_0(C,A))))) # label(dt_m4_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11665 (all A (l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_monoid_0(B,A) -> -v3_struct_0(B) & v4_group_1(B))))) # label(cc17_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11666 (all A all B (m3_monoid_0(B,A) & l1_group_1(A) -> (all C (m7_monoid_0(C,A,B) <-> m3_monoid_0(C,B))))) # label(redefinition_m7_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11667 (all A all B (v1_vectsp_1(B) & v1_vectsp_2(B) & m1_monoid_0(B,k18_monoid_0(A)) -> k19_monoid_0(A) = B)) # label(d41_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11668 (all A all B all C (m1_relset_1(B,A,A) & v1_funct_2(C,A,A) & m1_relset_1(C,A,A) & v1_funct_1(C) & v1_funct_2(B,A,A) & v1_funct_1(B) -> k5_relat_1(B,C) = k2_monoid_0(A,B,C))) # label(redefinition_k2_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11669 (all A (-v3_struct_0(A) & l1_group_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> B = k1_group_1(A,B,B))) <-> v10_monoid_0(A)))) # label(t9_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11670 (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) -> (v3_monoid_0(B,A) <-> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (exists E (k2_binop_1(A,A,A,B,E,C) = D & m1_subset_1(E,A)))))))))))) # label(d3_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11671 (all A (-v3_struct_0(A) & l1_group_1(A) -> (v13_monoid_0(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D ((exists E (k1_group_1(A,E,B) = C & C = k1_group_1(A,B,D) & m1_subset_1(E,u1_struct_0(A)))) & m1_subset_1(D,u1_struct_0(A))))))))))) # label(t12_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11672 (all A (-v3_struct_0(A) & l1_group_1(A) -> ((exists B (m1_subset_1(B,u1_struct_0(A)) & (all C (m1_subset_1(C,u1_struct_0(A)) -> C = k1_group_1(A,C,B) & C = k1_group_1(A,B,C))))) <-> v2_group_1(A)))) # label(t6_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11673 (all A all B (m1_subset_1(A,u1_struct_0(k15_monoid_0(B))) <-> m2_relset_1(A,B,B) & v1_funct_1(A))) # label(t77_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11674 (all A (l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_monoid_0(B,A) -> (v2_group_1(A) -> v2_group_1(B)) & (v13_monoid_0(A) -> v13_monoid_0(B)) & (v16_monoid_0(A) -> v16_monoid_0(B)) & (v17_monoid_0(A) -> v17_monoid_0(B)) & (v4_group_1(A) -> v4_group_1(B)) & (v7_group_1(A) -> v7_group_1(B)))))) # label(t21_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11675 (all A all B (m3_monoid_0(B,A) & l1_group_1(A) -> (exists C m7_monoid_0(C,A,B)))) # label(existence_m7_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11676 $T # label(t7_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11677 (all A (-v3_struct_0(A) & v17_monoid_0(A) & l1_group_1(A) -> (all B (m1_monoid_0(B,A) -> v17_monoid_0(B) & -v3_struct_0(B))))) # label(cc21_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11678 (all A all B (l1_group_1(A) & m1_monoid_0(B,A) -> (exists C m4_monoid_0(C,A,B)))) # label(existence_m4_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11679 (all A (l1_group_1(A) & -v3_struct_0(A) -> (v1_setwiseo(u1_group_1(A),u1_struct_0(A)) <-> v2_group_1(A)))) # label(d10_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11680 (all A (v7_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m2_monoid_0(B,A) -> (-v3_struct_0(B) -> v7_group_1(B) & -v3_struct_0(B)))))) # label(cc27_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11681 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> ((all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (exists E (m1_subset_1(E,A) & (exists F (m1_subset_1(F,A) & k2_binop_1(A,A,A,B,C,E) = D & D = k2_binop_1(A,A,A,B,F,C))))))))) <-> v5_monoid_0(B,A)))))) # label(d5_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11682 (all A (l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_monoid_0(B,A) -> -v3_struct_0(B))))) # label(cc13_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11683 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (v3_monoid_0(B,A) & v4_monoid_0(B,A) <-> v5_monoid_0(B,A)))))) # label(t1_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11684 (all A (l1_group_1(A) -> (all B (l1_vectsp_1(B) -> (m3_monoid_0(B,A) <-> (all C (l1_vectsp_1(C) -> (A = C -> u1_vectsp_1(C) = u1_vectsp_1(B)))) & r1_tarski(u1_group_1(B),u1_group_1(A))))))) # label(d24_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11685 (all A k6_partfun1(A) = k3_binop_1(u1_struct_0(k15_monoid_0(A)),u1_group_1(k15_monoid_0(A)))) # label(t78_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11686 (all A (-v3_struct_0(A) & l1_group_1(A) -> (all B (m2_monoid_0(B,A) & -v3_struct_0(B) -> (all C (m2_monoid_0(C,A) & -v3_struct_0(C) -> (r1_tarski(u1_struct_0(B),u1_struct_0(C)) -> m5_monoid_0(B,A,C)))))))) # label(t30_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11687 (all A (-v3_struct_0(A) & m2_monoid_0(A,k5_monoid_0) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,k1_numbers) -> (all E (m1_subset_1(E,k1_numbers) -> (E = C & B = D -> k10_group_1(A,B,C) = k9_binop_2(D,E)))))))))))) # label(t43_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11688 (all A (l1_group_1(A) -> (exists B (m2_monoid_0(B,A) & v1_group_1(B))))) # label(rc7_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11689 (all A (-v1_xboole_0(A) -> (all B (v2_monoid_0(B) & v16_monoid_0(B) & v17_monoid_0(B) & l1_group_1(B) & v4_group_1(B) & v2_group_1(B) & v1_group_1(B) & -v3_struct_0(B) -> (k12_monoid_0(A) = B <-> k3_finseq_2(A) = u1_struct_0(B) & (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k7_finseq_1(C,D) = k4_monoid_0(B,C,D)))))))))) # label(d34_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11690 (all A k17_monoid_0(A) = u1_group_1(k15_monoid_0(A))) # label(d39_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11691 (all A (v7_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m3_monoid_0(B,A) -> (-v3_struct_0(B) -> -v3_struct_0(B) & v7_group_1(B)))))) # label(cc28_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11692 (all A (l1_group_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m2_monoid_0(B,A) -> u1_group_1(B) = k1_realset1(u1_group_1(A),u1_struct_0(B)))))) # label(t26_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11693 (all A (-v3_struct_0(A) & l1_group_1(A) & v16_monoid_0(A) -> (all B (m2_monoid_0(B,A) -> (-v3_struct_0(B) -> v16_monoid_0(B) & v15_monoid_0(B) & v14_monoid_0(B) & -v3_struct_0(B)))))) # label(cc33_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11694 (all A all B (v1_funct_2(B,k2_zfmisc_1(k1_tarski(A),k1_tarski(A)),k1_tarski(A)) & m2_relset_1(B,k2_zfmisc_1(k1_tarski(A),k1_tarski(A)),k1_tarski(A)) & v1_funct_1(B) -> k2_funcop_1(k1_tarski(k4_tarski(A,A)),A) = B & v1_binop_1(B,k1_tarski(A)) & v9_monoid_0(B,k1_tarski(A)) & v8_monoid_0(B,k1_tarski(A)) & v5_monoid_0(B,k1_tarski(A)) & v3_binop_1(B,k1_tarski(A)) & v2_binop_1(B,k1_tarski(A)) & v1_setwiseo(B,k1_tarski(A)))) # label(t3_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11695 (all A (l1_vectsp_1(A) & -v3_struct_0(A) -> (v1_vectsp_2(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k1_group_1(A,u1_vectsp_1(A),B) & k1_group_1(A,B,u1_vectsp_1(A)) = B))))) # label(t18_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11696 (all A (-v1_xboole_0(A) -> (all B (-v3_struct_0(B) & m2_monoid_0(B,k12_monoid_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k7_finseq_1(C,D) = k4_monoid_0(B,C,D))))))))) # label(t72_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11697 (all A (l1_group_1(A) & -v3_struct_0(A) -> (exists B (-v3_struct_0(B) & v1_group_1(B) & m2_monoid_0(B,A))))) # label(rc8_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11698 (all A (-v3_struct_0(A) & l1_group_1(A) -> (all B (m2_monoid_0(B,A) & -v3_struct_0(B) -> (all C (m3_monoid_0(C,A) & -v3_struct_0(C) -> r1_tarski(u1_struct_0(B),u1_struct_0(A)) & r1_tarski(u1_struct_0(C),u1_struct_0(A)))))))) # label(t25_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11699 (all A (-v3_struct_0(A) & l1_group_1(A) -> (all B (m1_monoid_0(B,A) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (all F (m1_subset_1(F,u1_struct_0(A)) -> (F = D & E = C -> k1_group_1(B,C,D) = k1_group_1(A,E,F)))))))))) & u1_group_1(B) = u1_group_1(A) & u1_struct_0(A) = u1_struct_0(B))))) # label(t20_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11700 (all A (-v3_struct_0(A) & l1_group_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k1_group_1(A,D,B) = k1_group_1(A,C,B) -> C = D))))))) <-> v15_monoid_0(A)))) # label(t14_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11701 (all A (-v3_struct_0(A) & l1_group_1(A) -> (all B (m2_monoid_0(B,A) & -v3_struct_0(B) -> (v7_group_1(A) -> v7_group_1(B)))))) # label(t34_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11702 (all A (-v3_struct_0(A) & l1_group_1(A) -> (v12_monoid_0(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (C = k1_group_1(A,B,D) & m1_subset_1(D,u1_struct_0(A))))))))))) # label(t11_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11703 (all A (v1_funct_2(k17_monoid_0(A),k2_zfmisc_1(k4_partfun1(A,A),k4_partfun1(A,A)),k4_partfun1(A,A)) & m2_relset_1(k17_monoid_0(A),k2_zfmisc_1(k4_partfun1(A,A),k4_partfun1(A,A)),k4_partfun1(A,A)) & v1_funct_1(k17_monoid_0(A)))) # label(dt_k17_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11704 (all A (-v3_struct_0(A) & l1_group_1(A) -> (v11_monoid_0(A) <-> v3_monoid_0(u1_group_1(A),u1_struct_0(A))))) # label(d14_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11705 (all A (l1_struct_0(A) -> (v2_monoid_0(A) -> v1_monoid_0(A)))) # label(cc2_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11706 (all A (-v3_struct_0(A) & l1_vectsp_1(A) & v17_monoid_0(A) & v1_vectsp_2(A) -> (all B (m3_monoid_0(B,A) & -v3_struct_0(B) -> v17_monoid_0(B))))) # label(t39_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11707 (all A all B (v1_funct_2(A,B,B) & m2_relset_1(A,B,B) & v1_funct_1(A) <-> m1_subset_1(A,u1_struct_0(k18_monoid_0(B))))) # label(t82_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11708 (all A (-v3_struct_0(A) & l1_group_1(A) -> (exists B (-v3_struct_0(B) & v1_vectsp_1(B) & m3_monoid_0(B,A))))) # label(rc11_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11709 (all A all B (-v3_struct_0(B) & v2_group_1(B) & m2_monoid_0(B,k15_monoid_0(A)) & v1_group_1(B) -> (k1_funct_2(A,A) = u1_struct_0(B) <-> k18_monoid_0(A) = B))) # label(d40_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11710 (all A (v2_group_1(k18_monoid_0(A)) & m2_monoid_0(k18_monoid_0(A),k15_monoid_0(A)) & v1_group_1(k18_monoid_0(A)) & -v3_struct_0(k18_monoid_0(A)))) # label(dt_k18_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11711 (all A all B all C (m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_group_1(A) & -v3_struct_0(A) -> m1_subset_1(k4_monoid_0(A,B,C),u1_struct_0(A)))) # label(dt_k4_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11712 (exists A (v1_monoid_0(A) & l1_struct_0(A))) # label(rc1_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11713 (all A (-v3_struct_0(A) & v16_monoid_0(A) & l1_group_1(A) -> (all B (m3_monoid_0(B,A) -> (-v3_struct_0(B) -> v16_monoid_0(B) & v15_monoid_0(B) & v14_monoid_0(B) & -v3_struct_0(B)))))) # label(cc34_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11714 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m1_subset_1(C,u1_struct_0(k11_monoid_0)) -> (all D (m1_subset_1(D,u1_struct_0(k11_monoid_0)) -> (A = C & D = B -> k10_group_1(k11_monoid_0,C,D) = k24_binop_2(A,B)))))))))) # label(t64_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11715 (all A all B (v1_group_1(B) & v13_monoid_0(B) & m5_monoid_0(B,k15_monoid_0(A),k18_monoid_0(A)) & v2_group_1(B) & -v3_struct_0(B) -> (B = k20_monoid_0(A) <-> (all C (m1_subset_1(C,u1_struct_0(k18_monoid_0(A))) -> (m2_relset_1(C,A,A) & v3_funct_2(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) <-> r2_hidden(C,u1_struct_0(B)))))))) # label(d42_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11716 $T # label(t59_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11717 (all A (-v3_struct_0(A) & l1_vectsp_1(A) -> (v1_vectsp_2(A) <-> r3_binop_1(u1_struct_0(A),u1_vectsp_1(A),u1_group_1(A))))) # label(d21_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11718 (all A (l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m3_monoid_0(B,A) -> (-v3_struct_0(B) -> -v3_struct_0(B) & v4_group_1(B)))))) # label(cc30_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11719 (all A (l1_group_1(A) & -v3_struct_0(A) -> (v2_binop_1(u1_group_1(A),u1_struct_0(A)) <-> v4_group_1(A)))) # label(d12_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11720 (all A (-v3_struct_0(A) & v2_group_1(A) & l1_group_1(A) -> (all B (m2_monoid_0(B,A) -> (v13_monoid_0(B) & v4_group_1(B) & -v3_struct_0(B) -> -v3_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v16_monoid_0(B) & v15_monoid_0(B) & v14_monoid_0(B)))))) # label(cc36_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11721 (all A (-v3_struct_0(A) & l1_group_1(A) & v10_monoid_0(A) -> (all B (m2_monoid_0(B,A) -> (-v3_struct_0(B) -> -v3_struct_0(B) & v10_monoid_0(B)))))) # label(cc31_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11722 (all A (-v3_struct_0(A) & v1_vectsp_2(A) & l1_vectsp_1(A) & v17_monoid_0(A) -> (all B (m3_monoid_0(B,A) -> (-v3_struct_0(B) -> -v3_struct_0(B) & v2_group_1(B) & v6_vectsp_1(B) & v8_vectsp_1(B) & v1_vectsp_2(B) & v17_monoid_0(B)))))) # label(cc35_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11723 (all A (l1_group_1(A) -> (exists B (v1_vectsp_1(B) & m3_monoid_0(B,A))))) # label(rc10_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11724 (all A (l1_group_1(A) -> (exists B m2_monoid_0(B,A)))) # label(existence_m2_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11725 (all A (v1_group_1(A) & m2_monoid_0(A,k9_monoid_0) & v17_monoid_0(A) & v2_group_1(A) & -v3_struct_0(A) -> (u1_struct_0(A) = k5_numbers <-> A = k10_monoid_0))) # label(d31_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11726 (all A all B (l1_group_1(A) & m1_monoid_0(B,A) -> (all C (m4_monoid_0(C,A,B) <-> m2_monoid_0(C,B))))) # label(redefinition_m4_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11727 (exists A (l1_struct_0(A) & v2_monoid_0(A))) # label(rc2_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11728 (all A (-v3_struct_0(A) & v1_group_1(A) & m2_monoid_0(A,k5_monoid_0) -> (k6_monoid_0 = A <-> u1_struct_0(A) = k4_numbers))) # label(t46_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11729 (all A (l1_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> v1_funct_1(B) & v1_relat_1(B))) <-> v1_monoid_0(A)))) # label(d1_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11730 (all A (-v3_struct_0(A) & l1_group_1(A) & v2_monoid_0(A) -> (all B (m3_monoid_0(B,A) -> (-v3_struct_0(B) -> -v3_struct_0(B) & v2_monoid_0(B) & v1_monoid_0(B)))))) # label(cc25_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11731 (all A all B (r1_tarski(A,B) -> m2_monoid_0(k15_monoid_0(A),k15_monoid_0(B)))) # label(t81_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11732 (all A (-v3_struct_0(k20_monoid_0(A)) & v2_group_1(k20_monoid_0(A)) & m5_monoid_0(k20_monoid_0(A),k15_monoid_0(A),k18_monoid_0(A)) & v13_monoid_0(k20_monoid_0(A)) & v1_group_1(k20_monoid_0(A)))) # label(dt_k20_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11733 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m1_subset_1(C,u1_struct_0(k8_monoid_0)) -> (all D (m1_subset_1(D,u1_struct_0(k8_monoid_0)) -> (A = C & B = D -> k23_binop_2(A,B) = k10_group_1(k8_monoid_0,C,D)))))))))) # label(t51_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11734 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (r1_tarski(A,B) -> m2_monoid_0(k12_monoid_0(A),k12_monoid_0(B))))))) # label(t75_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11735 (all A (-v3_struct_0(A) & l1_group_1(A) -> (v12_monoid_0(A) <-> v4_monoid_0(u1_group_1(A),u1_struct_0(A))))) # label(d15_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11736 (all A (-v3_struct_0(A) & l1_group_1(A) & v2_group_1(A) -> (all B (m1_monoid_0(B,A) & v1_vectsp_2(B) & v1_vectsp_1(B) -> (all C (m1_monoid_0(C,A) & v1_vectsp_2(C) & v1_vectsp_1(C) -> B = C)))))) # label(t22_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11737 (all A (l1_group_1(A) & v13_monoid_0(A) & -v3_struct_0(A) -> (all B (m1_monoid_0(B,A) -> -v3_struct_0(B) & v12_monoid_0(B) & v13_monoid_0(B) & v11_monoid_0(B))))) # label(cc19_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11738 (all A all B (l1_group_1(A) & m3_monoid_0(B,A) -> (all C (m6_monoid_0(C,A,B) -> m2_monoid_0(C,A))))) # label(dt_m6_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11739 (all A all B (v2_group_1(B) & v4_group_1(B) & l1_group_1(B) & v1_monoid_0(B) & v1_group_1(B) & -v3_struct_0(B) -> (k4_partfun1(A,A) = u1_struct_0(B) & (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k5_relat_1(D,C) = k4_monoid_0(B,C,D))))) <-> B = k15_monoid_0(A)))) # label(d37_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11740 (all A (l1_group_1(A) & -v3_struct_0(A) -> (all B (m2_monoid_0(B,A) & -v3_struct_0(B) -> (r2_hidden(k3_binop_1(u1_struct_0(A),u1_group_1(A)),u1_struct_0(B)) & v2_group_1(A) -> v2_group_1(B) & k3_binop_1(u1_struct_0(A),u1_group_1(A)) = k3_binop_1(u1_struct_0(B),u1_group_1(B))))))) # label(t32_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11741 (all A (l1_group_1(A) -> (exists B m1_monoid_0(B,A)))) # label(existence_m1_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11742 (all A (l1_group_1(A) & -v3_struct_0(A) -> (all B (m2_monoid_0(B,A) & -v3_struct_0(B) -> (all C (m2_monoid_0(C,A) & -v3_struct_0(C) -> (u1_struct_0(C) = u1_struct_0(B) -> g1_group_1(u1_struct_0(C),u1_group_1(C)) = g1_group_1(u1_struct_0(B),u1_group_1(B))))))))) # label(t28_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11743 (all A all B all C (v1_funct_2(B,A,A) & m1_relset_1(B,A,A) & m1_relset_1(C,A,A) & v3_funct_2(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) & v3_funct_2(B,A,A) & v1_funct_1(B) -> v3_funct_2(k3_monoid_0(A,B,C),A,A) & m2_relset_1(k3_monoid_0(A,B,C),A,A) & v1_funct_2(k3_monoid_0(A,B,C),A,A) & v1_funct_1(k3_monoid_0(A,B,C)))) # label(dt_k3_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11744 (all A (v2_monoid_0(A) & l1_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> v1_funct_1(B) & v1_finseq_1(B) & v1_finset_1(B) & v1_relat_1(B))))) # label(cc4_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11745 (all A (-v3_struct_0(A) & l1_group_1(A) -> (v17_monoid_0(A) <-> v9_monoid_0(u1_group_1(A),u1_struct_0(A))))) # label(d20_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11746 (all A (l1_group_1(A) & v1_monoid_0(A) & -v3_struct_0(A) -> (all B (m3_monoid_0(B,A) -> (-v3_struct_0(B) -> v1_monoid_0(B) & -v3_struct_0(B)))))) # label(cc23_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11747 (all A (m1_subset_1(A,u1_struct_0(k6_monoid_0)) <-> v1_int_1(A))) # label(t47_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11748 (exists A (l1_group_1(A) & v4_group_1(A) & v7_group_1(A) & v1_monoid_0(A) & v2_monoid_0(A) & v13_monoid_0(A) & v17_monoid_0(A) & v16_monoid_0(A) & v10_monoid_0(A) & v2_group_1(A) & v1_group_1(A) & -v3_struct_0(A))) # label(rc3_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11749 (all A (-v3_struct_0(A) & l1_group_1(A) -> (all B (-v3_struct_0(B) & m2_monoid_0(B,A) -> (v16_monoid_0(A) -> v16_monoid_0(B)))))) # label(t37_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11750 (all A (-v1_xboole_0(A) -> (all B (-v3_struct_0(B) & m1_monoid_0(B,k12_monoid_0(A)) & v1_vectsp_2(B) & v1_vectsp_1(B) -> B = k13_monoid_0(A))))) # label(d35_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11751 (all A (-v1_xboole_0(A) -> v2_binop_1(k14_monoid_0(A),k3_finseq_2(A)) & k1_xboole_0 = k3_binop_1(k3_finseq_2(A),k14_monoid_0(A)) & v1_setwiseo(k14_monoid_0(A),k3_finseq_2(A)))) # label(t76_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11752 (all A (l1_group_1(A) & -v3_struct_0(A) -> (v4_group_1(A) -> (v1_finseqop(u1_group_1(A),u1_struct_0(A)) & v2_group_1(A) <-> v13_monoid_0(A))))) # label(t17_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11753 (all A (l1_group_1(A) -> (v2_monoid_0(A) -> v1_monoid_0(A)))) # label(cc3_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11754 (all A (l1_vectsp_1(A) -> (-v3_struct_0(A) & v1_vectsp_2(A) -> v8_vectsp_1(A) & v6_vectsp_1(A) & v2_group_1(A) & -v3_struct_0(A)))) # label(cc12_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11755 (all A (v2_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_monoid_0(B,A) -> v2_group_1(B) & v6_vectsp_1(B) & v8_vectsp_1(B) & -v3_struct_0(B))))) # label(cc16_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11756 (all A all B (-v3_struct_0(B) & m2_monoid_0(B,k15_monoid_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k4_monoid_0(B,C,D) = k5_relat_1(D,C))))))) # label(t79_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11757 (all A (-v3_struct_0(A) & m2_monoid_0(A,k9_monoid_0) & v2_group_1(A) -> np__0 = k3_binop_1(u1_struct_0(A),u1_group_1(A)) | k3_binop_1(u1_struct_0(A),u1_group_1(A)) = np__1)) # label(t60_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11758 $T # label(t8_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11759 (all A (l1_vectsp_1(A) & v1_vectsp_2(A) & -v3_struct_0(A) -> (all B (m3_monoid_0(B,A) & -v3_struct_0(B) -> v1_vectsp_2(B))))) # label(t33_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11760 (all A all B all C (m1_finseq_1(C,A) & m1_finseq_1(B,A) -> k1_monoid_0(A,B,C) = k7_finseq_1(B,C))) # label(redefinition_k1_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11761 $T # label(t48_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11762 (all A (v1_vectsp_2(k19_monoid_0(A)) & m1_monoid_0(k19_monoid_0(A),k18_monoid_0(A)) & v1_vectsp_1(k19_monoid_0(A)))) # label(dt_k19_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11763 (all A (l1_group_1(A) -> (exists B m3_monoid_0(B,A)))) # label(existence_m3_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11764 (all A k1_realset1(k17_monoid_0(A),k1_funct_2(A,A)) = u1_group_1(k18_monoid_0(A))) # label(t83_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11765 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,u1_struct_0(k13_monoid_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(k13_monoid_0(A))) -> k4_monoid_0(k13_monoid_0(A),B,C) = k7_finseq_1(B,C))))))) # label(t71_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11766 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m2_monoid_0(B,A) -> (-v3_struct_0(B) -> v4_group_1(B) & -v3_struct_0(B)))))) # label(cc29_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11767 (all A (l1_group_1(A) & v1_monoid_0(A) -> (all B (m1_monoid_0(B,A) -> v1_monoid_0(B))))) # label(cc14_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11768 (all A (-v1_xboole_0(A) -> v2_group_1(k12_monoid_0(A)) & v4_group_1(k12_monoid_0(A)) & v16_monoid_0(k12_monoid_0(A)) & v17_monoid_0(k12_monoid_0(A)) & l1_group_1(k12_monoid_0(A)) & v2_monoid_0(k12_monoid_0(A)) & v1_group_1(k12_monoid_0(A)) & -v3_struct_0(k12_monoid_0(A)))) # label(dt_k12_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11769 (all A (l1_group_1(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> k1_group_1(A,k3_binop_1(u1_struct_0(A),u1_group_1(A)),B) = B & k1_group_1(A,B,k3_binop_1(u1_struct_0(A),u1_group_1(A))) = B)) <-> v2_group_1(A)))) # label(t5_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11770 (all A (m1_subset_1(A,u1_struct_0(k9_monoid_0)) <-> m1_subset_1(A,k1_numbers))) # label(t56_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11771 (all A all B all C (v1_funct_1(B) & v1_funct_2(B,A,A) & v1_funct_1(C) & v1_funct_2(C,A,A) & v3_funct_2(C,A,A) & m1_relset_1(C,A,A) & m1_relset_1(B,A,A) & v3_funct_2(B,A,A) -> k5_relat_1(B,C) = k3_monoid_0(A,B,C))) # label(redefinition_k3_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11772 (all A (-v3_struct_0(A) & l1_group_1(A) -> (all B (-v3_struct_0(B) & m2_monoid_0(B,A) -> (v4_group_1(A) -> v4_group_1(B)))))) # label(t35_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11773 (all A (l1_group_1(A) -> (all B (m2_monoid_0(B,A) -> l1_group_1(B))))) # label(dt_m2_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11774 (all A all B (m1_subset_1(B,u1_struct_0(k20_monoid_0(A))) -> k3_group_1(k20_monoid_0(A),B) = k2_funct_1(B))) # label(t88_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11775 (all A all B (m3_monoid_0(B,A) & l1_group_1(A) -> (exists C m6_monoid_0(C,A,B)))) # label(existence_m6_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11776 (all A (-v3_struct_0(A) & l1_group_1(A) -> (all B (-v3_struct_0(B) & m2_monoid_0(B,A) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (all F (m1_subset_1(F,u1_struct_0(A)) -> (F = D & E = C -> k1_group_1(A,E,F) = k1_group_1(B,C,D)))))))))))))) # label(t27_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11777 (all A (l1_group_1(A) -> (all B (l1_vectsp_1(B) -> (g1_group_1(u1_struct_0(A),u1_group_1(A)) = g1_group_1(u1_struct_0(B),u1_group_1(B)) <-> m1_monoid_0(B,A)))))) # label(d22_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11778 (all A (-v3_struct_0(A) & l1_group_1(A) -> (all B (-v3_struct_0(B) & l1_vectsp_1(B) -> m2_monoid_0(A,A) & m3_monoid_0(B,B))))) # label(t24_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11779 (all A all B (m2_monoid_0(B,A) & l1_group_1(A) -> (all C (m5_monoid_0(C,A,B) -> m2_monoid_0(C,A))))) # label(dt_m5_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11780 $T # label(t45_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11781 (all A (k2_group_1(k20_monoid_0(A)) = k6_partfun1(A) & k6_partfun1(A) = k3_binop_1(u1_struct_0(k20_monoid_0(A)),u1_group_1(k20_monoid_0(A))))) # label(t87_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11782 (all A (l1_group_1(A) -> (exists B (m1_monoid_0(B,A) & v1_vectsp_1(B))))) # label(rc5_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11783 (all A (l1_group_1(A) & -v3_struct_0(A) -> (v14_monoid_0(A) <-> v6_monoid_0(u1_group_1(A),u1_struct_0(A))))) # label(d17_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11784 (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) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (k2_binop_1(A,A,A,B,C,D) = k2_binop_1(A,A,A,B,C,E) -> E = D))))))) <-> v6_monoid_0(B,A)))))) # label(d6_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11785 (all A all B (m2_monoid_0(B,A) & l1_group_1(A) -> (all C (m2_monoid_0(C,B) <-> m5_monoid_0(C,A,B))))) # label(redefinition_m5_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11786 (all A (-v3_struct_0(A) & l1_group_1(A) -> (v2_group_1(A) -> r3_binop_1(u1_struct_0(A),k3_binop_1(u1_struct_0(A),u1_group_1(A)),u1_group_1(A))))) # label(t4_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11787 (all A (l1_group_1(A) & -v3_struct_0(A) -> (v8_monoid_0(u1_group_1(A),u1_struct_0(A)) <-> v16_monoid_0(A)))) # label(d19_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11788 (all A (v1_vectsp_2(A) & m1_monoid_0(A,k7_monoid_0) & v1_vectsp_1(A) & -v3_struct_0(A) -> k8_monoid_0 = A)) # label(d28_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11789 (all A (l1_group_1(A) & -v3_struct_0(A) -> (v7_monoid_0(u1_group_1(A),u1_struct_0(A)) <-> v15_monoid_0(A)))) # label(d18_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11790 (all A (l1_group_1(A) -> (v16_monoid_0(A) & -v3_struct_0(A) -> v14_monoid_0(A) & v15_monoid_0(A) & -v3_struct_0(A)))) # label(cc9_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11791 (all A (l1_group_1(A) -> (v13_monoid_0(A) & v4_group_1(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v3_group_1(A) & v2_group_1(A)))) # label(cc6_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11792 (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) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (k2_binop_1(A,A,A,B,C,D) = k2_binop_1(A,A,A,B,C,E) | k2_binop_1(A,A,A,B,E,C) = k2_binop_1(A,A,A,B,D,C) -> E = D))))))) <-> v8_monoid_0(B,A)))))) # label(d8_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11793 (all A (l1_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B))) <-> v2_monoid_0(A)))) # label(d2_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11794 (all A (-v3_struct_0(A) & l1_group_1(A) -> (v13_monoid_0(A) <-> v5_monoid_0(u1_group_1(A),u1_struct_0(A))))) # label(d16_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11795 (all A (-v3_struct_0(A) & l1_group_1(A) -> (v10_monoid_0(A) <-> v3_binop_1(u1_group_1(A),u1_struct_0(A))))) # label(d13_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11796 (all A (-v3_struct_0(k16_monoid_0(A)) & m1_monoid_0(k16_monoid_0(A),k15_monoid_0(A)) & v1_vectsp_2(k16_monoid_0(A)) & v1_vectsp_1(k16_monoid_0(A)))) # label(dt_k16_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11797 (all A (l1_group_1(A) & v1_monoid_0(A) & -v3_struct_0(A) -> (all B (m2_monoid_0(B,A) -> (-v3_struct_0(B) -> -v3_struct_0(B) & v1_monoid_0(B)))))) # label(cc22_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11798 (all A all B all C (l1_group_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & -v3_struct_0(A) -> k1_group_1(A,B,C) = k4_monoid_0(A,B,C))) # label(redefinition_k4_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11799 (all A (v1_group_1(k15_monoid_0(A)) & v1_monoid_0(k15_monoid_0(A)) & l1_group_1(k15_monoid_0(A)) & v4_group_1(k15_monoid_0(A)) & v2_group_1(k15_monoid_0(A)) & -v3_struct_0(k15_monoid_0(A)))) # label(dt_k15_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11800 (all A (l1_group_1(A) -> (all B (m3_monoid_0(B,A) -> m2_monoid_0(B,A))))) # label(t23_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11801 (all A (l1_group_1(A) -> (all B (m3_monoid_0(B,A) -> l1_vectsp_1(B))))) # label(dt_m3_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11802 (all A (m1_subset_1(A,u1_struct_0(k8_monoid_0)) <-> m2_subset_1(A,k1_numbers,k5_numbers))) # label(t50_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11803 (all A (v2_monoid_0(A) & l1_group_1(A) -> (all B (m1_monoid_0(B,A) -> v1_monoid_0(B) & v2_monoid_0(B))))) # label(cc15_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11804 (all A (l1_group_1(A) & v10_monoid_0(A) & -v3_struct_0(A) -> (all B (m3_monoid_0(B,A) -> (-v3_struct_0(B) -> v10_monoid_0(B) & -v3_struct_0(B)))))) # label(cc32_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11805 (all A (m1_subset_1(A,u1_struct_0(k9_monoid_0)) -> (all B (m1_subset_1(B,u1_struct_0(k9_monoid_0)) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_subset_1(D,k1_numbers) -> (D = B & A = C -> k10_group_1(k9_monoid_0,A,B) = k11_binop_2(C,D)))))))))) # label(t55_monoid_0_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11806 (all A (l1_vectsp_1(A) & -v3_struct_0(A) -> (v1_vectsp_2(A) -> k3_binop_1(u1_struct_0(A),u1_group_1(A)) = u1_vectsp_1(A)))) # label(t19_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11807 (all A (-v1_xboole_0(A) -> g1_group_1(k3_finseq_2(A),k14_monoid_0(A)) = k12_monoid_0(A))) # label(t68_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11808 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m1_subset_1(C,u1_struct_0(k10_monoid_0)) -> (all D (m1_subset_1(D,u1_struct_0(k10_monoid_0)) -> (D = B & A = C -> k10_group_1(k10_monoid_0,C,D) = k24_binop_2(A,B)))))))))) # label(t62_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11809 (all A (v1_vectsp_2(A) & l1_vectsp_1(A) & -v3_struct_0(A) -> (all B (m3_monoid_0(B,A) -> (-v3_struct_0(B) -> v2_group_1(B) & v6_vectsp_1(B) & v8_vectsp_1(B) & v1_vectsp_2(B) & -v3_struct_0(B)))))) # label(cc26_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11810 (all A (l1_group_1(A) -> (all B (m1_monoid_0(B,A) -> l1_vectsp_1(B))))) # label(dt_m1_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11811 (all A (l1_vectsp_1(A) -> (all B (l1_vectsp_1(B) -> (m3_monoid_0(B,A) <-> u1_vectsp_1(B) = u1_vectsp_1(A) & r1_tarski(u1_group_1(B),u1_group_1(A))))))) # label(d25_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11812 (all A (l1_struct_0(A) -> (v1_fraenkel(u1_struct_0(A)) -> v1_monoid_0(A)))) # label(t89_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11813 (all A (l1_group_1(A) & -v3_struct_0(A) -> (v16_monoid_0(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k1_group_1(A,D,B) = k1_group_1(A,C,B) | k1_group_1(A,B,C) = k1_group_1(A,B,D) -> D = C)))))))))) # label(t15_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11814 (all A all B (m1_subset_1(A,u1_struct_0(k20_monoid_0(B))) <-> v1_funct_1(A) & v1_funct_2(A,B,B) & m2_relset_1(A,B,B) & v3_funct_2(A,B,B))) # label(t86_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11815 (all A (l1_group_1(A) & -v3_struct_0(A) -> (all B (m2_monoid_0(B,A) & -v3_struct_0(B) -> (v10_monoid_0(A) -> v10_monoid_0(B)))))) # label(t36_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11816 (all A all B (l1_group_1(A) & m3_monoid_0(B,A) -> (all C (m6_monoid_0(C,A,B) <-> m2_monoid_0(C,B))))) # label(redefinition_m6_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11817 (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) -> (v8_monoid_0(B,A) <-> v6_monoid_0(B,A) & v7_monoid_0(B,A)))))) # label(t2_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11818 (all A (-v3_struct_0(A) & l1_vectsp_1(A) & v1_vectsp_2(A) -> (exists B (m3_monoid_0(B,A) & v15_monoid_0(B) & v16_monoid_0(B) & v17_monoid_0(B) & v14_monoid_0(B) & v13_monoid_0(B) & v12_monoid_0(B) & v11_monoid_0(B) & v10_monoid_0(B) & v1_vectsp_2(B) & v8_vectsp_1(B) & v6_vectsp_1(B) & v1_vectsp_1(B) & v7_group_1(B) & v4_group_1(B) & v3_group_1(B) & v2_group_1(B) & -v3_struct_0(B))))) # label(rc12_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11819 (all A (v2_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (exists B (m2_monoid_0(B,A) & v1_group_1(B) & v4_group_1(B) & v7_group_1(B) & v16_monoid_0(B) & v17_monoid_0(B) & v15_monoid_0(B) & v14_monoid_0(B) & v13_monoid_0(B) & v12_monoid_0(B) & v11_monoid_0(B) & v10_monoid_0(B) & v3_group_1(B) & v2_group_1(B) & -v3_struct_0(B))))) # label(rc9_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11820 (all A k3_binop_1(u1_struct_0(k18_monoid_0(A)),u1_group_1(k18_monoid_0(A))) = k6_partfun1(A)) # label(t84_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11821 (all A (l1_group_1(A) & v7_group_1(A) & -v3_struct_0(A) -> (all B (m1_monoid_0(B,A) -> v7_group_1(B) & -v3_struct_0(B))))) # label(cc18_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11822 (all A (-v3_struct_0(A) & l1_vectsp_1(A) -> (all B (-v3_struct_0(B) & m3_monoid_0(B,A) -> (all C (-v3_struct_0(C) & m3_monoid_0(C,A) -> (r1_tarski(u1_struct_0(B),u1_struct_0(C)) -> m7_monoid_0(B,A,C)))))))) # label(t31_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11823 (all A (l1_group_1(A) -> (all B (l1_group_1(B) -> (m2_monoid_0(B,A) <-> r1_tarski(u1_group_1(B),u1_group_1(A))))))) # label(d23_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11824 (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) -> (all D (m1_subset_1(D,A) -> (exists E (m1_subset_1(E,A) & D = k2_binop_1(A,A,A,B,C,E))))))) <-> v4_monoid_0(B,A)))))) # label(d4_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11825 (all A (-v3_struct_0(A) & l1_group_1(A) -> (v1_setwiseo(u1_group_1(A),u1_struct_0(A)) & (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k3_binop_1(u1_struct_0(A),u1_group_1(A)) = k1_group_1(A,B,C) -> C = B & k3_binop_1(u1_struct_0(A),u1_group_1(A)) = C))))) <-> v17_monoid_0(A)))) # label(t16_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11826 (exists A (m1_subset_1(A,u1_struct_0(f1_s2_monoid_0)) & p1_s2_monoid_0(A))) & (all A (m1_subset_1(A,u1_struct_0(f1_s2_monoid_0)) -> (all B (m1_subset_1(B,u1_struct_0(f1_s2_monoid_0)) -> (p1_s2_monoid_0(A) & p1_s2_monoid_0(B) -> p1_s2_monoid_0(k1_group_1(f1_s2_monoid_0,A,B))))))) -> (exists A (-v3_struct_0(A) & m2_monoid_0(A,f1_s2_monoid_0) & (all B (m1_subset_1(B,u1_struct_0(f1_s2_monoid_0)) -> (p1_s2_monoid_0(B) <-> r2_hidden(B,u1_struct_0(A))))) & v1_group_1(A))) # label(s2_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11827 (all A (-v1_xboole_0(A) -> u1_group_1(k12_monoid_0(A)) = k14_monoid_0(A))) # label(d36_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11828 (all A (l1_group_1(A) -> (v11_monoid_0(A) & v12_monoid_0(A) & -v3_struct_0(A) -> v13_monoid_0(A) & -v3_struct_0(A)))) # label(cc8_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11829 (all A all B (l1_group_1(A) & m3_monoid_0(B,A) -> (all C (m7_monoid_0(C,A,B) -> m3_monoid_0(C,A))))) # label(dt_m7_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.76 11830 (all A (l1_group_1(A) -> (v4_group_1(A) & v13_monoid_0(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v16_monoid_0(A) & v2_group_1(A)))) # label(cc11_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11831 (all A all B (m2_monoid_0(B,A) & l1_group_1(A) -> (exists C m5_monoid_0(C,A,B)))) # label(existence_m5_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11832 (all A all B all C (-v1_xboole_0(A) & v1_funct_1(B) & m1_subset_1(C,A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> v1_vectsp_1(g1_vectsp_1(A,B,C)) & -v3_struct_0(g1_vectsp_1(A,B,C)))) # label(fc1_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11833 (all A (-v3_struct_0(A) & l1_group_1(A) & v2_monoid_0(A) -> (all B (m2_monoid_0(B,A) -> (-v3_struct_0(B) -> -v3_struct_0(B) & v2_monoid_0(B) & v1_monoid_0(B)))))) # label(cc24_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11834 (all A (-v3_struct_0(A) & v2_group_1(A) & m5_monoid_0(A,k5_monoid_0,k6_monoid_0) & v17_monoid_0(A) & v1_group_1(A) -> (k5_numbers = u1_struct_0(A) <-> A = k7_monoid_0))) # label(d27_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11835 (all A (-v1_xboole_0(A) -> (all B (m2_monoid_0(B,k12_monoid_0(A)) & v2_group_1(B) & -v3_struct_0(B) -> k1_xboole_0 = k3_binop_1(u1_struct_0(B),u1_group_1(B)))))) # label(t73_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11836 (all A all B all C (v1_funct_2(B,A,A) & m1_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) & m1_relset_1(B,A,A) & v1_funct_1(B) -> v1_funct_1(k2_monoid_0(A,B,C)) & v1_funct_2(k2_monoid_0(A,B,C),A,A) & m2_relset_1(k2_monoid_0(A,B,C),A,A))) # label(dt_k2_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11837 p1_s4_monoid_0(u1_vectsp_1(f1_s4_monoid_0)) & (all A (m1_subset_1(A,u1_struct_0(f1_s4_monoid_0)) -> (all B (m1_subset_1(B,u1_struct_0(f1_s4_monoid_0)) -> (p1_s4_monoid_0(A) & p1_s4_monoid_0(B) -> p1_s4_monoid_0(k1_group_1(f1_s4_monoid_0,A,B))))))) -> (exists A (-v3_struct_0(A) & v1_vectsp_1(A) & (all B (m1_subset_1(B,u1_struct_0(f1_s4_monoid_0)) -> (r2_hidden(B,u1_struct_0(A)) <-> p1_s4_monoid_0(B)))) & m3_monoid_0(A,f1_s4_monoid_0))) # label(s4_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11838 (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) -> (all D (m1_subset_1(D,A) -> (k3_binop_1(A,B) = k2_binop_1(A,A,A,B,C,D) -> D = C & k3_binop_1(A,B) = D))))) & v1_setwiseo(B,A) <-> v9_monoid_0(B,A)))))) # label(d9_monoid_0) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11839 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) & v1_tops_1(C,A) & r1_tarski(C,D) -> v1_tops_1(D,B)))))))))) # label(t83_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11840 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (u1_struct_0(B) = u1_struct_0(A) & (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (D = C -> k1_tops_1(B,D) = k1_tops_1(A,C)))))) -> g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))))))) # label(t74_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11841 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(C,A) | v3_tops_1(B,A) -> v3_tops_1(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t29_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11842 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_1(B,A) & v3_pre_topc(B,A) -> v1_tops_3(B,A)))))) # label(t36_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11843 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v1_tops_3(D,A) & u1_struct_0(A) = k4_subset_1(u1_struct_0(A),C,D) & k5_subset_1(u1_struct_0(A),C,D) = B & v2_tops_1(C,A) & v4_pre_topc(C,A)))))) & v3_tops_1(B,A)))))) # label(t51_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11844 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(C,A) -> k6_pre_topc(A,C) = k6_pre_topc(A,k5_subset_1(u1_struct_0(A),C,B))))) <-> v1_tops_1(B,A)))))) # label(t20_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11845 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r1_xboole_0(B,k1_tops_1(A,k6_pre_topc(A,B))) -> k1_xboole_0 = k1_tops_1(A,k6_pre_topc(A,B))))))) # label(t7_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11846 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tops_1(B,A) & r1_tarski(C,B) -> v2_tops_1(C,A)))))))) # label(t11_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11847 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_1(B,A) | v1_tops_1(C,A) -> v1_tops_1(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t21_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11848 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tops_1(B,A) | v2_tops_1(C,A) -> v2_tops_1(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t15_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11849 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) -> (v3_pre_topc(C,A) & r1_tarski(C,u1_struct_0(B)) & v2_tops_1(D,A) & D = E & r1_tarski(D,C) -> v2_tops_1(E,B)))))))))))) # label(t66_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11850 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (k4_subset_1(u1_struct_0(A),B,k6_pre_topc(A,k1_tops_1(A,B))) = u1_struct_0(A) -> u1_struct_0(A) = k6_pre_topc(A,k1_tops_1(A,B))))))) # label(t8_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11851 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v4_pre_topc(C,A) & g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) & C = D -> v4_pre_topc(D,B)))))))))) # label(t79_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11852 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(C,A) & v1_tops_1(C,A) & u1_struct_0(A) = k4_subset_1(u1_struct_0(A),C,D) & r1_xboole_0(C,D) & k4_subset_1(u1_struct_0(A),C,k5_subset_1(u1_struct_0(A),B,D)) = B & v2_tops_1(D,A) & v4_pre_topc(D,A)))))) & v1_tops_3(B,A)))))) # label(t50_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11853 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_3(C,A) & v1_tops_3(B,A) -> v1_tops_3(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t44_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11854 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(v1_tops_3(B,A) & B = k1_xboole_0))))) # label(t34_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11855 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(C,A) & r1_tarski(B,C) -> C = u1_struct_0(A)))) <-> v1_tops_1(B,A)))))) # label(t19_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11856 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (v1_tsep_1(B,A) & m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (C = D -> (v3_tops_1(C,A) <-> v3_tops_1(D,B))))))))))) # label(t70_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11857 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(C,A) -> r1_tarski(k1_tops_1(A,k4_subset_1(u1_struct_0(A),C,B)),k4_subset_1(u1_struct_0(A),C,k1_tops_1(A,B)))))))))) # label(t5_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11858 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_1(k1_tops_1(A,B),A) <-> v1_tops_3(B,A)))))) # label(t35_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11859 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & v1_tsep_1(B,A) & m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (C = D -> (v2_tops_1(D,B) <-> v2_tops_1(C,A))))))))))) # label(t67_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11860 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (r1_tarski(D,C) -> r1_tarski(k6_pre_topc(B,D),k6_pre_topc(A,C))))))))))) # label(t53_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11861 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_3(B,A) & v2_tops_1(C,A) -> v1_tops_1(k6_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t47_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11862 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tops_1(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(C,A) -> k1_tops_1(A,C) = k1_tops_1(A,k4_subset_1(u1_struct_0(A),C,B)))))))))) # label(t14_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11863 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (r1_tarski(D,C) & g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) & v2_tops_1(C,A) -> v2_tops_1(D,B)))))))))) # label(t82_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11864 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) & D = C -> k6_pre_topc(B,D) = k6_pre_topc(A,C)))))))))) # label(t80_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11865 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(v2_tops_1(B,A) & v1_tops_3(B,A)))))) # label(t37_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11866 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_1(B,A) <-> k6_pre_topc(A,B) = u1_struct_0(A)))))) # label(d2_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11867 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (k3_subset_1(u1_struct_0(A),B) = k1_pre_topc(A) -> k2_pre_topc(A) = B) & (u1_struct_0(A) = B -> k3_subset_1(u1_struct_0(A),B) = k1_xboole_0) & (k1_xboole_0 = k3_subset_1(u1_struct_0(A),B) -> B = u1_struct_0(A)) & (B = k2_pre_topc(A) -> k1_pre_topc(A) = k3_subset_1(u1_struct_0(A),B)))))) # label(t2_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11868 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (B = k1_pre_topc(A) -> k2_pre_topc(A) = k3_subset_1(u1_struct_0(A),B)) & (B = k1_xboole_0 -> u1_struct_0(A) = k3_subset_1(u1_struct_0(A),B)) & (u1_struct_0(A) = k3_subset_1(u1_struct_0(A),B) -> B = k1_xboole_0) & (k3_subset_1(u1_struct_0(A),B) = k2_pre_topc(A) -> B = k1_pre_topc(A)))))) # label(t1_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11869 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (C = D -> (v4_pre_topc(C,A) <-> v4_pre_topc(D,B))))))) & u1_struct_0(A) = u1_struct_0(B) -> g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))))))) # label(t73_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11870 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_3(B,A) | v1_tops_3(C,A) -> v1_tops_3(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t43_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11871 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(C != k1_xboole_0 & v3_pre_topc(C,A) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_xboole_0(B,D) & v3_pre_topc(D,A) & k1_xboole_0 != D & r1_tarski(D,C))))))) <-> v3_tops_1(B,A)))))) # label(t28_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11872 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) -> (r1_tarski(C,u1_struct_0(B)) & v3_tops_1(D,A) & E = D & r1_tarski(D,C) & v3_pre_topc(C,A) -> v3_tops_1(E,B)))))))))))) # label(t69_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11873 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (r1_tarski(D,C) & v3_tops_1(C,A) & g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) -> v3_tops_1(D,B)))))))))) # label(t84_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11874 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) & v1_tops_3(C,A) & r1_tarski(C,D) -> v1_tops_3(D,B)))))))))) # label(t85_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11875 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_3(B,A) & v1_tops_1(C,A) -> v1_tops_1(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t45_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11876 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_3(B,A) <-> (exists C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v1_tops_1(C,A) & v3_pre_topc(C,A) & r1_tarski(C,B)))))))) # label(t41_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11877 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(C,A) -> k1_tops_1(A,k4_subset_1(u1_struct_0(A),C,B)) = k1_tops_1(A,k4_subset_1(u1_struct_0(A),C,k1_tops_1(A,B)))))))))) # label(t6_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11878 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(B,A) & r1_tarski(C,B) -> v3_tops_1(C,A)))))))) # label(t26_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11879 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) & r1_tarski(C,D) -> r1_tarski(k6_pre_topc(A,C),k6_pre_topc(B,D))))))))))) # label(t81_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11880 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(k3_subset_1(u1_struct_0(A),B),A) <-> v1_tops_3(B,A)))))) # label(t39_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11881 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) -> (r1_tarski(C,u1_struct_0(B)) & r1_tarski(D,C) & E = D & v3_pre_topc(C,A) -> k1_tops_1(B,E) = k1_tops_1(A,D)))))))))))) # label(t57_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11882 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tops_1(k3_subset_1(u1_struct_0(A),B),A) <-> v1_tops_1(B,A)))))) # label(t18_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11883 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) -> (r1_tarski(C,u1_struct_0(B)) & E = D & r1_tarski(D,C) & v3_pre_topc(C,A) -> (v1_tops_3(E,B) & v1_tops_1(C,A) <-> v1_tops_3(D,A))))))))))))) # label(t62_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11884 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(B,A) -> v3_tops_1(k6_pre_topc(A,B),A)))))) # label(t24_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11885 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> v1_tops_3(k2_pre_topc(A),A))) # label(t31_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11886 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_3(B,A) -> v1_tops_3(k1_tops_1(A,B),A)))))) # label(t32_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11887 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_3(B,A) -> v1_tops_1(B,A)))))) # label(t33_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11888 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (C = D -> (v3_pre_topc(C,A) <-> v3_pre_topc(D,B))))))) & u1_struct_0(B) = u1_struct_0(A) -> g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))))))) # label(t72_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11889 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(v1_tops_1(B,A) & B = k1_xboole_0))))) # label(t17_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11890 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v2_tops_1(D,B) & r1_tarski(C,D) -> v2_tops_1(C,A)))))))))) # label(t65_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11891 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k5_subset_1(u1_struct_0(A),k1_tops_1(A,B),k6_pre_topc(A,C)),k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,C))))))))) # label(t3_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11892 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (D = C & g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) -> k1_tops_1(A,C) = k1_tops_1(B,D)))))))))) # label(t77_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11893 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(u1_struct_0(A) = B & v2_tops_1(B,A)))))) # label(t10_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11894 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(C,A) & r1_xboole_0(k3_subset_1(u1_struct_0(A),B),C) & k1_xboole_0 != C))) <-> v2_tops_1(B,A)))))) # label(t13_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11895 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(v1_tops_3(B,A) & (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v1_tops_1(C,A) & k4_subset_1(u1_struct_0(A),C,D) = B & r1_xboole_0(C,D) & v3_tops_1(D,A) & v3_pre_topc(C,A))))))))))) # label(t49_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11896 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (k1_xboole_0 = k1_tops_1(A,B) <-> v2_tops_1(B,A)))))) # label(d1_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11897 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v4_pre_topc(C,A) & v3_pre_topc(D,A) & v1_tops_1(D,A) & k4_subset_1(u1_struct_0(A),C,D) = u1_struct_0(A) & r1_xboole_0(C,D) & B = k5_subset_1(u1_struct_0(A),C,k4_subset_1(u1_struct_0(A),B,D)) & v2_tops_1(C,A)))))) & v3_tops_1(B,A)))))) # label(t52_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11898 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(B = u1_struct_0(A) & v3_tops_1(B,A)))))) # label(t23_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11899 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v1_borsuk_1(B,A) & m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (C = D -> k6_pre_topc(A,C) = k6_pre_topc(B,D)))))))))) # label(t55_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11900 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & v1_tsep_1(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) -> (u1_struct_0(B) = D & E = C -> (v1_tops_3(C,A) <-> v1_tops_1(D,A) & v1_tops_3(E,B))))))))))))) # label(t63_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11901 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(B,A) <-> (exists C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & r1_tarski(B,C) & v4_pre_topc(C,A) & v2_tops_1(C,A)))))))) # label(t27_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11902 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tops_1(C,A) & v3_tops_1(B,A) -> v2_tops_1(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t30_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11903 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> v2_tops_1(k1_pre_topc(A),A))) # label(t9_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11904 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) -> (r1_tarski(C,u1_struct_0(B)) & r1_tarski(D,C) & D = E -> (v1_tops_3(C,A) & v1_tops_3(E,B) <-> v1_tops_3(D,A))))))))))))) # label(t64_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11905 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v1_tops_1(C,A) & r1_tarski(C,D) -> v1_tops_1(D,B)))))))))) # label(t59_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11906 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(C,A) & v1_tops_1(B,A) -> v1_tops_1(k6_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t46_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11907 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_3(B,A) & r1_tarski(B,C) -> v1_tops_3(C,A)))))))) # label(t38_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11908 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v3_tops_1(D,B) & r1_tarski(C,D) -> v3_tops_1(C,A)))))))))) # label(t68_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11909 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (r1_tarski(C,D) & g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) -> r1_tarski(k1_tops_1(A,C),k1_tops_1(B,D))))))))))) # label(t78_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11910 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_tops_1(B,A) & v1_tops_1(B,A)))))) # label(t25_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11911 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (u1_struct_0(A) = u1_struct_0(B) & (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (D = C -> k6_pre_topc(B,D) = k6_pre_topc(A,C)))))) -> g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))))))) # label(t75_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11912 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(B,A) <-> v1_tops_3(k3_subset_1(u1_struct_0(A),B),A)))))) # label(t40_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11913 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_3(B,A) & v3_tops_1(C,A) -> v1_tops_3(k6_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t48_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11914 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_3(B,A) <-> k6_pre_topc(A,k1_tops_1(A,B)) = k2_pre_topc(A)))))) # label(d4_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11915 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) -> (r1_tarski(D,C) & E = D & r1_tarski(C,u1_struct_0(B)) -> (v1_tops_1(D,A) <-> v1_tops_1(C,A) & v1_tops_1(E,B))))))))))))) # label(t60_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11916 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(v4_pre_topc(C,A) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_tarski(C,D) & D != u1_struct_0(A) & u1_struct_0(A) = k4_subset_1(u1_struct_0(A),B,D) & v4_pre_topc(D,A)))) & C != u1_struct_0(A)))) <-> v1_tops_3(B,A)))))) # label(t42_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11917 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v1_tops_3(C,A) & r1_tarski(C,D) -> v1_tops_3(D,B)))))))))) # label(t61_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11918 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (C = D & v3_pre_topc(C,A) & g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) -> v3_pre_topc(D,B)))))))))) # label(t76_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11919 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) -> (r1_tarski(C,u1_struct_0(B)) & r1_tarski(D,C) & D = E & v4_pre_topc(C,A) -> k6_pre_topc(B,E) = k6_pre_topc(A,D)))))))))))) # label(t54_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11920 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) -> (u1_struct_0(B) = u1_struct_0(A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (k3_subset_1(u1_struct_0(A),C) = k3_subset_1(u1_struct_0(B),D) <-> C = D)))))))))) # label(t71_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11921 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (k1_xboole_0 = k1_tops_1(A,k6_pre_topc(A,B)) <-> v3_tops_1(B,A)))))) # label(d3_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11922 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k1_tops_1(A,k4_subset_1(u1_struct_0(A),B,C)),k4_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k1_tops_1(A,C))))))))) # label(t4_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11923 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tops_1(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(k3_subset_1(u1_struct_0(A),B),C) & v4_pre_topc(C,A) -> C = u1_struct_0(A))))))))) # label(t12_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11924 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) & v1_tsep_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (C = D -> k1_tops_1(A,C) = k1_tops_1(B,D)))))))))) # label(t58_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11925 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (r1_tarski(C,D) -> r1_tarski(k1_tops_1(A,C),k1_tops_1(B,D))))))))))) # label(t56_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11926 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_3(B,A) <-> k6_pre_topc(A,k1_tops_1(A,B)) = u1_struct_0(A)))))) # label(d5_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11927 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> v1_tops_1(k2_pre_topc(A),A))) # label(t16_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11928 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> v3_tops_1(k1_pre_topc(A),A))) # label(t22_tops_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11929 (all A (-v3_struct_0(A) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) -> (all B (m2_lattice4(B,A) -> (r2_hidden(k5_lattices(A),B) -> (all C (m1_subset_1(C,k5_finsub_1(u1_struct_0(A))) -> (r1_tarski(C,B) -> r2_hidden(k1_lattice4(A,C),B))))))))) # label(t24_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11930 (all A (v17_lattices(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> k7_lattices(A,k5_lattices(A)) = k6_lattices(A))) # label(t37_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11931 (all A all B (v17_lattices(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> -v1_xboole_0(k4_lattice4(A,B)))) # label(fc1_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11932 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l3_lattices(B) & v10_lattices(B) -> (all C (m1_lattice4(C,A,B) -> (r2_lattice4(A,B,C) <-> k6_lattices(B) = k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k6_lattices(A))))))))) # label(d7_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11933 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> (all C (m1_lattice4(C,A,B) -> (k5_lattices(B) = k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k5_lattices(A)) <-> r3_lattice4(A,B,C)))))))) # label(d8_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11934 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (-v3_struct_0(B) & l3_lattices(B) & v10_lattices(B) -> ((exists C (v3_lattice4(C,A,B) & m1_lattice4(C,A,B))) <-> r1_filter_1(A,B)))))) # label(d5_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11935 (all A (-v3_struct_0(A) & v17_lattices(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m2_lattice4(B,A) & -v1_xboole_0(B) -> (r2_hidden(k5_lattices(A),B) & r2_hidden(k6_lattices(A),B) -> k3_lattice4(A,B) = a_2_1_lattice4(A,B)))))) # label(t50_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11936 (all A (l3_lattices(A) & v17_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (exists B m3_lattice4(B,A)))) # label(existence_m3_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11937 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v17_lattices(A) -> (all B (m3_lattice4(B,A) -> m2_lattice4(B,A))))) # label(t42_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11938 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v2_lattice4(C,A,B) <-> k2_relat_1(C) = u1_struct_0(B)))))))) # label(d3_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11939 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & l3_lattices(A) & v17_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> m3_lattice4(k3_lattice4(A,B),A))) # label(dt_k3_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11940 (all A all B (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & -v3_struct_0(B) & l3_lattices(B) & v10_lattices(B) -> (all C (m1_lattice4(C,A,B) -> m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C))))) # label(dt_m1_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11941 (all A (-v3_struct_0(A) & v10_lattices(A) & v15_lattices(A) & l3_lattices(A) & v16_lattices(A) -> (all B (-v3_struct_0(B) & v17_lattices(B) & l3_lattices(B) & v10_lattices(B) -> (all C (m1_lattice4(C,B,A) -> (v2_lattice4(C,B,A) -> v17_lattices(A) & r4_lattice4(B,A,C)))))))) # label(t38_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11942 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) -> k2_lattice4(A,B) = k7_setwiseo(u1_struct_0(A),u1_struct_0(A),u1_lattices(A),B,k7_grcat_1(A)))))) # label(t14_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11943 (all A all B (v10_lattices(A) & v17_lattices(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & l3_lattices(A) & -v3_struct_0(A) -> m1_subset_1(k4_lattice4(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k4_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11944 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (exists B m2_lattice4(B,A)))) # label(existence_m2_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11945 (all A (v10_lattices(A) & l3_lattices(A) & v17_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (all C (m3_lattice4(C,A) -> (C = k3_lattice4(A,B) <-> r1_tarski(B,C) & (all D (m3_lattice4(D,A) -> (r1_tarski(B,D) -> r1_tarski(C,D))))))))))) # label(d15_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11946 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (v10_lattices(B) & l3_lattices(B) & -v3_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v2_lattice4(C,A,B) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (exists E (k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E) = D & m1_subset_1(E,u1_struct_0(A))))))))))))) # label(t9_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11947 (all A (-v3_struct_0(A) & l3_lattices(A) & v16_lattices(A) & v15_lattices(A) & v10_lattices(A) -> (all B (v10_lattices(B) & v3_filter_0(B) & l3_lattices(B) & -v3_struct_0(B) -> (all C (m1_lattice4(C,B,A) -> (v3_lattice4(C,B,A) -> r1_lattice4(B,A,C) & v3_filter_0(A)))))))) # label(t35_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11948 $T # label(t13_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11949 (all A (v10_lattices(A) & l3_lattices(A) & v14_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_lattice4(A,k5_setwiseo(u1_struct_0(A),B,k2_setwiseo(u1_struct_0(A),C))) = k4_lattices(A,k2_lattice4(A,B),C))))))) # label(t28_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11950 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (-v3_struct_0(B) & l3_lattices(B) & v10_lattices(B) -> (all C (m1_lattice4(C,A,B) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> k4_filter_0(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)) = k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k4_filter_0(A,D,E)))))) <-> r1_lattice4(A,B,C)))))))) # label(d6_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11951 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_lattice4(E,A,B) -> (r3_lattices(A,C,D) -> r3_lattices(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),E,C),k8_funct_2(u1_struct_0(A),u1_struct_0(B),E,D))))))))))))) # label(t7_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11952 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> k4_lattices(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)) = k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k4_lattices(A,D,E)) & k3_lattices(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)) = k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k3_lattices(A,D,E)))))) <-> m1_lattice4(C,A,B)))))))) # label(d1_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11953 (all A (-v3_struct_0(A) & l3_lattices(A) & v17_lattices(A) & v10_lattices(A) -> m3_lattice4(u1_struct_0(A),A))) # label(t41_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11954 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k1_lattice4(A,k2_setwiseo(u1_struct_0(A),B)))))) # label(t16_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11955 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) -> (all C (m1_lattice4(C,A,B) -> (v2_lattice4(C,A,B) & v1_lattice4(C,A,B) <-> v3_lattice4(C,A,B)))))))) # label(d4_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11956 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,B) & r2_hidden(C,B) -> r2_hidden(k4_lattices(A,C,D),B) & r2_hidden(k3_lattices(A,C,D),B)))))) <-> m2_lattice4(B,A)))))) # label(d10_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11957 (all A (-v3_struct_0(A) & l3_lattices(A) & v14_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (v1_funct_1(D) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(A)) -> k4_lattices(A,k3_lattice2(u1_struct_0(A),A,B,D),k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,C)) = k3_lattice2(u1_struct_0(A),A,k5_setwiseo(u1_struct_0(A),B,k2_setwiseo(u1_struct_0(A),C)),D))))))))) # label(t27_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11958 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (exists B (-v1_xboole_0(B) & m2_lattice4(B,A))))) # label(rc1_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11959 $T # label(t12_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11960 (all A (v17_lattices(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) -> k2_lattice2(u1_struct_0(A),A,B,k5_lattice4(A)) = k7_lattices(A,k2_lattice4(A,B)))))) # label(t48_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11961 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v1_lattice4(C,A,B) <-> v2_funct_1(C)))))))) # label(d2_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11962 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & v13_lattices(B) & l3_lattices(B) -> (all C (m1_lattice4(C,B,A) -> (v2_lattice4(C,B,A) -> v13_lattices(A) & r3_lattice4(B,A,C)))))))) # label(t19_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11963 $T # label(d11_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11964 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> v2_filter_0(k1_filter_0(A),A))) # label(t4_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.77 11965 (all A (v10_lattices(A) & l3_lattices(A) & v17_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(C,B) & r2_hidden(D,B) -> r2_hidden(k7_lattices(A,C),B) & r2_hidden(k4_lattices(A,C,D),B)))))) <-> m3_lattice4(B,A)))))) # label(d14_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 11966 (all A -((all B -(r2_hidden(B,A) & (all C -(r2_hidden(C,A) & B != C & r1_tarski(B,C))))) & (all B -(B != k1_xboole_0 & r1_tarski(B,A) & v6_ordinal1(B) & (all C -((all D (r2_hidden(D,B) -> r1_tarski(D,C))) & r2_hidden(C,A))))) & k1_xboole_0 != A)) # label(t3_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 11967 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m2_lattice4(B,A) -> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(dt_m2_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 11968 (all A (v10_lattices(A) & l3_lattices(A) & v17_lattices(A) & -v3_struct_0(A) -> (all B (m2_lattice4(B,A) & -v1_xboole_0(B) -> (r2_hidden(k5_lattices(A),B) & r2_hidden(k6_lattices(A),B) -> (all C (m1_subset_1(C,k5_finsub_1(u1_struct_0(A))) -> -((all D (m1_subset_1(D,k5_finsub_1(u1_struct_0(A))) -> -(k2_lattice2(u1_struct_0(A),A,C,k5_lattice4(A)) = k2_lattice4(A,D) & r1_tarski(D,k4_lattice4(A,B))))) & r1_tarski(C,k4_lattice4(A,B)))))))))) # label(t49_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 11969 (all A all B all C (-v3_struct_0(B) & v17_lattices(B) & -v1_xboole_0(C) & m2_lattice4(C,B) & l3_lattices(B) & v10_lattices(B) -> (r2_hidden(A,a_2_1_lattice4(B,C)) <-> (exists D (r1_tarski(D,k4_lattice4(B,C)) & A = k2_lattice4(B,D) & m1_subset_1(D,k5_finsub_1(u1_struct_0(B)))))))) # label(fraenkel_a_2_1_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 11970 (all A all B (-v3_struct_0(A) & v10_lattices(A) & m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) & l3_lattices(A) -> m1_subset_1(k1_lattice4(A,B),u1_struct_0(A)))) # label(dt_k1_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 11971 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_filter_0(C,A) -> r1_tarski(B,k3_filter_0(A,k1_finsub_1(k1_zfmisc_1(u1_struct_0(A)),B,C))) & r1_tarski(C,k3_filter_0(A,k1_finsub_1(k1_zfmisc_1(u1_struct_0(A)),B,C))))))))) # label(t5_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 11972 (all A (-v3_struct_0(A) & l3_lattices(A) & v13_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(D) -> k3_lattices(A,k2_lattice2(u1_struct_0(A),A,B,D),k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,C)) = k2_lattice2(u1_struct_0(A),A,k5_setwiseo(u1_struct_0(A),B,k2_setwiseo(u1_struct_0(A),C)),D))))))))) # label(t20_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 11973 $T # label(t1_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 11974 (all A (v10_lattices(A) & l3_lattices(A) & v17_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) -> k3_lattice2(u1_struct_0(A),A,B,k5_lattice4(A)) = k7_lattices(A,k1_lattice4(A,B)))))) # label(t46_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 11975 (all A (-v3_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) -> k7_lattices(A,k6_lattices(A)) = k5_lattices(A))) # label(t36_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 11976 (all A (-v3_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) -> (all B (m3_lattice4(B,A) -> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B))))) # label(dt_m3_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 11977 (all A (l3_lattices(A) & v17_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> m2_relset_1(k5_lattice4(A),u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(k5_lattice4(A),u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(k5_lattice4(A)))) # label(dt_k5_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 11978 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> m2_lattice4(u1_struct_0(A),A))) # label(t10_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 11979 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) -> k1_lattice4(A,B) = k7_setwiseo(u1_struct_0(A),u1_struct_0(A),u2_lattices(A),B,k7_grcat_1(A)))))) # label(t15_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 11980 (all A all B (-v3_struct_0(B) & l3_lattices(B) & v17_lattices(B) & v10_lattices(B) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (r2_hidden(A,k4_lattice4(B,C)) <-> (exists D (m1_subset_1(D,u1_struct_0(B)) & (exists E (m1_subset_1(E,u1_struct_0(B)) & A = k4_filter_0(B,D,E) & r2_hidden(E,C) & r2_hidden(D,C)))))))))) # label(t43_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 11981 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) -> k2_lattice2(u1_struct_0(A),A,B,k7_grcat_1(A)) = k1_lattice4(A,B))))) # label(d12_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 11982 (all A (v14_lattices(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m2_lattice4(B,A) -> (r2_hidden(k6_lattices(A),B) -> (all C (m1_subset_1(C,k5_finsub_1(u1_struct_0(A))) -> (r1_tarski(C,B) -> r2_hidden(k2_lattice4(A,C),B))))))))) # label(t31_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 11983 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k2_lattice4(A,k2_setwiseo(u1_struct_0(A),B)) = B)))) # label(t17_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 11984 (all A (v10_lattices(A) & l3_lattices(A) & v17_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> a_2_0_lattice4(A,B) = k4_lattice4(A,B))))) # label(d16_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 11985 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_lattice4(E,A,B) -> (v1_lattice4(E,A,B) -> (r3_lattices(A,C,D) <-> r3_lattices(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),E,C),k8_funct_2(u1_struct_0(A),u1_struct_0(B),E,D)))))))))))))) # label(t8_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 11986 (all A (v10_lattices(A) & l3_lattices(A) & v16_lattices(A) & v15_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) & v3_filter_0(B) -> (all C (m1_lattice4(C,B,A) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> (r3_lattices(A,k4_lattices(A,k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,D),k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,E)),k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,F)) & v1_lattice4(C,B,A) -> r3_lattices(A,k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,E),k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,k4_filter_0(B,D,F)))))))))))))))) # label(t34_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 11987 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> -(r2_hidden(C,k3_filter_0(A,k1_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k2_filter_0(A,D),B))) & (all E (m1_subset_1(E,u1_struct_0(A)) -> -(r2_hidden(E,B) & r3_lattices(A,k4_lattices(A,D,E),C))))))))))))) # label(t6_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 11988 (all A (-v3_struct_0(A) & l3_lattices(A) & v17_lattices(A) & v10_lattices(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> k7_lattices(A,C) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C))) <-> B = k5_lattice4(A)))))) # label(d17_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 11989 (all A (v17_lattices(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k5_finsub_1(u1_struct_0(A))) -> k3_lattice2(u1_struct_0(A),A,k5_setwiseo(u1_struct_0(A),C,k2_setwiseo(u1_struct_0(A),B)),k5_lattice4(A)) = k4_lattices(A,k3_lattice2(u1_struct_0(A),A,C,k5_lattice4(A)),k7_lattices(A,B)))))))) # label(t47_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 11990 (all A all B (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) -> m1_subset_1(k2_lattice4(A,B),u1_struct_0(A)))) # label(dt_k2_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 11991 $T # label(t2_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 11992 (all A (-v3_struct_0(A) & l3_lattices(A) & v17_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m3_lattice4(D,A) -> (r2_hidden(B,D) & r2_hidden(C,D) -> r2_hidden(k4_filter_0(A,B,C),D)))))))))) # label(t40_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 11993 (all A (-v3_struct_0(A) & v13_lattices(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k3_lattices(A,k1_lattice4(A,B),C) = k1_lattice4(A,k5_setwiseo(u1_struct_0(A),B,k2_setwiseo(u1_struct_0(A),C))))))))) # label(t21_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 11994 (all A all B all C (v10_lattices(B) & v17_lattices(B) & l3_lattices(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & -v1_xboole_0(C) & -v3_struct_0(B) -> (r2_hidden(A,a_2_0_lattice4(B,C)) <-> (exists D exists E (m1_subset_1(E,u1_struct_0(B)) & r2_hidden(D,C) & r2_hidden(E,C) & k4_filter_0(B,D,E) = A & m1_subset_1(D,u1_struct_0(B))))))) # label(fraenkel_a_2_0_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 11995 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & v14_lattices(B) & l3_lattices(B) -> (all C (m1_lattice4(C,B,A) -> (v2_lattice4(C,B,A) -> v14_lattices(A) & r2_lattice4(B,A,C)))))))) # label(t25_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 11996 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v17_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k5_finsub_1(u1_struct_0(A))) -> k2_lattice2(u1_struct_0(A),A,k5_setwiseo(u1_struct_0(A),C,k2_setwiseo(u1_struct_0(A),B)),k5_lattice4(A)) = k3_lattices(A,k2_lattice2(u1_struct_0(A),A,C,k5_lattice4(A)),k7_lattices(A,B)))))))) # label(t45_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 11997 (all A (l3_lattices(A) & v17_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,k4_lattice4(A,B)) <-> (exists D (m1_subset_1(D,u1_struct_0(A)) & (exists E (r2_hidden(D,B) & r2_hidden(E,B) & k3_lattices(A,k7_lattices(A,D),E) = C & m1_subset_1(E,u1_struct_0(A))))))))))))) # label(t44_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 11998 (all A (v10_lattices(A) & v14_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(A)) -> k3_lattice2(u1_struct_0(A),A,k8_setwiseo(u1_struct_0(A),u1_struct_0(A),C,B),D) = k3_lattice2(u1_struct_0(A),A,B,k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C,D)))))))))) # label(t29_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 11999 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) -> m2_lattice4(B,A))))) # label(t11_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12000 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) -> k2_lattice4(A,B) = k3_lattice2(u1_struct_0(A),A,B,k7_grcat_1(A)))))) # label(d13_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12001 (all A (v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (v10_lattices(B) & l3_lattices(B) & v3_filter_0(B) & -v3_struct_0(B) -> (all C (m1_lattice4(C,B,A) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> r3_lattices(A,k4_lattices(A,k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,D),k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,k4_filter_0(B,D,E))),k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,E)))))))))))) # label(t33_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12002 (all A (-v3_struct_0(A) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) -> k5_lattices(A) = k1_lattice4(A,k1_setwiseo(u1_struct_0(A))))) # label(t23_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12003 (all A (-v3_struct_0(A) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k5_finsub_1(u1_struct_0(A))) -> k3_lattices(A,k1_lattice4(A,B),k1_lattice4(A,C)) = k1_lattice4(A,k5_setwiseo(u1_struct_0(A),B,C)))))))) # label(t22_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12004 (all A (v17_lattices(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m3_lattice4(D,A) -> (r2_hidden(C,D) & r2_hidden(B,D) -> r2_hidden(k3_lattices(A,B,C),D)))))))))) # label(t39_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12005 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> (all C (m1_lattice4(C,A,B) -> (r4_lattice4(A,B,C) <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> k7_lattices(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D)) = k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k7_lattices(A,D))))))))))) # label(d9_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12006 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (v10_lattices(B) & v11_lattices(B) & l3_lattices(B) & -v3_struct_0(B) -> (all C (m1_lattice4(C,B,A) -> (v2_lattice4(C,B,A) -> v11_lattices(A)))))))) # label(t18_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12007 (all A (v10_lattices(A) & v14_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> k6_lattices(A) = k2_lattice4(A,k1_setwiseo(u1_struct_0(A))))) # label(t26_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12008 (all A (v10_lattices(A) & v11_lattices(A) & l3_lattices(A) & v14_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_lattice4(A,k8_setwiseo(u1_struct_0(A),u1_struct_0(A),k7_funcop_1(u1_struct_0(A),u1_struct_0(A),u2_lattices(A),k7_grcat_1(A),C),B)) = k3_lattices(A,k2_lattice4(A,B),C))))))) # label(t32_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12009 (all A all B (v10_lattices(A) & -v3_struct_0(B) & l3_lattices(B) & v10_lattices(B) & l3_lattices(A) & -v3_struct_0(A) -> (exists C m1_lattice4(C,A,B)))) # label(existence_m1_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12010 (all A (-v3_struct_0(A) & v14_lattices(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k5_finsub_1(u1_struct_0(A))) -> k2_lattice4(A,k5_setwiseo(u1_struct_0(A),B,C)) = k4_lattices(A,k2_lattice4(A,B),k2_lattice4(A,C)))))))) # label(t30_lattice4) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12011 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> m2_relset_1(k5_lopclset(A),k2_zfmisc_1(k1_lopclset(A),k1_lopclset(A)),k1_lopclset(A)) & v1_funct_2(k5_lopclset(A),k2_zfmisc_1(k1_lopclset(A),k1_lopclset(A)),k1_lopclset(A)) & v1_funct_1(k5_lopclset(A)))) # label(dt_k5_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12012 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m2_subset_1(B,k1_zfmisc_1(u1_struct_0(A)),k1_lopclset(A)) -> m2_subset_1(k3_subset_1(u1_struct_0(A),B),k1_zfmisc_1(u1_struct_0(A)),k1_lopclset(A)))))) # label(t9_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12013 (all A (-v3_struct_0(A) & l3_lattices(A) & -v3_realset2(A) & v17_lattices(A) & v10_lattices(A) -> m1_lattice4(k13_lopclset(A),A,k12_lopclset(A)))) # label(dt_k13_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12014 (all A all B all C (v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,k1_lopclset(A)) & m1_subset_1(C,k1_lopclset(A)) & -v3_struct_0(A) -> k2_lopclset(A,B,C) = k2_lopclset(A,C,B))) # label(commutativity_k2_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12015 (all A (-v3_struct_0(A) & v10_lattices(A) & v17_lattices(A) & -v3_realset2(A) & l3_lattices(A) -> k7_lopclset(A) = k8_funct_2(u1_struct_0(A),k1_zfmisc_1(k7_lopclset(A)),k9_lopclset(A),k6_lattices(A)))) # label(t37_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12016 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(k1_lopclset(A),k1_lopclset(A)),k1_lopclset(A)) & v1_funct_2(B,k2_zfmisc_1(k1_lopclset(A),k1_lopclset(A)),k1_lopclset(A)) & v1_funct_1(B) -> (k4_lopclset(A) = B <-> (all C (m2_subset_1(C,k1_zfmisc_1(u1_struct_0(A)),k1_lopclset(A)) -> (all D (m2_subset_1(D,k1_zfmisc_1(u1_struct_0(A)),k1_lopclset(A)) -> k2_lopclset(A,C,D) = k2_binop_1(k1_lopclset(A),k1_lopclset(A),k1_lopclset(A),B,C,D)))))))))) # label(d2_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12017 (all A all B (v10_lattices(B) & l3_lattices(B) & -v3_realset2(B) & v17_lattices(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> ((exists D (m1_filter_0(D,B) & r2_hidden(C,D) & v1_filter_0(D,B) & D = A)) <-> r2_hidden(A,k1_funct_1(k8_lopclset(B),C))))))) # label(t20_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12018 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> a_1_0_lopclset(A) = k1_lopclset(A))) # label(d1_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12019 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> v17_lattices(k6_lopclset(A)))) # label(t14_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12020 (all A (-v3_realset2(A) & l3_lattices(A) & v17_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (v1_pre_topc(B) & v2_pre_topc(B) & l1_pre_topc(B) -> (a_1_2_lopclset(A) = u1_pre_topc(B) & u1_struct_0(B) = k7_lopclset(A) <-> k11_lopclset(A) = B))))) # label(d8_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12021 (all A all B (-v3_struct_0(B) & -v3_realset2(B) & l3_lattices(B) & v17_lattices(B) & v10_lattices(B) -> ((exists C (A = C & v1_filter_0(C,B) & m1_filter_0(C,B))) <-> r2_hidden(A,a_1_1_lopclset(B))))) # label(fraenkel_a_1_1_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12022 (all A all B all C (-v3_struct_0(A) & m1_subset_1(B,k1_lopclset(A)) & m1_subset_1(C,k1_lopclset(A)) & l1_pre_topc(A) & v2_pre_topc(A) -> k3_lopclset(A,B,B) = B)) # label(idempotence_k3_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12023 (all A all B all C (l1_pre_topc(A) & m1_subset_1(B,k1_lopclset(A)) & m1_subset_1(C,k1_lopclset(A)) & v2_pre_topc(A) & -v3_struct_0(A) -> k2_lopclset(A,B,B) = B)) # label(idempotence_k2_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12024 (all A (-v1_xboole_0(A) -> -(all B (m1_subset_1(B,k5_finsub_1(A)) -> v1_xboole_0(B))))) # label(t32_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12025 (all A all B (-v3_struct_0(B) & v10_lattices(B) & -v3_realset2(B) & l3_lattices(B) & v17_lattices(B) -> ((exists C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(k7_lopclset(B)))) & r1_tarski(C,k10_lopclset(B)) & k5_setfam_1(k7_lopclset(B),C) = A)) <-> r2_hidden(A,a_1_2_lopclset(B))))) # label(fraenkel_a_1_2_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12026 (all A (-v3_struct_0(A) & l3_lattices(A) & -v3_realset2(A) & v17_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_filter_0(C,A) -> (r2_hidden(C,k1_funct_1(k8_lopclset(A),B)) <-> r2_hidden(B,C) & v1_filter_0(C,A)))))))) # label(t21_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12027 (all A (v10_lattices(A) & -v3_realset2(A) & l3_lattices(A) & v17_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_filter_0(C,A) -> -(-r2_hidden(C,k8_funct_2(u1_struct_0(A),k1_zfmisc_1(k7_lopclset(A)),k9_lopclset(A),B)) & r2_hidden(B,C) & v1_filter_0(C,A)))))))) # label(t27_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12028 (all A all B all C (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(C,k1_lopclset(A)) & m1_subset_1(B,k1_lopclset(A)) -> k2_xboole_0(B,C) = k2_lopclset(A,B,C))) # label(redefinition_k2_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12029 (all A (-v3_struct_0(A) & -v3_realset2(A) & l3_lattices(A) & v17_lattices(A) & v10_lattices(A) -> v1_funct_1(k9_lopclset(A)) & m2_relset_1(k9_lopclset(A),u1_struct_0(A),k1_zfmisc_1(k7_lopclset(A))) & v1_funct_2(k9_lopclset(A),u1_struct_0(A),k1_zfmisc_1(k7_lopclset(A))))) # label(dt_k9_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12030 (all A (-v3_struct_0(A) & -v3_realset2(A) & l3_lattices(A) & v17_lattices(A) & v10_lattices(A) -> -v1_xboole_0(k10_lopclset(A)))) # label(fc3_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12031 (all A (-v3_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) & -v3_realset2(A) -> m1_subset_1(k7_lopclset(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))) # label(dt_k7_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12032 (all A (v17_lattices(A) & l3_lattices(A) & -v3_realset2(A) & v10_lattices(A) & -v3_struct_0(A) -> r1_tarski(k10_lopclset(A),k1_zfmisc_1(k7_lopclset(A))))) # label(t25_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12033 (all A all B all C (-v3_struct_0(B) & v10_lattices(B) & m1_subset_1(C,u1_struct_0(B)) & l3_lattices(B) & -v3_realset2(B) & v17_lattices(B) -> ((exists D (m1_filter_0(D,B) & v1_filter_0(D,B) & r2_hidden(C,D) & A = D)) <-> r2_hidden(A,a_2_0_lopclset(B,C))))) # label(fraenkel_a_2_0_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12034 (all A (l3_lattices(A) & -v3_realset2(A) & v17_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_funct_1(k8_lopclset(A),k3_lattices(A,B,C)) = k2_xboole_0(k1_funct_1(k8_lopclset(A),B),k1_funct_1(k8_lopclset(A),C)))))))) # label(t24_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12035 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,k1_lopclset(A)) -> v4_pre_topc(B,A)))))) # label(t3_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12036 (all A (v10_lattices(A) & v17_lattices(A) & l3_lattices(A) & -v3_realset2(A) & -v3_struct_0(A) -> -v1_xboole_0(k7_lopclset(A)))) # label(fc2_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12037 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> m2_relset_1(k4_lopclset(A),k2_zfmisc_1(k1_lopclset(A),k1_lopclset(A)),k1_lopclset(A)) & v1_funct_2(k4_lopclset(A),k2_zfmisc_1(k1_lopclset(A),k1_lopclset(A)),k1_lopclset(A)) & v1_funct_1(k4_lopclset(A)))) # label(dt_k4_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12038 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & -v3_realset2(A) & v17_lattices(A) -> k10_lopclset(A) = k2_relat_1(k9_lopclset(A)))) # label(d7_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12039 (all A (-v3_struct_0(A) & v17_lattices(A) & l3_lattices(A) & -v3_realset2(A) & v10_lattices(A) -> k8_lopclset(A) = k13_lopclset(A))) # label(redefinition_k13_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12040 (all A (-v3_struct_0(A) & v13_lattices(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> -(v1_filter_0(B,A) & r2_hidden(k5_lattices(A),B)))))) # label(t35_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12041 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> m2_subset_1(k1_pre_topc(A),k1_zfmisc_1(u1_struct_0(A)),k1_lopclset(A)))) # label(t7_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12042 (all A (-v3_realset2(A) & l3_lattices(A) & v17_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> l3_lattices(k12_lopclset(A)) & v10_lattices(k12_lopclset(A)) & -v3_struct_0(k12_lopclset(A)))) # label(dt_k12_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12043 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(k6_lopclset(A))) -> (all C (m1_subset_1(C,u1_struct_0(k6_lopclset(A))) -> k3_xboole_0(B,C) = k4_lattices(k6_lopclset(A),B,C))))))) # label(t12_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12044 $T # label(t1_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12045 (all A (v10_lattices(A) & -v3_realset2(A) & l3_lattices(A) & v17_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_filter_0(D,A) -> (v1_filter_0(D,A) -> (r2_hidden(C,D) | r2_hidden(B,D) <-> r2_hidden(k3_lattices(A,B,C),D))))))))))) # label(t22_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12046 (all A (-v3_struct_0(A) & -v3_realset2(A) & l3_lattices(A) & v17_lattices(A) & v10_lattices(A) -> v2_funct_1(k9_lopclset(A)))) # label(t29_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12047 (all A (v10_lattices(A) & -v3_realset2(A) & l3_lattices(A) & v17_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k4_xboole_0(k7_lopclset(A),k8_funct_2(u1_struct_0(A),k1_zfmisc_1(k7_lopclset(A)),k9_lopclset(A),B)) = k8_funct_2(u1_struct_0(A),k1_zfmisc_1(k7_lopclset(A)),k9_lopclset(A),k7_lattices(A,B)))))) # label(t28_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12048 (all A all B (v17_lattices(B) & -v3_realset2(B) & l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> ((exists C (A = k8_funct_2(u1_struct_0(B),k1_zfmisc_1(k7_lopclset(B)),k9_lopclset(B),C) & m1_subset_1(C,u1_struct_0(B)))) <-> r2_hidden(A,k10_lopclset(B))))) # label(t26_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12049 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> -v3_struct_0(k6_lopclset(A)) & l3_lattices(k6_lopclset(A)) & v10_lattices(k6_lopclset(A)))) # label(dt_k6_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12050 (all A (-v1_xboole_0(A) -> (exists B (-v1_xboole_0(B) & v1_finset_1(B) & m1_subset_1(B,k5_finsub_1(A)))))) # label(rc2_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12051 (all A all B all C (m1_subset_1(C,k1_lopclset(A)) & m1_subset_1(B,k1_lopclset(A)) & l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> m2_subset_1(k2_lopclset(A,B,C),k1_zfmisc_1(u1_struct_0(A)),k1_lopclset(A)))) # label(dt_k2_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12052 $T # label(t33_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12053 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> m1_subset_1(k1_lopclset(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))) # label(dt_k1_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12054 (all A (v10_lattices(A) & v17_lattices(A) & l3_lattices(A) & -v3_realset2(A) & -v3_struct_0(A) -> k8_lopclset(A) = k9_lopclset(A))) # label(redefinition_k9_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12055 $T # label(dt_k10_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12056 (all A (-v3_struct_0(A) & v17_lattices(A) & l3_lattices(A) & -v3_realset2(A) & v10_lattices(A) -> (exists B (v2_pre_topc(B) & l1_pre_topc(B) & r1_filter_1(A,k6_lopclset(B)) & -v3_struct_0(B))))) # label(t44_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12057 (all A (-v3_struct_0(A) & v17_lattices(A) & l3_lattices(A) & -v3_realset2(A) & v10_lattices(A) -> l1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)) & v1_pre_topc(k11_lopclset(A)))) # label(dt_k11_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12058 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> g3_lattices(k1_lopclset(A),k4_lopclset(A),k5_lopclset(A)) = k6_lopclset(A))) # label(d4_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12059 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> m1_subset_1(k2_pre_topc(A),u1_struct_0(k6_lopclset(A))))) # label(t15_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12060 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> u1_struct_0(k6_lopclset(A)) = k1_lopclset(A))) # label(t13_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12061 (all A (v17_lattices(A) & -v3_realset2(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> a_1_1_lopclset(A) = k7_lopclset(A))) # label(d5_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12062 (all A (-v3_struct_0(A) & v10_lattices(A) & v17_lattices(A) & -v3_realset2(A) & l3_lattices(A) -> k2_relat_1(k13_lopclset(A)) = u1_struct_0(k12_lopclset(A)))) # label(t41_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12063 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> m1_subset_1(k1_pre_topc(A),u1_struct_0(k6_lopclset(A))))) # label(t16_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12064 (all A all B (-v3_struct_0(B) & l1_pre_topc(B) -> (r2_hidden(A,a_1_0_lopclset(B)) <-> (exists C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & v3_pre_topc(C,B) & v4_pre_topc(C,B)))))) # label(fraenkel_a_1_0_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12065 (all A (l3_lattices(A) & -v3_realset2(A) & v17_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> v1_funct_1(k8_lopclset(A)) & v1_relat_1(k8_lopclset(A)))) # label(dt_k8_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12066 (all A (l3_lattices(A) & -v3_realset2(A) & v17_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> v3_lattice4(k13_lopclset(A),A,k12_lopclset(A)))) # label(t42_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12067 (all A (-v3_struct_0(A) & v17_lattices(A) & -v3_realset2(A) & l3_lattices(A) & v10_lattices(A) -> r1_filter_1(A,k12_lopclset(A)))) # label(t43_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12068 (all A (-v3_struct_0(A) & v10_lattices(A) & -v3_realset2(A) & l3_lattices(A) & v17_lattices(A) -> -v3_struct_0(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)) & v1_pre_topc(k11_lopclset(A)))) # label(fc4_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12069 (all A (v10_lattices(A) & v17_lattices(A) & l3_lattices(A) & -v3_realset2(A) & -v3_struct_0(A) -> k12_lopclset(A) = k6_lopclset(k11_lopclset(A)))) # label(d9_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12070 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(g3_lattices(k1_lopclset(A),k4_lopclset(A),k5_lopclset(A)))) -> (all C (m1_subset_1(C,u1_struct_0(g3_lattices(k1_lopclset(A),k4_lopclset(A),k5_lopclset(A)))) -> (all D (m2_subset_1(D,k1_zfmisc_1(u1_struct_0(A)),k1_lopclset(A)) -> (all E (m2_subset_1(E,k1_zfmisc_1(u1_struct_0(A)),k1_lopclset(A)) -> (D = B & C = E -> k1_lattices(g3_lattices(k1_lopclset(A),k4_lopclset(A),k5_lopclset(A)),B,C) = k2_lopclset(A,D,E)))))))))))) # label(t5_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12071 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(k1_lopclset(A),k1_lopclset(A)),k1_lopclset(A)) & v1_funct_2(B,k2_zfmisc_1(k1_lopclset(A),k1_lopclset(A)),k1_lopclset(A)) & v1_funct_1(B) -> (k5_lopclset(A) = B <-> (all C (m2_subset_1(C,k1_zfmisc_1(u1_struct_0(A)),k1_lopclset(A)) -> (all D (m2_subset_1(D,k1_zfmisc_1(u1_struct_0(A)),k1_lopclset(A)) -> k3_lopclset(A,C,D) = k2_binop_1(k1_lopclset(A),k1_lopclset(A),k1_lopclset(A),B,C,D)))))))))) # label(d3_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12072 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> -v1_xboole_0(k1_lopclset(A)))) # label(fc1_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12073 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> m2_subset_1(k2_pre_topc(A),k1_zfmisc_1(u1_struct_0(A)),k1_lopclset(A)))) # label(t8_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12074 $T # label(t17_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12075 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(g3_lattices(k1_lopclset(A),k4_lopclset(A),k5_lopclset(A)))) -> (all C (m1_subset_1(C,u1_struct_0(g3_lattices(k1_lopclset(A),k4_lopclset(A),k5_lopclset(A)))) -> (all D (m2_subset_1(D,k1_zfmisc_1(u1_struct_0(A)),k1_lopclset(A)) -> (all E (m2_subset_1(E,k1_zfmisc_1(u1_struct_0(A)),k1_lopclset(A)) -> (B = D & C = E -> k2_lattices(g3_lattices(k1_lopclset(A),k4_lopclset(A),k5_lopclset(A)),B,C) = k3_lopclset(A,D,E)))))))))))) # label(t6_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12076 $T # label(t39_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12077 (all A all B all C (m1_subset_1(B,k1_lopclset(A)) & m1_subset_1(C,k1_lopclset(A)) & l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> k3_lopclset(A,B,C) = k3_xboole_0(B,C))) # label(redefinition_k3_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12078 (all A (-v3_realset2(A) & l3_lattices(A) & v17_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> k1_lopclset(k11_lopclset(A)) = k10_lopclset(A))) # label(t40_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12079 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) & v3_pre_topc(B,A) -> r2_hidden(B,k1_lopclset(A))))))) # label(t4_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12080 $T # label(t31_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12081 (all A (-v3_struct_0(A) & v10_lattices(A) & -v3_realset2(A) & l3_lattices(A) & v17_lattices(A) -> k1_xboole_0 = k8_funct_2(u1_struct_0(A),k1_zfmisc_1(k7_lopclset(A)),k9_lopclset(A),k5_lattices(A)))) # label(t36_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12082 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> v10_lattices(g3_lattices(k1_lopclset(A),k4_lopclset(A),k5_lopclset(A))) & l3_lattices(g3_lattices(k1_lopclset(A),k4_lopclset(A),k5_lopclset(A))) & -v3_struct_0(g3_lattices(k1_lopclset(A),k4_lopclset(A),k5_lopclset(A))))) # label(t10_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12083 (all A (-v3_realset2(A) & l3_lattices(A) & v17_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_funct_1(k8_lopclset(A),k4_lattices(A,B,C)) = k3_xboole_0(k1_funct_1(k8_lopclset(A),B),k1_funct_1(k8_lopclset(A),C)))))))) # label(t23_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12084 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & -v3_realset2(A) & v17_lattices(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_hidden(k5_lattices(A),k3_filter_0(A,B)) & (all C (m1_subset_1(C,k5_finsub_1(u1_struct_0(A))) & -v1_xboole_0(C) -> -(r1_tarski(C,B) & k2_lattice4(A,C) = k5_lattices(A))))))))) # label(t34_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12085 (exists A (v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v17_lattices(A) & -v3_realset2(A) & v16_lattices(A) & v12_lattices(A) & v10_lattices(A) & v9_lattices(A) & v8_lattices(A) & -v3_struct_0(A) & l3_lattices(A))) # label(rc1_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12086 (all A (v10_lattices(A) & -v3_realset2(A) & l3_lattices(A) & v17_lattices(A) & -v3_struct_0(A) -> k3_tarski(k10_lopclset(A)) = k7_lopclset(A))) # label(t30_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12087 (all A all B (-v3_struct_0(B) & v10_lattices(B) & v17_lattices(B) & l3_lattices(B) & -v3_realset2(B) -> (r2_hidden(A,k7_lopclset(B)) <-> (exists C (m1_filter_0(C,B) & C = A & v1_filter_0(C,B)))))) # label(t18_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12088 (all A (-v3_struct_0(A) & -v3_realset2(A) & l3_lattices(A) & v17_lattices(A) & v10_lattices(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(B) = u1_struct_0(A) & (all C (m1_subset_1(C,u1_struct_0(A)) -> a_2_0_lopclset(A,C) = k1_funct_1(B,C))) <-> B = k8_lopclset(A)))))) # label(d6_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12089 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,k1_lopclset(A)) -> v3_pre_topc(B,A)))))) # label(t2_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12090 (all A all B all C (-v3_struct_0(A) & v2_pre_topc(A) & m1_subset_1(C,k1_lopclset(A)) & m1_subset_1(B,k1_lopclset(A)) & l1_pre_topc(A) -> k3_lopclset(A,C,B) = k3_lopclset(A,B,C))) # label(commutativity_k3_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12091 (all A (-v3_struct_0(A) & -v3_realset2(A) & l3_lattices(A) & v17_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_tarski(a_2_0_lopclset(A,B),k7_lopclset(A)))))) # label(t19_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12092 (all A all B all C (-v3_struct_0(A) & m1_subset_1(C,k1_lopclset(A)) & m1_subset_1(B,k1_lopclset(A)) & l1_pre_topc(A) & v2_pre_topc(A) -> m2_subset_1(k3_lopclset(A,B,C),k1_zfmisc_1(u1_struct_0(A)),k1_lopclset(A)))) # label(dt_k3_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12093 (all A all B (-v3_struct_0(B) & v17_lattices(B) & l3_lattices(B) & -v3_realset2(B) & v10_lattices(B) -> -(k7_lopclset(B) = k3_tarski(A) & m1_subset_1(A,k1_zfmisc_1(k10_lopclset(B))) & (all C (m1_subset_1(C,k5_finsub_1(A)) -> k3_tarski(C) != k7_lopclset(B)))))) # label(t38_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12094 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(k6_lopclset(A))) -> (all C (m1_subset_1(C,u1_struct_0(k6_lopclset(A))) -> k2_xboole_0(B,C) = k3_lattices(k6_lopclset(A),B,C))))))) # label(t11_lopclset) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12095 (all A (l1_unialg_1(A) & v8_unialg_1(A) & v7_unialg_1(A) & v6_unialg_1(A) & -v3_struct_0(A) -> (all B (v6_unialg_1(B) & v8_unialg_1(B) & l1_unialg_1(B) & v7_unialg_1(B) & -v3_struct_0(B) -> (r1_unialg_2(A,B) -> (all C (m2_unialg_2(C,u1_struct_0(A),k1_unialg_2(A)) -> (all D (m2_unialg_2(D,u1_struct_0(B),k1_unialg_2(B)) -> (all E (m2_unialg_2(E,u1_struct_0(k5_pralg_1(A,B)),k1_unialg_2(k5_pralg_1(A,B))) -> (all F (m2_subset_1(F,k1_numbers,k5_numbers) -> (k1_funct_1(u1_unialg_1(A),F) = C & E = k1_funct_1(u1_unialg_1(k5_pralg_1(A,B)),F) & r2_hidden(F,k4_finseq_1(u1_unialg_1(A))) & k1_funct_1(u1_unialg_1(B),F) = D -> E = k3_pralg_1(u1_struct_0(A),u1_struct_0(B),C,D) & k2_unialg_1(u1_struct_0(k5_pralg_1(A,B)),E) = k2_unialg_1(u1_struct_0(B),D) & k2_unialg_1(u1_struct_0(k5_pralg_1(A,B)),E) = k2_unialg_1(u1_struct_0(A),C))))))))))))))) # label(t6_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12096 (all A all B (m1_pboole(B,A) & v2_relat_1(B) & -v1_xboole_0(A) -> (all C (m1_pralg_1(C,A,B) -> v1_funcop_1(C) & m1_pboole(C,A))))) # label(dt_m1_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12097 (all A (v4_ordinal2(A) -> m2_relset_1(k7_pralg_1(A),k3_finseq_2(k1_tarski(k1_xboole_0)),k1_tarski(k1_xboole_0)) & v1_funct_1(k7_pralg_1(A)))) # label(dt_k7_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12098 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) & v2_relat_1(B) -> (all C (m1_pboole(C,A) & v1_funcop_1(C) -> ((all D (m1_subset_1(D,A) -> -v1_xboole_0(k1_funct_1(C,D)) & v1_funct_1(k1_funct_1(C,D)) & v1_unialg_1(k1_funct_1(C,D),k1_funct_1(B,D)) & m2_relset_1(k1_funct_1(C,D),k3_finseq_2(k1_funct_1(B,D)),k1_funct_1(B,D)) & v2_unialg_1(k1_funct_1(C,D),k1_funct_1(B,D)))) <-> m1_pralg_1(C,A,B)))))))) # label(d15_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12099 (all A (-v1_xboole_0(A) -> (all B (v1_pralg_1(B) & m1_pboole(B,A) & v3_pralg_1(B) -> (all C (v4_ordinal2(C) -> (r2_hidden(C,k4_finseq_1(k13_pralg_1(A,B))) -> (all D (m1_pralg_1(D,A,k12_pralg_1(A,B)) & v4_pralg_1(D) -> (k23_pralg_1(A,B,C) = D <-> (all E (m1_subset_1(E,A) -> (all F (m2_unialg_2(F,u1_struct_0(k11_pralg_1(A,B,E)),k1_unialg_2(k11_pralg_1(A,B,E))) -> (F = k1_funct_1(u1_unialg_1(k11_pralg_1(A,B,E)),C) -> k14_pralg_1(A,k12_pralg_1(A,B),D,E) = F))))))))))))))) # label(d22_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12100 (all A (-v3_struct_0(A) & l1_unialg_1(A) & v8_unialg_1(A) & v7_unialg_1(A) & v6_unialg_1(A) -> (all B (v6_unialg_1(B) & v7_unialg_1(B) & l1_unialg_1(B) & v8_unialg_1(B) & -v3_struct_0(B) -> (r1_unialg_2(A,B) -> v1_funct_1(k6_pralg_1(u1_struct_0(A),u1_struct_0(B))) & v1_funct_2(k6_pralg_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k5_pralg_1(A,B)),u1_struct_0(k5_pralg_1(B,A))) & m2_relset_1(k6_pralg_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k5_pralg_1(A,B)),u1_struct_0(k5_pralg_1(B,A)))))))) # label(t5_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12101 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) & v1_funcop_1(B) -> k16_pralg_1(A,B,C) = k15_pralg_1(B,C))) # label(redefinition_k16_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.78 12102 (all A all B (m1_pboole(B,A) -> m1_pboole(k21_pralg_1(A,B),A))) # label(dt_k21_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12103 (all A all B (v2_relat_1(B) & m1_pboole(B,A) & -v1_xboole_0(A) -> (exists C (m1_pralg_1(C,A,B) & v1_funct_1(C) & v1_funcop_1(C) & v4_pralg_1(C) & v1_relat_1(C))))) # label(rc6_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12104 (all A all B (m1_pboole(B,A) & v3_pralg_1(B) & v1_pralg_1(B) & -v1_xboole_0(A) -> m2_finseq_1(k13_pralg_1(A,B),k5_numbers))) # label(dt_k13_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12105 (all A all B all C (m1_finseq_1(C,k2_zfmisc_1(A,B)) & -v1_xboole_0(B) & -v1_xboole_0(A) -> m2_finseq_1(k1_pralg_1(A,B,C),A))) # label(dt_k1_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12106 (all A all B (v2_pralg_1(B) & m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> ((all D -(r2_hidden(D,A) & (all E (l1_struct_0(E) -> -(u1_struct_0(E) = k1_funct_1(C,D) & k1_funct_1(B,D) = E))))) <-> C = k12_pralg_1(A,B)))))) # label(d13_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12107 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,B),k2_zfmisc_1(B,A)) & v1_funct_2(C,k2_zfmisc_1(A,B),k2_zfmisc_1(B,A)) & v1_funct_1(C) -> (C = k6_pralg_1(A,B) <-> (all D (m1_subset_1(D,k2_zfmisc_1(A,B)) -> k8_funct_2(k2_zfmisc_1(A,B),k2_zfmisc_1(B,A),C,D) = k1_domain_1(B,A,k3_domain_1(A,B,D),k2_domain_1(A,B,D))))))))))) # label(d6_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12108 (all A (v7_unialg_1(A) & v8_unialg_1(A) & l1_unialg_1(A) & v6_unialg_1(A) & -v3_struct_0(A) -> (all B (v6_unialg_1(B) & v7_unialg_1(B) & v8_unialg_1(B) & l1_unialg_1(B) & -v3_struct_0(B) -> (all C (v6_unialg_1(C) & v8_unialg_1(C) & l1_unialg_1(C) & v7_unialg_1(C) & -v3_struct_0(C) -> (all D (-v3_struct_0(D) & l1_unialg_1(D) & v8_unialg_1(D) & v7_unialg_1(D) & v6_unialg_1(D) -> (m3_unialg_2(A,B) & m3_unialg_2(C,D) & r1_unialg_2(B,D) -> m3_unialg_2(k5_pralg_1(A,C),k5_pralg_1(B,D))))))))))) # label(t8_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12109 (all A (m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k4_partfun1(k13_finseq_1(k1_tarski(k1_xboole_0)),k1_tarski(k1_xboole_0))) -> (B = k8_pralg_1(A) <-> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(C,k4_finseq_1(B)) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (k1_funct_1(A,C) = D -> k1_funct_1(B,C) = k7_pralg_1(D))))))) & k3_finseq_1(A) = k3_finseq_1(B)))))) # label(d8_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12110 (all A all B all C (-v1_xboole_0(B) & m1_pboole(C,k2_zfmisc_1(A,B)) -> k3_funct_5(C) = k19_pralg_1(A,B,C))) # label(redefinition_k19_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12111 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B (r2_hidden(B,k1_relat_1(A)) -> l1_struct_0(k1_funct_1(A,B)))) <-> v2_pralg_1(A)))) # label(d11_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12112 (all A all B all C (m1_pboole(C,k2_zfmisc_1(A,B)) -> k2_funct_4(C) = k18_pralg_1(A,B,C))) # label(redefinition_k18_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12113 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> v1_funct_2(k6_pralg_1(A,B),k2_zfmisc_1(A,B),k2_zfmisc_1(B,A)) & m2_relset_1(k6_pralg_1(A,B),k2_zfmisc_1(A,B),k2_zfmisc_1(B,A)) & v1_funct_1(k6_pralg_1(A,B)))) # label(dt_k6_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12114 (all A (-v1_xboole_0(A) -> (all B (v1_pralg_1(B) & v3_pralg_1(B) & m1_pboole(B,A) -> (all C (m2_finseq_1(C,k4_partfun1(k13_finseq_1(k4_card_3(k12_pralg_1(A,B))),k4_card_3(k12_pralg_1(A,B)))) -> (C = k24_pralg_1(A,B) <-> k3_finseq_1(k13_pralg_1(A,B)) = k3_finseq_1(C) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(C)) -> k22_pralg_1(A,k12_pralg_1(A,B),k23_pralg_1(A,B,D)) = k1_funct_1(C,D))))))))))) # label(d23_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12115 (all A all B all C (m1_pboole(C,k2_zfmisc_1(A,B)) & -v1_xboole_0(B) -> m1_pboole(k19_pralg_1(A,B,C),A))) # label(dt_k19_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12116 (all A all B all C all D (v2_relat_1(B) & m1_pralg_1(C,A,B) & m1_subset_1(D,A) & m1_pboole(B,A) & -v1_xboole_0(A) -> k14_pralg_1(A,B,C,D) = k1_funct_1(C,D))) # label(redefinition_k14_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12117 (all A all B all C (m1_pralg_1(C,A,B) & v4_pralg_1(C) & m1_pboole(B,A) & v2_relat_1(B) & -v1_xboole_0(A) -> -v1_xboole_0(k22_pralg_1(A,B,C)) & v1_unialg_1(k22_pralg_1(A,B,C),k4_card_3(B)) & m2_relset_1(k22_pralg_1(A,B,C),k3_finseq_2(k4_card_3(B)),k4_card_3(B)) & v2_unialg_1(k22_pralg_1(A,B,C),k4_card_3(B)) & v1_funct_1(k22_pralg_1(A,B,C)))) # label(dt_k22_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12118 (all A all B all C (-v1_xboole_0(A) & m1_pboole(B,A) & m1_subset_1(C,A) & v1_pralg_1(B) -> v7_unialg_1(k11_pralg_1(A,B,C)) & v8_unialg_1(k11_pralg_1(A,B,C)) & l1_unialg_1(k11_pralg_1(A,B,C)) & v6_unialg_1(k11_pralg_1(A,B,C)) & -v3_struct_0(k11_pralg_1(A,B,C)))) # label(dt_k11_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12119 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> k9_funcop_1(k2_zfmisc_1(A,B),B,A,k6_pralg_1(A,B)) = k2_zfmisc_1(B,A))))) # label(t3_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12120 (all A all B all C (-v1_xboole_0(A) & m1_finseq_1(C,k2_zfmisc_1(A,B)) & -v1_xboole_0(B) -> k1_pralg_1(A,B,C) = k15_mcart_1(C))) # label(redefinition_k1_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12121 (all A (-v1_xboole_0(A) & m1_finseq_1(A,k5_numbers) -> -v3_struct_0(k9_pralg_1(A)) & v7_unialg_1(k9_pralg_1(A)) & v8_unialg_1(k9_pralg_1(A)) & l1_unialg_1(k9_pralg_1(A)) & v6_unialg_1(k9_pralg_1(A)) & v3_unialg_1(k9_pralg_1(A)))) # label(dt_k9_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12122 (all A (m2_finseq_1(A,k5_numbers) -> (k1_xboole_0 != A -> v6_unialg_1(g1_unialg_1(k1_tarski(k1_xboole_0),k8_pralg_1(A))) & l1_unialg_1(g1_unialg_1(k1_tarski(k1_xboole_0),k8_pralg_1(A))) & v8_unialg_1(g1_unialg_1(k1_tarski(k1_xboole_0),k8_pralg_1(A))) & v7_unialg_1(g1_unialg_1(k1_tarski(k1_xboole_0),k8_pralg_1(A))) & v3_unialg_1(g1_unialg_1(k1_tarski(k1_xboole_0),k8_pralg_1(A))) & -v3_struct_0(g1_unialg_1(k1_tarski(k1_xboole_0),k8_pralg_1(A)))))) # label(t11_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12123 (all A all B all C (-v1_xboole_0(A) & v3_pralg_1(B) & v4_ordinal2(C) & m1_pboole(B,A) & v1_pralg_1(B) -> v4_pralg_1(k23_pralg_1(A,B,C)) & m1_pralg_1(k23_pralg_1(A,B,C),A,k12_pralg_1(A,B)))) # label(dt_k23_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12124 (all A all B all C (-v1_xboole_0(A) & m1_finseq_1(C,k2_zfmisc_1(A,B)) & -v1_xboole_0(B) -> m2_finseq_1(k2_pralg_1(A,B,C),B))) # label(dt_k2_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12125 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v3_pralg_1(A) <-> (all B all C (r2_hidden(B,k1_relat_1(A)) & r2_hidden(C,k1_relat_1(A)) -> (all D (v6_unialg_1(D) & l1_unialg_1(D) & v8_unialg_1(D) & v7_unialg_1(D) & -v3_struct_0(D) -> (all E (-v3_struct_0(E) & v8_unialg_1(E) & l1_unialg_1(E) & v7_unialg_1(E) & v6_unialg_1(E) -> (D = k1_funct_1(A,B) & k1_funct_1(A,C) = E -> k3_unialg_1(D) = k3_unialg_1(E))))))))))) # label(d12_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12126 (all A (-v1_xboole_0(A) -> (exists B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) & -v1_xboole_0(B) & m1_finseq_1(B,A))))) # label(rc1_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12127 (all A (v1_relat_1(A) & v1_pralg_1(A) & v1_funct_1(A) -> v1_relat_1(A) & v1_funct_1(A) & v2_pralg_1(A))) # label(cc1_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12128 (all A all B (v1_funct_1(A) & v1_funcop_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_relat_1(A) -> v1_relat_1(k15_pralg_1(A,B)) & v1_funct_1(k15_pralg_1(A,B)))) # label(dt_k15_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12129 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> v2_funct_1(k6_pralg_1(A,B)))))) # label(t4_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12130 (all A all B all C (-v1_xboole_0(A) & m1_finseq_1(C,k4_card_3(B)) & m1_pboole(B,A) & v2_relat_1(B) -> k4_funct_5(C) = k17_pralg_1(A,B,C))) # label(redefinition_k17_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12131 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_1(C,k2_zfmisc_1(A,B)) -> (all D (m2_finseq_1(D,B) -> (D = k2_pralg_1(A,B,C) <-> k3_finseq_1(D) = k3_finseq_1(C) & (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (r2_hidden(E,k4_finseq_1(D)) -> k1_funct_1(D,E) = k2_mcart_1(k1_funct_1(C,E)))))))))))))) # label(d2_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12132 (all A (m1_finseq_1(A,k5_numbers) -> m2_finseq_1(k8_pralg_1(A),k4_partfun1(k13_finseq_1(k1_tarski(k1_xboole_0)),k1_tarski(k1_xboole_0))))) # label(dt_k8_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12133 (all A (l1_unialg_1(A) & v8_unialg_1(A) & v7_unialg_1(A) & v6_unialg_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v8_unialg_1(B) & l1_unialg_1(B) & v7_unialg_1(B) & v6_unialg_1(B) -> (r1_unialg_2(A,B) -> -v3_struct_0(g1_unialg_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k4_pralg_1(A,B))) & v3_unialg_1(g1_unialg_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k4_pralg_1(A,B))) & v6_unialg_1(g1_unialg_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k4_pralg_1(A,B))) & v7_unialg_1(g1_unialg_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k4_pralg_1(A,B))) & l1_unialg_1(g1_unialg_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k4_pralg_1(A,B))) & v8_unialg_1(g1_unialg_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k4_pralg_1(A,B)))))))) # label(t2_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12134 (all A all B (-v1_xboole_0(A) & v3_pralg_1(B) & m1_pboole(B,A) & v1_pralg_1(B) -> v3_unialg_1(k25_pralg_1(A,B)) & v6_unialg_1(k25_pralg_1(A,B)) & v8_unialg_1(k25_pralg_1(A,B)) & l1_unialg_1(k25_pralg_1(A,B)) & v7_unialg_1(k25_pralg_1(A,B)) & -v3_struct_0(k25_pralg_1(A,B)))) # label(dt_k25_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12135 (all A (-v1_xboole_0(A) -> (all B (v2_relat_1(B) & m1_pboole(B,A) -> (all C (v4_pralg_1(C) & m1_pralg_1(C,A,B) -> (all D (-v1_xboole_0(D) & v1_unialg_1(D,k4_card_3(B)) & m2_relset_1(D,k3_finseq_2(k4_card_3(B)),k4_card_3(B)) & v2_unialg_1(D,k4_card_3(B)) & v1_funct_1(D) -> (k22_pralg_1(A,B,C) = D <-> (all E (m2_finseq_2(E,k4_card_3(B),k3_finseq_2(k4_card_3(B))) -> (r2_hidden(E,k1_relat_1(D)) -> (k4_finseq_1(E) = k1_xboole_0 -> k1_funct_1(D,E) = k16_pralg_1(A,C,k21_pralg_1(A,B))) & (k1_xboole_0 != k4_finseq_1(E) -> (all F (-v1_xboole_0(F) -> (all G (m1_pboole(G,k2_zfmisc_1(A,F)) -> (k18_pralg_1(k4_finseq_1(E),A,k17_pralg_1(A,B,E)) = G & k4_finseq_1(E) = F -> k16_pralg_1(A,C,k19_pralg_1(A,F,G)) = k1_funct_1(D,E)))))))))) & k1_relat_1(D) = k4_finseq_2(k20_pralg_1(A,B,C),k4_card_3(B))))))))))) # label(d21_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12136 (all A all B (-v1_xboole_0(A) & m1_pboole(B,A) & v1_pralg_1(B) -> v2_relat_1(k12_pralg_1(A,B)) & v1_funct_1(k12_pralg_1(A,B)) & -v3_relat_1(k12_pralg_1(A,B)) & v1_relat_1(k12_pralg_1(A,B)))) # label(fc2_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12137 (all A (-v1_xboole_0(A) -> (exists B (-v1_xboole_0(B) & v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) & m1_subset_1(B,k3_finseq_2(A)))))) # label(rc2_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12138 (all A all B all C (v2_relat_1(B) & m1_pboole(B,A) & m1_finseq_1(C,k4_card_3(B)) & -v1_xboole_0(A) -> m1_pboole(k17_pralg_1(A,B,C),k2_zfmisc_1(k4_finseq_1(C),A)))) # label(dt_k17_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12139 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_1(C,k2_zfmisc_1(A,B)) -> (all D (m2_finseq_1(D,A) -> (k1_pralg_1(A,B,C) = D <-> (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (r2_hidden(E,k4_finseq_1(D)) -> k1_funct_1(D,E) = k1_mcart_1(k1_funct_1(C,E))))) & k3_finseq_1(D) = k3_finseq_1(C)))))))))) # label(d1_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12140 (all A (v4_ordinal2(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k3_finseq_2(k1_tarski(k1_xboole_0)),k1_tarski(k1_xboole_0)) -> (k1_tarski(k1_xboole_0) = k2_relat_1(B) & k1_tarski(k2_finseq_2(A,k1_xboole_0)) = k1_relat_1(B) <-> B = k7_pralg_1(A)))))) # label(d7_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12141 (all A all B all C all D (-v1_xboole_0(A) & m1_pboole(B,A) & m1_subset_1(D,A) & m1_pralg_1(C,A,B) & v2_relat_1(B) -> m2_relset_1(k14_pralg_1(A,B,C,D),k3_finseq_2(k1_funct_1(B,D)),k1_funct_1(B,D)) & v2_unialg_1(k14_pralg_1(A,B,C,D),k1_funct_1(B,D)) & v1_unialg_1(k14_pralg_1(A,B,C,D),k1_funct_1(B,D)) & v1_funct_1(k14_pralg_1(A,B,C,D)) & -v1_xboole_0(k14_pralg_1(A,B,C,D)))) # label(dt_k14_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12142 (all A (-v1_xboole_0(A) -> (exists B (m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_pralg_1(B) & v3_pralg_1(B) & v2_pralg_1(B))))) # label(rc5_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12143 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(C) & v1_unialg_1(C,A) & v2_unialg_1(C,A) & m1_relset_1(C,k3_finseq_2(A),A) & m1_relset_1(D,k3_finseq_2(B),B) & v2_unialg_1(D,B) & v1_unialg_1(D,B) & v1_funct_1(D) & -v1_xboole_0(D) & v1_funct_1(C) & -v1_xboole_0(A) -> -v1_xboole_0(k3_pralg_1(A,B,C,D)) & v1_funct_1(k3_pralg_1(A,B,C,D)) & m2_relset_1(k3_pralg_1(A,B,C,D),k3_finseq_2(k2_zfmisc_1(A,B)),k2_zfmisc_1(A,B)) & v2_unialg_1(k3_pralg_1(A,B,C,D),k2_zfmisc_1(A,B)) & v1_unialg_1(k3_pralg_1(A,B,C,D),k2_zfmisc_1(A,B)))) # label(dt_k3_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12144 (all A exists B (m1_pboole(B,A) & v1_relat_1(B) & v2_pralg_1(B) & v1_funct_1(B))) # label(rc4_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12145 (all A all B (-v3_struct_0(A) & v7_unialg_1(A) & v8_unialg_1(A) & -v3_struct_0(B) & v7_unialg_1(B) & l1_unialg_1(B) & v8_unialg_1(B) & v6_unialg_1(B) & l1_unialg_1(A) & v6_unialg_1(A) -> m2_finseq_1(k4_pralg_1(A,B),k4_partfun1(k13_finseq_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))))) # label(dt_k4_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12146 (exists A (v1_relat_1(A) & v1_pralg_1(A) & v1_funct_1(A))) # label(rc3_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12147 (all A (m2_finseq_1(A,k5_numbers) & -v1_xboole_0(A) -> k9_pralg_1(A) = g1_unialg_1(k1_tarski(k1_xboole_0),k8_pralg_1(A)))) # label(d9_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12148 (all A all B all C (-v1_xboole_0(A) & v1_pralg_1(B) & m1_subset_1(C,A) & m1_pboole(B,A) -> k1_funct_1(B,C) = k11_pralg_1(A,B,C))) # label(redefinition_k11_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12149 (all A all B (-v1_xboole_0(A) & v2_relat_1(B) & m1_pboole(B,A) -> (exists C m1_pralg_1(C,A,B)))) # label(existence_m1_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12150 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) & v2_unialg_1(C,A) & m2_relset_1(C,k3_finseq_2(A),A) & v1_unialg_1(C,A) & v1_funct_1(C) -> (all D (v1_unialg_1(D,B) & m2_relset_1(D,k3_finseq_2(B),B) & v2_unialg_1(D,B) & v1_funct_1(D) & -v1_xboole_0(D) -> (k2_unialg_1(B,D) = k2_unialg_1(A,C) -> (all E (-v1_xboole_0(E) & m2_relset_1(E,k3_finseq_2(k2_zfmisc_1(A,B)),k2_zfmisc_1(A,B)) & v2_unialg_1(E,k2_zfmisc_1(A,B)) & v1_unialg_1(E,k2_zfmisc_1(A,B)) & v1_funct_1(E) -> (k3_pralg_1(A,B,C,D) = E <-> k4_finseq_2(k2_unialg_1(A,C),k2_zfmisc_1(A,B)) = k1_relat_1(E) & (all F (m2_finseq_1(F,k2_zfmisc_1(A,B)) -> (r2_hidden(F,k1_relat_1(E)) -> k4_tarski(k1_funct_1(C,k1_pralg_1(A,B,F)),k1_funct_1(D,k2_pralg_1(A,B,F))) = k1_funct_1(E,F)))))))))))))))) # label(d3_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12151 (all A all B all C (v1_funcop_1(B) & m1_pboole(B,A) & m1_pboole(C,A) -> m1_pboole(k16_pralg_1(A,B,C),A))) # label(dt_k16_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12152 (all A all B all C (-v1_xboole_0(A) & m1_pboole(B,A) & m1_subset_1(C,A) & v2_pralg_1(B) -> l1_struct_0(k10_pralg_1(A,B,C)))) # label(dt_k10_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12153 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B (r2_hidden(B,k1_relat_1(A)) -> -v3_struct_0(k1_funct_1(A,B)) & v6_unialg_1(k1_funct_1(A,B)) & v7_unialg_1(k1_funct_1(A,B)) & l1_unialg_1(k1_funct_1(A,B)) & v8_unialg_1(k1_funct_1(A,B)))) <-> v1_pralg_1(A)))) # label(d10_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12154 (all A all B (m1_pboole(B,A) & v2_pralg_1(B) -> m1_pboole(k12_pralg_1(A,B),A))) # label(dt_k12_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12155 (all A all B all C (-v1_xboole_0(A) & v2_pralg_1(B) & m1_subset_1(C,A) & m1_pboole(B,A) -> k10_pralg_1(A,B,C) = k1_funct_1(B,C))) # label(redefinition_k10_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12156 (all A (-v1_xboole_0(A) -> (all B (v1_pralg_1(B) & v3_pralg_1(B) & m1_pboole(B,A) -> g1_unialg_1(k4_card_3(k12_pralg_1(A,B)),k24_pralg_1(A,B)) = k25_pralg_1(A,B))))) # label(d24_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12157 (all A (v6_unialg_1(A) & v7_unialg_1(A) & l1_unialg_1(A) & v8_unialg_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v8_unialg_1(B) & l1_unialg_1(B) & v7_unialg_1(B) & v6_unialg_1(B) -> (r1_unialg_2(A,B) -> r1_unialg_2(k5_pralg_1(A,B),A)))))) # label(t7_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12158 (all A (v6_unialg_1(A) & l1_unialg_1(A) & v8_unialg_1(A) & v7_unialg_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v7_unialg_1(B) & l1_unialg_1(B) & v8_unialg_1(B) & v6_unialg_1(B) -> (r1_unialg_2(A,B) -> (all C (m2_finseq_1(C,k4_partfun1(k13_finseq_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) -> (k3_finseq_1(C) = k3_finseq_1(u1_unialg_1(A)) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(C)) -> (all E (v1_funct_1(E) & v1_unialg_1(E,u1_struct_0(A)) & m2_relset_1(E,k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)) & v2_unialg_1(E,u1_struct_0(A)) & -v1_xboole_0(E) -> (all F (v2_unialg_1(F,u1_struct_0(B)) & m2_relset_1(F,k3_finseq_2(u1_struct_0(B)),u1_struct_0(B)) & v1_unialg_1(F,u1_struct_0(B)) & v1_funct_1(F) & -v1_xboole_0(F) -> (k1_funct_1(u1_unialg_1(A),D) = E & k1_funct_1(u1_unialg_1(B),D) = F -> k3_pralg_1(u1_struct_0(A),u1_struct_0(B),E,F) = k1_funct_1(C,D))))))))) <-> k4_pralg_1(A,B) = C)))))))) # label(d4_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12159 (all A all B all C (m1_pralg_1(C,A,B) & v4_pralg_1(C) & m1_pboole(B,A) & v2_relat_1(B) & -v1_xboole_0(A) -> m2_subset_1(k20_pralg_1(A,B,C),k1_numbers,k5_numbers))) # label(dt_k20_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12160 (all A all B (-v3_struct_0(A) & -v3_struct_0(B) & v6_unialg_1(B) & l1_unialg_1(B) & v8_unialg_1(B) & v7_unialg_1(B) & l1_unialg_1(A) & v8_unialg_1(A) & v7_unialg_1(A) & v6_unialg_1(A) -> v8_unialg_1(k5_pralg_1(A,B)) & l1_unialg_1(k5_pralg_1(A,B)) & v7_unialg_1(k5_pralg_1(A,B)) & v6_unialg_1(k5_pralg_1(A,B)) & v3_unialg_1(k5_pralg_1(A,B)) & -v3_struct_0(k5_pralg_1(A,B)))) # label(dt_k5_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12161 (all A all B (v2_relat_1(B) & m1_pboole(B,A) & -v1_xboole_0(A) -> -v1_xboole_0(k4_card_3(B)) & v1_fraenkel(k4_card_3(B)))) # label(fc3_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12162 (all A (-v1_xboole_0(A) -> (all B (v3_pralg_1(B) & m1_pboole(B,A) & v1_pralg_1(B) -> (all C (m2_finseq_1(C,k5_numbers) -> (C = k13_pralg_1(A,B) <-> (all D (m1_subset_1(D,A) -> k3_unialg_1(k11_pralg_1(A,B,D)) = C))))))))) # label(d14_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12163 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v4_pralg_1(A) <-> (all B all C (r2_hidden(B,k1_relat_1(A)) & r2_hidden(C,k1_relat_1(A)) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_relat_1(E) -> (k1_funct_1(A,C) = E & D = k1_funct_1(A,B) -> (all F (m2_subset_1(F,k1_numbers,k5_numbers) -> (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (all H (-v1_xboole_0(H) -> (all I (-v1_xboole_0(I) -> (k1_relat_1(D) = k4_finseq_2(F,H) & k4_finseq_2(G,I) = k1_relat_1(E) -> (all J (-v1_xboole_0(J) & v1_funct_1(J) & m2_relset_1(J,k3_finseq_2(H),H) & v2_unialg_1(J,H) & v1_unialg_1(J,H) -> (all K (v1_funct_1(K) & v2_unialg_1(K,I) & m2_relset_1(K,k3_finseq_2(I),I) & v1_unialg_1(K,I) & -v1_xboole_0(K) -> (K = E & J = D -> k2_unialg_1(H,J) = k2_unialg_1(I,K))))))))))))))))))))))))) # label(d16_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12164 (all A (m2_finseq_1(A,k5_numbers) -> v5_unialg_1(k8_pralg_1(A),k1_tarski(k1_xboole_0)) & v2_relat_1(k8_pralg_1(A)) & v4_unialg_1(k8_pralg_1(A),k1_tarski(k1_xboole_0)))) # label(t10_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12165 (all A (v4_ordinal2(A) -> v1_unialg_1(k7_pralg_1(A),k1_tarski(k1_xboole_0)) & v2_unialg_1(k7_pralg_1(A),k1_tarski(k1_xboole_0)) & v1_funct_1(k7_pralg_1(A)) & v1_relat_1(k7_pralg_1(A)) & -v1_xboole_0(k7_pralg_1(A)))) # label(fc1_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12166 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (k4_finseq_2(D,B) = k4_finseq_2(C,A) -> C = D))))))))) # label(t1_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12167 (all A all B (v1_funcop_1(B) & m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (D = k16_pralg_1(A,B,C) <-> (all E (r2_hidden(E,A) -> (all F (v1_funct_1(F) & v1_relat_1(F) -> (k1_funct_1(B,E) = F -> k1_funct_1(D,E) = k1_funct_1(F,k1_funct_1(C,E)))))))))))))) # label(d18_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12168 (all A (-v1_xboole_0(A) -> (all B (v2_relat_1(B) & m1_pboole(B,A) -> (all C (m1_pralg_1(C,A,B) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> k2_unialg_1(k1_funct_1(B,E),k14_pralg_1(A,B,C,E)) = k2_unialg_1(k1_funct_1(B,D),k14_pralg_1(A,B,C,D)))))) <-> v4_pralg_1(C)))))))) # label(t12_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12169 (all A all B (v1_pralg_1(B) & m1_pboole(B,A) & v3_pralg_1(B) & -v1_xboole_0(A) -> m2_finseq_1(k24_pralg_1(A,B),k4_partfun1(k13_finseq_1(k4_card_3(k12_pralg_1(A,B))),k4_card_3(k12_pralg_1(A,B)))))) # label(dt_k24_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12170 (all A all B all C (m1_finseq_1(C,k2_zfmisc_1(A,B)) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k2_pralg_1(A,B,C) = k16_mcart_1(C))) # label(redefinition_k2_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12171 (all A all B all C (m1_pboole(C,k2_zfmisc_1(A,B)) -> m1_pboole(k18_pralg_1(A,B,C),k2_zfmisc_1(B,A)))) # label(dt_k18_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12172 (all A (v4_ordinal2(A) -> k2_unialg_1(k1_tarski(k1_xboole_0),k7_pralg_1(A)) = A)) # label(t9_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12173 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (C = k15_pralg_1(A,B) <-> (all D (r2_hidden(D,k1_relat_1(A)) -> k1_funct_1(C,D) = k1_funct_1(k1_funct_1(A,D),k1_funct_1(B,D)))) & k1_relat_1(C) = k1_relat_1(A)))))))) # label(d17_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12174 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> ((all D (r2_hidden(D,A) -> k1_funct_1(C,D) = k1_subset_1(k1_funct_1(B,D)))) <-> k21_pralg_1(A,B) = C))))) # label(d20_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12175 (all A (-v1_xboole_0(A) -> (all B (v2_relat_1(B) & m1_pboole(B,A) -> (all C (v4_pralg_1(C) & m1_pralg_1(C,A,B) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (D = k20_pralg_1(A,B,C) <-> (all E (m1_subset_1(E,A) -> k2_unialg_1(k1_funct_1(B,E),k14_pralg_1(A,B,C,E)) = D))))))))))) # label(d19_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12176 (all A (v7_unialg_1(A) & l1_unialg_1(A) & v8_unialg_1(A) & v6_unialg_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v7_unialg_1(B) & l1_unialg_1(B) & v8_unialg_1(B) & v6_unialg_1(B) -> (r1_unialg_2(A,B) -> g1_unialg_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k4_pralg_1(A,B)) = k5_pralg_1(A,B)))))) # label(d5_pralg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12177 (all A (l1_pre_topc(A) & v2_tdlat_3(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & -v5_tex_2(B,A) -> v2_tdlat_3(B) & v3_tdlat_3(B) & -v5_tex_2(B,A) & -v3_realset2(B) & v5_tdlat_3(B) & v4_tdlat_3(B) & -v1_tdlat_3(B) & v2_pre_topc(B) & -v3_struct_0(B)))))) # label(cc46_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12178 (all A (l1_pre_topc(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) & v4_pre_topc(C,A) -> v4_pre_topc(k4_subset_1(u1_struct_0(A),B,C),A) & v4_pre_topc(k5_subset_1(u1_struct_0(A),B,C),A)))))) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tex_2(B,A) & v3_tex_2(C,A) & v4_pre_topc(C,A) & v4_pre_topc(B,A) -> v3_tex_2(k4_subset_1(u1_struct_0(A),B,C),A))))))))) # label(t31_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12179 (all A (-v3_struct_0(A) & v1_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> r1_borsuk_1(A,B))))) # label(t73_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12180 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> v3_tex_2(k1_struct_0(A,B),A))))) # label(t36_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12181 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(k5_subset_1(u1_struct_0(A),B,D) = C & v3_pre_topc(D,A)))) & r1_tarski(C,B)))) <-> v3_tex_2(B,A)))))) # label(d5_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12182 (all A (v2_pre_topc(A) & l1_pre_topc(A) & v3_tdlat_3(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v1_tdlat_3(B) & m1_pre_topc(B,A) -> (exists C (v5_pre_topc(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v3_borsuk_1(C,A,B) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C))))))) # label(t78_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12183 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) & v2_tdlat_3(A) -> v2_tdlat_3(B)))))) # label(t18_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12184 (all A (-v3_struct_0(A) & v1_tdlat_3(A) & -v3_realset2(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (exists B (m1_pre_topc(B,A) & v1_pre_topc(B) & v2_pre_topc(B) & v1_tsep_1(B,A) & v1_borsuk_1(B,A) & v1_tdlat_3(B) & v3_tdlat_3(B) & v2_tex_2(B,A))))) # label(rc17_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12185 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (exists B (m1_pre_topc(B,A) & -v2_tex_2(B,A) & v1_pre_topc(B) & -v3_struct_0(B))))) # label(rc11_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12186 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (l1_pre_topc(B) & v2_tdlat_3(B) & v2_pre_topc(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> v5_pre_topc(C,A,B))))))) # label(t70_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12187 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v2_tex_2(B,A) -> v1_tsep_1(B,A) & v1_borsuk_1(B,A) & v2_pre_topc(B)))))) # label(cc28_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12188 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v1_tdlat_3(B) -> v2_pre_topc(B)))))) # label(cc16_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12189 $T # label(t22_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12190 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> -(v1_tex_2(k6_domain_1(A,B),k1_zfmisc_1(A)) & v1_realset1(A)))))) # label(t6_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12191 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> -(v2_tex_2(k1_tex_2(A,B),A) & v3_realset2(A)))))) # label(t21_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12192 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (exists B (v1_pre_topc(B) & v3_realset2(B) & -v3_struct_0(B) & m1_pre_topc(B,A))))) # label(rc12_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12193 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (C = u1_struct_0(B) -> (v1_tdlat_3(B) <-> v3_tex_2(C,A))))))))) # label(t26_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12194 (all A (l1_struct_0(A) & v3_realset2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (-v1_xboole_0(B) -> -v1_xboole_0(B) & -v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A)))))))) # label(cc8_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12195 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tex_2(B,A) & r1_tarski(C,B) -> v3_tex_2(C,A)))))))) # label(t28_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12196 (all A all B (m1_subset_1(B,A) -> (v1_tex_2(B,A) <-> k3_tarski(A) != B))) # label(d2_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12197 (all A (l1_struct_0(A) & -v3_realset2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (-v1_xboole_0(B) & -v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) -> -v1_realset1(B) & -v1_xboole_0(B)))))) # label(cc11_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12198 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) -> (v2_tex_2(B,A) & g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) -> v2_tex_2(C,A)))))))) # label(t14_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12199 (all A (-v3_struct_0(A) & v3_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & v5_tex_2(B,A) & m1_pre_topc(B,A) -> (exists C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v3_borsuk_1(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B) & v1_funct_1(C))))))) # label(t74_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12200 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) -> v3_tex_2(B,A))))) # label(t35_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12201 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v2_tdlat_3(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & v3_realset2(B) -> -v3_struct_0(B) & v5_tex_2(B,A) & v3_realset2(B) & v5_tdlat_3(B) & v4_tdlat_3(B) & v3_tdlat_3(B) & v2_tdlat_3(B) & v1_tdlat_3(B) & v2_pre_topc(B)))))) # label(cc45_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12202 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v3_realset2(B) & v1_tdlat_3(B) & -v3_struct_0(B) -> -v3_struct_0(B) & -v2_tdlat_3(B)))))) # label(cc26_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12203 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (-v1_tex_2(B,k1_zfmisc_1(A)) -> -v1_xboole_0(B)))))) # label(cc1_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12204 (all A (-v3_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k3_tarski(a_2_0_tex_2(A,B)) = k6_pre_topc(A,B))))) # label(t54_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12205 (all A (-v3_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_tex_2(B,A) -> v1_tops_1(B,A)))))) # label(t62_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12206 $T # label(t3_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12207 (all A (-v3_struct_0(A) & -v3_realset2(A) & l1_struct_0(A) -> (exists B (-v1_xboole_0(B) & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & v1_realset1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc8_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12208 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(B) = C -> (v1_tex_2(C,k1_zfmisc_1(u1_struct_0(A))) <-> v2_tex_2(B,A))))))))) # label(t13_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12209 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v1_tdlat_3(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (exists C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B) & v3_borsuk_1(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C))))))) # label(t72_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12210 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(C,A) & v3_tex_2(B,A) & v3_tex_2(C,A) & v3_pre_topc(B,A) -> v3_tex_2(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t38_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12211 (all A (v3_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_tex_2(B,A) -> k3_tarski(a_2_0_tex_2(A,B)) = u1_struct_0(A)))))) # label(t63_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12212 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & v2_tdlat_3(B) & -v3_realset2(B) -> -v3_struct_0(B) & -v1_tdlat_3(B)))))) # label(cc25_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12213 (all A (-v1_realset1(A) & -v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (v1_realset1(B) & -v1_xboole_0(B) -> -v1_xboole_0(B) & v1_tex_2(B,k1_zfmisc_1(A))))))) # label(cc6_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12214 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (exists B (m1_pre_topc(B,A) & -v3_struct_0(B) & v2_pre_topc(B) & v1_tdlat_3(B) & v4_tdlat_3(B) & v3_realset2(B) & v5_tdlat_3(B) & v3_tdlat_3(B) & v2_tdlat_3(B) & v1_pre_topc(B))))) # label(rc15_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12215 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_tex_2(B,A) & v3_pre_topc(B,A) -> v1_tops_1(B,A)))))) # label(t47_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12216 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (v2_pre_topc(A) & g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) -> v2_pre_topc(B)))))) # label(t12_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12217 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> -(r2_hidden(C,B) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(D,A) & k1_struct_0(A,C) = k5_subset_1(u1_struct_0(A),B,D))))))) -> v3_tex_2(B,A)))))) # label(t37_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12218 (all A (-v1_xboole_0(A) -> (exists B (v1_realset1(B) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)))))) # label(rc5_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12219 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v3_tdlat_3(B) -> -v2_tdlat_3(B)))))) # label(cc23_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12220 (all A (l1_pre_topc(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) & v3_pre_topc(C,A) -> v3_pre_topc(k5_subset_1(u1_struct_0(A),B,C),A) & v3_pre_topc(k4_subset_1(u1_struct_0(A),B,C),A)))))) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) & v3_tex_2(B,A) & v3_tex_2(C,A) & v3_pre_topc(C,A) -> v3_tex_2(k4_subset_1(u1_struct_0(A),B,C),A))))))))) # label(t30_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12221 (all A (v2_pre_topc(A) & v3_tdlat_3(A) & -v3_realset2(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (exists B (-v3_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & v5_tdlat_3(B) & v2_tex_2(B,A) & v4_tdlat_3(B) & v3_tdlat_3(B) & m1_pre_topc(B,A))))) # label(rc19_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12222 (all A all B (m1_subset_1(B,u1_struct_0(A)) & l1_pre_topc(A) & -v3_struct_0(A) -> v1_pre_topc(k1_tex_2(A,B)) & m1_pre_topc(k1_tex_2(A,B),A) & -v3_struct_0(k1_tex_2(A,B)))) # label(dt_k1_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12223 (all A (v3_realset2(A) & l1_struct_0(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (-v1_xboole_0(B) & -v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) -> v1_realset1(B) & -v1_xboole_0(B)))))) # label(cc9_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12224 (all A (-v3_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> -(r2_hidden(C,k6_pre_topc(A,B)) & (all D (m1_subset_1(D,u1_struct_0(A)) -> -(r2_hidden(D,B) & k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,k1_struct_0(A,C))) = k1_struct_0(A,D))))))) <-> v3_tex_2(B,A)))))) # label(t60_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12225 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v2_tdlat_3(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (v4_tex_2(B,A) <-> v1_realset1(B)))))) # label(t50_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12226 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v3_tdlat_3(A) -> (all B (v5_tex_2(B,A) & m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (v3_borsuk_1(C,A,B) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (D = E -> k5_pre_topc(A,B,C,D) = k6_pre_topc(A,E))))))))))))) # label(t76_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12227 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> ((all B (-v3_struct_0(B) & l1_pre_topc(B) & v2_pre_topc(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> v5_pre_topc(C,A,B))))) -> v1_tdlat_3(A)))) # label(t69_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12228 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v2_tex_2(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(B) = C -> v1_tex_2(C,k1_zfmisc_1(u1_struct_0(A))))))))))) # label(d3_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12229 (all A (v1_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_tex_2(B,A) <-> -v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A)))))))) # label(t49_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.79 12230 (all A (-v3_struct_0(A) & v1_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v3_realset2(B) & -v3_struct_0(B) -> v2_pre_topc(B) & -v2_tdlat_3(B) & v3_tdlat_3(B) & v4_tdlat_3(B) & -v3_realset2(B) & v5_tdlat_3(B) & v1_tdlat_3(B) & v1_borsuk_1(B,A) & v1_tsep_1(B,A) & -v3_struct_0(B)))))) # label(cc32_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12231 (all A (-v1_xboole_0(A) & -v1_realset1(A) -> (exists B (v1_tex_2(B,k1_zfmisc_1(A)) & v1_realset1(B) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)))))) # label(rc6_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12232 (all A (l1_pre_topc(A) & v2_tdlat_3(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & v5_tex_2(B,A) -> -v3_struct_0(B) & v1_tdlat_3(B) & v4_tdlat_3(B) & v3_realset2(B) & v5_tdlat_3(B) & v3_tdlat_3(B) & v2_tdlat_3(B) & v2_pre_topc(B)))))) # label(cc43_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12233 (all A (-v1_xboole_0(A) & -v1_realset1(A) -> (exists B (-v1_tex_2(B,k1_zfmisc_1(A)) & -v1_realset1(B) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)))))) # label(rc7_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12234 (all A (-v3_struct_0(A) & v2_pre_topc(A) & v2_tdlat_3(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & -v3_realset2(B) -> -v3_struct_0(B) & v2_pre_topc(B) & v2_tdlat_3(B) & v4_tdlat_3(B) & v5_tdlat_3(B) & -v3_realset2(B) & v3_tdlat_3(B) & -v1_tdlat_3(B)))))) # label(cc34_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12235 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_pre_topc(C,A) & v1_pre_topc(C) & -v3_struct_0(C) -> (k1_tex_2(A,B) = C <-> k1_struct_0(A,B) = u1_struct_0(C)))))))) # label(d4_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12236 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v1_borsuk_1(B,A) -> v2_tex_2(B,A) & v2_pre_topc(B)))))) # label(cc30_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12237 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v1_tex_2(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))) <-> v2_tex_2(k1_tex_2(A,B),A)))))) # label(t20_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12238 (all A all B (m1_subset_1(B,u1_struct_0(A)) & l1_pre_topc(A) & -v3_struct_0(A) -> v3_realset2(k1_tex_2(A,B)) & v1_pre_topc(k1_tex_2(A,B)) & -v3_struct_0(k1_tex_2(A,B)))) # label(fc2_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12239 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (v1_pre_topc(B) & v2_pre_topc(B) & v1_tsep_1(B,A) & v1_borsuk_1(B,A) & m1_pre_topc(B,A))))) # label(rc16_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12240 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v3_tdlat_3(A) & -v2_tdlat_3(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & v3_realset2(B) -> v3_tdlat_3(B) & v4_tdlat_3(B) & -v5_tex_2(B,A) & v5_tdlat_3(B) & v2_pre_topc(B) & -v3_struct_0(B)))))) # label(cc50_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12241 (all A (l1_pre_topc(A) & v3_realset2(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v2_tex_2(B,A) & -v3_struct_0(B) -> -v3_struct_0(B) & v3_realset2(B)))))) # label(cc13_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12242 (all A (l1_pre_topc(A) & v1_tdlat_3(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v5_tex_2(B,A) -> v1_borsuk_1(B,A) & v2_tex_2(B,A) & v3_tdlat_3(B) & v1_tdlat_3(B) & v1_tsep_1(B,A) & v2_pre_topc(B)))))) # label(cc42_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12243 (all A (v2_pre_topc(A) & l1_pre_topc(A) & v3_tdlat_3(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) & v5_tex_2(B,A) -> (all C (v1_funct_1(C) & v5_pre_topc(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (v3_borsuk_1(C,A,B) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (D = E -> k5_pre_topc(A,B,C,k1_struct_0(B,D)) = k6_pre_topc(A,k1_struct_0(A,E)))))))))))))) # label(t77_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12244 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (v1_tex_2(B,k1_zfmisc_1(A)) <-> A != B))) # label(t5_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12245 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(v4_tex_2(B,A) & (all C (v1_pre_topc(C) & m1_pre_topc(C,A) & -v3_struct_0(C) -> -(B = u1_struct_0(C) & v5_tex_2(C,A))))))))) # label(t53_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12246 (all A (v2_pre_topc(A) & l1_pre_topc(A) & v3_tdlat_3(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(v4_tex_2(B,A) & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & (v4_pre_topc(B,A) | v3_pre_topc(B,A))))))) # label(t61_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12247 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v3_tdlat_3(A) & -v1_tdlat_3(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & v5_tex_2(B,A) -> -v3_struct_0(B) & v3_tdlat_3(B) & v5_tdlat_3(B) & v2_tex_2(B,A) & v4_tdlat_3(B) & v2_pre_topc(B)))))) # label(cc47_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12248 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v2_pre_topc(k1_tex_2(A,B)) -> v1_tdlat_3(k1_tex_2(A,B)) & v2_tdlat_3(k1_tex_2(A,B))))))) # label(t24_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12249 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v2_tdlat_3(B) -> v2_pre_topc(B)))))) # label(cc17_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12250 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tex_2(B,A) & v1_tops_1(B,A) -> v4_tex_2(B,A)))))) # label(t48_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12251 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v3_tdlat_3(A) -> (exists B (-v3_struct_0(B) & v5_tdlat_3(B) & v5_tex_2(B,A) & v4_tdlat_3(B) & v3_tdlat_3(B) & v1_tdlat_3(B) & v2_pre_topc(B) & v1_pre_topc(B) & m1_pre_topc(B,A))))) # label(rc20_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12252 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tex_2(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -(r2_hidden(C,B) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(k5_subset_1(u1_struct_0(A),B,D) = k1_tarski(C) & v4_pre_topc(D,A)))))))))))) # label(t33_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12253 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & v1_realset1(B) -> (r1_tarski(A,B) -> B = A))))) # label(t1_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12254 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v3_tdlat_3(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> -((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v4_pre_topc(D,A) & k5_subset_1(u1_struct_0(A),B,D) = k1_struct_0(A,C)))) & r2_hidden(C,B)))) -> v3_tex_2(B,A)))))) # label(t57_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12255 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v1_tsep_1(B,A) -> v2_pre_topc(B) & v2_tex_2(B,A)))))) # label(cc29_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12256 (all A (-v1_realset1(A) & -v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> v1_tex_2(k6_domain_1(A,B),k1_zfmisc_1(A)))))) # label(t7_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12257 (all A (-v1_xboole_0(A) & -v1_realset1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (-v1_tex_2(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) -> -v1_xboole_0(B) & -v1_realset1(B)))))) # label(cc7_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12258 (all A (m1_subset_1(A,k1_zfmisc_1(u1_struct_0(f1_s1_tex_2))) -> -((all B (m1_subset_1(B,u1_struct_0(f1_s1_tex_2)) -> -p1_s1_tex_2(A,B))) & r2_hidden(A,f2_s1_tex_2)))) -> (exists A ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s1_tex_2))) -> (r2_hidden(B,f2_s1_tex_2) -> p1_s1_tex_2(B,k1_funct_1(A,B))))) & m2_relset_1(A,f2_s1_tex_2,u1_struct_0(f1_s1_tex_2)) & v1_funct_2(A,f2_s1_tex_2,u1_struct_0(f1_s1_tex_2)) & v1_funct_1(A))) # label(s1_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12259 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(B) = C -> (v5_tex_2(B,A) <-> v4_tex_2(C,A))))))))) # label(t51_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12260 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) & v3_tdlat_3(A) -> v3_tdlat_3(B)))))) # label(t19_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12261 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tex_2(B,A) | v3_tex_2(C,A) -> v3_tex_2(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t29_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12262 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v2_pre_topc(B) -> -v2_tdlat_3(B)))))) # label(cc19_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12263 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> -(v2_tex_2(B,A) & u1_struct_0(A) = u1_struct_0(B)))))) # label(t15_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12264 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (C = D & v3_tex_2(C,A) & g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) -> v3_tex_2(D,B)))))))))) # label(t25_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12265 (all A (l1_pre_topc(A) & v1_tdlat_3(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v2_tex_2(B,A) -> v2_pre_topc(B) & v1_tdlat_3(B) & v3_tdlat_3(B) & v5_tex_2(B,A) & v1_borsuk_1(B,A) & v1_tsep_1(B,A)))))) # label(cc41_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12266 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tex_2(B,A) & (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tex_2(C,A) & r1_tarski(B,C) -> C = B))) <-> v4_tex_2(B,A)))))) # label(d7_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12267 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (v1_tdlat_3(A) & g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) -> v1_tdlat_3(B)))))) # label(t17_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12268 (all A (-v3_struct_0(A) & v2_pre_topc(A) & v2_tdlat_3(A) & -v3_realset2(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & v2_tex_2(B,A) -> v2_pre_topc(B) & -v1_borsuk_1(B,A) & v2_tdlat_3(B) & v4_tdlat_3(B) & v2_tex_2(B,A) & v5_tdlat_3(B) & v3_tdlat_3(B) & -v1_tsep_1(B,A) & -v3_struct_0(B)))))) # label(cc35_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12269 (all A (-v3_struct_0(A) & -v3_realset2(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & -v2_tex_2(B,A) -> -v3_realset2(B) & -v3_struct_0(B)))))) # label(cc15_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12270 (all A (-v1_xboole_0(A) & v1_realset1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (-v1_xboole_0(B) -> -v1_xboole_0(B) & -v1_tex_2(B,k1_zfmisc_1(A))))))) # label(cc4_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12271 (all A all B (-v3_struct_0(A) & v2_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) & l1_pre_topc(A) -> -v3_struct_0(k1_tex_2(A,B)) & v1_pre_topc(k1_tex_2(A,B)) & v2_tdlat_3(k1_tex_2(A,B)) & v3_tdlat_3(k1_tex_2(A,B)) & v4_tdlat_3(k1_tex_2(A,B)) & v5_tdlat_3(k1_tex_2(A,B)) & v3_realset2(k1_tex_2(A,B)) & v1_tdlat_3(k1_tex_2(A,B)) & v2_pre_topc(k1_tex_2(A,B)))) # label(fc3_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12272 (all A (-v3_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,B) -> k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,k1_struct_0(A,C))) = k1_struct_0(A,C)))) -> v3_tex_2(B,A)))))) # label(t58_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12273 $T # label(t11_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12274 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(B) = C -> v4_tex_2(C,A)))) <-> v5_tex_2(B,A)))))) # label(d8_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12275 (all A (v2_pre_topc(A) & v2_tdlat_3(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v1_tdlat_3(B) & -v3_struct_0(B) -> -v3_struct_0(B) & v5_tdlat_3(B) & v3_realset2(B) & v4_tdlat_3(B) & v3_tdlat_3(B) & v2_tdlat_3(B) & v1_tdlat_3(B) & v2_pre_topc(B)))))) # label(cc33_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12276 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -v4_tex_2(B,A))))) # label(t46_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12277 (all A (-v3_struct_0(A) & l1_struct_0(A) & -v3_realset2(A) -> (exists B (v1_realset1(B) & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc10_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12278 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -((all C (v1_pre_topc(C) & v1_tdlat_3(C) & m1_pre_topc(C,A) & -v3_struct_0(C) -> B != u1_struct_0(C))) & v3_tex_2(B,A)))))) # label(t34_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12279 (all A (-v1_xboole_0(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(A)) & v1_tex_2(B,k1_zfmisc_1(A)))))) # label(rc3_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12280 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & v2_pre_topc(B) & v3_realset2(B) -> -v3_struct_0(B) & v1_tdlat_3(B) & v2_tdlat_3(B) & v3_tdlat_3(B) & v3_realset2(B) & v5_tdlat_3(B) & v4_tdlat_3(B) & v2_pre_topc(B)))))) # label(cc27_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12281 (all A (-v3_struct_0(A) & -v3_realset2(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v3_realset2(B) & -v3_struct_0(B) -> v2_tex_2(B,A) & -v3_struct_0(B)))))) # label(cc14_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12282 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (v1_xboole_0(B) -> v1_tex_2(B,k1_zfmisc_1(A))))))) # label(cc2_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12283 (all A (v2_tdlat_3(A) & -v3_realset2(A) & l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v1_tdlat_3(B) & -v3_struct_0(B) -> v2_pre_topc(B) & v2_tdlat_3(B) & v4_tdlat_3(B) & v5_tdlat_3(B) & v2_tex_2(B,A) & v3_realset2(B) & v3_tdlat_3(B) & v1_tdlat_3(B) & -v3_struct_0(B)))))) # label(cc36_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12284 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tex_2(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(C,B) -> k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,C)) = C)))))))) # label(t41_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12285 (all A (v1_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v5_tex_2(B,A) -> v2_pre_topc(B) & v1_tsep_1(B,A) & v1_tdlat_3(B) & -v2_tex_2(B,A) & v3_tdlat_3(B) & v1_borsuk_1(B,A)))))) # label(cc39_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12286 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tex_2(B,A) & v3_tex_2(C,A) & v4_pre_topc(C,A) & v4_pre_topc(B,A) -> v3_tex_2(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t39_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12287 (all A (-v3_struct_0(A) & -v3_realset2(A) & l1_struct_0(A) -> (exists B (-v1_xboole_0(B) & -v1_realset1(B) & -v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc9_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12288 (all A (v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & v2_tdlat_3(B) -> -v3_struct_0(B) & v2_pre_topc(B) & v1_tsep_1(B,A) & v1_tdlat_3(B) & v3_realset2(B) & v5_tdlat_3(B) & v4_tdlat_3(B) & v3_tdlat_3(B) & v2_tdlat_3(B) & v1_borsuk_1(B,A)))))) # label(cc31_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12289 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v3_tdlat_3(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(C,B) & r2_hidden(D,B) -> D = C | r1_xboole_0(k6_pre_topc(A,k1_struct_0(A,C)),k6_pre_topc(A,k1_struct_0(A,D)))))))) <-> v3_tex_2(B,A)))))) # label(t59_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12290 (all A (l1_pre_topc(A) & v1_tdlat_3(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v2_tex_2(B,A) -> v2_pre_topc(B) & v1_tsep_1(B,A) & v1_borsuk_1(B,A) & v3_tdlat_3(B) & -v5_tex_2(B,A) & v1_tdlat_3(B)))))) # label(cc40_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12291 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) -> (v3_realset2(A) & u1_struct_0(B) = u1_struct_0(A) -> v3_realset2(B)))))) # label(t4_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12292 (all A (v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(v4_tex_2(C,A) & r1_tarski(B,C)))) & v3_tex_2(B,A)))))) # label(t65_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12293 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v2_pre_topc(B) -> -v1_tdlat_3(B)))))) # label(cc18_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12294 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v4_tex_2(C,A) & D = C & g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) -> v4_tex_2(D,B)))))))))) # label(t45_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12295 (all A (v2_pre_topc(A) & l1_pre_topc(A) & v1_tdlat_3(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> v5_pre_topc(C,A,B))))))) # label(t68_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12296 (all A (-v1_xboole_0(k1_tarski(A)) & v1_realset1(k1_tarski(A)) & v1_finset_1(k1_tarski(A)))) # label(fc1_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12297 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tex_2(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -(r2_hidden(C,B) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(D,A) & k1_tarski(C) = k5_subset_1(u1_struct_0(A),B,D)))))))))))) # label(t32_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12298 (all A (v2_pre_topc(A) & l1_pre_topc(A) & v1_tdlat_3(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v3_tex_2(B,A))))) # label(t43_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12299 (all A (l1_pre_topc(A) & v2_tdlat_3(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v3_realset2(B) & -v3_struct_0(B) -> v4_tdlat_3(B) & v5_tdlat_3(B) & -v5_tex_2(B,A) & v3_tdlat_3(B) & v2_tdlat_3(B) & v2_pre_topc(B) & -v3_struct_0(B)))))) # label(cc44_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12300 (all A (-v1_xboole_0(A) -> (v1_realset1(A) <-> (exists B (m1_subset_1(B,A) & k6_domain_1(A,B) = A))))) # label(d1_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12301 (all A (-v3_realset2(A) & l1_struct_0(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_realset1(B) & -v1_xboole_0(B) -> -v1_xboole_0(B) & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A)))))))) # label(cc10_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12302 (all A (-v3_struct_0(A) & -v3_realset2(A) & l1_pre_topc(A) & v2_tdlat_3(A) & v2_pre_topc(A) -> (exists B (-v1_tsep_1(B,A) & -v1_borsuk_1(B,A) & v2_tdlat_3(B) & v2_tex_2(B,A) & v3_tdlat_3(B) & v2_pre_topc(B) & v1_pre_topc(B) & m1_pre_topc(B,A))))) # label(rc18_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12303 (all A (v1_realset1(A) & -v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (v1_tex_2(B,k1_zfmisc_1(A)) -> v1_xboole_0(B) & v5_membered(B) & v1_tex_2(B,k1_zfmisc_1(A)) & v4_membered(B) & v3_membered(B) & v2_membered(B) & v1_membered(B)))))) # label(cc3_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12304 (all A (-v1_xboole_0(A) & v1_realset1(A) -> (all B (-v1_xboole_0(k3_xboole_0(A,B)) -> r1_tarski(A,B))))) # label(t2_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12305 (all A (l1_pre_topc(A) & v3_tdlat_3(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & v1_tdlat_3(B) & -v3_struct_0(B) -> r1_borsuk_1(A,B))))) # label(t79_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12306 (all A (-v1_xboole_0(A) & v1_realset1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (-v1_xboole_0(B) & -v1_tex_2(B,k1_zfmisc_1(A)) -> v1_realset1(B) & -v1_tex_2(B,k1_zfmisc_1(A)) & -v1_xboole_0(B)))))) # label(cc5_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12307 (all A (-v1_tdlat_3(A) & v3_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v2_tex_2(B,A) & -v3_struct_0(B) -> -v3_struct_0(B) & v3_tdlat_3(B) & v4_tdlat_3(B) & -v5_tex_2(B,A) & v5_tdlat_3(B) & v2_pre_topc(B)))))) # label(cc48_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12308 (all A (-v3_struct_0(A) & v2_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (v3_tex_2(B,A) <-> v1_realset1(B)))))) # label(t44_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12309 (all A (v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (exists B (v4_tex_2(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(t66_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12310 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tex_2(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,B) -> k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,k1_struct_0(A,C))) = k1_struct_0(A,C))))))))) # label(t42_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12311 (all A (-v3_realset2(A) & l1_struct_0(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> v1_tex_2(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))))))) # label(t9_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12312 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (v5_tex_2(B,A) <-> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) & v1_tdlat_3(C) -> (m1_pre_topc(B,C) -> g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(C),u1_pre_topc(C))))) & v1_tdlat_3(B)))))) # label(t52_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12313 (exists A (v1_realset1(A) & -v1_xboole_0(A))) # label(rc1_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12314 (all A (-v3_realset2(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (exists B (v2_tex_2(B,A) & v3_realset2(B) & v1_pre_topc(B) & -v3_struct_0(B) & m1_pre_topc(B,A))))) # label(rc13_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12315 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v5_tex_2(B,A) & -v3_struct_0(B) -> -v3_struct_0(B) & v3_tdlat_3(B) & v5_tdlat_3(B) & v4_tdlat_3(B) & v1_tdlat_3(B) & v2_pre_topc(B)))))) # label(cc37_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12316 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v3_tdlat_3(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (m1_subset_1(D,u1_struct_0(A)) & k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,k1_struct_0(A,C))) = k1_struct_0(A,D) & r2_hidden(D,B))))) <-> v4_tex_2(B,A)))))) # label(t64_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12317 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tex_2(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_tarski(C,B) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(C = k5_subset_1(u1_struct_0(A),B,D) & v4_pre_topc(D,A)))))))))))) # label(d6_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12318 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v3_tdlat_3(A) -> (all B (-v3_struct_0(B) & v5_tex_2(B,A) & m1_pre_topc(B,A) -> r1_borsuk_1(A,B))))) # label(t75_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12319 (all A exists B (-v1_tex_2(B,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)))) # label(rc2_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12320 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_3(B,A) & v3_tex_2(B,A) -> v3_pre_topc(B,A)))))) # label(t40_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12321 (all A (-v3_struct_0(A) & v3_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(B,k6_pre_topc(A,k1_struct_0(A,C))) -> k6_pre_topc(A,k1_struct_0(A,C)) = k6_pre_topc(A,k1_struct_0(A,B))))))))) # label(t55_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12322 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v1_tdlat_3(B) -> v3_tdlat_3(B)))))) # label(cc20_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12323 (all A (-v3_struct_0(A) & v2_pre_topc(A) & -v2_tdlat_3(A) & l1_pre_topc(A) & v3_tdlat_3(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & v5_tex_2(B,A) -> -v3_realset2(B) & v5_tdlat_3(B) & v4_tdlat_3(B) & v3_tdlat_3(B) & v2_pre_topc(B) & -v3_struct_0(B)))))) # label(cc49_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12324 (all A all B (-v3_struct_0(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) & v2_pre_topc(A) -> -v3_struct_0(k1_tex_2(A,B)) & v3_tdlat_3(k1_tex_2(A,B)) & v4_tdlat_3(k1_tex_2(A,B)) & v3_realset2(k1_tex_2(A,B)) & v5_tdlat_3(k1_tex_2(A,B)) & v2_tdlat_3(k1_tex_2(A,B)) & v1_tdlat_3(k1_tex_2(A,B)) & v2_pre_topc(k1_tex_2(A,B)) & v1_pre_topc(k1_tex_2(A,B)))) # label(fc4_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12325 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) & v3_realset2(B) -> (exists C (m1_subset_1(C,u1_struct_0(A)) & g1_pre_topc(u1_struct_0(k1_tex_2(A,C)),u1_pre_topc(k1_tex_2(A,C))) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)))))))) # label(t23_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12326 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v1_tdlat_3(B) & v2_tdlat_3(B) & -v3_struct_0(B) -> -v3_struct_0(B) & v3_realset2(B)))))) # label(cc24_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12327 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v3_tdlat_3(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & v1_tdlat_3(B) & -v3_struct_0(B) -> (exists C (m1_pre_topc(C,A) & m1_pre_topc(B,C) & v5_tex_2(C,A) & v1_pre_topc(C) & -v3_struct_0(C))))))) # label(t67_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12328 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v1_tdlat_3(B) & -v3_struct_0(B) -> -v5_tex_2(B,A) & -v3_struct_0(B)))))) # label(cc38_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12329 (all A (l1_pre_topc(A) & v3_realset2(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) -> -v2_tex_2(B,A) & -v3_struct_0(B)))))) # label(cc12_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12330 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> ((all B (-v3_struct_0(B) & l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(C) -> v5_pre_topc(C,B,A))))) -> v2_tdlat_3(A)))) # label(t71_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12331 (all A all B all C (-v3_struct_0(B) & v2_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & l1_pre_topc(B) & v3_tdlat_3(B) -> ((exists D (r2_hidden(D,C) & k6_pre_topc(B,k1_struct_0(B,D)) = A & m1_subset_1(D,u1_struct_0(B)))) <-> r2_hidden(A,a_2_0_tex_2(B,C))))) # label(fraenkel_a_2_0_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12332 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (-v2_tex_2(B,A) & m1_pre_topc(B,A) -> g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)))))) # label(t16_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12333 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v3_tdlat_3(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r1_xboole_0(k6_pre_topc(A,k1_struct_0(A,B)),k6_pre_topc(A,k1_struct_0(A,C))) | k6_pre_topc(A,k1_struct_0(A,C)) = k6_pre_topc(A,k1_struct_0(A,B)))))))) # label(t56_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12334 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v3_tdlat_3(B) -> -v1_tdlat_3(B)))))) # label(cc21_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12335 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(A) = B -> (v1_tdlat_3(A) <-> v3_tex_2(B,A))))))) # label(t27_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12336 $T # label(t10_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12337 (all A (-v1_xboole_0(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) & -v1_tex_2(B,k1_zfmisc_1(A)))))) # label(rc4_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12338 (all A (l1_struct_0(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> -(v1_tex_2(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))) & v3_realset2(A)))))) # label(t8_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12339 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (exists B (-v3_struct_0(B) & v1_pre_topc(B) & v4_tdlat_3(B) & v5_tdlat_3(B) & v3_realset2(B) & v3_tdlat_3(B) & v2_tdlat_3(B) & v1_tdlat_3(B) & v2_pre_topc(B) & m1_pre_topc(B,A))))) # label(rc14_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12340 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v2_tdlat_3(B) -> v3_tdlat_3(B)))))) # label(cc22_tex_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12341 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v2_tex_3(B,A) <-> (exists C (v1_tex_3(C,A) & m1_pre_topc(C,A) & m1_pre_topc(C,B) & v1_tsep_1(C,A) & v1_pre_topc(C)))))))) # label(t24_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12342 (all A (-v3_struct_0(A) & -v3_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (exists B (-v3_struct_0(B) & v2_pre_topc(B) & v3_tex_3(B,A) & v4_tex_3(B,A) & -v2_tex_3(B,A) & -v1_tex_3(B,A) & v2_tex_2(B,A) & -v1_tsep_1(B,A) & v1_pre_topc(B) & m1_pre_topc(B,A))))) # label(rc10_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12343 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_realset2(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v2_tex_2(B,A) & m1_pre_topc(B,A) -> (exists C (m1_pre_topc(C,A) & r4_tsep_2(A,B,C) & v2_tex_2(C,A) & v1_pre_topc(C) & -v3_struct_0(C))))))) # label(t8_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12344 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) -> (all C (-v3_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) -> (C = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) -> (v1_tex_3(B,A) & m1_pre_topc(B,A) <-> m1_pre_topc(C,A) & v1_tex_3(C,A))))))))) # label(t15_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12345 (all A (v2_pre_topc(A) & -v3_tdlat_3(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> ((exists C (v3_tex_3(C,A) & m1_pre_topc(B,C) & m1_pre_topc(C,A) & v1_borsuk_1(C,A) & v1_pre_topc(C) & -v3_struct_0(C))) <-> v4_tex_3(B,A)))))) # label(t71_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12346 (all A (v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (exists B (m1_pre_topc(B,A) & -v4_tex_3(B,A) & -v3_tex_3(B,A) & v5_tdlat_3(B) & v4_tdlat_3(B) & v3_tdlat_3(B) & v1_tdlat_3(B) & v1_tsep_1(B,A) & v1_borsuk_1(B,A) & v2_pre_topc(B) & v1_pre_topc(B) & -v3_struct_0(B))))) # label(rc4_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12347 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & -v3_tdlat_3(A) -> (all B (-v3_struct_0(B) & v2_tex_2(B,A) & m1_pre_topc(B,A) & v2_tex_3(B,A) -> (exists C (-v3_struct_0(C) & m1_pre_topc(C,A) & r4_tsep_2(A,B,C) & v4_tex_3(C,A) & v1_pre_topc(C))))))) # label(t65_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12348 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) -> (r3_tsep_2(A,B,C) -> (v3_tex_3(C,A) <-> v1_tex_3(B,A))))))))) # label(t31_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12349 (all A (-v3_struct_0(A) & v3_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v1_tex_3(B,A) & v2_tex_2(B,A) -> -v1_tsep_1(B,A) & v2_tex_2(B,A) & v2_pre_topc(B)))))) # label(cc30_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12350 (all A (l1_pre_topc(A) & -v3_tdlat_3(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (v4_tex_3(B,A) & m1_pre_topc(B,A) & -v3_struct_0(B) -> -(-(v1_borsuk_1(B,A) & v3_tex_3(B,A)) & (all C (v2_tex_2(C,A) & m1_pre_topc(C,A) & v2_tex_3(C,A) & v1_pre_topc(C) & -v3_struct_0(C) -> (all D (v1_borsuk_1(D,A) & m1_pre_topc(D,A) & v3_tex_3(D,A) & v1_pre_topc(D) & -v3_struct_0(D) -> -(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = k1_tsep_1(A,C,D) & k2_tsep_1(A,C,D) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)))))))))))) # label(t72_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12351 (all A (v2_pre_topc(A) & -v3_tdlat_3(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (exists B (m1_pre_topc(B,A) & v1_pre_topc(B) & v2_pre_topc(B) & v1_borsuk_1(B,A) & -v2_tex_3(B,A) & v4_tex_3(B,A) & v3_tex_3(B,A) & -v1_tex_3(B,A) & v2_tex_2(B,A) & -v1_tsep_1(B,A) & -v3_struct_0(B))))) # label(rc12_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12352 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) -> (r3_tsep_2(A,B,C) -> (v2_tex_3(B,A) <-> v4_tex_3(C,A))))))))) # label(t37_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12353 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (r4_tsep_2(A,B,C) -> (v3_tex_3(B,A) <-> v1_tex_3(C,A))))))))) # label(t32_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12354 (all A (-v3_struct_0(A) & v2_pre_topc(A) & -v1_tdlat_3(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> -(v1_tops_1(B,A) & (all C (v1_pre_topc(C) & v2_tex_2(C,A) & m1_pre_topc(C,A) & v1_tex_3(C,A) -> B != u1_struct_0(C)))))))) # label(t52_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12355 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) & v2_tex_3(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,B) & v2_tex_3(C,B) -> v2_tex_3(C,A) & m1_pre_topc(C,A))))))) # label(t21_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12356 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v4_tex_3(B,A) -> v2_tex_2(B,A) & v3_tex_3(B,A) & -v2_tex_3(B,A) & v2_pre_topc(B)))))) # label(cc15_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12357 (all A (v2_pre_topc(A) & l1_pre_topc(A) & v1_tdlat_3(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v1_tex_3(B,A) -> v1_borsuk_1(B,A) & v1_tdlat_3(B) & v1_tex_3(B,A) & -v4_tex_3(B,A) & -v3_tex_3(B,A) & v2_tex_3(B,A) & v5_tex_2(B,A) & -v2_tex_2(B,A) & v3_tdlat_3(B) & v1_tsep_1(B,A) & v2_pre_topc(B)))))) # label(cc24_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12358 (all A (v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v1_tsep_1(B,A) & v2_tex_2(B,A) -> -v1_tex_3(B,A) & -v2_tex_3(B,A) & v2_tex_2(B,A) & v2_pre_topc(B)))))) # label(cc32_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12359 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) -> (v4_tex_3(B,A) & m1_pre_topc(C,B) -> v4_tex_3(C,A)))))))) # label(t40_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12360 (all A (v2_pre_topc(A) & l1_pre_topc(A) & v3_tdlat_3(A) & -v3_struct_0(A) -> (exists B (m1_pre_topc(B,A) & -v3_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & v4_tdlat_3(B) & -v4_tex_3(B,A) & v5_tdlat_3(B) & v3_tdlat_3(B))))) # label(rc8_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12361 (all A (-v3_struct_0(A) & v1_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v2_tex_2(B,A) -> v2_pre_topc(B) & v2_tex_2(B,A) & -v2_tex_3(B,A) & -v1_tex_3(B,A) & -v5_tex_2(B,A) & v3_tdlat_3(B) & v1_tdlat_3(B) & v1_tsep_1(B,A) & v1_borsuk_1(B,A)))))) # label(cc23_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12362 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (v1_tex_3(C,A) | v1_tex_3(B,A) -> v1_tex_3(k1_tsep_1(A,B,C),A) & m1_pre_topc(k1_tsep_1(A,B,C),A)))))))) # label(t25_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12363 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> -(v2_tops_1(B,A) & (all C (m1_pre_topc(C,A) & v1_pre_topc(C) -> -(v3_tex_3(C,A) & u1_struct_0(C) = B)))))))) # label(t30_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12364 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v1_tex_3(B,A) -> -v4_tex_3(B,A) & v2_pre_topc(B)))))) # label(cc18_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12365 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (v1_tex_3(C,A) & v2_tex_3(B,A) | v1_tex_3(B,A) & v2_tex_3(C,A) -> v1_tex_3(k2_tsep_1(A,B,C),A) & m1_pre_topc(k2_tsep_1(A,B,C),A)))))))) # label(t28_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12366 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v3_tex_3(B,A) -> v2_pre_topc(B) & -v2_tex_3(B,A) & v2_tex_2(B,A)))))) # label(cc14_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12367 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v1_tex_3(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(B) = C -> v1_tops_1(C,A))))))))) # label(d1_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12368 (all A (v2_pre_topc(A) & -v1_tdlat_3(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v2_tex_2(B,A) & v1_tex_3(B,A) & m1_pre_topc(B,A) -> (exists C (r4_tsep_2(A,B,C) & m1_pre_topc(C,A) & v3_tex_3(C,A) & v1_pre_topc(C) & -v3_struct_0(C))))))) # label(t54_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12369 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(v1_tops_1(B,A) & (all C (v1_pre_topc(C) & v1_tsep_1(C,A) & v1_tex_3(C,A) & m1_pre_topc(C,A) & -v3_struct_0(C) -> B != u1_struct_0(C))) & v3_pre_topc(B,A)))))) # label(t23_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.80 12370 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & -v1_tdlat_3(A) -> (exists B (m1_pre_topc(B,A) & -v3_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & v2_tex_2(B,A) & v1_tex_3(B,A) & -v4_tex_3(B,A) & -v1_borsuk_1(B,A))))) # label(rc7_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12371 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(B) = C -> (v1_tex_3(B,A) <-> v1_tops_1(C,A))))))))) # label(t9_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12372 (all A (v1_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) -> -v3_struct_0(B) & v1_tsep_1(B,A) & v1_tdlat_3(B) & v3_tdlat_3(B) & v4_tdlat_3(B) & v5_tdlat_3(B) & -v3_tex_3(B,A) & -v4_tex_3(B,A) & v1_borsuk_1(B,A) & v2_pre_topc(B)))))) # label(cc22_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12373 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> -(v1_tops_3(B,A) & (all C (v2_tex_3(C,A) & m1_pre_topc(C,A) & v1_pre_topc(C) & -v3_struct_0(C) -> u1_struct_0(C) != B))))))) # label(t17_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12374 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> -(-r1_tsep_1(A,B,C) & -v4_tex_3(k2_tsep_1(A,B,C),A) & (v4_tex_3(B,A) | v4_tex_3(C,A))))))))) # label(t46_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12375 (all A (-v3_struct_0(A) & -v3_realset2(A) & l1_pre_topc(A) & v1_tdlat_3(A) & v2_pre_topc(A) -> (exists B (v2_pre_topc(B) & v1_tsep_1(B,A) & v3_tdlat_3(B) & v2_tex_2(B,A) & -v5_tex_2(B,A) & -v1_tex_3(B,A) & -v2_tex_3(B,A) & v1_tdlat_3(B) & v1_borsuk_1(B,A) & v1_pre_topc(B) & m1_pre_topc(B,A))))) # label(rc5_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12376 (all A (v2_pre_topc(A) & -v3_tdlat_3(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> -(v1_tops_3(B,A) & (all C (v1_pre_topc(C) & v2_tex_2(C,A) & m1_pre_topc(C,A) & v2_tex_3(C,A) -> u1_struct_0(C) != B))))))) # label(t63_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12377 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & v3_tex_3(B,A) -> v2_tex_2(B,A) & -v1_tsep_1(B,A) & v2_pre_topc(B) & -v3_struct_0(B)))))) # label(cc12_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12378 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & -v3_realset2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (exists C (v2_tex_2(C,A) & m1_pre_topc(C,A) & B = u1_struct_0(C) & v1_pre_topc(C) & -v3_struct_0(C))))))) # label(t7_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12379 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v2_tex_2(B,A) -> v2_pre_topc(B) & v2_tex_3(B,A)))))) # label(cc6_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12380 (all A (v2_pre_topc(A) & -v3_tdlat_3(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (v2_tex_2(B,A) & m1_pre_topc(B,A) & v2_tex_3(B,A) -> (exists C (v1_tsep_1(C,A) & (exists D (v1_pre_topc(D) & r3_tsep_2(A,C,D) & m1_pre_topc(C,B) & m1_pre_topc(D,A) & v3_tex_3(D,A) & v1_borsuk_1(D,A))) & m1_pre_topc(C,A) & v1_tex_3(C,A) & v2_tex_2(C,A) & v1_pre_topc(C))))))) # label(t75_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12381 (all A (-v3_struct_0(A) & v3_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) -> v4_tdlat_3(B) & v5_tdlat_3(B) & -v4_tex_3(B,A) & v3_tdlat_3(B) & v2_pre_topc(B) & -v3_struct_0(B)))))) # label(cc25_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12382 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v2_tex_3(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(B) = C -> v1_tops_3(C,A))))))))) # label(d2_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12383 (all A (-v3_struct_0(A) & -v3_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v3_tex_3(B,A) & m1_pre_topc(B,A) & v1_borsuk_1(B,A) & -v3_struct_0(B) -> (exists C (-v3_struct_0(C) & v1_tsep_1(C,A) & v2_tex_2(C,A) & v1_tex_3(C,A) & r4_tsep_2(A,B,C) & m1_pre_topc(C,A) & v1_pre_topc(C))))))) # label(t69_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12384 (all A (-v3_struct_0(A) & v2_pre_topc(A) & -v3_tdlat_3(A) & l1_pre_topc(A) -> (all B (v1_tsep_1(B,A) & v2_tex_2(B,A) & v1_tex_3(B,A) & m1_pre_topc(B,A) & -v3_struct_0(B) -> (exists C (-v3_struct_0(C) & v1_pre_topc(C) & v1_borsuk_1(C,A) & m1_pre_topc(C,A) & r4_tsep_2(A,B,C) & v3_tex_3(C,A))))))) # label(t70_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12385 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> -(-v3_tex_3(k2_tsep_1(A,B,C),A) & -r1_tsep_1(A,B,C) & (v3_tex_3(B,A) | v3_tex_3(C,A))))))))) # label(t43_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12386 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & -v1_tdlat_3(A) -> (exists B (m1_pre_topc(B,A) & v2_pre_topc(B) & -v1_tsep_1(B,A) & v2_tex_2(B,A) & -v2_tex_3(B,A) & v3_tex_3(B,A) & v1_pre_topc(B) & -v3_struct_0(B))))) # label(rc6_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12387 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v3_tex_3(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(C,u1_struct_0(B)) -> v2_tops_1(C,A))))))))) # label(t33_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12388 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(B) = C -> v2_tops_1(C,A)))) <-> v3_tex_3(B,A)))))) # label(d3_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12389 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_tsep_2(A,B,C) -> (v3_tops_1(C,A) <-> v1_tops_3(B,A))))))))) # label(t4_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12390 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (C = u1_struct_0(B) -> (v2_tex_3(B,A) <-> v1_tops_3(C,A))))))))) # label(t16_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12391 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(B) = C -> (v4_tex_3(B,A) <-> v3_tops_1(C,A))))))))) # label(t35_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12392 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v1_tex_3(B,A) -> -v2_tex_3(B,A) & v2_pre_topc(B)))))) # label(cc5_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12393 (all A (-v3_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_tex_3(B,A) & m1_pre_topc(B,A) -> (exists C (v1_pre_topc(C) & v2_tex_2(C,A) & m1_pre_topc(C,A) & r4_tsep_2(A,B,C) & v2_tex_3(C,A) & -v3_struct_0(C))))))) # label(t64_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12394 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_tsep_2(A,B,C) -> (v1_tops_1(C,A) <-> v2_tops_1(B,A))))))))) # label(t3_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12395 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> -(v1_tdlat_3(A) & (exists B (-v3_struct_0(B) & v3_tex_3(B,A) & m1_pre_topc(B,A)))))) # label(t49_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12396 (all A (v2_pre_topc(A) & -v3_realset2(A) & l1_pre_topc(A) & -v3_struct_0(A) -> ((all B (m1_pre_topc(B,A) & v2_tex_2(B,A) -> -v1_tex_3(B,A))) -> v1_tdlat_3(A)))) # label(t48_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12397 (all A (-v3_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_tops_1(B,A) & (all C (-v3_struct_0(C) & v4_tex_3(C,A) & m1_pre_topc(C,A) & v1_pre_topc(C) -> B != u1_struct_0(C)))))))) # label(t62_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12398 (all A (-v3_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(v4_pre_topc(B,A) & (all C (v1_pre_topc(C) & v3_tex_3(C,A) & m1_pre_topc(C,A) & v1_borsuk_1(C,A) & -v3_struct_0(C) -> B != u1_struct_0(C))) & v2_tops_1(B,A)))))) # label(t67_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12399 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> -(v3_tops_1(B,A) & (all C (v1_pre_topc(C) & m1_pre_topc(C,A) -> -(B = u1_struct_0(C) & v4_tex_3(C,A))))))))) # label(t36_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12400 (all A (-v3_struct_0(A) & l1_pre_topc(A) & -v3_tdlat_3(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> -(v1_tops_1(B,A) & (all C (v2_tex_2(C,A) & v1_tex_3(C,A) & m1_pre_topc(C,A) & v1_tsep_1(C,A) & v1_pre_topc(C) -> u1_struct_0(C) != B)) & v3_pre_topc(B,A)))))) # label(t68_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12401 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v1_tex_3(B,A) & m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (C = D -> (v1_tops_1(D,B) <-> v1_tops_1(C,A))))))))))) # label(t11_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12402 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v1_borsuk_1(B,A) & v3_tex_3(B,A) -> v2_pre_topc(B) & v2_tex_2(B,A) & -v2_tex_3(B,A) & v4_tex_3(B,A) & v3_tex_3(B,A) & -v1_tex_3(B,A)))))) # label(cc19_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12403 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (v2_tex_3(C,A) & v2_tex_3(B,A) -> v2_tex_3(k2_tsep_1(A,B,C),A) & m1_pre_topc(k2_tsep_1(A,B,C),A)))))))) # label(t27_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12404 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> -(v3_tdlat_3(A) & (exists B (m1_pre_topc(B,A) & v2_tex_2(B,A) & v1_tsep_1(B,A) & v1_tex_3(B,A) & -v3_struct_0(B)))))) # label(t61_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12405 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v1_tsep_1(B,A) & -v3_struct_0(B) -> -v3_struct_0(B) & v2_pre_topc(B) & -v3_tex_3(B,A)))))) # label(cc11_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12406 (all A (-v3_struct_0(A) & v3_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v1_tex_3(B,A) & v1_tsep_1(B,A) -> v1_tsep_1(B,A) & -v4_tex_3(B,A) & -v3_tex_3(B,A) & v2_tex_3(B,A) & v1_tex_3(B,A) & -v2_tex_2(B,A) & v1_borsuk_1(B,A) & v2_pre_topc(B)))))) # label(cc31_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12407 (all A (-v3_struct_0(A) & l1_pre_topc(A) & -v3_realset2(A) & v2_pre_topc(A) -> ((all B (v2_tex_2(B,A) & m1_pre_topc(B,A) -> -v2_tex_3(B,A))) -> v3_tdlat_3(A)))) # label(t57_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12408 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v2_tex_3(B,A) & v1_tsep_1(B,A) -> v2_tex_2(B,A) & -v1_tex_3(B,A) & -v2_tex_3(B,A) & v2_pre_topc(B)))))) # label(cc10_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12409 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v2_tex_2(B,A) & v1_tex_3(B,A) -> v2_pre_topc(B) & v2_tex_2(B,A) & -v1_borsuk_1(B,A)))))) # label(cc2_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12410 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v1_tdlat_3(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_tex_3(B,A) & m1_pre_topc(B,A) -> (exists C (v1_pre_topc(C) & v2_tex_2(C,A) & v1_tex_3(C,A) & r4_tsep_2(A,B,C) & m1_pre_topc(C,A) & -v3_struct_0(C))))))) # label(t53_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12411 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v1_tex_3(B,A) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) -> (m1_pre_topc(B,C) -> v1_tex_3(C,A)))))))) # label(t12_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12412 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_tsep_2(A,B,C) -> (v2_tops_1(C,A) <-> v1_tops_1(B,A))))))))) # label(t2_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12413 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> ((exists C (m1_pre_topc(C,A) & v3_tex_3(C,A) & m1_pre_topc(B,C) & v1_borsuk_1(C,A) & v1_pre_topc(C) & -v3_struct_0(C))) <-> v4_tex_3(B,A)))))) # label(t42_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12414 (all A (-v3_struct_0(A) & v3_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v2_tex_3(B,A) -> v1_tsep_1(B,A) & v2_tex_3(B,A) & -v4_tex_3(B,A) & -v3_tex_3(B,A) & v1_tex_3(B,A) & -v2_tex_2(B,A) & v1_borsuk_1(B,A) & v2_pre_topc(B)))))) # label(cc27_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12415 (all A (l1_pre_topc(A) & -v3_tdlat_3(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_tex_3(B,A) & m1_pre_topc(B,A) -> (exists C (-v3_struct_0(C) & v2_tex_2(C,A) & m1_pre_topc(C,A) & (exists D (v1_pre_topc(D) & m1_pre_topc(D,A) & m1_pre_topc(B,D) & r4_tsep_2(A,C,D) & v3_tex_3(D,A) & v1_borsuk_1(D,A) & -v3_struct_0(D))) & v1_tex_3(C,A) & v1_tsep_1(C,A) & v1_pre_topc(C))))))) # label(t74_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12416 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (v4_tex_3(C,A) & v4_tex_3(B,A) -> v4_tex_3(k1_tsep_1(A,B,C),A)))))))) # label(t44_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12417 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v1_borsuk_1(B,A) & v2_tex_2(B,A) -> -v1_tex_3(B,A) & v2_pre_topc(B)))))) # label(cc3_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12418 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> (all C (v2_pre_topc(C) & l1_pre_topc(C) & -v3_struct_0(C) -> (g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = C -> (v2_tex_3(C,A) & m1_pre_topc(C,A) <-> v2_tex_3(B,A) & m1_pre_topc(B,A))))))))) # label(t22_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12419 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(v2_tops_1(B,A) & v4_pre_topc(B,A) & (all C (v1_pre_topc(C) & v1_borsuk_1(C,A) & m1_pre_topc(C,A) & -v3_struct_0(C) -> -(v3_tex_3(C,A) & u1_struct_0(C) = B)))))))) # label(t41_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12420 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v2_tex_3(B,A) -> v2_pre_topc(B) & v1_tex_3(B,A)))))) # label(cc4_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12421 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (v1_tex_3(B,A) & m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & v1_tex_3(C,B) & m1_pre_topc(C,B) -> -v3_struct_0(C) & v1_tex_3(C,A) & m1_pre_topc(C,A))))))) # label(t14_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12422 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & -v3_tdlat_3(A) -> (exists B (-v3_struct_0(B) & -v1_borsuk_1(B,A) & v2_tex_3(B,A) & -v4_tex_3(B,A) & -v3_tex_3(B,A) & v1_tex_3(B,A) & v2_tex_2(B,A) & v2_pre_topc(B) & v1_pre_topc(B) & m1_pre_topc(B,A))))) # label(rc11_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12423 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v4_tex_3(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (C = u1_struct_0(B) -> v3_tops_1(C,A))))))))) # label(d4_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12424 (all A (-v3_struct_0(A) & -v3_realset2(A) & l1_pre_topc(A) & v3_tdlat_3(A) & v2_pre_topc(A) -> (exists B (m1_pre_topc(B,A) & v1_pre_topc(B) & v2_tex_2(B,A) & -v2_tex_3(B,A) & v2_pre_topc(B))))) # label(rc9_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12425 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (r4_tsep_2(A,B,C) -> (v2_tex_3(C,A) <-> v4_tex_3(B,A))))))))) # label(t38_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12426 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) & v1_tex_3(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (m1_pre_topc(B,C) -> v1_tex_3(B,C) & m1_pre_topc(B,C)))))))) # label(t13_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12427 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v1_tex_3(B,A) & v1_tsep_1(B,A) -> v2_tex_3(B,A) & v1_tex_3(B,A) & v2_pre_topc(B)))))) # label(cc8_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12428 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v2_tex_3(B,A) -> -v3_tex_3(B,A) & v2_pre_topc(B)))))) # label(cc13_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12429 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & v2_tex_3(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (m1_pre_topc(B,C) -> m1_pre_topc(B,C) & v2_tex_3(B,C)))))))) # label(t20_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12430 (all A (-v3_struct_0(A) & l1_pre_topc(A) & -v3_tdlat_3(A) & v2_pre_topc(A) -> (exists B (v2_pre_topc(B) & -v1_borsuk_1(B,A) & v1_tsep_1(B,A) & v2_tex_3(B,A) & -v3_tex_3(B,A) & -v4_tex_3(B,A) & v1_tex_3(B,A) & v2_tex_2(B,A) & v1_pre_topc(B) & -v3_struct_0(B) & m1_pre_topc(B,A))))) # label(rc13_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12431 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (exists B (m1_pre_topc(B,A) & -v3_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & v1_tex_3(B,A) & v2_tex_3(B,A) & v1_tsep_1(B,A))))) # label(rc3_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12432 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_tsep_2(A,B,C) -> (-v1_xboole_0(B) <-> v1_tex_2(C,k1_zfmisc_1(u1_struct_0(A))))))))))) # label(t1_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12433 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> -((exists B (-v3_struct_0(B) & v2_tex_2(B,A) & v2_tex_3(B,A) & m1_pre_topc(B,A))) & v3_tdlat_3(A)))) # label(t60_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12434 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> ((all B (m1_pre_topc(B,A) -> -v4_tex_3(B,A))) -> v3_tdlat_3(A)))) # label(t56_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12435 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> ((all B (m1_pre_topc(B,A) -> -v3_tex_3(B,A))) -> v1_tdlat_3(A)))) # label(t47_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12436 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v1_borsuk_1(B,A) & v1_tex_3(B,A) -> v2_pre_topc(B) & v1_borsuk_1(B,A) & -v2_tex_2(B,A) & v1_tsep_1(B,A)))))) # label(cc1_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12437 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v2_tex_3(B,A) -> v2_pre_topc(B) & v2_tex_2(B,A)))))) # label(cc7_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12438 (all A (v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v2_tex_2(B,A) -> v2_pre_topc(B) & v2_tex_2(B,A) & -v2_tex_3(B,A)))))) # label(cc26_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12439 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_tsep_2(A,B,C) -> (v3_tops_1(B,A) <-> v1_tops_3(C,A))))))))) # label(t5_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12440 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v3_tex_3(B,A) & -v4_tex_3(B,A) -> v2_tex_2(B,A) & -v1_borsuk_1(B,A) & v2_pre_topc(B)))))) # label(cc20_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12441 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v3_tex_3(B,A) -> -v4_tex_3(B,A) & v2_pre_topc(B)))))) # label(cc16_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12442 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v4_tex_3(B,A) & v1_borsuk_1(B,A) -> -v4_tex_3(B,A) & -v3_tex_3(B,A) & v2_pre_topc(B)))))) # label(cc21_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12443 (all A (v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v1_borsuk_1(B,A) & -v3_struct_0(B) -> v2_pre_topc(B) & v4_tdlat_3(B) & v5_tdlat_3(B) & -v3_tex_3(B,A) & -v4_tex_3(B,A) & v3_tdlat_3(B) & -v3_struct_0(B)))))) # label(cc29_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12444 (all A (-v3_struct_0(A) & l1_pre_topc(A) & -v1_tdlat_3(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & l1_pre_topc(B) & v2_pre_topc(B) -> (all C (v2_pre_topc(C) & l1_pre_topc(C) & -v3_struct_0(C) -> (C = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) -> (v3_tex_3(C,A) & m1_pre_topc(C,A) <-> m1_pre_topc(B,A) & v3_tex_3(B,A))))))))) # label(t55_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12445 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v4_tex_3(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(C,u1_struct_0(B)) -> v3_tops_1(C,A))))))))) # label(t39_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12446 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (v2_tex_3(C,A) | v2_tex_3(B,A) -> m1_pre_topc(k1_tsep_1(A,B,C),A) & v2_tex_3(k1_tsep_1(A,B,C),A)))))))) # label(t26_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12447 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v4_tex_3(B,A) -> v2_pre_topc(B) & v2_tex_2(B,A) & -v2_tex_3(B,A) & -v1_tex_3(B,A)))))) # label(cc17_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12448 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & -v1_tdlat_3(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> -((all C (v1_pre_topc(C) & m1_pre_topc(C,A) & v3_tex_3(C,A) -> u1_struct_0(C) != B)) & v2_tops_1(B,A)))))) # label(t51_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12449 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (exists B (v2_pre_topc(B) & v2_tex_3(B,A) & v1_tex_3(B,A) & v1_pre_topc(B) & -v3_struct_0(B) & m1_pre_topc(B,A))))) # label(rc2_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12450 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v2_tex_3(B,A) & m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (D = C -> (v1_tops_3(D,B) <-> v1_tops_3(C,A))))))))))) # label(t18_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12451 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> -((exists B (-v3_struct_0(B) & m1_pre_topc(B,A) & v2_tex_2(B,A) & v1_tex_3(B,A))) & v1_tdlat_3(A)))) # label(t50_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12452 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> -((exists B (-v3_struct_0(B) & m1_pre_topc(B,A) & v3_tex_3(B,A) & v1_borsuk_1(B,A))) & v3_tdlat_3(A)))) # label(t59_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12453 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (r4_tsep_2(A,B,C) -> v2_tex_2(B,A) & v2_tex_2(C,A)))))))) # label(t6_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12454 (all A (-v3_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & v3_tex_3(B,A) -> v2_pre_topc(B) & v3_tdlat_3(B) & v4_tdlat_3(B) & v2_tex_2(B,A) & v5_tdlat_3(B) & -v1_borsuk_1(B,A) & -v3_struct_0(B)))))) # label(cc28_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12455 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> -((exists B (m1_pre_topc(B,A) & v4_tex_3(B,A) & -v3_struct_0(B))) & v3_tdlat_3(A)))) # label(t58_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12456 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_tex_3(B,A) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) -> (m1_pre_topc(B,C) -> v2_tex_3(C,A)))))))) # label(t19_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12457 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) -> (v3_tex_3(B,A) & m1_pre_topc(C,B) -> v3_tex_3(C,A)))))))) # label(t34_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12458 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (C = u1_struct_0(B) -> (v3_tex_3(B,A) <-> v2_tops_1(C,A))))))))) # label(t29_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12459 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -((all C (-v3_struct_0(C) & v1_pre_topc(C) & m1_pre_topc(C,A) & v1_tex_3(C,A) -> B != u1_struct_0(C))) & v1_tops_1(B,A)))))) # label(t10_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12460 (all A (l1_pre_topc(A) & -v3_tdlat_3(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l1_pre_topc(B) & v2_pre_topc(B) -> (all C (v2_pre_topc(C) & l1_pre_topc(C) & -v3_struct_0(C) -> (C = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) -> (m1_pre_topc(C,A) & v4_tex_3(C,A) <-> m1_pre_topc(B,A) & v4_tex_3(B,A))))))))) # label(t66_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12461 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (v3_tex_3(B,A) & v4_tex_3(C,A) | v3_tex_3(C,A) & v4_tex_3(B,A) -> v3_tex_3(k1_tsep_1(A,B,C),A)))))))) # label(t45_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12462 (all A (l1_pre_topc(A) & -v3_tdlat_3(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & v2_tex_3(B,A) & -v3_struct_0(B) -> -(-(v1_tsep_1(B,A) & v1_tex_3(B,A)) & (all C (v1_tsep_1(C,A) & v1_tex_3(C,A) & m1_pre_topc(C,A) & v2_tex_2(C,A) & v1_pre_topc(C) & -v3_struct_0(C) -> (all D (-v3_struct_0(D) & v4_tex_3(D,A) & m1_pre_topc(D,A) & v1_pre_topc(D) -> -(r1_tsep_1(A,C,D) & g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = k1_tsep_1(A,C,D))))))))))) # label(t73_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12463 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v1_tex_3(B,A) & -v2_tex_3(B,A) -> v2_tex_2(B,A) & -v1_tsep_1(B,A) & v2_pre_topc(B)))))) # label(cc9_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12464 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (v1_tex_3(B,A) & v2_pre_topc(B) & v1_pre_topc(B) & -v3_struct_0(B) & m1_pre_topc(B,A))))) # label(rc1_tex_3) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12465 (all A all B all C (-v3_struct_0(A) & l3_msualg_1(C,A) & m1_subset_1(B,u1_msualg_1(A)) & l1_msualg_1(A) & -v2_msualg_1(A) -> m1_subset_1(k4_msualg_1(A,B,C),k2_relat_1(u4_msualg_1(A,C))))) # label(dt_k4_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12466 $T # label(d2_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12467 (all A (-v3_struct_0(A) & v6_unialg_1(A) & v8_unialg_1(A) & l1_unialg_1(A) & v7_unialg_1(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k4_finseq_1(k6_msualg_1(A)),k3_finseq_2(k1_tarski(np__0))) & m2_relset_1(B,k4_finseq_1(k6_msualg_1(A)),k3_finseq_2(k1_tarski(np__0))) -> (B = k1_partfun1(k5_numbers,k5_numbers,k5_numbers,k3_finseq_2(k1_tarski(np__0)),k6_msualg_1(A),k9_pboole(np__0)) -> g1_msualg_1(k1_tarski(np__0),k4_finseq_1(k6_msualg_1(A)),B,k10_pboole(k4_finseq_1(k6_msualg_1(A)),np__0)) = k7_msualg_1(A)))))) # label(t16_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12468 (all A (l1_struct_0(A) -> (exists B (v3_msualg_1(B,A) & l2_msualg_1(B,A))))) # label(rc4_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12469 (all A all B all C all D (v1_funct_2(C,B,k3_finseq_2(A)) & m1_relset_1(C,B,k3_finseq_2(A)) & m1_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_1(D) & v1_funct_1(C) -> (all E all F all G all H (g1_msualg_1(A,B,C,D) = g1_msualg_1(E,F,G,H) -> G = C & D = H & B = F & E = A)))) # label(free_g1_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12470 (exists A (l1_msualg_1(A) & -v3_struct_0(A) & v1_msualg_1(A) & -v2_msualg_1(A))) # label(rc3_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12471 (all A (v6_unialg_1(A) & l1_unialg_1(A) & v8_unialg_1(A) & v7_unialg_1(A) & -v3_struct_0(A) -> k10_pboole(k1_tarski(np__0),u1_struct_0(A)) = k8_msualg_1(A))) # label(d14_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12472 (all A (l1_msualg_1(A) -> l1_struct_0(A))) # label(dt_l1_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12473 (all A (l1_struct_0(A) -> (exists B (l2_msualg_1(B,A) & v3_msualg_1(B,A) & v5_msualg_1(B,A))))) # label(rc7_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12474 (all A (-v3_struct_0(A) & l1_unialg_1(A) & v8_unialg_1(A) & v7_unialg_1(A) & v6_unialg_1(A) -> k10_msualg_1(A) = g3_msualg_1(k7_msualg_1(A),k8_msualg_1(A),k9_msualg_1(A)))) # label(d16_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12475 $T # label(t2_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12476 (all A all B (l1_struct_0(A) & l2_msualg_1(B,A) -> (v3_msualg_1(B,A) -> g2_msualg_1(A,u4_msualg_1(A,B)) = B))) # label(abstractness_v3_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12477 (all A (l1_msualg_1(A) -> v1_funct_2(u3_msualg_1(A),u1_msualg_1(A),u1_struct_0(A)) & m2_relset_1(u3_msualg_1(A),u1_msualg_1(A),u1_struct_0(A)) & v1_funct_1(u3_msualg_1(A)))) # label(dt_u3_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12478 (all A (v7_unialg_1(A) & v8_unialg_1(A) & l1_unialg_1(A) & v6_unialg_1(A) & -v3_struct_0(A) -> -v3_struct_0(k7_msualg_1(A)) & v1_msualg_1(k7_msualg_1(A)) & -v2_msualg_1(k7_msualg_1(A)) & v6_msualg_1(k7_msualg_1(A)) & v3_realset2(k7_msualg_1(A)))) # label(fc2_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12479 $T # label(t1_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12480 (all A all B (l2_msualg_1(B,A) & l1_struct_0(A) -> m1_pboole(u4_msualg_1(A,B),u1_struct_0(A)))) # label(dt_u4_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12481 (all A (-v3_struct_0(A) & v6_unialg_1(A) & v7_unialg_1(A) & v8_unialg_1(A) & l1_unialg_1(A) -> (all B (v3_realset2(B) & v1_msualg_1(B) & l1_msualg_1(B) & v6_msualg_1(B) & -v2_msualg_1(B) -> (k1_tarski(np__0) = u1_struct_0(B) & k4_finseq_1(k6_msualg_1(A)) = u1_msualg_1(B) & k10_pboole(k4_finseq_1(k6_msualg_1(A)),np__0) = u3_msualg_1(B) & k1_partfun1(k5_numbers,k5_numbers,k5_numbers,k3_finseq_2(k1_tarski(np__0)),k6_msualg_1(A),k9_pboole(np__0)) = u2_msualg_1(B) <-> B = k7_msualg_1(A)))))) # label(d13_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12482 (all A all B (-v3_struct_0(A) & l3_msualg_1(B,A) & l1_msualg_1(A) -> (v4_msualg_1(B,A) -> g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)) = B))) # label(abstractness_v4_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12483 (all A all B (-v2_msualg_1(A) & l1_msualg_1(A) & m1_subset_1(B,u1_msualg_1(A)) & -v3_struct_0(A) -> m2_finseq_2(k1_msualg_1(A,B),u1_struct_0(A),k3_finseq_2(u1_struct_0(A))))) # label(dt_k1_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12484 (all A (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) & v6_msualg_1(A) & v3_realset2(A) -> (all B (l3_msualg_1(B,A) & v5_msualg_1(B,A) -> g1_unialg_1(k11_msualg_1(A,B),k12_msualg_1(A,B)) = k13_msualg_1(A,B))))) # label(d19_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12485 (all A (l1_struct_0(A) -> (exists B l2_msualg_1(B,A)))) # label(existence_l2_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12486 $T # label(t4_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12487 (all A all B all C (l1_msualg_1(A) & m1_pboole(B,u1_struct_0(A)) & m3_pboole(C,u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),B)),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),B)) & -v3_struct_0(A) -> (all D all E all F (g3_msualg_1(A,B,C) = g3_msualg_1(D,E,F) -> D = A & F = C & B = E)))) # label(free_g3_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12488 (all A all B all C (l3_msualg_1(C,A) & m1_subset_1(B,u1_msualg_1(A)) & l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> m1_subset_1(k3_msualg_1(A,B,C),k2_relat_1(k6_pboole(u1_struct_0(A),u4_msualg_1(A,C)))))) # label(dt_k3_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12489 (all A (l1_msualg_1(A) & -v3_struct_0(A) -> (exists B (l3_msualg_1(B,A) & v5_msualg_1(B,A) & v4_msualg_1(B,A))))) # label(rc6_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12490 (all A (-v3_struct_0(A) & l1_unialg_1(A) & v8_unialg_1(A) & v7_unialg_1(A) & v6_unialg_1(A) & v3_unialg_1(A) -> k13_msualg_1(k7_msualg_1(A),k10_msualg_1(A)) = A)) # label(t15_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12491 (all A (-v3_struct_0(A) & l1_msualg_1(A) & -v2_msualg_1(A) -> (all B (m1_subset_1(B,u1_msualg_1(A)) -> k1_msualg_1(A,B) = k1_funct_1(u2_msualg_1(A),B))))) # label(d6_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12492 (all A (-v3_struct_0(A) & v6_unialg_1(A) & l1_unialg_1(A) & v8_unialg_1(A) & v7_unialg_1(A) -> -v1_xboole_0(k3_unialg_1(A)))) # label(t9_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12493 (all A (l1_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> l2_msualg_1(B,A))))) # label(dt_l3_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12494 (all A (-v3_struct_0(A) & v6_unialg_1(A) & l1_unialg_1(A) & v8_unialg_1(A) & v7_unialg_1(A) -> v2_relat_1(k8_msualg_1(A)) & m1_pboole(k8_msualg_1(A),u1_struct_0(k7_msualg_1(A))))) # label(dt_k8_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12495 (exists A (l1_msualg_1(A) & v1_msualg_1(A))) # label(rc1_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12496 (all A all B all C (-v3_struct_0(A) & m1_subset_1(B,u1_msualg_1(A)) & l3_msualg_1(C,A) & l1_msualg_1(A) & -v2_msualg_1(A) -> v1_funct_1(k5_msualg_1(A,B,C)) & v1_funct_2(k5_msualg_1(A,B,C),k3_msualg_1(A,B,C),k4_msualg_1(A,B,C)) & m2_relset_1(k5_msualg_1(A,B,C),k3_msualg_1(A,B,C),k4_msualg_1(A,B,C)))) # label(dt_k5_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12497 (all A all B (l1_struct_0(A) & v5_msualg_1(B,A) & l2_msualg_1(B,A) -> v1_relat_1(u4_msualg_1(A,B)) & v1_funct_1(u4_msualg_1(A,B)) & v2_relat_1(u4_msualg_1(A,B)))) # label(fc1_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12498 (all A (l1_unialg_1(A) & v8_unialg_1(A) & v7_unialg_1(A) & v6_unialg_1(A) & -v3_struct_0(A) -> m2_finseq_1(k6_msualg_1(A),k5_numbers))) # label(dt_k6_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12499 $T # label(d3_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12500 (exists A (v3_realset2(A) & v1_msualg_1(A) & -v2_msualg_1(A) & v6_msualg_1(A) & -v3_struct_0(A) & l1_msualg_1(A))) # label(rc8_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12501 (all A (v3_realset2(A) & v6_msualg_1(A) & l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_msualg_1(A)) -> (all C (l3_msualg_1(C,A) & v5_msualg_1(C,A) -> r1_tarski(k3_msualg_1(A,B,C),k3_finseq_2(k11_msualg_1(A,C))))))))) # label(t13_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12502 (all A all B (-v3_struct_0(A) & l1_msualg_1(A) & l3_msualg_1(B,A) & v5_msualg_1(B,A) & v3_realset2(A) -> -v1_xboole_0(k11_msualg_1(A,B)))) # label(fc4_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12503 (all A (l1_msualg_1(A) & -v3_struct_0(A) -> (exists B l3_msualg_1(B,A)))) # label(existence_l3_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12504 (all A (l1_msualg_1(A) -> m2_relset_1(u2_msualg_1(A),u1_msualg_1(A),k3_finseq_2(u1_struct_0(A))) & v1_funct_2(u2_msualg_1(A),u1_msualg_1(A),k3_finseq_2(u1_struct_0(A))) & v1_funct_1(u2_msualg_1(A)))) # label(dt_u2_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12505 (all A (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) -> (all B (m1_subset_1(B,u1_msualg_1(A)) -> (all C (l3_msualg_1(C,A) & v5_msualg_1(C,A) -> -v1_xboole_0(k5_msualg_1(A,B,C)))))))) # label(t6_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12506 $T # label(t3_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12507 (all A (l1_msualg_1(A) -> (v1_msualg_1(A) -> g1_msualg_1(u1_struct_0(A),u1_msualg_1(A),u2_msualg_1(A),u3_msualg_1(A)) = A))) # label(abstractness_v1_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12508 (all A (-v3_struct_0(A) & l1_unialg_1(A) & v8_unialg_1(A) & v7_unialg_1(A) & v6_unialg_1(A) -> v5_msualg_1(k10_msualg_1(A),k7_msualg_1(A)) & v4_msualg_1(k10_msualg_1(A),k7_msualg_1(A)))) # label(fc3_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12509 $T # label(dt_u1_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12510 (all A (l1_msualg_1(A) & v6_msualg_1(A) & -v2_msualg_1(A) & v3_realset2(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) & v5_msualg_1(B,A) -> u5_msualg_1(A,B) = k12_msualg_1(A,B))))) # label(d18_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12511 $T # label(d1_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12512 (all A (v7_unialg_1(A) & v8_unialg_1(A) & l1_unialg_1(A) & v6_unialg_1(A) & -v3_struct_0(A) -> m3_pboole(k9_msualg_1(A),u1_msualg_1(k7_msualg_1(A)),k8_pboole(u1_msualg_1(k7_msualg_1(A)),k3_finseq_2(u1_struct_0(k7_msualg_1(A))),u2_msualg_1(k7_msualg_1(A)),k6_pboole(u1_struct_0(k7_msualg_1(A)),k8_msualg_1(A))),k8_pboole(u1_msualg_1(k7_msualg_1(A)),u1_struct_0(k7_msualg_1(A)),u3_msualg_1(k7_msualg_1(A)),k8_msualg_1(A))))) # label(dt_k9_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12513 (exists A l1_msualg_1(A)) # label(existence_l1_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12514 (all A (v3_realset2(A) & v6_msualg_1(A) & l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_msualg_1(A)) -> (all C (l3_msualg_1(C,A) & v5_msualg_1(C,A) -> k3_msualg_1(A,B,C) = k4_finseq_2(k3_finseq_1(k1_msualg_1(A,B)),k11_msualg_1(A,C)))))))) # label(t11_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12515 (all A (l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_msualg_1(A)) -> (all C (l3_msualg_1(C,A) -> k4_msualg_1(A,B,C) = k1_funct_1(k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,C)),B))))))) # label(d10_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12516 (all A all B (l1_msualg_1(A) & l3_msualg_1(B,A) & v5_msualg_1(B,A) & -v3_struct_0(A) -> (all C (m1_subset_1(C,k2_relat_1(k6_pboole(u1_struct_0(A),u4_msualg_1(A,B)))) -> -v1_xboole_0(C))))) # label(cc2_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12517 $T # label(d4_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12518 (all A all B (v3_realset2(A) & -v2_msualg_1(A) & v6_msualg_1(A) & l3_msualg_1(B,A) & v5_msualg_1(B,A) & l1_msualg_1(A) & -v3_struct_0(A) -> m2_finseq_1(k12_msualg_1(A,B),k4_partfun1(k13_finseq_1(k11_msualg_1(A,B)),k11_msualg_1(A,B))))) # label(dt_k12_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12519 $T # label(dt_l2_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12520 (all A all B (-v3_struct_0(A) & v3_realset2(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) & v6_msualg_1(A) & -v2_msualg_1(A) -> -v3_struct_0(k13_msualg_1(A,B)) & l1_unialg_1(k13_msualg_1(A,B)) & v8_unialg_1(k13_msualg_1(A,B)) & v7_unialg_1(k13_msualg_1(A,B)) & v6_unialg_1(k13_msualg_1(A,B)) & v3_unialg_1(k13_msualg_1(A,B)))) # label(dt_k13_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12521 (all A (-v2_msualg_1(A) & l1_msualg_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_msualg_1(A)) -> (all C (l3_msualg_1(C,A) -> k3_msualg_1(A,B,C) = k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),u4_msualg_1(A,C))),B))))))) # label(d9_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12522 (all A (l1_struct_0(A) -> (all B (l2_msualg_1(B,A) -> (v5_msualg_1(B,A) <-> v2_relat_1(u4_msualg_1(A,B))))))) # label(d8_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12523 (all A (v6_unialg_1(A) & v8_unialg_1(A) & l1_unialg_1(A) & v7_unialg_1(A) & -v3_struct_0(A) -> v4_msualg_1(k10_msualg_1(A),k7_msualg_1(A)) & l3_msualg_1(k10_msualg_1(A),k7_msualg_1(A)))) # label(dt_k10_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12524 (all A all B (l1_msualg_1(A) & l3_msualg_1(B,A) & v5_msualg_1(B,A) & -v3_struct_0(A) -> (all C (m1_subset_1(C,k2_relat_1(u4_msualg_1(A,B))) -> -v1_xboole_0(C))))) # label(cc1_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12525 (all A (l1_msualg_1(A) -> (v6_msualg_1(A) <-> (exists B (m2_subset_1(B,k1_numbers,k5_numbers) & k2_finseq_1(B) = u1_msualg_1(A)))))) # label(d12_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12526 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m2_relset_1(E,B,C) & v1_funct_2(E,B,C) & v1_funct_1(E) -> v1_funct_2(k1_partfun1(A,B,B,C,D,E),k1_relat_1(D),C) & m2_relset_1(k1_partfun1(A,B,B,C,D,E),k1_relat_1(D),C) & v1_funct_1(k1_partfun1(A,B,B,C,D,E)))))))))) # label(t7_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12527 (all A all B (-v3_struct_0(A) & l1_msualg_1(A) & l3_msualg_1(B,A) -> m3_pboole(u5_msualg_1(A,B),u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),u4_msualg_1(A,B))),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,B))))) # label(dt_u5_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12528 (exists A (v2_msualg_1(A) & v1_msualg_1(A) & -v3_struct_0(A) & l1_msualg_1(A))) # label(rc2_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12529 (all A (-v3_struct_0(A) & l1_msualg_1(A) -> (v3_realset2(A) -> (all B (l3_msualg_1(B,A) -> (all C (m1_subset_1(C,k2_relat_1(u4_msualg_1(A,B))) -> (all D (m1_subset_1(D,k2_relat_1(u4_msualg_1(A,B))) -> D = C))))))))) # label(t10_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12530 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k3_finseq_2(A),A) & v2_unialg_1(B,A) & v1_unialg_1(B,A) & -v1_xboole_0(B) -> k1_relat_1(B) = k1_funct_2(k2_finseq_1(k2_unialg_1(A,B)),A))))) # label(t8_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12531 (all A (-v1_xboole_0(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> r1_tarski(k4_finseq_2(B,A),k3_finseq_2(A)))))) # label(t12_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12532 $T # label(t5_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12533 (all A (-v3_struct_0(A) & l1_msualg_1(A) & -v2_msualg_1(A) -> (all B (m1_subset_1(B,u1_msualg_1(A)) -> k1_funct_1(u3_msualg_1(A),B) = k2_msualg_1(A,B))))) # label(d7_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12534 (all A all B (l1_struct_0(A) & m1_pboole(B,u1_struct_0(A)) -> (all C all D (g2_msualg_1(A,B) = g2_msualg_1(C,D) -> A = C & B = D)))) # label(free_g2_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12535 (all A (-v3_struct_0(A) & v3_realset2(A) & -v2_msualg_1(A) & v6_msualg_1(A) & l1_msualg_1(A) -> (all B (l3_msualg_1(B,A) & v5_msualg_1(B,A) -> m2_finseq_1(u5_msualg_1(A,B),k4_partfun1(k3_finseq_2(k11_msualg_1(A,B)),k11_msualg_1(A,B))))))) # label(t14_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12536 (all A all B (m1_pboole(B,u1_struct_0(A)) & l1_struct_0(A) -> v3_msualg_1(g2_msualg_1(A,B),A) & l2_msualg_1(g2_msualg_1(A,B),A))) # label(dt_g2_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12537 (all A (v3_realset2(A) & l1_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> (all C (k11_msualg_1(A,B) = C <-> m1_subset_1(C,k2_relat_1(u4_msualg_1(A,B))))))))) # label(d17_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12538 (all A all B all C all D (v1_funct_1(C) & v1_funct_2(C,B,k3_finseq_2(A)) & v1_funct_1(D) & v1_funct_2(D,B,A) & m1_relset_1(D,B,A) & m1_relset_1(C,B,k3_finseq_2(A)) -> v1_msualg_1(g1_msualg_1(A,B,C,D)) & l1_msualg_1(g1_msualg_1(A,B,C,D)))) # label(dt_g1_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12539 (all A (-v3_struct_0(A) & l1_msualg_1(A) & -v2_msualg_1(A) -> (all B (m1_subset_1(B,u1_msualg_1(A)) -> (all C (l3_msualg_1(C,A) -> k5_msualg_1(A,B,C) = k1_funct_1(u5_msualg_1(A,C),B))))))) # label(d11_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12540 (all A (v6_unialg_1(A) & v7_unialg_1(A) & l1_unialg_1(A) & v8_unialg_1(A) & -v3_struct_0(A) -> v1_msualg_1(k7_msualg_1(A)) & v6_msualg_1(k7_msualg_1(A)) & l1_msualg_1(k7_msualg_1(A)) & -v2_msualg_1(k7_msualg_1(A)) & v3_realset2(k7_msualg_1(A)))) # label(dt_k7_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12541 (all A (l1_unialg_1(A) & v8_unialg_1(A) & v7_unialg_1(A) & v6_unialg_1(A) & -v3_struct_0(A) -> k3_unialg_1(A) = k6_msualg_1(A))) # label(redefinition_k6_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12542 (all A (l1_msualg_1(A) & -v3_struct_0(A) -> (exists B (v4_msualg_1(B,A) & l3_msualg_1(B,A))))) # label(rc5_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12543 (all A all B (m1_subset_1(B,u1_msualg_1(A)) & l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> m1_subset_1(k2_msualg_1(A,B),u1_struct_0(A)))) # label(dt_k2_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12544 (all A all B all C (l1_msualg_1(A) & m1_pboole(B,u1_struct_0(A)) & m3_pboole(C,u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),B)),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),B)) & -v3_struct_0(A) -> l3_msualg_1(g3_msualg_1(A,B,C),A) & v4_msualg_1(g3_msualg_1(A,B,C),A))) # label(dt_g3_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12545 (all A (l1_msualg_1(A) -> (k1_xboole_0 = u1_msualg_1(A) <-> v2_msualg_1(A)))) # label(d5_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12546 (all A (-v3_struct_0(A) & v7_unialg_1(A) & v8_unialg_1(A) & l1_unialg_1(A) & v6_unialg_1(A) -> u1_unialg_1(A) = k9_msualg_1(A))) # label(d15_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12547 $T # label(dt_k11_msualg_1) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12548 (all A (-v3_struct_0(A) & v1_group_1(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)) -> (all C (m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)) -> m2_fraenkel(k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C,B),u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)))))))) # label(t8_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.81 12549 (all A (v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(k3_autgroup(A))) -> (all C (m1_subset_1(C,u1_struct_0(k3_autgroup(A))) -> (all D (m2_fraenkel(D,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)) -> (all E (m2_fraenkel(E,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)) -> (C = E & B = D -> k1_group_1(k3_autgroup(A),B,C) = k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),E,D)))))))))))) # label(t9_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12550 (all A (v1_group_1(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_group_2(B,A) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (m1_subset_1(D,u1_struct_0(B)) -> r1_rlvect_1(B,k2_group_3(A,D,C))))))) <-> v1_group_3(B,A)))))) # label(t1_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12551 (all A (v1_group_1(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> r2_group_6(k5_autgroup(A),k6_group_6(A,k10_group_5(A))))) # label(t31_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12552 (all A (-v3_struct_0(A) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),k6_autgroup(A,k3_group_1(A,B)),k6_autgroup(A,B)) = k6_autgroup(A,k2_group_1(A)))))) # label(t26_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12553 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & v1_group_1(A) -> (all B (m1_fraenkel(B,u1_struct_0(A),u1_struct_0(A)) -> ((all C (v1_group_6(C,A,A) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(C) -> (v3_group_6(C,A,A) & v2_funct_1(C) <-> r2_hidden(C,B)))) & (all C (m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),B) -> v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) & v1_group_6(C,A,A))) <-> B = k1_autgroup(A)))))) # label(d1_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12554 (all A (-v3_struct_0(A) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> v1_funct_2(k2_autgroup(A),k2_zfmisc_1(k1_autgroup(A),k1_autgroup(A)),k1_autgroup(A)) & m2_relset_1(k2_autgroup(A),k2_zfmisc_1(k1_autgroup(A),k1_autgroup(A)),k1_autgroup(A)) & v1_funct_1(k2_autgroup(A)))) # label(dt_k2_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12555 (all A all B (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & m1_subset_1(B,u1_struct_0(A)) & v4_group_1(A) & v1_group_1(A) -> m2_fraenkel(k6_autgroup(A,B),u1_struct_0(A),u1_struct_0(A),k4_autgroup(A)))) # label(dt_k6_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12556 (all A (-v3_struct_0(A) & v1_group_1(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> r1_tarski(k4_autgroup(A),k1_fraenkel(u1_struct_0(A),u1_struct_0(A))))) # label(t12_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12557 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_1(A) -> (all B (m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)) -> v1_funct_1(k2_funct_1(B)) & v1_group_6(k2_funct_1(B),A,A) & m2_relset_1(k2_funct_1(B),u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(k2_funct_1(B),u1_struct_0(A),u1_struct_0(A)))))) # label(t6_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12558 (all A (v1_group_1(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> r1_tarski(k1_autgroup(A),k1_fraenkel(u1_struct_0(A),u1_struct_0(A))))) # label(t3_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12559 (all A (v1_group_1(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> m2_fraenkel(k6_partfun1(u1_struct_0(A)),u1_struct_0(A),u1_struct_0(A),k4_autgroup(A)))) # label(t16_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12560 (all A (v1_group_1(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> m1_fraenkel(k1_autgroup(A),u1_struct_0(A),u1_struct_0(A)))) # label(dt_k1_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12561 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k6_autgroup(A,k1_group_1(A,B,C)) = k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),k6_autgroup(A,B),k6_autgroup(A,C)))))))) # label(t23_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12562 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & v1_group_1(A) -> k6_autgroup(A,k2_group_1(A)) = k6_partfun1(u1_struct_0(A)))) # label(t24_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12563 (all A (v1_group_1(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (v1_group_1(B) & v1_group_3(B,k3_autgroup(A)) & m1_group_2(B,k3_autgroup(A)) -> (k5_autgroup(A) = B <-> k4_autgroup(A) = u1_struct_0(B)))))) # label(d5_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12564 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & v1_group_1(A) & -v3_struct_0(A) -> (all B (m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A)) -> (all C (m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A)) -> k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C,B) = k1_binop_1(k2_autgroup(A),B,C))))))) # label(t15_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12565 (all A (-v3_struct_0(A) & v1_group_1(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A)) -> m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)))))) # label(t13_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12566 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & v1_group_1(A) -> r1_tarski(k4_autgroup(A),k1_autgroup(A)))) # label(t14_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12567 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & v1_group_1(A) & -v3_struct_0(A) -> m2_fraenkel(k6_partfun1(u1_struct_0(A)),u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)))) # label(t4_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12568 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & v1_group_1(A) -> (all B (m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A)) -> (all C (m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A)) -> m2_fraenkel(k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C,B),u1_struct_0(A),u1_struct_0(A),k4_autgroup(A)))))))) # label(t18_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12569 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_1(A) & -v3_struct_0(A) -> k2_group_1(k5_autgroup(A)) = k6_partfun1(u1_struct_0(A)))) # label(t21_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12570 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & v1_group_1(A) & -v3_struct_0(A) -> (all B (m1_fraenkel(B,u1_struct_0(A),u1_struct_0(A)) -> (B = k4_autgroup(A) <-> (all C (m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),k1_fraenkel(u1_struct_0(A),u1_struct_0(A))) -> ((exists D ((all E (m1_subset_1(E,u1_struct_0(A)) -> k2_group_3(A,E,D) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),C,E))) & m1_subset_1(D,u1_struct_0(A)))) <-> r2_hidden(C,B))))))))) # label(d4_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12571 (all A (-v3_struct_0(A) & v1_group_1(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A)) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> k2_group_3(A,D,B) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),C,D))) <-> C = k6_autgroup(A,B)))))))) # label(d6_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12572 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & v1_group_1(A) -> v1_group_1(k5_autgroup(A)) & m1_group_2(k5_autgroup(A),k3_autgroup(A)) & v1_group_3(k5_autgroup(A),k3_autgroup(A)))) # label(dt_k5_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12573 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & v1_group_1(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_group_6(B,A,A) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) -> (v4_group_6(B,A,A) <-> r2_hidden(B,k1_autgroup(A))))))) # label(t5_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12574 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_1(A) & -v3_struct_0(A) -> k3_autgroup(A) = g1_group_1(k1_autgroup(A),k2_autgroup(A)))) # label(d3_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12575 (all A (-v3_struct_0(A) & v1_group_1(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> k6_partfun1(u1_struct_0(A)) = k2_group_1(k3_autgroup(A)))) # label(t10_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12576 (all A (-v3_struct_0(A) & v1_group_1(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),k6_autgroup(A,B),k6_autgroup(A,k3_group_1(A,B))) = k6_autgroup(A,k2_group_1(A)))))) # label(t27_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12577 (all A (-v3_struct_0(A) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)) -> m2_fraenkel(k2_funct_1(B),u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)))))) # label(t7_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12578 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & v1_group_1(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(k1_autgroup(A),k1_autgroup(A)),k1_autgroup(A)) & m2_relset_1(B,k2_zfmisc_1(k1_autgroup(A),k1_autgroup(A)),k1_autgroup(A)) & v1_funct_1(B) -> ((all C (m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)) -> (all D (m2_fraenkel(D,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)) -> k2_binop_1(k1_autgroup(A),k1_autgroup(A),k1_autgroup(A),B,C,D) = k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),D,C))))) <-> B = k2_autgroup(A)))))) # label(d2_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12579 $T # label(t2_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12580 (all A (v1_group_1(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A)) -> m2_fraenkel(k2_funct_1(B),u1_struct_0(A),u1_struct_0(A),k4_autgroup(A)))))) # label(t17_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12581 $T # label(t19_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12582 (all A (-v3_struct_0(A) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> m1_fraenkel(k4_autgroup(A),u1_struct_0(A),u1_struct_0(A)))) # label(dt_k4_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12583 (all A (-v3_struct_0(A) & v1_group_1(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> -v3_struct_0(k3_autgroup(A)) & v1_group_1(k3_autgroup(A)) & v3_group_1(k3_autgroup(A)) & l1_group_1(k3_autgroup(A)) & v4_group_1(k3_autgroup(A)))) # label(dt_k3_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12584 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & v1_group_1(A) -> (v3_group_1(A) & v7_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(k5_autgroup(A))) -> B = k2_group_1(k5_autgroup(A))))))) # label(t32_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12585 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & v1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k8_funct_2(u1_struct_0(A),u1_struct_0(A),k6_autgroup(A,k2_group_1(A)),B))))) # label(t25_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12586 (all A (-v3_struct_0(A) & v1_group_1(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_autgroup(A,B) = k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),k6_autgroup(A,k2_group_1(A)),k6_autgroup(A,B)) & k6_autgroup(A,B) = k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),k6_autgroup(A,B),k6_autgroup(A,k2_group_1(A))))))) # label(t29_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12587 (all A (-v3_struct_0(A) & v1_group_1(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(k5_autgroup(A))) -> (all C (m1_subset_1(C,u1_struct_0(k5_autgroup(A))) -> (all D (m2_fraenkel(D,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A)) -> (all E (m2_fraenkel(E,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A)) -> (E = C & D = B -> k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),E,D) = k1_group_1(k5_autgroup(A),B,C)))))))))))) # label(t20_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12588 (all A (v1_group_1(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A)) -> (all C (m1_subset_1(C,u1_struct_0(k5_autgroup(A))) -> (B = C -> k3_group_1(k5_autgroup(A),C) = k2_funct_1(B)))))))) # label(t22_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12589 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & v1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k2_funct_1(k6_autgroup(A,B)) = k6_autgroup(A,k3_group_1(A,B)))))) # label(t28_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12590 (all A (-v3_struct_0(A) & v1_group_1(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)) -> (all C (m1_subset_1(C,u1_struct_0(k3_autgroup(A))) -> (B = C -> k3_group_1(k3_autgroup(A),C) = k2_funct_1(B)))))))) # label(t11_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12591 (all A (-v3_struct_0(A) & v1_group_1(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A)) -> B = k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),k6_autgroup(A,k2_group_1(A)),B) & B = k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),B,k6_autgroup(A,k2_group_1(A))))))) # label(t30_autgroup) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12592 (all A all B (-v3_struct_0(A) & -v2_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) & l1_msualg_1(A) -> m2_relset_1(k15_msualg_2(A,B),k2_zfmisc_1(k14_msualg_2(A,B),k14_msualg_2(A,B)),k14_msualg_2(A,B)) & v1_funct_2(k15_msualg_2(A,B),k2_zfmisc_1(k14_msualg_2(A,B),k14_msualg_2(A,B)),k14_msualg_2(A,B)) & v1_funct_1(k15_msualg_2(A,B)))) # label(dt_k15_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12593 (all A (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) -> (all B (l3_msualg_1(B,A) -> (all C (m1_msualg_2(C,A,B) -> m4_pboole(k2_msualg_2(A,B),u1_struct_0(A),u4_msualg_1(A,C)))))))) # label(t11_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12594 (all A all B (-v2_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) & l1_msualg_1(A) & -v3_struct_0(A) -> v3_lattices(k17_msualg_2(A,B)) & v4_lattices(k17_msualg_2(A,B)) & v5_lattices(k17_msualg_2(A,B)) & v7_lattices(k17_msualg_2(A,B)) & v8_lattices(k17_msualg_2(A,B)) & v13_lattices(k17_msualg_2(A,B)) & v14_lattices(k17_msualg_2(A,B)) & v15_lattices(k17_msualg_2(A,B)) & v10_lattices(k17_msualg_2(A,B)) & v9_lattices(k17_msualg_2(A,B)) & v6_lattices(k17_msualg_2(A,B)) & -v3_struct_0(k17_msualg_2(A,B)))) # label(fc12_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12595 (all A all B all C (m1_pboole(B,A) & v2_relat_1(C) & m1_pboole(C,A) -> v1_funct_1(k2_pboole(A,B,C)) & v2_relat_1(k2_pboole(A,B,C)) & v1_relat_1(k2_pboole(A,B,C)))) # label(fc1_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12596 (all A all B (l3_msualg_1(B,A) & v5_msualg_1(B,A) & l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> v1_funct_2(k16_msualg_2(A,B),k2_zfmisc_1(k14_msualg_2(A,B),k14_msualg_2(A,B)),k14_msualg_2(A,B)) & m2_relset_1(k16_msualg_2(A,B),k2_zfmisc_1(k14_msualg_2(A,B),k14_msualg_2(A,B)),k14_msualg_2(A,B)) & v1_funct_1(k16_msualg_2(A,B)))) # label(dt_k16_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12597 (all A (-v2_msualg_1(A) & l1_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> (all C (m1_msualg_2(C,A,B) -> (all D (m1_msualg_2(D,A,B) -> (all E (v4_msualg_1(E,A) & m1_msualg_2(E,A,B) -> (E = k11_msualg_2(A,B,C,D) <-> r6_pboole(u1_struct_0(A),u4_msualg_1(A,E),k3_pboole(u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))) & (all F (m4_pboole(F,u1_struct_0(A),u4_msualg_1(A,B)) -> (r6_pboole(u1_struct_0(A),F,u4_msualg_1(A,E)) -> v3_msualg_2(F,A,B) & r6_pboole(u1_msualg_1(A),u5_msualg_1(A,E),k4_msualg_2(A,B,F)))))))))))))))) # label(d17_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12598 (all A all B all C all D (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) & m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B)) & m1_subset_1(C,u1_msualg_1(A)) & l3_msualg_1(B,A) -> m2_relset_1(k3_msualg_2(A,B,C,D),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),D)),C),k1_funct_1(k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),D),C)) & v1_funct_2(k3_msualg_2(A,B,C,D),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),D)),C),k1_funct_1(k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),D),C)) & v1_funct_1(k3_msualg_2(A,B,C,D)))) # label(dt_k3_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12599 $T # label(d1_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12600 (all A (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) -> (all B (v5_msualg_1(B,A) & l3_msualg_1(B,A) -> g3_lattices(k14_msualg_2(A,B),k15_msualg_2(A,B),k16_msualg_2(A,B)) = k17_msualg_2(A,B))))) # label(d23_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12601 (all A (-v3_struct_0(A) & l1_msualg_1(A) & -v2_msualg_1(A) -> (all B (l3_msualg_1(B,A) -> (all C (v4_msualg_1(C,A) & m1_msualg_2(C,A,B) -> (all D (m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B)) -> (r6_pboole(u1_struct_0(A),D,u4_msualg_1(A,C)) -> C = k12_msualg_2(A,B,D)))))))))) # label(t23_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12602 (all A all B all C (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(C) & m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) & l3_msualg_1(B,A) & v5_msualg_1(B,A) -> v4_msualg_1(k12_msualg_2(A,B,C),A) & v5_msualg_1(k12_msualg_2(A,B,C),A))) # label(fc10_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12603 (all A (l1_msualg_1(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> v1_msualg_2(B,A))) <-> v2_msualg_2(A)))) # label(d3_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12604 (all A (-v3_struct_0(A) & l1_msualg_1(A) & -v2_msualg_1(A) -> (all B (l3_msualg_1(B,A) -> m1_msualg_2(B,A,B))))) # label(t6_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12605 (all A (-v2_msualg_1(A) & l1_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) & v5_msualg_1(B,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(k14_msualg_2(A,B),k14_msualg_2(A,B)),k14_msualg_2(A,B)) & v1_funct_2(C,k2_zfmisc_1(k14_msualg_2(A,B),k14_msualg_2(A,B)),k14_msualg_2(A,B)) -> (C = k15_msualg_2(A,B) <-> (all D (m1_subset_1(D,k14_msualg_2(A,B)) -> (all E (m1_subset_1(E,k14_msualg_2(A,B)) -> (all F (v4_msualg_1(F,A) & m1_msualg_2(F,A,B) -> (all G (m1_msualg_2(G,A,B) & v4_msualg_1(G,A) -> (F = D & G = E -> k13_msualg_2(A,B,F,G) = k2_binop_1(k14_msualg_2(A,B),k14_msualg_2(A,B),k14_msualg_2(A,B),C,D,E))))))))))))))))) # label(d21_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12606 (all A all B all C (-v3_struct_0(A) & l1_msualg_1(A) & l3_msualg_1(B,A) & m1_subset_1(C,k6_msualg_2(A,B)) & -v2_msualg_1(A) -> m4_pboole(k7_msualg_2(A,B,C),u1_struct_0(A),u4_msualg_1(A,B)))) # label(dt_k7_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12607 $T # label(dt_k8_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12608 $T # label(dt_k6_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12609 (all A (-v2_msualg_1(A) & l1_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) & v5_msualg_1(B,A) -> (all C (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> (r6_pboole(u1_struct_0(A),C,u4_msualg_1(A,B)) -> k12_msualg_2(A,B,C) = k6_lattices(k17_msualg_2(A,B))))))))) # label(t36_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12610 (all A all B all C all D (-v2_msualg_1(A) & l3_msualg_1(B,A) & m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) & m1_subset_1(D,u1_struct_0(A)) & l1_msualg_1(A) & -v3_struct_0(A) -> -v1_xboole_0(k8_msualg_2(A,B,C,D)))) # label(fc9_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12611 (all A (-v3_struct_0(A) & l1_msualg_1(A) & -v2_msualg_1(A) -> (all B (m1_subset_1(B,u1_msualg_1(A)) -> (all C (l3_msualg_1(C,A) -> (all D (m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,C)) -> (all E (m4_pboole(E,u1_struct_0(A),u4_msualg_1(A,C)) -> (r2_hidden(E,k5_msualg_2(A,C,D)) -> r1_tarski(k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k9_msualg_2(A,C,D))),B),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),E)),B))))))))))))) # label(t18_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12612 (all A (-v2_msualg_1(A) & l1_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> (all C (m1_subset_1(C,u1_msualg_1(A)) -> (all D (m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B)) -> (r1_msualg_2(A,B,C,D) -> k7_relat_1(k5_msualg_1(A,C,B),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),D)),C)) = k3_msualg_2(A,B,C,D)))))))))) # label(d8_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12613 (all A all B all C all D (l3_msualg_1(B,A) & m1_msualg_2(D,A,B) & m1_msualg_2(C,A,B) & l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> m1_msualg_2(k11_msualg_2(A,B,C,D),A,B) & v4_msualg_1(k11_msualg_2(A,B,C,D),A))) # label(dt_k11_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12614 (all A (-v3_struct_0(A) & l1_msualg_1(A) & -v2_msualg_1(A) -> (all B (l3_msualg_1(B,A) -> (all C (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> k1_msualg_2(A,B,D) = k1_funct_1(C,D))) <-> k2_msualg_2(A,B) = C))))))) # label(d5_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12615 (all A (-v3_struct_0(A) & l1_msualg_1(A) & -v2_msualg_1(A) -> (all B (v5_msualg_1(B,A) & l3_msualg_1(B,A) -> v2_binop_1(k16_msualg_2(A,B),k14_msualg_2(A,B)))))) # label(t33_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12616 $T # label(t39_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12617 (all A (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) -> (all B (l3_msualg_1(B,A) & v5_msualg_1(B,A) -> (all C (m1_msualg_2(C,A,B) -> (all D (m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B)) -> (all E (m4_pboole(E,u1_struct_0(A),u4_msualg_1(A,B)) -> (r6_pboole(u1_struct_0(A),E,k2_pboole(u1_struct_0(A),D,u4_msualg_1(A,C))) -> k12_msualg_2(A,B,E) = k13_msualg_2(A,B,k12_msualg_2(A,B,D),C)))))))))))) # label(t25_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12618 (all A all B all C all D (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) & m1_msualg_2(D,A,B) & m1_msualg_2(C,A,B) & l3_msualg_1(B,A) & v5_msualg_1(B,A) -> m1_msualg_2(k13_msualg_2(A,B,C,D),A,B) & v4_msualg_1(k13_msualg_2(A,B,C,D),A))) # label(dt_k13_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12619 (all A (-v3_struct_0(A) & l1_msualg_1(A) & -v2_msualg_1(A) -> (all B (l3_msualg_1(B,A) & v5_msualg_1(B,A) -> (all C (m1_msualg_2(C,A,B) -> k12_msualg_2(A,B,k2_msualg_2(A,B)) = k11_msualg_2(A,B,k12_msualg_2(A,B,k2_msualg_2(A,B)),C))))))) # label(t24_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12620 (exists A (-v3_struct_0(A) & -v2_msualg_1(A) & v2_msualg_2(A) & v1_msualg_1(A) & l1_msualg_1(A))) # label(rc1_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12621 (all A (-v2_msualg_1(A) & l1_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_funct_1(u4_msualg_1(A,B),C))) -> (k1_xboole_0 != k1_funct_1(u4_msualg_1(A,B),C) -> (D = k1_msualg_2(A,B,C) <-> (exists E (-v1_xboole_0(E) & E = k1_funct_1(u4_msualg_1(A,B),C) & D = a_4_0_msualg_2(A,B,C,E))))) & (k1_funct_1(u4_msualg_1(A,B),C) = k1_xboole_0 -> (D = k1_xboole_0 <-> k1_msualg_2(A,B,C) = D)))))))))) # label(d4_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12622 (all A (-v2_msualg_1(A) & l1_msualg_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_msualg_1(A)) -> (all C (l3_msualg_1(C,A) -> (all D (m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,C)) -> r1_tarski(k2_relat_1(k7_relat_1(k5_msualg_1(A,B,C),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k9_msualg_2(A,C,D))),B))),k1_funct_1(k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k9_msualg_2(A,C,D)),B)))))))))) # label(t20_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12623 (all A (-v2_msualg_1(A) & l1_msualg_1(A) & -v3_struct_0(A) -> (all B (v4_msualg_1(B,A) & l3_msualg_1(B,A) & v5_msualg_1(B,A) -> k6_lattices(k17_msualg_2(A,B)) = B)))) # label(t37_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12624 (all A (-v3_struct_0(A) & l1_msualg_1(A) & -v2_msualg_1(A) -> (all B (l3_msualg_1(B,A) -> (all C ((all D (r2_hidden(D,C) <-> m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B)) & (all E (m4_pboole(E,u1_struct_0(A),u4_msualg_1(A,B)) -> (E = D -> v3_msualg_2(E,A,B)))) & r2_hidden(D,k1_funct_2(u1_struct_0(A),k1_zfmisc_1(k3_card_3(u4_msualg_1(A,B))))))) <-> C = k6_msualg_2(A,B))))))) # label(d12_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12625 (all A (-v2_msualg_1(A) & l1_msualg_1(A) & -v3_struct_0(A) -> (all B (v5_msualg_1(B,A) & l3_msualg_1(B,A) -> (all C (m1_msualg_2(C,A,B) -> (all D (m1_msualg_2(D,A,B) -> (all E (m1_msualg_2(E,A,B) & v4_msualg_1(E,A) -> (k13_msualg_2(A,B,C,D) = E <-> (all F (m4_pboole(F,u1_struct_0(A),u4_msualg_1(A,B)) -> (r6_pboole(u1_struct_0(A),F,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))) -> k12_msualg_2(A,B,F) = E)))))))))))))) # label(d19_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12626 (all A (-v2_msualg_1(A) & l1_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> (all C (l3_msualg_1(C,A) -> (all D (l3_msualg_1(D,A) -> (m1_msualg_2(C,A,D) & m1_msualg_2(B,A,C) -> m1_msualg_2(B,A,D)))))))))) # label(t7_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12627 (all A all B (l1_msualg_1(A) & l3_msualg_1(B,A) & v5_msualg_1(B,A) & -v2_msualg_1(A) & -v3_struct_0(A) -> v5_msualg_1(g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)),A) & v4_msualg_1(g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)),A))) # label(fc6_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12628 (all A all B all C (-v3_struct_0(A) & l1_msualg_1(A) & l3_msualg_1(B,A) & m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) & -v2_msualg_1(A) -> m1_msualg_2(k10_msualg_2(A,B,C),A,B) & v4_msualg_1(k10_msualg_2(A,B,C),A))) # label(dt_k10_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12629 (all A (-v3_struct_0(A) & l1_msualg_1(A) & -v2_msualg_1(A) -> (all B (l3_msualg_1(B,A) & v5_msualg_1(B,A) -> (all C (v4_msualg_1(C,A) & m1_msualg_2(C,A,B) -> (all D (m1_msualg_2(D,A,B) & v4_msualg_1(D,A) -> C = k11_msualg_2(A,B,C,k13_msualg_2(A,B,C,D)))))))))) # label(t28_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12630 $T # label(t1_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12631 (all A (l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> (all B (v5_msualg_1(B,A) & l3_msualg_1(B,A) -> (all C (m2_relset_1(C,k2_zfmisc_1(k14_msualg_2(A,B),k14_msualg_2(A,B)),k14_msualg_2(A,B)) & v1_funct_2(C,k2_zfmisc_1(k14_msualg_2(A,B),k14_msualg_2(A,B)),k14_msualg_2(A,B)) & v1_funct_1(C) -> ((all D (m1_subset_1(D,k14_msualg_2(A,B)) -> (all E (m1_subset_1(E,k14_msualg_2(A,B)) -> (all F (v4_msualg_1(F,A) & m1_msualg_2(F,A,B) -> (all G (v4_msualg_1(G,A) & m1_msualg_2(G,A,B) -> (F = D & G = E -> k2_binop_1(k14_msualg_2(A,B),k14_msualg_2(A,B),k14_msualg_2(A,B),C,D,E) = k11_msualg_2(A,B,F,G)))))))))) <-> C = k16_msualg_2(A,B)))))))) # label(d22_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12632 (all A (-v2_msualg_1(A) & l1_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> (all C (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E ((all F ((exists G (m4_pboole(G,u1_struct_0(A),u4_msualg_1(A,B)) & r2_hidden(G,k5_msualg_2(A,B,C)) & k1_funct_1(G,D) = F)) <-> r2_hidden(F,E))) <-> k8_msualg_2(A,B,C,D) = E)))))))))) # label(d14_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12633 (all A (-v2_msualg_1(A) & l1_msualg_1(A) & -v3_struct_0(A) -> (all B (v5_msualg_1(B,A) & l3_msualg_1(B,A) -> (all C (m1_msualg_2(C,A,B) & v4_msualg_1(C,A) -> (all D (m1_msualg_2(D,A,B) & v4_msualg_1(D,A) -> D = k13_msualg_2(A,B,k11_msualg_2(A,B,C,D),D))))))))) # label(t29_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12634 (all A (-v2_msualg_1(A) & l1_msualg_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_msualg_1(A)) -> (all C (l3_msualg_1(C,A) -> (all D (m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,C)) -> (all E (m4_pboole(E,u1_struct_0(A),u4_msualg_1(A,C)) -> (r2_hidden(E,k5_msualg_2(A,C,D)) -> r1_tarski(k2_relat_1(k7_relat_1(k5_msualg_1(A,B,C),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k9_msualg_2(A,C,D))),B))),k1_funct_1(k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),E),B))))))))))))) # label(t19_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12635 $T # label(dt_k5_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12636 (all A (-v3_struct_0(A) & l1_msualg_1(A) & -v2_msualg_1(A) -> (all B (l3_msualg_1(B,A) -> (all C (m1_subset_1(C,k6_msualg_2(A,B)) -> C = k7_msualg_2(A,B,C))))))) # label(d13_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12637 (all A all B all C (-v2_msualg_1(A) & m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) & l3_msualg_1(B,A) & l1_msualg_1(A) & -v3_struct_0(A) -> m1_msualg_2(k12_msualg_2(A,B,C),A,B) & v4_msualg_1(k12_msualg_2(A,B,C),A))) # label(dt_k12_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12638 (all A all B (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) & l3_msualg_1(B,A) -> -v1_xboole_0(k14_msualg_2(A,B)))) # label(fc11_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12639 (all A (-v3_struct_0(A) & l1_msualg_1(A) & -v2_msualg_1(A) -> (all B (l3_msualg_1(B,A) -> (all C (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> (all D ((all E (r2_hidden(E,D) <-> r2_hidden(E,k1_funct_2(u1_struct_0(A),k1_zfmisc_1(k3_card_3(u4_msualg_1(A,B))))) & m4_pboole(E,u1_struct_0(A),u4_msualg_1(A,B)) & (all F (m4_pboole(F,u1_struct_0(A),u4_msualg_1(A,B)) -> (E = F -> r2_pboole(u1_struct_0(A),k2_msualg_2(A,B),F) & r2_pboole(u1_struct_0(A),C,F) & v3_msualg_2(F,A,B)))))) <-> D = k5_msualg_2(A,B,C))))))))) # label(d11_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12640 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m2_finseq_2(D,A,k3_finseq_2(A)) -> k4_card_3(k5_relat_1(D,k3_pboole(A,B,C))) = k3_xboole_0(k4_card_3(k5_relat_1(D,B)),k4_card_3(k5_relat_1(D,C))))))))))) # label(t2_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12641 (all A (l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> (all C (m1_subset_1(C,u1_msualg_1(A)) -> (all D (m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B)) -> (r1_tarski(k2_relat_1(k7_relat_1(k5_msualg_1(A,C,B),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),D)),C))),k1_funct_1(k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),D),C)) <-> r1_msualg_2(A,B,C,D)))))))))) # label(d6_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12642 (all A (-v3_struct_0(A) & l1_msualg_1(A) & -v2_msualg_1(A) -> (all B (l3_msualg_1(B,A) & v4_msualg_1(B,A) -> (all C (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> (r6_pboole(u1_struct_0(A),C,u4_msualg_1(A,B)) -> k12_msualg_2(A,B,C) = B))))))) # label(t22_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12643 (all A (l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) & v5_msualg_1(B,A) -> v2_binop_1(k15_msualg_2(A,B),k14_msualg_2(A,B)))))) # label(t31_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12644 (all A (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) -> (all B (l3_msualg_1(B,A) -> (all C (m1_msualg_2(C,A,B) -> (all D (m1_msualg_2(D,A,B) -> (r2_pboole(u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D)) -> m1_msualg_2(C,A,D)))))))))) # label(t9_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12645 (all A all B all C (m1_pboole(C,A) & v2_relat_1(C) & m1_pboole(B,A) -> v1_funct_1(k2_pboole(A,C,B)) & v2_relat_1(k2_pboole(A,C,B)) & v1_relat_1(k2_pboole(A,C,B)))) # label(fc2_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12646 (all A (l1_msualg_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v1_msualg_2(B,A) <-> (exists C (m1_subset_1(C,u1_msualg_1(A)) & B = k1_funct_1(u3_msualg_1(A),C) & k1_funct_1(u2_msualg_1(A),C) = k1_xboole_0))))))) # label(d2_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12647 (all A all B (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) & l3_msualg_1(B,A) & v5_msualg_1(B,A) -> (exists C (v4_msualg_1(C,A) & v5_msualg_1(C,A) & m1_msualg_2(C,A,B))))) # label(rc3_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12648 (all A (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) -> (all B (l3_msualg_1(B,A) -> (all C (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> r1_tarski(k5_msualg_2(A,B,C),k6_msualg_2(A,B)))))))) # label(t41_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12649 (all A (-v2_msualg_1(A) & l1_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> (all C (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> (all D (m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B)) -> (k9_msualg_2(A,B,C) = D <-> (all E (m1_subset_1(E,u1_struct_0(A)) -> k1_setfam_1(k8_msualg_2(A,B,C,E)) = k1_funct_1(D,E)))))))))))) # label(d15_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12650 (all A (l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> (all C (l3_msualg_1(C,A) -> ((all D (m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B)) -> (r6_pboole(u1_struct_0(A),D,u4_msualg_1(A,C)) -> r6_pboole(u1_msualg_1(A),u5_msualg_1(A,C),k4_msualg_2(A,B,D)) & v3_msualg_2(D,A,B)))) & m4_pboole(u4_msualg_1(A,C),u1_struct_0(A),u4_msualg_1(A,B)) <-> m1_msualg_2(C,A,B)))))))) # label(d10_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12651 (all A (l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> m1_msualg_2(g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)),A,B))))) # label(t38_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12652 (all A (-v2_msualg_1(A) & l1_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> (all C (C = k14_msualg_2(A,B) <-> (all D (v4_msualg_1(D,A) & m1_msualg_2(D,A,B) <-> r2_hidden(D,C))))))))) # label(d20_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12653 (all A (-v3_struct_0(A) & l1_msualg_1(A) & -v2_msualg_1(A) -> (all B (l3_msualg_1(B,A) -> (all C (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> (all D (m3_pboole(D,u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),C)),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),C)) -> ((all E (m1_subset_1(E,u1_msualg_1(A)) -> k3_msualg_2(A,B,E,C) = k1_funct_1(D,E))) <-> k4_msualg_2(A,B,C) = D))))))))) # label(d9_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12654 (all A (-v2_msualg_1(A) & l1_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> (all C (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> (v3_msualg_2(C,A,B) <-> r2_hidden(C,k6_msualg_2(A,B))))))))) # label(t15_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12655 (all A (l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> (all C (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> (r6_pboole(u1_struct_0(A),C,u4_msualg_1(A,B)) -> v3_msualg_2(C,A,B) & (all D (m1_subset_1(D,u1_msualg_1(A)) -> k3_msualg_2(A,B,D,C) = k5_msualg_1(A,D,B)))))))))) # label(t4_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12656 (all A (-v3_struct_0(A) & l1_msualg_1(A) & -v2_msualg_1(A) -> (all B (l3_msualg_1(B,A) & v5_msualg_1(B,A) -> v15_lattices(k17_msualg_2(A,B)))))) # label(t34_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12657 (all A all B (-v3_struct_0(A) & -v2_msualg_1(A) & l3_msualg_1(B,A) & l1_msualg_1(A) -> (exists C (m1_msualg_2(C,A,B) & v4_msualg_1(C,A))))) # label(rc2_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12658 (all A (l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> (all C (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> v3_msualg_2(k9_msualg_2(A,B,C),A,B) & r2_pboole(u1_struct_0(A),C,k9_msualg_2(A,B,C)))))))) # label(t21_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12659 (all A (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) -> (all B (l3_msualg_1(B,A) -> (all C (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> (v3_msualg_2(C,A,B) <-> (all D (m1_subset_1(D,u1_msualg_1(A)) -> r1_msualg_2(A,B,D,C)))))))))) # label(d7_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12660 (all A all B (l1_msualg_1(A) & l3_msualg_1(B,A) & -v2_msualg_1(A) & -v3_struct_0(A) -> -v1_xboole_0(k6_msualg_2(A,B)))) # label(fc8_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12661 (all A (-v3_struct_0(A) & -v2_msualg_1(A) & v2_msualg_2(A) & l1_msualg_1(A) -> (all B (v5_msualg_1(B,A) & l3_msualg_1(B,A) -> (all C (m1_msualg_2(C,A,B) & v5_msualg_1(C,A) -> (all D (v5_msualg_1(D,A) & m1_msualg_2(D,A,B) -> v2_relat_1(k3_pboole(u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))))))))))) # label(t13_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12662 (all A all B (l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) & v2_msualg_2(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> v2_relat_1(k2_msualg_2(A,B)) & v1_funct_1(k2_msualg_2(A,B)) & -v3_relat_1(k2_msualg_2(A,B)) & v1_relat_1(k2_msualg_2(A,B)))) # label(fc5_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12663 (all A all B (l3_msualg_1(B,A) & l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> (exists C m1_msualg_2(C,A,B)))) # label(existence_m1_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12664 (all A all B all C (-v2_msualg_1(A) & l1_msualg_1(A) & m1_subset_1(C,u1_struct_0(A)) & l3_msualg_1(B,A) & -v3_struct_0(A) -> m1_subset_1(k1_msualg_2(A,B,C),k1_zfmisc_1(k1_funct_1(u4_msualg_1(A,B),C))))) # label(dt_k1_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12665 (all A all B (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) & l3_msualg_1(B,A) -> (all C (m1_msualg_2(C,A,B) -> l3_msualg_1(C,A))))) # label(dt_m1_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12666 (all A (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) -> (all B (l3_msualg_1(B,A) -> (all C (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> (all D (m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B)) -> (v3_msualg_2(D,A,B) & r2_pboole(u1_struct_0(A),C,D) & r2_pboole(u1_struct_0(A),k2_msualg_2(A,B),D) <-> r2_hidden(D,k5_msualg_2(A,B,C))))))))))) # label(t14_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12667 (all A all B all C (l1_msualg_1(A) & l3_msualg_1(B,A) & m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) & -v2_msualg_1(A) & -v3_struct_0(A) -> m3_pboole(k4_msualg_2(A,B,C),u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),C)),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),C)))) # label(dt_k4_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12668 (all A (-v3_struct_0(A) & l1_msualg_1(A) & -v2_msualg_1(A) -> (all B (l3_msualg_1(B,A) -> (all C (m1_msualg_2(C,A,B) & v4_msualg_1(C,A) -> (all D (v4_msualg_1(D,A) & m1_msualg_2(D,A,B) -> (r6_pboole(u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D)) -> D = C))))))))) # label(t10_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12669 (all A all B all C (-v2_msualg_1(A) & l1_msualg_1(A) & l3_msualg_1(B,A) & m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) & -v3_struct_0(A) -> m4_pboole(k9_msualg_2(A,B,C),u1_struct_0(A),u4_msualg_1(A,B)))) # label(dt_k9_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12670 (all A (-v2_msualg_1(A) & l1_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> (all C (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> r2_pboole(u1_struct_0(A),k2_pboole(u1_struct_0(A),k2_msualg_2(A,B),C),k9_msualg_2(A,B,C)))))))) # label(t16_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12671 (all A (l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> (all B (v5_msualg_1(B,A) & l3_msualg_1(B,A) -> (all C (m1_msualg_2(C,A,B) -> (all D (m1_msualg_2(D,A,B) -> k13_msualg_2(A,B,D,C) = k13_msualg_2(A,B,C,D))))))))) # label(t27_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12672 (all A all B all C all D (-v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(C,B,k3_finseq_2(A)) & m1_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_1(D) & m1_relset_1(C,B,k3_finseq_2(A)) -> -v3_struct_0(g1_msualg_1(A,B,C,D)) & v1_msualg_1(g1_msualg_1(A,B,C,D)))) # label(fc3_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12673 (all A all B all C all D all E (l1_msualg_1(B) & -v1_xboole_0(E) & m1_subset_1(D,u1_struct_0(B)) & l3_msualg_1(C,B) & -v2_msualg_1(B) & -v3_struct_0(B) -> ((exists F ((exists G (k1_funct_1(u2_msualg_1(B),G) = k1_xboole_0 & D = k1_funct_1(u3_msualg_1(B),G) & r2_hidden(F,k2_relat_1(k5_msualg_1(B,G,C))) & m1_subset_1(G,u1_msualg_1(B)))) & F = A & m1_subset_1(F,E))) <-> r2_hidden(A,a_4_0_msualg_2(B,C,D,E))))) # label(fraenkel_a_4_0_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12674 (all A (-v2_msualg_1(A) & l1_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> (all C (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> (v2_relat_1(k2_pboole(u1_struct_0(A),k2_msualg_2(A,B),C)) -> v2_relat_1(k9_msualg_2(A,B,C))))))))) # label(t17_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12675 $T # label(dt_k14_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12676 (all A (l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> (all C (l3_msualg_1(C,A) -> (v4_msualg_1(B,A) & v4_msualg_1(C,A) & m1_msualg_2(C,A,B) & m1_msualg_2(B,A,C) -> B = C))))))) # label(t8_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12677 (all A (l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> (all C (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> (v3_msualg_2(C,A,B) -> g3_msualg_1(A,C,k4_msualg_2(A,B,C)) = k10_msualg_2(A,B,C)))))))) # label(d16_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12678 (all A (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) -> (all B (l3_msualg_1(B,A) -> (all C (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> (all D (m1_msualg_2(D,A,B) & v4_msualg_1(D,A) -> (D = k12_msualg_2(A,B,C) <-> (all E (m1_msualg_2(E,A,B) -> (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,E)) -> m1_msualg_2(D,A,E)))) & m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,D))))))))))) # label(d18_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12679 (all A (-v3_struct_0(A) & l1_msualg_1(A) & -v2_msualg_1(A) -> (all B (m1_subset_1(B,u1_msualg_1(A)) -> (all C (l3_msualg_1(C,A) -> (all D (m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,C)) -> (all E (m4_pboole(E,u1_struct_0(A),u4_msualg_1(A,C)) -> (r2_pboole(u1_struct_0(A),D,E) -> r1_tarski(k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),D)),B),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),E)),B))))))))))))) # label(t3_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12680 (all A all B all C (-v3_struct_0(A) & -v2_msualg_1(A) & m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) & l3_msualg_1(B,A) & l1_msualg_1(A) -> -v1_xboole_0(k5_msualg_2(A,B,C)))) # label(fc7_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12681 (all A all B (-v3_struct_0(A) & l3_msualg_1(B,A) & v5_msualg_1(B,A) & l1_msualg_1(A) & -v2_msualg_1(A) -> v3_lattices(k17_msualg_2(A,B)) & l3_lattices(k17_msualg_2(A,B)) & v10_lattices(k17_msualg_2(A,B)) & -v3_struct_0(k17_msualg_2(A,B)))) # label(dt_k17_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.45/125.82 12682 (all A (-v2_msualg_1(A) & l1_msualg_1(A) & -v3_struct_0(A) -> (all B (v5_msualg_1(B,A) & l3_msualg_1(B,A) -> k5_lattices(k17_msualg_2(A,B)) = k12_msualg_2(A,B,k2_msualg_2(A,B)))))) # label(t35_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12683 (all A (l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> (all C (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> r2_hidden(u4_msualg_1(A,B),k5_msualg_2(A,B,C)))))))) # label(t40_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12684 (all A (-v3_struct_0(A) & l1_msualg_1(A) & -v2_msualg_1(A) -> (all B (l3_msualg_1(B,A) & v5_msualg_1(B,A) -> (all C (m1_msualg_2(C,A,B) -> (all D (m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B)) -> (r6_pboole(u1_struct_0(A),D,u4_msualg_1(A,B)) -> k12_msualg_2(A,B,D) = k13_msualg_2(A,B,k12_msualg_2(A,B,D),C)))))))))) # label(t26_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12685 (all A (-v3_struct_0(A) & l1_msualg_1(A) & -v2_msualg_1(A) -> (all B (l3_msualg_1(B,A) & v5_msualg_1(B,A) -> v1_binop_1(k16_msualg_2(A,B),k14_msualg_2(A,B)))))) # label(t32_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12686 (all A all B (-v3_struct_0(A) & l1_msualg_1(A) & l3_msualg_1(B,A) & -v2_msualg_1(A) -> m4_pboole(k2_msualg_2(A,B),u1_struct_0(A),u4_msualg_1(A,B)))) # label(dt_k2_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12687 (all A all B all C (-v2_msualg_1(A) & l3_msualg_1(B,A) & m1_subset_1(C,u1_struct_0(A)) & v5_msualg_1(B,A) & l1_msualg_1(A) & v2_msualg_2(A) & -v3_struct_0(A) -> -v1_xboole_0(k1_msualg_2(A,B,C)))) # label(fc4_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12688 (all A (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) -> (all B (l3_msualg_1(B,A) & v5_msualg_1(B,A) -> v1_binop_1(k15_msualg_2(A,B),k14_msualg_2(A,B)))))) # label(t30_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12689 (all A (-v3_struct_0(A) & l1_msualg_1(A) & v2_msualg_2(A) & -v2_msualg_1(A) -> (all B (v5_msualg_1(B,A) & l3_msualg_1(B,A) -> (all C (m1_msualg_2(C,A,B) & v5_msualg_1(C,A) -> m4_pboole(k2_msualg_2(A,B),u1_struct_0(A),u4_msualg_1(A,C)) & v2_relat_1(k2_msualg_2(A,B)))))))) # label(t12_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12690 (all A (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) -> (all B (l3_msualg_1(B,A) -> (all C (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> (r6_pboole(u1_struct_0(A),C,u4_msualg_1(A,B)) -> r6_pboole(u1_msualg_1(A),k4_msualg_2(A,B,C),u5_msualg_1(A,B))))))))) # label(t5_msualg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12691 (all A all B all C all D (-v3_struct_0(B) & m1_subset_1(D,A) & m2_pralg_2(C,A,B) & l1_msualg_1(B) & -v1_xboole_0(A) -> l3_msualg_1(k6_pralg_2(A,B,C,D),B) & v5_msualg_1(k6_pralg_2(A,B,C,D),B))) # label(dt_k6_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12692 (all A (v1_pralg_2(A) <-> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,A) & r2_hidden(C,A) -> k1_relat_1(C) = k1_relat_1(B)))))))) # label(d1_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12693 (all A all B all C all D (m1_subset_1(D,u1_msualg_1(B)) & m2_pralg_2(C,A,B) & l1_msualg_1(B) & -v2_msualg_1(B) & -v3_struct_0(B) -> m1_pboole(k13_pralg_2(A,B,C,D),A) & v1_funcop_1(k13_pralg_2(A,B,C,D)))) # label(dt_k13_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12694 (all A (-v1_xboole_0(A) -> (all B all C (v2_relat_1(C) & m1_pboole(C,A) -> (all D (v2_relat_1(D) & m1_pboole(D,A) -> (all E (v1_funct_1(E) & m2_relset_1(E,B,k3_finseq_2(A)) & v1_funct_2(E,B,k3_finseq_2(A)) -> (all F (v1_funct_2(F,B,A) & m2_relset_1(F,B,A) & v1_funct_1(F) -> (all G all H (v1_funct_1(H) & m2_relset_1(H,k1_funct_1(k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,C)),G),k1_funct_1(k8_pboole(B,A,F,C),G)) & v1_funct_2(H,k1_funct_1(k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,C)),G),k1_funct_1(k8_pboole(B,A,F,C),G)) -> (all I (v1_funct_1(I) & v1_funct_2(I,k1_funct_1(k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,D)),G),k1_funct_1(k8_pboole(B,A,F,D),G)) & m2_relset_1(I,k1_funct_1(k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,D)),G),k1_funct_1(k8_pboole(B,A,F,D),G)) -> (r2_hidden(G,B) -> (all J (m2_relset_1(J,k1_funct_1(k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,k11_pboole(A,C,D))),G),k1_funct_1(k8_pboole(B,A,F,k11_pboole(A,C,D)),G)) & v1_funct_2(J,k1_funct_1(k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,k11_pboole(A,C,D))),G),k1_funct_1(k8_pboole(B,A,F,k11_pboole(A,C,D)),G)) & v1_funct_1(J) -> (k4_pralg_2(A,B,C,D,E,F,G,H,I) = J <-> (all K (v1_funct_1(K) & v1_relat_1(K) -> (r2_hidden(K,k1_funct_1(k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,k11_pboole(A,C,D))),G)) -> k1_funct_1(J,K) = k4_tarski(k1_funct_1(H,k15_mcart_1(K)),k1_funct_1(I,k16_mcart_1(K)))))))))))))))))))))))) # label(d10_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12695 (all A (-v1_xboole_0(A) -> (all B all C (m1_pboole(C,A) & v2_relat_1(C) -> (all D (v2_relat_1(D) & m1_pboole(D,A) -> (all E (m2_relset_1(E,B,k3_finseq_2(A)) & v1_funct_2(E,B,k3_finseq_2(A)) & v1_funct_1(E) -> (all F (v1_funct_2(F,B,A) & m2_relset_1(F,B,A) & v1_funct_1(F) -> (all G (m3_pboole(G,B,k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,C)),k8_pboole(B,A,F,C)) -> (all H (m3_pboole(H,B,k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,D)),k8_pboole(B,A,F,D)) -> (all I (m3_pboole(I,B,k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,k11_pboole(A,C,D))),k8_pboole(B,A,F,k11_pboole(A,C,D))) -> (I = k5_pralg_2(A,B,C,D,E,F,G,H) <-> (all J (r2_hidden(J,B) -> (all K (v1_funct_2(K,k1_funct_1(k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,C)),J),k1_funct_1(k8_pboole(B,A,F,C),J)) & m2_relset_1(K,k1_funct_1(k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,C)),J),k1_funct_1(k8_pboole(B,A,F,C),J)) & v1_funct_1(K) -> (all L (m2_relset_1(L,k1_funct_1(k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,D)),J),k1_funct_1(k8_pboole(B,A,F,D),J)) & v1_funct_2(L,k1_funct_1(k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,D)),J),k1_funct_1(k8_pboole(B,A,F,D),J)) & v1_funct_1(L) -> (K = k1_funct_1(G,J) & k1_funct_1(H,J) = L -> k4_pralg_2(A,B,C,D,E,F,J,K,L) = k1_funct_1(I,J))))))))))))))))))))))))) # label(d11_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12696 (all A (-v1_xboole_0(A) -> (all B (-v3_struct_0(B) & -v2_msualg_1(B) & l1_msualg_1(B) -> (all C (m2_pralg_2(C,A,B) -> (all D (m1_subset_1(D,u1_msualg_1(B)) -> (all E (v1_relat_1(E) & v1_funct_1(E) -> (r2_hidden(E,k2_relat_1(k3_pralg_2(k13_pralg_2(A,B,C,D)))) -> (all F (m1_subset_1(F,A) -> r2_hidden(k1_funct_1(E,F),k4_msualg_1(B,D,k6_pralg_2(A,B,C,F))))) & A = k1_relat_1(E)))))))))))) # label(t16_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12697 (all A (-v1_xboole_0(A) -> (all B (-v2_msualg_1(B) & l1_msualg_1(B) & -v3_struct_0(B) -> (all C (m2_pralg_2(C,A,B) -> (all D (m1_subset_1(D,u1_msualg_1(B)) -> r2_hidden(k10_funct_6(k12_pralg_2(A,B,C)),k1_funct_2(u1_msualg_1(B),k1_funct_2(A,k2_relat_1(k4_funct_5(k12_pralg_2(A,B,C)))))))))))))) # label(t13_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12698 $T # label(t7_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12699 (all A (v1_relat_1(A) & v1_funct_1(A) -> (k1_relat_1(A) = k1_tarski(k1_xboole_0) -> A = k2_pralg_2(A)))) # label(t8_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12700 (all A (-v1_xboole_0(A) & v1_fraenkel(A) & v1_pralg_2(A) -> (all B (m1_pralg_2(B,A) <-> m1_subset_1(B,A))))) # label(redefinition_m1_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12701 (all A (-v1_xboole_0(A) -> (all B (-v3_struct_0(B) & -v2_msualg_1(B) & l1_msualg_1(B) -> (all C (m2_pralg_2(C,A,B) -> (all D (m1_subset_1(D,u1_msualg_1(B)) -> (all E (v1_funct_1(E) & v1_relat_1(E) -> (r2_hidden(E,k1_relat_1(k3_pralg_2(k13_pralg_2(A,B,C,D)))) -> r1_tarski(k2_relat_1(E),k1_fraenkel(k1_relat_1(k1_msualg_1(B,D)),k8_pralg_2(A,B,C))) & (all F (m1_subset_1(F,A) -> r2_hidden(k1_funct_1(E,F),k3_msualg_1(B,D,k6_pralg_2(A,B,C,F))))) & k1_relat_1(E) = A))))))))))) # label(t17_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12702 (all A (v1_relat_1(A) & v1_funcop_1(A) & v1_funct_1(A) -> v1_funcop_1(k3_pralg_2(A)) & m1_pboole(k3_pralg_2(A),k4_card_3(k2_funct_6(A))))) # label(dt_k3_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12703 (all A all B (l1_msualg_1(B) & -v3_struct_0(B) -> (all C (m2_pralg_2(C,A,B) -> (all D (v1_funcop_1(D) & m1_pboole(D,A) -> (k1_xboole_0 != A -> (D = k12_pralg_2(A,B,C) <-> (all E -(r2_hidden(E,A) & (all F (l3_msualg_1(F,B) -> -(u5_msualg_1(B,F) = k1_funct_1(D,E) & F = k1_funct_1(C,E)))))))) & (A = k1_xboole_0 -> (D = k12_pralg_2(A,B,C) <-> k1_xboole_0 = D)))))))) # label(d18_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12704 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (-v3_struct_0(C) & -v2_msualg_1(C) & l1_msualg_1(C) -> (all D (m2_pralg_2(D,A,C) -> (all E (m1_subset_1(E,u1_msualg_1(C)) -> k5_msualg_1(C,E,k6_pralg_2(A,C,D,B)) = k1_funct_1(k13_pralg_2(A,C,D,E),B))))))))))) # label(t14_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12705 (all A all B (-v3_struct_0(B) & l1_msualg_1(B) & -v2_msualg_1(B) -> (all C (m2_pralg_2(C,A,B) -> r6_pboole(u1_struct_0(B),u4_msualg_1(B,k15_pralg_2(A,B,C)),k11_pralg_2(A,B,C)) & r6_pboole(u1_msualg_1(B),u5_msualg_1(B,k15_pralg_2(A,B,C)),k14_pralg_2(A,B,C)))))) # label(t20_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12706 (all A (v1_pralg_2(A) & v1_fraenkel(A) & -v1_xboole_0(A) -> (all B (m1_pralg_2(B,A) -> m1_pboole(B,k1_pralg_2(A)))))) # label(dt_m1_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12707 $T # label(d3_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12708 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C ((exists D (v1_relat_1(D) & v1_funct_1(D) & r2_hidden(D,k1_relat_1(A)) & C = k10_funct_6(D))) <-> r2_hidden(C,k1_relat_1(B)))) & (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(C,k1_relat_1(B)) -> k1_funct_1(B,C) = k1_funct_1(A,k10_funct_6(C))))) <-> B = k2_pralg_2(A)))))) # label(d6_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12709 (all A all B all C (-v2_msualg_1(B) & l1_msualg_1(B) & m2_pralg_2(C,A,B) & -v3_struct_0(B) -> m3_pboole(k14_pralg_2(A,B,C),u1_msualg_1(B),k8_pboole(u1_msualg_1(B),k3_finseq_2(u1_struct_0(B)),u2_msualg_1(B),k6_pboole(u1_struct_0(B),k11_pralg_2(A,B,C))),k8_pboole(u1_msualg_1(B),u1_struct_0(B),u3_msualg_1(B),k11_pralg_2(A,B,C))))) # label(dt_k14_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12710 (exists A (v1_fraenkel(A) & v1_pralg_2(A) & -v1_xboole_0(A))) # label(rc1_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12711 (all A (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) -> (all B (l3_msualg_1(B,A) -> (all C (m1_subset_1(C,u1_msualg_1(A)) -> (k1_xboole_0 = k1_msualg_1(A,C) -> k3_msualg_1(A,C,B) = k1_tarski(k1_xboole_0)))))))) # label(t11_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12712 (all A (v1_fraenkel(A) & v1_pralg_2(A) -> (k1_tarski(k1_xboole_0) = A -> k1_pralg_2(A) = k1_xboole_0))) # label(t2_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12713 (all A (l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> (all C (m1_subset_1(C,u1_msualg_1(A)) -> k4_card_3(k5_relat_1(k1_msualg_1(A,C),u4_msualg_1(A,B))) = k3_msualg_1(A,C,B) & k1_relat_1(k5_relat_1(k1_msualg_1(A,C),u4_msualg_1(A,B))) = k1_relat_1(k1_msualg_1(A,C)) & k4_msualg_1(A,C,B) = k1_funct_1(u4_msualg_1(A,B),k2_msualg_1(A,C)))))))) # label(t10_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12714 (all A all B (v2_relat_1(B) & m1_pboole(B,A) -> v1_fraenkel(k4_card_3(B)) & v1_pralg_2(k4_card_3(B)) & -v1_xboole_0(k4_card_3(B)))) # label(fc1_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12715 (all A all B all C (-v3_struct_0(B) & m2_pralg_2(C,A,B) & l1_msualg_1(B) -> m1_pboole(k11_pralg_2(A,B,C),u1_struct_0(B)))) # label(dt_k11_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12716 (all A all B all C (-v3_struct_0(B) & l1_msualg_1(B) & m2_pralg_2(C,A,B) & -v1_xboole_0(A) -> -v1_xboole_0(k8_pralg_2(A,B,C)))) # label(fc4_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12717 (all A all B (-v3_struct_0(B) & l1_msualg_1(B) & -v2_msualg_1(B) -> (all C (m2_pralg_2(C,A,B) -> (all D (m3_pboole(D,u1_msualg_1(B),k8_pboole(u1_msualg_1(B),k3_finseq_2(u1_struct_0(B)),u2_msualg_1(B),k6_pboole(u1_struct_0(B),k11_pralg_2(A,B,C))),k8_pboole(u1_msualg_1(B),u1_struct_0(B),u3_msualg_1(B),k11_pralg_2(A,B,C))) -> (A != k1_xboole_0 -> (D = k14_pralg_2(A,B,C) <-> (all E (m1_subset_1(E,u1_msualg_1(B)) -> k1_funct_1(D,E) = k1_cqc_lang(k1_msualg_1(B,E),k1_xboole_0,k10_funct_6(k13_pralg_2(A,B,C,E)),k2_pralg_2(k3_pralg_2(k13_pralg_2(A,B,C,E)))))))) & (k1_xboole_0 = A -> k14_pralg_2(A,B,C) = D))))))) # label(d20_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12718 (all A (-v1_xboole_0(A) & v1_pralg_2(A) & v1_fraenkel(A) -> (exists B m1_pralg_2(B,A)))) # label(existence_m1_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12719 (all A all B all C all D (-v3_struct_0(B) & m2_pralg_2(D,A,B) & m1_subset_1(C,u1_struct_0(B)) & l1_msualg_1(B) -> v1_funct_1(k10_pralg_2(A,B,C,D)) & v2_relat_1(k10_pralg_2(A,B,C,D)) & v1_relat_1(k10_pralg_2(A,B,C,D)))) # label(fc6_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12720 (all A all B all C all D all E all F all G all H (-v1_xboole_0(A) & v2_relat_1(D) & v1_funct_1(E) & m1_relset_1(E,B,k3_finseq_2(A)) & v1_funct_1(F) & v1_funct_2(F,B,A) & m3_pboole(G,B,k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,C)),k8_pboole(B,A,F,C)) & m3_pboole(H,B,k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,D)),k8_pboole(B,A,F,D)) & m1_relset_1(F,B,A) & v1_funct_2(E,B,k3_finseq_2(A)) & m1_pboole(D,A) & m1_pboole(C,A) & v2_relat_1(C) -> m3_pboole(k5_pralg_2(A,B,C,D,E,F,G,H),B,k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,k11_pboole(A,C,D))),k8_pboole(B,A,F,k11_pboole(A,C,D))))) # label(dt_k5_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12721 (all A (v1_funcop_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (m1_pboole(B,k4_card_3(k2_funct_6(A))) & v1_funcop_1(B) -> (k3_pralg_2(A) = B <-> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(C,k4_card_3(k2_funct_6(A))) -> k1_funct_1(B,C) = k15_pralg_1(A,C))))))))) # label(d8_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12722 (all A (-v1_xboole_0(A) -> (all B (-v3_struct_0(B) & l1_msualg_1(B) & -v2_msualg_1(B) -> (all C (m2_pralg_2(C,A,B) -> (all D (m1_subset_1(D,u1_msualg_1(B)) -> (all E (m1_subset_1(E,A) -> k3_msualg_1(B,D,k6_pralg_2(A,B,C,E)) = k1_funct_1(k2_funct_6(k13_pralg_2(A,B,C,D)),E))) & k1_relat_1(k2_funct_6(k13_pralg_2(A,B,C,D))) = A)))))))) # label(t18_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12723 (all A all B (-v3_struct_0(B) & l1_msualg_1(B) & -v2_msualg_1(B) -> (all C (m2_pralg_2(C,A,B) -> (all D (m1_subset_1(D,u1_msualg_1(B)) -> k13_pralg_2(A,B,C,D) = k1_funct_1(k10_funct_6(k12_pralg_2(A,B,C)),D))))))) # label(d19_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12724 (all A all B (-v3_struct_0(B) & l1_msualg_1(B) & -v2_msualg_1(B) -> (all C (m2_pralg_2(C,A,B) -> g3_msualg_1(B,k11_pralg_2(A,B,C),k14_pralg_2(A,B,C)) = k15_pralg_2(A,B,C))))) # label(d21_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12725 (all A (v1_fraenkel(A) & v1_pralg_2(A) -> (all B ((A = k1_xboole_0 -> (B = k1_xboole_0 <-> B = k1_pralg_2(A))) & (k1_xboole_0 != A -> (k1_pralg_2(A) = B <-> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(C,A) -> k1_relat_1(C) = B))))))))) # label(d2_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12726 (all A all B all C (v2_relat_1(B) & v2_relat_1(C) & m1_pboole(C,A) & m1_pboole(B,A) -> v1_relat_1(k11_pboole(A,B,C)) & v2_relat_1(k11_pboole(A,B,C)) & v1_funct_1(k11_pboole(A,B,C)))) # label(fc2_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12727 $T # label(t5_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12728 (all A (-v1_xboole_0(A) -> (all B (-v2_msualg_1(B) & l1_msualg_1(B) & -v3_struct_0(B) -> (all C (m2_pralg_2(C,A,B) -> (all D (m1_subset_1(D,u1_msualg_1(B)) -> (all E (r2_hidden(E,k2_relat_1(k3_pralg_2(k13_pralg_2(A,B,C,D)))) -> v1_relat_1(E) & v1_funct_1(E))))))))))) # label(t15_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12729 (all A all B all C (-v3_struct_0(B) & -v2_msualg_1(B) & m2_pralg_2(C,A,B) & l1_msualg_1(B) -> v4_msualg_1(k15_pralg_2(A,B,C),B))) # label(fc8_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12730 $T # label(t6_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12731 (all A (-v1_xboole_0(A) -> (all B (l1_msualg_1(B) & -v3_struct_0(B) -> (all C (m2_pralg_2(C,A,B) -> k8_pralg_2(A,B,C) = k3_tarski(a_3_0_pralg_2(A,B,C)))))))) # label(d14_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12732 (all A all B all C all D (-v3_struct_0(C) & l1_msualg_1(C) & m2_pralg_2(D,B,C) & -v1_xboole_0(B) -> (r2_hidden(A,a_3_0_pralg_2(B,C,D)) <-> (exists E (A = k7_pralg_2(C,k6_pralg_2(B,C,D,E)) & m1_subset_1(E,B)))))) # label(fraenkel_a_3_0_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12733 $T # label(t19_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12734 (all A all B (-v3_struct_0(A) & l3_msualg_1(B,A) & v5_msualg_1(B,A) & l1_msualg_1(A) -> -v1_xboole_0(k7_pralg_2(A,B)))) # label(fc3_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12735 (all A all B (l1_msualg_1(B) & -v3_struct_0(B) -> (all C (m2_pralg_2(C,A,B) -> k1_relat_1(k4_funct_5(k12_pralg_2(A,B,C))) = k2_zfmisc_1(A,u1_msualg_1(B)))))) # label(t12_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12736 $T # label(d5_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12737 (all A all B all C (-v3_struct_0(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & v5_msualg_1(C,A) & l3_msualg_1(C,A) & l3_msualg_1(B,A) -> v4_msualg_1(k9_pralg_2(A,B,C),A))) # label(fc5_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12738 $T # label(t3_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12739 $T # label(d9_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12740 (all A all B (l1_msualg_1(B) & -v3_struct_0(B) -> (exists C m2_pralg_2(C,A,B)))) # label(existence_m2_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12741 (all A (-v1_xboole_0(A) -> (all B all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,A) & m2_relset_1(E,B,A) -> r6_pboole(B,k7_pboole(B,A,E,k11_pboole(A,C,D)),k11_pboole(B,k7_pboole(B,A,E,C),k7_pboole(B,A,E,D))))))))))) # label(t9_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12742 (all A all B all C all D (l1_msualg_1(B) & m1_subset_1(D,A) & m2_pralg_2(C,A,B) & -v3_struct_0(B) & -v1_xboole_0(A) -> k1_funct_1(C,D) = k6_pralg_2(A,B,C,D))) # label(redefinition_k6_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12743 (all A all B (l1_msualg_1(B) & -v3_struct_0(B) -> (all C (m2_pralg_2(C,A,B) -> (all D (m1_pboole(D,u1_struct_0(B)) -> ((all E (m1_subset_1(E,u1_struct_0(B)) -> k1_funct_1(D,E) = k4_card_3(k10_pralg_2(A,B,E,C)))) <-> D = k11_pralg_2(A,B,C)))))))) # label(d17_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12744 (all A all B all C all D (m2_pralg_2(D,A,B) & m1_subset_1(C,u1_struct_0(B)) & l1_msualg_1(B) & -v3_struct_0(B) -> m1_pboole(k10_pralg_2(A,B,C,D),A))) # label(dt_k10_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12745 $T # label(d4_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12746 (all A all B all C (-v3_struct_0(B) & l1_msualg_1(B) & m2_pralg_2(C,A,B) & -v2_msualg_1(B) -> l3_msualg_1(k15_pralg_2(A,B,C),B))) # label(dt_k15_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12747 (all A all B all C all D all E all F all G all H all I (v2_relat_1(D) & v1_funct_1(E) & v1_funct_2(E,B,k3_finseq_2(A)) & m1_relset_1(E,B,k3_finseq_2(A)) & m1_relset_1(F,B,A) & m1_relset_1(I,k1_funct_1(k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,D)),G),k1_funct_1(k8_pboole(B,A,F,D),G)) & v1_funct_2(I,k1_funct_1(k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,D)),G),k1_funct_1(k8_pboole(B,A,F,D),G)) & v1_funct_1(I) & m1_relset_1(H,k1_funct_1(k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,C)),G),k1_funct_1(k8_pboole(B,A,F,C),G)) & v1_funct_2(H,k1_funct_1(k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,C)),G),k1_funct_1(k8_pboole(B,A,F,C),G)) & v1_funct_1(H) & v1_funct_2(F,B,A) & v1_funct_1(F) & m1_pboole(D,A) & m1_pboole(C,A) & v2_relat_1(C) & -v1_xboole_0(A) -> m2_relset_1(k4_pralg_2(A,B,C,D,E,F,G,H,I),k1_funct_1(k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,k11_pboole(A,C,D))),G),k1_funct_1(k8_pboole(B,A,F,k11_pboole(A,C,D)),G)) & v1_funct_2(k4_pralg_2(A,B,C,D,E,F,G,H,I),k1_funct_1(k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,k11_pboole(A,C,D))),G),k1_funct_1(k8_pboole(B,A,F,k11_pboole(A,C,D)),G)) & v1_funct_1(k4_pralg_2(A,B,C,D,E,F,G,H,I)))) # label(dt_k4_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12748 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) -> k3_pralg_2(A) = k7_funct_6(A))) # label(redefinition_k3_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12749 (all A all B all C (l1_msualg_1(B) & m2_pralg_2(C,A,B) & -v3_struct_0(B) -> v1_funct_1(k11_pralg_2(A,B,C)) & -v3_relat_1(k11_pralg_2(A,B,C)) & v2_relat_1(k11_pralg_2(A,B,C)) & v1_relat_1(k11_pralg_2(A,B,C)))) # label(fc7_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12750 $T # label(d7_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12751 (all A all B (l1_msualg_1(B) & -v3_struct_0(B) -> (all C (m1_pboole(C,A) -> ((all D (r2_hidden(D,A) -> l3_msualg_1(k1_funct_1(C,D),B) & v5_msualg_1(k1_funct_1(C,D),B))) <-> m2_pralg_2(C,A,B)))))) # label(d12_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12752 (all A (-v3_struct_0(A) & l1_msualg_1(A) -> (all B (v5_msualg_1(B,A) & l3_msualg_1(B,A) -> (all C (v5_msualg_1(C,A) & l3_msualg_1(C,A) -> k9_pralg_2(A,B,C) = g3_msualg_1(A,k11_pboole(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)),k5_pralg_2(u1_struct_0(A),u1_msualg_1(A),u4_msualg_1(A,B),u4_msualg_1(A,C),u2_msualg_1(A),u3_msualg_1(A),u5_msualg_1(A,B),u5_msualg_1(A,C))))))))) # label(d15_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12753 (all A all B (-v3_struct_0(B) & l1_msualg_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m2_pralg_2(D,A,B) -> (all E (m1_pboole(E,A) -> (A != k1_xboole_0 -> ((all F -((all G (l3_msualg_1(G,B) -> -(k1_funct_1(u4_msualg_1(B,G),C) = k1_funct_1(E,F) & k1_funct_1(D,F) = G))) & r2_hidden(F,A))) <-> k10_pralg_2(A,B,C,D) = E)) & (k1_xboole_0 = A -> (E = k10_pralg_2(A,B,C,D) <-> k1_xboole_0 = E)))))))))) # label(d16_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12754 (all A all B (l1_msualg_1(B) & -v3_struct_0(B) -> (all C (m2_pralg_2(C,A,B) -> m1_pboole(C,A))))) # label(dt_m2_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12755 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k2_pralg_2(A)) & v1_relat_1(k2_pralg_2(A)))) # label(dt_k2_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12756 $T # label(dt_k1_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12757 $T # label(t4_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12758 (all A (-v3_struct_0(A) & l1_msualg_1(A) -> (all B (l3_msualg_1(B,A) -> k3_tarski(k2_relat_1(u4_msualg_1(A,B))) = k7_pralg_2(A,B))))) # label(d13_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12759 (all A all B all C (-v3_struct_0(A) & l3_msualg_1(C,A) & v5_msualg_1(C,A) & l3_msualg_1(B,A) & v5_msualg_1(B,A) & l1_msualg_1(A) -> l3_msualg_1(k9_pralg_2(A,B,C),A))) # label(dt_k9_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12760 $T # label(dt_k7_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12761 (all A all B all C (-v3_struct_0(B) & l1_msualg_1(B) & m2_pralg_2(C,A,B) -> v1_funcop_1(k12_pralg_2(A,B,C)) & m1_pboole(k12_pralg_2(A,B,C),A))) # label(dt_k12_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12762 $T # label(dt_k8_pralg_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12763 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & v2_t_0topsp(B) & l1_pre_topc(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r2_hidden(k8_borsuk_1(A,A,D,E),k1_t_0topsp(A)) -> k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D) = k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)))))))))))) # label(t15_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12764 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> k1_relat_1(k4_t_0topsp(A)) = u1_struct_0(A) & r1_tarski(k2_relat_1(k4_t_0topsp(A)),u1_struct_0(k3_t_0topsp(A))))) # label(t4_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12765 (all A (-v1_xboole_0(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) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (k8_funct_2(A,B,C,E) = k8_funct_2(A,B,C,F) & r2_hidden(E,D) -> r2_hidden(F,D)))))) -> D = k3_funct_2(A,B,C,k2_funct_2(A,B,C,D))))))))))) # label(t2_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12766 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(k3_t_0topsp(A))) <-> (exists C (m1_subset_1(C,u1_struct_0(A)) & k6_eqrel_1(u1_struct_0(A),k1_t_0topsp(A),C) = B)))))) # label(t7_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12767 (all A (l1_pre_topc(A) -> (v2_t_0topsp(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -(B != C & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -((r2_hidden(B,D) & -r2_hidden(C,D) | -r2_hidden(B,D) & r2_hidden(C,D)) & v3_pre_topc(D,A))))))))) | v3_struct_0(A)))) # label(d7_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12768 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_pre_topc(B) & v2_t_0topsp(B) & l1_pre_topc(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k4_pre_topc(A,B,C,k6_eqrel_1(u1_struct_0(A),k1_t_0topsp(A),D)) = k1_struct_0(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D)))))))))) # label(t16_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12769 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> k8_eqrel_1(u1_struct_0(A),k1_t_0topsp(A)) = k2_t_0topsp(A))) # label(d4_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12770 (all A all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> (r2_hidden(A,a_1_0_t_0topsp(B)) <-> (exists C (C = A & r2_hidden(k3_tarski(C),u1_pre_topc(B)) & m1_subset_1(C,k1_zfmisc_1(k2_t_0topsp(B)))))))) # label(fraenkel_a_1_0_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12771 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> k17_borsuk_1(A,k2_t_0topsp(A)) = k4_t_0topsp(A))) # label(d6_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12772 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> v1_t_0topsp(k4_t_0topsp(A),A,k3_t_0topsp(A)))) # label(t12_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12773 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) -> ((all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> (r2_hidden(k4_tarski(E,F),D) <-> r2_hidden(k4_tarski(E,F),C)))))) -> D = C))))))))) # label(t1_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12774 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v1_t_0topsp(C,A,B) <-> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(D,A) -> v3_pre_topc(k4_pre_topc(A,B,C,D),B))))))))))) # label(d2_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12775 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> -v1_xboole_0(k2_t_0topsp(A)) & m1_eqrel_1(k2_t_0topsp(A),u1_struct_0(A)))) # label(dt_k2_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12776 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> a_1_0_t_0topsp(A) = u1_pre_topc(k3_t_0topsp(A)) & k2_t_0topsp(A) = u1_struct_0(k3_t_0topsp(A)))) # label(t5_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12777 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) & -v3_struct_0(B) -> ((exists C (m2_relset_1(C,u1_struct_0(k3_t_0topsp(B)),u1_struct_0(k3_t_0topsp(A))) & v3_tops_2(C,k3_t_0topsp(B),k3_t_0topsp(A)) & r1_rfinseq(k4_t_0topsp(A),k7_funct_2(u1_struct_0(B),u1_struct_0(k3_t_0topsp(B)),u1_struct_0(k3_t_0topsp(A)),k4_t_0topsp(B),C)) & v1_funct_2(C,u1_struct_0(k3_t_0topsp(B)),u1_struct_0(k3_t_0topsp(A))) & v1_funct_1(C))) -> r1_t_0topsp(A,B)))))) # label(t14_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12778 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,k2_t_0topsp(A)) -> r1_tarski(C,B) | r1_xboole_0(C,B))))))))) # label(t11_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12779 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> k16_borsuk_1(A,k2_t_0topsp(A)) = k3_t_0topsp(A))) # label(d5_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12780 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_t_0topsp(A)))) -> (r2_hidden(k3_tarski(B),u1_pre_topc(A)) <-> v3_pre_topc(B,k3_t_0topsp(A))))))) # label(t6_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12781 (exists A (l1_pre_topc(A) & -v3_struct_0(A) & v2_t_0topsp(A) & v2_pre_topc(A))) # label(rc1_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12782 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k8_funct_2(u1_struct_0(A),u1_struct_0(k3_t_0topsp(A)),k4_t_0topsp(A),C) = k8_funct_2(u1_struct_0(A),u1_struct_0(k3_t_0topsp(A)),k4_t_0topsp(A),D) & r2_hidden(C,B) -> r2_hidden(D,B))))))))))) # label(t10_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12783 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(k8_borsuk_1(A,A,C,B),k1_t_0topsp(A)) <-> k8_funct_2(u1_struct_0(A),u1_struct_0(k3_t_0topsp(A)),k4_t_0topsp(A),B) = k8_funct_2(u1_struct_0(A),u1_struct_0(k3_t_0topsp(A)),k4_t_0topsp(A),C)))))))) # label(t9_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12784 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> l1_pre_topc(k3_t_0topsp(A)) & v2_pre_topc(k3_t_0topsp(A)))) # label(dt_k3_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12785 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> l1_pre_topc(k3_t_0topsp(A)) & v2_t_0topsp(k3_t_0topsp(A)) & v2_pre_topc(k3_t_0topsp(A)) & -v3_struct_0(k3_t_0topsp(A)))) # label(t13_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12786 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_eqrel_1(u1_struct_0(A),k1_t_0topsp(A),B) = k8_funct_2(u1_struct_0(A),u1_struct_0(k3_t_0topsp(A)),k4_t_0topsp(A),B))))) # label(t8_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12787 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r2_hidden(B,k8_funct_2(u1_struct_0(A),u1_struct_0(k3_t_0topsp(A)),k4_t_0topsp(A),B)))))) # label(t3_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12788 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> v1_funct_1(k4_t_0topsp(A)) & v1_funct_2(k4_t_0topsp(A),u1_struct_0(A),u1_struct_0(k3_t_0topsp(A))) & v5_pre_topc(k4_t_0topsp(A),A,k3_t_0topsp(A)) & m2_relset_1(k4_t_0topsp(A),u1_struct_0(A),u1_struct_0(k3_t_0topsp(A))))) # label(dt_k4_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12789 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_partfun1(B,u1_struct_0(A),u1_struct_0(A)) & v8_relat_2(B) & v3_relat_2(B) -> (B = k1_t_0topsp(A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(k4_tarski(C,D),B) <-> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(E,A) -> (r2_hidden(D,E) <-> r2_hidden(C,E))))))))))))))) # label(d3_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12790 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> v2_pre_topc(k3_t_0topsp(A)) & -v3_struct_0(k3_t_0topsp(A)))) # label(fc1_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12791 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> v8_relat_2(k1_t_0topsp(A)) & m2_relset_1(k1_t_0topsp(A),u1_struct_0(A),u1_struct_0(A)) & v1_partfun1(k1_t_0topsp(A),u1_struct_0(A),u1_struct_0(A)) & v3_relat_2(k1_t_0topsp(A)))) # label(dt_k1_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12792 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> ((exists C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v3_tops_2(C,A,B) & v1_funct_1(C))) <-> r1_t_0topsp(A,B)))))) # label(d1_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12793 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_pre_topc(B) & v2_t_0topsp(B) & l1_pre_topc(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v5_pre_topc(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (exists D (v1_funct_1(D) & v5_pre_topc(D,k3_t_0topsp(A),B) & m2_relset_1(D,u1_struct_0(k3_t_0topsp(A)),u1_struct_0(B)) & C = k4_borsuk_1(A,k3_t_0topsp(A),B,k4_t_0topsp(A),D) & v1_funct_2(D,u1_struct_0(k3_t_0topsp(A)),u1_struct_0(B)))))))))) # label(t17_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12794 (all A (l3_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l3_lattices(B) -> (g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) = g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> (E = C & D = F -> k2_lattices(B,E,F) = k2_lattices(A,C,D) & (r1_lattices(A,C,D) -> r1_lattices(B,E,F)) & (r1_lattices(B,E,F) -> r1_lattices(A,C,D)) & k1_lattices(A,C,D) = k1_lattices(B,E,F))))))))))))))) # label(t1_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12795 (all A (v7_quantal1(A) & v8_quantal1(A) & l1_quantal1(A) & v4_group_1(A) & v4_lattice3(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v18_quantal1(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r3_lattices(A,k4_monoid_0(A,C,D),B) -> r3_lattices(A,k4_monoid_0(A,D,C),B))))))))))) # label(t15_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12796 (all A (v10_lattices(A) & v7_quantal1(A) & l1_quantal1(A) & v8_quantal1(A) & v4_group_1(A) & v4_lattice3(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A)) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> k1_quantal1(A,k1_quantal1(A,D,B),B) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),C,D))) -> v14_quantal1(C,A)))))))) # label(t14_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12797 (all A (v2_group_1(A) & v4_group_1(A) & v8_quantal1(A) & v20_quantal1(A) & l3_quantal1(A) & v21_quantal1(A) & v7_quantal1(A) & v4_lattice3(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k9_quantal1(A,B,k3_quantal1(A)) = B & k9_quantal1(A,k3_quantal1(A),B) = B)))) # label(t33_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.83 12798 (all A (-v3_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & v4_group_1(A) & v7_quantal1(A) & v8_quantal1(A) & l1_quantal1(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) -> -(v11_quantal1(B) & (all C (-v3_struct_0(C) & l3_lattices(C) & v4_lattice3(C) & v10_lattices(C) -> -((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) -> k15_lattice3(C,D) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,k15_lattice3(A,D)))) & u1_struct_0(C) = k2_relat_1(B)))) & v15_quantal1(B,A) & v14_quantal1(B,A)))))) # label(t34_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12799 (exists A (-v3_struct_0(A) & v4_quantal1(A) & v5_quantal1(A) & v6_quantal1(A) & l1_group_1(A))) # label(rc5_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12800 (exists A (v2_quantal1(A) & l1_quantal1(A))) # label(rc1_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12801 (all A all B all C all D (-v3_struct_0(B) & l1_quantal1(B) & m1_subset_1(C,u1_struct_0(B)) -> (r2_hidden(A,a_3_1_quantal1(B,C,D)) <-> (exists E (k4_monoid_0(B,E,C) = A & r2_hidden(E,D) & m1_subset_1(E,u1_struct_0(B))))))) # label(fraenkel_a_3_1_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12802 (all A (-v3_struct_0(A) & v4_lattice3(A) & v4_group_1(A) & v7_quantal1(A) & v8_quantal1(A) & l1_quantal1(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v17_quantal1(B,A) -> k1_quantal1(A,B,B) = k3_binop_1(u1_struct_0(A),u1_group_1(A)) & k3_binop_1(u1_struct_0(A),u1_group_1(A)) = k2_quantal1(A,B,B) & v2_group_1(A)))))) # label(t19_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12803 (all A all B all C (-v3_struct_0(A) & l1_quantal1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> m1_subset_1(k1_quantal1(A,B,C),u1_struct_0(A)))) # label(dt_k1_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12804 (all A (v4_lattice3(A) & v8_quantal1(A) & l1_quantal1(A) & v7_quantal1(A) & v4_group_1(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (v17_quantal1(B,A) -> k2_quantal1(A,k4_monoid_0(A,k1_quantal1(A,D,B),C),B) = k2_quantal1(A,C,D) & k1_quantal1(A,k4_monoid_0(A,C,k2_quantal1(A,D,B)),B) = k1_quantal1(A,C,D)))))))))) # label(t20_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12805 (exists A (l1_quantal1(A) & -v3_struct_0(A))) # label(rc2_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12806 (all A (l3_lattices(A) & -v3_struct_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> r1_lattices(A,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),C))) <-> v13_quantal1(B,A)))))) # label(d11_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12807 (all A all B all C all D (-v3_struct_0(B) & l3_lattices(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) -> ((exists E (m1_subset_1(E,u1_struct_0(B)) & r2_hidden(E,D) & A = k8_funct_2(u1_struct_0(B),u1_struct_0(B),C,E))) <-> r2_hidden(A,a_3_4_quantal1(B,C,D))))) # label(fraenkel_a_3_4_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12808 (all A (l3_quantal1(A) & -v3_struct_0(A) -> (v18_quantal1(u1_quantal1(A),A) <-> v20_quantal1(A)))) # label(d19_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12809 (all A (-v3_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) -> (all B (v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> (v14_quantal1(B,A) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k15_lattice3(A,a_3_5_quantal1(A,B,C)) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,k15_lattice3(A,C)))) <-> v15_quantal1(B,A))))))) # label(t10_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12810 (all A (-v3_struct_0(A) & v2_group_1(A) & v4_group_1(A) & v7_quantal1(A) & v8_quantal1(A) & v20_quantal1(A) & l3_quantal1(A) & v21_quantal1(A) & v4_lattice3(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k5_quantal1(A,k5_quantal1(A,B)))))) # label(t22_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12811 (all A (-v3_struct_0(A) & v10_lattices(A) & l1_quantal1(A) & v8_quantal1(A) & v7_quantal1(A) & v4_lattice3(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k3_lattices(A,k4_monoid_0(A,D,B),k4_monoid_0(A,D,C)) = k4_monoid_0(A,D,k3_lattices(A,B,C)) & k3_lattices(A,k4_monoid_0(A,B,D),k4_monoid_0(A,C,D)) = k4_monoid_0(A,k3_lattices(A,B,C),D))))))))) # label(t6_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12812 (all A all B (l3_quantal1(A) & m1_subset_1(B,u1_struct_0(A)) & -v3_struct_0(A) -> m1_subset_1(k5_quantal1(A,B),u1_struct_0(A)))) # label(dt_k5_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12813 (all A (-v3_struct_0(A) & v4_lattice3(A) & v2_group_1(A) & v7_quantal1(A) & v8_quantal1(A) & v21_quantal1(A) & l3_quantal1(A) & v20_quantal1(A) & v4_group_1(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k5_quantal1(A,k3_lattices(A,B,C)) = k4_lattices(A,k5_quantal1(A,B),k5_quantal1(A,C)) & k5_quantal1(A,k4_lattices(A,B,C)) = k3_lattices(A,k5_quantal1(A,B),k5_quantal1(A,C)))))))) # label(t26_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12814 (all A ((exists B (A = f2_s2_quantal1(B) & p1_s2_quantal1(B) & m1_subset_1(B,f1_s2_quantal1))) <-> r2_hidden(A,a_0_3_quantal1))) # label(fraenkel_a_0_3_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12815 (exists A (l2_quantal1(A) & v3_quantal1(A))) # label(rc3_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12816 (all A all B all C all D all E (-v1_xboole_0(A) & v1_funct_1(B) & 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,k2_zfmisc_1(A,A),A) & m1_subset_1(E,A) & m1_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> -v3_struct_0(g2_quantal1(A,B,C,D,E)) & v3_quantal1(g2_quantal1(A,B,C,D,E)))) # label(fc2_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12817 (all A (-v3_struct_0(A) & l1_quantal1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C k4_monoid_0(A,B,k15_lattice3(A,C)) = k15_lattice3(A,a_3_0_quantal1(A,B,C))))) <-> v7_quantal1(A)))) # label(d5_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12818 (all A all B all C all D (v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & m1_relset_1(D,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> l1_quantal1(g1_quantal1(A,B,C,D)) & v2_quantal1(g1_quantal1(A,B,C,D)))) # label(dt_g1_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12819 (all A (-v3_struct_0(A) & v7_quantal1(A) & l1_quantal1(A) & v8_quantal1(A) & v4_group_1(A) & v4_lattice3(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (v18_quantal1(B,A) -> r3_lattices(A,k4_monoid_0(A,k1_quantal1(A,k1_quantal1(A,C,B),B),k1_quantal1(A,k1_quantal1(A,D,B),B)),k1_quantal1(A,k1_quantal1(A,k4_monoid_0(A,C,D),B),B))))))))))) # label(t18_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12820 (all A (l1_quantal1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k15_lattice3(A,a_3_6_quantal1(A,B,C)) = k1_quantal1(A,B,C))))))) # label(d15_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12821 (all A (l1_quantal1(A) -> (v2_quantal1(A) -> g1_quantal1(u1_struct_0(A),u2_lattices(A),u1_lattices(A),u1_group_1(A)) = A))) # label(abstractness_v2_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12822 (all A (l1_group_1(A) -> (v4_quantal1(A) & v5_quantal1(A) & -v3_struct_0(A) -> v6_quantal1(A) & -v3_struct_0(A)))) # label(cc2_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12823 (all A all B (-v3_struct_0(A) & l3_quantal1(A) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) -> v1_funct_1(k7_quantal1(A,B)) & m2_relset_1(k7_quantal1(A,B),u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(k7_quantal1(A,B),u1_struct_0(A),u1_struct_0(A)))) # label(dt_k7_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12824 (all A all B all C all D all E all F (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & 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,k2_zfmisc_1(A,A),A) & m1_relset_1(D,k2_zfmisc_1(A,A),A) & m1_subset_1(E,A) & m1_subset_1(F,A) & v1_funct_1(C) & m1_relset_1(B,k2_zfmisc_1(A,A),A) -> (all G all H all I all J all K all L (g3_quantal1(A,B,C,D,E,F) = g3_quantal1(G,H,I,J,K,L) -> C = I & E = K & L = F & J = D & H = B & G = A)))) # label(free_g3_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12825 (all A (r2_hidden(A,a_0_4_quantal1) <-> (exists B (r2_hidden(B,f3_s3_quantal1) & k15_lattice3(f1_s3_quantal1,a_1_0_quantal1(B)) = A & m1_subset_1(B,u1_struct_0(f1_s3_quantal1)))))) # label(fraenkel_a_0_4_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12826 (all A (-v3_struct_0(A) & v2_group_1(A) & v8_quantal1(A) & v21_quantal1(A) & l3_quantal1(A) & v20_quantal1(A) & v7_quantal1(A) & v4_group_1(A) & v4_lattice3(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r3_lattices(A,B,C) -> r3_lattices(A,k5_quantal1(A,C),k5_quantal1(A,B))))))))) # label(t23_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12827 (all A all B (l3_quantal1(A) & v1_funct_1(B) & m1_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & -v3_struct_0(A) -> m2_relset_1(k8_quantal1(A,B),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_2(k8_quantal1(A,B),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_1(k8_quantal1(A,B)))) # label(dt_k8_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12828 (all A (-v3_struct_0(A) & v20_quantal1(A) & l3_quantal1(A) & v21_quantal1(A) & v8_quantal1(A) & v7_quantal1(A) & v4_group_1(A) & v2_group_1(A) & v4_lattice3(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k4_lattices(A,k9_quantal1(A,C,B),k9_quantal1(A,D,B)) = k9_quantal1(A,k4_lattices(A,C,D),B) & k9_quantal1(A,B,k4_lattices(A,C,D)) = k4_lattices(A,k9_quantal1(A,B,C),k9_quantal1(A,B,D)))))))))) # label(t29_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12829 (all A all B all C all D (v10_lattices(B) & v4_lattice3(B) & v8_quantal1(B) & l1_quantal1(B) & v7_quantal1(B) & -v3_struct_0(B) -> ((exists E exists F (k4_monoid_0(B,E,F) = A & r2_hidden(F,D) & r2_hidden(E,C) & m1_subset_1(F,u1_struct_0(B)) & m1_subset_1(E,u1_struct_0(B)))) <-> r2_hidden(A,a_3_3_quantal1(B,C,D))))) # label(fraenkel_a_3_3_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12830 (all A all B all C all D all E (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & m1_relset_1(D,k2_zfmisc_1(A,A),A) & m1_subset_1(E,A) & v1_funct_1(D) & m1_relset_1(B,k2_zfmisc_1(A,A),A) -> v3_quantal1(g2_quantal1(A,B,C,D,E)) & l2_quantal1(g2_quantal1(A,B,C,D,E)))) # label(dt_g2_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12831 (all A (-v3_struct_0(A) & l3_lattices(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(v1_xboole_0(B) & v1_quantal1(B,A)))))) # label(t3_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12832 (all A (-v3_struct_0(A) & l3_quantal1(A) -> (v17_quantal1(u1_quantal1(A),A) <-> v21_quantal1(A)))) # label(d20_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12833 (all A all B all C all D (m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & m1_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all E all F all G all H (g1_quantal1(A,B,C,D) = g1_quantal1(E,F,G,H) -> A = E & G = C & H = D & B = F)))) # label(free_g1_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12834 (all A all B all C all D (v7_quantal1(B) & v20_quantal1(B) & m1_subset_1(C,u1_struct_0(B)) & l3_quantal1(B) & v21_quantal1(B) & v8_quantal1(B) & v4_group_1(B) & v2_group_1(B) & v4_lattice3(B) & v10_lattices(B) & -v3_struct_0(B) -> ((exists E (m1_subset_1(E,u1_struct_0(B)) & k4_monoid_0(B,C,E) = A & r2_hidden(E,D))) <-> r2_hidden(A,a_3_8_quantal1(B,C,D))))) # label(fraenkel_a_3_8_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12835 (all A (l1_quantal1(A) -> l1_group_1(A) & l3_lattices(A))) # label(dt_l1_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12836 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (exists B (v1_relat_1(B) & v13_quantal1(B,A) & v14_quantal1(B,A) & v12_quantal1(B,A) & v1_partfun1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & -v1_xboole_0(B) & v1_funct_1(B) & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)))))) # label(rc9_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12837 (all A (-v3_struct_0(A) & l3_lattices(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) -> (v14_quantal1(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattices(A,C,D) -> r1_lattices(A,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D)))))))))))) # label(d12_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12838 (all A (v4_group_1(A) & v8_quantal1(A) & v20_quantal1(A) & v21_quantal1(A) & l3_quantal1(A) & v7_quantal1(A) & v2_group_1(A) & v4_lattice3(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (k9_quantal1(A,k16_lattice3(A,C),B) = k16_lattice3(A,a_3_11_quantal1(A,B,C)) & k4_monoid_0(A,k15_lattice3(A,C),B) = k15_lattice3(A,a_3_10_quantal1(A,B,C)))))))) # label(t28_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12839 (all A (-v3_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & v4_group_1(A) & v21_quantal1(A) & l3_quantal1(A) & v20_quantal1(A) & v8_quantal1(A) & v7_quantal1(A) & v2_group_1(A) -> (all B k5_quantal1(A,k15_lattice3(A,B)) = k16_lattice3(A,a_2_0_quantal1(A,B))))) # label(t24_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12840 (all A (m1_subset_1(A,f1_s2_quantal1) -> -p1_s2_quantal1(A))) -> a_0_3_quantal1 = k1_xboole_0 # label(s2_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12841 (all A (-v3_struct_0(A) & l1_quantal1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v18_quantal1(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_quantal1(A,C,B) = k1_quantal1(A,C,B)))))))) # label(d18_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12842 (all A all B all C all D (-v3_struct_0(B) & l1_quantal1(B) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(C,u1_struct_0(B)) -> ((exists E (r1_lattices(B,k4_monoid_0(B,C,E),D) & A = E & m1_subset_1(E,u1_struct_0(B)))) <-> r2_hidden(A,a_3_7_quantal1(B,C,D))))) # label(fraenkel_a_3_7_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12843 (all A (-v3_struct_0(A) & l3_quantal1(A) -> m1_subset_1(k4_quantal1(A),u1_struct_0(A)))) # label(dt_k4_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12844 (all A (l2_quantal1(A) -> (v3_quantal1(A) -> g2_quantal1(u1_struct_0(A),u2_lattices(A),u1_lattices(A),u1_group_1(A),u1_vectsp_1(A)) = A))) # label(abstractness_v3_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12845 (all A (l2_quantal1(A) & v2_group_1(A) & -v3_struct_0(A) -> (-v3_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & v4_group_1(A) & v7_quantal1(A) & l1_quantal1(A) & v8_quantal1(A) -> -v3_struct_0(A) & v10_lattices(A) & v2_group_1(A) & v4_group_1(A) & v4_quantal1(A) & v6_quantal1(A) & v9_quantal1(A) & l2_quantal1(A) & v10_quantal1(A) & v4_lattice3(A)))) # label(t7_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12846 (all A (-v3_struct_0(A) & v10_lattices(A) & l1_quantal1(A) & v8_quantal1(A) & v7_quantal1(A) & v4_group_1(A) & v4_lattice3(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r3_lattices(A,B,C) -> r3_lattices(A,k4_monoid_0(A,D,B),k4_monoid_0(A,D,C)) & r3_lattices(A,k4_monoid_0(A,B,D),k4_monoid_0(A,C,D))))))))))) # label(t8_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12847 (exists A l3_quantal1(A)) # label(existence_l3_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12848 (all A (l3_quantal1(A) -> m1_subset_1(k3_quantal1(A),u1_struct_0(A)))) # label(dt_k3_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12849 (all A all B all C all D (v10_lattices(B) & l3_lattices(B) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B)) & v1_funct_1(C) & v4_lattice3(B) & -v3_struct_0(B) -> ((exists E (k8_funct_2(u1_struct_0(B),u1_struct_0(B),C,E) = A & r2_hidden(E,D) & m1_subset_1(E,u1_struct_0(B)))) <-> r2_hidden(A,a_3_5_quantal1(B,C,D))))) # label(fraenkel_a_3_5_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12850 (all A all B all C all D (-v3_struct_0(B) & v4_lattice3(B) & v4_group_1(B) & v7_quantal1(B) & v8_quantal1(B) & v20_quantal1(B) & m1_subset_1(C,u1_struct_0(B)) & l3_quantal1(B) & v21_quantal1(B) & v2_group_1(B) & v10_lattices(B) -> ((exists E (m1_subset_1(E,u1_struct_0(B)) & r2_hidden(E,D) & A = k4_monoid_0(B,E,C))) <-> r2_hidden(A,a_3_10_quantal1(B,C,D))))) # label(fraenkel_a_3_10_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12851 (all A all B all C all D (l1_quantal1(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) & -v3_struct_0(B) -> ((exists E (m1_subset_1(E,u1_struct_0(B)) & E = A & r1_lattices(B,k4_monoid_0(B,E,C),D))) <-> r2_hidden(A,a_3_6_quantal1(B,C,D))))) # label(fraenkel_a_3_6_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12852 (all A (-v3_struct_0(A) & l3_quantal1(A) -> (all B (m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> k2_monoid_0(u1_struct_0(A),B,k6_quantal1(A)) = k7_quantal1(A,B))))) # label(d25_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12853 (all A (l3_quantal1(A) & -v3_struct_0(A) -> (g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = k1_lattice3(k1_xboole_0) -> v21_quantal1(A) & v20_quantal1(A)))) # label(t21_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12854 (all A (l1_quantal1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v17_quantal1(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> C = k1_quantal1(A,k2_quantal1(A,C,B),B) & C = k2_quantal1(A,k1_quantal1(A,C,B),B)))))))) # label(d17_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12855 (all A (l3_quantal1(A) -> m1_subset_1(u1_quantal1(A),u1_struct_0(A)))) # label(dt_u1_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12856 (all A (l1_quantal1(A) & -v3_struct_0(A) -> (all B (m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> (v16_quantal1(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> r1_lattices(A,k4_monoid_0(A,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D)),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,k4_monoid_0(A,C,D)))))))))))) # label(d14_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12857 (all A (-v3_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & v2_group_1(A) & v20_quantal1(A) & l3_quantal1(A) & v21_quantal1(A) & v8_quantal1(A) & v7_quantal1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k9_quantal1(A,B,k9_quantal1(A,C,D)) = k9_quantal1(A,k9_quantal1(A,B,C),D))))))))) # label(t31_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12858 (all A (l1_group_1(A) -> (v6_quantal1(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v5_quantal1(A) & v4_quantal1(A)))) # label(cc1_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12859 (all A (v2_group_1(A) & v7_quantal1(A) & v20_quantal1(A) & v21_quantal1(A) & l3_quantal1(A) & v8_quantal1(A) & v4_group_1(A) & v4_lattice3(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k4_monoid_0(A,B,k4_quantal1(A)) = B & k4_monoid_0(A,k4_quantal1(A),B) = B)))) # label(t32_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12860 (all A (-v3_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & v4_group_1(A) & v20_quantal1(A) & l3_quantal1(A) & v21_quantal1(A) & v8_quantal1(A) & v7_quantal1(A) & v2_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r3_lattices(A,B,C) & r3_lattices(A,D,E) -> r3_lattices(A,k9_quantal1(A,B,D),k9_quantal1(A,C,E))))))))))))) # label(t30_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12861 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v11_quantal1(A) <-> A = k5_relat_1(A,A)))) # label(d9_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12862 (all A (l2_quantal1(A) -> (v7_quantal1(A) & v8_quantal1(A) & v4_lattice3(A) & v10_lattices(A) & -v3_struct_0(A) -> v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v9_lattices(A) & v4_lattice3(A) & v9_quantal1(A) & v10_quantal1(A) & v10_lattices(A) & v8_lattices(A) & -v3_struct_0(A)))) # label(cc3_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12863 (exists A (v19_quantal1(A) & l3_quantal1(A))) # label(rc10_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12864 (all A (-v3_struct_0(A) & l1_quantal1(A) -> (v8_quantal1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C k15_lattice3(A,a_3_1_quantal1(A,B,C)) = k4_monoid_0(A,k15_lattice3(A,C),B))))))) # label(d6_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12865 (exists A l1_quantal1(A)) # label(existence_l1_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12866 (all A (-v3_struct_0(A) & l3_lattices(A) -> (all B (l3_lattices(B) & -v3_struct_0(B) -> (g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (D = C -> (r3_lattice3(B,D,E) -> r3_lattice3(A,C,E)) & (r4_lattice3(B,D,E) -> r4_lattice3(A,C,E)) & (r4_lattice3(A,C,E) -> r4_lattice3(B,D,E)) & (r3_lattice3(A,C,E) -> r3_lattice3(B,D,E))))))))))))) # label(t2_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12867 (all A (r2_hidden(A,a_0_5_quantal1) <-> (exists B exists C (m1_subset_1(B,u1_struct_0(f1_s3_quantal1)) & m1_subset_1(C,u1_struct_0(f1_s3_quantal1)) & A = f2_s3_quantal1(B,C) & r2_hidden(B,f3_s3_quantal1) & r2_hidden(C,f4_s3_quantal1))))) # label(fraenkel_a_0_5_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12868 (all A (-v3_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & v4_group_1(A) & l1_quantal1(A) & v8_quantal1(A) & v7_quantal1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (v18_quantal1(B,A) -> r3_lattices(A,C,k2_quantal1(A,k2_quantal1(A,C,B),B)) & r3_lattices(A,C,k1_quantal1(A,k1_quantal1(A,C,B),B))))))))) # label(t16_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12869 (all A (-v3_struct_0(A) & v10_lattices(A) & v7_quantal1(A) & l1_quantal1(A) & v8_quantal1(A) & v4_group_1(A) & v4_lattice3(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r3_lattices(A,k4_monoid_0(A,B,C),D) <-> r3_lattices(A,C,k2_quantal1(A,B,D))))))))))) # label(t11_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12870 (all A (l1_group_1(A) & -v3_struct_0(A) -> (v4_quantal1(A) <-> (exists B ((all C (m1_subset_1(C,u1_struct_0(A)) -> B = k1_group_1(A,B,C))) & m1_subset_1(B,u1_struct_0(A))))))) # label(d2_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12871 (all A ((exists B (m1_subset_1(B,f1_s1_quantal1) & A = f3_s1_quantal1(f4_s1_quantal1(B)) & p1_s1_quantal1(B))) <-> r2_hidden(A,a_0_2_quantal1))) # label(fraenkel_a_0_2_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12872 (all A (v4_lattice3(A) & l1_quantal1(A) & v8_quantal1(A) & v7_quantal1(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B all C k15_lattice3(A,a_3_3_quantal1(A,B,C)) = k4_monoid_0(A,k15_lattice3(A,B),k15_lattice3(A,C))))) # label(t5_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12873 (all A (l1_group_1(A) & -v3_struct_0(A) -> ((exists B ((all C (m1_subset_1(C,u1_struct_0(A)) -> B = k1_group_1(A,C,B))) & m1_subset_1(B,u1_struct_0(A)))) <-> v5_quantal1(A)))) # label(d3_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12874 (all A (-v3_struct_0(A) & l3_quantal1(A) -> k1_quantal1(A,k3_quantal1(A),k3_quantal1(A)) = k4_quantal1(A))) # label(d22_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12875 (all A (l3_quantal1(A) -> (v19_quantal1(A) -> A = g3_quantal1(u1_struct_0(A),u2_lattices(A),u1_lattices(A),u1_group_1(A),u1_vectsp_1(A),u1_quantal1(A))))) # label(abstractness_v19_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12876 (all A (-v3_struct_0(A) & l1_quantal1(A) & v8_quantal1(A) & v7_quantal1(A) & v4_group_1(A) & v4_lattice3(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r3_lattices(A,D,E) & r3_lattices(A,B,C) -> r3_lattices(A,k4_monoid_0(A,B,D),k4_monoid_0(A,C,E))))))))))))) # label(t9_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12877 (all A (-v3_struct_0(A) & l3_quantal1(A) -> (all B (v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> k5_quantal1(A,C) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C))) <-> B = k6_quantal1(A)))))) # label(d24_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12878 (exists A (-v3_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v9_lattices(A) & v10_lattices(A) & v2_group_1(A) & v4_quantal1(A) & v6_quantal1(A) & v7_quantal1(A) & v8_quantal1(A) & v5_quantal1(A) & v7_group_1(A) & v4_group_1(A) & v4_lattice3(A) & v8_lattices(A) & v7_lattices(A) & v6_lattices(A) & l1_quantal1(A))) # label(rc6_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12879 (all A all B (m1_subset_1(B,u1_struct_0(f1_s3_quantal1)) -> (r2_hidden(A,a_1_0_quantal1(B)) <-> (exists C (m1_subset_1(C,u1_struct_0(f1_s3_quantal1)) & r2_hidden(C,f4_s3_quantal1) & A = f2_s3_quantal1(B,C)))))) # label(fraenkel_a_1_0_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12880 (all A all B all C all D (-v3_struct_0(B) & m1_subset_1(C,u1_struct_0(B)) & l1_quantal1(B) -> (r2_hidden(A,a_3_0_quantal1(B,C,D)) <-> (exists E (m1_subset_1(E,u1_struct_0(B)) & r2_hidden(E,D) & A = k4_monoid_0(B,C,E)))))) # label(fraenkel_a_3_0_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12881 (all A (v4_lattice3(A) & v7_quantal1(A) & v8_quantal1(A) & l1_quantal1(A) & v4_group_1(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (v18_quantal1(B,A) -> k1_quantal1(A,C,B) = k1_quantal1(A,k1_quantal1(A,k1_quantal1(A,C,B),B),B) & k2_quantal1(A,C,B) = k2_quantal1(A,k2_quantal1(A,k2_quantal1(A,C,B),B),B)))))))) # label(t17_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12882 (all A (v4_lattice3(A) & v4_group_1(A) & v8_quantal1(A) & l1_quantal1(A) & v7_quantal1(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r3_lattices(A,C,D) -> r3_lattices(A,k2_quantal1(A,D,B),k2_quantal1(A,C,B)) & r3_lattices(A,k1_quantal1(A,D,B),k1_quantal1(A,C,B))))))))))) # label(t13_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12883 (all A all B all C (-v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_quantal1(A) -> m1_subset_1(k2_quantal1(A,B,C),u1_struct_0(A)))) # label(dt_k2_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12884 (all A (l3_lattices(A) & -v3_struct_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_lattices(A,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,k15_lattice3(A,C)),k15_lattice3(A,a_3_4_quantal1(A,B,C))))) <-> v15_quantal1(B,A)))))) # label(d13_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12885 (all A (l3_quantal1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_quantal1(A,B,k3_quantal1(A)) = k5_quantal1(A,B))))) # label(d23_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12886 (all A (-v3_struct_0(A) & v10_lattices(A) & v7_quantal1(A) & v8_quantal1(A) & l1_quantal1(A) & v4_group_1(A) & v4_lattice3(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r3_lattices(A,B,k1_quantal1(A,C,D)) <-> r3_lattices(A,k4_monoid_0(A,B,C),D)))))))))) # label(t12_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12887 (exists A (-v3_struct_0(A) & l2_quantal1(A))) # label(rc4_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12888 (all A all B all C all D all E all F (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & m1_subset_1(F,A) & m1_subset_1(E,A) & m1_relset_1(D,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) -> v19_quantal1(g3_quantal1(A,B,C,D,E,F)) & l3_quantal1(g3_quantal1(A,B,C,D,E,F)))) # label(dt_g3_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12889 (all A (-v3_struct_0(A) & l1_group_1(A) -> (v5_quantal1(A) & v4_quantal1(A) <-> v6_quantal1(A)))) # label(d4_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12890 (all A (-v3_struct_0(A) & l3_lattices(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) -> (v12_quantal1(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> r1_lattices(A,C,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C))))))))) # label(d10_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12891 (all A (l1_quantal1(A) & -v3_struct_0(A) -> (k1_lattice3(k1_xboole_0) = g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) -> v2_group_1(A) & v6_quantal1(A) & v4_lattice3(A) & v7_quantal1(A) & v10_lattices(A) & v8_quantal1(A) & v7_group_1(A) & v4_group_1(A)))) # label(t4_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12892 (all A all B all C all D all E (v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & m1_subset_1(E,A) & m1_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all F all G all H all I all J (g2_quantal1(F,G,H,I,J) = g2_quantal1(A,B,C,D,E) -> C = H & I = D & J = E & B = G & F = A)))) # label(free_g2_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12893 (all A all B all C all D (-v3_struct_0(B) & l1_quantal1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (r2_hidden(A,a_3_2_quantal1(B,C,D)) <-> (exists E exists F (A = k4_monoid_0(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) & m1_subset_1(F,u1_struct_0(B)) & m1_subset_1(E,u1_struct_0(B))))))) # label(fraenkel_a_3_2_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12894 (all A all B all C all D (-v3_struct_0(B) & v4_lattice3(B) & v4_group_1(B) & v20_quantal1(B) & l3_quantal1(B) & m1_subset_1(C,u1_struct_0(B)) & v21_quantal1(B) & v8_quantal1(B) & v7_quantal1(B) & v2_group_1(B) & v10_lattices(B) -> ((exists E (k9_quantal1(B,C,E) = A & r2_hidden(E,D) & m1_subset_1(E,u1_struct_0(B)))) <-> r2_hidden(A,a_3_9_quantal1(B,C,D))))) # label(fraenkel_a_3_9_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12895 (all A (l3_quantal1(A) -> u1_quantal1(A) = k3_quantal1(A))) # label(d21_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12896 (all A all B all C all D (-v3_struct_0(B) & v4_lattice3(B) & v20_quantal1(B) & l3_quantal1(B) & m1_subset_1(C,u1_struct_0(B)) & v21_quantal1(B) & v8_quantal1(B) & v7_quantal1(B) & v4_group_1(B) & v2_group_1(B) & v10_lattices(B) -> (r2_hidden(A,a_3_11_quantal1(B,C,D)) <-> (exists E (m1_subset_1(E,u1_struct_0(B)) & r2_hidden(E,D) & k9_quantal1(B,E,C) = A))))) # label(fraenkel_a_3_11_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12897 (exists A (l2_quantal1(A) & -v3_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v10_lattices(A) & v4_lattice3(A) & v2_group_1(A) & v4_group_1(A) & v7_group_1(A) & v4_quantal1(A) & v6_quantal1(A) & v8_quantal1(A) & v10_quantal1(A) & v9_quantal1(A) & v7_quantal1(A) & v5_quantal1(A) & v9_lattices(A) & v8_lattices(A) & v7_lattices(A) & v6_lattices(A))) # label(rc8_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12898 (exists A l2_quantal1(A)) # label(existence_l2_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12899 (all A all B all C (v10_lattices(A) & v4_lattice3(A) & v4_group_1(A) & v20_quantal1(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l3_quantal1(A) & v21_quantal1(A) & v8_quantal1(A) & v7_quantal1(A) & v2_group_1(A) & -v3_struct_0(A) -> m1_subset_1(k9_quantal1(A,B,C),u1_struct_0(A)))) # label(dt_k9_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12900 (all A all B all C all D all E all F (v1_funct_1(B) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & m1_subset_1(F,A) & m1_subset_1(E,A) & m1_relset_1(D,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & -v1_xboole_0(A) -> -v3_struct_0(g3_quantal1(A,B,C,D,E,F)) & v19_quantal1(g3_quantal1(A,B,C,D,E,F)))) # label(fc3_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12901 (all A (l2_quantal1(A) -> l1_vectsp_1(A) & l1_quantal1(A))) # label(dt_l2_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12902 (all A (r2_hidden(A,a_0_1_quantal1) <-> (exists B (p1_s1_quantal1(B) & f4_s1_quantal1(B) = A & m1_subset_1(B,f1_s1_quantal1))))) # label(fraenkel_a_0_1_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12903 (exists A (l3_quantal1(A) & -v3_struct_0(A))) # label(rc11_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12904 (all A (l3_quantal1(A) -> l2_quantal1(A))) # label(dt_l3_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12905 (exists A (l2_quantal1(A) & v4_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v4_lattice3(A) & v10_lattices(A) & v6_lattices(A) & v5_lattices(A) & -v3_struct_0(A))) # label(rc7_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12906 (all A all B all C all D (m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & m1_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & v1_funct_1(C) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & -v1_xboole_0(A) -> -v3_struct_0(g1_quantal1(A,B,C,D)) & v2_quantal1(g1_quantal1(A,B,C,D)))) # label(fc1_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12907 (all A (r2_hidden(A,a_0_0_quantal1) <-> (exists B (f3_s1_quantal1(B) = A & r2_hidden(B,a_0_1_quantal1) & m1_subset_1(B,f2_s1_quantal1))))) # label(fraenkel_a_0_0_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12908 (all A (v10_lattices(A) & v4_lattice3(A) & v21_quantal1(A) & l3_quantal1(A) & v20_quantal1(A) & v8_quantal1(A) & v7_quantal1(A) & v4_group_1(A) & v2_group_1(A) & -v3_struct_0(A) -> (all B k15_lattice3(A,a_2_0_quantal1(A,B)) = k5_quantal1(A,k16_lattice3(A,B))))) # label(t25_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12909 (all A (-v3_struct_0(A) & v7_quantal1(A) & v20_quantal1(A) & v21_quantal1(A) & l3_quantal1(A) & v8_quantal1(A) & v4_group_1(A) & v2_group_1(A) & v4_lattice3(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k9_quantal1(A,B,C) = k5_quantal1(A,k4_monoid_0(A,k5_quantal1(A,B),k5_quantal1(A,C))))))))) # label(d27_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12910 (all A (-v3_struct_0(A) & v4_lattice3(A) & v7_quantal1(A) & l3_quantal1(A) & v21_quantal1(A) & v20_quantal1(A) & v8_quantal1(A) & v4_group_1(A) & v2_group_1(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (k16_lattice3(A,a_3_9_quantal1(A,B,C)) = k9_quantal1(A,B,k16_lattice3(A,C)) & k15_lattice3(A,a_3_8_quantal1(A,B,C)) = k4_monoid_0(A,B,k15_lattice3(A,C)))))))) # label(t27_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12911 (all A (l3_quantal1(A) & -v3_struct_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) -> k8_quantal1(A,B) = k7_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A),u1_struct_0(A),B,k6_quantal1(A)))))) # label(d26_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12912 (all A all B all C (-v3_struct_0(B) & v8_quantal1(B) & v20_quantal1(B) & v21_quantal1(B) & l3_quantal1(B) & v7_quantal1(B) & v4_group_1(B) & v2_group_1(B) & v4_lattice3(B) & v10_lattices(B) -> ((exists D (A = k5_quantal1(B,D) & r2_hidden(D,C) & m1_subset_1(D,u1_struct_0(B)))) <-> r2_hidden(A,a_2_0_quantal1(B,C))))) # label(fraenkel_a_2_0_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12913 (all A (l1_quantal1(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_lattices(A,k4_monoid_0(A,D,B),k4_monoid_0(A,D,C)) = k4_monoid_0(A,D,k1_lattices(A,B,C)) & k1_lattices(A,k4_monoid_0(A,B,D),k4_monoid_0(A,C,D)) = k4_monoid_0(A,k1_lattices(A,B,C),D))))))) <-> v9_quantal1(A)))) # label(d7_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12914 (exists A (l3_quantal1(A) & v4_lattices(A) & v5_lattices(A) & v10_lattices(A) & v4_lattice3(A) & v2_group_1(A) & v4_group_1(A) & v7_group_1(A) & v7_quantal1(A) & v9_quantal1(A) & v20_quantal1(A) & v21_quantal1(A) & v19_quantal1(A) & v10_quantal1(A) & v8_quantal1(A) & v9_lattices(A) & v8_lattices(A) & v7_lattices(A) & v6_lattices(A) & -v3_struct_0(A))) # label(rc12_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12915 (all A (l3_quantal1(A) & -v3_struct_0(A) -> v1_funct_1(k6_quantal1(A)) & m2_relset_1(k6_quantal1(A),u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(k6_quantal1(A),u1_struct_0(A),u1_struct_0(A)))) # label(dt_k6_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12916 (all A (-v3_struct_0(A) & l3_lattices(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(B)) & v1_finset_1(C) -> (exists D (m1_subset_1(D,u1_struct_0(A)) & r1_lattices(A,k15_lattice3(A,C),D) & r2_hidden(D,B))))) <-> v1_quantal1(B,A)))))) # label(d1_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12917 (all A (l1_quantal1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k15_lattice3(A,a_3_7_quantal1(A,B,C)) = k2_quantal1(A,B,C))))))) # label(d16_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12918 (all A (-v3_struct_0(A) & l1_quantal1(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v1_quantal1(C,A) & v1_quantal1(B,A) -> k15_lattice3(A,a_3_2_quantal1(A,B,C)) = k4_monoid_0(A,k15_lattice3(A,B),k15_lattice3(A,C))))))) <-> v10_quantal1(A)))) # label(d8_quantal1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12919 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k6_tex_4(A,B)))))))) # label(t81_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12920 (all A all B (-v3_struct_0(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & l1_pre_topc(A) & v2_pre_topc(A) -> v1_xboole_0(k1_tops_1(A,B)) & v3_tops_1(k1_tops_1(A,B),A) & v1_tex_2(k1_tops_1(A,B),k1_zfmisc_1(u1_struct_0(A))) & v4_membered(k1_tops_1(A,B)) & v5_membered(k1_tops_1(A,B)) & v3_membered(k1_tops_1(A,B)) & v2_membered(k1_tops_1(A,B)) & v1_membered(k1_tops_1(A,B)) & v2_tops_1(k1_tops_1(A,B),A) & v4_pre_topc(k1_tops_1(A,B),A) & v3_pre_topc(k1_tops_1(A,B),A))) # label(fc7_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12921 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> v1_tex_4(k5_setfam_1(u1_struct_0(A),k1_tex_4(A,B)),A))))) # label(t15_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12922 (all A all B (-v3_struct_0(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> v1_pre_topc(k7_tex_4(A,B)) & -v3_struct_0(k7_tex_4(A,B)))) # label(fc19_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12923 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) | v4_pre_topc(C,A) -> k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,C)) = k5_subset_1(u1_struct_0(A),k3_tex_4(A,B),k3_tex_4(A,C))))))))) # label(t66_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12924 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_realset1(B) & -v1_xboole_0(B) & l1_pre_topc(A) & -v3_realset2(A) & -v3_struct_0(A) -> -v3_struct_0(k6_tex_4(A,B)) & -v3_realset2(k6_tex_4(A,B)) & v1_pre_topc(k6_tex_4(A,B)))) # label(fc17_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12925 (all A all B (v2_pre_topc(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) & -v3_struct_0(A) -> -v1_xboole_0(k6_pre_topc(A,B)) & v4_pre_topc(k6_pre_topc(A,B),A))) # label(fc1_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12926 (all A all B all C (-v3_struct_0(B) & l1_pre_topc(B) & m1_subset_1(C,u1_struct_0(B)) -> (r2_hidden(A,a_2_4_tex_4(B,C)) <-> (exists D (A = D & v4_pre_topc(D,B) & r2_hidden(C,D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))))))) # label(fraenkel_a_2_4_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12927 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) -> (r1_tarski(B,C) -> m1_pre_topc(k7_tex_4(A,B),k7_tex_4(A,C))))))))) # label(t86_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12928 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r1_subset_1(u1_struct_0(k5_tex_4(A,B)),u1_struct_0(k5_tex_4(A,C))) | g1_pre_topc(u1_struct_0(k5_tex_4(A,C)),u1_pre_topc(k5_tex_4(A,C))) = g1_pre_topc(u1_struct_0(k5_tex_4(A,B)),u1_pre_topc(k5_tex_4(A,B))))))))) # label(t77_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12929 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (v3_pre_topc(B,A) & v1_tex_4(B,A) -> v3_tex_4(B,A)))))) # label(t18_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12930 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k3_tex_4(A,k3_tex_4(A,B)) = k3_tex_4(A,B))))) # label(t35_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12931 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (exists B (m1_pre_topc(B,A) & v2_pre_topc(B) & v3_tdlat_3(B) & v4_tex_4(B,A) & v2_tdlat_3(B) & v1_pre_topc(B))))) # label(rc1_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12932 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_tdlat_3(B) & m1_pre_topc(B,A) -> (all C (v1_tsep_1(C,A) & m1_pre_topc(C,A) -> r1_tsep_1(A,B,C) | m1_pre_topc(B,C))))))) # label(t72_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.84 12933 (all A all B all C (l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & -v3_struct_0(B) -> ((exists D (D = A & v3_pre_topc(D,B) & r1_tarski(C,D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))))) <-> r2_hidden(A,a_2_7_tex_4(B,C))))) # label(fraenkel_a_2_7_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12934 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (v1_tsep_1(B,A) & m1_pre_topc(B,A) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> m1_pre_topc(k7_tex_4(A,C),B)))))))) # label(t90_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12935 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v2_tex_4(B,A) -> v1_tex_4(k6_setfam_1(u1_struct_0(A),B),A)))))) # label(t11_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12936 (all A all B all C (l1_pre_topc(B) & m1_subset_1(C,u1_struct_0(B)) & v2_pre_topc(B) & -v3_struct_0(B) -> ((exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & D = A & r2_hidden(C,D) & v4_pre_topc(D,B))) <-> r2_hidden(A,a_2_1_tex_4(B,C))))) # label(fraenkel_a_2_1_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12937 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & l1_pre_topc(B) & -v3_struct_0(B) -> ((exists D (m1_subset_1(D,u1_struct_0(B)) & r2_hidden(D,C) & A = k2_tex_4(B,D))) <-> r2_hidden(A,a_2_6_tex_4(B,C))))) # label(fraenkel_a_2_6_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12938 (all A all B (-v3_realset2(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_realset1(B) & l1_pre_topc(A) & -v3_struct_0(A) -> -v3_struct_0(k7_tex_4(A,B)) & -v3_realset2(k7_tex_4(A,B)) & v1_pre_topc(k7_tex_4(A,B)))) # label(fc20_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12939 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) & v1_tex_4(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,B) -> B = k6_pre_topc(A,k1_struct_0(A,C)))))))))) # label(t45_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12940 (all A all B (-v3_struct_0(A) & l1_pre_topc(A) & -v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -v1_xboole_0(k3_tex_4(A,B)) & -v1_tex_2(k3_tex_4(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(fc12_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12941 (all A all B (m1_subset_1(B,u1_struct_0(A)) & l1_pre_topc(A) -> m1_subset_1(k2_tex_4(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k2_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12942 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_struct_0(A,B) = k6_setfam_1(u1_struct_0(A),k1_tex_4(A,B)))))) # label(t13_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12943 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v4_tex_4(B,A) -> v2_pre_topc(B) & v2_tdlat_3(B) & v3_tdlat_3(B)))))) # label(cc1_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12944 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) & v1_tsep_1(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (m1_subset_1(C,u1_struct_0(B)) -> m1_pre_topc(k5_tex_4(A,C),B)))))))) # label(t79_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12945 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,B) & v3_pre_topc(B,A) -> r1_tarski(k2_tex_4(A,C),B)))))))) # label(t26_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12946 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & l1_pre_topc(B) & v2_pre_topc(B) & -v3_struct_0(B) -> ((exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & D = A & r1_tarski(D,C) & v3_pre_topc(D,B))) <-> r2_hidden(A,a_2_2_tex_4(B,C))))) # label(fraenkel_a_2_2_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12947 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,B) -> k6_pre_topc(A,B) = k6_pre_topc(A,k1_struct_0(A,C))))) <-> v1_tex_4(B,A)))))) # label(d13_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12948 (all A all B all C (m1_subset_1(C,u1_struct_0(B)) & l1_pre_topc(B) & -v3_struct_0(B) -> (r2_hidden(A,a_2_5_tex_4(B,C)) <-> (exists D (r2_hidden(C,D) & v3_pre_topc(D,B) & A = D & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))))))) # label(fraenkel_a_2_5_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12949 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(B) = C -> (v4_tex_4(B,A) <-> v3_tex_4(C,A))))))))) # label(t74_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12950 (all A all B (l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) & -v3_struct_0(A) -> -v1_xboole_0(k2_tex_4(A,B)))) # label(fc9_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12951 (all A (-v3_struct_0(A) & -v3_realset2(A) & l1_pre_topc(A) -> (exists B (v1_pre_topc(B) & -v2_tex_2(B,A) & m1_pre_topc(B,A))))) # label(rc2_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12952 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> v1_tex_4(k1_struct_0(A,B),A))))) # label(t8_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12953 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v2_tdlat_3(B) -> -v4_tex_4(B,A)))))) # label(cc2_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12954 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k3_tex_4(A,B),k6_pre_topc(A,B)))))) # label(t61_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12955 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) | v3_pre_topc(C,A) -> k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,C)) = k5_subset_1(u1_struct_0(A),k3_tex_4(A,B),k3_tex_4(A,C))))))))) # label(t67_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12956 (all A all B (-v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & l1_pre_topc(A) -> -v1_xboole_0(k1_tex_4(A,B)))) # label(fc8_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12957 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> v3_tex_4(k2_tex_4(A,B),A))))) # label(t22_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12958 (all A all B all C (l1_pre_topc(B) & m1_subset_1(C,u1_struct_0(B)) -> ((exists D (D = A & r2_hidden(C,D) & v1_tex_4(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))))) <-> r2_hidden(A,a_2_3_tex_4(B,C))))) # label(fraenkel_a_2_3_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12959 (all A all B (l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_realset1(B) & -v1_xboole_0(B) & -v3_realset2(A) & -v3_struct_0(A) -> -v1_realset1(k3_tex_4(A,B)) & -v1_xboole_0(k3_tex_4(A,B)))) # label(fc13_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12960 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> m1_pre_topc(k6_tex_4(A,B),k7_tex_4(A,B)))))) # label(t84_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12961 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tex_4(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) & r2_hidden(C,D) & v3_pre_topc(D,A) -> r1_tarski(B,D))))))))))) # label(d1_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12962 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_tarski(k2_tex_4(A,B),k6_pre_topc(A,k1_struct_0(A,B))))))) # label(t50_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12963 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) & r2_hidden(C,D) & v4_pre_topc(D,A) -> r1_tarski(B,D)))))) <-> v1_tex_4(B,A)))))) # label(d2_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12964 (all A all B (-v3_struct_0(A) & l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> m1_pre_topc(k7_tex_4(A,B),A) & v1_pre_topc(k7_tex_4(A,B)))) # label(dt_k7_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12965 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v1_pre_topc(C) & m1_pre_topc(C,A) -> (u1_struct_0(C) = k2_tex_4(A,B) <-> C = k5_tex_4(A,B)))))))) # label(d17_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12966 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k1_tops_1(A,B) = k3_tex_4(A,k1_tops_1(A,B)))))) # label(t59_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12967 (all A all B (v2_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) & -v3_struct_0(A) -> -v1_tex_2(k6_pre_topc(A,B),k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(k6_pre_topc(A,B),A) & -v1_xboole_0(k6_pre_topc(A,B)))) # label(fc3_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12968 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,B) & v3_tex_4(B,A) -> k2_tex_4(A,C) = B))))))) # label(t29_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12969 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k6_pre_topc(A,k1_struct_0(A,C)) = k6_pre_topc(A,k1_struct_0(A,B)) <-> k2_tex_4(A,B) = k2_tex_4(A,C)))))))) # label(t51_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12970 (all A all B (v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) & -v3_struct_0(A) -> -v3_struct_0(k5_tex_4(A,B)) & v1_pre_topc(k5_tex_4(A,B)) & v2_pre_topc(k5_tex_4(A,B)) & v4_tex_4(k5_tex_4(A,B),A) & v3_tdlat_3(k5_tex_4(A,B)) & v2_tdlat_3(k5_tex_4(A,B)))) # label(fc15_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12971 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k3_tex_4(A,k1_struct_0(A,B)) = k2_tex_4(A,B))))) # label(t30_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12972 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v1_tsep_1(B,A) & -v4_tex_4(B,A) & -v3_struct_0(B) -> -v3_struct_0(B) & v2_pre_topc(B) & -v2_tdlat_3(B) & -v4_tex_4(B,A) & -v3_realset2(B)))))) # label(cc4_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12973 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tex_4(B,A) <-> (exists C (m1_subset_1(C,u1_struct_0(A)) & k2_tex_4(A,C) = B & r2_hidden(C,B)))))))) # label(d9_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12974 (all A all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) & -v3_struct_0(A) -> -v1_xboole_0(k3_tex_4(A,B)))) # label(fc10_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12975 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k1_xboole_0 != a_2_5_tex_4(A,B) -> r1_tarski(k2_tex_4(A,B),k1_setfam_1(a_2_5_tex_4(A,B)))))))) # label(t28_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12976 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> g1_pre_topc(u1_struct_0(k7_tex_4(A,k3_tex_4(A,B))),u1_pre_topc(k7_tex_4(A,k3_tex_4(A,B)))) = g1_pre_topc(u1_struct_0(k7_tex_4(A,B)),u1_pre_topc(k7_tex_4(A,B))))))) # label(t87_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12977 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(C,B) & v3_pre_topc(B,A) -> r1_tarski(k3_tex_4(A,C),B)))))))) # label(t40_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12978 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_tarski(k1_setfam_1(a_2_9_tex_4(A,C)),k1_setfam_1(a_2_9_tex_4(A,B))) <-> r1_tarski(k6_pre_topc(A,k1_struct_0(A,B)),k6_pre_topc(A,k1_struct_0(A,C)))))))))) # label(t53_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12979 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (v1_pre_topc(C) & m1_pre_topc(C,A) -> (k7_tex_4(A,B) = C <-> u1_struct_0(C) = k3_tex_4(A,B)))))))) # label(d19_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12980 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k6_pre_topc(A,B) = k6_pre_topc(A,k3_tex_4(A,B)))))) # label(t64_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12981 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (v2_tdlat_3(B) & m1_pre_topc(B,A) -> (all C (v1_borsuk_1(C,A) & m1_pre_topc(C,A) -> m1_pre_topc(B,C) | r1_tsep_1(A,B,C))))))) # label(t73_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12982 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & -v4_tex_4(B,A) & v1_borsuk_1(B,A) -> -v3_realset2(B) & -v4_tex_4(B,A) & -v2_tdlat_3(B) & v2_pre_topc(B) & -v3_struct_0(B)))))) # label(cc7_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12983 (all A all B (-v3_struct_0(A) & l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> m1_subset_1(k3_tex_4(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k3_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12984 (all A all B (v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_realset1(B) & -v1_xboole_0(B) & -v3_realset2(A) & -v3_struct_0(A) -> -v1_xboole_0(k6_pre_topc(A,B)) & v4_pre_topc(k6_pre_topc(A,B),A) & -v1_realset1(k6_pre_topc(A,B)))) # label(fc4_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12985 (all A all B (-v3_struct_0(A) & v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) & v2_pre_topc(A) -> v1_xboole_0(k6_pre_topc(A,B)) & v3_pre_topc(k6_pre_topc(A,B),A) & v4_pre_topc(k6_pre_topc(A,B),A) & v1_tex_2(k6_pre_topc(A,B),k1_zfmisc_1(u1_struct_0(A))) & v3_membered(k6_pre_topc(A,B)) & v5_membered(k6_pre_topc(A,B)) & v4_membered(k6_pre_topc(A,B)) & v2_membered(k6_pre_topc(A,B)) & v1_membered(k6_pre_topc(A,B)) & v3_tops_1(k6_pre_topc(A,B),A) & v2_tops_1(k6_pre_topc(A,B),A))) # label(fc2_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12986 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tex_4(B,A) -> v2_tops_1(B,A) | v3_pre_topc(B,A)))))) # label(t46_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12987 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) & r1_tarski(C,B) -> r1_tarski(k3_tex_4(A,C),B)))))))) # label(t42_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12988 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,k2_tex_4(A,B)) <-> k2_tex_4(A,C) = k2_tex_4(A,B)))))))) # label(t23_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12989 (all A all B (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & -v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -v1_xboole_0(k1_tops_1(A,B)) & -v1_tex_2(k1_tops_1(A,B),k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(k1_tops_1(A,B),A))) # label(fc5_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12990 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -(r1_xboole_0(k2_tex_4(A,C),B) & -r1_xboole_0(k2_tex_4(A,C),k3_tex_4(A,B))))))))) # label(t31_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12991 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_tarski(k1_struct_0(A,B),k5_setfam_1(u1_struct_0(A),k1_tex_4(A,B))))))) # label(t14_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12992 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,C) -> r1_tarski(k3_tex_4(A,B),k3_tex_4(A,C))))))))) # label(t33_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12993 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) -> (g1_pre_topc(u1_struct_0(k7_tex_4(A,B)),u1_pre_topc(k7_tex_4(A,B))) = g1_pre_topc(u1_struct_0(k7_tex_4(A,C)),u1_pre_topc(k7_tex_4(A,C))) <-> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k7_tex_4(A,C)))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k7_tex_4(A,B))))))))))) # label(t89_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12994 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v2_tex_4(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> v1_tex_4(C,A))))))))) # label(d5_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12995 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_pre_topc(A,k1_struct_0(A,B)) = k1_setfam_1(a_2_1_tex_4(A,B)))))) # label(t2_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12996 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k3_tex_4(A,B) = k3_tarski(a_2_6_tex_4(A,B)))))) # label(d11_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12997 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v2_tdlat_3(B) & v1_tsep_1(B,A) & -v3_struct_0(B) -> -v3_struct_0(B) & v2_tdlat_3(B) & v4_tex_4(B,A) & v3_tdlat_3(B) & v2_pre_topc(B)))))) # label(cc3_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12998 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k1_xboole_0 != a_2_4_tex_4(A,B) -> r1_tarski(k2_tex_4(A,B),k1_setfam_1(a_2_4_tex_4(A,B)))))))) # label(t27_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 12999 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (-r1_xboole_0(k2_tex_4(A,C),k3_tex_4(A,B)) -> r1_tarski(k2_tex_4(A,C),k3_tex_4(A,B))))))))) # label(t32_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13000 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> ((all C (v1_tsep_1(C,A) & m1_pre_topc(C,A) -> r1_tsep_1(A,B,C) | m1_pre_topc(B,C))) -> v2_tdlat_3(B)))))) # label(t70_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13001 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_tarski(k2_tex_4(A,B),k1_setfam_1(a_2_1_tex_4(A,B))))))) # label(t49_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13002 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> k3_tex_4(A,B) = B))))) # label(t58_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13003 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> a_2_3_tex_4(A,B) = k1_tex_4(A,B))))) # label(d6_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13004 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tex_4(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(-r1_xboole_0(B,C) & -r1_tarski(B,C) & v3_pre_topc(C,A))))))))) # label(d3_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13005 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k6_pre_topc(A,k1_struct_0(A,B)) = k1_struct_0(A,B) -> v4_tex_4(k1_tex_2(A,B),A)))))) # label(t80_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13006 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & v2_tdlat_3(B) & v1_borsuk_1(B,A) -> v2_tdlat_3(B) & v3_tdlat_3(B) & v4_tex_4(B,A) & v2_pre_topc(B) & -v3_struct_0(B)))))) # label(cc6_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13007 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,k3_tex_4(A,C)) -> r1_tarski(k3_tex_4(A,B),k3_tex_4(A,C))))))))) # label(t36_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13008 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k3_xboole_0(k6_pre_topc(A,k1_struct_0(A,B)),k1_setfam_1(a_2_9_tex_4(A,B))) = k4_tex_4(A,B))))) # label(d15_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13009 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k3_tarski(a_2_2_tex_4(A,B)) = k1_tops_1(A,B))))) # label(t4_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13010 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_pre_topc(C,A) & v1_pre_topc(C) -> (u1_struct_0(C) = B <-> C = k6_tex_4(A,B)))))))) # label(d18_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13011 (all A all B (v2_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) & l1_pre_topc(A) & -v3_struct_0(A) -> k2_tex_4(A,B) = k4_tex_4(A,B))) # label(redefinition_k4_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13012 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (v4_pre_topc(B,A) & r2_hidden(C,B) -> r1_tarski(k2_tex_4(A,C),B)))))))) # label(t25_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13013 $T # label(t5_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13014 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(B,k3_tex_4(A,B)))))) # label(t34_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13015 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v3_tex_4(C,A) & C = D & g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) -> v3_tex_4(D,B)))))))))) # label(t16_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13016 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> ((all C (v1_borsuk_1(C,A) & m1_pre_topc(C,A) -> m1_pre_topc(B,C) | r1_tsep_1(A,B,C))) -> v2_tdlat_3(B)))))) # label(t71_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13017 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tex_4(C,A) & r1_tarski(k6_pre_topc(A,k1_struct_0(A,B)),C) -> C = k6_pre_topc(A,k1_struct_0(A,B))))))))) # label(t44_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13018 (all A all B all C (v2_pre_topc(B) & m1_subset_1(C,u1_struct_0(B)) & l1_pre_topc(B) & -v3_struct_0(B) -> ((exists D (v3_pre_topc(D,B) & r2_hidden(C,D) & D = A & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))))) <-> r2_hidden(A,a_2_9_tex_4(B,C))))) # label(fraenkel_a_2_9_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13019 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> g1_pre_topc(u1_struct_0(k7_tex_4(A,k1_struct_0(A,B))),u1_pre_topc(k7_tex_4(A,k1_struct_0(A,B)))) = g1_pre_topc(u1_struct_0(k5_tex_4(A,B)),u1_pre_topc(k5_tex_4(A,B))))))) # label(t85_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13020 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v1_tex_4(B,A))))) # label(t9_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13021 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tex_4(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,B) -> r1_tarski(B,k6_pre_topc(A,k1_struct_0(A,C))))))))))) # label(d12_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13022 (all A all B (-v3_struct_0(A) & l1_pre_topc(A) & -v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> -v2_tex_2(k7_tex_4(A,B),A) & v1_pre_topc(k7_tex_4(A,B)) & -v3_struct_0(k7_tex_4(A,B)))) # label(fc21_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13023 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> m1_pre_topc(k6_tex_4(A,B),A) & v1_pre_topc(k6_tex_4(A,B)))) # label(dt_k6_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13024 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_tarski(k4_tex_4(A,C),k1_setfam_1(a_2_9_tex_4(A,B))) <-> r1_tarski(k6_pre_topc(A,k1_struct_0(A,B)),k6_pre_topc(A,k1_struct_0(A,C)))))))))) # label(t54_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13025 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> m1_pre_topc(k1_tex_2(A,B),k5_tex_4(A,B)))))) # label(t75_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13026 (all A all B all C (-v3_struct_0(B) & v2_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & l1_pre_topc(B) -> (r2_hidden(A,a_2_10_tex_4(B,C)) <-> (exists D (A = D & r1_tarski(C,D) & v3_pre_topc(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))))))) # label(fraenkel_a_2_10_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13027 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,C)),k5_subset_1(u1_struct_0(A),k3_tex_4(A,B),k3_tex_4(A,C))))))))) # label(t39_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13028 (all A all B (l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) -> m1_subset_1(k1_tex_4(A,B),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))) # label(dt_k1_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13029 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_subset_1(k2_tex_4(A,B),k2_tex_4(A,C)) <-> k6_pre_topc(A,k1_struct_0(A,C)) != k6_pre_topc(A,k1_struct_0(A,B))))))))) # label(t52_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13030 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(C,B) & v1_tex_4(B,A) -> v1_tex_4(C,A)))))))) # label(t7_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13031 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (-((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v4_pre_topc(D,A) & r1_tarski(k4_tex_4(A,B),D) & r1_xboole_0(D,k4_tex_4(A,C))))) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v4_pre_topc(D,A) & r1_xboole_0(D,k4_tex_4(A,B)) & r1_tarski(k4_tex_4(A,C),D))))) <-> r1_subset_1(k4_tex_4(A,B),k4_tex_4(A,C))))))))) # label(t56_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13032 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tex_4(B,A) & v4_pre_topc(B,A) -> v3_tex_4(B,A)))))) # label(t19_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13033 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v2_tdlat_3(B) & -v4_tex_4(B,A) & -v3_struct_0(B) -> -v1_borsuk_1(B,A) & v2_tex_2(B,A) & v2_pre_topc(B) & -v3_struct_0(B)))))) # label(cc8_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13034 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v2_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (C = u1_struct_0(B) & v1_tex_4(C,A) -> v2_tdlat_3(B))))))))) # label(t69_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13035 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k7_tex_4(A,C)))) -> m1_pre_topc(k7_tex_4(A,B),k7_tex_4(A,C))))))))) # label(t88_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13036 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k7_tex_4(A,B)))))))) # label(t83_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13037 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) -> -v3_tex_4(B,A))))) # label(t17_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13038 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v2_tex_4(B,A) -> v1_tex_4(k5_setfam_1(u1_struct_0(A),B),A) | k6_setfam_1(u1_struct_0(A),B) = k1_xboole_0))))) # label(t10_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13039 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & l1_pre_topc(A) & -v3_struct_0(A) -> v2_membered(k3_tex_4(A,B)) & v5_membered(k3_tex_4(A,B)) & v4_membered(k3_tex_4(A,B)) & v3_membered(k3_tex_4(A,B)) & v1_membered(k3_tex_4(A,B)) & v1_tex_2(k3_tex_4(A,B),k1_zfmisc_1(u1_struct_0(A))) & v2_tops_1(k3_tex_4(A,B),A) & v1_xboole_0(k3_tex_4(A,B)))) # label(fc11_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13040 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (k3_tex_4(A,C) = k3_tex_4(A,B) -> k6_pre_topc(A,C) = k6_pre_topc(A,B)))))))) # label(t65_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13041 (all A all B (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) -> m1_subset_1(k4_tex_4(A,B),k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(k4_tex_4(A,B)))) # label(dt_k4_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13042 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> v2_tex_4(k1_tex_4(A,B),A))))) # label(t12_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13043 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k4_subset_1(u1_struct_0(A),k3_tex_4(A,B),k3_tex_4(A,C)) = k3_tex_4(A,k4_subset_1(u1_struct_0(A),B,C)))))))) # label(t38_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13044 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) -> k3_tex_4(A,B) = B))))) # label(t62_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13045 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v4_tex_4(B,A) <-> v2_tdlat_3(B) & (all C (m1_pre_topc(C,A) -> (v2_tdlat_3(C) & r1_tarski(u1_struct_0(B),u1_struct_0(C)) -> u1_struct_0(C) = u1_struct_0(B))))))))) # label(d16_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13046 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & v1_borsuk_1(B,A) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> m1_pre_topc(k7_tex_4(A,C),B)))))))) # label(t91_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13047 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (k1_xboole_0 != a_2_8_tex_4(A,B) -> r1_tarski(k3_tex_4(A,B),k1_setfam_1(a_2_8_tex_4(A,B)))))))) # label(t43_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13048 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & l1_pre_topc(B) & v2_pre_topc(B) & -v3_struct_0(B) -> ((exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & v4_pre_topc(D,B) & r1_tarski(C,D) & A = D)) <-> r2_hidden(A,a_2_0_tex_4(B,C))))) # label(fraenkel_a_2_0_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13049 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_subset_1(k4_tex_4(A,B),k4_tex_4(A,C)) <-> -((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(D,A) & r1_xboole_0(D,k4_tex_4(A,C)) & r1_tarski(k4_tex_4(A,B),D)))) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(D,A) & r1_xboole_0(D,k4_tex_4(A,B)) & r1_tarski(k4_tex_4(A,C),D)))))))))))) # label(t55_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13050 (all A all B (-v3_struct_0(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) -> v1_pre_topc(k5_tex_4(A,B)) & -v3_struct_0(k5_tex_4(A,B)))) # label(fc14_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13051 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v1_tex_4(C,A) & C = D & g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) -> v1_tex_4(D,B)))))))))) # label(t6_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13052 (all A all B (m1_subset_1(B,u1_struct_0(A)) & l1_pre_topc(A) -> m1_pre_topc(k5_tex_4(A,B),A) & v1_pre_topc(k5_tex_4(A,B)))) # label(dt_k5_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13053 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_tarski(k1_struct_0(A,B),k2_tex_4(A,B)))))) # label(t20_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13054 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (g1_pre_topc(u1_struct_0(k5_tex_4(A,B)),u1_pre_topc(k5_tex_4(A,B))) = g1_pre_topc(u1_struct_0(k5_tex_4(A,C)),u1_pre_topc(k5_tex_4(A,C))) <-> m1_subset_1(C,u1_struct_0(k5_tex_4(A,B)))))))))) # label(t76_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13055 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (k3_tex_4(A,B) = k3_tex_4(A,C) <-> r1_tarski(B,k3_tex_4(A,C)) & r1_tarski(C,k3_tex_4(A,B))))))))) # label(t37_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13056 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,B) -> k2_tex_4(A,C) = B))) <-> v3_tex_4(B,A)))))) # label(d10_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13057 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_tarski(k2_tex_4(A,B),k1_setfam_1(a_2_9_tex_4(A,B))))))) # label(t48_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13058 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> m1_pre_topc(k6_tex_4(A,C),B)))))))) # label(t82_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13059 (all A all B (-v3_struct_0(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> -v3_struct_0(k6_tex_4(A,B)) & v1_pre_topc(k6_tex_4(A,B)))) # label(fc16_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13060 (all A all B (-v3_struct_0(A) & -v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & l1_pre_topc(A) -> v1_pre_topc(k6_tex_4(A,B)) & -v2_tex_2(k6_tex_4(A,B),A) & -v3_struct_0(k6_tex_4(A,B)))) # label(fc18_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13061 (all A all B (l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & v2_pre_topc(A) & -v3_struct_0(A) -> v1_tex_2(k1_tops_1(A,B),k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(k1_tops_1(A,B),A))) # label(fc6_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13062 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k3_tex_4(A,B),k1_setfam_1(a_2_10_tex_4(A,B))))))) # label(t57_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13063 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k1_struct_0(A,B) = k6_pre_topc(A,k1_struct_0(A,B)) -> v3_tex_4(k1_struct_0(A,B),A)))))) # label(t47_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13064 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tex_4(B,A) <-> v1_tex_4(B,A) & (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tex_4(C,A) & r1_tarski(B,C) -> C = B)))))))) # label(d7_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13065 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k2_tex_4(A,B) = k5_setfam_1(u1_struct_0(A),k1_tex_4(A,B)))))) # label(d8_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13066 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v2_tdlat_3(B) & -v4_tex_4(B,A) & -v3_struct_0(B) -> -v3_struct_0(B) & -v1_tsep_1(B,A) & v2_tex_2(B,A) & v2_pre_topc(B)))))) # label(cc5_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13067 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tex_4(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,B) & r2_hidden(C,B) -> k6_pre_topc(A,k1_struct_0(A,D)) = k6_pre_topc(A,k1_struct_0(A,C)))))))))))) # label(d14_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13068 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tdlat_3(B) & u1_struct_0(B) = C -> v1_tex_4(C,A)))))))) # label(t68_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13069 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(v4_pre_topc(C,A) & -r1_tarski(B,C) & -r1_xboole_0(B,C)))) <-> v1_tex_4(B,A)))))) # label(d4_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13070 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k3_tex_4(A,B),k1_setfam_1(a_2_0_tex_4(A,B))))))) # label(t60_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13071 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (k1_xboole_0 != a_2_7_tex_4(A,B) -> r1_tarski(k3_tex_4(A,B),k1_setfam_1(a_2_7_tex_4(A,B)))))))) # label(t41_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13072 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & v1_borsuk_1(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (m1_subset_1(C,u1_struct_0(B)) -> m1_pre_topc(k5_tex_4(A,C),B)))))))) # label(t78_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13073 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k1_setfam_1(a_2_0_tex_4(A,B)) = k6_pre_topc(A,B))))) # label(t1_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13074 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k3_tex_4(A,k6_pre_topc(A,B)) = k6_pre_topc(A,B))))) # label(t63_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.85 13075 (all A all B all C (l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & -v3_struct_0(B) -> ((exists D (r1_tarski(C,D) & v4_pre_topc(D,B) & A = D & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))))) <-> r2_hidden(A,a_2_8_tex_4(B,C))))) # label(fraenkel_a_2_8_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13076 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,B) & v1_tex_4(B,A) -> r1_tarski(B,k2_tex_4(A,C))))))))) # label(t21_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13077 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_tex_4(A,C) = k2_tex_4(A,B) | r1_subset_1(k2_tex_4(A,B),k2_tex_4(A,C)))))))) # label(t24_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13078 $T # label(t3_tex_4) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13079 (all A (l1_pre_topc(A) -> (v2_t_0topsp(A) <-> v3_struct_0(A) | (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -(B != C & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v4_pre_topc(D,A) & -r2_hidden(C,D) & r2_hidden(B,D)))) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(-r2_hidden(B,D) & r2_hidden(C,D) & v4_pre_topc(D,A)))))))))))) # label(d4_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13080 (all A (l1_pre_topc(A) -> (exists B m2_tsp_1(B,A)))) # label(existence_m2_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13081 $T # label(t3_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13082 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> -(r2_hidden(D,B) & D != C & (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(v4_pre_topc(E,A) & r2_hidden(D,E) & -r2_hidden(C,E)))) & (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(-r2_hidden(D,E) & r2_hidden(C,E) & v4_pre_topc(E,A)))) & r2_hidden(C,B)))))) <-> v1_tsp_1(B,A)))))) # label(d9_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13083 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tsp_1(C,A) & v1_tsp_1(B,A) -> -v3_pre_topc(B,A) & -v3_pre_topc(C,A) | v1_tsp_1(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t9_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13084 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v1_tsp_1(C,A) & C = D & g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) -> v1_tsp_1(D,B)))))))))) # label(t5_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13085 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> -(r2_hidden(D,B) & D != C & r2_hidden(C,k6_pre_topc(A,k1_struct_0(A,D))) & r2_hidden(D,k6_pre_topc(A,k1_struct_0(A,C))) & r2_hidden(C,B)))))) <-> v1_tsp_1(B,A)))))) # label(d11_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13086 (exists A (l1_pre_topc(A) & -v3_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & -v2_tdlat_3(A) & v2_t_0topsp(A) & -v3_realset2(A))) # label(rc3_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13087 (exists A (l1_pre_topc(A) & -v3_struct_0(A) & -v3_realset2(A) & v1_pre_topc(A) & -v2_t_0topsp(A) & -v1_tdlat_3(A) & v2_pre_topc(A))) # label(rc4_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13088 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> ((exists D (C = k3_xboole_0(D,u1_struct_0(B)) & v3_pre_topc(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))))) <-> v3_pre_topc(C,B)))) & r1_tarski(u1_struct_0(B),u1_struct_0(A)) <-> m1_tsp_1(B,A)))))) # label(d1_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13089 (all A (l1_pre_topc(A) -> (all B (m2_tsp_1(B,A) -> l1_pre_topc(B))))) # label(dt_m2_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13090 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & -v2_t_0topsp(A) -> (all B (m1_pre_topc(B,A) -> (v2_t_0topsp(B) & -v3_struct_0(B) -> v2_tex_2(B,A) & -v3_struct_0(B)))))) # label(cc13_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13091 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> v1_tsp_1(k1_struct_0(A,B),A))))) # label(t14_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13092 (all A (l1_pre_topc(A) -> (all B (m2_tsp_1(B,A) -> (v3_struct_0(B) | (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> -(m1_subset_1(D,u1_struct_0(B)) & (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_hidden(D,E) & -r2_hidden(C,E) & v3_pre_topc(E,A)))) & (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(E,A) & -r2_hidden(D,E) & r2_hidden(C,E)))) & C != D & m1_subset_1(C,u1_struct_0(B))))))) <-> v2_t_0topsp(B)))))) # label(d13_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13093 (all A (-v3_struct_0(A) & l1_pre_topc(A) & -v2_t_0topsp(A) & v2_pre_topc(A) -> (exists B (m1_pre_topc(B,A) & -v2_t_0topsp(B) & v1_pre_topc(B))))) # label(rc7_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13094 (all A (l1_pre_topc(A) -> (-v3_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & v2_t_0topsp(A) -> v1_tdlat_3(A) & v3_tdlat_3(A) & v4_tdlat_3(A) & v2_t_0topsp(A) & v5_tdlat_3(A) & v2_pre_topc(A) & -v3_struct_0(A)))) # label(cc8_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13095 (all A (l1_pre_topc(A) -> (-v3_struct_0(A) & -v3_realset2(A) & v2_pre_topc(A) & v2_tdlat_3(A) -> v2_pre_topc(A) & -v2_t_0topsp(A) & -v3_realset2(A) & -v3_struct_0(A)))) # label(cc5_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13096 (all A (l1_pre_topc(A) -> (all B (m1_tsp_1(B,A) -> l1_pre_topc(B))))) # label(dt_m1_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13097 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & m2_tsp_1(B,A) & v2_t_0topsp(B) -> (all C (m2_tsp_1(C,A) & v2_t_0topsp(C) & -v3_struct_0(C) -> (v1_tsep_1(B,A) | v1_tsep_1(C,A) -> v2_t_0topsp(k1_tsep_1(A,B,C))))))))) # label(t18_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13098 (all A (l1_pre_topc(A) -> (v3_realset2(A) & -v3_struct_0(A) -> v2_t_0topsp(A) & -v3_struct_0(A)))) # label(cc1_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13099 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> ((exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & C = k3_xboole_0(D,u1_struct_0(B)) & v4_pre_topc(D,A))) <-> v4_pre_topc(C,B)))) & r1_tarski(u1_struct_0(B),u1_struct_0(A)) <-> m2_tsp_1(B,A)))))) # label(d2_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13100 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -(C != B & r2_hidden(B,k6_pre_topc(A,k1_struct_0(A,C))) & r2_hidden(C,k6_pre_topc(A,k1_struct_0(A,B)))))))) <-> v2_t_0topsp(A)))) # label(d6_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13101 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -(k6_pre_topc(A,k1_struct_0(A,B)) = k6_pre_topc(A,k1_struct_0(A,C)) & C != B))))) <-> v2_t_0topsp(A)))) # label(d5_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13102 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m2_tsp_1(B,A) -> (all C (m2_tsp_1(C,A) & v2_t_0topsp(C) & -v3_struct_0(C) -> (m2_tsp_1(B,C) -> v2_t_0topsp(B)))))))) # label(t16_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13103 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tsp_1(B,A) | v1_tsp_1(C,A) -> v1_tsp_1(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t8_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13104 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(v1_tex_4(B,A) & -v1_realset1(B) & v1_tsp_1(B,A)))))) # label(t12_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13105 (all A (-v3_realset2(A) & v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (exists B (v2_t_0topsp(B) & v2_tex_2(B,A) & v1_pre_topc(B) & -v3_struct_0(B) & m1_pre_topc(B,A))))) # label(rc6_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13106 (all A (l1_pre_topc(A) -> (v2_pre_topc(A) & -v1_tdlat_3(A) & v3_tdlat_3(A) & -v3_struct_0(A) -> -v3_realset2(A) & v2_pre_topc(A) & -v1_tdlat_3(A) & -v2_t_0topsp(A) & -v3_struct_0(A)))) # label(cc9_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13107 (exists A (-v3_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & -v2_t_0topsp(A) & -v3_realset2(A) & l1_pre_topc(A))) # label(rc2_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13108 (all A (l1_pre_topc(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -(C != B & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(D,A) & -r2_hidden(C,D) & r2_hidden(B,D)))) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(D,A) & r2_hidden(C,D) & -r2_hidden(B,D))))))))) | v3_struct_0(A) <-> v2_t_0topsp(A)))) # label(d3_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13109 (all A (l1_pre_topc(A) -> (all B (m2_tsp_1(B,A) <-> m1_pre_topc(B,A))))) # label(redefinition_m2_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13110 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (exists B (m1_pre_topc(B,A) & -v3_struct_0(B) & v1_pre_topc(B) & v2_t_0topsp(B))))) # label(rc5_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13111 (all A (l1_pre_topc(A) -> (v2_pre_topc(A) & -v1_tdlat_3(A) & v2_t_0topsp(A) & -v3_struct_0(A) -> -v3_realset2(A) & -v1_tdlat_3(A) & -v3_tdlat_3(A) & -v2_tdlat_3(A) & v2_pre_topc(A) & -v3_struct_0(A)))) # label(cc10_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13112 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (v2_t_0topsp(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -(C != B & r1_tarski(k6_pre_topc(A,k1_struct_0(A,C)),k6_pre_topc(A,k1_struct_0(A,B))) & r2_hidden(B,k6_pre_topc(A,k1_struct_0(A,C))))))))))) # label(d7_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13113 (all A (l1_pre_topc(A) -> (all B (m2_tsp_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> -(v4_pre_topc(D,B) & D = k3_xboole_0(C,u1_struct_0(B))))) & v4_pre_topc(C,A)))))))) # label(t4_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13114 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) <-> m1_tsp_1(B,A))))) # label(redefinition_m1_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13115 (exists A (v2_t_0topsp(A) & v2_pre_topc(A) & v1_pre_topc(A) & -v3_struct_0(A) & l1_pre_topc(A))) # label(rc1_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13116 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tsp_1(C,A) & v1_tsp_1(B,A) -> -v4_pre_topc(C,A) & -v4_pre_topc(B,A) | v1_tsp_1(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t10_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13117 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) -> v1_tsp_1(B,A))))) # label(t13_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13118 (all A (l1_pre_topc(A) -> (all B (m2_tsp_1(B,A) -> (v3_struct_0(B) | (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> -(m1_subset_1(D,u1_struct_0(B)) & (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(v4_pre_topc(E,A) & r2_hidden(C,E) & -r2_hidden(D,E)))) & (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(v4_pre_topc(E,A) & -r2_hidden(C,E) & r2_hidden(D,E)))) & D != C & m1_subset_1(C,u1_struct_0(B))))))) <-> v2_t_0topsp(B)))))) # label(d14_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13119 (all A (l1_pre_topc(A) -> (-v3_struct_0(A) & v2_t_0topsp(A) & v2_pre_topc(A) & -v3_realset2(A) -> v2_pre_topc(A) & -v2_tdlat_3(A) & -v3_realset2(A) & -v3_struct_0(A)))) # label(cc7_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13120 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m2_tsp_1(B,A) & v2_t_0topsp(B) & -v3_struct_0(B) -> (all C (m2_tsp_1(C,A) & -v3_struct_0(C) -> (-r1_tsep_1(A,B,C) -> v2_t_0topsp(k2_tsep_1(A,B,C))))))))) # label(t17_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13121 (all A (-v3_struct_0(A) & v2_pre_topc(A) & -v2_t_0topsp(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & -v2_tex_2(B,A) -> -v3_struct_0(B) & -v3_realset2(B) & -v2_t_0topsp(B)))))) # label(cc12_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13122 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -((all C (v2_t_0topsp(C) & m2_tsp_1(C,A) & v1_pre_topc(C) & -v3_struct_0(C) -> u1_struct_0(C) != B)) & v1_tsp_1(B,A)))))) # label(t20_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13123 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tsp_1(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> -(k6_pre_topc(A,k1_struct_0(A,D)) = k6_pre_topc(A,k1_struct_0(A,C)) & C != D & r2_hidden(D,B) & r2_hidden(C,B))))))))))) # label(d10_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13124 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tsp_1(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> -(r2_hidden(D,B) & C != D & (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(E,A) & r2_hidden(D,E) & -r2_hidden(C,E)))) & (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(-r2_hidden(D,E) & r2_hidden(C,E) & v3_pre_topc(E,A)))) & r2_hidden(C,B))))))))))) # label(d8_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13125 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tex_2(B,A) -> v1_tsp_1(B,A)))))) # label(t11_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13126 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tsp_1(B,A) & r1_tarski(C,B) -> v1_tsp_1(C,A)))))))) # label(t7_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13127 (all A (l1_pre_topc(A) -> (v2_pre_topc(A) & v1_tdlat_3(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v2_pre_topc(A) & v2_t_0topsp(A)))) # label(cc3_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13128 $T # label(t1_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13129 (all A (l1_pre_topc(A) -> (-v2_t_0topsp(A) & -v3_struct_0(A) -> -v3_struct_0(A) & -v3_realset2(A)))) # label(cc2_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13130 (all A (-v3_struct_0(A) & v2_pre_topc(A) & -v2_t_0topsp(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -((all C (v1_pre_topc(C) & m2_tsp_1(C,A) & -v2_t_0topsp(C) -> u1_struct_0(C) != B)) & -v1_tsp_1(B,A)))))) # label(t21_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13131 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (v2_t_0topsp(B) & m2_tsp_1(B,A) & -v3_struct_0(B) -> (all C (m2_tsp_1(C,A) & v2_t_0topsp(C) & -v3_struct_0(C) -> (v1_borsuk_1(B,A) | v1_borsuk_1(C,A) -> v2_t_0topsp(k1_tsep_1(A,B,C))))))))) # label(t19_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13132 (all A all B (l1_pre_topc(A) & m1_pre_topc(B,A) -> (v2_t_0topsp(B) <-> v3_tsp_1(B,A)))) # label(redefinition_v3_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13133 (all A (l1_pre_topc(A) -> (-v3_struct_0(A) & -v2_t_0topsp(A) & v2_pre_topc(A) -> -v3_realset2(A) & -v1_tdlat_3(A) & v2_pre_topc(A) & -v3_struct_0(A)))) # label(cc4_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13134 (all A (l1_pre_topc(A) -> (all B (m1_tsp_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(C,A) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> -(v3_pre_topc(D,B) & k3_xboole_0(C,u1_struct_0(B)) = D)))))))))) # label(t2_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13135 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m2_tsp_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(B) = C -> (v1_tsp_1(C,A) <-> v2_t_0topsp(B))))))))) # label(t15_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13136 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(A) = B -> (v2_t_0topsp(A) <-> v1_tsp_1(B,A))))))) # label(t6_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13137 (all A (v2_pre_topc(A) & v2_t_0topsp(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) -> v2_t_0topsp(B) & -v3_struct_0(B)))))) # label(cc11_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13138 (all A (l1_pre_topc(A) -> (exists B m1_tsp_1(B,A)))) # label(existence_m1_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13139 (all A all B (l1_pre_topc(A) & m1_pre_topc(B,A) -> (v2_tsp_1(B,A) <-> v2_t_0topsp(B)))) # label(redefinition_v2_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13140 (all A (l1_pre_topc(A) -> (-v3_struct_0(A) & v2_tdlat_3(A) & v2_t_0topsp(A) & v2_pre_topc(A) -> -v3_struct_0(A) & v1_tdlat_3(A) & v3_tdlat_3(A) & v4_tdlat_3(A) & v2_t_0topsp(A) & v5_tdlat_3(A) & v2_tdlat_3(A) & v2_pre_topc(A) & v3_realset2(A)))) # label(cc6_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13141 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> -(r2_hidden(D,B) & D != C & r2_hidden(C,k6_pre_topc(A,k1_struct_0(A,D))) & r1_tarski(k6_pre_topc(A,k1_struct_0(A,D)),k6_pre_topc(A,k1_struct_0(A,C))) & r2_hidden(C,B)))))) <-> v1_tsp_1(B,A)))))) # label(d12_tsp_1) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13142 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v2_tsp_2(B,A) & m2_tsp_1(B,A) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B) & v1_funct_1(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> ((all E (m1_subset_1(E,u1_struct_0(A)) -> k1_struct_0(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)) = k5_subset_1(u1_struct_0(A),D,k4_tex_4(A,E)))) & D = u1_struct_0(B) -> v3_borsuk_1(C,A,B)))))))))) # label(t20_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13143 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v2_tsp_2(B,A) -> v2_pre_topc(B) & v1_tex_3(B,A)))))) # label(cc3_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13144 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v2_tsp_2(B,A) & v2_tex_2(B,A) -> v2_pre_topc(B) & -v1_tsep_1(B,A)))))) # label(cc7_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13145 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m2_tsp_1(B,A) & v2_tsp_2(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(C,A) -> v4_pre_topc(k4_pre_topc(A,B,k4_tsp_2(A,B),C),B)))))))) # label(t35_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13146 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tsp_2(B,A) <-> v1_tsp_1(B,A) & k3_tex_4(A,B) = u1_struct_0(A)))))) # label(d5_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13147 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tsp_2(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (r2_hidden(D,B) & k5_subset_1(u1_struct_0(A),B,k4_tex_4(A,C)) = k1_struct_0(A,D) & m1_subset_1(D,u1_struct_0(A))))))))))) # label(d6_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13148 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m2_tsp_1(B,A) & v2_tsp_2(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(D,A) | v3_pre_topc(C,A) -> k4_pre_topc(A,B,k4_tsp_2(A,B),k5_subset_1(u1_struct_0(A),C,D)) = k5_subset_1(u1_struct_0(B),k4_pre_topc(A,B,k4_tsp_2(A,B),C),k4_pre_topc(A,B,k4_tsp_2(A,B),D))))))))))) # label(t32_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13149 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,C) & v1_tsp_1(C,A) -> B = C))) & v1_tsp_1(B,A) <-> v1_tsp_2(B,A)))))) # label(d4_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13150 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(v1_tsp_2(B,A) & (all C (v1_pre_topc(C) & m2_tsp_1(C,A) & -v3_struct_0(C) -> -(v2_tsp_2(C,A) & u1_struct_0(C) = B)))))))) # label(t12_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13151 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m2_tsp_1(B,A) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (C = u1_struct_0(B) -> v1_tsp_2(C,A)))) <-> v2_tsp_2(B,A)))))) # label(d7_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13152 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & v2_tsp_2(B,A) & m2_tsp_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k4_pre_topc(A,B,k4_tsp_2(A,B),C) = k4_pre_topc(A,B,k4_tsp_2(A,B),k3_tex_4(A,C)))))))) # label(t30_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13153 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tsp_2(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(C,A) -> k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,C)) = C)))))))) # label(t5_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13154 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v2_tsp_2(B,A) & m2_tsp_1(B,A) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B) & v1_funct_1(C) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> r2_hidden(k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k4_tex_4(A,D)))) <-> k3_tsp_2(A,B) = C))))))) # label(d11_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13155 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (v2_tsp_2(B,A) & m2_tsp_1(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> k4_subset_1(u1_struct_0(B),k4_pre_topc(A,B,k4_tsp_2(A,B),C),k4_pre_topc(A,B,k4_tsp_2(A,B),D)) = k4_pre_topc(A,B,k4_tsp_2(A,B),k4_subset_1(u1_struct_0(A),C,D)))))))))) # label(t31_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13156 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & v2_tsp_2(B,A) & m2_tsp_1(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k4_pre_topc(A,B,k3_tsp_2(A,B),k1_struct_0(A,C)) = k4_pre_topc(A,B,k3_tsp_2(A,B),k4_tex_4(A,C)))))))) # label(t28_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13157 (all A all B (-v3_struct_0(A) & -v3_struct_0(B) & v2_tsp_2(B,A) & m1_pre_topc(B,A) & l1_pre_topc(A) & v2_pre_topc(A) -> v1_funct_1(k4_tsp_2(A,B)) & v5_pre_topc(k4_tsp_2(A,B),A,B) & m2_relset_1(k4_tsp_2(A,B),u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(k4_tsp_2(A,B),u1_struct_0(A),u1_struct_0(B)))) # label(dt_k4_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13158 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v2_t_0topsp(B) & -v3_struct_0(B) -> -v2_tsp_2(B,A) & -v3_struct_0(B)))))) # label(cc2_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13159 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & v2_tsp_2(B,A) -> v2_t_0topsp(B) & -v3_struct_0(B)))))) # label(cc1_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13160 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m2_tsp_1(B,A) & v2_tsp_2(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (D = C -> k6_pre_topc(A,k1_struct_0(A,C)) = k5_pre_topc(A,B,k1_tsp_2(A,B),k6_pre_topc(B,k1_struct_0(B,D)))))))))))) # label(t24_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13161 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m2_tsp_1(B,A) & v2_tsp_2(B,A) & -v3_struct_0(B) -> r1_borsuk_1(A,B))))) # label(t23_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13162 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m2_tsp_1(B,A) & v2_tsp_2(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(D,A) | v4_pre_topc(C,A) -> k4_pre_topc(A,B,k4_tsp_2(A,B),k5_subset_1(u1_struct_0(A),C,D)) = k5_subset_1(u1_struct_0(B),k4_pre_topc(A,B,k4_tsp_2(A,B),C),k4_pre_topc(A,B,k4_tsp_2(A,B),D))))))))))) # label(t33_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13163 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tsp_2(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k1_tops_1(A,C) = k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,k1_tops_1(A,C)))))))))) # label(t8_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13164 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v1_tex_3(B,A) -> v2_pre_topc(B) & -v2_tsp_2(B,A)))))) # label(cc4_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13165 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(v1_tsp_2(B,A) & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & (v3_pre_topc(B,A) | v4_pre_topc(B,A))))))) # label(t3_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13166 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & v2_tsp_2(B,A) & m2_tsp_1(B,A) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (C = k1_tsp_2(A,B) <-> v3_borsuk_1(C,A,B)))))))) # label(d9_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13167 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tsp_2(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(C,A) -> C = k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,C)))))))))) # label(t6_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13168 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & v2_tsp_2(B,A) & m2_tsp_1(B,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> r2_hidden(k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k4_tex_4(A,D)))) -> v3_borsuk_1(C,A,B)))))))) # label(t21_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13169 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (exists B (-v3_struct_0(B) & v1_pre_topc(B) & v1_tex_3(B,A) & v2_t_0topsp(B) & v2_tsp_2(B,A) & v2_pre_topc(B) & m1_pre_topc(B,A))))) # label(rc1_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13170 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m2_tsp_1(B,A) & v2_tsp_2(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (C = k3_tex_4(A,C) & (exists D (D = k3_xboole_0(C,u1_struct_0(B)) & v4_pre_topc(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))))) <-> v4_pre_topc(C,A)))))))) # label(t17_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13171 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m2_tsp_1(B,A) & v2_tsp_2(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (D = C -> k3_tex_4(A,C) = k5_pre_topc(A,B,k1_tsp_2(A,B),D)))))))))) # label(t26_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13172 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tsp_1(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,B) -> k5_subset_1(u1_struct_0(A),B,k4_tex_4(A,C)) = k1_struct_0(A,C))))))))) # label(d2_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13173 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,B) & r2_hidden(C,B) -> C = D | r1_subset_1(k4_tex_4(A,C),k4_tex_4(A,D))))))) <-> v1_tsp_1(B,A)))))) # label(d1_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13174 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tsp_2(B,A) -> v1_tops_1(B,A)))))) # label(t2_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13175 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (v2_tsp_2(B,A) & m2_tsp_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (D = C -> (v4_pre_topc(D,B) <-> v4_pre_topc(k3_tex_4(A,C),A) & k3_xboole_0(k3_tex_4(A,C),u1_struct_0(B)) = D)))))))))) # label(t16_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13176 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m2_tsp_1(B,A) & v2_tsp_2(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k5_pre_topc(A,B,k4_tsp_2(A,B),k4_pre_topc(A,B,k4_tsp_2(A,B),C)) = k3_tex_4(A,C))))))) # label(t29_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13177 (all A all B (-v3_struct_0(A) & l1_pre_topc(A) & m1_pre_topc(B,A) & v2_tsp_2(B,A) & -v3_struct_0(B) & v2_pre_topc(A) -> k4_tsp_2(A,B) = k1_tsp_2(A,B))) # label(redefinition_k4_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13178 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & v2_tsp_2(B,A) & m2_tsp_1(B,A) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (D = u1_struct_0(B) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> k4_pre_topc(A,B,C,E) = k5_subset_1(u1_struct_0(A),D,k3_tex_4(A,E))))))) <-> C = k4_tsp_2(A,B)))))))) # label(d12_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13179 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v1_tsep_1(B,A) & v2_tex_2(B,A) -> v2_pre_topc(B) & -v2_tsp_2(B,A)))))) # label(cc6_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13180 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_tsp_2(B,A) & m2_tsp_1(B,A) & -v3_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> ((all E (m1_subset_1(E,u1_struct_0(A)) -> k5_subset_1(u1_struct_0(A),D,k4_tex_4(A,E)) = k1_struct_0(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)))) & u1_struct_0(B) = D -> v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))))))))))) # label(t18_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13181 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_tarski(B,C) & v1_tsp_2(C,A)))) & v1_tsp_1(B,A)))))) # label(t9_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13182 (all A all B (-v3_struct_0(A) & m1_pre_topc(B,A) & v2_tsp_2(B,A) & -v3_struct_0(B) & l1_pre_topc(A) & v2_pre_topc(A) -> v1_funct_1(k3_tsp_2(A,B)) & m2_relset_1(k3_tsp_2(A,B),u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A,B),A,B) & v1_funct_2(k3_tsp_2(A,B),u1_struct_0(A),u1_struct_0(B)))) # label(dt_k3_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13183 (all A all B (-v3_struct_0(A) & l1_pre_topc(A) & -v3_struct_0(B) & v2_tsp_2(B,A) & m1_pre_topc(B,A) & v2_pre_topc(A) -> v1_funct_2(k1_tsp_2(A,B),u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(k1_tsp_2(A,B),u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(k1_tsp_2(A,B),A,B) & v1_funct_1(k1_tsp_2(A,B)))) # label(dt_k1_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13184 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_tsp_2(B,A) & m2_tsp_1(B,A) & -v3_struct_0(B) -> (exists C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v3_borsuk_1(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B) & v1_funct_1(C))))))) # label(t22_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13185 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tsp_2(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k6_pre_topc(A,C) = k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,C)))))))))) # label(t7_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13186 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & v2_tsp_2(B,A) & m2_tsp_1(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (D = C -> k4_tex_4(A,C) = k5_pre_topc(A,B,k1_tsp_2(A,B),k1_struct_0(B,D))))))))))) # label(t25_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13187 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v1_borsuk_1(B,A) & v2_tex_2(B,A) -> -v2_tsp_2(B,A) & v2_pre_topc(B)))))) # label(cc9_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13188 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m2_tsp_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(B) = C -> (v1_tsp_2(C,A) <-> v2_tsp_2(B,A))))))))) # label(t11_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13189 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) & v1_tsp_2(C,A) & D = C -> v1_tsp_2(D,B)))))))))) # label(t1_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13190 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v1_tsep_1(B,A) & v2_tsp_2(B,A) -> v2_pre_topc(B) & -v2_tex_2(B,A)))))) # label(cc5_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13191 (all A all B (l1_pre_topc(A) & m1_pre_topc(B,A) & v2_tsp_2(B,A) & -v3_struct_0(B) & v2_pre_topc(A) & -v3_struct_0(A) -> m2_relset_1(k2_tsp_2(A,B),u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(k2_tsp_2(A,B),A,B) & v1_funct_2(k2_tsp_2(A,B),u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(k2_tsp_2(A,B)))) # label(dt_k2_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13192 (all A all B (-v3_struct_0(B) & v2_tsp_2(B,A) & m1_pre_topc(B,A) & l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> k1_tsp_2(A,B) = k3_tsp_2(A,B))) # label(redefinition_k3_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13193 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v1_borsuk_1(B,A) & v2_tsp_2(B,A) -> -v2_tex_2(B,A) & v2_pre_topc(B)))))) # label(cc8_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13194 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & v2_tsp_2(B,A) & m2_tsp_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(C,A) -> v3_pre_topc(k4_pre_topc(A,B,k4_tsp_2(A,B),C),B)))))))) # label(t34_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13195 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v2_tsp_2(B,A) & v2_tex_2(B,A) -> v2_pre_topc(B) & -v1_borsuk_1(B,A)))))) # label(cc10_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13196 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_tsp_2(B,A))))) # label(t10_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13197 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (v2_tsp_2(B,A) & m2_tsp_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (D = C -> (k3_xboole_0(k3_tex_4(A,C),u1_struct_0(B)) = D & v3_pre_topc(k3_tex_4(A,C),A) <-> v3_pre_topc(D,B))))))))))) # label(t14_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13198 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m2_tsp_1(B,A) & v2_tsp_2(B,A) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (D = u1_struct_0(B) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> k1_struct_0(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)) = k5_subset_1(u1_struct_0(A),D,k4_tex_4(A,E))))))) <-> C = k2_tsp_2(A,B)))))))) # label(d10_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13199 (all A all B (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(B) & v2_tsp_2(B,A) & m1_pre_topc(B,A) & -v3_struct_0(A) -> k2_tsp_2(A,B) = k1_tsp_2(A,B))) # label(redefinition_k2_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13200 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (v2_t_0topsp(B) & m2_tsp_1(B,A) & -v3_struct_0(B) -> (exists C (v1_pre_topc(C) & m2_tsp_1(C,A) & m2_tsp_1(B,C) & v2_tsp_2(C,A))))))) # label(t13_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13201 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & v2_tsp_2(B,A) & m2_tsp_1(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k4_tex_4(A,C) = k5_pre_topc(A,B,k3_tsp_2(A,B),k1_struct_0(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),k3_tsp_2(A,B),C))))))))) # label(t27_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13202 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_tsp_2(B,A) & m2_tsp_1(B,A) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> r2_hidden(k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k4_tex_4(A,D)))) -> v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B)))))))) # label(t19_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13203 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> -(r2_hidden(C,B) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(k5_subset_1(u1_struct_0(A),B,D) = k1_struct_0(A,C) & v3_tex_4(D,A))))))) <-> v1_tsp_1(B,A)))))) # label(d3_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13204 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_tsp_2(B,A) & m2_tsp_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & k3_xboole_0(C,u1_struct_0(B)) = D & v3_pre_topc(D,B))) & C = k3_tex_4(A,C) <-> v3_pre_topc(C,A)))))))) # label(t15_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13205 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -v1_tsp_2(B,A))))) # label(t4_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.86 13206 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m2_tsp_1(B,A) & -v3_struct_0(B) -> ((all C (m2_tsp_1(C,A) & v2_t_0topsp(C) & -v3_struct_0(C) -> (m2_tsp_1(B,C) -> g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))))) & v2_t_0topsp(B) <-> v2_tsp_2(B,A)))))) # label(d8_tsp_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13207 (all A all B (m2_lattice4(B,A) & -v1_xboole_0(B) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> v4_lattices(k23_filter_2(A,B)) & v8_lattices(k23_filter_2(A,B)) & v9_lattices(k23_filter_2(A,B)) & v10_lattices(k23_filter_2(A,B)) & v7_lattices(k23_filter_2(A,B)) & v6_lattices(k23_filter_2(A,B)) & v5_lattices(k23_filter_2(A,B)) & v3_lattices(k23_filter_2(A,B)) & -v3_struct_0(k23_filter_2(A,B)))) # label(fc5_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13208 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m2_filter_2(B,A) -> r1_filter_2(u1_struct_0(A),k19_filter_2(A,B),B))))) # label(t38_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13209 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v14_lattices(A) -> (all B (v14_lattices(B) & l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> (g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) -> k6_lattices(A) = k6_lattices(B)))))) # label(t10_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13210 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = k23_filter_2(A,k1_filter_2(A)) & k23_filter_2(A,k17_filter_2(A)) = g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)))) # label(t72_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13211 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (v10_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A)) & -v3_struct_0(k1_lattice2(A)) <-> -v3_struct_0(A) & l3_lattices(A) & v17_lattices(A) & v10_lattices(A)))) # label(t54_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13212 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(k1_lattice2(A))) -> B = k6_filter_2(A,B))))) # label(d5_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13213 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_filter_2(B,A) -> k23_filter_2(A,B) = k8_filter_0(A,B))))) # label(t70_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13214 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(D) -> -((all E (m1_subset_1(E,u1_struct_0(A)) -> (all F (m1_subset_1(F,u1_struct_0(A)) -> -(k3_lattices(A,E,F) = B & r2_hidden(F,D) & r2_hidden(E,C)))))) & r2_hidden(B,k20_filter_2(A,C,D))))))))) # label(t47_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13215 $T # label(d2_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13216 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (v10_lattices(B) & l3_lattices(B) & -v3_struct_0(B) -> (all C (m1_filter_2(C,A) -> (all D (m1_filter_2(D,B) -> (C = D & g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) -> k8_filter_0(B,D) = k8_filter_0(A,C)))))))))) # label(t68_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13217 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) <-> m1_filter_2(B,A))))) # label(redefinition_m1_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13218 (all A all B (-v3_struct_0(A) & l3_lattices(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & v10_lattices(A) -> m2_filter_2(k19_filter_2(A,B),A))) # label(dt_k19_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13219 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (exists B m2_filter_2(B,A)))) # label(existence_m2_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13220 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m2_filter_2(B,A) -> (r2_filter_2(A,B) <-> (all C (m2_filter_2(C,A) -> (r1_tarski(B,C) -> C = u1_struct_0(A) | r1_filter_2(u1_struct_0(A),B,C)))) & u1_struct_0(A) != B))))) # label(d10_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13221 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v14_lattices(A) -> r1_filter_2(u1_struct_0(A),k2_filter_2(A,B),k22_filter_2(A,B,k6_lattices(A)))))))) # label(t66_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13222 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) -> (all D (-v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) & -v1_xboole_0(E) -> k5_filter_0(k1_lattice2(A),k7_filter_2(A,B),k7_filter_2(A,C)) = k20_filter_2(A,B,C) & k5_filter_0(A,k8_filter_2(A,D),k8_filter_2(A,E)) = k20_filter_2(k1_lattice2(A),D,E) & k5_filter_0(k1_lattice2(A),D,E) = k20_filter_2(A,k8_filter_2(A,D),k8_filter_2(A,E)) & k20_filter_2(k1_lattice2(A),k7_filter_2(A,B),k7_filter_2(A,C)) = k5_filter_0(A,B,C))))))))))) # label(t45_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13223 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m2_filter_2(B,A) -> -v1_xboole_0(B) & m2_lattice4(B,A))))) # label(dt_m2_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13224 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> (C = B <-> r1_filter_2(A,B,C)))) # label(redefinition_r1_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13225 (all A all B all C all D (-v3_struct_0(B) & -v1_xboole_0(C) & -v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & l3_lattices(B) & v10_lattices(B) -> ((exists E exists F (m1_subset_1(F,u1_struct_0(B)) & r2_hidden(F,D) & r2_hidden(E,C) & A = k3_lattices(B,E,F) & m1_subset_1(E,u1_struct_0(B)))) <-> r2_hidden(A,a_3_0_filter_2(B,C,D))))) # label(fraenkel_a_3_0_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13226 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r3_lattices(A,B,C) -> v15_lattices(k23_filter_2(A,k22_filter_2(A,B,C))) & k5_lattices(k23_filter_2(A,k22_filter_2(A,B,C))) = B & C = k6_lattices(k23_filter_2(A,k22_filter_2(A,B,C)))))))))) # label(t84_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13227 (all A (-v3_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) -> (all B (m2_filter_2(B,A) -> (r2_filter_2(A,B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (-r2_hidden(k7_lattices(A,C),B) <-> r2_hidden(C,B))))))))) # label(t59_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13228 (all A all B (m1_filter_0(B,k1_lattice2(A)) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> m2_filter_2(k14_filter_2(A,B),A))) # label(dt_k14_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13229 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> -(u1_struct_0(A) = k18_filter_2(A,B) & -(all C (m1_subset_1(C,u1_struct_0(A)) -> B = k3_lattices(A,B,C)))))))) # label(t35_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13230 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(B,k18_filter_2(A,C)) <-> r3_lattices(A,B,C)))))))) # label(t29_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13231 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) -> k3_filter_2(k1_lattice2(A),k7_filter_2(A,B)) = k19_filter_2(A,B) & k3_filter_2(k1_lattice2(A),C) = k19_filter_2(A,k8_filter_2(A,C)) & k19_filter_2(k1_lattice2(A),C) = k3_filter_2(A,k8_filter_2(A,C)) & k3_filter_2(A,B) = k19_filter_2(k1_lattice2(A),k7_filter_2(A,B)))))))) # label(t37_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13232 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_lattices(k23_filter_2(A,k18_filter_2(A,B))) = B)))) # label(t81_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13233 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,B) & r2_hidden(C,B) <-> r2_hidden(k3_lattices(A,C,D),B)))))) -> m2_lattice4(B,A)))))) # label(t14_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13234 (all A all B all C (-v3_struct_0(A) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A) & m2_filter_2(C,A) & m2_filter_2(B,A) -> k20_filter_2(A,B,C) = k21_filter_2(A,B,C))) # label(redefinition_k21_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13235 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> m1_subset_1(k8_filter_2(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k8_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13236 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) -> (r1_filter_2(u1_struct_0(A),C,k6_domain_1(u1_struct_0(A),B)) -> r1_filter_2(u1_struct_0(A),k19_filter_2(A,C),k18_filter_2(A,B))))))))) # label(t41_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13237 (all A all B (-v3_struct_0(A) & l3_lattices(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v10_lattices(A) -> m1_subset_1(k7_filter_2(A,B),k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) # label(dt_k7_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13238 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (v14_lattices(A) -> (all B (m2_filter_2(B,A) -> -((all C (m2_filter_2(C,A) -> -(r1_tarski(B,C) & r2_filter_2(A,C)))) & B != u1_struct_0(A))))))) # label(t34_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13239 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k2_filter_2(A,B) = k18_filter_2(k1_lattice2(A),k5_filter_2(A,B)) & k2_filter_2(k1_lattice2(A),k5_filter_2(A,B)) = k18_filter_2(A,B))))) # label(t30_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13240 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> m2_filter_2(k17_filter_2(A),A))) # label(dt_k17_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13241 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (v10_lattices(B) & l3_lattices(B) & -v3_struct_0(B) -> (g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) -> (all C (m2_filter_2(C,A) -> m2_filter_2(C,B)))))))) # label(t17_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13242 (all A all B all C (m1_subset_1(C,u1_struct_0(B)) & l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> ((exists D (r3_lattices(B,D,C) & D = A & m1_subset_1(D,u1_struct_0(B)))) <-> r2_hidden(A,a_2_0_filter_2(B,C))))) # label(fraenkel_a_2_0_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13243 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (exists B m1_filter_2(B,A)))) # label(existence_m1_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13244 (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)) -> (r1_filter_2(A,B,C) <-> (all D (m1_subset_1(D,A) -> (r2_hidden(D,B) <-> r2_hidden(D,C))))))))))) # label(d1_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13245 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> u1_struct_0(A) = k17_filter_2(A))) # label(d8_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13246 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) -> B = k8_filter_2(A,B))))) # label(d7_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13247 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (-v1_xboole_0(B) & m2_lattice4(B,A) -> k1_realset1(u2_lattices(A),B) = u2_lattices(k23_filter_2(A,B)) & k1_realset1(u1_lattices(A),B) = u1_lattices(k23_filter_2(A,B)) & B = u1_struct_0(k23_filter_2(A,B)))))) # label(t73_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13248 (all A (v13_lattices(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (v10_lattices(B) & l3_lattices(B) & v13_lattices(B) & -v3_struct_0(B) -> (g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) = g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) -> k5_lattices(A) = k5_lattices(B)))))) # label(t9_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13249 (all A (l3_lattices(A) -> (all B (l3_lattices(B) -> (g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) = g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) -> k1_lattice2(B) = k1_lattice2(A)))))) # label(t6_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13250 (all A all B all C (v10_lattices(A) & l3_lattices(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) & -v3_struct_0(A) -> m1_subset_1(k20_filter_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k20_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13251 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (-v1_xboole_0(B) & m2_lattice4(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(k23_filter_2(A,B))) -> (all F (m1_subset_1(F,u1_struct_0(k23_filter_2(A,B))) -> (F = D & E = C -> k3_lattices(k23_filter_2(A,B),E,F) = k3_lattices(A,C,D) & k4_lattices(k23_filter_2(A,B),E,F) = k4_lattices(A,C,D)))))))))))))) # label(t74_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13252 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m2_lattice4(B,A) & -v1_xboole_0(B) -> k24_filter_2(k1_lattice2(A),k23_filter_2(k1_lattice2(A),k10_filter_2(A,B))) = k23_filter_2(A,B))))) # label(t71_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13253 (all A all B (v10_lattices(A) & l3_lattices(A) & m2_lattice4(B,k1_lattice2(A)) & -v3_struct_0(A) -> m2_lattice4(k11_filter_2(A,B),A))) # label(dt_k11_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13254 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k18_filter_2(A,B) = a_2_0_filter_2(A,B))))) # label(d9_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13255 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m2_filter_2(B,A) -> (v2_filter_0(k15_filter_2(A,B),k1_lattice2(A)) <-> v1_filter_2(B,A)))))) # label(t44_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13256 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) & -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,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) -> (all E (v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(B,B),B) & m2_relset_1(E,k2_zfmisc_1(B,B),B) -> (all F (v1_funct_1(F) & v1_funct_2(F,k2_zfmisc_1(B,B),B) & m2_relset_1(F,k2_zfmisc_1(B,B),B) -> (F = k1_realset1(D,B) & r1_lattice2(A,C,D) & k1_realset1(C,B) = E -> r1_lattice2(B,E,F)))))))))))))) # label(t5_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13257 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r3_lattices(A,B,C) -> r2_hidden(C,k22_filter_2(A,B,C)) & r2_hidden(B,k22_filter_2(A,B,C))))))))) # label(t64_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13258 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) -> (all E (m2_relset_1(E,k2_zfmisc_1(B,B),B) & v1_funct_2(E,k2_zfmisc_1(B,B),B) & v1_funct_1(E) -> (all F (v1_funct_1(F) & v1_funct_2(F,k2_zfmisc_1(B,B),B) & m2_relset_1(F,k2_zfmisc_1(B,B),B) -> (k1_realset1(C,B) = E & F = k1_realset1(D,B) -> (r5_binop_1(A,C,D) -> r5_binop_1(B,E,F)) & (r4_binop_1(A,C,D) -> r4_binop_1(B,E,F))))))))))))))) # label(t3_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13259 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (m2_filter_2(k6_domain_1(u1_struct_0(A),B),A) -> v13_lattices(A)))))) # label(t27_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13260 (all A all B (v10_lattices(A) & l3_lattices(A) & -v1_xboole_0(B) & m2_lattice4(B,A) & -v3_struct_0(A) -> m2_lattice4(k10_filter_2(A,B),k1_lattice2(A)) & -v1_xboole_0(k10_filter_2(A,B)))) # label(dt_k10_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13261 (all A all B (-v3_struct_0(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l3_lattices(A) & v10_lattices(A) -> m1_filter_2(k3_filter_2(A,B),A))) # label(dt_k3_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13262 (all A all B (l3_lattices(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & v10_lattices(A) & -v3_struct_0(A) -> k3_filter_2(A,B) = k3_filter_0(A,B))) # label(redefinition_k3_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13263 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (v13_lattices(A) -> m2_filter_2(k6_domain_1(u1_struct_0(A),k5_lattices(A)),A)))) # label(t26_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13264 (all A all B (l3_lattices(A) & m1_filter_0(B,A) & v10_lattices(A) & -v3_struct_0(A) -> k13_filter_2(A,B) = k7_filter_2(A,B))) # label(redefinition_k13_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13265 (all A all B (v10_lattices(A) & m2_nat_lat(B,A) & l3_lattices(A) & -v3_struct_0(A) -> v3_lattices(k24_filter_2(A,B)) & m2_nat_lat(k24_filter_2(A,B),k1_lattice2(A)))) # label(dt_k24_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13266 (all A all B all C all D (-v3_struct_0(B) & v10_lattices(B) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(C,u1_struct_0(B)) & l3_lattices(B) -> ((exists E (r3_lattices(B,C,E) & r3_lattices(B,E,D) & A = E & m1_subset_1(E,u1_struct_0(B)))) <-> r2_hidden(A,a_3_2_filter_2(B,C,D))))) # label(fraenkel_a_3_2_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13267 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> r1_filter_2(A,B,B))) # label(reflexivity_r1_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13268 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) -> (r2_hidden(B,C) -> r1_tarski(k18_filter_2(A,B),k19_filter_2(A,C))))))))) # label(t40_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13269 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(k1_lattice2(A))) -> (all E (m1_subset_1(E,u1_struct_0(k1_lattice2(A))) -> k3_lattices(k1_lattice2(A),k5_filter_2(A,B),k5_filter_2(A,C)) = k4_lattices(A,B,C) & k4_lattices(k1_lattice2(A),k5_filter_2(A,B),k5_filter_2(A,C)) = k3_lattices(A,B,C) & k3_lattices(A,k6_filter_2(A,D),k6_filter_2(A,E)) = k4_lattices(k1_lattice2(A),D,E) & k4_lattices(A,k6_filter_2(A,D),k6_filter_2(A,E)) = k3_lattices(k1_lattice2(A),D,E))))))))))) # label(t19_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13270 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k5_filter_2(A,B) = B)))) # label(d4_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13271 (all A all B (m1_subset_1(B,u1_struct_0(k1_lattice2(A))) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> m1_subset_1(k6_filter_2(A,B),u1_struct_0(A)))) # label(dt_k6_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13272 (all A (-v3_struct_0(A) & l3_lattices(A) -> (all B (-v3_struct_0(B) & l3_lattices(B) -> (g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> (D = F & C = E -> k2_lattices(A,C,D) = k2_lattices(B,E,F) & (r1_lattices(B,E,F) -> r1_lattices(A,C,D)) & (r1_lattices(A,C,D) -> r1_lattices(B,E,F)) & k1_lattices(B,E,F) = k1_lattices(A,C,D))))))))))))))) # label(t8_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13273 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v13_lattices(A) -> r1_filter_2(u1_struct_0(A),k18_filter_2(A,B),k22_filter_2(A,k5_lattices(A),B))))))) # label(t67_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13274 (all A (-v3_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) -> (all B (m2_filter_2(B,A) -> (r2_filter_2(A,B) <-> v1_filter_2(B,A) & B != k17_filter_2(A)))))) # label(t58_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13275 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> m2_filter_2(u1_struct_0(A),A))) # label(t28_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13276 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(k3_lattices(A,C,D),B) <-> r2_hidden(C,B) & r2_hidden(D,B)))))) -> m2_filter_2(B,A)))))) # label(t15_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13277 (all A all B (-v3_struct_0(A) & v10_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & l3_lattices(A) -> m1_filter_2(k2_filter_2(A,B),A))) # label(dt_k2_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13278 (all A all B (v10_lattices(A) & l3_lattices(A) & m2_lattice4(B,A) & -v3_struct_0(A) -> m2_lattice4(k9_filter_2(A,B),k1_lattice2(A)))) # label(dt_k9_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13279 (all A all B (v10_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & l3_lattices(A) & -v3_struct_0(A) -> m1_subset_1(k5_filter_2(A,B),u1_struct_0(k1_lattice2(A))))) # label(dt_k5_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13280 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r2_hidden(k4_lattices(A,C,B),k18_filter_2(A,B)) & r2_hidden(k4_lattices(A,B,C),k18_filter_2(A,B)) & r2_hidden(B,k18_filter_2(A,B)))))))) # label(t31_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13281 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & m2_relset_1(D,k2_zfmisc_1(A,A),A) -> (all E (v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(B,B),B) & m2_relset_1(E,k2_zfmisc_1(B,B),B) -> (all F (v1_funct_1(F) & m2_relset_1(F,k2_zfmisc_1(B,B),B) & v1_funct_2(F,k2_zfmisc_1(B,B),B) -> (r6_binop_1(A,C,D) & F = k1_realset1(D,B) & k1_realset1(C,B) = E -> r6_binop_1(B,E,F)))))))))))))) # label(t4_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13282 (all A all B (v10_lattices(A) & m1_filter_0(B,k1_lattice2(A)) & l3_lattices(A) & -v3_struct_0(A) -> k8_filter_2(A,B) = k14_filter_2(A,B))) # label(redefinition_k14_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13283 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v14_lattices(A) & r2_hidden(k6_lattices(A),B) -> k19_filter_2(A,B) = u1_struct_0(A) & r1_filter_2(u1_struct_0(A),k19_filter_2(A,B),k17_filter_2(A))))))) # label(t42_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13284 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m2_filter_2(B,A) -> (v13_lattices(A) -> v13_lattices(k23_filter_2(A,B))))))) # label(t76_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13285 (all A all B (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B,u1_struct_0(A)) -> m2_filter_2(k18_filter_2(A,B),A))) # label(dt_k18_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13286 (all A (-v3_struct_0(A) & l3_lattices(A) & v17_lattices(A) & v10_lattices(A) -> (all B (m2_filter_2(B,A) -> (r2_filter_2(A,B) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> r2_hidden(C,B) | r2_hidden(k7_lattices(A,C),B))) & u1_struct_0(A) != B))))) # label(t57_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13287 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (-v3_struct_0(B) & l3_lattices(B) & v10_lattices(B) -> (m2_nat_lat(B,A) <-> (exists C ((exists D (v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(C,C),C) & m2_relset_1(D,k2_zfmisc_1(C,C),C) & (exists E (v1_funct_1(E) & D = k1_realset1(u2_lattices(A),C) & k1_realset1(u1_lattices(A),C) = E & g3_lattices(C,D,E) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) & m2_relset_1(E,k2_zfmisc_1(C,C),C) & v1_funct_2(E,k2_zfmisc_1(C,C),C))))) & m2_lattice4(C,A) & -v1_xboole_0(C)))))))) # label(d15_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13288 (all A all B (v10_lattices(A) & m2_lattice4(B,A) & -v1_xboole_0(B) & l3_lattices(A) & -v3_struct_0(A) -> k10_filter_2(A,B) = k7_filter_2(A,B))) # label(redefinition_k10_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13289 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v17_lattices(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & v17_lattices(B) & l3_lattices(B) -> (g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (D = C -> k7_lattices(A,C) = k7_lattices(B,D))))))))))) # label(t12_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13290 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) & -v1_xboole_0(B) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> -v1_xboole_0(k8_filter_2(A,B)))) # label(fc2_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13291 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m2_filter_2(B,A) -> (all C (m2_filter_2(C,A) -> r1_filter_2(u1_struct_0(A),k19_filter_2(A,k4_subset_1(u1_struct_0(A),B,C)),k19_filter_2(A,k20_filter_2(A,B,C))))))))) # label(t52_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13292 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> v14_lattices(k23_filter_2(A,k18_filter_2(A,B))))))) # label(t80_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13293 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(k1_lattice2(A))) -> C = k5_filter_2(A,k6_filter_2(A,C)) & B = k6_filter_2(A,k5_filter_2(A,B)))))))) # label(t18_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13294 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (-v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(E) -> (r2_hidden(B,D) & r2_hidden(C,E) -> r2_hidden(k3_lattices(A,C,B),k20_filter_2(A,D,E)) & r2_hidden(k3_lattices(A,B,C),k20_filter_2(A,D,E))))))))))))) # label(t46_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13295 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m2_filter_2(B,A) -> (r2_hidden(k6_lattices(A),B) & v14_lattices(A) -> r1_filter_2(u1_struct_0(A),B,k17_filter_2(A)) & u1_struct_0(A) = B))))) # label(t43_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13296 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) -> r1_filter_2(u1_struct_0(A),k20_filter_2(A,B,C),k20_filter_2(A,C,B)))))))) # label(t48_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13297 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = k1_lattice2(k1_lattice2(A)))) # label(t7_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13298 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (v10_lattices(B) & l3_lattices(B) & -v3_struct_0(B) -> (g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) -> (all C (m1_filter_2(C,A) -> m1_filter_2(C,B)))))))) # label(t16_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13299 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r3_lattices(A,B,C) -> k22_filter_2(A,B,C) = a_3_2_filter_2(A,B,C)))))))) # label(d14_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13300 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m2_filter_2(B,A) -> (all C (m2_filter_2(C,A) -> a_3_1_filter_2(A,B,C) = k19_filter_2(A,k4_subset_1(u1_struct_0(A),B,C)))))))) # label(t50_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13301 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m2_filter_2(B,A) -> (v1_filter_2(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(C,B) | r2_hidden(D,B) <-> r2_hidden(k4_lattices(A,C,D),B))))))))))) # label(d12_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13302 (all A all B (v10_lattices(A) & l3_lattices(A) & m2_filter_2(B,k1_lattice2(A)) & -v3_struct_0(A) -> m1_filter_2(k16_filter_2(A,B),A))) # label(dt_k16_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13303 (all A all B (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B,A) -> m1_filter_2(k15_filter_2(A,B),k1_lattice2(A)))) # label(dt_k15_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13304 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (m2_filter_2(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(C,B) & r2_hidden(D,B) -> r2_hidden(k3_lattices(A,C,D),B)))))) & (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(C,B) & r3_lattices(A,D,C) -> r2_hidden(D,B))))))))))) # label(t22_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13305 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (v14_lattices(A) -> r1_filter_2(u1_struct_0(A),k17_filter_2(A),k18_filter_2(A,k6_lattices(A)))))) # label(t32_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13306 (all A (v10_lattices(A) & v17_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -((all D (m2_filter_2(D,A) -> -(r2_filter_2(A,D) & (r2_hidden(B,D) & -r2_hidden(C,D) | -r2_hidden(B,D) & r2_hidden(C,D))))) & C != B))))))) # label(t60_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13307 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (-v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(C,D) -> r1_tarski(k19_filter_2(A,C),k19_filter_2(A,D))) & r1_tarski(k19_filter_2(A,k19_filter_2(A,B)),k19_filter_2(A,B)))))))))) # label(t39_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13308 (all A all B all C (-v3_struct_0(A) & v11_lattices(A) & l3_lattices(A) & m1_filter_0(B,A) & m1_filter_0(C,A) & v10_lattices(A) -> m1_filter_2(k4_filter_2(A,B,C),A))) # label(dt_k4_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13309 (all A all B (v10_lattices(A) & l3_lattices(A) & m2_lattice4(B,k1_lattice2(A)) & -v1_xboole_0(B) & -v3_struct_0(A) -> -v1_xboole_0(k12_filter_2(A,B)) & m2_lattice4(k12_filter_2(A,B),A))) # label(dt_k12_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13310 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m2_filter_2(B,A) -> (exists C (r2_hidden(C,B) & m1_subset_1(C,u1_struct_0(A)))))))) # label(t24_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13311 (all A all B (v10_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & l3_lattices(A) & -v3_struct_0(A) -> k2_filter_0(A,B) = k2_filter_2(A,B))) # label(redefinition_k2_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13312 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r3_lattices(A,B,C) -> (r2_hidden(D,k22_filter_2(A,B,C)) <-> r3_lattices(A,B,D) & r3_lattices(A,D,C))))))))))) # label(t63_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13313 (all A all B (l3_lattices(A) & m2_lattice4(B,k1_lattice2(A)) & v10_lattices(A) & -v3_struct_0(A) -> k8_filter_2(A,B) = k11_filter_2(A,B))) # label(redefinition_k11_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13314 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m2_filter_2(B,A) -> (all C (m2_filter_2(C,A) -> r1_tarski(B,k20_filter_2(A,B,C)) & r1_tarski(C,k20_filter_2(A,B,C)))))))) # label(t51_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13315 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v13_lattices(A) -> k5_lattices(k23_filter_2(A,k18_filter_2(A,B))) = k5_lattices(A) & v13_lattices(k23_filter_2(A,k18_filter_2(A,B)))))))) # label(t82_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13316 (all A all B (-v3_struct_0(A) & l3_lattices(A) & m2_filter_2(B,k1_lattice2(A)) & v10_lattices(A) -> k8_filter_2(A,B) = k16_filter_2(A,B))) # label(redefinition_k16_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13317 (all A all B all C (-v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> -v1_xboole_0(k20_filter_2(A,B,C)))) # label(fc3_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13318 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_filter_2(u1_struct_0(A),k19_filter_2(A,k4_subset_1(u1_struct_0(A),B,C)),k19_filter_2(A,k4_subset_1(u1_struct_0(A),B,k19_filter_2(A,C)))) & r1_filter_2(u1_struct_0(A),k19_filter_2(A,k4_subset_1(u1_struct_0(A),B,C)),k19_filter_2(A,k4_subset_1(u1_struct_0(A),k19_filter_2(A,B),C))))))))) # label(t49_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13319 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) & m2_lattice4(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(k23_filter_2(A,B))) -> (all F (m1_subset_1(F,u1_struct_0(k23_filter_2(A,B))) -> (F = D & E = C -> (r3_lattices(k23_filter_2(A,B),E,F) <-> r3_lattices(A,C,D))))))))))))))) # label(t75_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13320 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (-v1_xboole_0(B) & m2_lattice4(B,A) -> (all C (m2_nat_lat(C,A) -> ((exists D (v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(B,B),B) & (exists E (k1_realset1(u1_lattices(A),B) = E & C = g3_lattices(B,D,E) & k1_realset1(u2_lattices(A),B) = D & m2_relset_1(E,k2_zfmisc_1(B,B),B) & v1_funct_2(E,k2_zfmisc_1(B,B),B) & v1_funct_1(E))) & m2_relset_1(D,k2_zfmisc_1(B,B),B))) <-> C = k23_filter_2(A,B)))))))) # label(d16_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13321 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v13_lattices(A) -> v15_lattices(k23_filter_2(A,k18_filter_2(A,B)))))))) # label(t83_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13322 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (-v3_struct_0(A) & l3_lattices(A) & r3_lattices(A,B,C) & v12_lattices(A) & v16_lattices(A) & v15_lattices(A) & v10_lattices(A) -> v10_lattices(k23_filter_2(A,k22_filter_2(A,B,C))) & v16_lattices(k23_filter_2(A,k22_filter_2(A,B,C))) & l3_lattices(k23_filter_2(A,k22_filter_2(A,B,C))) & v15_lattices(k23_filter_2(A,k22_filter_2(A,B,C))) & -v3_struct_0(k23_filter_2(A,k22_filter_2(A,B,C)))))))))) # label(t86_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13323 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m2_lattice4(B,A) & -v1_xboole_0(B) -> (v12_lattices(A) -> v12_lattices(k23_filter_2(A,B))))))) # label(t77_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13324 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (v3_filter_0(A) & r3_lattices(A,B,C) -> v3_filter_0(k23_filter_2(A,k22_filter_2(A,B,C)))))))))) # label(t79_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13325 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> k1_filter_0(A) = k1_filter_2(A))) # label(redefinition_k1_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13326 (all A (l3_lattices(A) & v17_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(k1_lattice2(A))) -> k7_lattices(A,k6_filter_2(A,C)) = k7_lattices(k1_lattice2(A),C) & k7_lattices(k1_lattice2(A),k5_filter_2(A,B)) = k7_lattices(A,B))))))) # label(t55_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13327 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_2(D,k2_zfmisc_1(B,B),B) & m2_relset_1(D,k2_zfmisc_1(B,B),B) & v1_funct_1(D) -> (D = k1_realset1(C,B) -> (v1_binop_1(C,A) -> v1_binop_1(D,B)) & (v3_binop_1(C,A) -> v3_binop_1(D,B)) & (v2_binop_1(C,A) -> v2_binop_1(D,B))))))))))) # label(t1_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13328 (all A (l3_lattices(A) & v17_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m2_filter_2(B,A) -> (all C (m2_filter_2(C,A) -> r1_filter_2(u1_struct_0(A),k19_filter_2(A,k4_subset_1(u1_struct_0(A),B,C)),k21_filter_2(A,B,C)))))))) # label(t56_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13329 (all A all B (l3_lattices(A) & m2_lattice4(B,A) & v10_lattices(A) & -v3_struct_0(A) -> k9_filter_2(A,B) = k7_filter_2(A,B))) # label(redefinition_k9_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13330 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k20_filter_2(A,B,C) = a_3_0_filter_2(A,B,C))))))) # label(d13_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.87 13331 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m2_nat_lat(B,A) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> m1_subset_1(C,u1_struct_0(A)))))))) # label(t69_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.88 13332 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (all C (m2_filter_2(C,A) -> (k19_filter_2(A,B) = C <-> (all D (m2_filter_2(D,A) -> (r1_tarski(B,D) -> r1_tarski(C,D)))) & r1_tarski(B,C)))))))) # label(d11_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.88 13333 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m2_lattice4(B,A) & -v1_xboole_0(B) -> v1_funct_1(k1_realset1(u1_lattices(A),B)) & v1_funct_2(k1_realset1(u1_lattices(A),B),k2_zfmisc_1(B,B),B) & m2_relset_1(k1_realset1(u1_lattices(A),B),k2_zfmisc_1(B,B),B) & m2_relset_1(k1_realset1(u2_lattices(A),B),k2_zfmisc_1(B,B),B) & v1_funct_2(k1_realset1(u2_lattices(A),B),k2_zfmisc_1(B,B),B) & v1_funct_1(k1_realset1(u2_lattices(A),B)))))) # label(t61_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.88 13334 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> m1_filter_2(k1_filter_2(A),A))) # label(dt_k1_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.88 13335 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (v10_lattices(A) & r3_lattices(A,B,C) & l3_lattices(A) & v17_lattices(A) & -v3_struct_0(A) -> -v3_struct_0(k23_filter_2(A,k22_filter_2(A,B,C))) & v10_lattices(k23_filter_2(A,k22_filter_2(A,B,C))) & l3_lattices(k23_filter_2(A,k22_filter_2(A,B,C))) & v17_lattices(k23_filter_2(A,k22_filter_2(A,B,C)))))))))) # label(t87_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.88 13336 (all A all B (l3_lattices(A) & m2_nat_lat(B,A) & v10_lattices(A) & -v3_struct_0(A) -> k24_filter_2(A,B) = k1_lattice2(B))) # label(redefinition_k24_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.88 13337 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(k4_lattices(A,C,D),B) <-> r2_hidden(D,B) & r2_hidden(C,B)))))) -> m2_lattice4(B,A)))))) # label(t13_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.88 13338 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (-v3_struct_0(A) & v16_lattices(A) & l3_lattices(A) & v15_lattices(A) & v10_lattices(A) <-> -v3_struct_0(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A))))) # label(t53_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.88 13339 (all A all B all C (m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> m2_lattice4(k22_filter_2(A,B,C),A) & -v1_xboole_0(k22_filter_2(A,B,C)))) # label(dt_k22_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.88 13340 (all A all B (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -v1_xboole_0(k7_filter_2(A,B)))) # label(fc1_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.88 13341 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m2_lattice4(B,A) & -v1_xboole_0(B) -> (v11_lattices(A) -> v11_lattices(k23_filter_2(A,B))))))) # label(t78_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.88 13342 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_filter_2(u1_struct_0(A),k22_filter_2(A,B,B),k6_domain_1(u1_struct_0(A),B)))))) # label(t65_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.88 13343 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_filter_2(A,B,C) -> r1_filter_2(A,C,B)))) # label(symmetry_r1_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.88 13344 (all A all B (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & -v1_xboole_0(B) & m2_lattice4(B,A) -> m2_nat_lat(k23_filter_2(A,B),A))) # label(dt_k23_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.88 13345 (all A all B (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B,A) -> m2_filter_2(k13_filter_2(A,B),k1_lattice2(A)))) # label(dt_k13_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.88 13346 (all A all B (v10_lattices(A) & m2_lattice4(B,k1_lattice2(A)) & -v1_xboole_0(B) & l3_lattices(A) & -v3_struct_0(A) -> k8_filter_2(A,B) = k12_filter_2(A,B))) # label(redefinition_k12_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.88 13347 (all A all B all C (v10_lattices(A) & m2_filter_2(C,A) & m2_filter_2(B,A) & l3_lattices(A) & v11_lattices(A) & -v3_struct_0(A) -> m2_filter_2(k21_filter_2(A,B,C),A))) # label(dt_k21_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.88 13348 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m2_filter_2(D,A) -> (r2_hidden(B,D) -> r2_hidden(k4_lattices(A,B,C),D) & r2_hidden(k4_lattices(A,C,B),D)))))))))) # label(t23_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.88 13349 (all A all B (-v3_struct_0(A) & m2_filter_2(B,A) & l3_lattices(A) & v10_lattices(A) -> k7_filter_2(A,B) = k15_filter_2(A,B))) # label(redefinition_k15_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.88 13350 (all A (v10_lattices(A) & v16_lattices(A) & l3_lattices(A) & v15_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & v15_lattices(B) & l3_lattices(B) & v16_lattices(B) -> (g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> (r2_lattices(A,C,D) & F = D & C = E -> r2_lattices(B,E,F))))))))))))))) # label(t11_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.88 13351 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> -((all C (m2_filter_2(C,A) -> -(r2_filter_2(A,C) & r2_hidden(B,C)))) & B != k6_lattices(A) & v14_lattices(A)))))) # label(t36_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.88 13352 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (-v1_xboole_0(B) & m2_lattice4(B,A) -> (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,k2_zfmisc_1(B,B),B) & v1_funct_2(D,k2_zfmisc_1(B,B),B) -> (C = k1_realset1(u2_lattices(A),B) & D = k1_realset1(u1_lattices(A),B) -> v1_binop_1(C,B) & r1_lattice2(B,C,D) & r1_lattice2(B,D,C) & v2_binop_1(D,B) & v1_binop_1(D,B) & v2_binop_1(C,B)))))))))) # label(t62_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.88 13353 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(k1_lattice2(A))) -> (all E (m1_subset_1(E,u1_struct_0(k1_lattice2(A))) -> (r3_lattices(A,B,C) -> r3_lattices(k1_lattice2(A),k5_filter_2(A,C),k5_filter_2(A,B))) & (r3_lattices(k1_lattice2(A),k5_filter_2(A,C),k5_filter_2(A,B)) -> r3_lattices(A,B,C)) & (r3_lattices(k1_lattice2(A),D,E) -> r3_lattices(A,k6_filter_2(A,E),k6_filter_2(A,D))) & (r3_lattices(A,k6_filter_2(A,E),k6_filter_2(A,D)) -> r3_lattices(k1_lattice2(A),D,E)))))))))))) # label(t20_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.88 13354 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (-v1_xboole_0(B) & m2_lattice4(B,A) -> (m2_filter_2(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,B) & r2_hidden(C,B) <-> r2_hidden(k3_lattices(A,C,D),B))))))))))) # label(d3_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.88 13355 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v17_lattices(A) -> v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & -v3_struct_0(k1_lattice2(A)))) # label(fc4_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.88 13356 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (-v3_struct_0(A) & v10_lattices(A) & v16_lattices(A) & v12_lattices(A) & l3_lattices(A) & v15_lattices(A) -> v10_lattices(k23_filter_2(A,k18_filter_2(A,B))) & l3_lattices(k23_filter_2(A,k18_filter_2(A,B))) & v16_lattices(k23_filter_2(A,k18_filter_2(A,B))) & v15_lattices(k23_filter_2(A,k18_filter_2(A,B))) & -v3_struct_0(k23_filter_2(A,k18_filter_2(A,B)))))))) # label(t85_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.88 13357 (all A all B all C (m1_filter_0(C,A) & m1_filter_0(B,A) & l3_lattices(A) & v11_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> k5_filter_0(A,B,C) = k4_filter_2(A,B,C))) # label(redefinition_k4_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.88 13358 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_2(B,A) -> m2_lattice4(B,A) & -v1_xboole_0(B))))) # label(dt_m1_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.88 13359 (all A all B all C all D (l3_lattices(B) & m2_filter_2(C,B) & m2_filter_2(D,B) & v10_lattices(B) & -v3_struct_0(B) -> ((exists E (A = E & (exists F (m1_subset_1(F,u1_struct_0(B)) & (exists G (r3_lattices(B,E,k3_lattices(B,F,G)) & r2_hidden(F,C) & r2_hidden(G,D) & m1_subset_1(G,u1_struct_0(B)))))) & m1_subset_1(E,u1_struct_0(B)))) <-> r2_hidden(A,a_3_1_filter_2(B,C,D))))) # label(fraenkel_a_3_1_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.88 13360 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m2_filter_2(B,A) <-> m1_filter_2(B,k1_lattice2(A)))))) # label(t21_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.88 13361 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_2(D,k2_zfmisc_1(B,B),B) & m2_relset_1(D,k2_zfmisc_1(B,B),B) & v1_funct_1(D) -> (all E (m1_subset_1(E,A) -> (all F (m2_subset_1(F,A,B) -> (k1_realset1(C,B) = D & F = E -> (r1_binop_1(A,E,C) -> r1_binop_1(B,F,D)) & (r2_binop_1(A,E,C) -> r2_binop_1(B,F,D)) & (r3_binop_1(A,E,C) -> r3_binop_1(B,F,D))))))))))))))) # label(t2_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.88 13362 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m2_filter_2(B,A) -> (v1_filter_0(k15_filter_2(A,B),k1_lattice2(A)) <-> r2_filter_2(A,B)))))) # label(t33_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.88 13363 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> B = k7_filter_2(A,B))))) # label(d6_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.88 13364 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m2_filter_2(B,A) -> (v13_lattices(A) -> r2_hidden(k5_lattices(A),B)))))) # label(t25_filter_2) # label(axiom) # label(non_clause). [assumption]. 126.56/125.88 13365 (all A all B (v2_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) & l1_cat_1(A) -> v2_cat_1(k14_cat_5(A,B)) & l1_cat_1(k14_cat_5(A,B)) & v1_cat_5(k14_cat_5(A,B)) & v1_cat_1(k14_cat_5(A,B)))) # label(dt_k14_cat_5) # label(axiom) # label(non_clause). [assumption]. 126.56/125.88 13366 (exists A (-v1_xboole_0(A) & v2_cat_5(A))) # label(rc2_cat_5) # label(axiom) # label(non_clause). [assumption]. 126.56/125.88 13367 (all A all B all C (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(C,k2_zfmisc_1(A,B)) -> k3_cat_5(A,B,C) = k2_mcart_1(C))) # label(redefinition_k3_cat_5) # label(axiom) # label(non_clause). [assumption]. 126.56/125.88 13368 (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_subset_1(u2_cat_1(A),k13_cat_5(A,B),k12_cat_5(A,C)) = k6_cat_1(A,B,C))))))) # label(t25_cat_5) # label(axiom) # label(non_clause). [assumption]. 130.85/130.11 13369 (all A all B (v2_cat_1(A) & l1_cat_1(A) & m1_subset_1(B,u2_cat_1(A)) & v3_cat_5(A) -> l1_cat_1(k8_cat_5(A,B)) & v2_cat_1(k8_cat_5(A,B)))) # label(dt_k8_cat_5) # label(axiom) # label(non_clause). [assumption]. 130.85/130.11 13370 (all A (m1_subset_1(A,f1_s1_cat_5) -> (exists B (m1_subset_1(B,f2_s1_cat_5) & p1_s1_cat_5(A,A,B) & (all C (m1_subset_1(C,f1_s1_cat_5) -> (all D (m1_subset_1(D,f2_s1_cat_5) -> (p1_s1_cat_5(C,A,D) -> f3_s1_cat_5(B,D) = D) & (p1_s1_cat_5(A,C,D) -> D = f3_s1_cat_5(D,B)))))))))) & (all A (m1_subset_1(A,f1_s1_cat_5) -> (all B (m1_subset_1(B,f1_s1_cat_5) -> (all C (m1_subset_1(C,f1_s1_cat_5) -> (all D (m1_subset_1(D,f1_s1_cat_5) -> (all E (m1_subset_1(E,f2_s1_cat_5) -> (all F (m1_subset_1(F,f2_s1_cat_5) -> (all G (m1_subset_1(G,f2_s1_cat_5) -> (p1_s1_cat_5(A,B,E) & p1_s1_cat_5(B,C,F) & p1_s1_cat_5(C,D,G) -> f3_s1_cat_5(f3_s1_cat_5(G,F),E) = f3_s1_cat_5(G,f3_s1_cat_5(F,E))))))))))))))))) & (all A (m1_subset_1(A,f1_s1_cat_5) -> (all B (m1_subset_1(B,f1_s1_cat_5) -> (all C (m1_subset_1(C,f1_s1_cat_5) -> (all D (m1_subset_1(D,f2_s1_cat_5) -> (all E (m1_subset_1(E,f2_s1_cat_5) -> (p1_s1_cat_5(A,B,D) & p1_s1_cat_5(B,C,E) -> p1_s1_cat_5(A,C,f3_s1_cat_5(E,D)) & r2_hidden(f3_s1_cat_5(E,D),f2_s1_cat_5)))))))))))) -> (exists A (v2_cat_1(A) & v1_cat_5(A) & (all B (m1_subset_1(B,u2_cat_1(A)) -> (exists C ((exists D (m1_subset_1(D,f1_s1_cat_5) & (exists E (p1_s1_cat_5(C,D,E) & k1_domain_1(k2_zfmisc_1(f1_s1_cat_5,f1_s1_cat_5),f2_s1_cat_5,k1_domain_1(f1_s1_cat_5,f1_s1_cat_5,C,D),E) = B & m1_subset_1(E,f2_s1_cat_5))))) & m1_subset_1(C,f1_s1_cat_5))))) & (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,f1_s1_cat_5) -> (all E (m1_subset_1(E,f1_s1_cat_5) -> (all F (m1_subset_1(F,f1_s1_cat_5) -> (all G (m1_subset_1(G,f2_s1_cat_5) -> (all H (m1_subset_1(H,f2_s1_cat_5) -> (C = k1_domain_1(k2_zfmisc_1(f1_s1_cat_5,f1_s1_cat_5),f2_s1_cat_5,k1_domain_1(f1_s1_cat_5,f1_s1_cat_5,E,F),H) & B = k1_domain_1(k2_zfmisc_1(f1_s1_cat_5,f1_s1_cat_5),f2_s1_cat_5,k1_domain_1(f1_s1_cat_5,f1_s1_cat_5,D,E),G) -> k4_cat_1(A,B,C) = k4_tarski(k1_domain_1(f1_s1_cat_5,f1_s1_cat_5,D,F),f3_s1_cat_5(H,G))))))))))))))))) & (all B (m1_subset_1(B,f1_s1_cat_5) -> (all C (m1_subset_1(C,f1_s1_cat_5) -> (all D (m1_subset_1(D,f2_s1_cat_5) -> (p1_s1_cat_5(B,C,D) -> m1_subset_1(k1_domain_1(k2_zfmisc_1(f1_s1_cat_5,f1_s1_cat_5),f2_s1_cat_5,k1_domain_1(f1_s1_cat_5,f1_s1_cat_5,B,C),D),u2_cat_1(A))))))))) & u1_cat_1(A) = f1_s1_cat_5 & l1_cat_1(A) & v1_cat_1(A))) # label(s1_cat_5) # label(axiom) # label(non_clause). [assumption]. 130.85/130.11 13371 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> v2_cat_1(B) & l1_cat_1(B))) <-> v2_cat_5(A)))) # label(d5_cat_5) # label(axiom) # label(non_clause). [assumption]. 130.85/130.11 13372 (all A all B (v2_cat_1(A) & l1_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) -> l1_cat_1(k15_cat_5(A,B)) & v1_cat_5(k15_cat_5(A,B)) & v2_cat_1(k15_cat_5(A,B)) & v1_cat_1(k15_cat_5(A,B)))) # label(dt_k15_cat_5) # label(axiom) # label(non_clause). [assumption]. 130.85/130.11 13373 (all A (-v1_xboole_0(A) & v2_cat_5(A) -> (all B (-v1_xboole_0(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) & v3_cat_5(C) & v1_cat_1(C) -> (all D (v2_cat_1(D) & l1_cat_1(D) & v3_cat_5(D) & v1_cat_1(D) -> (A = u1_cat_1(C) & (all E (m1_cat_5(E,A) -> (all F (m1_cat_5(F,A) -> (all G (m2_cat_1(G,E,F) -> (r2_hidden(G,B) <-> m1_subset_1(k1_domain_1(k2_zfmisc_1(A,A),k1_zfmisc_1(k2_zfmisc_1(u2_cat_1(E),u2_cat_1(F))),k1_domain_1(A,A,E,F),G),u2_cat_1(C))))))))) & (all E (m1_cat_5(E,A) -> (all F (m1_cat_5(F,A) -> (all G (m2_cat_1(G,E,F) -> (r2_hidden(G,B) <-> m1_subset_1(k1_domain_1(k2_zfmisc_1(A,A),k1_zfmisc_1(k2_zfmisc_1(u2_cat_1(E),u2_cat_1(F))),k1_domain_1(A,A,E,F),G),u2_cat_1(D))))))))) & u1_cat_1(D) = A -> C = D))))))))) # label(t18_cat_5) # label(axiom) # label(non_clause). [assumption]. 130.85/130.11 13374 (all A (v1_cat_5(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> k4_tarski(k1_domain_1(u1_cat_1(A),u1_cat_1(A),k2_cat_1(A,B),k3_cat_1(A,B)),k2_mcart_1(B)) = B & k18_mcart_1(B) = k3_cat_1(A,B) & k2_cat_1(A,B) = k17_mcart_1(B))))) # label(t2_cat_5) # label(axiom) # label(non_clause). [assumption]. 130.85/130.12 13375 (all A (v2_cat_1(A) & l1_cat_1(A) & v3_cat_5(A) -> (all B (v2_cat_1(B) & v3_cat_5(B) & v4_cat_5(B) & l1_cat_1(B) -> (r1_tarski(u1_cat_1(A),u1_cat_1(B)) -> m3_cat_2(A,B)))))) # label(t21_cat_5) # label(axiom) # label(non_clause). [assumption]. 130.85/130.12 13376 (all A (v2_cat_1(A) & l1_cat_1(A) -> A = k10_cat_5(A))) # label(d7_cat_5) # label(axiom) # label(non_clause). [assumption]. 130.85/130.12 13377 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m3_cat_2(B,A) -> (all C (m3_cat_2(C,B) -> m3_cat_2(C,A))))))) # label(t4_cat_5) # label(axiom) # label(non_clause). [assumption]. 130.85/130.12 13378 (all A (v2_cat_1(A) & l1_cat_1(A) & v3_cat_5(A) -> (all B (m3_cat_2(B,A) -> v3_cat_5(B))))) # label(cc2_cat_5) # label(axiom) # label(non_clause). [assumption]. 130.85/130.12 13379 (all A all B (m1_subset_1(B,u1_cat_1(A)) & l1_cat_1(A) & v2_cat_1(A) -> m1_subset_1(k13_cat_5(A,B),k1_zfmisc_1(u2_cat_1(A))))) # label(dt_k13_cat_5) # label(axiom) # label(non_clause). [assumption]. 130.85/130.12 13380 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (l1_cat_1(C) & v1_cat_5(C) & v2_cat_1(C) & v1_cat_1(C) -> ((all D (m1_subset_1(D,u2_cat_1(C)) -> (exists E (m2_subset_1(E,u2_cat_1(A),k12_cat_5(A,B)) & (exists F (m2_subset_1(F,u2_cat_1(A),k12_cat_5(A,B)) & (exists G (m1_subset_1(G,u2_cat_1(A)) & k4_cat_1(A,G,F) = E & k2_cat_1(A,F) = k3_cat_1(A,G) & D = k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,E,F),G))))))))) & (all D (m1_subset_1(D,u2_cat_1(C)) -> (all E (m1_subset_1(E,u2_cat_1(C)) -> (all F (m2_subset_1(F,u2_cat_1(A),k12_cat_5(A,B)) -> (all G (m2_subset_1(G,u2_cat_1(A),k12_cat_5(A,B)) -> (all H (m2_subset_1(H,u2_cat_1(A),k12_cat_5(A,B)) -> (all I (m1_subset_1(I,u2_cat_1(A)) -> (all J (m1_subset_1(J,u2_cat_1(A)) -> (k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,F,G),I) = D & k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,G,H),J) = E -> k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,F,H),k4_cat_1(A,I,J)) = k4_cat_1(C,D,E)))))))))))))))) & (all D (m2_subset_1(D,u2_cat_1(A),k12_cat_5(A,B)) -> (all E (m2_subset_1(E,u2_cat_1(A),k12_cat_5(A,B)) -> (all F (m1_subset_1(F,u2_cat_1(A)) -> (D = k4_cat_1(A,F,E) & k3_cat_1(A,F) = k2_cat_1(A,E) -> m1_subset_1(k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,D,E),F),u2_cat_1(C))))))))) & u1_cat_1(C) = k12_cat_5(A,B) <-> k14_cat_5(A,B) = C))))))) # label(d11_cat_5) # label(axiom) # label(non_clause). [assumption]. 130.85/130.12 13381 (exists A (v1_cat_1(A) & v1_cat_5(A) & v3_cat_5(A) & v4_cat_5(A) & v2_cat_1(A) & l1_cat_1(A))) # label(rc4_cat_5) # label(axiom) # label(non_clause). [assumption]. 130.85/130.12 13382 (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) -> m2_cat_1(C,A,k7_cat_5(A,B,C)))))))) # label(t8_cat_5) # label(axiom) # label(non_clause). [assumption]. 130.85/130.12 13383 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v3_cat_5(B) & l1_cat_1(B) & v2_cat_1(B) -> (all C (l1_cat_1(C) & v3_cat_5(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,C) -> (E = D -> k7_cat_5(A,C,E) = k7_cat_5(A,B,D)))))))))))) # label(t22_cat_5) # label(axiom) # label(non_clause). [assumption]. 130.85/130.12 13384 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m2_subset_1(C,u2_cat_1(A),k13_cat_5(A,B)) -> (all D (m1_subset_1(D,u1_cat_1(k15_cat_5(A,B))) -> (C = D -> k10_cat_1(k15_cat_5(A,B),D) = k1_domain_1(u1_cat_1(k11_cat_2(k15_cat_5(A,B),k15_cat_5(A,B))),u2_cat_1(A),k12_cat_2(k15_cat_5(A,B),k15_cat_5(A,B),D,D),k10_cat_1(A,k3_cat_1(A,C)))))))))))) # label(t32_cat_5) # label(axiom) # label(non_clause). [assumption]. 130.85/130.12 13385 (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) -> m3_cat_2(k7_cat_5(A,B,C),B) & v1_cat_1(k7_cat_5(A,B,C)))) # label(dt_k7_cat_5) # label(axiom) # label(non_clause). [assumption]. 130.85/130.12 13386 (all A all B (l1_cat_1(A) & m1_subset_1(B,u2_cat_1(A)) & v1_cat_5(A) -> m1_subset_1(k4_cat_5(A,B),u1_cat_1(A)))) # label(dt_k4_cat_5) # label(axiom) # label(non_clause). [assumption]. 130.85/130.12 13387 (all A (v3_cat_5(A) & l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) & v3_cat_5(B) -> (u2_cat_1(A) = u2_cat_1(B) & u1_cat_1(B) = u1_cat_1(A) -> g1_cat_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A)) = g1_cat_1(u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),u5_cat_1(B),u6_cat_1(B))))))) # label(t14_cat_5) # label(axiom) # label(non_clause). [assumption]. 130.85/130.12 13388 (all A (l1_cat_1(A) & v2_cat_1(A) -> v3_cat_5(k8_cat_1(A,k4_tarski(k4_tarski(A,A),k15_cat_1(A)))))) # label(t11_cat_5) # label(axiom) # label(non_clause). [assumption]. 130.85/130.12 13389 (all A (l1_cat_1(A) -> (v1_cat_5(A) <-> (all B (m1_subset_1(B,u2_cat_1(A)) -> (exists C B = k4_tarski(k1_domain_1(u1_cat_1(A),u1_cat_1(A),k2_cat_1(A,B),k3_cat_1(A,B)),C))))))) # label(d1_cat_5) # label(axiom) # label(non_clause). [assumption]. 130.85/130.12 13390 (all A all B (v1_cat_5(A) & l1_cat_1(A) & m1_subset_1(B,u2_cat_1(A)) -> k4_cat_5(A,B) = k17_mcart_1(B))) # label(redefinition_k4_cat_5) # label(axiom) # label(non_clause). [assumption]. 130.85/130.12 13391 (all A (v2_cat_1(k10_cat_5(A)) & l1_cat_1(k10_cat_5(A)))) # label(dt_k10_cat_5) # label(axiom) # label(non_clause). [assumption]. 130.85/130.12 13392 (all A (v2_cat_1(A) & v3_cat_5(A) & l1_cat_1(A) -> (all B (v3_cat_5(B) & l1_cat_1(B) & v2_cat_1(B) -> (r1_tarski(u2_cat_1(A),u2_cat_1(B)) -> m3_cat_2(A,B)))))) # label(t15_cat_5) # label(axiom) # label(non_clause). [assumption]. 130.85/130.12 13393 (all A all B all C (v2_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) & m1_subset_1(C,u2_cat_1(k14_cat_5(A,B))) & l1_cat_1(A) -> k18_mcart_1(C) = k18_cat_5(A,B,C))) # label(redefinition_k18_cat_5) # label(axiom) # label(non_clause). [assumption]. 130.85/130.12 13394 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> k13_cat_5(A,B) = k3_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k6_domain_1(u1_cat_1(A),B)))))) # label(d10_cat_5) # label(axiom) # label(non_clause). [assumption]. 130.85/130.12 13395 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) & -v1_xboole_0(C) & -v1_xboole_0(A) -> k1_cat_5(A,B,C,D) = k17_mcart_1(D))) # label(redefinition_k1_cat_5) # label(axiom) # label(non_clause). [assumption]. 130.85/130.12 13396 (all A all B (v3_cat_5(A) & l1_cat_1(A) & m1_subset_1(B,u2_cat_1(A)) & v2_cat_1(A) -> k9_cat_5(A,B) = k18_mcart_1(B))) # label(redefinition_k9_cat_5) # label(axiom) # label(non_clause). [assumption]. 130.85/130.12 13397 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> k3_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k6_domain_1(u1_cat_1(A),B)) = k12_cat_5(A,B))))) # label(d9_cat_5) # label(axiom) # label(non_clause). [assumption]. 130.85/130.12 13398 (all A all B (m1_subset_1(B,u2_cat_1(A)) & l1_cat_1(A) & v1_cat_5(A) -> k5_cat_5(A,B) = k18_mcart_1(B))) # label(redefinition_k5_cat_5) # label(axiom) # label(non_clause). [assumption]. 130.85/130.12 13399 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> r2_hidden(B,k12_cat_5(A,k3_cat_1(A,B))) & r2_hidden(B,k13_cat_5(A,k2_cat_1(A,B))))))) # label(t26_cat_5) # label(axiom) # label(non_clause). [assumption]. 130.85/130.12 13400 (all A (m1_subset_1(A,u2_cat_1(f1_s3_cat_5)) -> (all B (m1_subset_1(B,u2_cat_1(f1_s3_cat_5)) -> (all C (m1_subset_1(C,u2_cat_1(f2_s3_cat_5)) -> (all D (m1_subset_1(D,u2_cat_1(f2_s3_cat_5)) -> (D = f4_s3_cat_5(B) & k2_cat_1(f1_s3_cat_5,B) = k3_cat_1(f1_s3_cat_5,A) & C = f4_s3_cat_5(A) -> f4_s3_cat_5(k4_cat_1(f1_s3_cat_5,A,B)) = k4_cat_1(f2_s3_cat_5,C,D)))))))))) & (all A (m1_subset_1(A,u1_cat_1(f1_s3_cat_5)) -> k10_cat_1(f2_s3_cat_5,f3_s3_cat_5(A)) = f4_s3_cat_5(k10_cat_1(f1_s3_cat_5,A)))) & (all A (m1_subset_1(A,u2_cat_1(f1_s3_cat_5)) -> (all B (m1_subset_1(B,u2_cat_1(f2_s3_cat_5)) -> (f4_s3_cat_5(A) = B -> k2_cat_1(f2_s3_cat_5,B) = f3_s3_cat_5(k2_cat_1(f1_s3_cat_5,A)) & k3_cat_1(f2_s3_cat_5,B) = f3_s3_cat_5(k3_cat_1(f1_s3_cat_5,A))))) & m1_subset_1(f4_s3_cat_5(A),u2_cat_1(f2_s3_cat_5)))) -> (exists A ((all B (m1_subset_1(B,u2_cat_1(f1_s3_cat_5)) -> k8_funct_2(u2_cat_1(f1_s3_cat_5),u2_cat_1(f2_s3_cat_5),A,B) = f4_s3_cat_5(B))) & m2_cat_1(A,f1_s3_cat_5,f2_s3_cat_5))) # label(s3_cat_5) # label(axiom) # label(non_clause). Cputime limit exceeded (core dumped) 180.08/179.34 EOF