0.10/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.10/0.11 % Command : tptp2X_and_run_prover9 %d %s 0.10/0.31 % Computer : n018.cluster.edu 0.10/0.31 % Model : x86_64 x86_64 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.31 % Memory : 8042.1875MB 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.31 % CPULimit : 1200 0.10/0.31 % DateTime : Tue Jul 13 16:26:25 EDT 2021 0.10/0.32 % CPUTime : 28.04/27.67 ============================== Prover9 =============================== 28.04/27.67 Prover9 (32) version 2009-11A, November 2009. 28.04/27.67 Process 24788 was started by sandbox2 on n018.cluster.edu, 28.04/27.67 Tue Jul 13 16:26:49 2021 28.04/27.67 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1200 -f /tmp/Prover9_24440_n018.cluster.edu". 28.04/27.67 ============================== end of head =========================== 28.04/27.67 28.04/27.67 ============================== INPUT ================================= 28.04/27.67 28.04/27.67 % Reading from file /tmp/Prover9_24440_n018.cluster.edu 28.04/27.67 28.04/27.67 set(prolog_style_variables). 28.04/27.67 set(auto2). 28.04/27.67 % set(auto2) -> set(auto). 28.04/27.67 % set(auto) -> set(auto_inference). 28.04/27.67 % set(auto) -> set(auto_setup). 28.04/27.67 % set(auto_setup) -> set(predicate_elim). 28.04/27.67 % set(auto_setup) -> assign(eq_defs, unfold). 28.04/27.67 % set(auto) -> set(auto_limits). 28.04/27.67 % set(auto_limits) -> assign(max_weight, "100.000"). 28.04/27.67 % set(auto_limits) -> assign(sos_limit, 20000). 28.04/27.67 % set(auto) -> set(auto_denials). 28.04/27.67 % set(auto) -> set(auto_process). 28.04/27.67 % set(auto2) -> assign(new_constants, 1). 28.04/27.67 % set(auto2) -> assign(fold_denial_max, 3). 28.04/27.67 % set(auto2) -> assign(max_weight, "200.000"). 28.04/27.67 % set(auto2) -> assign(max_hours, 1). 28.04/27.67 % assign(max_hours, 1) -> assign(max_seconds, 3600). 28.04/27.67 % set(auto2) -> assign(max_seconds, 0). 28.04/27.67 % set(auto2) -> assign(max_minutes, 5). 28.04/27.67 % assign(max_minutes, 5) -> assign(max_seconds, 300). 28.04/27.67 % set(auto2) -> set(sort_initial_sos). 28.04/27.67 % set(auto2) -> assign(sos_limit, -1). 28.04/27.67 % set(auto2) -> assign(lrs_ticks, 3000). 28.04/27.67 % set(auto2) -> assign(max_megs, 400). 28.04/27.67 % set(auto2) -> assign(stats, some). 28.04/27.67 % set(auto2) -> clear(echo_input). 28.04/27.67 % set(auto2) -> set(quiet). 28.04/27.67 % set(auto2) -> clear(print_initial_clauses). 28.04/27.67 % set(auto2) -> clear(print_given). 28.04/27.67 assign(lrs_ticks,-1). 28.04/27.67 assign(sos_limit,10000). 28.04/27.67 assign(order,kbo). 28.04/27.67 set(lex_order_vars). 28.04/27.67 clear(print_given). 28.04/27.67 28.04/27.67 % formulas(sos). % not echoed (10546 formulas) 28.04/27.67 28.04/27.67 ============================== end of input ========================== 28.04/27.67 28.04/27.67 % From the command line: assign(max_seconds, 1200). 28.04/27.67 28.04/27.67 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 28.04/27.67 28.04/27.67 % Formulas that are not ordinary clauses: 28.04/27.67 1 (all A all B (r2_hidden(A,B) -> -r2_hidden(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 2 $T # label(t8_tarski) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 3 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 4 (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]. 28.04/27.67 5 (all A all B ((all C (A = C <-> r2_hidden(C,B))) <-> B = k1_tarski(A))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 6 (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]. 28.04/27.67 7 (all A all B r1_tarski(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 8 (all A all B -((all C -(r2_hidden(C,B) & (all D -(r2_hidden(D,C) & r2_hidden(D,B))))) & r2_hidden(A,B))) # label(t7_tarski) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 9 (all A all B ((all C (r2_hidden(C,B) <-> (exists D (r2_hidden(C,D) & r2_hidden(D,A))))) <-> B = k3_tarski(A))) # label(d4_tarski) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 10 (all A exists 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 -(-r2_tarski(C,B) & -r2_hidden(C,B) & r1_tarski(C,B))) & (all C all D (r2_hidden(C,B) & r1_tarski(D,C) -> r2_hidden(D,B))) & r2_hidden(A,B))) # label(t9_tarski) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 11 (all A all B (r2_tarski(A,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(F,G),C) & r2_hidden(k4_tarski(D,E),C) -> (D = F <-> E = G))) & (all D -((all E -(r2_hidden(E,B) & r2_hidden(k4_tarski(D,E),C))) & r2_hidden(D,A))))))) # label(d6_tarski) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 12 $T # label(t3_tarski) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 13 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 14 $T # label(dt_k3_tarski) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 15 $T # label(t4_tarski) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 16 (all A all B all C (p1_s1_tarski(A,C) & p1_s1_tarski(A,B) -> B = C)) -> (exists A all B ((exists C (p1_s1_tarski(C,B) & r2_hidden(C,f1_s1_tarski))) <-> r2_hidden(B,A))) # label(s1_tarski) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 17 (all A all B ((all C (r2_hidden(C,A) -> r2_hidden(C,B))) <-> r1_tarski(A,B))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 18 $T # label(t6_tarski) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 19 (all A all B all C ((all D (r2_hidden(D,C) <-> D = B | D = A)) <-> k2_tarski(A,B) = C)) # label(d2_tarski) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 20 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 21 (all A all B k2_tarski(B,A) = k2_tarski(A,B)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 22 $T # label(t5_tarski) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 23 $T # label(t1_tarski) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 24 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 25 (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]. 28.04/27.67 26 (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]. 28.04/27.67 27 (all A all B r3_xboole_0(A,A)) # label(reflexivity_r3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 28 (all A ((all B -r2_hidden(B,A)) <-> A = k1_xboole_0)) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 29 (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]. 28.04/27.67 30 (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,A) & -r2_hidden(C,B)))) # label(t5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 31 (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]. 28.04/27.67 32 (all A all B A = k3_xboole_0(A,A)) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 33 (all A all B (r1_xboole_0(A,B) <-> k1_xboole_0 = k3_xboole_0(A,B))) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 34 (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]. 28.04/27.67 35 (exists A -v1_xboole_0(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 36 (all A all B (r1_tarski(B,A) & r1_tarski(A,B) <-> A = B)) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 37 (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]. 28.04/27.67 38 (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]. 28.04/27.67 39 (exists A all B (r2_hidden(B,A) <-> r2_hidden(B,f1_s1_xboole_0) & p1_s1_xboole_0(B))) # label(s1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 40 (all A all B all C ((all D ((r2_hidden(D,C) <-> r2_hidden(D,B)) <-> -r2_hidden(D,A))) -> k5_xboole_0(B,C) = A)) # label(t2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 41 (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]. 28.04/27.67 42 (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]. 28.04/27.67 43 (all A (A = k1_xboole_0 <-> v1_xboole_0(A))) # label(d5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 44 (all A all B k2_xboole_0(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 45 (all A all B (r2_xboole_0(A,B) <-> r1_tarski(A,B) & B != A)) # label(d8_xboole_0) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 46 (all A all B (-((exists C (r2_hidden(C,B) & r2_hidden(C,A))) & r1_xboole_0(A,B)) & -((all C -(r2_hidden(C,A) & r2_hidden(C,B))) & -r1_xboole_0(A,B)))) # label(t3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 47 (all A all B -r2_xboole_0(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 48 (all A all B k5_xboole_0(A,B) = k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(B,A))) # label(d6_xboole_0) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 49 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 50 (all A all B (-(r1_xboole_0(A,B) & (exists C r2_hidden(C,k3_xboole_0(A,B)))) & -((all C -r2_hidden(C,k3_xboole_0(A,B))) & -r1_xboole_0(A,B)))) # label(t4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 51 (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]. 28.04/27.67 52 (all A all B all C (k4_xboole_0(A,B) = C <-> (all D (r2_hidden(D,C) <-> -r2_hidden(D,B) & r2_hidden(D,A))))) # label(d4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 53 (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]. 28.04/27.67 54 $T # label(dt_k5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 55 (exists A v1_xboole_0(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 56 (all A all B all C ((all D (r2_hidden(D,C) <-> r2_hidden(D,A) | r2_hidden(D,B))) <-> k2_xboole_0(A,B) = C)) # label(d2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 57 (all A all B all C (k3_xboole_0(A,B) = C <-> (all D (r2_hidden(D,C) <-> r2_hidden(D,B) & r2_hidden(D,A))))) # label(d3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 58 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 59 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 60 (all A all B all C (-(r2_hidden(A,C) <-> r2_hidden(A,B)) <-> r2_hidden(A,k5_xboole_0(B,C)))) # label(t1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 61 (all A all B -(v1_xboole_0(B) & A != B & v1_xboole_0(A))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 62 (all A k1_xboole_0 = k3_xboole_0(A,k1_xboole_0)) # label(t2_boole) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 63 (all A A = k4_xboole_0(A,k1_xboole_0)) # label(t3_boole) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 64 (all A k1_xboole_0 = k4_xboole_0(k1_xboole_0,A)) # label(t4_boole) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 65 (all A A = k2_xboole_0(A,k1_xboole_0)) # label(t1_boole) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 66 (all A (v1_xboole_0(A) -> A = k1_xboole_0)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 67 (all A A = k5_xboole_0(A,k1_xboole_0)) # label(t5_boole) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 68 (all A all B -(v1_xboole_0(B) & r2_hidden(A,B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 69 (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]. 28.04/27.67 70 (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]. 28.04/27.67 71 (all A all B all C (r1_tarski(A,B) & r1_tarski(C,B) -> r1_tarski(k5_xboole_0(A,C),B))) # label(t110_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 72 (all A k1_xboole_0 = k5_xboole_0(A,A)) # label(t92_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 73 (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]. 28.04/27.67 74 (all A all B all C k2_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(k2_xboole_0(A,C),k2_xboole_0(B,C))) # label(t5_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 75 (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]. 28.04/27.67 76 (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]. 28.04/27.67 77 (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]. 28.04/27.67 78 (all A all B all C all D (r1_xboole_0(C,D) & r1_xboole_0(B,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]. 28.04/27.67 79 (all A r1_tarski(k1_xboole_0,A)) # label(t2_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 80 (all A all B k2_xboole_0(A,B) = k2_xboole_0(k5_xboole_0(A,B),k3_xboole_0(A,B))) # label(t93_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 81 (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]. 28.04/27.67 82 (all A all B (k1_xboole_0 = k4_xboole_0(A,B) <-> r1_tarski(A,B))) # label(t37_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 83 (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]. 28.04/27.67 84 (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]. 28.04/27.67 85 (all A all B all C all D (r1_xboole_0(B,D) & r1_tarski(C,D) & r1_tarski(A,B) -> r1_xboole_0(A,C))) # label(t64_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 86 (all A all B all C (r1_tarski(A,B) & r1_xboole_0(B,C) & r1_tarski(A,C) -> k1_xboole_0 = A)) # label(t67_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 87 (all A all B all C (r1_tarski(A,k5_xboole_0(B,C)) <-> r1_tarski(A,k2_xboole_0(B,C)) & r1_xboole_0(A,k3_xboole_0(B,C)))) # label(t107_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 88 (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]. 28.04/27.67 89 (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]. 28.04/27.67 90 (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]. 28.04/27.67 91 (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]. 28.04/27.67 92 (all A (-(-r1_xboole_0(A,A) & A = k1_xboole_0) & -(A != k1_xboole_0 & r1_xboole_0(A,A)))) # label(t66_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 93 (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]. 28.04/27.67 94 (all A all B all C k3_xboole_0(A,k3_xboole_0(B,C)) = k3_xboole_0(k3_xboole_0(A,B),C)) # label(t16_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 95 (all A all B r1_tarski(A,k2_xboole_0(A,B))) # label(t7_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 96 (all A all B all C r1_tarski(k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C)),k2_xboole_0(B,C))) # label(t31_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 97 (all A all B all C k3_xboole_0(k4_xboole_0(A,B),k4_xboole_0(A,C)) = k4_xboole_0(A,k2_xboole_0(B,C))) # label(t53_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.67 98 (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]. 28.04/27.67 99 (all A all B all C k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(A,C)) = k4_xboole_0(A,k3_xboole_0(B,C))) # label(t54_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 100 (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]. 28.04/27.68 101 (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]. 28.04/27.68 102 (all A all B (k4_xboole_0(B,A) = k4_xboole_0(A,B) -> A = B)) # label(t32_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 103 (all A all B all C k3_xboole_0(A,k4_xboole_0(B,C)) = k4_xboole_0(k3_xboole_0(A,B),C)) # label(t49_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 104 (all A all B all C (-(-(r1_xboole_0(A,C) & r1_xboole_0(A,B)) & r1_xboole_0(A,k2_xboole_0(B,C))) & -(-r1_xboole_0(A,k2_xboole_0(B,C)) & r1_xboole_0(A,B) & r1_xboole_0(A,C)))) # label(t70_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 105 (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]. 28.04/27.68 106 (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]. 28.04/27.68 107 (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]. 28.04/27.68 108 (all A all B all C k4_xboole_0(A,k2_xboole_0(B,C)) = k4_xboole_0(k4_xboole_0(A,B),C)) # label(t41_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 109 (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]. 28.04/27.68 110 (all A all B -(r2_xboole_0(B,A) & r2_xboole_0(A,B))) # label(t57_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 111 (all A all B all C k2_xboole_0(k4_xboole_0(A,B),k3_xboole_0(A,C)) = k4_xboole_0(A,k4_xboole_0(B,C))) # label(t52_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 112 (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]. 28.04/27.68 113 (all A all B -(r2_xboole_0(A,B) & k4_xboole_0(B,A) = k1_xboole_0)) # label(t105_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 114 (all A all B k4_xboole_0(k2_xboole_0(A,B),k3_xboole_0(A,B)) = k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(B,A))) # label(t55_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 115 (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]. 28.04/27.68 116 (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]. 28.04/27.68 117 (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]. 28.04/27.68 118 (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]. 28.04/27.68 119 (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]. 28.04/27.68 120 (all A all B -(r2_xboole_0(B,A) & r1_tarski(A,B))) # label(t60_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 121 (all A all B (r1_tarski(A,B) -> B = k2_xboole_0(A,B))) # label(t12_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 122 (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]. 28.04/27.68 123 (all A all B all C (k2_xboole_0(A,B) = k2_xboole_0(C,B) & r1_xboole_0(C,B) & r1_xboole_0(A,B) -> A = C)) # label(t71_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 124 (all A all B all C (r1_tarski(A,B) & r1_xboole_0(B,C) -> r1_xboole_0(A,C))) # label(t63_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 125 (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) -> C = B)) # label(t72_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 126 (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]. 28.04/27.68 127 (all A all B all C k4_xboole_0(A,k5_xboole_0(B,C)) = k2_xboole_0(k4_xboole_0(A,k2_xboole_0(B,C)),k3_xboole_0(k3_xboole_0(A,B),C))) # label(t102_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 128 (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]. 28.04/27.68 129 (all A all B all C (r1_xboole_0(A,B) -> k2_xboole_0(k4_xboole_0(C,A),B) = k4_xboole_0(k2_xboole_0(C,B),A))) # label(t87_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 130 (all A (r1_tarski(A,k1_xboole_0) -> A = k1_xboole_0)) # label(t3_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 131 (all A all B r1_tarski(k3_xboole_0(A,B),A)) # label(t17_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 132 (all A all B all C (r2_xboole_0(B,C) & r1_tarski(A,B) -> r2_xboole_0(A,C))) # label(t59_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 133 (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]. 28.04/27.68 134 (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]. 28.04/27.68 135 (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]. 28.04/27.68 136 (all A all B all C (r1_tarski(A,k2_xboole_0(B,C)) & r1_xboole_0(A,C) -> r1_tarski(A,B))) # label(t73_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 137 (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]. 28.04/27.68 138 (all A all B all C (r1_tarski(k4_xboole_0(A,B),C) & r1_tarski(k4_xboole_0(B,A),C) -> r1_tarski(k5_xboole_0(A,B),C))) # label(t97_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 139 (all A all B k4_xboole_0(k2_xboole_0(A,B),B) = k4_xboole_0(A,B)) # label(t40_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 140 (all A all B (r1_xboole_0(A,B) <-> A = k4_xboole_0(A,B))) # label(t83_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 141 (all A all B k4_xboole_0(k2_xboole_0(A,B),k3_xboole_0(A,B)) = k5_xboole_0(A,B)) # label(t101_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 142 (all A all B all C all D (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k3_xboole_0(A,C),k3_xboole_0(B,D)))) # label(t27_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 143 (all A all B all C all D k2_xboole_0(A,k2_xboole_0(k2_xboole_0(B,C),D)) = k2_xboole_0(k2_xboole_0(k2_xboole_0(A,B),C),D)) # label(t113_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 144 (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]. 28.04/27.68 145 (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]. 28.04/27.68 146 (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]. 28.04/27.68 147 (all A all B (-v1_xboole_0(B) -> -(r1_tarski(B,A) & r1_xboole_0(B,A)))) # label(t69_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 148 (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]. 28.04/27.68 149 (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]. 28.04/27.68 150 (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]. 28.04/27.68 151 (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]. 28.04/27.68 152 (all A all B r1_tarski(k4_xboole_0(A,B),A)) # label(t36_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 153 (all A all B all C -(-r1_xboole_0(A,B) & r1_xboole_0(A,k3_xboole_0(B,C)) & r1_tarski(A,C))) # label(t77_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 154 (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]. 28.04/27.68 155 (all A all B k2_xboole_0(A,k3_xboole_0(A,B)) = A) # label(t22_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 156 (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]. 28.04/27.68 157 (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]. 28.04/27.68 158 (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]. 28.04/27.68 159 (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]. 28.04/27.68 160 (all A all B all C (r1_tarski(A,B) & r1_tarski(C,B) & (all D (r1_tarski(C,D) & r1_tarski(A,D) -> r1_tarski(B,D))) -> B = k2_xboole_0(A,C))) # label(t14_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 161 (all A r1_xboole_0(A,k1_xboole_0)) # label(t65_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 162 (all A -r2_xboole_0(A,k1_xboole_0)) # label(t62_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 163 (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]. 28.04/27.68 164 (all A all B A = k3_xboole_0(A,k2_xboole_0(A,B))) # label(t21_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 165 (all A all B (-(-r2_xboole_0(A,B) & -r2_xboole_0(B,A) & A != B) <-> r3_xboole_0(A,B))) # label(t104_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 166 (all A all B k2_xboole_0(A,B) = k5_xboole_0(A,k4_xboole_0(B,A))) # label(t98_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 167 (all A all B all C (r1_xboole_0(A,C) & r1_tarski(A,B) -> r1_tarski(A,k4_xboole_0(B,C)))) # label(t86_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 168 (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]. 28.04/27.68 169 (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]. 28.04/27.68 170 (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]. 28.04/27.68 171 (all A all B r1_xboole_0(k4_xboole_0(A,B),B)) # label(t79_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 172 (all A all B all C -(-r1_xboole_0(A,B) & r1_xboole_0(A,C) & r1_xboole_0(A,k4_xboole_0(B,C)))) # label(t84_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 173 (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]. 28.04/27.68 174 (all A all B all C k2_xboole_0(A,k3_xboole_0(B,C)) = k3_xboole_0(k2_xboole_0(A,B),k2_xboole_0(A,C))) # label(t24_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 175 (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]. 28.04/27.68 176 (all A (A != k1_xboole_0 -> r2_xboole_0(k1_xboole_0,A))) # label(t61_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 177 (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]. 28.04/27.68 178 (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]. 28.04/27.68 179 (all A all B (r1_tarski(A,B) -> A = k3_xboole_0(A,B))) # label(t28_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 180 (all A all B all C ((all D (r1_tarski(D,B) & r1_tarski(D,C) -> r1_tarski(D,A))) & r1_tarski(A,C) & r1_tarski(A,B) -> k3_xboole_0(B,C) = A)) # label(t20_xboole_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 181 (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]. 28.04/27.68 182 (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]. 28.04/27.68 183 (all A all B all C all D (k2_zfmisc_1(C,D) = k2_zfmisc_1(A,B) -> A = k1_xboole_0 | k1_xboole_0 = B | B = D & C = A)) # label(t134_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 184 (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]. 28.04/27.68 185 (all A all B (k4_xboole_0(k1_tarski(A),B) = k1_xboole_0 | k1_tarski(A) = k4_xboole_0(k1_tarski(A),B))) # label(t69_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 186 (all A all B (r1_tarski(k1_tarski(A),k1_tarski(B)) -> A = B)) # label(t24_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 187 (all A all B k2_zfmisc_1(k1_tarski(A),k1_tarski(B)) = k1_tarski(k4_tarski(A,B))) # label(t35_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 188 $T # label(t4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 189 (all A all B all C all D k2_xboole_0(k2_zfmisc_1(k4_xboole_0(A,C),B),k2_zfmisc_1(A,k4_xboole_0(B,D))) = k4_xboole_0(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D))) # label(t126_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 190 (all A all B -((all C -(B != C & r2_hidden(C,A))) & k1_xboole_0 != A & A != k1_tarski(B))) # label(t41_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 191 $T # label(t71_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 192 $T # label(t85_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 193 (all A all B (A = k1_tarski(B) | k1_xboole_0 = A <-> r1_tarski(A,k1_tarski(B)))) # label(t39_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 194 (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]. 28.04/27.68 195 $T # label(t76_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 196 (all A all B all C -((all D all E k4_tarski(D,E) != A) & r2_hidden(A,k2_zfmisc_1(B,C)))) # label(t102_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 197 (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]. 28.04/27.68 198 (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]. 28.04/27.68 199 (all A r1_tarski(A,k1_zfmisc_1(k3_tarski(A)))) # label(t100_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 200 (all A all B -v1_xboole_0(k4_tarski(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 201 (all A k3_tarski(k1_zfmisc_1(A)) = A) # label(t99_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 202 (all A all B (k2_zfmisc_1(B,B) = k2_zfmisc_1(A,A) -> A = B)) # label(t115_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 203 $T # label(dt_k4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 204 $T # label(t61_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 205 (all A all B all C -(k2_tarski(A,B) != k4_xboole_0(k2_tarski(A,B),C) & k1_tarski(B) != k4_xboole_0(k2_tarski(A,B),C) & k4_xboole_0(k2_tarski(A,B),C) != k1_tarski(A) & k1_xboole_0 != k4_xboole_0(k2_tarski(A,B),C))) # label(t74_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 206 (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]. 28.04/27.68 207 (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]. 28.04/27.68 208 (all A all B r1_tarski(k1_tarski(A),k2_tarski(A,B))) # label(t12_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 209 (all A all B all C (k2_tarski(B,C) = k1_tarski(A) -> C = B)) # label(t9_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 210 (all A all B all C -(-r2_hidden(A,B) & -r2_hidden(C,B) & -r1_xboole_0(k2_tarski(A,C),B))) # label(t57_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 211 $T # label(t89_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 212 (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]. 28.04/27.68 213 (all A all B (r2_hidden(A,B) -> r1_tarski(A,k3_tarski(B)))) # label(t92_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 214 $T # label(t3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 215 (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]. 28.04/27.68 216 (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]. 28.04/27.68 217 (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]. 28.04/27.68 218 $T # label(t5_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 219 (all A all B all C -(r1_tarski(k1_tarski(A),k2_tarski(B,C)) & C != A & A != B)) # label(t25_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 220 (all A all B all C all D (r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D)) <-> r2_hidden(A,C) & r2_hidden(B,D))) # label(t106_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 221 (all A all B all C (k2_tarski(B,C) = k1_tarski(A) -> A = B)) # label(t8_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 222 (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]. 28.04/27.68 223 (all A all B all C (r1_tarski(A,k2_tarski(B,C)) <-> -(A != k1_xboole_0 & A != k2_tarski(B,C) & A != k1_tarski(C) & A != k1_tarski(B)))) # label(t42_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 224 (all A all B k4_xboole_0(k1_tarski(A),k2_tarski(A,B)) = k1_xboole_0) # label(t22_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 225 (all A all B all C (k2_zfmisc_1(C,k3_xboole_0(A,B)) = k3_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) & k2_zfmisc_1(k3_xboole_0(A,B),C) = k3_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)))) # label(t122_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 226 $T # label(t77_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 227 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 228 (all A all B all C -(B != C & B != k1_xboole_0 & k1_xboole_0 != C & k1_tarski(A) = k2_xboole_0(B,C))) # label(t44_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 229 (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]. 28.04/27.68 230 (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]. 28.04/27.68 231 $T # label(t78_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 232 (all A all B k3_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B)) = k1_zfmisc_1(k3_xboole_0(A,B))) # label(t83_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 233 (all A all B ((all C all D (r2_hidden(k4_tarski(C,D),B) <-> r2_hidden(k4_tarski(C,D),A))) & (all C -(r2_hidden(C,B) & (all D all E k4_tarski(D,E) != C))) & (all C -((all D all E C != k4_tarski(D,E)) & r2_hidden(C,A))) -> A = B)) # label(t112_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 234 (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]. 28.04/27.68 235 $T # label(t15_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 236 $T # label(t7_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 237 (all A all B all C -(-r1_tarski(B,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))) & k1_xboole_0 != A)) # label(t117_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 238 (all A all B all C (r2_hidden(A,C) & r2_hidden(B,C) <-> r1_tarski(k2_tarski(A,B),C))) # label(t38_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 239 (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]. 28.04/27.68 240 (all A all B all C all D (r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,k1_tarski(D))) <-> r2_hidden(A,C) & B = D)) # label(t129_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 241 (all A all B all C all D (r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) -> r1_tarski(A,C) & r1_tarski(B,D) | k2_zfmisc_1(A,B) = k1_xboole_0)) # label(t138_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 242 (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]. 28.04/27.68 243 (all A all B (k4_xboole_0(k1_tarski(A),B) = k1_xboole_0 <-> r2_hidden(A,B))) # label(t68_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 244 (all A A = k3_tarski(k1_tarski(A))) # label(t31_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 245 (all A all B all C all D all E -((all F all G -(k4_tarski(F,G) = A & r2_hidden(G,k3_xboole_0(C,E)) & r2_hidden(F,k3_xboole_0(B,D)))) & r2_hidden(A,k3_xboole_0(k2_zfmisc_1(B,C),k2_zfmisc_1(D,E))))) # label(t104_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 246 (all A all B all C all D -(C != A & A != D & k2_tarski(C,D) = k2_tarski(A,B))) # label(t10_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 247 (all A all B (r1_tarski(k1_tarski(A),k1_tarski(B)) -> A = B)) # label(t6_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 248 (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]. 28.04/27.68 249 (all A all B all C -(-(k1_xboole_0 = C & k1_tarski(A) = B) & -(k1_tarski(A) = C & k1_xboole_0 = B) & -(k1_tarski(A) = B & C = k1_tarski(A)) & k2_xboole_0(B,C) = k1_tarski(A))) # label(t43_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 250 (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]. 28.04/27.68 251 (all A (-v1_xboole_0(A) -> (all B all C all D (r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) | r1_tarski(k2_zfmisc_1(B,A),k2_zfmisc_1(D,C)) -> r1_tarski(B,D))))) # label(t139_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 252 $T # label(t90_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 253 (all A all B ((all C all D (r2_hidden(k4_tarski(C,D),A) -> r2_hidden(k4_tarski(C,D),B))) & (all C -(r2_hidden(C,A) & (all D all E C != k4_tarski(D,E)))) -> r1_tarski(A,B))) # label(t111_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 254 (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]. 28.04/27.68 255 (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]. 28.04/27.68 256 (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]. 28.04/27.68 257 (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]. 28.04/27.68 258 (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]. 28.04/27.68 259 (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]. 28.04/27.68 260 (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]. 28.04/27.68 261 (all A all B (k2_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_tarski(A) -> A = B)) # label(t13_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 262 (all A all B (B != A -> k4_xboole_0(k2_tarski(A,B),k1_tarski(B)) = k1_tarski(A))) # label(t23_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 263 (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]. 28.04/27.68 264 (all A all B all C all D (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)))) # label(t119_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 265 (all A all B all C all D (A != B -> r1_xboole_0(k2_zfmisc_1(C,k1_tarski(A)),k2_zfmisc_1(D,k1_tarski(B))) & r1_xboole_0(k2_zfmisc_1(k1_tarski(A),C),k2_zfmisc_1(k1_tarski(B),D)))) # label(t131_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 266 (all A all B all C (k4_xboole_0(A,k2_tarski(B,C)) = k1_xboole_0 <-> -(k2_tarski(B,C) != A & A != k1_tarski(C) & A != k1_tarski(B) & k1_xboole_0 != A))) # label(t75_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 267 $T # label(t133_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 268 (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]. 28.04/27.68 269 (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]. 28.04/27.68 270 (all A all B (k2_zfmisc_1(A,B) = k2_zfmisc_1(B,A) -> k1_xboole_0 = B | A = B | k1_xboole_0 = A)) # label(t114_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 271 (all A all B all C all D (D = B & C = A <-> r2_hidden(k4_tarski(A,B),k2_zfmisc_1(k1_tarski(C),k1_tarski(D))))) # label(t34_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 272 (all A all B all C (k2_zfmisc_1(k1_tarski(A),k2_tarski(B,C)) = k2_tarski(k4_tarski(A,B),k4_tarski(A,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]. 28.04/27.68 273 (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]. 28.04/27.68 274 (all A all B (r1_tarski(A,k2_zfmisc_1(B,A)) | r1_tarski(A,k2_zfmisc_1(A,B)) -> k1_xboole_0 = A)) # label(t135_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.68 275 (all A all B all C (-r2_hidden(B,C) & -r2_hidden(A,C) <-> k2_tarski(A,B) = k4_xboole_0(k2_tarski(A,B),C))) # label(t72_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 276 (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]. 28.04/27.69 277 (all A all B (k1_tarski(B) = k3_xboole_0(A,k1_tarski(B)) -> r2_hidden(B,A))) # label(t51_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 278 $T # label(t91_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 279 (all A all B (k4_xboole_0(A,k1_tarski(B)) = A <-> -r2_hidden(B,A))) # label(t65_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 280 (all A all B all C (k3_xboole_0(k2_tarski(A,B),C) = k2_tarski(A,B) -> r2_hidden(A,C))) # label(t63_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 281 (all A all B all C all D (r1_xboole_0(A,B) | r1_xboole_0(C,D) -> r1_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)))) # label(t127_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 282 (all A all B all C all D -(A != C & A != D & r1_tarski(k2_tarski(A,B),k2_tarski(C,D)))) # label(t28_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 283 (all A all B (k1_zfmisc_1(A) = B <-> (all C (r1_tarski(C,A) <-> r2_hidden(C,B))))) # label(d1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 284 (all A all B all C all D all E all F (r1_tarski(A,k2_zfmisc_1(B,C)) & (all G all H (r2_hidden(k4_tarski(G,H),A) <-> r2_hidden(k4_tarski(G,H),D))) & r1_tarski(D,k2_zfmisc_1(E,F)) -> D = A)) # label(t110_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 285 (all A (r1_tarski(A,k2_zfmisc_1(A,A)) -> A = k1_xboole_0)) # label(t116_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 286 (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]. 28.04/27.69 287 (all A all B (r1_tarski(k1_tarski(A),B) <-> r2_hidden(A,B))) # label(t37_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 288 (all A r1_tarski(k1_tarski(A),k1_zfmisc_1(A))) # label(t80_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 289 (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]. 28.04/27.69 290 (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]. 28.04/27.69 291 (all A all B all C (r2_hidden(A,B) -> r2_hidden(C,B) & A != C | k1_tarski(A) = k3_xboole_0(k2_tarski(A,C),B))) # label(t60_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 292 (all A all B all C all D k2_zfmisc_1(k2_xboole_0(A,B),k2_xboole_0(C,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))) # label(t121_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 293 (all A all B all C (r2_hidden(A,B) & A != C <-> r2_hidden(A,k4_xboole_0(B,k1_tarski(C))))) # label(t64_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 294 $T # label(t62_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 295 (all A all B -(k1_xboole_0 = k4_xboole_0(A,k1_tarski(B)) & A != k1_xboole_0 & A != k1_tarski(B))) # label(t66_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 296 (all A all B (k1_xboole_0 = k4_xboole_0(k1_tarski(A),k1_tarski(B)) -> A = B)) # label(t21_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 297 (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]. 28.04/27.69 298 (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]. 28.04/27.69 299 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 300 (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]. 28.04/27.69 301 $T # label(t11_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 302 (all A all B (A != B <-> k4_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_tarski(A))) # label(t20_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 303 $T # label(t88_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 304 (all A all B all C all D -(r2_hidden(D,A) & (all E all F -(r2_hidden(E,B) & D = k4_tarski(E,F) & r2_hidden(F,C))) & r1_tarski(A,k2_zfmisc_1(B,C)))) # label(t103_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 305 (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]. 28.04/27.69 306 (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]. 28.04/27.69 307 (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]. 28.04/27.69 308 (all A exists B ((all C -(-r2_tarski(C,B) & -r2_hidden(C,B) & r1_tarski(C,B))) & (all C (r2_hidden(C,B) -> r2_hidden(k1_zfmisc_1(C),B))) & (all C all D (r1_tarski(D,C) & r2_hidden(C,B) -> r2_hidden(D,B))) & r2_hidden(A,B))) # label(t136_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 309 (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]. 28.04/27.69 310 (all A all B all C all D ((all E all F (r2_hidden(k4_tarski(E,F),k2_zfmisc_1(A,B)) <-> r2_hidden(k4_tarski(E,F),k2_zfmisc_1(C,D)))) -> k2_zfmisc_1(C,D) = k2_zfmisc_1(A,B))) # label(t108_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 311 (all A all B all C ((B = A | r2_hidden(B,C)) & -r2_hidden(A,C) <-> k1_tarski(A) = k4_xboole_0(k2_tarski(A,B),C))) # label(t70_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 312 (all A all B all C (k2_zfmisc_1(k2_xboole_0(A,B),C) = k2_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)) & k2_zfmisc_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)))) # label(t120_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 313 (all A all B k3_tarski(k2_tarski(k1_tarski(A),k1_tarski(B))) = k2_tarski(A,B)) # label(t32_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 314 (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]. 28.04/27.69 315 (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]. 28.04/27.69 316 (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]. 28.04/27.69 317 (all A k1_zfmisc_1(k1_tarski(A)) = k2_tarski(k1_xboole_0,k1_tarski(A))) # label(t30_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 318 (all A all B (A != k1_xboole_0 -> k1_xboole_0 != k2_zfmisc_1(k1_tarski(B),A) & k1_xboole_0 != k2_zfmisc_1(A,k1_tarski(B)))) # label(t130_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 319 (all A all B all C all D (r2_hidden(k4_tarski(A,B),k2_zfmisc_1(k1_tarski(C),D)) <-> A = C & r2_hidden(B,D))) # label(t128_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 320 (all A all B k1_xboole_0 != k2_xboole_0(k1_tarski(A),B)) # label(t49_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 321 (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]. 28.04/27.69 322 (all A all B -(A = B & r1_xboole_0(k1_tarski(A),k1_tarski(B)))) # label(t16_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 323 (all A all B all C all D (k4_tarski(C,D) = k4_tarski(A,B) -> A = C & D = B)) # label(t33_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 324 $T # label(dt_k3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 325 (all A all B all C (k2_zfmisc_1(A,B) = C <-> (all D (r2_hidden(D,C) <-> (exists E exists F (r2_hidden(E,A) & k4_tarski(E,F) = D & r2_hidden(F,B))))))) # label(d2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 326 $T # label(t87_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 327 (all A all B (k4_xboole_0(k1_tarski(A),B) = k1_tarski(A) <-> -r2_hidden(A,B))) # label(t67_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 328 (all A all B (r2_hidden(A,B) -> B = k2_xboole_0(k1_tarski(A),B))) # label(t46_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 329 (all A all B (k2_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B)) = k1_zfmisc_1(k2_xboole_0(A,B)) -> r3_xboole_0(A,B))) # label(t82_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 330 (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]. 28.04/27.69 331 $T # label(t1_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 332 (all A all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(A) -> (all C (m2_subset_1(C,A,B) -> m1_subset_1(C,A))))) # label(dt_m2_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 333 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k5_subset_1(A,B,C) = k5_subset_1(A,C,B))) # label(commutativity_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 334 $T # label(t13_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 335 (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]. 28.04/27.69 336 (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]. 28.04/27.69 337 (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]. 28.04/27.69 338 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,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]. 28.04/27.69 339 (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]. 28.04/27.69 340 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r1_tarski(B,C) & r1_xboole_0(D,C) -> r1_tarski(B,k3_subset_1(A,D))))))))) # label(t47_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 341 $T # label(t3_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 342 (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]. 28.04/27.69 343 (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]. 28.04/27.69 344 $T # label(t6_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 345 $T # label(t14_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 346 (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]. 28.04/27.69 347 (all A (A != k1_xboole_0 -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,A) -> (-r2_hidden(C,B) -> r2_hidden(C,k3_subset_1(A,B))))))))) # label(t50_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 348 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,C) | r2_hidden(E,D) <-> r2_hidden(E,B)))) -> B = k4_subset_1(A,C,D)))))))) # label(t15_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 349 (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,k3_subset_1(A,C)) <-> r1_tarski(B,C)))))) # label(t44_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 350 $T # label(t9_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 351 $T # label(t27_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 352 (all A (m1_subset_1(A,f1_s4_subset_1) -> (r2_hidden(A,f3_s4_subset_1) <-> p1_s4_subset_1(A)))) & (all A (m1_subset_1(A,f1_s4_subset_1) -> (p1_s4_subset_1(A) <-> r2_hidden(A,f2_s4_subset_1)))) -> f2_s4_subset_1 = f3_s4_subset_1 # label(s4_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 353 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> (r2_subset_1(A,B) <-> r1_xboole_0(A,B)))) # label(redefinition_r2_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 354 $T # label(t11_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 355 (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]. 28.04/27.69 356 (all A m1_subset_1(k1_xboole_0,k1_zfmisc_1(A))) # label(t4_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 357 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,B) <-> r2_hidden(E,D) & r2_hidden(E,C)))) -> B = k5_subset_1(A,C,D)))))))) # label(t16_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 358 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k3_subset_1(A,k7_subset_1(A,B,C)) = k4_subset_1(A,k5_subset_1(A,B,C),k5_subset_1(A,k3_subset_1(A,B),k3_subset_1(A,C))))))) # label(t34_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 359 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k4_subset_1(A,k3_subset_1(A,B),C) = k3_subset_1(A,k6_subset_1(A,B,C)))))) # label(t33_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 360 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k4_xboole_0(B,C) = k6_subset_1(A,B,C))) # label(redefinition_k6_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 361 (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]. 28.04/27.69 362 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,C) & -r2_hidden(E,D) <-> r2_hidden(E,B)))) -> k6_subset_1(A,C,D) = B))))))) # label(t17_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 363 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,A) -> (A != k1_xboole_0 -> m1_subset_1(k4_enumset1(B,C,D,E,F,G),k1_zfmisc_1(A))))))))))))))) # label(t60_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 364 (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]. 28.04/27.69 365 (all A k1_xboole_0 = k1_subset_1(A)) # label(d3_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 366 (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]. 28.04/27.69 367 (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_tarski(k3_subset_1(A,C),k3_subset_1(A,B))))))) # label(t31_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 368 (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]. 28.04/27.69 369 (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]. 28.04/27.69 370 (all A all B ((v1_xboole_0(A) -> (m1_subset_1(B,A) <-> v1_xboole_0(B))) & (-v1_xboole_0(A) -> (m1_subset_1(B,A) <-> r2_hidden(B,A))))) # label(d2_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 371 (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]. 28.04/27.69 372 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (r1_tarski(k3_subset_1(A,B),B) <-> k2_subset_1(A) = B))) # label(t39_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 373 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,A) -> (k1_xboole_0 != A -> m1_subset_1(k5_enumset1(B,C,D,E,F,G,H),k1_zfmisc_1(A))))))))))))))))) # label(t61_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 374 (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,k5_subset_1(A,B,C)) = k4_subset_1(A,k3_subset_1(A,B),k3_subset_1(A,C)))))) # label(t30_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 375 (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]. 28.04/27.69 376 (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]. 28.04/27.69 377 $T # label(t2_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 378 (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]. 28.04/27.69 379 (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]. 28.04/27.69 380 $T # label(t37_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 381 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> k4_subset_1(A,B,B) = B)) # label(idempotence_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 382 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 383 (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]. 28.04/27.69 384 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> -(r2_hidden(D,B) <-> r2_hidden(D,C)))) -> B = k3_subset_1(A,C)))))) # label(t53_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 385 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> k5_subset_1(A,B,C) = k3_xboole_0(B,C))) # label(redefinition_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 386 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> -(k1_xboole_0 != B & (all C (m1_subset_1(C,A) -> -r2_hidden(C,B)))))) # label(t10_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 387 $T # label(d1_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 388 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k3_subset_1(A,B) = k4_xboole_0(A,B))) # label(d5_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 389 (all A all B all C (-v1_xboole_0(A) & -v1_xboole_0(C) & -v1_xboole_0(B) -> -v1_xboole_0(k3_zfmisc_1(A,B,C)))) # label(fc5_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 390 (all A m1_subset_1(k8_subset_1(A),A)) # label(dt_k8_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 391 (all A k2_subset_1(A) = k3_subset_1(A,k1_subset_1(A))) # label(t22_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 392 (all A -v1_xboole_0(k1_zfmisc_1(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 393 (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]. 28.04/27.69 394 $T # label(t19_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 395 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) -> -(r2_hidden(B,C) & r2_hidden(B,k3_subset_1(A,C))))) # label(t54_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 396 (exists A ((all B (m1_subset_1(B,f1_s3_subset_1) -> (r2_hidden(B,A) <-> p1_s3_subset_1(B)))) & m1_subset_1(A,k1_zfmisc_1(f1_s3_subset_1)))) # label(s3_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 397 (all A k3_subset_1(A,k2_subset_1(A)) = k1_subset_1(A)) # label(t21_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 398 $T # label(t20_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 399 (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]. 28.04/27.69 400 (all A (v1_xboole_0(k1_subset_1(A)) & m1_subset_1(k1_subset_1(A),k1_zfmisc_1(A)))) # label(dt_k1_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 401 (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]. 28.04/27.69 402 (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]. 28.04/27.69 403 (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]. 28.04/27.69 404 $T # label(t45_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 405 (all A all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(A) -> (exists C m2_subset_1(C,A,B)))) # label(existence_m2_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 406 (all A exists B m1_subset_1(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 407 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> B = k5_subset_1(A,B,B))) # label(idempotence_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 408 (exists A ((all B (r2_hidden(B,A) <-> p1_s1_subset_1(B) & r2_hidden(B,f1_s1_subset_1))) & m1_subset_1(A,k1_zfmisc_1(f1_s1_subset_1)))) # label(s1_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 409 $T # label(t5_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 410 (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]. 28.04/27.69 411 (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]. 28.04/27.69 412 (all A k2_subset_1(A) = A) # label(d4_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 413 $T # label(t12_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.69 414 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_xboole_0(B,C) & r1_xboole_0(k3_subset_1(A,B),k3_subset_1(A,C)) -> k3_subset_1(A,C) = B))))) # label(t46_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 415 (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]. 28.04/27.70 416 (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]. 28.04/27.70 417 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k5_subset_1(A,B,k3_subset_1(A,C)) = k6_subset_1(A,B,C))))) # label(t32_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 418 (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]. 28.04/27.70 419 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> (r1_subset_1(A,B) <-> r1_xboole_0(A,B)))) # label(redefinition_r1_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 420 $T # label(t24_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 421 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> m1_subset_1(k7_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k7_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 422 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> (r2_hidden(D,C) <-> r2_hidden(D,B)))) -> B = C))))) # label(t8_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 423 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k3_subset_1(A,k3_subset_1(A,B)) = B)) # label(involutiveness_k3_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 424 (all A (-$T -> (all B (m1_subset_1(B,A) -> k8_subset_1(A) = B)))) # label(d6_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 425 (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]. 28.04/27.70 426 (all A all B all C all D (-v1_xboole_0(D) & -v1_xboole_0(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> -v1_xboole_0(k4_zfmisc_1(A,B,C,D)))) # label(fc6_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 427 (all A exists B (v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 428 (all A m1_subset_1(k2_subset_1(A),k1_zfmisc_1(A))) # label(dt_k2_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 429 (all A -v1_xboole_0(k1_tarski(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 430 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (k1_xboole_0 != A -> m1_subset_1(k2_enumset1(B,C,D,E),k1_zfmisc_1(A))))))))))) # label(t58_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 431 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(B,k3_subset_1(A,C)) <-> r1_xboole_0(B,C)))))) # label(t43_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 432 (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]. 28.04/27.70 433 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (k1_xboole_0 != A -> m1_subset_1(k1_enumset1(B,C,D),k1_zfmisc_1(A))))))))) # label(t57_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 434 (all A (-v1_xboole_0(A) -> (exists B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 435 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> (r2_hidden(D,C) <-> -r2_hidden(D,B)))) -> k3_subset_1(A,C) = B))))) # label(t52_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 436 (all A all B -v1_xboole_0(k2_tarski(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 437 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (k1_subset_1(A) = B <-> r1_tarski(B,k3_subset_1(A,B))))) # label(t38_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 438 $T # label(t23_subset_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 439 (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]. 28.04/27.70 440 (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]. 28.04/27.70 441 (all A all B ((all C (r2_hidden(C,A) -> r1_tarski(B,C))) -> r1_tarski(B,k1_setfam_1(A)) | A = k1_xboole_0)) # label(t6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 442 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r2_hidden(B,A) -> (r2_hidden(B,k8_setfam_1(A,C)) <-> (all D (r2_hidden(D,C) -> r2_hidden(B,D))))))) # label(t58_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 443 $T # label(t15_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 444 (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]. 28.04/27.70 445 (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]. 28.04/27.70 446 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> ((all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(D,B) <-> r2_hidden(D,C)))) -> B = C))))) # label(t44_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 447 (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]. 28.04/27.70 448 (all A all B r1_setfam_1(A,A)) # label(reflexivity_r1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 449 (all A all B all C (C = k2_setfam_1(A,B) <-> (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]. 28.04/27.70 450 (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]. 28.04/27.70 451 $T # label(t26_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 452 $T # label(t13_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 453 $T # label(t14_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 454 (all A all B all C (r1_tarski(A,C) & r2_hidden(A,B) -> r1_tarski(k1_setfam_1(B),C))) # label(t8_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 455 (all A all B all C (r1_setfam_1(C,k2_tarski(A,B)) -> (all D -(r2_hidden(D,C) & -r1_tarski(D,A) & -r1_tarski(D,B))))) # label(t25_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 456 (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]. 28.04/27.70 457 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> -(k1_xboole_0 != B & k7_setfam_1(A,B) = k1_xboole_0))) # label(t46_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 458 (all A all B all C (k3_setfam_1(A,B) = C <-> (all D (r2_hidden(D,C) <-> (exists E exists F (r2_hidden(F,B) & D = k3_xboole_0(E,F) & r2_hidden(E,A))))))) # label(d5_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 459 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (B = k1_xboole_0 -> A = k8_setfam_1(A,B)) & (k1_xboole_0 != B -> k8_setfam_1(A,B) = k6_setfam_1(A,B)))) # label(d10_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 460 (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]. 28.04/27.70 461 (all A (-r2_hidden(k1_xboole_0,A) <-> v1_setfam_1(A))) # label(d9_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 462 $T # label(t32_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 463 (all A all B -(B != k1_xboole_0 & -r1_tarski(k2_xboole_0(k1_setfam_1(A),k1_setfam_1(B)),k1_setfam_1(k2_setfam_1(A,B))) & k1_xboole_0 != A)) # label(t40_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 464 $T # label(t28_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 465 (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]. 28.04/27.70 466 $T # label(dt_k3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 467 (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]. 28.04/27.70 468 (exists A -v2_setfam_1(A)) # label(rc2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 469 (all A all B -(k1_setfam_1(k2_xboole_0(A,B)) != k3_xboole_0(k1_setfam_1(A),k1_setfam_1(B)) & k1_xboole_0 != B & k1_xboole_0 != A)) # label(t10_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 470 (all A all B (r2_setfam_1(B,A) -> k1_xboole_0 = A | r1_tarski(k1_setfam_1(B),k1_setfam_1(A)))) # label(t19_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 471 (all A all B ((A = k1_xboole_0 -> (B = k1_xboole_0 <-> k1_setfam_1(A) = B)) & (A != k1_xboole_0 -> ((all C ((all D (r2_hidden(D,A) -> r2_hidden(C,D))) <-> r2_hidden(C,B))) <-> B = k1_setfam_1(A))))) # label(d1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 472 (all A all B (B != k1_xboole_0 -> k2_xboole_0(A,k1_setfam_1(B)) = k1_setfam_1(k2_setfam_1(k1_tarski(A),B)))) # label(t35_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 473 (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]. 28.04/27.70 474 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> -v1_xboole_0(k2_tarski(A,B)) & v1_setfam_1(k2_tarski(A,B)))) # label(fc3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 475 $T # label(t22_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 476 $T # label(t43_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 477 (all A (-v2_setfam_1(A) -> -v1_xboole_0(A))) # label(cc2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 478 (all A all B (B != k1_xboole_0 -> 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]. 28.04/27.70 479 (all A all B (v1_setfam_1(B) & v1_setfam_1(A) -> v1_setfam_1(k2_xboole_0(A,B)))) # label(fc4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 480 (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]. 28.04/27.70 481 (all A all B all C ((all D (r2_hidden(D,C) <-> (exists E exists F (r2_hidden(F,B) & D = k4_xboole_0(E,F) & r2_hidden(E,A))))) <-> C = k4_setfam_1(A,B))) # label(d6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 482 (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]. 28.04/27.70 483 (all A all B (k1_xboole_0 != B -> k4_xboole_0(A,k1_setfam_1(B)) = k3_tarski(k4_setfam_1(k1_tarski(A),B)))) # label(t38_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 484 (all A all B all C (r2_hidden(C,A) & r1_tarski(k3_tarski(A),B) -> r1_tarski(C,B))) # label(t56_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 485 $T # label(t45_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 486 $T # label(t33_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 487 (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]. 28.04/27.70 488 $T # label(t27_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 489 $T # label(dt_k4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 490 $T # label(t16_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 491 (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]. 28.04/27.70 492 (all A all B r2_setfam_1(B,B)) # label(reflexivity_r2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 493 (all A r1_setfam_1(k3_setfam_1(A,A),A)) # label(t30_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 494 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k7_setfam_1(A,C) = k7_setfam_1(A,B) -> B = C))))) # label(t53_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 495 $T # label(dt_k1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 496 (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]. 28.04/27.70 497 (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),k5_setfam_1(A,B)) = k6_setfam_1(A,k7_setfam_1(A,B))))) # label(t47_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 498 (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]. 28.04/27.70 499 (all A all B ((all C -(r2_hidden(C,A) & (all D -(r2_hidden(D,B) & r1_tarski(C,D))))) <-> r1_setfam_1(A,B))) # label(d2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 500 (all A ((all B (-v1_xboole_0(B) -> -r2_hidden(B,A))) <-> v2_setfam_1(A))) # label(d11_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 501 $T # label(t1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 502 (all A r1_setfam_1(A,k2_setfam_1(A,A))) # label(t29_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 503 (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]. 28.04/27.70 504 (all A (r2_hidden(k1_xboole_0,A) -> k1_xboole_0 = k1_setfam_1(A))) # label(t5_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 505 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> B = k7_setfam_1(A,k7_setfam_1(A,B)))) # label(involutiveness_k7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 506 (all A (r1_setfam_1(A,k1_xboole_0) -> k1_xboole_0 = A)) # label(t21_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 507 (all A all B (r1_tarski(A,B) -> r1_setfam_1(A,B))) # label(t17_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 508 (all A all B k3_tarski(k3_setfam_1(k1_tarski(A),B)) = k3_xboole_0(A,k3_tarski(B))) # label(t36_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 509 $T # label(d7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 510 (all A r1_setfam_1(k4_setfam_1(A,A),A)) # label(t31_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 511 (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)) = k6_subset_1(A,k2_subset_1(A),k6_setfam_1(A,B))))) # label(t48_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 512 $T # label(t50_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 513 (all A all B k3_xboole_0(k3_tarski(A),k3_tarski(B)) = k3_tarski(k3_setfam_1(A,B))) # label(t39_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 514 (all A all B k1_setfam_1(k2_tarski(A,B)) = k3_xboole_0(A,B)) # label(t12_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 515 (all A all B all C (r1_setfam_1(A,B) & r1_setfam_1(B,C) -> r1_setfam_1(A,C))) # label(t23_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 516 (all A all B ((all C -((all D -(r2_hidden(D,A) & r1_tarski(D,C))) & r2_hidden(C,B))) <-> r2_setfam_1(A,B))) # label(d3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 517 $T # label(t42_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 518 (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]. 28.04/27.70 519 (all A r1_setfam_1(k1_xboole_0,A)) # label(t20_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 520 (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]. 28.04/27.70 521 (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]. 28.04/27.70 522 (all A all B all C (r1_xboole_0(A,C) & r2_hidden(A,B) -> r1_xboole_0(k1_setfam_1(B),C))) # label(t9_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 523 (all A k1_setfam_1(k1_tarski(A)) = A) # label(t11_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 524 $T # label(dt_k2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 525 (all A r1_tarski(k1_setfam_1(A),k3_tarski(A))) # label(t3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 526 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> k6_setfam_1(A,B) = k1_setfam_1(B))) # label(redefinition_k6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 527 (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]. 28.04/27.70 528 (exists A (-v1_xboole_0(A) & v1_setfam_1(A))) # label(rc1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 529 (all A (-v1_xboole_0(A) -> -v1_xboole_0(k1_tarski(A)) & v1_setfam_1(k1_tarski(A)))) # label(fc2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 530 (all A all B (r1_tarski(A,B) -> r1_tarski(k1_setfam_1(B),k1_setfam_1(A)) | A = k1_xboole_0)) # label(t7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 531 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (B = k1_tarski(A) -> k1_tarski(k1_xboole_0) = k7_setfam_1(A,B)))) # label(t55_setfam_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 532 (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]. 28.04/27.70 533 (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]. 28.04/27.70 534 (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]. 28.04/27.70 535 (all A all B (r2_hidden(A,B) -> m1_subset_1(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 536 (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]. 28.04/27.70 537 (all A all B all C -(m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) & r2_hidden(A,B))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 538 (all A all B all C (r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) -> m1_subset_1(A,C))) # label(t4_subset) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 539 $T # label(t113_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 540 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k7_relat_1(C,A),k7_relat_1(D,B))))))) # label(t106_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 541 (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]. 28.04/27.70 542 (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]. 28.04/27.70 543 (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]. 28.04/27.70 544 (all A k1_xboole_0 = k8_relat_1(A,k1_xboole_0)) # label(t138_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 545 $T # label(t61_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 546 (all A k4_relat_1(k6_relat_1(A)) = k6_relat_1(A)) # label(t72_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 547 (all A all B (v1_relat_1(B) -> k3_xboole_0(B,k2_zfmisc_1(A,k2_relat_1(B))) = k7_relat_1(B,A))) # label(t96_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 548 (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]. 28.04/27.70 549 $T # label(t63_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 550 (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]. 28.04/27.70 551 $T # label(t43_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 552 (all A (v1_relat_1(A) -> ((all B all C -r2_hidden(k4_tarski(B,C),A)) -> A = k1_xboole_0))) # label(t56_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.04/27.70 553 (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]. 28.04/27.70 554 (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]. 28.04/27.70 555 (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]. 28.04/27.70 556 (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]. 28.04/27.70 557 (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]. 28.04/27.70 558 (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]. 28.04/27.70 559 (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]. 28.04/27.70 560 (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]. 28.04/27.70 561 (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]. 28.13/27.70 562 (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]. 28.13/27.70 563 (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]. 28.13/27.70 564 $T # label(t2_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.70 565 (all A all B all C all D (v1_relat_1(D) -> (r2_hidden(k4_tarski(A,B),k5_relat_1(k6_relat_1(C),D)) <-> r2_hidden(A,C) & r2_hidden(k4_tarski(A,B),D)))) # label(t74_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.70 566 (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]. 28.13/27.70 567 (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]. 28.13/27.70 568 $T # label(t42_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.70 569 (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]. 28.13/27.70 570 (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]. 28.13/27.70 571 (all A all B (v1_relat_1(B) -> k3_xboole_0(k2_relat_1(B),A) = k2_relat_1(k8_relat_1(A,B)))) # label(t119_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.70 572 (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]. 28.13/27.70 573 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k3_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k3_relat_1(A),k3_relat_1(B)))))) # label(t33_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.70 574 (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]. 28.13/27.70 575 (all A all B all C (v1_relat_1(C) -> k7_relat_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)))) # label(t107_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.70 576 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k2_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k2_relat_1(A),k2_relat_1(B)))))) # label(t26_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.70 577 (all A (k2_relat_1(k6_relat_1(A)) = A & k1_relat_1(k6_relat_1(A)) = A)) # label(t71_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.70 578 (all A (v1_relat_1(A) -> v1_relat_1(k4_relat_1(A)))) # label(dt_k4_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.70 579 $T # label(t85_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.70 580 (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]. 28.13/27.70 581 (all A k7_relat_1(k1_xboole_0,A) = k1_xboole_0) # label(t111_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.70 582 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k7_relat_1(A,k1_relat_1(k7_relat_1(B,k1_relat_1(A)))) = k7_relat_1(A,k1_relat_1(B)))))) # label(t189_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.70 583 $T # label(t70_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.70 584 (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]. 28.13/27.70 585 (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]. 28.13/27.70 586 (all A all B (v3_relat_1(A) & v1_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]. 28.13/27.71 587 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(k7_relat_1(C,B))) <-> r2_hidden(A,k1_relat_1(C)) & r2_hidden(A,B)))) # label(t86_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 588 (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]. 28.13/27.71 589 (all A all B (v1_relat_1(B) -> r1_tarski(k5_relat_1(B,k6_relat_1(A)),B) & r1_tarski(k5_relat_1(k6_relat_1(A),B),B))) # label(t76_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 590 (all A all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> k5_relat_1(B,k6_relat_1(A)) = B))) # label(t79_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 591 (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]. 28.13/27.71 592 (exists A (v1_relat_1(A) & -v1_xboole_0(A))) # label(rc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 593 (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]. 28.13/27.71 594 (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]. 28.13/27.71 595 (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]. 28.13/27.71 596 (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]. 28.13/27.71 597 (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]. 28.13/27.71 598 (all A (v1_relat_1(A) -> k2_relat_1(A) = k9_relat_1(A,k1_relat_1(A)))) # label(t146_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 599 (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]. 28.13/27.71 600 (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]. 28.13/27.71 601 (all A (v1_relat_1(A) -> (k1_xboole_0 = k2_relat_1(A) <-> k1_relat_1(A) = k1_xboole_0))) # label(t65_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 602 (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]. 28.13/27.71 603 $T # label(t165_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 604 (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]. 28.13/27.71 605 (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]. 28.13/27.71 606 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k4_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k4_relat_1(A),k4_relat_1(B)))))) # label(t40_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 607 $T # label(t83_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 608 (exists A (v1_relat_1(A) & v3_relat_1(A))) # label(rc3_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 609 (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]. 28.13/27.71 610 (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]. 28.13/27.71 611 $T # label(t58_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 612 (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]. 28.13/27.71 613 (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]. 28.13/27.71 614 (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]. 28.13/27.71 615 $T # label(t114_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 616 (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]. 28.13/27.71 617 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k2_relat_1(k5_relat_1(A,B)) = k9_relat_1(B,k2_relat_1(A)))))) # label(t160_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 618 (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]. 28.13/27.71 619 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (C = k5_relat_1(A,B) <-> (all D all E ((exists F (r2_hidden(k4_tarski(F,E),B) & r2_hidden(k4_tarski(D,F),A))) <-> r2_hidden(k4_tarski(D,E),C)))))))))) # label(d8_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 620 (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]. 28.13/27.71 621 (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]. 28.13/27.71 622 $T # label(t141_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 623 $T # label(t12_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 624 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k7_relat_1(k5_relat_1(B,C),A) = k5_relat_1(k7_relat_1(B,A),C))))) # label(t112_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 625 (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]. 28.13/27.71 626 (all A all B (v1_relat_1(B) -> -(-v3_relat_1(k7_relat_1(B,A)) & v3_relat_1(B)))) # label(t190_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 627 $T # label(dt_k3_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 628 $T # label(t142_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 629 (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]. 28.13/27.71 630 $T # label(t84_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 631 (all A (v1_relat_1(A) -> (all B all C (k10_relat_1(A,B) = C <-> (all D (r2_hidden(D,C) <-> (exists E (r2_hidden(E,B) & r2_hidden(k4_tarski(D,E),A))))))))) # label(d14_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 632 (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]. 28.13/27.71 633 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C all D (k7_relat_1(A,D) = k7_relat_1(B,D) & r1_tarski(C,D) -> k7_relat_1(B,C) = k7_relat_1(A,C))))))) # label(t188_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 634 (all A all B (v1_relat_1(A) & v1_relat_1(B) -> v1_relat_1(k3_xboole_0(A,B)))) # label(fc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 635 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k5_relat_1(A,k5_relat_1(B,C)) = k5_relat_1(k5_relat_1(A,B),C))))))) # label(t55_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 636 (all A all B (v1_relat_1(B) -> k8_relat_1(A,B) = k8_relat_1(A,k8_relat_1(A,B)))) # label(t128_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 637 (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(k8_relat_1(A,C),k8_relat_1(B,D))))))) # label(t133_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 638 (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]. 28.13/27.71 639 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C all D (k7_relat_1(B,C) = k7_relat_1(A,C) & k7_relat_1(A,D) = k7_relat_1(B,D) -> k7_relat_1(A,k2_xboole_0(C,D)) = k7_relat_1(B,k2_xboole_0(C,D)))))))) # label(t185_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 640 (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]. 28.13/27.71 641 (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]. 28.13/27.71 642 (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]. 28.13/27.71 643 (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]. 28.13/27.71 644 (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]. 28.13/27.71 645 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (k8_relat_1(A,B) = C <-> (all D all E (r2_hidden(k4_tarski(D,E),B) & r2_hidden(E,A) <-> r2_hidden(k4_tarski(D,E),C)))))))) # label(d12_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 646 (all A (v1_relat_1(A) -> A = k5_relat_1(k6_relat_1(k1_relat_1(A)),A))) # label(t78_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 647 (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]. 28.13/27.71 648 (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]. 28.13/27.71 649 $T # label(t8_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 650 (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]. 28.13/27.71 651 $T # label(t16_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 652 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> ((all C all D (r2_hidden(k4_tarski(D,C),A) <-> r2_hidden(k4_tarski(C,D),B))) <-> k4_relat_1(A) = B))))) # label(d7_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 653 (all A (v1_relat_1(A) -> k2_relat_1(k4_relat_1(A)) = k1_relat_1(A) & k1_relat_1(k4_relat_1(A)) = k2_relat_1(A))) # label(t37_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 654 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (k1_relat_1(B) = A & r1_tarski(k2_relat_1(C),A) & k5_relat_1(C,B) = k6_relat_1(k1_relat_1(D)) & k5_relat_1(B,D) = k6_relat_1(A) -> C = D))))))) # label(t82_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 655 $T # label(t36_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 656 (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]. 28.13/27.71 657 (all A all B (v1_relat_1(B) -> (r1_tarski(k1_relat_1(B),A) -> B = k7_relat_1(B,A)))) # label(t97_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 658 (exists A (v1_xboole_0(A) & v1_relat_1(A))) # label(rc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 659 (all A all B (v1_relat_1(B) -> (r1_xboole_0(k1_relat_1(B),A) <-> k1_xboole_0 = k9_relat_1(B,A)))) # label(t151_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 660 (all A (v1_relat_1(A) -> A = k8_relat_1(k2_relat_1(A),A))) # label(t126_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 661 (all A (v1_relat_1(A) & -v1_xboole_0(A) -> -v1_xboole_0(k2_relat_1(A)))) # label(fc6_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 662 (all A (v1_relat_1(A) -> A = k4_relat_1(k4_relat_1(A)))) # label(involutiveness_k4_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 663 (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]. 28.13/27.71 664 (all A all B all C all D all E (v1_relat_1(E) -> (E = k2_tarski(k4_tarski(A,B),k4_tarski(C,D)) -> 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]. 28.13/27.71 665 (all A all B (v1_relat_1(B) & v1_relat_1(A) -> v1_relat_1(k2_xboole_0(A,B)))) # label(fc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 666 $T # label(t1_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 667 (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]. 28.13/27.71 668 (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]. 28.13/27.71 669 (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]. 28.13/27.71 670 (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]. 28.13/27.71 671 (all A v1_relat_1(k6_relat_1(A))) # label(dt_k6_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 672 (all A (v1_relat_1(A) -> k7_relat_1(A,k1_relat_1(A)) = A)) # label(t98_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 673 (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]. 28.13/27.71 674 (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]. 28.13/27.71 675 $T # label(t69_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 676 (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]. 28.13/27.71 677 (all A (v1_relat_1(A) <-> (all B -((all C all D k4_tarski(C,D) != B) & r2_hidden(B,A))))) # label(d1_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 678 (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]. 28.13/27.71 679 (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]. 28.13/27.71 680 (all A k9_relat_1(k1_xboole_0,A) = k1_xboole_0) # label(t150_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 681 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k2_xboole_0(k1_relat_1(A),k1_relat_1(B)) = k1_relat_1(k2_xboole_0(A,B)))))) # label(t13_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 682 $T # label(t59_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 683 (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]. 28.13/27.71 684 (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]. 28.13/27.71 685 $T # label(t164_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 686 (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]. 28.13/27.71 687 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k9_relat_1(C,A),k9_relat_1(D,B))))))) # label(t158_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 688 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(C,B) & r1_tarski(k1_relat_1(C),A) -> r1_tarski(C,k7_relat_1(B,A))))))) # label(t186_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 689 (all A all B (v1_relat_1(B) -> ((all C all D (r2_hidden(C,A) & C = D <-> r2_hidden(k4_tarski(C,D),B))) <-> k6_relat_1(A) = B))) # label(d10_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 690 (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]. 28.13/27.71 691 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 692 (all A all B v1_relat_1(k1_tarski(k4_tarski(A,B)))) # label(t4_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 693 (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]. 28.13/27.71 694 (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]. 28.13/27.71 695 (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]. 28.13/27.71 696 (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]. 28.13/27.71 697 (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]. 28.13/27.71 698 (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]. 28.13/27.71 699 (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]. 28.13/27.71 700 (all A (v1_xboole_0(A) -> v1_xboole_0(k2_relat_1(A)) & v1_relat_1(k2_relat_1(A)))) # label(fc8_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 701 (exists A (v1_relat_1(A) & (all B all C (p1_s1_relat_1(B,C) & r2_hidden(C,f2_s1_relat_1) & r2_hidden(B,f1_s1_relat_1) <-> r2_hidden(k4_tarski(B,C),A))))) # label(s1_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 702 (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]. 28.13/27.71 703 (all A all B (v1_relat_1(B) -> (r1_tarski(A,k2_relat_1(B)) -> A = k2_relat_1(k8_relat_1(A,B))))) # label(t120_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 704 (all A (v1_relat_1(A) -> r1_tarski(k1_relat_1(A),k3_relat_1(A)) & r1_tarski(k2_relat_1(A),k3_relat_1(A)))) # label(t29_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 705 (all A all B all C (v1_relat_1(C) -> k3_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)) = k8_relat_1(k3_xboole_0(A,B),C))) # label(t135_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 706 (all A (v1_relat_1(A) -> k1_relat_1(A) = k10_relat_1(A,k2_relat_1(A)))) # label(t169_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 707 (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]. 28.13/27.71 708 $T # label(t17_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 709 (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]. 28.13/27.71 710 (all A (v1_relat_1(A) -> k7_relat_1(A,k1_xboole_0) = k1_xboole_0)) # label(t110_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 711 (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]. 28.13/27.71 712 (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]. 28.13/27.71 713 (all A all B (v1_relat_1(B) -> -(A != k1_xboole_0 & r1_tarski(A,k2_relat_1(B)) & k10_relat_1(B,A) = k1_xboole_0))) # label(t174_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 714 (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]. 28.13/27.71 715 (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]. 28.13/27.71 716 (all A all B (v1_xboole_0(A) & v1_relat_1(B) -> 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]. 28.13/27.71 717 $T # label(t68_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 718 $T # label(t7_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 719 (all A (v1_relat_1(A) -> (all B all C (v1_relat_1(C) -> ((all D all E (r2_hidden(k4_tarski(D,E),C) <-> r2_hidden(k4_tarski(D,E),A) & r2_hidden(D,B))) <-> k7_relat_1(A,B) = C))))) # label(d11_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 720 (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]. 28.13/27.71 721 $T # label(dt_k10_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 722 (all A all B all C (v1_relat_1(C) -> k4_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)) = k8_relat_1(k4_xboole_0(A,B),C))) # label(t136_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 723 (all A (v1_relat_1(A) -> (k1_xboole_0 = k2_relat_1(A) | k1_relat_1(A) = k1_xboole_0 -> A = k1_xboole_0))) # label(t64_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 724 (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]. 28.13/27.71 725 (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]. 28.13/27.71 726 $T # label(t162_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 727 (all A (v1_relat_1(A) -> k3_relat_1(k4_relat_1(A)) = k3_relat_1(A))) # label(t38_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 728 (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]. 28.13/27.71 729 $T # label(t57_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 730 (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]. 28.13/27.71 731 (all A all B v1_relat_1(k2_zfmisc_1(A,B))) # label(t6_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.71 732 $T # label(t35_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 733 (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]. 28.13/27.72 734 (all A (v1_relat_1(A) -> (all B all C (k9_relat_1(A,B) = C <-> (all D ((exists E (r2_hidden(E,B) & r2_hidden(k4_tarski(E,D),A))) <-> r2_hidden(D,C))))))) # label(d13_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 735 (all A all B all C (v1_relat_1(C) -> k2_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)) = k9_relat_1(C,k2_xboole_0(A,B)))) # label(t153_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 736 (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(k5_relat_1(A,B)) = k1_relat_1(A)))))) # label(t46_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 737 (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]. 28.13/27.72 738 (all A all B (v1_relat_1(B) -> (r1_xboole_0(k1_relat_1(B),A) <-> k7_relat_1(B,A) = k1_xboole_0))) # label(t95_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 739 (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]. 28.13/27.72 740 (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]. 28.13/27.72 741 (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]. 28.13/27.72 742 (all A (v1_xboole_0(A) -> v1_xboole_0(k1_relat_1(A)) & v1_relat_1(k1_relat_1(A)))) # label(fc7_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 743 (all A all B (v1_relat_1(B) -> k10_relat_1(B,A) = k10_relat_1(B,k3_xboole_0(k2_relat_1(B),A)))) # label(t168_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 744 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 745 (all A all B (v1_relat_1(B) -> k5_relat_1(B,k6_relat_1(A)) = k8_relat_1(A,B))) # label(t123_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 746 (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]. 28.13/27.72 747 (all A all B all C (v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),C) -> r2_hidden(A,k3_relat_1(C)) & r2_hidden(B,k3_relat_1(C))))) # label(t30_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 748 (all A all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> B = k8_relat_1(A,B)))) # label(t125_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 749 $T # label(dt_k9_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 750 (all A (v1_xboole_0(A) -> v1_xboole_0(k4_relat_1(A)) & v1_relat_1(k4_relat_1(A)))) # label(fc11_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 751 (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]. 28.13/27.72 752 (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]. 28.13/27.72 753 (all A all B (v1_relat_1(B) & v1_xboole_0(A) -> v1_xboole_0(k5_relat_1(B,A)) & v1_relat_1(k5_relat_1(B,A)))) # label(fc10_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 754 $T # label(t11_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 755 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k10_relat_1(k5_relat_1(B,C),A) = k10_relat_1(B,k10_relat_1(C,A)))))) # label(t181_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 756 (all A all B all C (v1_relat_1(C) -> ((exists D (r2_hidden(D,k1_relat_1(C)) & r2_hidden(D,B) & r2_hidden(k4_tarski(D,A),C))) <-> r2_hidden(A,k9_relat_1(C,B))))) # label(t143_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 757 (all A (-v1_xboole_0(A) & v1_relat_1(A) -> -v1_xboole_0(k1_relat_1(A)))) # label(fc5_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 758 (all A (v1_relat_1(A) -> (all B (k1_relat_1(A) = B <-> (all C (r2_hidden(C,B) <-> (exists D r2_hidden(k4_tarski(C,D),A)))))))) # label(d4_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 759 (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]. 28.13/27.72 760 (all A all B (v1_relat_1(B) -> k9_relat_1(B,A) = k2_relat_1(k7_relat_1(B,A)))) # label(t148_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 761 (all A k10_relat_1(k1_xboole_0,A) = k1_xboole_0) # label(t172_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 762 (all A all B (v1_relat_1(B) -> -(k9_relat_1(B,A) = k1_xboole_0 & r1_tarski(A,k1_relat_1(B)) & k1_xboole_0 != A))) # label(t152_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 763 (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]. 28.13/27.72 764 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k10_relat_1(C,A),k10_relat_1(D,B))))))) # label(t180_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 765 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k9_relat_1(C,k9_relat_1(B,A)) = k9_relat_1(k5_relat_1(B,C),A))))) # label(t159_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 766 (all A (v1_xboole_0(A) -> v1_relat_1(A))) # label(cc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 767 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k3_xboole_0(k4_relat_1(A),k4_relat_1(B)) = k4_relat_1(k3_xboole_0(A,B)))))) # label(t39_relat_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 768 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k2_relat_1(B) = k1_relat_1(A) & v2_funct_1(k5_relat_1(B,A)) -> v2_funct_1(B) & v2_funct_1(A)))))) # label(t48_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 769 $T # label(d11_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 770 (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 (r2_hidden(D,k1_relat_1(A)) & r2_hidden(k1_funct_1(A,D),k1_relat_1(B)) <-> r2_hidden(D,k1_relat_1(C)))) & (all D (r2_hidden(D,k1_relat_1(C)) -> k1_funct_1(C,D) = k1_funct_1(B,k1_funct_1(A,D)))) -> k5_relat_1(A,B) = C))))))) # label(t20_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 771 $T # label(t92_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 772 $T # label(t113_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 773 $T # label(t112_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 774 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) <-> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k5_relat_1(C,A) = k5_relat_1(B,A) & k1_relat_1(C) = k1_relat_1(B) & r1_tarski(k2_relat_1(C),k1_relat_1(A)) & r1_tarski(k2_relat_1(B),k1_relat_1(A)) -> B = C)))))))) # label(t49_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 775 (all A (v1_funct_1(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(E,k1_relat_1(A)) & r2_hidden(E,B) & k1_funct_1(A,E) = D)))))))) # label(d12_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 776 (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]. 28.13/27.72 777 $T # label(t4_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 778 $T # label(t91_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 779 (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]. 28.13/27.72 780 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C all D (r2_hidden(D,k1_relat_1(B)) & r2_hidden(C,k1_relat_1(A)) -> (D = k1_funct_1(A,C) <-> k1_funct_1(B,D) = C))) & k1_relat_1(B) = k2_relat_1(A) & k2_relat_1(B) = k1_relat_1(A) & v2_funct_1(A) -> k2_funct_1(A) = B))))) # label(t60_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 781 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) & r2_hidden(A,k1_relat_1(B)) -> A = k1_funct_1(k2_funct_1(B),k1_funct_1(B,A)) & A = k1_funct_1(k5_relat_1(B,k2_funct_1(B)),A)))) # label(t56_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 782 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> k9_relat_1(B,k1_tarski(A)) = k1_tarski(k1_funct_1(B,A))))) # label(t117_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 783 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C ((-r2_hidden(B,k1_relat_1(A)) -> (C = k1_xboole_0 <-> k1_funct_1(A,B) = C)) & (r2_hidden(B,k1_relat_1(A)) -> (C = k1_funct_1(A,B) <-> r2_hidden(k4_tarski(B,C),A))))))) # label(d4_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 784 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (k6_relat_1(A) = B <-> A = k1_relat_1(B) & (all C (r2_hidden(C,A) -> C = k1_funct_1(B,C)))))) # label(t34_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 785 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B (r2_hidden(B,k1_relat_1(A)) -> v1_xboole_0(k1_funct_1(A,B)))) <-> v3_relat_1(A)))) # label(d14_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 786 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(k1_funct_1(C,A),k1_relat_1(B)) & r2_hidden(A,k1_relat_1(C)) <-> r2_hidden(A,k1_relat_1(k5_relat_1(C,B)))))))) # label(t21_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 787 $T # label(t100_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 788 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k2_funct_1(A)) & v1_relat_1(k2_funct_1(A)))) # label(dt_k2_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 789 $T # label(t69_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 790 (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]. 28.13/27.72 791 (all A k2_funct_1(k6_relat_1(A)) = k6_relat_1(A)) # label(t67_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 792 $T # label(t140_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 793 (exists A (v1_relat_1(A) & f1_s4_funct_1 = k1_relat_1(A) & (all B (m1_subset_1(B,f1_s4_funct_1) -> k1_funct_1(A,B) = f2_s4_funct_1(B))) & v1_funct_1(A))) # label(s4_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 794 (all A ((all B all C all D (r2_hidden(k4_tarski(B,C),A) & r2_hidden(k4_tarski(B,D),A) -> D = C)) <-> v1_funct_1(A))) # label(d1_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 795 (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]. 28.13/27.72 796 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,B) -> k7_relat_1(k7_relat_1(C,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]. 28.13/27.72 797 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B all C k9_relat_1(A,k3_xboole_0(B,C)) = k3_xboole_0(k9_relat_1(A,B),k9_relat_1(A,C))) -> v2_funct_1(A)))) # label(t122_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 798 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B -((all C k1_tarski(C) != k10_relat_1(A,k1_tarski(B))) & r2_hidden(B,k2_relat_1(A)))) <-> v2_funct_1(A)))) # label(t144_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 799 $T # label(t98_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 800 $T # label(t26_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 801 $T # label(t96_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 802 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(k5_relat_1(C,B))) -> k1_funct_1(B,k1_funct_1(C,A)) = k1_funct_1(k5_relat_1(C,B),A)))))) # label(t22_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 803 $T # label(t31_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 804 $T # label(t94_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 805 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B all C k9_relat_1(A,k4_xboole_0(B,C)) = k4_xboole_0(k9_relat_1(A,B),k9_relat_1(A,C))) -> v2_funct_1(A)))) # label(t124_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 806 $T # label(t115_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 807 (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]. 28.13/27.72 808 $T # label(t135_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 809 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(A) & k5_relat_1(A,B) = k6_relat_1(k1_relat_1(A)) & k2_relat_1(A) = k1_relat_1(B) -> B = k2_funct_1(A)))))) # label(t63_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 810 $T # label(t7_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 811 $T # label(t141_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 812 (all A (v1_funct_1(A) & v1_xboole_0(A) & v1_relat_1(A) -> v1_relat_1(A) & v2_funct_1(A) & v1_funct_1(A))) # label(cc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 813 $T # label(t119_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 814 (all A all B all C (r2_hidden(A,f1_s2_funct_1) & p1_s2_funct_1(A,C) & p1_s2_funct_1(A,B) -> C = B)) & (all A -((all B -p1_s2_funct_1(A,B)) & r2_hidden(A,f1_s2_funct_1))) -> (exists A (k1_relat_1(A) = f1_s2_funct_1 & (all B (r2_hidden(B,f1_s2_funct_1) -> p1_s2_funct_1(B,k1_funct_1(A,B)))) & v1_funct_1(A) & v1_relat_1(A))) # label(s2_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 815 $T # label(t93_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 816 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(B,C) = k1_funct_1(A,C))) & k1_relat_1(A) = k1_relat_1(B) -> B = A))))) # label(t9_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 817 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k7_relat_1(C,A) = B <-> (all D (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(B,D) = k1_funct_1(C,D))) & k1_relat_1(B) = k3_xboole_0(k1_relat_1(C),A)))))) # label(t68_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 818 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(C)) & k1_funct_1(C,A) = B <-> r2_hidden(k4_tarski(A,B),C)))) # label(t8_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 819 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k3_xboole_0(k1_relat_1(C),A)) -> k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B)))) # label(t71_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 820 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k3_xboole_0(k1_relat_1(C),A)) -> k1_funct_1(C,B) = k1_funct_1(k5_relat_1(k6_relat_1(A),C),B)))) # label(t38_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 821 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (A = k1_relat_1(B) & r1_tarski(k2_relat_1(C),A) & B = k5_relat_1(C,B) & v2_funct_1(B) & k1_relat_1(C) = A -> k6_relat_1(A) = C))))) # label(t50_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 822 (exists A (v1_funct_1(A) & v1_relat_1(A))) # label(rc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 823 $T # label(t104_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 824 $T # label(t136_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 825 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B r1_tarski(k10_relat_1(A,k9_relat_1(A,B)),B)) -> v2_funct_1(A)))) # label(t153_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 826 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> k3_xboole_0(k1_relat_1(B),A) = k1_relat_1(k5_relat_1(k6_relat_1(A),B)))) # label(t37_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 827 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),k1_relat_1(A)) & v2_funct_1(k5_relat_1(B,A)) -> v2_funct_1(B)))))) # label(t47_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 828 $T # label(t105_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 829 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(A) & v2_funct_1(B) -> 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]. 28.13/27.72 830 (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]. 28.13/27.72 831 $T # label(t101_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 832 $T # label(t127_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 833 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(A) & k1_relat_1(A) = k2_relat_1(B) & k5_relat_1(B,A) = k6_relat_1(k2_relat_1(A)) -> B = k2_funct_1(A)))))) # label(t64_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 834 (all A all B -(-(A = k1_xboole_0 & B != k1_xboole_0) & (all C (v1_funct_1(C) & v1_relat_1(C) -> -(k1_relat_1(C) = B & r1_tarski(k2_relat_1(C),A)))))) # label(t18_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 835 (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(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]. 28.13/27.72 836 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B all C (r2_hidden(B,k1_relat_1(A)) & k1_funct_1(A,C) = k1_funct_1(A,B) & r2_hidden(C,k1_relat_1(A)) -> B = C)) <-> v2_funct_1(A)))) # label(d8_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 837 (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]. 28.13/27.72 838 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(A) & k2_relat_1(k5_relat_1(B,A)) = k2_relat_1(A) -> r1_tarski(k1_relat_1(A),k2_relat_1(B))))))) # label(t51_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 839 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k1_relat_1(A) = k2_relat_1(k5_relat_1(A,k2_funct_1(A))) & k1_relat_1(A) = k1_relat_1(k5_relat_1(A,k2_funct_1(A)))))) # label(t58_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 840 $T # label(t24_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 841 $T # label(t11_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 842 $T # label(t74_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 843 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k1_relat_1(k8_relat_1(A,B)),k1_relat_1(B)) & r1_tarski(k2_relat_1(k8_relat_1(A,B)),k2_relat_1(B)))) # label(t89_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 844 (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(B) = A & k1_relat_1(C) = A -> C = B))))) -> k1_xboole_0 = A)) # label(t16_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 845 $T # label(t95_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 846 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k2_relat_1(C) = k1_tarski(A) & k1_tarski(A) = k2_relat_1(B) & k1_relat_1(B) = k1_relat_1(C) -> B = C))))) # label(t17_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 847 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> k2_relat_1(A) = k1_relat_1(k2_funct_1(A)) & k2_relat_1(k2_funct_1(A)) = k1_relat_1(A)))) # label(t55_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 848 (all A all B (v1_relat_1(B) -> (r2_hidden(A,k2_relat_1(B)) <-> k10_relat_1(B,k1_tarski(A)) != k1_xboole_0))) # label(t142_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 849 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k2_relat_1(B),A) & (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k5_relat_1(B,C) = k5_relat_1(B,D) & k1_relat_1(D) = A & k1_relat_1(C) = A -> D = C))))) -> A = k2_relat_1(B)))) # label(t33_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 850 (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]. 28.13/27.72 851 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C all D ((r2_hidden(D,k1_relat_1(A)) & k1_funct_1(A,D) = C -> r2_hidden(C,k2_relat_1(A)) & k1_funct_1(B,C) = D) & (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) <-> B = k2_funct_1(A))))))) # label(t54_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 852 $T # label(t29_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 853 (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]. 28.13/27.72 854 $T # label(t6_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 855 $T # label(t81_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 856 (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]. 28.13/27.72 857 (all A (v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)))) # label(fc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 858 (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_funct_1(D) & v1_relat_1(D) -> (k5_relat_1(B,D) = k5_relat_1(B,C) & k1_relat_1(D) = A & k1_relat_1(C) = A & k2_relat_1(B) = A -> C = D))))))) # label(t156_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 859 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> k10_relat_1(C,k3_xboole_0(A,B)) = k3_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)))) # label(t137_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 860 (all A all B (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k7_relat_1(A,B)) & v1_relat_1(k7_relat_1(A,B)))) # label(fc4_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 861 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k10_relat_1(C,A),k10_relat_1(C,B)) & r1_tarski(A,k2_relat_1(C)) -> r1_tarski(A,B)))) # label(t158_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 862 (all A (v1_xboole_0(A) -> v1_funct_1(A))) # label(cc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 863 $T # label(t108_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 864 $T # label(t10_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 865 (all A (A != k1_xboole_0 -> (all B exists C (v1_funct_1(C) & k1_tarski(B) = k2_relat_1(C) & k1_relat_1(C) = A & v1_relat_1(C))))) # label(t15_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 866 (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]. 28.13/27.72 867 $T # label(t5_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.72 868 (exists A (v1_relat_1(A) & v1_funct_1(A) & v3_relat_1(A))) # label(rc4_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 869 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) -> k3_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)) = k9_relat_1(C,k3_xboole_0(A,B))))) # label(t121_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 870 $T # label(t79_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 871 $T # label(t41_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 872 $T # label(t39_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 873 (all A all B all C (v1_relat_1(C) & v1_funct_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]. 28.13/27.73 874 (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]. 28.13/27.73 875 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k1_relat_1(k8_relat_1(A,C))) -> k1_funct_1(C,B) = k1_funct_1(k8_relat_1(A,C),B)))) # label(t87_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 876 (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]. 28.13/27.73 877 (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)) -> k1_funct_1(B,D) = k1_funct_1(C,D))) & (all D (r2_hidden(D,k1_relat_1(B)) <-> r2_hidden(D,k1_relat_1(C)) & r2_hidden(k1_funct_1(C,D),A))) <-> k8_relat_1(A,C) = B))))) # label(t85_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 878 (all A (v1_funct_1(A) & v1_relat_1(A) -> k5_relat_1(k6_relat_1(k1_relat_1(A)),A) = A & k5_relat_1(A,k6_relat_1(k2_relat_1(A))) = A)) # label(t42_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 879 $T # label(t45_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 880 $T # label(t30_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 881 $T # label(t114_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 882 (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]. 28.13/27.73 883 (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]. 28.13/27.73 884 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(B) = k2_relat_1(A) & A = k5_relat_1(A,B) -> B = k6_relat_1(k1_relat_1(B))))))) # label(t44_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 885 $T # label(t88_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 886 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> v2_funct_1(k2_funct_1(A))))) # label(t62_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 887 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) -> r1_tarski(k10_relat_1(B,k9_relat_1(B,A)),A)))) # label(t152_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 888 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k1_relat_1(k7_relat_1(C,A))) -> k1_funct_1(C,B) = k1_funct_1(k7_relat_1(C,A),B)))) # label(t70_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 889 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> A = k2_funct_1(k2_funct_1(A))))) # label(t65_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 890 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k2_relat_1(B)) & v2_funct_1(B) -> A = k1_funct_1(B,k1_funct_1(k2_funct_1(B),A)) & A = k1_funct_1(k5_relat_1(k2_funct_1(B),B),A)))) # label(t57_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 891 (all A ((all B all C all D (r2_hidden(k4_tarski(B,D),A) & r2_hidden(k4_tarski(B,C),A) -> D = C)) & (all B -((all C all D k4_tarski(C,D) != B) & r2_hidden(B,A))) -> v1_funct_1(A) & v1_relat_1(A))) # label(t2_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 892 $T # label(d6_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 893 (all A all B (r2_hidden(B,A) -> B = k1_funct_1(k6_relat_1(A),B))) # label(t35_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 894 (all A v2_funct_1(k6_relat_1(A))) # label(t52_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 895 $T # label(t128_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 896 (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,k8_relat_1(B,C)) = k8_relat_1(A,C)))) # label(t97_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 897 $T # label(t129_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 898 (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]. 28.13/27.73 899 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k2_relat_1(k5_relat_1(C,B))) -> r2_hidden(A,k2_relat_1(B))))))) # label(t25_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 900 $T # label(t78_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 901 $T # label(t28_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 902 $T # label(t134_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 903 $T # label(t32_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 904 (exists A (v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A))) # label(rc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 905 (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]. 28.13/27.73 906 $T # label(d10_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 907 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(B) = k1_tarski(A) -> k1_tarski(k1_funct_1(B,A)) = k2_relat_1(B)))) # label(t14_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 908 (all A all B all C (v1_relat_1(C) -> k10_relat_1(k7_relat_1(C,A),B) = k3_xboole_0(A,k10_relat_1(C,B)))) # label(t139_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 909 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) -> k10_relat_1(k2_funct_1(B),A) = k9_relat_1(B,A)))) # label(t154_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 910 $T # label(dt_k1_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 911 (exists A (v1_relat_1(A) & (all B (r2_hidden(B,f1_s3_funct_1) -> f2_s3_funct_1(B) = k1_funct_1(A,B))) & k1_relat_1(A) = f1_s3_funct_1 & v1_funct_1(A))) # label(s3_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 912 (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]. 28.13/27.73 913 $T # label(d3_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 914 (exists A (v1_relat_1(A) & v2_funct_1(A) & v1_funct_1(A))) # label(rc3_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 915 $T # label(d2_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 916 $T # label(t75_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 917 (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]. 28.13/27.73 918 (all A all B (v1_funct_1(B) & v1_relat_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]. 28.13/27.73 919 $T # label(t106_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 920 $T # label(t77_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 921 $T # label(t3_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 922 $T # label(t102_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 923 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((exists B (v1_funct_1(B) & k5_relat_1(A,B) = k6_relat_1(k1_relat_1(A)) & v1_relat_1(B))) -> v2_funct_1(A)))) # label(t53_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 924 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_funct_1(B) & v1_relat_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]. 28.13/27.73 925 (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]. 28.13/27.73 926 $T # label(t132_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 927 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C ((all D (r2_hidden(D,k1_relat_1(A)) & r2_hidden(k1_funct_1(A,D),B) <-> r2_hidden(D,C))) <-> C = k10_relat_1(A,B))))) # label(d13_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 928 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k2_relat_1(k5_relat_1(k2_funct_1(A),A)) = k2_relat_1(A) & k1_relat_1(k5_relat_1(k2_funct_1(A),A)) = k2_relat_1(A)))) # label(t59_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 929 $T # label(t109_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 930 $T # label(t83_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 931 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k9_relat_1(C,A),k9_relat_1(C,B)) & r1_tarski(A,k1_relat_1(C)) & v2_funct_1(C) -> r1_tarski(A,B)))) # label(t157_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 932 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (B = k2_relat_1(A) <-> (all C ((exists D (r2_hidden(D,k1_relat_1(A)) & C = k1_funct_1(A,D))) <-> r2_hidden(C,B))))))) # label(d5_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 933 (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]. 28.13/27.73 934 (all A all B all C (p1_s1_funct_1(A,C) & p1_s1_funct_1(A,B) -> B = C)) -> (exists A (v1_funct_1(A) & (all B all C (r2_hidden(B,f1_s1_funct_1) & p1_s1_funct_1(B,C) <-> r2_hidden(k4_tarski(B,C),A))) & v1_relat_1(A))) # label(s1_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 935 $T # label(t133_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 936 $T # label(t80_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 937 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) -> k9_relat_1(C,k4_xboole_0(A,B)) = k4_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B))))) # label(t123_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 938 (all A (v1_relat_1(A) & v1_funct_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]. 28.13/27.73 939 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(k5_relat_1(B,A)) = k1_relat_1(B) -> r1_tarski(k2_relat_1(B),k1_relat_1(A))))))) # label(t27_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 940 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k1_relat_1(C)) & r2_hidden(B,A) -> r2_hidden(k1_funct_1(C,B),k2_relat_1(k7_relat_1(C,A)))))) # label(t73_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 941 (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]. 28.13/27.73 942 (all A (v1_relat_1(A) & v1_funct_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]. 28.13/27.73 943 $T # label(t107_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 944 (all A all B all C (v1_funct_1(C) & v1_relat_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]. 28.13/27.73 945 $T # label(t103_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 946 $T # label(t111_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 947 $T # label(t90_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 948 $T # label(t1_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 949 (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]. 28.13/27.73 950 $T # label(t116_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 951 (all A all B (v1_relat_1(B) -> ((all C -(k10_relat_1(B,k1_tarski(C)) = k1_xboole_0 & r2_hidden(C,A))) -> r1_tarski(A,k2_relat_1(B))))) # label(t143_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 952 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k1_relat_1(k8_relat_1(A,C))) <-> r2_hidden(B,k1_relat_1(C)) & r2_hidden(k1_funct_1(C,B),A)))) # label(t86_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 953 (all A all B (v1_relat_1(B) & v1_funct_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]. 28.13/27.73 954 (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]. 28.13/27.73 955 $T # label(d7_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 956 $T # label(t131_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 957 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k9_relat_1(k6_relat_1(A),B) = B)) # label(t162_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 958 (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]. 28.13/27.73 959 $T # label(t13_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 960 $T # label(t110_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 961 $T # label(t36_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 962 (exists A (v1_funct_1(A) & v2_relat_1(A) & v1_relat_1(A))) # label(rc5_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 963 $T # label(t130_funct_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 964 (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]. 28.13/27.73 965 $T # label(t4_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 966 (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]. 28.13/27.73 967 $T # label(t21_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 968 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v3_relat_2(A) & v3_relat_2(B) -> v3_relat_2(k2_xboole_0(A,B)) & v3_relat_2(k3_xboole_0(A,B)) & v3_relat_2(k4_xboole_0(A,B))))))) # label(t35_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 969 (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]. 28.13/27.73 970 $T # label(t9_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 971 (all A (v1_relat_1(A) -> (all B (r8_relat_2(A,B) <-> (all C all D all E (r2_hidden(C,B) & r2_hidden(D,B) & r2_hidden(k4_tarski(C,D),A) & r2_hidden(k4_tarski(D,E),A) & r2_hidden(E,B) -> r2_hidden(k4_tarski(C,E),A))))))) # label(d8_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 972 (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]. 28.13/27.73 973 (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]. 28.13/27.73 974 (all A (v1_relat_1(A) -> (r1_relat_2(A,k3_relat_1(A)) <-> v1_relat_2(A)))) # label(d9_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 975 (all A (v1_relat_1(A) -> (r4_relat_2(A,k3_relat_1(A)) <-> v4_relat_2(A)))) # label(d12_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 976 (all A (v1_relat_1(A) -> (v1_relat_2(A) -> k2_relat_1(A) = k2_relat_1(k4_relat_1(A)) & k1_relat_1(k4_relat_1(A)) = k1_relat_1(A)))) # label(t29_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 977 (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]. 28.13/27.73 978 (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]. 28.13/27.73 979 (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]. 28.13/27.73 980 (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]. 28.13/27.73 981 (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]. 28.13/27.73 982 (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]. 28.13/27.73 983 (all A (v1_relat_1(A) -> (v2_relat_2(A) & v8_relat_2(A) -> v5_relat_2(A)))) # label(t25_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 984 (all A (v1_relat_1(A) -> (v2_relat_2(A) -> v2_relat_2(k4_relat_1(A))))) # label(t28_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 985 $T # label(t16_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 986 (all A (v1_relat_1(A) -> (v5_relat_2(A) <-> r5_relat_2(A,k3_relat_1(A))))) # label(d13_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 987 $T # label(t1_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 988 (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]. 28.13/27.73 989 $T # label(t11_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 990 $T # label(t15_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 991 (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]. 28.13/27.73 992 $T # label(t10_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 993 $T # label(t8_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 994 (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]. 28.13/27.73 995 $T # label(t5_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 996 $T # label(t7_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 997 (all A (v1_relat_1(A) -> (A = k4_relat_1(A) <-> v3_relat_2(A)))) # label(t30_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 998 (all A (v1_relat_1(A) -> (all B ((all C -(r2_hidden(k4_tarski(C,C),A) & r2_hidden(C,B))) <-> r2_relat_2(A,B))))) # label(d2_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 999 (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))) <-> r5_relat_2(A,B))))) # label(d5_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 1000 $T # label(t6_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 1001 $T # label(t14_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 1002 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v2_relat_2(B) & v2_relat_2(A) -> v2_relat_2(k2_xboole_0(A,B)) & v2_relat_2(k3_xboole_0(A,B))))))) # label(t32_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 1003 (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]. 28.13/27.73 1004 (all A (v1_relat_1(A) -> (r3_relat_2(A,k3_relat_1(A)) <-> v3_relat_2(A)))) # label(d11_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 1005 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v4_relat_2(A) -> v4_relat_2(k3_xboole_0(A,B)) & v4_relat_2(k4_xboole_0(A,B))))))) # label(t41_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 1006 $T # label(t2_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 1007 $T # label(t13_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 1008 (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]. 28.13/27.73 1009 (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]. 28.13/27.73 1010 (all A (v1_relat_1(A) -> (all B ((all C all D -(r2_hidden(D,B) & C != D & -r2_hidden(k4_tarski(D,C),A) & -r2_hidden(k4_tarski(C,D),A) & r2_hidden(C,B))) <-> r6_relat_2(A,B))))) # label(d6_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 1011 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v8_relat_2(A) & v8_relat_2(B) -> v8_relat_2(k3_xboole_0(A,B))))))) # label(t43_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 1012 $T # label(t3_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 1013 (all A (v1_relat_1(A) -> (all B (r4_relat_2(A,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) -> C = D)))))) # label(d4_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 1014 (all A (v1_relat_1(A) -> (v3_relat_2(A) & v8_relat_2(A) -> v1_relat_2(A)))) # label(t22_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 1015 (all A (v1_relat_1(A) -> (all B ((all C all D (r2_hidden(D,B) & r2_hidden(k4_tarski(C,D),A) & r2_hidden(C,B) -> r2_hidden(k4_tarski(D,C),A))) <-> r3_relat_2(A,B))))) # label(d3_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 1016 (all A (v1_relat_1(A) -> (v6_relat_2(A) <-> r1_tarski(k4_xboole_0(k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A)),k6_relat_1(k3_relat_1(A))),k2_xboole_0(A,k4_relat_1(A)))))) # label(t45_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 1017 (all A (v1_relat_1(A) -> (v5_relat_2(A) -> v4_relat_2(A) & v2_relat_2(A)))) # label(t26_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 1018 $T # label(t12_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 1019 (all A (v1_relat_1(A) -> (all B (r7_relat_2(A,B) <-> (all C all D -(-r2_hidden(k4_tarski(D,C),A) & -r2_hidden(k4_tarski(C,D),A) & r2_hidden(D,B) & r2_hidden(C,B))))))) # label(d7_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 1020 (all A (v1_relat_1(A) -> (r1_tarski(k3_xboole_0(A,k4_relat_1(A)),k6_relat_1(k1_relat_1(A))) <-> v4_relat_2(A)))) # label(t39_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 1021 (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]. 28.13/27.73 1022 (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]. 28.13/27.73 1023 (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]. 28.13/27.73 1024 (all A (v1_relat_1(A) -> (v7_relat_2(A) <-> k2_xboole_0(A,k4_relat_1(A)) = k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A))))) # label(t47_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 1025 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v5_relat_2(A) & v5_relat_2(B) -> v5_relat_2(k3_xboole_0(A,B))))))) # label(t37_relat_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.73 1026 (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]. 28.13/27.74 1027 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> (r1_ordinal1(A,B) <-> r1_tarski(A,B)))) # label(redefinition_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1028 $T # label(t16_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1029 (all A exists B m1_ordinal1(B,A)) # label(existence_m1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1030 $T # label(t17_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1031 $T # label(dt_k1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1032 (all A (v3_ordinal1(A) -> v1_ordinal1(k3_tarski(A)) & v2_ordinal1(k3_tarski(A)) & v3_ordinal1(k3_tarski(A)))) # label(fc4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1033 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v3_ordinal1(k1_relat_1(A)) <-> v5_ordinal1(A)))) # label(d7_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1034 $T # label(t15_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1035 (exists A (v2_ordinal1(A) & v3_ordinal1(A) & v1_ordinal1(A) & -v1_xboole_0(A))) # label(rc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1036 (all A all B (r2_hidden(A,k1_ordinal1(B)) <-> A = B | r2_hidden(A,B))) # label(t13_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1037 $T # label(t40_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1038 (all A all B (k1_ordinal1(A) = k1_ordinal1(B) -> B = A)) # label(t12_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1039 (all A all B (v3_ordinal1(B) -> -(r1_tarski(A,B) & (all C (v3_ordinal1(C) -> -(r2_hidden(C,A) & (all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> r1_ordinal1(C,D))))))) & k1_xboole_0 != A))) # label(t32_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1040 (all A -(all B (v3_ordinal1(B) <-> r2_hidden(B,A)))) # label(t37_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1041 (all A exists B ((all C (v3_ordinal1(C) -> (-r2_hidden(C,A) -> r1_ordinal1(B,C)))) & -r2_hidden(B,A) & v3_ordinal1(B))) # label(t39_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1042 (all A ((all B (r2_hidden(B,A) -> v3_ordinal1(B) & r1_tarski(B,A))) -> v3_ordinal1(A))) # label(t31_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1043 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(A,B) <-> r1_ordinal1(k1_ordinal1(A),B)))))) # label(t33_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1044 (all A all B all C all D -(r2_hidden(D,A) & r2_hidden(C,D) & r2_hidden(B,C) & r2_hidden(A,B))) # label(t4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1045 (all A all B all C all D all E -(r2_hidden(A,B) & r2_hidden(B,C) & r2_hidden(C,D) & r2_hidden(E,A) & r2_hidden(D,E))) # label(t5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1046 (all A all B (m1_ordinal1(B,A) -> v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B))) # label(dt_m1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1047 (all A all B (v3_ordinal1(B) -> (r2_hidden(A,B) -> v3_ordinal1(A)))) # label(t23_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1048 (all A -v1_xboole_0(k1_ordinal1(A))) # label(fc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1049 (all A (v3_ordinal1(A) -> v1_ordinal1(k1_ordinal1(A)) & v3_ordinal1(k1_ordinal1(A)) & v2_ordinal1(k1_ordinal1(A)) & -v1_xboole_0(k1_ordinal1(A)))) # label(fc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1050 (exists A (p1_s1_ordinal1(A) & v3_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]. 28.13/27.74 1051 (all A (v3_ordinal1(A) -> v3_ordinal1(k3_tarski(A)))) # label(t30_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1052 (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]. 28.13/27.74 1053 (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]. 28.13/27.74 1054 $T # label(t9_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1055 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> r1_ordinal1(A,B) | r1_ordinal1(B,A))) # label(connectedness_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1056 (all A (v3_ordinal1(A) <-> v1_ordinal1(A) & v2_ordinal1(A))) # label(d4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1057 $T # label(t28_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1058 $T # label(t1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1059 (all A ((all B (r2_hidden(B,A) -> v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B))) & v6_ordinal1(A) -> 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]. 28.13/27.74 1060 (exists A (v1_relat_1(A) & v1_xboole_0(A) & v1_ordinal1(A) & v3_ordinal1(A) & v2_ordinal1(A) & v2_funct_1(A) & v1_funct_1(A))) # label(rc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1061 (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]. 28.13/27.74 1062 (all A all B (v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) -> (m1_ordinal1(B,A) <-> r1_tarski(k2_relat_1(B),A)))) # label(d8_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1063 (all A (v1_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_tarski(A,B) & r2_hidden(B,C) -> r2_hidden(A,C)))))))) # label(t22_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1064 (exists A (v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1065 (all A ((all B all C (r2_hidden(B,A) & r2_hidden(C,A) -> r3_xboole_0(B,C))) <-> v6_ordinal1(A))) # label(d9_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1066 $T # label(t11_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1067 (all A r2_hidden(A,k1_ordinal1(A))) # label(t10_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1068 (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]. 28.13/27.74 1069 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v3_ordinal1(k1_relat_1(A)) -> m1_ordinal1(A,k2_relat_1(A))))) # label(t46_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1070 (all A (v1_ordinal1(A) & v2_ordinal1(A) -> v3_ordinal1(A))) # label(cc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1071 (all A (v3_ordinal1(A) -> ((all B (v3_ordinal1(B) -> (r2_hidden(B,A) -> r2_hidden(k1_ordinal1(B),A)))) <-> v4_ordinal1(A)))) # label(t41_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1072 (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]. 28.13/27.74 1073 $T # label(t18_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1074 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -(-r2_xboole_0(A,B) & B != A & -r2_xboole_0(B,A)))))) # label(t50_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1075 $T # label(t8_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1076 (all A (v3_ordinal1(A) -> v2_ordinal1(A) & v1_ordinal1(A))) # label(cc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1077 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v3_ordinal1(B) & v5_ordinal1(A) -> m1_ordinal1(k2_ordinal1(A,B),k2_relat_1(A)))) # label(dt_k2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1078 $T # label(t2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1079 $T # label(t44_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1080 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> r1_ordinal1(A,A))) # label(reflexivity_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1081 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v3_ordinal1(B) -> k7_relat_1(A,B) = k2_ordinal1(A,B))) # label(redefinition_k2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1082 $T # label(t43_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1083 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> r3_xboole_0(A,B))))) # label(t25_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1084 (exists A (v2_ordinal1(A) & v3_ordinal1(A) & v1_ordinal1(A))) # label(rc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1085 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> r1_ordinal1(A,B) | r2_hidden(B,A))))) # label(t26_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1086 (all A (v2_ordinal1(A) <-> (all B all C -(r2_hidden(B,A) & -r2_hidden(B,C) & C != B & -r2_hidden(C,B) & r2_hidden(C,A))))) # label(d3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1087 $T # label(d5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1088 (all A k1_ordinal1(A) != A) # label(t14_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1089 (all A (v1_xboole_0(A) -> v2_ordinal1(A) & v3_ordinal1(A) & v1_ordinal1(A))) # label(cc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1090 (all A all B all C -(r2_hidden(A,B) & r2_hidden(B,C) & r2_hidden(C,A))) # label(t3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1091 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -(-r2_hidden(A,B) & A != B & -r2_hidden(B,A)))))) # label(t24_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1092 (all A all B all C all D all E all F -(r2_hidden(A,B) & r2_hidden(B,C) & r2_hidden(D,E) & r2_hidden(E,F) & r2_hidden(F,A) & r2_hidden(C,D))) # label(t6_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1093 (all A (v3_ordinal1(A) -> -((all B (v3_ordinal1(B) -> k1_ordinal1(B) != A)) & -v4_ordinal1(A)) & -((exists B (v3_ordinal1(B) & k1_ordinal1(B) = A)) & v4_ordinal1(A)))) # label(t42_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1094 (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]. 28.13/27.74 1095 (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]. 28.13/27.74 1096 (all A k2_xboole_0(A,k1_tarski(A)) = k1_ordinal1(A)) # label(d1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1097 (exists A (v1_relat_1(A) & v5_ordinal1(A) & (all B (v3_ordinal1(B) -> (all C (v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,f1_s4_ordinal1) & C = k2_ordinal1(A,B) -> f2_s4_ordinal1(C) = k1_funct_1(A,B)))))) & k1_relat_1(A) = f1_s4_ordinal1 & v1_funct_1(A))) # label(s4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1098 (all A m1_ordinal1(k1_xboole_0,A)) # label(t45_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1099 $T # label(t20_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1100 (all A -(all B (v3_ordinal1(B) -> r2_hidden(B,A)))) # label(t38_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1101 (all A (v1_ordinal1(A) <-> (all B (r2_hidden(B,A) -> r1_tarski(B,A))))) # label(d2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1102 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) -> v2_ordinal1(k1_relat_1(A)) & v3_ordinal1(k1_relat_1(A)) & v1_ordinal1(k1_relat_1(A)))) # label(fc5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1103 (all A (v3_ordinal1(A) -> v3_ordinal1(k1_ordinal1(A)))) # label(t29_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1104 (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]. 28.13/27.74 1105 k1_relat_1(f3_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) & B = k2_ordinal1(f3_s3_ordinal1,A) -> f2_s3_ordinal1(B) = k1_funct_1(f3_s3_ordinal1,A)))))) & 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)))))) -> f4_s3_ordinal1 = f3_s3_ordinal1 # label(s3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1106 (all A (A = k3_tarski(A) <-> v4_ordinal1(A))) # label(d6_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1107 (all A all B -(r2_hidden(A,B) & r1_tarski(B,A))) # label(t7_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1108 (all A (v3_ordinal1(A) -> (all B ((exists C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & A = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> f3_s5_ordinal1(k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & B = f3_s5_ordinal1(C))) <-> f2_s5_ordinal1(A) = B)))) & (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s5_ordinal1)) -> f2_s5_ordinal1(A) = k1_funct_1(f1_s5_ordinal1,A)))) -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s5_ordinal1)) -> f3_s5_ordinal1(k2_ordinal1(f1_s5_ordinal1,A)) = k1_funct_1(f1_s5_ordinal1,A)))) # label(s5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1109 (all A (v1_relat_1(A) -> r4_wellord1(A,A))) # label(t48_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1110 $T # label(t6_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1111 $T # label(t14_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1112 (all A all B all C all D (v1_relat_1(D) -> (all E (v1_relat_1(E) -> (v2_wellord1(E) & r2_hidden(A,k3_relat_1(D)) & r2_hidden(C,k3_relat_1(E)) & r4_wellord1(D,k2_wellord1(E,k1_wellord1(E,B))) & r4_wellord1(k2_wellord1(D,k1_wellord1(D,A)),k2_wellord1(E,k1_wellord1(E,C))) & r2_hidden(B,k3_relat_1(E)) & v2_wellord1(D) -> r1_tarski(k1_wellord1(E,C),k1_wellord1(E,B)) & r2_hidden(k4_tarski(C,B),E)))))) # label(t62_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1113 (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]. 28.13/27.74 1114 (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]. 28.13/27.74 1115 (all A all B all C (v1_relat_1(C) -> -(r4_wellord1(k2_wellord1(C,k1_wellord1(C,A)),k2_wellord1(C,k1_wellord1(C,B))) & A != B & r2_hidden(B,k3_relat_1(C)) & r2_hidden(A,k3_relat_1(C)) & v2_wellord1(C)))) # label(t58_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1116 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (v2_wellord1(B) & r1_tarski(A,k3_relat_1(B)) & r3_wellord1(B,C,D) -> r3_wellord1(k2_wellord1(B,A),k2_wellord1(C,k9_relat_1(D,A)),k7_relat_1(D,A)) & r4_wellord1(k2_wellord1(B,A),k2_wellord1(C,k9_relat_1(D,A)))))))))) # label(t59_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1117 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> ((exists C (v1_relat_1(C) & v1_funct_1(C) & r3_wellord1(A,B,C))) <-> r4_wellord1(A,B)))))) # label(d8_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1118 (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]. 28.13/27.74 1119 (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]. 28.13/27.74 1120 $T # label(t3_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1121 (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]. 28.13/27.74 1122 (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]. 28.13/27.74 1123 $T # label(t56_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1124 (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]. 28.13/27.74 1125 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> (all B -(r4_wellord1(A,k2_wellord1(A,k1_wellord1(A,B))) & r2_hidden(B,k3_relat_1(A))))))) # label(t57_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1126 $T # label(t34_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1127 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r3_wellord1(A,B,C) -> (all D all E (r2_hidden(k4_tarski(D,E),A) -> E = D | 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)))))))))) # label(t45_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1128 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r3_wellord1(A,B,C) & v2_wellord1(A) -> v2_wellord1(B)))))))) # label(t54_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1129 (all A all B (v1_relat_1(B) -> (v2_wellord1(B) -> k3_relat_1(k2_wellord1(B,k1_wellord1(B,A))) = k1_wellord1(B,A)))) # label(t40_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1130 (all A all B (v1_relat_1(B) & v1_relat_1(A) -> v1_funct_1(k3_wellord1(A,B)) & v1_relat_1(k3_wellord1(A,B)))) # label(dt_k3_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1131 $T # label(t4_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1132 (all A (v1_relat_1(A) -> (all B (r1_wellord1(A,B) <-> (all C -(r1_tarski(C,B) & (all D -(r2_hidden(D,C) & r1_xboole_0(k1_wellord1(A,D),C))) & C != k1_xboole_0)))))) # label(d3_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1133 (all A all B all C (v1_relat_1(C) -> (v2_wellord1(C) & r2_hidden(B,k3_relat_1(C)) & (all D (r2_hidden(D,k1_wellord1(C,A)) -> r2_hidden(k4_tarski(D,B),C) & D != B)) & r2_hidden(A,k3_relat_1(C)) -> r2_hidden(k4_tarski(A,B),C)))) # label(t42_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1134 (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]. 28.13/27.74 1135 (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]. 28.13/27.74 1136 (all A all B (v1_relat_1(B) -> (r2_wellord1(B,A) -> (all C -(r1_tarski(C,A) & k1_xboole_0 != C & (all D -((all E (r2_hidden(E,C) -> r2_hidden(k4_tarski(D,E),B))) & r2_hidden(D,C)))))))) # label(t9_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1137 $T # label(dt_k1_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1138 (all A (v1_relat_1(A) -> (v2_wellord1(A) <-> v1_relat_2(A) & v6_relat_2(A) & v1_wellord1(A) & v4_relat_2(A) & v8_relat_2(A)))) # label(d4_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1139 (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]. 28.13/27.74 1140 (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]. 28.13/27.74 1141 (all A all B (v1_relat_1(B) -> (r1_tarski(A,k3_relat_1(B)) & v2_wellord1(B) -> A = k3_relat_1(k2_wellord1(B,A))))) # label(t39_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1142 (all A all B (v1_relat_1(B) -> r2_hidden(A,k3_relat_1(B)) | k1_wellord1(B,A) = k1_xboole_0)) # label(t2_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1143 $T # label(t44_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1144 (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))) & k1_xboole_0 != B))))) # label(t10_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1145 (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]. 28.13/27.74 1146 $T # label(t1_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1147 (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]. 28.13/27.74 1148 (all A all B (v1_relat_1(B) -> k7_relat_1(k8_relat_1(A,B),A) = k2_wellord1(B,A))) # label(t17_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1149 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k3_relat_1(A) = k1_relat_1(C) & (all D all E (r2_hidden(D,k3_relat_1(A)) & r2_hidden(k4_tarski(k1_funct_1(C,D),k1_funct_1(C,E)),B) & r2_hidden(E,k3_relat_1(A)) <-> r2_hidden(k4_tarski(D,E),A))) & v2_funct_1(C) & k3_relat_1(B) = k2_relat_1(C) <-> r3_wellord1(A,B,C)))))))) # label(d7_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1150 (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]. 28.13/27.74 1151 $T # label(t46_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1152 (all A all B (v1_relat_1(B) -> (v2_wellord1(B) & r1_tarski(A,k3_relat_1(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]. 28.13/27.74 1153 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v2_wellord1(A) -> (all C (v1_relat_1(C) & v1_funct_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]. 28.13/27.74 1154 (all A all B all C (v1_relat_1(C) -> (v2_wellord1(C) & r2_hidden(B,k1_wellord1(C,A)) & r2_hidden(A,k3_relat_1(C)) -> k1_wellord1(C,B) = k1_wellord1(k2_wellord1(C,k1_wellord1(C,A)),B)))) # label(t35_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1155 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> (all B -(r2_hidden(B,k3_relat_1(A)) & (exists C (r2_hidden(C,k3_relat_1(A)) & -r2_hidden(k4_tarski(C,B),A))) & (all C -((all D -(r2_hidden(D,k3_relat_1(A)) & r2_hidden(k4_tarski(B,D),A) & B != D & -r2_hidden(k4_tarski(C,D),A))) & r2_hidden(k4_tarski(B,C),A) & r2_hidden(C,k3_relat_1(A)))))) | k3_relat_1(A) = k1_xboole_0))) # label(t12_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1156 (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 -(r2_hidden(E,k3_relat_1(B)) & k9_relat_1(C,k1_wellord1(A,D)) = k1_wellord1(B,E))) & r2_hidden(D,k3_relat_1(A))))))))))) # label(t60_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1157 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k2_wellord1(C,B)) <-> r2_hidden(A,C) & r2_hidden(A,k2_zfmisc_1(B,B))))) # label(t16_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1158 (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]. 28.13/27.74 1159 (all A (v1_relat_1(A) -> k2_wellord1(A,k3_relat_1(A)) = A)) # label(t30_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.74 1160 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_wellord1(A) & r1_tarski(k2_relat_1(B),k3_relat_1(A)) & (all C all D (r2_hidden(k4_tarski(C,D),A) -> D = C | k1_funct_1(B,D) != k1_funct_1(B,C) & r2_hidden(k4_tarski(k1_funct_1(B,C),k1_funct_1(B,D)),A))) & k1_relat_1(B) = k3_relat_1(A) -> (all C (r2_hidden(C,k3_relat_1(A)) -> r2_hidden(k4_tarski(C,k1_funct_1(B,C)),A)))))))) # label(t43_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1161 (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]. 28.13/27.75 1162 (all A (v1_relat_1(A) -> ((all B -(r1_tarski(B,k3_relat_1(A)) & k1_xboole_0 != B & (all C -(r2_hidden(C,B) & r1_xboole_0(k1_wellord1(A,C),B))))) <-> v1_wellord1(A)))) # label(d2_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1163 (all A all B (v1_relat_1(B) -> -(r1_tarski(A,k3_relat_1(B)) & v2_wellord1(B) & (all C -(r4_wellord1(k2_wellord1(B,k1_wellord1(B,C)),k2_wellord1(B,A)) & r2_hidden(C,k3_relat_1(B)))) & -r4_wellord1(B,k2_wellord1(B,A))))) # label(t64_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1164 (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)) <-> A = B | r2_hidden(A,k1_wellord1(C,B)))))) # label(t38_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1165 (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]. 28.13/27.75 1166 $T # label(t7_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1167 (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]. 28.13/27.75 1168 (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]. 28.13/27.75 1169 (all A (v1_relat_1(A) -> (r2_wellord1(A,k3_relat_1(A)) <-> v2_wellord1(A)))) # label(t8_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1170 (all A (v1_relat_1(A) -> -((all B -((all C (r2_hidden(C,k3_relat_1(A)) -> r2_hidden(k4_tarski(B,C),A))) & r2_hidden(B,k3_relat_1(A)))) & k1_xboole_0 != k3_relat_1(A) & v2_wellord1(A)))) # label(t11_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1171 (all A (v1_relat_1(A) -> (all B all C (k1_wellord1(A,B) = C <-> (all D (r2_hidden(k4_tarski(D,B),A) & B != D <-> r2_hidden(D,C))))))) # label(d1_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1172 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k3_relat_1(k2_wellord1(C,B))) -> r2_hidden(A,B) & r2_hidden(A,k3_relat_1(C))))) # label(t19_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1173 (all A all B (v1_relat_1(B) -> k2_wellord1(B,A) = k2_wellord1(k2_wellord1(B,A),A))) # label(t28_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1174 (all A all B all C (v1_relat_1(C) -> (r2_hidden(B,k3_relat_1(C)) & r2_hidden(A,k3_relat_1(C)) & v2_wellord1(C) -> (r2_hidden(k4_tarski(A,B),C) <-> r1_tarski(k1_wellord1(C,A),k1_wellord1(C,B)))))) # label(t37_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1175 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r3_wellord1(A,B,C) -> (v1_wellord1(A) -> v1_wellord1(B)) & (v4_relat_2(A) -> v4_relat_2(B)) & (v6_relat_2(A) -> v6_relat_2(B)) & (v8_relat_2(A) -> v8_relat_2(B)) & (v1_relat_2(A) -> v1_relat_2(B))))))))) # label(t53_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1176 (all A (v1_relat_1(A) -> (all B (r2_wellord1(A,B) <-> r8_relat_2(A,B) & r6_relat_2(A,B) & r1_wellord1(A,B) & r4_relat_2(A,B) & r1_relat_2(A,B))))) # label(d5_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1177 (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]. 28.13/27.75 1178 (all A all B (v1_relat_1(B) -> k2_wellord1(B,A) = k8_relat_1(A,k7_relat_1(B,A)))) # label(t18_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1179 (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]. 28.13/27.75 1180 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r4_wellord1(A,B) & v2_wellord1(A) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k3_wellord1(A,B) = C <-> r3_wellord1(A,B,C))))))))) # label(d9_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1181 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> -(v2_wellord1(A) & v2_wellord1(B) & -r4_wellord1(A,B) & (all C -(r2_hidden(C,k3_relat_1(B)) & r4_wellord1(A,k2_wellord1(B,k1_wellord1(B,C))))) & (all C -(r2_hidden(C,k3_relat_1(A)) & r4_wellord1(k2_wellord1(A,k1_wellord1(A,C)),B)))))))) # label(t63_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1182 (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]. 28.13/27.75 1183 (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]. 28.13/27.75 1184 (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_funct_1(E) & v1_relat_1(E) -> (r3_wellord1(A,B,D) & r3_wellord1(B,C,E) -> r3_wellord1(A,C,k5_relat_1(D,E))))))))))))) # label(t51_wellord1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1185 (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]. 28.13/27.75 1186 (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]. 28.13/27.75 1187 $T # label(t41_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1188 (all A all B m2_relset_1(k1_xboole_0,A,B)) # label(t25_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1189 (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]. 28.13/27.75 1190 (all A all B all C (m1_relset_1(C,A,B) -> m1_subset_1(k5_relset_1(A,B,C),k1_zfmisc_1(B)))) # label(dt_k5_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1191 (all A (-v1_xboole_0(A) -> k6_relat_1(A) != k1_xboole_0)) # label(t46_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1192 $T # label(t44_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1193 (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]. 28.13/27.75 1194 (all A all B all C (m1_relset_1(C,A,B) <-> m2_relset_1(C,A,B))) # label(redefinition_m2_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1195 (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]. 28.13/27.75 1196 (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]. 28.13/27.75 1197 (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]. 28.13/27.75 1198 $T # label(t1_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1199 $T # label(t3_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1200 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> k4_xboole_0(C,D) = k3_relset_1(A,B,C,D))) # label(redefinition_k3_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1201 (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]. 28.13/27.75 1202 (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]. 28.13/27.75 1203 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> k2_relset_1(A,B,C,C) = C)) # label(idempotence_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1204 (all A all B all C (m2_relset_1(C,B,A) -> (m2_relset_1(C,B,k1_xboole_0) -> C = k1_xboole_0))) # label(t27_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1205 (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]. 28.13/27.75 1206 (all A all B all C (m1_relset_1(C,A,B) -> C = k6_relset_1(A,B,k6_relset_1(A,B,C)))) # label(involutiveness_k6_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1207 $T # label(t37_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1208 (exists A (m2_relset_1(A,f1_s1_relset_1,f2_s1_relset_1) & (all B all C (r2_hidden(k4_tarski(B,C),A) <-> r2_hidden(C,f2_s1_relset_1) & p1_s1_relset_1(B,C) & r2_hidden(B,f1_s1_relset_1))))) # label(s1_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1209 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> k1_relset_1(A,B,C,C) = C)) # label(idempotence_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1210 $T # label(t42_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1211 (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]. 28.13/27.75 1212 (all A all B all C all D all E all F (m1_relset_1(F,C,D) & m1_relset_1(E,A,B) -> m2_relset_1(k7_relset_1(A,B,C,D,E,F),A,D))) # label(dt_k7_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1213 (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 (r2_hidden(k4_tarski(E,D),C) & m1_subset_1(E,B))) <-> r2_hidden(D,k5_relset_1(B,A,C))))))))))) # label(t48_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1214 (all A all B all C all D (m2_relset_1(D,A,B) -> -((all E all F -(C = k4_tarski(E,F) & r2_hidden(E,A) & r2_hidden(F,B))) & r2_hidden(C,D)))) # label(t6_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1215 (all A r1_tarski(k6_relat_1(A),k2_zfmisc_1(A,A))) # label(t28_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1216 (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]. 28.13/27.75 1217 $T # label(t2_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1218 (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]. 28.13/27.75 1219 (all A all B all C (m1_relset_1(C,A,B) -> k4_relset_1(A,B,C) = k1_relat_1(C))) # label(redefinition_k4_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1220 $T # label(t40_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1221 (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]. 28.13/27.75 1222 (all A all B all C (m1_relset_1(C,A,B) -> k6_relset_1(A,B,C) = k4_relat_1(C))) # label(redefinition_k6_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1223 (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]. 28.13/27.75 1224 (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]. 28.13/27.75 1225 (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]. 28.13/27.75 1226 (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]. 28.13/27.75 1227 (all A all B all C (m2_relset_1(C,A,B) -> (r1_tarski(k6_relat_1(B),C) -> k5_relset_1(A,B,C) = B & r1_tarski(B,k4_relset_1(A,B,C))))) # label(t32_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1228 (all A all B all C (m1_relset_1(C,A,B) <-> r1_tarski(C,k2_zfmisc_1(A,B)))) # label(d1_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1229 (all A all B (m2_relset_1(B,A,A) -> B = k5_relat_1(k6_relat_1(A),B) & B = k5_relat_1(B,k6_relat_1(A)))) # label(t45_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1230 (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) -> ((exists F (m1_subset_1(F,C) & r2_hidden(F,B) & r2_hidden(k4_tarski(E,F),D))) <-> r2_hidden(E,k11_relset_1(A,C,D,B))))))))))))) # label(t53_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1231 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> m2_relset_1(k3_relset_1(A,B,C,D),A,B))) # label(dt_k3_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1232 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) -> (all D (m1_subset_1(D,A) -> (r2_hidden(D,k4_relset_1(A,B,C)) <-> (exists E (m1_subset_1(E,B) & r2_hidden(k4_tarski(D,E),C)))))))))))) # label(t47_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1233 (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]. 28.13/27.75 1234 (all A all B all C (m1_relset_1(C,A,B) -> k5_relset_1(A,B,C) = k2_relat_1(C))) # label(redefinition_k5_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1235 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1236 (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]. 28.13/27.75 1237 (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]. 28.13/27.75 1238 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,B) -> (all E (m2_relset_1(E,B,C) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,C) -> ((exists H (m1_subset_1(H,B) & r2_hidden(k4_tarski(F,H),D) & r2_hidden(k4_tarski(H,G),E))) <-> r2_hidden(k4_tarski(F,G),k7_relset_1(A,B,B,C,D,E))))))))))))))))) # label(t51_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1239 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) -> (all D (m1_subset_1(D,A) -> -((all E (m1_subset_1(E,B) -> -r2_hidden(E,k5_relset_1(A,B,C)))) & r2_hidden(D,k4_relset_1(A,B,C))))))))))) # label(t49_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1240 (all A all B all C all D (m1_relset_1(C,A,B) -> k9_relat_1(C,D) = k10_relset_1(A,B,C,D))) # label(redefinition_k10_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1241 $T # label(t5_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1242 $T # label(t18_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1243 (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]. 28.13/27.75 1244 (all A all B all C (v1_relat_1(C) -> (r1_tarski(k2_relat_1(C),B) & r1_tarski(k1_relat_1(C),A) -> m2_relset_1(C,A,B)))) # label(t11_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1245 (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]. 28.13/27.75 1246 $T # label(t7_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1247 (all A all B all C (m2_relset_1(C,B,A) -> ((all D -((all E -r2_hidden(k4_tarski(D,E),C)) & r2_hidden(D,B))) <-> B = k4_relset_1(B,A,C)))) # label(t22_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1248 (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]. 28.13/27.75 1249 (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]. 28.13/27.75 1250 (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]. 28.13/27.75 1251 (all A all B exists C m1_relset_1(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1252 (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]. 28.13/27.75 1253 (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]. 28.13/27.75 1254 (all A all B all C all D (m1_relset_1(D,A,B) -> k8_relat_1(C,D) = k9_relset_1(A,B,C,D))) # label(redefinition_k9_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1255 (all A all B exists C m2_relset_1(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1256 (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]. 28.13/27.75 1257 (exists A (m2_relset_1(A,f1_s2_relset_1,f2_s2_relset_1) & (all B (m1_subset_1(B,f1_s2_relset_1) -> (all C (m1_subset_1(C,f2_s2_relset_1) -> (p1_s2_relset_1(B,C) <-> r2_hidden(k4_tarski(B,C),A)))))))) # label(s2_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1258 $T # label(t20_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1259 (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)) & B = k4_relset_1(B,A,C)))) # label(t31_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1260 (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]. 28.13/27.75 1261 (all A m2_relset_1(k6_relat_1(A),A,A)) # label(t29_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1262 (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]. 28.13/27.75 1263 (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]. 28.13/27.75 1264 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,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]. 28.13/27.75 1265 (all A all B all C (m2_relset_1(C,A,B) -> k5_relset_1(A,B,C) = k10_relset_1(A,B,C,A) & k11_relset_1(A,B,C,B) = k4_relset_1(A,B,C))) # label(t38_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1266 (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]. 28.13/27.75 1267 (all A all B all C (m2_relset_1(C,A,B) -> k5_relset_1(A,B,C) = k4_relset_1(B,A,k6_relset_1(A,B,C)) & 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]. 28.13/27.75 1268 (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]. 28.13/27.75 1269 (all A all B all C all D (m1_relset_1(C,A,B) -> k7_relat_1(C,D) = k8_relset_1(A,B,C,D))) # label(redefinition_k8_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1270 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,C,A) -> (all E (m1_subset_1(E,A) -> ((exists F (m1_subset_1(F,C) & r2_hidden(F,B) & r2_hidden(k4_tarski(F,E),D))) <-> r2_hidden(E,k10_relset_1(C,A,D,B))))))))))))) # label(t52_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1271 $T # label(t43_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1272 $T # label(t21_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1273 (all A all B all C (m2_relset_1(C,B,A) -> k11_relset_1(B,A,C,k10_relset_1(B,A,C,B)) = k4_relset_1(B,A,C) & k5_relset_1(B,A,C) = k10_relset_1(B,A,C,k11_relset_1(B,A,C,A)))) # label(t39_relset_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1274 $T # label(t164_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1275 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_funct_1(A) & v1_relat_1(A) -> (r1_partfun1(A,B) -> r1_partfun1(B,A)))) # label(symmetry_r1_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1276 $T # label(t104_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1277 $T # label(t124_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1278 $T # label(d1_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1279 $T # label(t108_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1280 $T # label(t173_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1281 $T # label(t102_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1282 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((exists C (v1_relat_1(C) & v1_funct_1(C) & r1_tarski(B,C) & r1_tarski(A,C))) <-> r1_partfun1(A,B)))))) # label(t131_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1283 $T # label(t170_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1284 (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]. 28.13/27.75 1285 (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]. 28.13/27.75 1286 (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]. 28.13/27.75 1287 $T # label(t52_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1288 (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) -> -(C = k1_funct_1(D,E) & r2_hidden(E,k4_relset_1(A,B,D)))))))) # label(t26_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1289 $T # label(t21_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1290 (all A all B k3_partfun1(k1_xboole_0,A,B) = k1_xboole_0) # label(t91_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1291 (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 (m1_subset_1(E,A) -> (r2_hidden(E,k4_relset_1(A,B,C)) -> k1_funct_1(C,E) = k1_funct_1(D,E)))) & k4_relset_1(A,B,D) = k4_relset_1(A,B,C) -> D = C))))) # label(t34_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1292 (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]. 28.13/27.75 1293 $T # label(t157_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1294 (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)) -> m2_relset_1(D,A,B) & v1_funct_1(D))))) # label(t168_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.75 1295 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> k4_relset_1(k1_xboole_0,A,B) = k1_xboole_0 & k2_relat_1(B) = k1_xboole_0)) # label(t54_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1296 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r1_tarski(A,C) -> v1_funct_1(D) & m2_relset_1(D,C,B)))) # label(t30_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1297 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r1_tarski(C,D) -> r1_tarski(k3_partfun1(C,A,B),k3_partfun1(D,A,B))))))) # label(t81_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1298 (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]. 28.13/27.76 1299 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k2_xboole_0(A,B) = C -> (all D (r2_hidden(D,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(B,D) = k1_funct_1(A,D)))))))))) # label(t3_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1300 (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]. 28.13/27.76 1301 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> m2_relset_1(k8_relset_1(A,B,D,C),C,B) & v1_funct_1(k8_relset_1(A,B,D,C)))) # label(t43_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1302 (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]. 28.13/27.76 1303 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(A,k4_relset_1(B,C,k3_partfun1(D,B,C))) -> k1_funct_1(k3_partfun1(D,B,C),A) = k1_funct_1(D,A)))) # label(t80_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1304 (all A all B all C all D (m2_relset_1(D,A,k1_tarski(B)) & v1_funct_1(D) -> (r2_hidden(C,k4_relset_1(A,k1_tarski(B),D)) -> B = k1_funct_1(D,C)))) # label(t73_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1305 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_relat_1(E) -> (r1_tarski(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]. 28.13/27.76 1306 (all A all B all C (m2_relset_1(C,A,k1_tarski(B)) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,k1_tarski(B)) -> (k4_relset_1(A,k1_tarski(B),D) = k4_relset_1(A,k1_tarski(B),C) -> C = D))))) # label(t74_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1307 $T # label(t12_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1308 $T # label(t160_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1309 (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]. 28.13/27.76 1310 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (-r1_xboole_0(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) -> r1_partfun1(C,D)))))) # label(t185_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1311 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r1_tarski(A,B) -> r1_tarski(k3_partfun1(D,A,C),k3_partfun1(D,B,C))))) # label(t82_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1312 $T # label(t106_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1313 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> m2_relset_1(k7_relat_1(k8_relat_1(A,C),B),B,A) & v1_funct_1(k7_relat_1(k8_relat_1(A,C),B)))) # label(t47_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1314 $T # label(d2_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1315 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_partfun1(k7_relat_1(k8_relat_1(A,C),B),C))) # label(t146_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1316 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(B,C) -> m2_relset_1(D,A,C) & v1_funct_1(D)))) # label(t31_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1317 (all A (v1_relat_1(A) & v1_funct_1(A) -> m2_relset_1(A,k1_relat_1(A),k2_relat_1(A)) & v1_funct_1(A))) # label(t24_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1318 (all A all B all C (v1_funct_1(A) & v1_relat_1(A) -> m2_relset_1(k3_partfun1(A,B,C),B,C) & v1_funct_1(k3_partfun1(A,B,C)))) # label(dt_k3_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1319 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(A,k1_relat_1(D)) & r2_hidden(k1_funct_1(D,A),C) & r2_hidden(A,B) -> k1_funct_1(D,A) = k1_funct_1(k3_partfun1(D,B,C),A)))) # label(t79_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1320 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> r2_hidden(C,k4_partfun1(A,B)))) # label(t119_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1321 $T # label(t182_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1322 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (v2_funct_1(C) -> v1_funct_1(k2_funct_1(C)) & m2_relset_1(k2_funct_1(C),B,A)))) # label(t39_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1323 $T # label(t118_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1324 $T # label(t101_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1325 (exists A (v1_funct_1(A) & k1_relat_1(A) = f1_s1_partfun1 & (all B (r2_hidden(B,f1_s1_partfun1) -> (p1_s1_partfun1(B) -> f2_s1_partfun1(B) = k1_funct_1(A,B)) & (-p1_s1_partfun1(B) -> f3_s1_partfun1(B) = k1_funct_1(A,B)))) & v1_relat_1(A))) # label(s1_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1326 $T # label(t88_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1327 $T # label(t177_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1328 $T # label(t17_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1329 (all A (v1_funct_1(A) & v1_relat_1(A) -> k3_partfun1(A,k1_relat_1(A),k2_relat_1(A)) = A)) # label(t86_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1330 $T # label(t161_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1331 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r1_tarski(k2_relat_1(D),C) -> m2_relset_1(D,A,C) & v1_funct_1(D)))) # label(t29_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1332 (all A all B all C all D all E (v1_funct_1(E) & m2_relset_1(E,A,B) -> (r1_tarski(B,D) & r1_tarski(A,C) -> m2_relset_1(E,C,D) & v1_funct_1(E)))) # label(t32_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1333 (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]. 28.13/27.76 1334 (all A all B (v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_relat_1(A) -> r1_partfun1(A,A))) # label(reflexivity_r1_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1335 (all A k4_partfun1(k1_xboole_0,A) = k1_tarski(k1_xboole_0)) # label(t122_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1336 $T # label(t184_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1337 $T # label(t103_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1338 (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) -> m2_relset_1(D,C,B) & v1_funct_1(D)))) # label(t28_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1339 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> k2_partfun1(A,B,k3_partfun1(D,A,B),C) = k3_partfun1(D,k3_xboole_0(A,C),B))) # label(t96_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1340 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C k3_partfun1(A,B,C) = k7_relat_1(k8_relat_1(C,A),B)))) # label(d3_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1341 $T # label(t9_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1342 $T # label(t107_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1343 (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)) -> k1_funct_1(A,B) = f3_s3_partfun1(B))) & (all B (p1_s3_partfun1(B) & r2_hidden(B,f1_s3_partfun1) <-> 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]. 28.13/27.76 1344 $T # label(t165_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1345 (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]. 28.13/27.76 1346 $T # label(t23_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1347 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,k1_xboole_0,A) -> k1_xboole_0 = k10_relat_1(C,B))) # label(t61_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1348 $T # label(t154_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1349 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,k1_xboole_0) -> k2_relat_1(B) = k1_xboole_0 & k1_xboole_0 = k4_relset_1(A,k1_xboole_0,B))) # label(t62_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1350 $T # label(t156_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1351 (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]. 28.13/27.76 1352 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> k5_partfun1(k1_xboole_0,A,B) = k1_tarski(k1_xboole_0))) # label(t176_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1353 (all A k6_partfun1(A) = k6_relat_1(A)) # label(redefinition_k6_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1354 (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) -> k1_partfun1(A,B,C,D,E,F) = k5_relat_1(E,F))) # label(redefinition_k1_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1355 $T # label(t150_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1356 (all A exists B (m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v4_relat_2(B) & v3_relat_2(B) & v1_relat_2(B) & v1_relat_1(B))) # label(rc3_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1357 $T # label(t109_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1358 (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) -> m2_relset_1(k1_partfun1(A,B,C,D,E,F),A,D) & v1_funct_1(k1_partfun1(A,B,C,D,E,F)))) # label(dt_k1_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1359 (all A (v8_relat_2(A) & v3_relat_2(A) & v1_relat_1(A) -> v1_relat_2(A) & v1_relat_1(A))) # label(cc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1360 $T # label(t166_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1361 $T # label(t20_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1362 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((exists C (v1_funct_1(C) & C = k2_xboole_0(A,B) & v1_relat_1(C))) <-> r1_partfun1(A,B)))))) # label(t130_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1363 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r1_tarski(A,B) -> r1_tarski(k3_partfun1(D,C,A),k3_partfun1(D,C,B))))) # label(t83_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1364 (all A all B (m2_relset_1(B,A,k1_xboole_0) & v1_funct_1(B) -> (k1_xboole_0 != A -> k1_xboole_0 = k5_partfun1(A,k1_xboole_0,B)))) # label(t172_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1365 (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) -> -((k1_xboole_0 = B -> k1_xboole_0 = A) & r1_partfun1(C,D) & (all E (m2_relset_1(E,A,B) & v1_funct_1(E) -> -(r1_partfun1(C,E) & r1_partfun1(D,E) & v1_partfun1(E,A,B))))))))) # label(t162_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1366 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> k1_xboole_0 = B)) # label(t57_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1367 $T # label(t183_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1368 (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]. 28.13/27.76 1369 (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)) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(A,C) = k1_funct_1(B,C))) <-> r1_partfun1(A,B))))))) # label(t132_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1370 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_tarski(k4_relset_1(A,B,k3_partfun1(C,A,B)),k1_relat_1(C)) & r1_tarski(k2_relat_1(k3_partfun1(C,A,B)),k2_relat_1(C)))) # label(t77_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1371 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_xboole_0) -> k1_xboole_0 = k9_relat_1(C,B))) # label(t67_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1372 $T # label(t89_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1373 (all A all B all C (v1_relat_1(C) & v1_funct_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]. 28.13/27.76 1374 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> v2_funct_1(B))) # label(t59_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1375 $T # label(t6_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1376 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_relat_1(E) & v1_funct_1(E) -> (r1_tarski(D,C) & r1_partfun1(C,E) -> r1_partfun1(D,E)))))))) # label(t140_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1377 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_xboole_0) -> k10_relat_1(C,B) = k1_xboole_0)) # label(t68_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1378 $T # label(t149_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1379 $T # label(t13_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1380 (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]. 28.13/27.76 1381 $T # label(t134_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1382 $T # label(t98_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1383 (all A all B (v1_partfun1(k3_partfun1(k1_xboole_0,A,B),A,B) -> A = k1_xboole_0)) # label(t114_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1384 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> 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]. 28.13/27.76 1385 $T # label(t41_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1386 (all A all B all C (m1_subset_1(C,k4_partfun1(A,B)) -> m2_relset_1(C,A,B) & v1_funct_1(C))) # label(t121_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1387 $T # label(t14_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1388 (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]. 28.13/27.76 1389 $T # label(t159_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1390 $T # label(t15_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1391 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (v1_partfun1(C,A,B) & k1_xboole_0 = B -> A = k1_xboole_0))) # label(t99_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1392 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_relat_1(C),B) & r1_tarski(k1_relat_1(C),A) -> C = k3_partfun1(C,A,B)))) # label(t85_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1393 (all A all B (p1_s5_partfun1(A,B) -> r2_hidden(f4_s5_partfun1(A,B),f3_s5_partfun1))) -> (exists A (v1_funct_1(A) & (all B all C (r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1,A)) -> f4_s5_partfun1(B,C) = k1_funct_1(A,k4_tarski(B,C)))) & (all B all C (r2_hidden(B,f1_s5_partfun1) & p1_s5_partfun1(B,C) & r2_hidden(C,f2_s5_partfun1) <-> r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1,A)))) & m2_relset_1(A,k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1))) # label(s5_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1394 (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]. 28.13/27.76 1395 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k2_relat_1(B),A) -> v1_funct_1(B) & m2_relset_1(B,k1_relat_1(B),A)))) # label(t25_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1396 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> m2_relset_1(k8_relset_1(A,B,D,C),A,B) & v1_funct_1(k8_relset_1(A,B,D,C)))) # label(t44_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1397 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(D,k5_partfun1(A,B,C)) -> r1_partfun1(C,D)))))) # label(t171_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1398 (all A (m2_relset_1(k6_partfun1(A),A,A) & v1_partfun1(k6_partfun1(A),A,A))) # label(dt_k6_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1399 (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]. 28.13/27.76 1400 (all A all B all C (C = k4_partfun1(A,B) <-> (all D ((exists E (v1_relat_1(E) & r1_tarski(k2_relat_1(E),B) & r1_tarski(k1_relat_1(E),A) & E = D & v1_funct_1(E))) <-> r2_hidden(D,C))))) # label(d5_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1401 (all A all B all C (m2_relset_1(C,A,k1_xboole_0) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,k1_xboole_0) -> C = D)))) # label(t65_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1402 (all A all B all C all D all E all F (r1_tarski(D,k2_zfmisc_1(E,F)) & r1_tarski(A,k2_zfmisc_1(B,C)) -> r1_tarski(k2_xboole_0(A,D),k2_zfmisc_1(k2_xboole_0(B,E),k2_xboole_0(C,F))))) # label(t1_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1403 $T # label(t179_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1404 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_xboole_0 = k1_relat_1(C) -> v1_funct_1(C) & m2_relset_1(C,A,B)))) # label(t55_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1405 $T # label(t133_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1406 $T # label(t90_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1407 (all A (v1_relat_1(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)) & v8_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)))) # label(fc2_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1408 (all A all B all C all D (m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (all E (m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_1(E) -> (k4_relset_1(k2_zfmisc_1(A,B),C,D) = k4_relset_1(k2_zfmisc_1(A,B),C,E) & (all F all G (r2_hidden(k4_tarski(F,G),k4_relset_1(k2_zfmisc_1(A,B),C,D)) -> k1_funct_1(E,k4_tarski(F,G)) = k1_funct_1(D,k4_tarski(F,G)))) -> D = E))))) # label(t35_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.76 1409 $T # label(t153_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1410 $T # label(t40_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1411 (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]. 28.13/27.77 1412 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (r2_hidden(D,k4_relset_1(A,B,C)) & r2_hidden(E,k4_relset_1(A,B,C)) & k1_funct_1(C,D) = k1_funct_1(C,E) -> E = D))))) -> v2_funct_1(C)))) # label(t38_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1413 (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(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]. 28.13/27.77 1414 (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) -> C != k2_xboole_0(A,B))) & (all C (r2_hidden(C,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(A,C) = k1_funct_1(B,C)))))))) # label(t2_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1415 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> -((all E (m1_subset_1(E,A) -> -(r2_hidden(E,k4_relset_1(A,B,D)) & k1_funct_1(D,E) = C))) & r2_hidden(C,k9_relat_1(D,A))))) # label(t49_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1416 (exists A (v1_funct_1(A) & v1_xboole_0(A) & v2_funct_1(A) & v1_relat_1(A))) # label(rc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1417 $T # label(t137_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1418 $T # label(t19_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1419 $T # label(t4_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1420 (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]. 28.13/27.77 1421 (all A k1_tarski(k1_xboole_0) = k4_partfun1(A,k1_xboole_0)) # label(t123_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1422 (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]. 28.13/27.77 1423 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,B) -> r1_partfun1(A,B)))))) # label(t135_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1424 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m2_relset_1(E,A,B) & v1_funct_1(E) -> (v1_partfun1(E,A,B) & r1_partfun1(D,E) & r1_partfun1(C,E) -> r1_partfun1(C,D)))))))) # label(t158_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1425 $T # label(t129_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1426 $T # label(t163_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1427 (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]. 28.13/27.77 1428 (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]. 28.13/27.77 1429 $T # label(dt_k5_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1430 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> v1_partfun1(B,k1_xboole_0,A))) # label(t112_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1431 $T # label(t75_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1432 (all A all B all C (r2_hidden(A,f1_s4_partfun1) & p1_s4_partfun1(A,B,C) & r2_hidden(B,f2_s4_partfun1) -> r2_hidden(C,f3_s4_partfun1))) & (all A all B all C all D (p1_s4_partfun1(A,B,C) & p1_s4_partfun1(A,B,D) & r2_hidden(B,f2_s4_partfun1) & r2_hidden(A,f1_s4_partfun1) -> C = D)) -> (exists A (m2_relset_1(A,k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1) & (all B all C (r2_hidden(C,f2_s4_partfun1) & (exists D p1_s4_partfun1(B,C,D)) & r2_hidden(B,f1_s4_partfun1) <-> r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1,A)))) & (all B all C (r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1,A)) -> p1_s4_partfun1(B,C,k1_funct_1(A,k4_tarski(B,C))))) & v1_funct_1(A))) # label(s4_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1433 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r2_hidden(D,k5_partfun1(A,B,C)) -> v1_partfun1(D,A,B)))))) # label(t169_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1434 $T # label(t110_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1435 (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]. 28.13/27.77 1436 (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]. 28.13/27.77 1437 $T # label(t105_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1438 (all A all B all C all D (m2_relset_1(D,k1_tarski(A),B) & v1_funct_1(D) -> r1_tarski(k9_relat_1(D,C),k1_tarski(k1_funct_1(D,A))))) # label(t71_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1439 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(k1_funct_1(D,A),C) & r2_hidden(A,B) & k1_relat_1(D) = k1_tarski(A) -> m2_relset_1(D,B,C) & v1_funct_1(D)))) # label(t72_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1440 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> k10_relat_1(C,B) = k4_relset_1(A,B,C))) # label(t53_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1441 $T # label(t11_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1442 (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]. 28.13/27.77 1443 $T # label(t5_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1444 (all A all B (m2_relset_1(B,A,k1_xboole_0) & v1_funct_1(B) -> k1_xboole_0 = B)) # label(t64_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1445 (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,B) & r2_hidden(k1_funct_1(D,A),C) & r2_hidden(A,k1_relat_1(D))))) # label(t78_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1446 (all A all B all C (m2_relset_1(C,A,B) -> (A = k4_relset_1(A,B,C) <-> v1_partfun1(C,A,B)))) # label(d4_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1447 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> r1_partfun1(A,B)))))) # label(t138_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1448 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r2_hidden(C,k4_relset_1(A,B,D)) -> r2_hidden(k1_funct_1(D,C),B)))) # label(t27_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1449 $T # label(t50_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1450 (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]. 28.13/27.77 1451 $T # label(t48_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1452 (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]. 28.13/27.77 1453 $T # label(t180_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1454 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,k1_xboole_0,A) -> k9_relat_1(C,B) = k1_xboole_0)) # label(t60_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1455 (all A all B exists C (v1_funct_1(C) & v1_relat_1(C) & m1_relset_1(C,A,B))) # label(rc2_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1456 $T # label(dt_k4_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1457 (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]. 28.13/27.77 1458 $T # label(t100_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1459 $T # label(t16_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1460 (all A all B -v1_xboole_0(k4_partfun1(A,B))) # label(fc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1461 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (v1_partfun1(C,A,B) & r1_partfun1(C,D) & v1_partfun1(D,A,B) -> C = D))))) # label(t148_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1462 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_partfun1(k7_relat_1(B,A),B))) # label(t144_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1463 $T # label(t42_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1464 $T # label(t152_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1465 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> -((k1_xboole_0 = B -> A = k1_xboole_0) & r1_partfun1(C,D) & r1_xboole_0(k5_partfun1(A,B,C),k5_partfun1(A,B,D))))))) # label(t186_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1466 $T # label(t167_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1467 (all A all B all C (m2_relset_1(C,A,B) -> k5_relat_1(C,k6_relat_1(B)) = C)) # label(t37_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1468 (all A all B all C (r2_hidden(A,f1_s2_partfun1) & p1_s2_partfun1(A,C) & p1_s2_partfun1(A,B) -> B = C)) & (all A all B (r2_hidden(A,f1_s2_partfun1) & p1_s2_partfun1(A,B) -> 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 ((exists C p1_s2_partfun1(B,C)) & r2_hidden(B,f1_s2_partfun1) <-> r2_hidden(B,k4_relset_1(f1_s2_partfun1,f2_s2_partfun1,A)))))) # label(s2_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1469 (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)) -> r1_partfun1(C,D))))) # label(t143_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1470 $T # label(t8_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1471 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (D = k5_partfun1(A,B,C) <-> (all E ((exists F (v1_funct_1(F) & m2_relset_1(F,A,B) & v1_partfun1(F,A,B) & r1_partfun1(C,F) & E = F)) <-> r2_hidden(E,D))))))) # label(d7_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1472 (all A all B all C (m2_relset_1(C,k1_xboole_0,A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k1_xboole_0,B) -> D = C)))) # label(t58_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1473 $T # label(t111_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1474 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_xboole_0 = k2_relat_1(C) -> v1_funct_1(C) & m2_relset_1(C,A,B)))) # label(t63_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1475 $T # label(t151_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1476 $T # label(t18_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1477 $T # label(t155_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1478 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (v1_partfun1(k3_partfun1(C,A,B),A,B) -> r1_tarski(A,k1_relat_1(C))))) # label(t113_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1479 (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]. 28.13/27.77 1480 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(A) = k1_relat_1(B) & r1_partfun1(A,B) -> B = A))))) # label(t136_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1481 $T # label(t22_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1482 (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]. 28.13/27.77 1483 $T # label(t7_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1484 $T # label(t181_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1485 $T # label(t178_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1486 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> k1_tarski(B) = k5_partfun1(k1_xboole_0,A,B))) # label(t175_partfun1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1487 (all A all B all C (v1_relat_1(C) & v1_funct_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]. 28.13/27.77 1488 (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]. 28.13/27.77 1489 (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]. 28.13/27.77 1490 (all A all B all C all D all E k2_enumset1(k3_mcart_1(A,B,D),k3_mcart_1(A,C,D),k3_mcart_1(A,B,E),k3_mcart_1(A,C,E)) = k3_zfmisc_1(k1_tarski(A),k2_tarski(B,C),k2_tarski(D,E))) # label(t45_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1491 (all A all B all C all D k3_zfmisc_1(k1_tarski(A),k2_tarski(B,C),k1_tarski(D)) = k2_tarski(k3_mcart_1(A,B,D),k3_mcart_1(A,C,D))) # label(t41_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1492 (all A all B all C all D k3_mcart_1(k4_tarski(A,B),C,D) = k4_mcart_1(A,B,C,D)) # label(t32_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1493 (all A all B (k1_xboole_0 != k2_zfmisc_1(A,B) -> (all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> k1_mcart_1(C) != C & C != k2_mcart_1(C))))) # label(t66_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1494 (all A all B all C -(B != k1_xboole_0 & (exists D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) & (exists E exists F exists G (D = k3_mcart_1(E,F,G) & -(k5_mcart_1(A,B,C,D) = E & k6_mcart_1(A,B,C,D) = F & G = k7_mcart_1(A,B,C,D)))))) & C != k1_xboole_0 & k1_xboole_0 != A)) # label(t47_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1495 (all A all B all C all D k2_tarski(k3_mcart_1(A,B,C),k3_mcart_1(A,B,D)) = k3_zfmisc_1(k1_tarski(A),k1_tarski(B),k2_tarski(C,D))) # label(t42_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1496 (all A -(k1_xboole_0 != A & (all B -(r2_hidden(B,A) & (all C all D -((r2_hidden(D,A) | r2_hidden(C,A)) & k4_tarski(C,D) = B)))))) # label(t9_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1497 (all A all B all C (r2_hidden(A,k2_zfmisc_1(B,C)) -> A != k1_mcart_1(A) & k2_mcart_1(A) != A)) # label(t67_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1498 (all A all B all C all D all E all F all G all H (r1_tarski(C,D) & r1_tarski(G,H) & r1_tarski(E,F) & r1_tarski(A,B) -> r1_tarski(k4_zfmisc_1(A,C,E,G),k4_zfmisc_1(B,D,F,H)))) # label(t88_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1499 (all A all B all C all D all E k3_zfmisc_1(k2_tarski(A,B),k1_tarski(C),k2_tarski(D,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))) # label(t44_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1500 $T # label(dt_k3_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1501 $T # label(dt_k2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1502 (all A all B all C all D all E all F all G all H (-r1_xboole_0(k4_zfmisc_1(A,B,C,D),k4_zfmisc_1(E,F,G,H)) -> -r1_xboole_0(B,F) & -r1_xboole_0(D,H) & -r1_xboole_0(C,G) & -r1_xboole_0(A,E))) # label(t64_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1503 $T # label(dt_k19_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1504 (all A all B all C all D all E all F all G all H -(A != k1_xboole_0 & k1_xboole_0 != B & k1_xboole_0 != D & F != k1_xboole_0 & k1_xboole_0 != G & H != k1_xboole_0 & (exists I ((exists J (J = I & -(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) & k9_mcart_1(E,F,G,H,J) = k9_mcart_1(A,B,C,D,I) & k8_mcart_1(E,F,G,H,J) = k8_mcart_1(A,B,C,D,I)) & m1_subset_1(J,k4_zfmisc_1(E,F,G,H)))) & m1_subset_1(I,k4_zfmisc_1(A,B,C,D)))) & k1_xboole_0 != E & k1_xboole_0 != C)) # label(t86_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1505 (all A ((exists B exists C A = k4_tarski(B,C)) -> (all B (B = k2_mcart_1(A) <-> (all C all D (k4_tarski(C,D) = A -> B = D)))))) # label(d2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1506 (all A all B all C -(B != k1_xboole_0 & k1_xboole_0 != C & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> k3_mcart_1(k5_mcart_1(A,B,C,D),k6_mcart_1(A,B,C,D),k7_mcart_1(A,B,C,D)) = D)) & k1_xboole_0 != A)) # label(t48_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1507 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(k2_tarski(B,C),k1_tarski(D))) -> (C = k1_mcart_1(A) | k1_mcart_1(A) = B) & k2_mcart_1(A) = D)) # label(t17_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1508 (all A all B all C all D -(k1_xboole_0 != A & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> k9_mcart_1(A,B,C,D,E) != E & k11_mcart_1(A,B,C,D,E) != E & k10_mcart_1(A,B,C,D,E) != E & k8_mcart_1(A,B,C,D,E) != E)) & k1_xboole_0 != D & C != k1_xboole_0 & k1_xboole_0 != B)) # label(t62_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1509 (all A all B all C all D all E all F (m1_subset_1(D,k1_zfmisc_1(A)) & m1_subset_1(F,k1_zfmisc_1(C)) & m1_subset_1(E,k1_zfmisc_1(B)) -> 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]. 28.13/27.77 1510 (all A all B all C all D -(k1_xboole_0 != A & k1_xboole_0 != C & -(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)) & D != k1_xboole_0 & B != k1_xboole_0)) # label(t60_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1511 (all A all B all C (r2_hidden(k1_mcart_1(A),B) & r2_hidden(k2_mcart_1(A),C) -> r2_hidden(A,k2_zfmisc_1(B,C)) | (all D all E k4_tarski(D,E) != A))) # label(t11_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1512 $T # label(dt_k4_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1513 (all A all B all C -(A != k1_xboole_0 & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> D != k6_mcart_1(A,B,C,D) & D != k7_mcart_1(A,B,C,D) & D != k5_mcart_1(A,B,C,D))) & k1_xboole_0 != C & k1_xboole_0 != B)) # label(t51_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1514 (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]. 28.13/27.77 1515 (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(C,G) & r2_hidden(D,H) & r2_hidden(B,F) & r2_hidden(A,E))) # label(t84_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1516 (all A -((all B -(r2_hidden(B,A) & (all C all D all E (r2_hidden(E,B) & r2_hidden(D,E) & r2_hidden(C,D) -> r1_xboole_0(C,A))))) & A != k1_xboole_0)) # label(t4_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1517 (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]. 28.13/27.77 1518 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (all E (m1_subset_1(E,k1_zfmisc_1(B)) -> (all F (m1_subset_1(F,k1_zfmisc_1(C)) -> (all G (m1_subset_1(G,k3_zfmisc_1(A,B,C)) -> (r2_hidden(G,k3_zfmisc_1(D,E,F)) -> r2_hidden(k5_mcart_1(A,B,C,G),D) & r2_hidden(k6_mcart_1(A,B,C,G),E) & r2_hidden(k7_mcart_1(A,B,C,G),F)))))))))) # label(t76_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1519 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k15_mcart_1(A)) & v1_relat_1(k15_mcart_1(A)))) # label(dt_k15_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1520 (all A all B all C all D all E all F (k3_mcart_1(A,B,C) = k3_mcart_1(D,E,F) -> C = F & B = E & A = D)) # label(t28_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1521 (all A all B all C all D all E all F -(A != k1_xboole_0 & k1_xboole_0 != D & k1_xboole_0 != F & (exists G (m1_subset_1(G,k3_zfmisc_1(A,B,C)) & (exists H (H = G & -(k5_mcart_1(A,B,C,G) = k5_mcart_1(D,E,F,H) & k6_mcart_1(D,E,F,H) = k6_mcart_1(A,B,C,G) & k7_mcart_1(A,B,C,G) = k7_mcart_1(D,E,F,H)) & m1_subset_1(H,k3_zfmisc_1(D,E,F)))))) & E != k1_xboole_0 & k1_xboole_0 != C & k1_xboole_0 != B)) # label(t75_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1522 (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]. 28.13/27.77 1523 (all A all B all C all D k3_zfmisc_1(k2_zfmisc_1(A,B),C,D) = k4_zfmisc_1(A,B,C,D)) # label(t54_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1524 (all A all B all C (k3_zfmisc_1(A,B,C) != k1_xboole_0 <-> A != k1_xboole_0 & B != k1_xboole_0 & C != k1_xboole_0)) # label(t35_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1525 (all A all B all C -(C != k1_xboole_0 & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> (all E (m1_subset_1(E,C) -> (E = k7_mcart_1(A,B,C,D) <-> (all F all G all H (k3_mcart_1(F,G,H) = D -> H = E))))))) & B != k1_xboole_0 & k1_xboole_0 != A)) # label(d7_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1526 (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) -> C = k1_xboole_0 | D = k1_xboole_0 | G = C & H = D & B = F & E = A | k1_xboole_0 = B | k1_xboole_0 = A)) # label(t56_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1527 (all A all B all C all D all E (m1_subset_1(E,k3_zfmisc_1(A,B,C)) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (k3_mcart_1(F,G,H) = E -> D = F))))))) -> k1_xboole_0 = B | k1_xboole_0 = C | k5_mcart_1(A,B,C,E) = D | A = k1_xboole_0))) # label(t69_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1528 (all A all B all C (r2_hidden(A,k2_zfmisc_1(B,C)) -> r2_hidden(k1_mcart_1(A),B) & r2_hidden(k2_mcart_1(A),C))) # label(t10_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1529 (all A all B (k3_zfmisc_1(B,B,B) = k3_zfmisc_1(A,A,A) -> A = B)) # label(t38_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1530 (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]. 28.13/27.77 1531 (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)) -> 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]. 28.13/27.77 1532 (all A -(A != k1_xboole_0 & (all B -(r2_hidden(B,A) & r1_xboole_0(B,A))))) # label(t1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1533 (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) -> D = H & G = C & B = F & E = A | k1_xboole_0 = k4_zfmisc_1(A,B,C,D))) # label(t57_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.77 1534 (all A all B all C all D all E all F (A = k17_mcart_1(k4_tarski(k4_tarski(A,B),C)) & B = k18_mcart_1(k4_tarski(k4_tarski(A,B),C)) & k20_mcart_1(k4_tarski(F,k4_tarski(D,E))) = E & k19_mcart_1(k4_tarski(F,k4_tarski(D,E))) = D)) # label(t89_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1535 (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]. 28.13/27.78 1536 (all A all B -(-(all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> C = k4_tarski(k1_mcart_1(C),k2_mcart_1(C)))) & k1_xboole_0 != B & k1_xboole_0 != A)) # label(t24_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1537 (all A all B all C all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> -(A != k1_xboole_0 & k1_xboole_0 != C & (exists E exists F exists G (-(k5_mcart_1(A,B,C,D) = E & G = k7_mcart_1(A,B,C,D) & F = k6_mcart_1(A,B,C,D)) & D = k3_mcart_1(E,F,G))) & B != k1_xboole_0))) # label(t68_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1538 (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]. 28.13/27.78 1539 (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]. 28.13/27.78 1540 $T # label(dt_k1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1541 (all A all B all C all D all E all F (r1_tarski(A,B) & r1_tarski(E,F) & r1_tarski(C,D) -> r1_tarski(k3_zfmisc_1(A,C,E),k3_zfmisc_1(B,D,F)))) # label(t77_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1542 (all A all B all C all D k4_mcart_1(A,B,C,D) = k4_tarski(k3_mcart_1(A,B,C),D)) # label(d4_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1543 (all A -(A != k1_xboole_0 & (all B -((all C all D all E all F -((r2_hidden(C,A) | r2_hidden(D,A)) & B = k4_mcart_1(C,D,E,F))) & r2_hidden(B,A))))) # label(t34_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1544 (all A all B all C all D all E all F all G all H (m1_subset_1(G,k1_zfmisc_1(C)) & m1_subset_1(H,k1_zfmisc_1(D)) & m1_subset_1(F,k1_zfmisc_1(B)) & m1_subset_1(E,k1_zfmisc_1(A)) -> k14_mcart_1(A,B,C,D,E,F,G,H) = k4_zfmisc_1(E,F,G,H))) # label(redefinition_k14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1545 (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]. 28.13/27.78 1546 $T # label(t21_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1547 (all A all B all C all D all E all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,D) -> (k4_mcart_1(G,H,I,J) = F -> G = E))))))))) -> k1_xboole_0 = B | D = k1_xboole_0 | E = k8_mcart_1(A,B,C,D,F) | C = k1_xboole_0 | k1_xboole_0 = A))) # label(t79_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1548 (all A all B all C all D all E (m1_subset_1(E,k3_zfmisc_1(A,B,C)) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (k3_mcart_1(F,G,H) = E -> H = D))))))) -> C = k1_xboole_0 | D = k7_mcart_1(A,B,C,E) | B = k1_xboole_0 | A = k1_xboole_0))) # label(t71_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1549 (all A all B all C all D all E all F (k3_zfmisc_1(D,E,F) = k3_zfmisc_1(A,B,C) -> k3_zfmisc_1(A,B,C) = k1_xboole_0 | D = A & E = B & C = F)) # label(t37_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1550 (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))))))) -> A = k1_xboole_0 | k6_mcart_1(A,B,C,E) = D | C = k1_xboole_0 | k1_xboole_0 = B))) # label(t70_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1551 (all A all B all C (r2_hidden(A,k2_zfmisc_1(k1_tarski(B),k1_tarski(C))) -> k1_mcart_1(A) = B & k2_mcart_1(A) = C)) # label(t14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1552 (all A all B all C all D all E all F k6_enumset1(k3_mcart_1(A,C,E),k3_mcart_1(A,D,E),k3_mcart_1(A,C,F),k3_mcart_1(A,D,F),k3_mcart_1(B,C,E),k3_mcart_1(B,D,E),k3_mcart_1(B,C,F),k3_mcart_1(B,D,F)) = k3_zfmisc_1(k2_tarski(A,B),k2_tarski(C,D),k2_tarski(E,F))) # label(t46_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1553 (all A all B all C all D (-(-r1_tarski(A,k4_zfmisc_1(A,B,C,D)) & -r1_tarski(A,k4_zfmisc_1(B,C,D,A)) & -r1_tarski(A,k4_zfmisc_1(D,A,B,C)) & -r1_tarski(A,k4_zfmisc_1(C,D,A,B))) -> k1_xboole_0 = A)) # label(t63_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1554 (all A all B all C all D k2_tarski(k3_mcart_1(A,C,D),k3_mcart_1(B,C,D)) = k3_zfmisc_1(k2_tarski(A,B),k1_tarski(C),k1_tarski(D))) # label(t40_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1555 (all A -((all B -(r2_hidden(B,A) & (all C all D (r2_hidden(D,B) & r2_hidden(C,D) -> r1_xboole_0(C,A))))) & k1_xboole_0 != A)) # label(t3_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1556 (all A all B all C all D all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> -(k1_xboole_0 != C & (exists F exists G exists H exists I (-(k10_mcart_1(A,B,C,D,E) = H & I = k11_mcart_1(A,B,C,D,E) & G = k9_mcart_1(A,B,C,D,E) & F = k8_mcart_1(A,B,C,D,E)) & E = k4_mcart_1(F,G,H,I))) & k1_xboole_0 != D & B != k1_xboole_0 & A != k1_xboole_0))) # label(t78_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1557 (all A all B all C all D -(C != k1_xboole_0 & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,B) -> ((all G all H all I all J (k4_mcart_1(G,H,I,J) = E -> F = H)) <-> F = k9_mcart_1(A,B,C,D,E)))))) & k1_xboole_0 != D & B != k1_xboole_0 & k1_xboole_0 != A)) # label(d9_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1558 $T # label(dt_k17_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1559 (all A all B -(B != k1_xboole_0 & -(all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> k2_mcart_1(C) != C & C != k1_mcart_1(C))) & k1_xboole_0 != A)) # label(t26_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1560 (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) & k4_mcart_1(G,H,I,J) = F & r2_hidden(J,E) & r2_hidden(H,C))))) -> A = k4_zfmisc_1(B,C,D,E))) # label(t85_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1561 (all A -(k1_xboole_0 != A & (all B -((all C all D all E -((r2_hidden(D,A) | r2_hidden(C,A)) & B = k3_mcart_1(C,D,E))) & r2_hidden(B,A))))) # label(t29_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1562 (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]. 28.13/27.78 1563 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(B,C) = k1_mcart_1(k1_funct_1(A,C)))) & k1_relat_1(B) = k1_relat_1(A) <-> k15_mcart_1(A) = B))))) # label(d12_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1564 (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]. 28.13/27.78 1565 (all A all B all C all D all E all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,D) -> (F = k4_mcart_1(G,H,I,J) -> E = H))))))))) -> D = k1_xboole_0 | E = k9_mcart_1(A,B,C,D,F) | C = k1_xboole_0 | B = k1_xboole_0 | A = k1_xboole_0))) # label(t80_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1566 (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(C,F) & -r1_xboole_0(B,E) & -r1_xboole_0(A,D))) # label(t52_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1567 (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]. 28.13/27.78 1568 (all A k20_mcart_1(A) = k2_mcart_1(k2_mcart_1(A))) # label(d17_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1569 (all A all B all C all D -(-(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,C) -> (k10_mcart_1(A,B,C,D,E) = F <-> (all G all H all I all J (E = k4_mcart_1(G,H,I,J) -> F = I))))))) & k1_xboole_0 != D & k1_xboole_0 != C & B != k1_xboole_0 & A != k1_xboole_0)) # label(d10_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1570 $T # label(t30_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1571 $T # label(dt_k20_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1572 $T # label(dt_k18_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1573 (all A ((exists B exists C k4_tarski(B,C) = A) -> k2_mcart_1(A) != A & k1_mcart_1(A) != A)) # label(t20_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1574 (all A all B all C all D ((all E ((exists F exists G exists H (r2_hidden(F,B) & r2_hidden(H,D) & k3_mcart_1(F,G,H) = E & r2_hidden(G,C))) <-> r2_hidden(E,A))) -> A = k3_zfmisc_1(B,C,D))) # label(t74_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1575 (all A all B (k2_mcart_1(k4_tarski(A,B)) = B & k1_mcart_1(k4_tarski(A,B)) = A)) # label(t7_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1576 $T # label(t22_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1577 (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]. 28.13/27.78 1578 (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]. 28.13/27.78 1579 (all A all B all C all D -(C != k1_xboole_0 & k1_xboole_0 != D & (exists E ((exists F exists G exists H exists I (E = k4_mcart_1(F,G,H,I) & -(G = k9_mcart_1(A,B,C,D,E) & k11_mcart_1(A,B,C,D,E) = I & k10_mcart_1(A,B,C,D,E) = H & F = k8_mcart_1(A,B,C,D,E)))) & m1_subset_1(E,k4_zfmisc_1(A,B,C,D)))) & k1_xboole_0 != B & k1_xboole_0 != A)) # label(t59_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1580 (all A all B all C all D -(k1_xboole_0 != B & D != k1_xboole_0 & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,D) -> ((all G all H all I all J (k4_mcart_1(G,H,I,J) = E -> F = J)) <-> k11_mcart_1(A,B,C,D,E) = F))))) & C != k1_xboole_0 & A != k1_xboole_0)) # label(d11_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1581 (all A all B all C all D all E all F (m1_subset_1(F,k1_zfmisc_1(C)) & m1_subset_1(E,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(A)) -> 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]. 28.13/27.78 1582 (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]. 28.13/27.78 1583 (all A k1_mcart_1(k2_mcart_1(A)) = k19_mcart_1(A)) # label(d16_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1584 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k16_mcart_1(A)) & v1_funct_1(k16_mcart_1(A)))) # label(dt_k16_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1585 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C (r2_hidden(C,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) <-> B = k16_mcart_1(A)))))) # label(d13_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1586 (all A all B all C all D all E all F (k3_zfmisc_1(D,E,F) = k3_zfmisc_1(A,B,C) -> k1_xboole_0 = A | C = k1_xboole_0 | D = A & E = B & F = C | k1_xboole_0 = B)) # label(t36_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1587 (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,A) -> (k5_mcart_1(A,B,C,D) = E <-> (all F all G all H (D = k3_mcart_1(F,G,H) -> F = E))))))) & k1_xboole_0 != C & k1_xboole_0 != A)) # label(d5_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1588 (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]. 28.13/27.78 1589 (all A all B all C all D all E -((all F all G all H all I -(r2_hidden(H,D) & r2_hidden(I,E) & k4_mcart_1(F,G,H,I) = A & r2_hidden(G,C) & r2_hidden(F,B))) & r2_hidden(A,k4_zfmisc_1(B,C,D,E)))) # label(t83_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1590 (all A all B all C -(k1_xboole_0 != A & k1_xboole_0 != B & k1_xboole_0 != C & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> k2_mcart_1(k1_mcart_1(D)) = k6_mcart_1(A,B,C,D) & k2_mcart_1(D) = k7_mcart_1(A,B,C,D) & k5_mcart_1(A,B,C,D) = k1_mcart_1(k1_mcart_1(D)))))) # label(t50_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1591 (all A k18_mcart_1(A) = k2_mcart_1(k1_mcart_1(A))) # label(d15_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1592 (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))))))))) -> B = k1_xboole_0 | C = k1_xboole_0 | k10_mcart_1(A,B,C,D,F) = E | D = k1_xboole_0 | k1_xboole_0 = A))) # label(t81_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1593 (all A all B (k4_zfmisc_1(A,A,A,A) = k4_zfmisc_1(B,B,B,B) -> A = B)) # label(t58_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1594 (all A -((all B -(r2_hidden(B,A) & (all C (r2_hidden(C,B) -> r1_xboole_0(C,A))))) & A != k1_xboole_0)) # label(t2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1595 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(k1_tarski(B),k2_tarski(C,D))) -> (D = k2_mcart_1(A) | C = k2_mcart_1(A)) & k1_mcart_1(A) = B)) # label(t18_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1596 (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))) -> A = k1_xboole_0)) # label(t49_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1597 (all A all B all C all D (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(D,k1_zfmisc_1(B)) -> k2_zfmisc_1(C,D) = k12_mcart_1(A,B,C,D))) # label(redefinition_k12_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1598 (all A all B all C all D all E k2_enumset1(k3_mcart_1(A,C,E),k3_mcart_1(B,C,E),k3_mcart_1(A,D,E),k3_mcart_1(B,D,E)) = k3_zfmisc_1(k2_tarski(A,B),k2_tarski(C,D),k1_tarski(E))) # label(t43_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1599 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(k2_tarski(B,C),D)) -> (k1_mcart_1(A) = C | B = k1_mcart_1(A)) & r2_hidden(k2_mcart_1(A),D))) # label(t15_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1600 (all A ((exists B exists C k4_tarski(B,C) = A) -> (all B ((all C all D (k4_tarski(C,D) = A -> B = C)) <-> B = k1_mcart_1(A))))) # label(d1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1601 (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) -> (E = k6_mcart_1(A,B,C,D) <-> (all F all G all H (D = k3_mcart_1(F,G,H) -> E = G))))))) & C != k1_xboole_0 & A != k1_xboole_0)) # label(d6_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1602 (all A all B all C all D -(k1_xboole_0 != A & k1_xboole_0 != B & 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))) & k11_mcart_1(A,B,C,D,E) = k2_mcart_1(E) & k2_mcart_1(k1_mcart_1(E)) = k10_mcart_1(A,B,C,D,E))) & k1_xboole_0 != C)) # label(t61_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1603 (all A -((all B -(r2_hidden(B,A) & (all C all D all E all F all G (r2_hidden(C,D) & r2_hidden(F,G) & r2_hidden(G,B) & r2_hidden(E,F) & r2_hidden(D,E) -> r1_xboole_0(C,A))))) & A != k1_xboole_0)) # label(t6_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1604 (all A all B all C all D all E all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,D) -> (k4_mcart_1(G,H,I,J) = F -> E = J))))))))) -> k1_xboole_0 = A | k11_mcart_1(A,B,C,D,F) = E | k1_xboole_0 = D | k1_xboole_0 = C | k1_xboole_0 = B))) # label(t82_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1605 (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]. 28.13/27.78 1606 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(B,k2_tarski(C,D))) -> r2_hidden(k1_mcart_1(A),B) & (k2_mcart_1(A) = C | k2_mcart_1(A) = D))) # label(t16_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1607 (all A k1_mcart_1(k1_mcart_1(A)) = k17_mcart_1(A)) # label(d14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1608 (all A all B all C all D -(r2_hidden(A,k3_zfmisc_1(B,C,D)) & (all E all F all G -(r2_hidden(F,C) & k3_mcart_1(E,F,G) = A & r2_hidden(G,D) & r2_hidden(E,B))))) # label(t72_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1609 (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 & H = D & G = C & F = B)) # label(t33_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1610 $T # label(t27_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1611 (all A all B all C all D -(k1_xboole_0 != A & C != 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) -> (F = k8_mcart_1(A,B,C,D,E) <-> (all G all H all I all J (k4_mcart_1(G,H,I,J) = E -> G = F))))))) & k1_xboole_0 != B)) # label(d8_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1612 (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) = E | k2_mcart_1(A) = D) & (k1_mcart_1(A) = C | B = k1_mcart_1(A)))) # label(t19_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1613 (all A all B all C all D (k4_zfmisc_1(A,B,C,D) != k1_xboole_0 <-> B != k1_xboole_0 & k1_xboole_0 != D & k1_xboole_0 != C & A != k1_xboole_0)) # label(t55_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1614 (all A -((all B -((all C all D all E all F (r2_hidden(D,E) & r2_hidden(E,F) & r2_hidden(F,B) & r2_hidden(C,D) -> r1_xboole_0(C,A))) & r2_hidden(B,A))) & k1_xboole_0 != A)) # label(t5_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1615 (all A all B all C all D all E (m1_subset_1(E,k1_zfmisc_1(A)) -> (all F (m1_subset_1(F,k1_zfmisc_1(B)) -> (all G (m1_subset_1(G,k1_zfmisc_1(C)) -> (all H (m1_subset_1(H,k1_zfmisc_1(D)) -> (all I (m1_subset_1(I,k4_zfmisc_1(A,B,C,D)) -> (r2_hidden(I,k4_zfmisc_1(E,F,G,H)) -> r2_hidden(k8_mcart_1(A,B,C,D,I),E) & r2_hidden(k9_mcart_1(A,B,C,D,I),F) & r2_hidden(k11_mcart_1(A,B,C,D,I),H) & r2_hidden(k10_mcart_1(A,B,C,D,I),G)))))))))))) # label(t87_mcart_1) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1616 (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]. 28.13/27.78 1617 $T # label(t19_wellord2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1618 (all A v4_relat_2(k1_wellord2(A))) # label(t5_wellord2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1619 (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]. 28.13/27.78 1620 $T # label(t1_wellord2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1621 $T # label(t21_wellord2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1622 $T # label(t15_wellord2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1623 (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]. 28.13/27.78 1624 $T # label(t24_wellord2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1625 (all A (-v1_xboole_0(A) -> -((all B (v1_relat_1(B) & v1_funct_1(B) -> -((all C (r2_hidden(C,A) -> r2_hidden(k1_funct_1(B,C),C))) & k1_relat_1(B) = A))) & (all B -(k1_xboole_0 = B & r2_hidden(B,A)))))) # label(t28_wellord2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1626 (all A all B (v1_relat_1(B) -> (B = k1_wellord2(A) <-> A = k3_relat_1(B) & (all C all D (r2_hidden(D,A) & r2_hidden(C,A) -> (r1_tarski(C,D) <-> r2_hidden(k4_tarski(C,D),B))))))) # label(d1_wellord2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1627 (all A all B r2_wellord2(A,A)) # label(reflexivity_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1628 (all A -((all B -(p1_s1_wellord2(A,B) & r2_hidden(B,f2_s1_wellord2))) & r2_hidden(A,f1_s1_wellord2))) -> (exists 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) & v1_relat_1(A))) # label(s1_wellord2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1629 (all A all B (r2_wellord2(A,B) -> r2_wellord2(B,A))) # label(symmetry_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1630 (all A all B ((exists C (v1_funct_1(C) & k1_relat_1(C) = A & B = k2_relat_1(C) & v2_funct_1(C) & v1_relat_1(C))) <-> r2_wellord2(A,B))) # label(d4_wellord2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1631 (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]. 28.13/27.78 1632 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) -> (r1_wellord2(A,B) <-> A = k2_wellord2(B)))))) # label(d3_wellord2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1633 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r4_wellord1(k1_wellord2(A),k1_wellord2(B)) -> A = B))))) # label(t11_wellord2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1634 (all A v1_relat_2(k1_wellord2(A))) # label(t2_wellord2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1635 (all A all B all C (r2_wellord2(B,C) & r2_wellord2(A,B) -> r2_wellord2(A,C))) # label(t22_wellord2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1636 (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]. 28.13/27.78 1637 (all A (v3_ordinal1(A) -> v1_wellord1(k1_wellord2(A)))) # label(t6_wellord2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1638 (all A -((all B all C -(r2_hidden(B,f2_s2_wellord2) & r2_hidden(C,f3_s2_wellord2) & p1_s2_wellord2(A,B,C))) & r2_hidden(A,f1_s2_wellord2))) -> (exists A (v1_relat_1(A) & v1_funct_1(A) & (exists B (k1_relat_1(B) = f1_s2_wellord2 & (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(A) = f1_s2_wellord2 & v1_funct_1(B) & v1_relat_1(B))))) # label(s2_wellord2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1639 (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]. 28.13/27.78 1640 (all A all B (r2_wellord2(A,B) <-> r2_tarski(A,B))) # label(redefinition_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1641 (all A v8_relat_2(k1_wellord2(A))) # label(t3_wellord2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1642 (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]. 28.13/27.78 1643 (all A (v1_relat_1(A) -> v3_ordinal1(k2_wellord2(A)))) # label(dt_k2_wellord2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1644 (all A exists B (r2_wellord1(B,A) & v1_relat_1(B))) # label(t26_wellord2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.78 1645 (all A all B (v1_relat_1(B) -> (r2_wellord1(B,A) -> v2_wellord1(k2_wellord1(B,A)) & A = k3_relat_1(k2_wellord1(B,A))))) # label(t25_wellord2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.79 1646 $T # label(t20_wellord2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.79 1647 $T # label(t16_wellord2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.79 1648 $T # label(t18_wellord2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.79 1649 (all A (-v1_xboole_0(A) -> -((all B all C (r2_hidden(B,A) & r2_hidden(C,A) -> r1_xboole_0(B,C) | C = B)) & (all B exists C (r2_hidden(C,A) & (all D k1_tarski(D) != k3_xboole_0(B,C)))) & (all B -(r2_hidden(B,A) & B = k1_xboole_0))))) # label(t27_wellord2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.79 1650 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> (all B (v3_ordinal1(B) -> (B = k2_wellord2(A) <-> r4_wellord1(A,k1_wellord2(B)))))))) # label(d2_wellord2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.79 1651 (all A v1_relat_1(k1_wellord2(A))) # label(dt_k1_wellord2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.79 1652 $T # label(t23_wellord2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.79 1653 (all A (v3_ordinal1(A) -> v2_wellord1(k1_wellord2(A)))) # label(t7_wellord2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.79 1654 (all A (v3_ordinal1(A) -> v6_relat_2(k1_wellord2(A)))) # label(t4_wellord2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.79 1655 (all A all B (r1_tarski(A,B) -> k2_wellord1(k1_wellord2(B),A) = k1_wellord2(A))) # label(t8_wellord2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.79 1656 (all A all B all C (v1_funct_2(C,k1_xboole_0,A) & m2_relset_1(C,k1_xboole_0,A) & v1_funct_1(C) -> k1_xboole_0 = k3_funct_2(k1_xboole_0,A,C,B))) # label(t60_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.79 1657 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(C,A,A) -> (A = k2_relat_1(C) & 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]. 28.13/27.79 1658 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,k1_tarski(B)) & m2_relset_1(C,A,k1_tarski(B)) -> (all D (v1_funct_2(D,A,k1_tarski(B)) & m2_relset_1(D,A,k1_tarski(B)) & v1_funct_1(D) -> C = D)))) # label(t66_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.79 1659 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,A,B) & v1_funct_2(C,A,B) -> m1_subset_1(k2_funct_2(A,B,C,D),k1_zfmisc_1(B)))) # label(dt_k2_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.79 1660 (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]. 28.13/27.79 1661 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r1_tarski(D,C) -> r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D))))))) # label(t165_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.79 1662 (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) -> (exists E (r2_hidden(E,k4_relset_1(A,B,C)) & k1_funct_1(D,E) != k1_funct_1(C,E))))) & (k1_xboole_0 = B -> A = k1_xboole_0)))) # label(t136_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.79 1663 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (k4_relset_1(A,B,C) = A -> v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B)))) # label(t130_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.79 1664 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) -> (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]. 28.13/27.79 1665 $T # label(t39_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.79 1666 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(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(t85_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.79 1667 $T # label(t57_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.79 1668 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> ((B = k1_xboole_0 -> k1_xboole_0 = A) -> v1_partfun1(k3_partfun1(C,A,B),A,B)))) # label(t133_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.79 1669 $T # label(t104_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.79 1670 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> -(A != k1_xboole_0 & B != k1_xboole_0 & -((all D all E (v1_funct_1(E) & m2_relset_1(E,D,A) & v1_funct_2(E,D,A) -> (all F (v1_funct_1(F) & v1_funct_2(F,D,A) & m2_relset_1(F,D,A) -> (k1_partfun1(D,A,A,B,F,C) = k1_partfun1(D,A,A,B,E,C) -> E = F))))) <-> v2_funct_1(C))))) # label(t27_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.79 1671 $T # label(t139_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.79 1672 $T # label(t124_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.79 1673 (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) -> (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)))) -> D = E))))) # label(t118_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.79 1674 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & v3_funct_2(B,A,A) & m2_relset_1(B,A,A) -> k6_partfun1(A) = k5_funct_2(A,B,k6_funct_2(A,B)) & k5_funct_2(A,k6_funct_2(A,B),B) = k6_partfun1(A))) # label(t88_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.79 1675 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(k4_relset_1(A,B,D),k4_relset_1(A,B,C)) & r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) -> r1_tarski(D,C)))))) # label(t166_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.79 1676 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> ((k1_xboole_0 = B -> A = k1_xboole_0) -> (r1_partfun1(C,D) <-> (all E (r2_hidden(E,k4_relset_1(A,B,C)) -> k1_funct_1(C,E) = k1_funct_1(D,E))))))))) # label(t145_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.79 1677 $T # label(t105_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.79 1678 $T # label(t97_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.79 1679 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> (v2_funct_1(B) & k2_relat_1(B) = A -> v1_funct_1(B) & m2_relset_1(B,A,A) & v3_funct_2(B,A,A) & v1_funct_2(B,A,A)))) # label(t83_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.79 1680 $T # label(t112_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.79 1681 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> ((k1_xboole_0 = B -> k1_xboole_0 = A) -> k3_funct_2(A,B,C,B) = A))) # label(t48_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.79 1682 (exists A (v1_funct_1(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))) # label(s4_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.79 1683 (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),k2_relat_1(D)) | B = k1_xboole_0))) # label(t6_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.79 1684 $T # label(t101_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.79 1685 (exists A (f4_s10_funct_2 = k8_funct_2(f1_s10_funct_2,f2_s10_funct_2,A,f3_s10_funct_2) & (all B (m1_subset_1(B,f1_s10_funct_2) -> (f3_s10_funct_2 != B -> k8_funct_2(f1_s10_funct_2,f2_s10_funct_2,A,B) = f5_s10_funct_2(B)))) & m2_relset_1(A,f1_s10_funct_2,f2_s10_funct_2) & v1_funct_2(A,f1_s10_funct_2,f2_s10_funct_2) & v1_funct_1(A))) # label(s10_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.13/27.79 1686 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(C,A,A) & v3_funct_2(C,A,A) -> (r1_tarski(B,A) -> B = k2_funct_2(A,A,C,k3_funct_2(A,A,C,B)) & k3_funct_2(A,A,C,k2_funct_2(A,A,C,B)) = B))) # label(t92_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1687 (all A (m1_subset_1(A,f1_s7_funct_2) -> (all B (m1_subset_1(B,f2_s7_funct_2) -> (exists C (m1_subset_1(C,f3_s7_funct_2) & p1_s7_funct_2(A,B,C))))))) -> (exists A (v1_funct_2(A,k2_zfmisc_1(f1_s7_funct_2,f2_s7_funct_2),f3_s7_funct_2) & 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_1(A))) # label(s7_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1688 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (k6_partfun1(A) = k1_partfun1(A,B,B,A,C,D) -> B = k1_xboole_0 | v2_funct_1(C) & k2_relat_1(D) = A))))) # label(t29_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1689 $T # label(t52_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1690 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> A = k3_funct_2(A,A,B,k2_funct_2(A,A,B,A)))) # label(t82_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1691 (all A all B all C (m1_relset_1(C,A,B) -> (v1_funct_1(C) & v2_funct_1(C) & v1_funct_2(C,A,B) & v2_funct_2(C,A,B) -> v1_funct_1(C) & v1_funct_2(C,A,B) & v3_funct_2(C,A,B)))) # label(cc3_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1692 $T # label(t100_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1693 $T # label(t69_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1694 (all A all B (m1_relset_1(B,A,A) -> (v1_funct_1(B) & v1_funct_2(B,A,A) & v1_relat_2(B) & v1_partfun1(B,A,A) -> v1_funct_1(B) & v2_funct_1(B) & v3_funct_2(B,A,A) & v2_funct_2(B,A,A) & v1_funct_2(B,A,A)))) # label(cc4_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1695 $T # label(t128_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1696 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> ((B = k1_xboole_0 -> 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]. 28.21/27.79 1697 $T # label(t144_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1698 (all A all B all C (m2_relset_1(C,A,B) -> C = k7_relset_1(A,B,B,B,C,k6_partfun1(B)) & k7_relset_1(A,A,A,B,k6_partfun1(A),C) = C)) # label(t23_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1699 (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) & m2_relset_1(E,B,C) & v1_funct_2(E,B,C) -> (v2_funct_1(E) & k2_relat_1(k1_partfun1(A,B,B,C,D,E)) = C -> k2_relat_1(D) = B | C = k1_xboole_0))))) # label(t28_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1700 (all A all B all C (m2_relset_1(k9_funct_2(A,B,C),k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & v1_funct_2(k9_funct_2(A,B,C),k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & v1_funct_1(k9_funct_2(A,B,C)))) # label(dt_k9_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1701 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,A,B) -> k10_relat_1(C,D) = k3_funct_2(A,B,C,D))) # label(redefinition_k3_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1702 $T # label(t54_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1703 (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(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) & (all E k1_tarski(E) != B) -> r1_tarski(D,C)))))) # label(t167_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1704 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,A,B) -> m1_subset_1(k3_funct_2(A,B,C,D),k1_zfmisc_1(A)))) # label(dt_k3_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1705 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (k1_partfun1(B,A,A,B,D,C) = k6_partfun1(B) -> k2_relat_1(C) = B))))) # label(t24_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1706 $T # label(t58_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1707 (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 (m2_relset_1(A,f1_s9_funct_2,f2_s9_funct_2) & (all B (r2_hidden(B,f1_s9_funct_2) -> (-p1_s9_funct_2(B) -> k1_funct_1(A,B) = f4_s9_funct_2(B)) & (p1_s9_funct_2(B) -> f3_s9_funct_2(B) = k1_funct_1(A,B)))) & v1_funct_2(A,f1_s9_funct_2,f2_s9_funct_2) & v1_funct_1(A))) # label(s9_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1708 $T # label(t42_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1709 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,k1_tarski(A),B) & m2_relset_1(C,k1_tarski(A),B) -> (k1_xboole_0 != B -> r2_hidden(k1_funct_1(C,A),B)))) # label(t61_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1710 (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) -> r2_hidden(C,k1_funct_2(A,B))))) # label(t11_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1711 (all A -((all B -(r2_hidden(B,f2_s1_funct_2) & p1_s1_funct_2(A,B))) & r2_hidden(A,f1_s1_funct_2))) -> (exists A ((all B (r2_hidden(B,f1_s1_funct_2) -> p1_s1_funct_2(B,k1_funct_1(A,B)))) & m2_relset_1(A,f1_s1_funct_2,f2_s1_funct_2) & v1_funct_2(A,f1_s1_funct_2,f2_s1_funct_2) & v1_funct_1(A))) # label(s1_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1712 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (B != k1_xboole_0 -> (all E ((exists F (r2_hidden(F,A) & E = k1_funct_1(D,F) & r2_hidden(F,C))) -> r2_hidden(E,k9_relat_1(D,C))))))) # label(t43_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1713 (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) -> D = k2_partfun1(A,B,D,C)))) # label(t40_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1714 $T # label(t109_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1715 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_2(D,A,B) & v1_funct_1(E) & m1_relset_1(E,B,C) & v1_funct_2(E,B,C) & m1_relset_1(D,A,B) & v1_funct_1(D) -> v1_funct_2(k7_funct_2(A,B,C,D,E),A,C) & m2_relset_1(k7_funct_2(A,B,C,D,E),A,C) & v1_funct_1(k7_funct_2(A,B,C,D,E)))) # label(dt_k7_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1716 (all A all B k1_funct_2(A,B) = k5_partfun1(A,B,k3_partfun1(k1_xboole_0,A,B))) # label(t160_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1717 (all A all B all C (m1_relset_1(B,A,A) & v1_funct_1(C) & m1_relset_1(C,A,A) & v3_funct_2(C,A,A) & v1_funct_2(C,A,A) & v3_funct_2(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> k5_relat_1(B,C) = k5_funct_2(A,B,C))) # label(redefinition_k5_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1718 (all A all B all C ((all D ((exists E (E = D & A = k1_relat_1(E) & r1_tarski(k2_relat_1(E),B) & v1_funct_1(E) & v1_relat_1(E))) <-> r2_hidden(D,C))) <-> C = k1_funct_2(A,B))) # label(d2_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1719 $T # label(t99_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1720 $T # label(t123_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1721 $T # label(t127_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1722 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(C,A) -> k1_xboole_0 != A & B = k1_xboole_0 | r1_tarski(C,k3_funct_2(A,B,D,k2_funct_2(A,B,D,C)))))) # label(t50_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1723 $T # label(t147_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1724 (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) -> v1_funct_1(D) & v1_funct_2(D,A,C) & m2_relset_1(D,A,C) | A != k1_xboole_0 & B = k1_xboole_0))) # label(t9_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1725 (all A all B all C (v3_funct_2(B,A,A) & m1_relset_1(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) & v1_funct_2(B,A,A) & v1_funct_1(B) -> v3_funct_2(k5_funct_2(A,B,C),A,A) & m2_relset_1(k5_funct_2(A,B,C),A,A) & v1_funct_2(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]. 28.21/27.79 1726 (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) -> (v2_funct_1(k1_partfun1(A,B,B,C,D,E)) -> v2_funct_1(D) | B = k1_xboole_0 & k1_xboole_0 != A | k1_xboole_0 != B & C = k1_xboole_0))))) # label(t26_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1727 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> v1_partfun1(k3_partfun1(B,A,A),A,A))) # label(t134_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1728 (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]. 28.21/27.79 1729 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(C) = A & (all D (r2_hidden(D,A) -> r2_hidden(k1_funct_1(C,D),B))) -> v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C)))) # label(t5_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1730 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_xboole_0 = k1_relat_1(B) -> m2_relset_1(B,k1_xboole_0,A) & v1_funct_2(B,k1_xboole_0,A) & v1_funct_1(B)))) # label(t55_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1731 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(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) -> (B = k4_funct_2(A,B,C) & k2_relat_1(B) = A -> k6_partfun1(A) = C))))) # label(t75_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1732 $T # label(t72_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1733 (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_relat_1(E) -> (r2_hidden(C,A) -> k1_funct_1(k5_relat_1(D,E),C) = k1_funct_1(E,k1_funct_1(D,C)) | B = k1_xboole_0))))) # label(t21_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1734 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(C,A,A) -> (r1_partfun1(B,C) -> B = C))))) # label(t143_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1735 (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_funct_2(D,A,B) -> (r1_partfun1(C,D) -> k1_xboole_0 = B & A != k1_xboole_0 | r2_hidden(D,k5_partfun1(A,B,C))))))) # label(t155_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1736 $T # label(t89_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1737 (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) -> m2_relset_1(k2_partfun1(A,B,D,C),C,B) & v1_funct_2(k2_partfun1(A,B,D,C),C,B) & v1_funct_1(k2_partfun1(A,B,D,C)) | k1_xboole_0 != A & B = k1_xboole_0))) # label(t38_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1738 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> ((all E (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]. 28.21/27.79 1739 $T # label(t157_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1740 $T # label(t106_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.79 1741 (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]. 28.21/27.79 1742 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> r1_tarski(k5_partfun1(A,B,C),k1_funct_2(A,B)))) # label(t159_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1743 (all A all B (r2_hidden(A,f1_s6_funct_2) & r2_hidden(B,f2_s6_funct_2) -> r2_hidden(f4_s6_funct_2(A,B),f3_s6_funct_2))) -> (exists A (v1_funct_1(A) & (all B all C (r2_hidden(B,f1_s6_funct_2) & r2_hidden(C,f2_s6_funct_2) -> k1_funct_1(A,k4_tarski(B,C)) = f4_s6_funct_2(B,C))) & m2_relset_1(A,k2_zfmisc_1(f1_s6_funct_2,f2_s6_funct_2),f3_s6_funct_2) & v1_funct_2(A,k2_zfmisc_1(f1_s6_funct_2,f2_s6_funct_2),f3_s6_funct_2))) # label(s6_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1744 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (v2_funct_2(C,A,B) <-> B = k2_relat_1(C)))) # label(d3_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1745 (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(k2_relat_1(D),C) -> A != k1_xboole_0 & k1_xboole_0 = B | v1_funct_1(D) & v1_funct_2(D,A,C) & m2_relset_1(D,A,C)))) # label(t8_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1746 (all A all B (m2_relset_1(B,A,A) -> k7_relset_1(A,A,A,A,k6_partfun1(A),B) = B & B = k7_relset_1(A,A,A,A,B,k6_partfun1(A)))) # label(t74_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1747 (all A all B all C (v1_relat_1(C) & v1_funct_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]. 28.21/27.80 1748 $T # label(t103_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1749 $T # label(t111_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1750 $T # label(t90_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1751 $T # label(t84_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1752 $T # label(t63_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1753 (all A all B all C (m1_relset_1(B,A,A) & v1_funct_1(C) & v1_funct_2(C,A,A) & m1_relset_1(C,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> k4_funct_2(A,B,C) = k5_relat_1(B,C))) # label(redefinition_k4_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1754 (all A all B all C all D (m2_relset_1(D,k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & v1_funct_2(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]. 28.21/27.80 1755 (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]. 28.21/27.80 1756 $T # label(dt_k1_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1757 (all A (v1_relat_1(A) & v1_funct_1(A) -> m2_relset_1(A,k1_relat_1(A),k2_relat_1(A)) & v1_funct_2(A,k1_relat_1(A),k2_relat_1(A)) & v1_funct_1(A))) # label(t3_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1758 (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_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (v2_funct_1(C) & k1_partfun1(A,B,B,A,C,D) = k6_partfun1(A) & B = k2_relat_1(C) -> k1_xboole_0 = B | D = k2_funct_1(C) | A = k1_xboole_0))))) # label(t36_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1759 (all A all B (-v1_xboole_0(B) -> (all C (m1_relset_1(C,A,B) -> (v1_funct_2(C,A,B) & v1_funct_1(C) -> v1_funct_1(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B)))))) # label(cc5_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1760 (all A exists B (v1_relat_1(B) & v1_funct_1(B) & v1_funct_2(B,A,A) & v2_funct_2(B,A,A) & v3_funct_2(B,A,A) & v2_funct_1(B) & m1_relset_1(B,A,A))) # label(rc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1761 (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) -> (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]. 28.21/27.80 1762 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> ((all C all D (r2_hidden(D,A) & k1_funct_1(B,D) = k1_funct_1(B,C) & r2_hidden(C,A) -> D = C)) <-> v2_funct_1(B)))) # label(t77_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1763 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) & m2_relset_1(A,f1_s11_funct_2,f2_s11_funct_2) & (all B (m1_subset_1(B,f1_s11_funct_2) -> -(k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,B) != f7_s11_funct_2(B) & f4_s11_funct_2 != B & f3_s11_funct_2 != B))) & k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,f4_s11_funct_2) = f6_s11_funct_2 & k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,f3_s11_funct_2) = f5_s11_funct_2)) # label(s11_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1764 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (r1_partfun1(C,D) -> k1_xboole_0 != A & B = k1_xboole_0 | D = C))))) # label(t142_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1765 $T # label(t93_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1766 $T # label(t126_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1767 (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) -> (k1_xboole_0 != B -> r1_tarski(k2_funct_2(k1_tarski(A),B,D,C),k1_tarski(k1_funct_1(D,A)))))) # label(t64_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1768 $T # label(t163_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1769 (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]. 28.21/27.80 1770 (all A all B all C (m2_relset_1(C,A,k1_tarski(B)) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,k1_tarski(B)) & v1_funct_2(D,A,k1_tarski(B)) -> k1_tarski(D) = k5_partfun1(A,k1_tarski(B),C))))) # label(t164_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1771 $T # label(t33_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1772 $T # label(t122_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1773 $T # label(t1_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1774 $T # label(t94_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1775 (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]. 28.21/27.80 1776 (all A all B all C (m1_relset_1(C,A,B) -> (v1_funct_2(C,A,B) & v3_funct_2(C,A,B) & v1_funct_1(C) -> v1_funct_2(C,A,B) & v2_funct_2(C,A,B) & v2_funct_1(C) & v1_funct_1(C)))) # label(cc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1777 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (k2_relat_1(C) = B <-> (all D -(r2_hidden(D,B) & k1_xboole_0 = k3_funct_2(A,B,C,k1_tarski(D))))))) # label(t49_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1778 $T # label(t125_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1779 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> ((all E (m1_subset_1(E,A) -> k1_funct_1(C,E) = k1_funct_1(D,E))) -> D = C))))) # label(t113_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1780 (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 -((all F -(k1_funct_1(D,F) = E & r2_hidden(F,C) & r2_hidden(F,A))) & r2_hidden(E,k2_funct_2(A,B,D,C)))))) # label(t115_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1781 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (B = k2_relat_1(C) & v2_funct_1(C) -> k1_xboole_0 = B | k5_relat_1(C,k2_funct_1(C)) = k6_partfun1(A) & k6_partfun1(B) = k5_relat_1(k2_funct_1(C),C)))) # label(t35_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1782 $T # label(t96_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1783 (all A all B all C (m2_relset_1(C,A,B) -> ((B = k1_xboole_0 -> A = k1_xboole_0) -> (v1_funct_2(C,A,B) <-> A = k4_relset_1(A,B,C))) & (B = k1_xboole_0 -> A = k1_xboole_0 | (v1_funct_2(C,A,B) <-> C = k1_xboole_0)))) # label(d1_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1784 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> -((all E -(r2_hidden(E,A) & k1_funct_1(D,E) = C)) & B = k2_relat_1(D) & r2_hidden(C,B)))) # label(t17_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1785 $T # label(t117_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1786 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E -(r2_hidden(E,k2_funct_2(A,B,D,C)) & (all F (m1_subset_1(F,A) -> -(k1_funct_1(D,F) = E & r2_hidden(F,C)))))))) # label(t116_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1787 $T # label(t15_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1788 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> ((B = k1_xboole_0 -> A = k1_xboole_0) -> ((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]. 28.21/27.80 1789 $T # label(t80_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1790 (exists A (v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(f1_s8_funct_2,f2_s8_funct_2),f3_s8_funct_2) & (all B (m1_subset_1(B,f1_s8_funct_2) -> (all C (m1_subset_1(C,f2_s8_funct_2) -> k1_funct_1(A,k4_tarski(B,C)) = f4_s8_funct_2(B,C))))) & v1_funct_2(A,k2_zfmisc_1(f1_s8_funct_2,f2_s8_funct_2),f3_s8_funct_2))) # label(s8_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1791 (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 (v1_funct_1(F) & m2_relset_1(F,B,C) & v1_funct_2(F,B,C) -> -((k1_xboole_0 = C -> B = 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))) & (k1_xboole_0 = B -> k1_xboole_0 = A)))))) # label(t53_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1792 (all A -v1_xboole_0(k1_funct_2(A,A))) # label(fc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1793 (all A all B all C all D (-v1_xboole_0(A) & m1_relset_1(C,A,B) & m1_subset_1(D,A) & v1_funct_2(C,A,B) & v1_funct_1(C) -> k1_funct_1(C,D) = k8_funct_2(A,B,C,D))) # label(redefinition_k8_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1794 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_2(E,B,C) & m2_relset_1(E,B,C) & v1_funct_1(E) -> (v2_funct_1(k1_partfun1(A,B,B,C,D,E)) & k2_relat_1(D) = B -> k1_xboole_0 != B & C = k1_xboole_0 | v2_funct_1(E) & v2_funct_1(D)))))) # label(t30_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1795 $T # label(t135_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1796 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> r2_hidden(B,k1_funct_2(A,A)))) # label(t12_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1797 (all A all B all C all D all E (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> (r2_hidden(C,A) & r2_hidden(k1_funct_1(E,C),D) -> k1_funct_1(k9_relset_1(A,B,D,E),C) = k1_funct_1(E,C) | k1_xboole_0 = B))) # label(t41_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1798 (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]. 28.21/27.80 1799 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(E,B,C) & m1_relset_1(E,B,C) & v1_funct_1(E) & m1_relset_1(D,A,B) & v1_funct_2(D,A,B) -> k5_relat_1(D,E) = k7_funct_2(A,B,C,D,E))) # label(redefinition_k7_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1800 $T # label(t150_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1801 (all A all B -(r2_hidden(A,f1_s5_funct_2) & r2_hidden(B,f2_s5_funct_2) & (all C -(p1_s5_funct_2(A,B,C) & r2_hidden(C,f3_s5_funct_2))))) -> (exists A ((all B all C (r2_hidden(C,f2_s5_funct_2) & r2_hidden(B,f1_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) & v1_funct_1(A))) # label(s5_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1802 $T # label(t13_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1803 (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) & m2_relset_1(k6_funct_2(A,B),A,A) & v3_funct_2(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]. 28.21/27.80 1804 (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_1(E) & m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_2(E,k2_zfmisc_1(A,B),C) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> k1_funct_1(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]. 28.21/27.80 1805 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (m2_relset_1(E,B,C) & v1_funct_2(E,B,C) & v1_funct_1(E) -> (k2_relat_1(E) = C & B = k2_relat_1(D) -> k2_relat_1(k1_partfun1(A,B,B,C,D,E)) = C | C = k1_xboole_0 | B = k1_xboole_0))))) # label(t20_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1806 (all A all B all C all D all E all F (m2_relset_1(F,k2_zfmisc_1(A,B),C) & v1_funct_2(F,k2_zfmisc_1(A,B),C) & v1_funct_1(F) -> (r2_hidden(D,A) & r2_hidden(E,B) -> 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]. 28.21/27.80 1807 $T # label(t114_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1808 $T # label(t91_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1809 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,C) & m2_relset_1(E,B,C) -> (-(A != k1_xboole_0 & k1_xboole_0 != C & k1_xboole_0 = B) -> v1_funct_1(k1_partfun1(A,B,B,C,D,E)) & m2_relset_1(k1_partfun1(A,B,B,C,D,E),A,C) & v1_funct_2(k1_partfun1(A,B,B,C,D,E),A,C)))))) # label(t19_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1810 $T # label(t153_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1811 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (B != k1_xboole_0 -> (B = k2_relat_1(C) <-> (all D (k1_xboole_0 != D -> (all E (v1_funct_1(E) & m2_relset_1(E,B,D) & v1_funct_2(E,B,D) -> (all F (m2_relset_1(F,B,D) & v1_funct_2(F,B,D) & v1_funct_1(F) -> (k1_partfun1(A,B,B,D,C,F) = k1_partfun1(A,B,B,D,C,E) -> E = F))))))))))) # label(t22_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1812 (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) & v1_funct_2(A,f1_s13_funct_2,f2_s13_funct_2) & (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))) # label(s13_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1813 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> (all C (m2_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) -> (B = k4_funct_2(A,C,B) & v2_funct_1(B) -> C = k6_partfun1(A)))))) # label(t76_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1814 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> r1_tarski(k9_relat_1(D,C),B))) # label(t44_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1815 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> k5_partfun1(A,A,k3_partfun1(B,A,A)) = k1_tarski(B))) # label(t162_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1816 (all A all B all C all D (v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) -> k2_funct_2(A,B,C,D) = k9_relat_1(C,D))) # label(redefinition_k2_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1817 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (r2_hidden(C,A) & v2_funct_1(D) -> C = k1_funct_1(k2_funct_1(D),k1_funct_1(D,C)) | B = k1_xboole_0))) # label(t32_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1818 (all A (m1_subset_1(A,f1_s3_funct_2) -> (exists B (m1_subset_1(B,f2_s3_funct_2) & p1_s3_funct_2(A,B))))) -> (exists A (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)))) & v1_funct_2(A,f1_s3_funct_2,f2_s3_funct_2) & v1_funct_1(A))) # label(s3_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1819 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) -> ((all D (r2_hidden(D,k4_relset_1(A,A,B)) -> k1_funct_1(B,D) = k1_funct_1(C,D))) <-> r1_partfun1(B,C)))))) # label(t146_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1820 $T # label(t68_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1821 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & v3_funct_2(B,A,A) & m2_relset_1(B,A,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,A) & v3_funct_2(C,A,A) & m2_relset_1(C,A,A) -> (k5_funct_2(A,B,C) = C -> k6_partfun1(A) = B))))) # label(t86_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1822 $T # label(t71_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1823 (all A all B all C (r2_hidden(C,k1_funct_2(A,B)) -> v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B))) # label(t121_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1824 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> ((all E B != k1_tarski(E)) & k5_partfun1(A,B,D) = k5_partfun1(A,B,C) -> C = D))))) # label(t168_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1825 (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 -(D = k1_funct_1(C,E) & r2_hidden(E,A))))) -> k2_relat_1(C) = B | k1_xboole_0 = B))) # label(t16_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1826 $T # label(t110_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1827 $T # label(t2_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1828 $T # label(t129_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1829 (all A all B (v1_funct_1(B) & m1_relset_1(B,A,A) & v3_funct_2(B,A,A) & v1_funct_2(B,A,A) -> k2_funct_1(B) = k6_funct_2(A,B))) # label(redefinition_k6_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1830 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (B != k1_xboole_0 -> (all E (r2_hidden(E,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]. 28.21/27.80 1831 (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]. 28.21/27.80 1832 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> (all C (m1_relset_1(C,A,B) -> (v1_funct_2(C,A,B) & v1_funct_1(C) -> v1_funct_2(C,A,B) & v1_partfun1(C,A,B) & -v1_xboole_0(C) & v1_funct_1(C)))))) # label(cc6_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1833 $T # label(t56_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1834 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> -(-v2_funct_1(C) & (exists D (m2_relset_1(D,B,A) & k6_partfun1(A) = k1_partfun1(A,B,B,A,C,D) & v1_funct_2(D,B,A) & v1_funct_1(D))) & B != k1_xboole_0))) # label(t37_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1835 (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]. 28.21/27.80 1836 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(B,A) -> k1_funct_1(D,k1_funct_1(C,B)) = k1_funct_1(k5_relat_1(C,D),B)))))) # label(t70_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1837 $T # label(t98_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1838 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> k2_funct_2(A,A,B,A) = k2_relat_1(B))) # label(t79_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1839 (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_2(C,A,A) & m2_relset_1(C,A,A) & v3_funct_2(C,A,A) & v1_funct_1(C) -> (k5_funct_2(A,B,C) = k6_partfun1(A) -> C = k6_funct_2(A,B)))))) # label(t87_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1840 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (v2_funct_1(C) & v2_funct_2(C,A,B) <-> v3_funct_2(C,A,B)))) # label(d4_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1841 (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) -> k1_funct_1(A,B) = f3_s2_funct_2(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]. 28.21/27.80 1842 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) -> (r1_partfun1(B,C) -> r2_hidden(C,k5_partfun1(A,A,B))))))) # label(t156_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1843 $T # label(t137_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1844 (all A (k1_xboole_0 != A -> k1_xboole_0 = k1_funct_2(A,k1_xboole_0))) # label(t14_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 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) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (r1_partfun1(D,E) & r1_partfun1(C,E) -> r1_partfun1(C,D) | B = k1_xboole_0 & k1_xboole_0 != A))))))) # label(t151_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1846 (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 -> A = k1_xboole_0) -> A = k3_funct_2(A,B,C,k2_funct_2(A,B,C,A))))) # label(t51_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1847 (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))) & (B = k1_xboole_0 -> k1_xboole_0 = A)))) # label(t148_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1848 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (v1_partfun1(C,A,B) -> v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C)))) # label(t131_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1849 $T # label(t140_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1850 $T # label(t10_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1851 $T # label(t138_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1852 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> v1_partfun1(C,A,B) | k1_xboole_0 != A & B = k1_xboole_0))) # label(t132_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.80 1853 (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) | k1_xboole_0 = B))) # label(t7_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1854 (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) -> -((B = k1_xboole_0 -> A = k1_xboole_0) & (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> -(r1_partfun1(C,E) & r1_partfun1(D,E)))) & r1_partfun1(C,D)))))) # label(t154_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1855 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (v2_funct_1(C) & k2_relat_1(C) = B -> 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]. 28.21/27.81 1856 $T # label(t78_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1857 (all A all B all C (v1_funct_1(B) & 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(k4_funct_2(A,B,C)) & m2_relset_1(k4_funct_2(A,B,C),A,A) & v1_funct_2(k4_funct_2(A,B,C),A,A))) # label(dt_k4_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1858 $T # label(t95_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1859 $T # label(t102_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1860 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> r1_tarski(k2_relat_1(B),A) & A = k4_relset_1(A,A,B))) # label(t67_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1861 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> r1_tarski(k10_relat_1(D,C),A))) # label(t47_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1862 (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]. 28.21/27.81 1863 $T # label(t108_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1864 (all A all B exists C (m1_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) & v1_relat_1(C))) # label(rc1_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1865 (all A (m1_subset_1(A,f1_s14_funct_2) -> (exists B (m1_subset_1(B,f2_s14_funct_2) & p1_s14_funct_2(A,B))))) -> (exists A (v1_funct_2(A,f1_s14_funct_2,f2_s14_funct_2) & (all B (m1_subset_1(B,f1_s14_funct_2) -> p1_s14_funct_2(B,k8_funct_2(f1_s14_funct_2,f2_s14_funct_2,A,B)))) & m2_relset_1(A,f1_s14_funct_2,f2_s14_funct_2) & v1_funct_1(A))) # label(s14_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1866 $T # label(t107_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1867 (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]. 28.21/27.81 1868 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (all D (m2_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_1(D) -> (B = k2_relat_1(C) & (all E all F ((E = k1_funct_1(C,F) & r2_hidden(F,A) -> r2_hidden(E,B) & F = k1_funct_1(D,E)) & (r2_hidden(E,B) & k1_funct_1(D,E) = F -> r2_hidden(F,A) & k1_funct_1(C,F) = E))) & v2_funct_1(C) -> k1_xboole_0 = A | k2_funct_1(C) = D | k1_xboole_0 = B))))) # label(t34_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1869 $T # label(t81_funct_2) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1870 $T # label(t23_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1871 $T # label(t11_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1872 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(C) = A & A = k1_relat_1(B) -> 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]. 28.21/27.81 1873 (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) -> (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]. 28.21/27.81 1874 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k10_relat_1(k1_funct_3(B),A),k1_zfmisc_1(k1_relat_1(B))))) # label(t13_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1875 (all A all B (v1_funct_1(k7_funct_3(A,B)) & v1_relat_1(k7_funct_3(A,B)))) # label(dt_k7_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1876 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> k15_funct_3(k5_relat_1(B,A),k5_relat_1(D,C)) = k5_relat_1(k15_funct_3(B,D),k15_funct_3(A,C)))))))))) # label(t92_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1877 $T # label(t46_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1878 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,C) & m2_relset_1(E,A,C) -> (all F (m1_subset_1(F,A) -> k4_tarski(k8_funct_2(A,B,D,F),k8_funct_2(A,C,E,F)) = k8_funct_2(A,k2_zfmisc_1(B,C),k14_funct_3(A,B,C,D,E),F))))))))))))) # label(t79_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1879 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k9_relat_1(B,A),k1_relat_1(C)) & r1_tarski(A,k1_relat_1(B)) -> r1_tarski(A,k1_relat_1(k5_relat_1(B,C)))))))) # label(t3_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1880 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_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]. 28.21/27.81 1881 $T # label(t54_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1882 (all A all 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) & v1_funct_1(k9_funct_3(A,B)))) # label(dt_k9_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1883 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k1_relat_1(C) = k1_relat_1(D) & k13_funct_3(D,C) = k13_funct_3(A,B) & k1_relat_1(B) = k1_relat_1(A) -> D = A & B = C))))))))) # label(t74_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1884 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k9_relat_1(k1_funct_3(B),A),k1_zfmisc_1(k2_relat_1(B))))) # label(t12_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1885 (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(C) & r2_hidden(A,B) & B = k1_relat_1(D) -> k1_funct_1(k13_funct_3(C,D),A) = k4_tarski(k1_funct_1(C,A),k1_funct_1(D,A))))))) # label(t69_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1886 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) & r1_tarski(A,k1_zfmisc_1(k1_relat_1(B))) -> k9_relat_1(B,k3_tarski(A)) = k3_tarski(k10_relat_1(k3_funct_3(B),A))))) # label(t32_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1887 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (C = k7_funct_3(A,B) <-> k1_relat_1(C) = k2_zfmisc_1(A,B) & (all D all E (r2_hidden(D,A) & r2_hidden(E,B) -> k1_funct_1(C,k4_tarski(D,E)) = D))))) # label(d5_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1888 (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]. 28.21/27.81 1889 (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]. 28.21/27.81 1890 (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(k10_relat_1(k1_funct_3(B),A))))) # label(t19_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1891 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k1_relat_1(D) = k1_relat_1(C) & r1_tarski(k2_relat_1(D),B) & r1_tarski(k2_relat_1(C),A) -> D = k5_relat_1(k13_funct_3(C,D),k10_funct_3(A,B)) & k5_relat_1(k13_funct_3(C,D),k9_funct_3(A,B)) = C))))) # label(t72_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1892 (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]. 28.21/27.81 1893 $T # label(t41_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1894 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (A = k1_relat_1(C) & A = k1_relat_1(B) -> A = k1_relat_1(k13_funct_3(B,C))))))) # label(t70_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1895 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) -> k9_relat_1(k3_funct_3(B),A) = k10_relat_1(k1_funct_3(B),A)))) # label(t34_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1896 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C (r1_tarski(C,k1_relat_1(A)) -> k1_funct_1(B,C) = k9_relat_1(A,C))) & k1_relat_1(B) = k1_zfmisc_1(k1_relat_1(A)) <-> B = k1_funct_3(A)))))) # label(d1_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1897 (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 all E (r2_hidden(D,k1_relat_1(A)) & r2_hidden(E,k1_relat_1(B)) -> k1_funct_1(C,k4_tarski(D,E)) = k4_tarski(k1_funct_1(A,D),k1_funct_1(B,E)))) & k1_relat_1(C) = k2_zfmisc_1(k1_relat_1(A),k1_relat_1(B)) <-> k15_funct_3(A,B) = C))))))) # label(d9_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1898 $T # label(t55_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1899 (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]. 28.21/27.81 1900 (all A all B all C all D all E all F (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) -> m2_relset_1(k16_funct_3(A,B,C,D,E,F),k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) & v1_funct_2(k16_funct_3(A,B,C,D,E,F),k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) & v1_funct_1(k16_funct_3(A,B,C,D,E,F)))) # label(dt_k16_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1901 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (m2_relset_1(E,A,C) & v1_funct_2(E,A,C) & v1_funct_1(E) -> -((B = k1_xboole_0 -> A = k1_xboole_0) & -(k5_relat_1(k13_funct_3(D,E),k9_funct_3(B,C)) = D & k5_relat_1(k13_funct_3(D,E),k10_funct_3(B,C)) = E) & (C = k1_xboole_0 -> A = k1_xboole_0)))))) # label(t81_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1902 (all A all B all C all D all E all F (v1_funct_1(E) & v1_funct_2(E,A,C) & m1_relset_1(E,A,C) & v1_funct_1(F) & m1_relset_1(F,B,D) & v1_funct_2(F,B,D) -> 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]. 28.21/27.81 1903 (all A all B all C (k4_funct_3(C,B) = k4_funct_3(A,B) & r1_tarski(C,B) & r1_tarski(A,B) -> C = A)) # label(t47_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1904 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,C) & v1_funct_2(E,A,C) -> k7_funct_2(A,k2_zfmisc_1(B,C),C,k14_funct_3(A,B,C,D,E),k10_funct_3(B,C)) = E & k7_funct_2(A,k2_zfmisc_1(B,C),B,k14_funct_3(A,B,C,D,E),k9_funct_3(B,C)) = D)))))))) # label(t82_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1905 $T # label(t57_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1906 (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,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]. 28.21/27.81 1907 (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]. 28.21/27.81 1908 $T # label(t65_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1909 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (B = k11_funct_3(A) <-> (all C (r2_hidden(C,A) -> k4_tarski(C,C) = k1_funct_1(B,C))) & A = k1_relat_1(B)))) # label(d7_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1910 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B)) = k2_relat_1(k15_funct_3(A,B)))))) # label(t88_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1911 $T # label(t40_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1912 (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]. 28.21/27.81 1913 (all A all B (A != k1_xboole_0 -> B = k2_relat_1(k7_funct_3(B,A)))) # label(t60_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1914 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> k2_zfmisc_1(k10_relat_1(C,A),k10_relat_1(D,B)) = k10_relat_1(k15_funct_3(C,D),k2_zfmisc_1(A,B)))))) # label(t94_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1915 $T # label(t58_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1916 $T # label(t26_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1917 (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]. 28.21/27.81 1918 (all A all B k6_relat_1(k2_zfmisc_1(A,B)) = k15_funct_3(k6_relat_1(A),k6_relat_1(B))) # label(t90_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1919 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> k9_relat_1(k15_funct_3(C,D),k2_zfmisc_1(A,B)) = k2_zfmisc_1(k9_relat_1(C,A),k9_relat_1(D,B)))))) # label(t93_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1920 (all A all B (v1_funct_1(k4_funct_3(A,B)) & v1_relat_1(k4_funct_3(A,B)))) # label(dt_k4_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1921 (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]. 28.21/27.81 1922 (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]. 28.21/27.81 1923 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(C) = k2_zfmisc_1(A,B) & (all D all E (r2_hidden(D,A) & r2_hidden(E,B) -> E = k1_funct_1(C,k4_tarski(D,E)))) <-> C = k8_funct_3(A,B)))) # label(d6_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1924 $T # label(t64_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1925 (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]. 28.21/27.81 1926 (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]. 28.21/27.81 1927 (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) -> k9_relat_1(k1_funct_3(A),B) = k10_relat_1(k3_funct_3(A),B))))) # label(t37_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1928 (all A (v1_relat_1(A) & v1_funct_1(A) -> m2_relset_1(k3_funct_3(A),k1_zfmisc_1(k2_relat_1(A)),k1_zfmisc_1(k1_relat_1(A))) & v1_funct_2(k3_funct_3(A),k1_zfmisc_1(k2_relat_1(A)),k1_zfmisc_1(k1_relat_1(A))) & v1_funct_1(k3_funct_3(A)))) # label(t39_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1929 (exists A (v1_relat_1(A) & v1_funct_1(A) & (all B all C (r2_hidden(B,f1_s2_funct_3) & r2_hidden(C,f2_s2_funct_3) -> k1_funct_1(A,k4_tarski(B,C)) = f3_s2_funct_3(B,C))) & k1_relat_1(A) = k2_zfmisc_1(f1_s2_funct_3,f2_s2_funct_3))) # label(s2_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1930 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> k13_funct_3(k5_relat_1(k9_funct_3(k1_relat_1(A),k1_relat_1(B)),A),k5_relat_1(k10_funct_3(k1_relat_1(A),k1_relat_1(B)),B)) = k15_funct_3(A,B))))) # label(t87_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1931 (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]. 28.21/27.81 1932 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (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]. 28.21/27.81 1933 (all A all B k4_funct_3(A,B) = k5_funct_3(A,B)) # label(redefinition_k5_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1934 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k3_tarski(k9_relat_1(k1_funct_3(B),A)),k9_relat_1(B,k3_tarski(A))))) # label(t15_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1935 (all A all B k13_funct_3(k9_funct_3(A,B),k10_funct_3(A,B)) = k6_relat_1(k2_zfmisc_1(A,B))) # label(t73_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1936 (all A all B (m2_relset_1(k5_funct_3(A,B),B,k2_tarski(np__0,np__1)) & v1_funct_2(k5_funct_3(A,B),B,k2_tarski(np__0,np__1)) & v1_funct_1(k5_funct_3(A,B)))) # label(dt_k5_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1937 (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(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]. 28.21/27.81 1938 (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(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]. 28.21/27.81 1939 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_1(D) & m1_relset_1(E,A,C) & v1_funct_2(E,A,C) & v1_funct_1(E) & m1_relset_1(D,A,B) & v1_funct_2(D,A,B) & -v1_xboole_0(C) -> k14_funct_3(A,B,C,D,E) = k13_funct_3(D,E))) # label(redefinition_k14_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1940 (all A all B all C all D all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (all F (v1_funct_1(F) & m2_relset_1(F,C,D) & v1_funct_2(F,C,D) -> v1_funct_1(k15_funct_3(E,F)) & v1_funct_2(k15_funct_3(E,F),k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) & m2_relset_1(k15_funct_3(E,F),k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)))))) # label(t95_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1941 (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]. 28.21/27.81 1942 (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 (v1_funct_1(F) & m2_relset_1(F,C,D) & v1_funct_2(F,C,D) -> -(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) & (k1_xboole_0 = D -> C = k1_xboole_0) & (k1_xboole_0 = B -> A = k1_xboole_0)))))) # label(t97_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1943 (all A all B (v1_funct_1(B) & v1_relat_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]. 28.21/27.81 1944 $T # label(t85_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1945 (all A all B (k1_xboole_0 != A -> k2_relat_1(k8_funct_3(A,B)) = B)) # label(t62_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1946 (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]. 28.21/27.81 1947 (all A all B all C (-v1_xboole_0(B) & v1_funct_1(C) & m1_relset_1(C,A,B) & v1_funct_2(C,A,B) -> k2_funct_3(A,B,C) = k1_funct_3(C))) # label(redefinition_k2_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1948 (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]. 28.21/27.81 1949 (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]. 28.21/27.81 1950 (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]. 28.21/27.81 1951 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,k1_relat_1(k5_relat_1(B,C))) -> r1_tarski(k9_relat_1(B,A),k1_relat_1(C))))))) # label(t2_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1952 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> (all F (v1_funct_1(F) & v1_funct_2(F,A,C) & m2_relset_1(F,A,C) -> (all G (v1_funct_2(G,A,C) & m2_relset_1(G,A,C) & v1_funct_1(G) -> (k14_funct_3(A,B,C,D,F) = k14_funct_3(A,B,C,E,G) -> E = D & G = F))))))))))))) # label(t84_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1953 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k2_zfmisc_1(A,B) = k1_relat_1(D) & (all E all F (r2_hidden(F,B) & r2_hidden(E,A) -> k1_funct_1(D,k4_tarski(E,F)) = k1_funct_1(C,k4_tarski(E,F)))) & k2_zfmisc_1(A,B) = k1_relat_1(C) -> D = C))))) # label(t6_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1954 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) -> k3_funct_3(k5_relat_1(A,B)) = k5_relat_1(k3_funct_3(B),k3_funct_3(A))))))) # label(t38_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1955 (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]. 28.21/27.81 1956 (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]. 28.21/27.81 1957 $T # label(t7_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1958 (all A all B all C all D all E (-v1_xboole_0(C) & v1_funct_2(D,A,B) & m1_relset_1(D,A,B) & v1_funct_1(E) & v1_funct_2(E,A,C) & m1_relset_1(E,A,C) & v1_funct_1(D) & -v1_xboole_0(B) -> m2_relset_1(k14_funct_3(A,B,C,D,E),A,k2_zfmisc_1(B,C)) & v1_funct_2(k14_funct_3(A,B,C,D,E),A,k2_zfmisc_1(B,C)) & v1_funct_1(k14_funct_3(A,B,C,D,E)))) # label(dt_k14_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1959 (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]. 28.21/27.81 1960 $T # label(t67_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1961 $T # label(d4_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1962 (all A k11_funct_3(A) = k12_funct_3(A)) # label(redefinition_k12_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1963 $T # label(t44_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1964 $T # label(t52_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1965 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,C) & m2_relset_1(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]. 28.21/27.81 1966 (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_zfmisc_1(k2_relat_1(A)) & (all C (r1_tarski(C,k2_relat_1(A)) -> k10_relat_1(A,C) = k1_funct_1(B,C))) <-> B = k3_funct_3(A)))))) # label(d2_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1967 (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]. 28.21/27.81 1968 (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]. 28.21/27.81 1969 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(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]. 28.21/27.81 1970 $T # label(t45_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1971 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (r1_tarski(B,k1_zfmisc_1(k1_relat_1(A))) -> r1_tarski(k10_relat_1(k3_funct_3(A),B),k9_relat_1(k1_funct_3(A),B)))))) # label(t35_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1972 (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]. 28.21/27.81 1973 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,k2_relat_1(C)) & r1_tarski(k10_relat_1(C,A),k2_relat_1(B)) -> r1_tarski(A,k2_relat_1(k5_relat_1(B,C)))))))) # label(t5_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1974 (all A all B all C (-v1_xboole_0(B) & v1_funct_1(C) & m1_relset_1(C,A,B) & v1_funct_2(C,A,B) -> 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)) & v1_funct_1(k2_funct_3(A,B,C)))) # label(dt_k2_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1975 (all A all B (v1_funct_1(B) & v1_relat_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]. 28.21/27.81 1976 (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]. 28.21/27.81 1977 (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]. 28.21/27.81 1978 (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]. 28.21/27.81 1979 (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,B) & m2_relset_1(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) -> E = D & G = F | k1_xboole_0 = C & A != k1_xboole_0 | B = k1_xboole_0 & A != k1_xboole_0))))))))) # label(t83_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1980 (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) -> -((B = k1_xboole_0 -> k1_xboole_0 = A) & -(v1_funct_1(k13_funct_3(D,E)) & 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))) & (C = k1_xboole_0 -> k1_xboole_0 = A)))))) # label(t78_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.81 1981 (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]. 28.21/27.81 1982 (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 (v1_funct_1(F) & m2_relset_1(F,B,D) & v1_funct_2(F,B,D) -> k13_funct_3(k5_relat_1(k9_funct_3(A,B),E),k5_relat_1(k10_funct_3(A,B),F)) = k16_funct_3(A,B,C,D,E,F))))))))) # label(t98_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 1983 (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) -> 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]. 28.21/27.82 1984 (all A all B (v1_relat_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_funct_1(A) -> 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]. 28.21/27.82 1985 $T # label(t51_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 1986 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,k2_tarski(np__0,np__1)) & v1_funct_2(B,A,k2_tarski(np__0,np__1)) -> 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]. 28.21/27.82 1987 (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 (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> (all F (v1_funct_1(F) & v1_funct_2(F,C,D) & m2_relset_1(F,C,D) -> (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]. 28.21/27.82 1988 (all A all B all C all D (r2_hidden(A,f1_s1_funct_3) & p1_s1_funct_3(A,B,C) & p1_s1_funct_3(A,B,D) & r2_hidden(B,f2_s1_funct_3) -> D = C)) & (all A all B -(r2_hidden(B,f2_s1_funct_3) & (all C -p1_s1_funct_3(A,B,C)) & r2_hidden(A,f1_s1_funct_3))) -> (exists A (k2_zfmisc_1(f1_s1_funct_3,f2_s1_funct_3) = k1_relat_1(A) & (all B all C (r2_hidden(B,f1_s1_funct_3) & r2_hidden(C,f2_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]. 28.21/27.82 1989 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k4_funct_3(A,B) = C <-> k1_relat_1(C) = B & (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]. 28.21/27.82 1990 (all A all B all C (-v1_xboole_0(C) -> (all D (v1_funct_2(D,A,C) & m2_relset_1(D,A,C) & v1_funct_1(D) -> (r1_tarski(B,k1_zfmisc_1(A)) -> k2_funct_2(A,C,D,k3_tarski(B)) = k3_tarski(k9_relat_1(k1_funct_3(D),B))))))) # label(t17_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 1991 (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]. 28.21/27.82 1992 $T # label(t50_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 1993 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_2(E,A,C) & m2_relset_1(E,A,C) & v1_funct_1(E) -> 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]. 28.21/27.82 1994 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C all D (r2_hidden(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]. 28.21/27.82 1995 (all A (v1_funct_1(A) & v1_relat_1(A) -> k1_xboole_0 = k1_funct_1(k1_funct_3(A),k1_xboole_0))) # label(t9_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 1996 (all A (v1_relat_1(A) & v1_funct_1(A) -> r1_tarski(k2_relat_1(k3_funct_3(A)),k1_zfmisc_1(k1_relat_1(A))))) # label(t25_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 1997 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_2(k1_funct_3(A),k1_zfmisc_1(k1_relat_1(A)),k1_zfmisc_1(k2_relat_1(A))) & m2_relset_1(k1_funct_3(A),k1_zfmisc_1(k1_relat_1(A)),k1_zfmisc_1(k2_relat_1(A))) & v1_funct_1(k1_funct_3(A)))) # label(t21_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 1998 $T # label(t63_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 1999 (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]. 28.21/27.82 2000 (all A all B (-v1_xboole_0(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> k3_xboole_0(k10_relat_1(C,A),k10_relat_1(D,B)) = k10_relat_1(k13_funct_3(C,D),k2_zfmisc_1(A,B)))))))) # label(t77_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2001 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k6_relat_1(B) = k6_funct_3(A,B))) # label(redefinition_k6_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2002 (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]. 28.21/27.82 2003 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,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]. 28.21/27.82 2004 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k3_tarski(k10_relat_1(k1_funct_3(B),A)),k10_relat_1(B,k3_tarski(A))))) # label(t18_funct_3) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2005 $T # label(t3_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2006 (all A (-v1_xboole_0(A) -> (all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (v1_funct_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) -> 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]. 28.21/27.82 2007 (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_funct_2(A,k2_zfmisc_1(k1_xboole_0,k1_xboole_0),k1_xboole_0) & v1_binop_1(A,k1_xboole_0) & v2_binop_1(A,k1_xboole_0) & v1_xboole_0(A)))) # label(cc1_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2008 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (v1_binop_1(C,A) -> (r6_binop_1(A,C,B) <-> r5_binop_1(A,C,B))))))))) # label(t27_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2009 $T # label(t9_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2010 (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) -> (v3_binop_1(B,A) <-> (all C (m1_subset_1(C,A) -> k1_binop_1(B,C,C) = C))))) # label(d4_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2011 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (r3_binop_1(A,C,B) <-> (all D (m1_subset_1(D,A) -> D = k1_binop_1(B,D,C) & D = k1_binop_1(B,C,D)))))))) # label(t11_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2012 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (r5_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k2_binop_1(A,A,A,B,k2_binop_1(A,A,A,C,D,E),F) = k2_binop_1(A,A,A,C,k2_binop_1(A,A,A,B,D,F),k2_binop_1(A,A,A,B,E,F))))))))))))))) # label(d19_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2013 $T # label(t7_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2014 $T # label(t8_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2015 (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) -> (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]. 28.21/27.82 2016 (all A all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (r4_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k1_binop_1(C,k1_binop_1(B,D,E),k1_binop_1(B,D,F)) = k1_binop_1(B,D,k1_binop_1(C,E,F))))))))))))) # label(d9_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2017 (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]. 28.21/27.82 2018 $T # label(t10_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2019 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (v1_binop_1(C,A) -> (r6_binop_1(A,C,B) <-> (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)))))))))))))))) # label(t25_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2020 $T # label(t20_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2021 (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,C,k2_binop_1(A,A,A,B,D,E),k2_binop_1(A,A,A,B,D,F)) = k2_binop_1(A,A,A,B,D,k2_binop_1(A,A,A,C,E,F)))))))) <-> r4_binop_1(A,B,C)))))))) # label(d18_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2022 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> ((all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> k1_binop_1(B,C,D) = k1_binop_1(B,D,C))))) <-> v1_binop_1(B,A)))) # label(d2_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2023 (all A all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (r4_binop_1(A,B,C) & r5_binop_1(A,B,C) <-> r6_binop_1(A,B,C)))))) # label(d11_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2024 (all A all B all C all D all E all F (-v1_xboole_0(A) & -v1_xboole_0(B) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m1_subset_1(F,B) & m1_subset_1(E,A) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> 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]. 28.21/27.82 2025 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (v1_binop_1(B,A) -> (r3_binop_1(A,C,B) <-> (all D (m1_subset_1(D,A) -> D = k1_binop_1(B,D,C))))))))) # label(t13_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2026 (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) -> (r3_binop_1(A,C,B) <-> r2_binop_1(A,C,B))))))) # label(t15_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2027 (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) <-> r2_binop_1(A,C,B))))))) # label(t16_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2028 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> ((all D (m1_subset_1(D,A) -> D = 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]. 28.21/27.82 2029 $T # label(t5_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2030 $T # label(t6_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2031 (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) -> (v1_binop_1(C,A) -> (r6_binop_1(A,C,B) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k2_binop_1(A,A,A,C,D,k2_binop_1(A,A,A,B,E,F)) = k2_binop_1(A,A,A,B,k2_binop_1(A,A,A,C,D,E),k2_binop_1(A,A,A,C,D,F)))))))))))))))) # label(t24_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2032 (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]. 28.21/27.82 2033 (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) -> m1_subset_1(k3_binop_1(A,B),A))) # label(dt_k3_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2034 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (v3_binop_1(B,A) <-> (all C (m1_subset_1(C,A) -> C = k2_binop_1(A,A,A,B,C,C)))))))) # label(d15_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2035 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (v1_binop_1(B,A) -> (r3_binop_1(A,C,B) <-> r1_binop_1(A,C,B))))))) # label(t14_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2036 (all A all B (m1_subset_1(B,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (r3_binop_1(A,B,C) <-> r2_binop_1(A,B,C) & r1_binop_1(A,B,C)))))) # label(d7_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2037 (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) -> (k3_binop_1(A,B) = C <-> r3_binop_1(A,C,B))))))) # label(d8_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2038 $T # label(t4_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2039 (exists A (v1_funct_2(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))))) & m2_relset_1(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]. 28.21/27.82 2040 (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) -> (all D (m1_subset_1(D,A) -> (r2_binop_1(A,D,B) & r1_binop_1(A,C,B) -> D = C))))))) # label(t17_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2041 (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) -> ((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]. 28.21/27.82 2042 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,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) -> 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]. 28.21/27.82 2043 (all A all B all C all D all E all F (v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m1_subset_1(F,B) & m1_subset_1(E,A) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> m1_subset_1(k2_binop_1(A,B,C,D,E,F),C))) # label(dt_k2_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2044 (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]. 28.21/27.82 2045 (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_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]. 28.21/27.82 2046 $T # label(t1_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2047 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) -> (all E (v1_funct_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))))) -> E = D))))))))))) # label(t2_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2048 (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) & 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) <-> r4_binop_1(A,C,B))))))))) # label(t26_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2049 (all A (m1_subset_1(A,f1_s1_binop_1) -> (all B (m1_subset_1(B,f1_s1_binop_1) -> (exists C (m1_subset_1(C,f1_s1_binop_1) & p1_s1_binop_1(A,B,C))))))) -> (exists A (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]. 28.21/27.82 2050 $T # label(dt_k1_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2051 (all A all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (r3_binop_1(A,C,B) & r3_binop_1(A,D,B) -> C = D))))))) # label(t18_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2052 $T # label(t21_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2053 $T # label(t22_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2054 (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) -> (r5_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k1_binop_1(B,k1_binop_1(C,D,E),F) = k1_binop_1(C,k1_binop_1(B,D,F),k1_binop_1(B,E,F))))))))))))) # label(d10_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.82 2055 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> ((all D (m1_subset_1(D,A) -> D = k2_binop_1(A,A,A,C,D,B))) <-> r2_binop_1(A,B,C)))))))) # label(d17_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2056 (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) -> (r3_binop_1(A,C,B) <-> (all D (m1_subset_1(D,A) -> D = k1_binop_1(B,C,D))))))))) # label(t12_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2057 (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) -> (all E (m1_subset_1(E,A) -> k2_binop_1(A,A,A,B,C,k2_binop_1(A,A,A,B,D,E)) = k2_binop_1(A,A,A,B,k2_binop_1(A,A,A,B,C,D),E))))))) <-> v2_binop_1(B,A)))))) # label(d14_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2058 (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 (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (r6_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k1_binop_1(C,k1_binop_1(B,D,E),k1_binop_1(B,D,F)) = k1_binop_1(B,D,k1_binop_1(C,E,F)) & k1_binop_1(C,k1_binop_1(B,D,F),k1_binop_1(B,E,F)) = k1_binop_1(B,k1_binop_1(C,D,E),F)))))))))))) # label(t23_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2059 $T # label(t19_binop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2060 (all A all B all C all D (-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) & -v1_xboole_0(A) -> m2_relset_1(k9_funcop_1(A,B,C,D),B,C))) # label(dt_k9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2061 (all A all B all C (v1_funct_1(A) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_1(B) & v1_relat_1(B) & v1_relat_1(A) -> v1_funct_1(k3_funcop_1(A,B,C)) & v1_relat_1(k3_funcop_1(A,B,C)))) # label(fc4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2062 (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,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))) -> k7_funcop_1(A,B,C,E,F) = D))))))))))))) # label(t61_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2063 (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]. 28.21/27.83 2064 (all A all B all C (v1_relat_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_funct_1(A) -> v1_funct_1(k4_funcop_1(A,B,C)) & v1_relat_1(k4_funcop_1(A,B,C)))) # label(fc5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2065 (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]. 28.21/27.83 2066 (all A all B all C all D all E (-v1_xboole_0(A) & -v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(D,B,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_1(D) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> 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]. 28.21/27.83 2067 (all A all B k10_relat_1(k2_funcop_1(A,B),k1_tarski(B)) = A) # label(t21_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2068 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (all E (v1_funct_2(E,B,A) & m2_relset_1(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]. 28.21/27.83 2069 $T # label(t62_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2070 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_2(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) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & -v1_xboole_0(A) -> v1_funct_2(k8_funcop_1(A,B,C,D,E),B,A) & m2_relset_1(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]. 28.21/27.83 2071 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) -> (all E (m1_subset_1(E,A) -> k1_funct_1(k1_funcop_1(D),E) = k4_tarski(k2_mcart_1(k8_funct_2(A,k2_zfmisc_1(B,C),D,E)),k1_mcart_1(k8_funct_2(A,k2_zfmisc_1(B,C),D,E))))))))))))) # label(t71_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2072 (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) -> ((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))) & k1_relat_1(k3_funcop_1(C,A,B)) = k1_relat_1(D) -> k3_funcop_1(C,A,B) = D))))))))) # label(t27_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2073 (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,E,k8_funcop_1(B,A,C,F,D)) = k8_funcop_1(B,A,C,k2_binop_1(B,B,B,C,E,F),D)))))))))))))) # label(t77_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2074 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(C) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_2(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]. 28.21/27.83 2075 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,A) & m2_relset_1(E,B,A) -> (all F (m1_subset_1(F,B) -> k8_funct_2(B,A,k6_funcop_1(A,B,C,D,E),F) = k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,F),k8_funct_2(B,A,E,F)))))))))))))) # label(t48_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2076 (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]. 28.21/27.83 2077 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(A) = k1_relat_1(B) & (all C (r2_hidden(C,k1_relat_1(A)) -> -((all D all E k4_tarski(D,E) != k1_funct_1(A,C)) & k1_funct_1(A,C) != k1_funct_1(B,C)) & (all D all E (k4_tarski(D,E) = k1_funct_1(A,C) -> k4_tarski(E,D) = k1_funct_1(B,C))))) <-> k1_funcop_1(A) = B))))) # label(d1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2078 (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]. 28.21/27.83 2079 (all A all B (v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(B) & v1_funcop_1(A) & v1_relat_1(A) -> v1_funct_1(k5_relat_1(B,A)) & v1_funcop_1(k5_relat_1(B,A)) & v1_relat_1(k5_relat_1(B,A)))) # label(fc8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2080 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C k3_funcop_1(B,k2_funcop_1(k1_relat_1(A),C),A) = k5_funcop_1(B,C,A)))))) # label(t41_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2081 (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_funct_1(D) & v1_relat_1(D) -> k5_relat_1(k3_funcop_1(D,B,C),A) = k3_funcop_1(k5_relat_1(D,A),B,C))))))))) # label(t32_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2082 (all A k13_funct_3(k6_partfun1(A),k6_partfun1(A)) = k12_funct_3(A)) # label(t2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2083 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> k2_binop_1(A,A,A,B,C,C) = k8_funct_2(A,A,k8_funcop_1(A,A,B,C,k6_partfun1(A)),C))))))) # label(t70_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2084 (all A all B (v1_xboole_0(B) -> v2_funct_1(k2_funcop_1(B,A)) & v1_funct_1(k2_funcop_1(B,A)) & v1_relat_1(k2_funcop_1(B,A)) & v1_xboole_0(k2_funcop_1(B,A)))) # label(fc3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2085 $T # label(t68_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2086 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D k5_relat_1(k4_funcop_1(C,B,D),A) = k4_funcop_1(k5_relat_1(C,A),B,D)))))))) # label(t38_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2087 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C k5_relat_1(A,k2_funcop_1(B,C)) = k2_funcop_1(k10_relat_1(A,B),C)))) # label(t25_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2088 (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) -> k7_funct_2(A,B,B,D,k8_funcop_1(B,B,C,E,k6_partfun1(B))) = k8_funcop_1(B,A,C,E,D))))))))))) # label(t69_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2089 (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]. 28.21/27.83 2090 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> (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]. 28.21/27.83 2091 $T # label(dt_k5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2092 (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_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]. 28.21/27.83 2093 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C k5_relat_1(k13_funct_3(B,k2_funcop_1(k1_relat_1(B),C)),A) = k4_funcop_1(A,B,C)))))) # label(d4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2094 $T # label(t8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2095 (all A all B k2_zfmisc_1(A,k1_tarski(B)) = k2_funcop_1(A,B)) # label(d2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2096 (all A all B all C all D all E (-v1_xboole_0(A) & v1_funct_1(C) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(D,B,A) & m1_subset_1(E,A) & m1_relset_1(D,B,A) & v1_funct_1(D) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & -v1_xboole_0(B) -> m2_relset_1(k7_funcop_1(A,B,C,D,E),B,A) & v1_funct_2(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]. 28.21/27.83 2097 (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) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (m1_subset_1(E,B) -> v1_funct_1(k4_funcop_1(C,D,E)) & v1_funct_2(k4_funcop_1(C,D,E),A,B) & m2_relset_1(k4_funcop_1(C,D,E),A,B))))))))))) # label(t59_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2098 (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 (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]. 28.21/27.83 2099 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> (all F (v1_funct_2(F,A,B) & m2_relset_1(F,A,B) & v1_funct_1(F) -> ((all G (m1_subset_1(G,A) -> k8_funct_2(A,B,F,G) = k2_binop_1(B,B,B,C,k8_funct_2(A,B,D,G),k8_funct_2(A,B,E,G)))) -> k6_funcop_1(B,A,C,D,E) = F))))))))))))) # label(t49_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2100 $T # label(t40_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2101 (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]. 28.21/27.83 2102 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (r2_hidden(C,k1_relat_1(A)) -> k2_funcop_1(B,k1_funct_1(A,C)) = k5_relat_1(k2_funcop_1(B,C),A))))) # label(t23_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2103 (all A all B (A != k1_xboole_0 -> k1_tarski(B) = k2_relat_1(k2_funcop_1(A,B)))) # label(t14_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2104 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D all E (v1_funct_1(E) & v1_relat_1(E) -> (k7_relat_1(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]. 28.21/27.83 2105 (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]. 28.21/27.83 2106 (all A all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,B) -> m2_relset_1(k2_funcop_1(A,C),A,B) & v1_funct_2(k2_funcop_1(A,C),A,B) & v1_funct_1(k2_funcop_1(A,C)))))) # label(t58_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2107 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & -v1_xboole_0(C) & v1_funct_1(D) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) -> v1_funct_1(k10_funcop_1(A,B,C,D)) & v1_funct_2(k10_funcop_1(A,B,C,D),A,k2_zfmisc_1(C,B)) & m2_relset_1(k10_funcop_1(A,B,C,D),A,k2_zfmisc_1(C,B)))) # label(dt_k10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2108 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (v2_binop_1(C,B) -> k7_funcop_1(B,A,C,k8_funcop_1(B,A,C,E,D),F) = k8_funcop_1(B,A,C,E,k7_funcop_1(B,A,C,D,F))))))))))))))) # label(t74_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2109 (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]. 28.21/27.83 2110 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,A) & v1_funct_2(D,A,A) -> k8_funct_2(A,A,k6_funcop_1(A,A,B,k6_partfun1(A),D),C) = k2_binop_1(A,A,A,B,C,k8_funct_2(A,A,D,C)))))))))) # label(t54_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2111 (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_funct_1(k4_funcop_1(B,A,D),C) = k1_binop_1(B,k1_funct_1(A,C),D))))))) # label(t35_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2112 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C k7_relat_1(k13_funct_3(A,B),C) = k13_funct_3(k7_relat_1(A,C),B)))))) # label(t10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2113 (all A all B (v1_funcop_1(A) & v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k1_funct_1(A,B)) & v1_relat_1(k1_funct_1(A,B)))) # label(fc7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2114 $T # label(t5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2115 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C all D (v1_funct_1(D) & v1_relat_1(D) -> (all E (k7_relat_1(B,C) = k7_relat_1(A,C) -> k7_relat_1(k5_funcop_1(D,E,B),C) = k7_relat_1(k5_funcop_1(D,E,A),C))))))))) # label(t43_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2116 (all A (v1_relat_1(A) -> (all B all C (k2_zfmisc_1(B,C) = A -> B = k1_xboole_0 | B = k1_relat_1(A) & k2_relat_1(A) = C | C = k1_xboole_0)))) # label(t1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2117 (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_funct_1(D) & v1_relat_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]. 28.21/27.83 2118 (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]. 28.21/27.83 2119 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(C) & 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(A) -> k2_relat_1(D) = k9_funcop_1(A,B,C,D))) # label(redefinition_k9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2120 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> 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]. 28.21/27.83 2121 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (all D (v1_funct_2(D,A,A) & m2_relset_1(D,A,A) & v1_funct_1(D) -> k2_binop_1(A,A,A,B,k8_funct_2(A,A,D,C),C) = k8_funct_2(A,A,k6_funcop_1(A,A,B,D,k6_partfun1(A)),C))))))))) # label(t55_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2122 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,B) & m2_relset_1(E,B,B) -> k6_funcop_1(B,A,C,k7_funct_2(A,B,B,D,E),D) = k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,E,k6_partfun1(B))))))))))))) # label(t52_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2123 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (all F (v1_funct_1(F) & m2_relset_1(F,A,B) & v1_funct_2(F,A,B) -> (v2_binop_1(C,B) -> k6_funcop_1(B,A,C,D,k6_funcop_1(B,A,C,E,F)) = k6_funcop_1(B,A,C,k6_funcop_1(B,A,C,D,E),F)))))))))))))) # label(t76_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2124 (all A all B all C all D all E (m1_relset_1(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) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k8_funcop_1(A,B,C,D,E) = k5_funcop_1(C,D,E))) # label(redefinition_k8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2125 (all A (v1_funct_1(A) & v1_relat_1(A) -> k1_funcop_1(k1_funcop_1(A)) = A)) # label(involutiveness_k1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2126 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_xboole_0 = k1_relat_1(B) & k1_relat_1(A) = k1_xboole_0 -> B = A))))) # label(t4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2127 (all A (v1_relat_1(A) & v1_funct_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]. 28.21/27.83 2128 (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_relat_1(B) = k1_relat_1(A) -> k1_relat_1(k5_relat_1(C,A)) = k1_relat_1(k5_relat_1(C,B))))))))) # label(t3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2129 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D k5_relat_1(B,k5_funcop_1(C,D,A)) = k5_funcop_1(C,D,k5_relat_1(B,A))))))))) # label(t44_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2130 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D k5_relat_1(k6_partfun1(B),k5_funcop_1(C,D,A)) = k5_funcop_1(C,D,k7_relat_1(A,B))))))) # label(t46_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2131 (all A all B (-v1_xboole_0(B) -> v1_funct_1(k2_funcop_1(A,B)) & v2_relat_1(k2_funcop_1(A,B)) & v1_relat_1(k2_funcop_1(A,B)))) # label(fc9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2132 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (v1_funct_1(C) & v1_relat_1(C) -> k5_funcop_1(A,B,C) = k5_relat_1(k13_funct_3(k2_funcop_1(k1_relat_1(C),B),C),A))))) # label(d5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2133 (exists A (v1_funcop_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2134 (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) -> (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]. 28.21/27.83 2135 (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) & m1_subset_1(E,A) & v1_funct_1(C) & -v1_xboole_0(B) -> k7_funcop_1(A,B,C,D,E) = k4_funcop_1(C,D,E))) # label(redefinition_k7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2136 (all A all B (r1_tarski(k2_relat_1(k2_funcop_1(A,B)),k1_tarski(B)) & A = k1_relat_1(k2_funcop_1(A,B)))) # label(t19_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2137 (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]. 28.21/27.83 2138 (all A (v1_xboole_0(k2_funcop_1(k1_xboole_0,A)) & v2_funct_1(k2_funcop_1(k1_xboole_0,A)) & v1_funct_1(k2_funcop_1(k1_xboole_0,A)) & v1_relat_1(k2_funcop_1(k1_xboole_0,A)))) # label(fc2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2139 (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,A) -> (all F (m1_subset_1(F,B) -> k8_funct_2(B,A,k8_funcop_1(A,B,C,E,D),F) = k2_binop_1(A,A,A,C,E,k8_funct_2(B,A,D,F)))))))))))))) # label(t66_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2140 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> k7_funcop_1(B,A,C,D,E) = k7_funct_2(A,B,B,D,k7_funcop_1(B,B,C,k6_partfun1(B),E)))))))))))) # label(t63_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2141 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C k4_funcop_1(B,A,C) = k3_funcop_1(B,A,k2_funcop_1(k1_relat_1(A),C))))))) # label(t34_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2142 (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) -> (v3_binop_1(C,B) -> k6_funcop_1(B,A,C,D,D) = D))))))))) # label(t81_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2143 $T # label(t12_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2144 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C all D (v1_relat_1(D) & v1_funct_1(D) -> (all E (k7_relat_1(B,C) = k7_relat_1(A,C) -> k7_relat_1(k4_funcop_1(D,B,E),C) = k7_relat_1(k4_funcop_1(D,A,E),C))))))))) # label(t36_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2145 (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]. 28.21/27.83 2146 (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]. 28.21/27.83 2147 (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) -> 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]. 28.21/27.83 2148 (all A all B all C (r2_hidden(C,B) -> v1_funct_1(k2_funcop_1(A,C)) & v1_funct_2(k2_funcop_1(A,C),A,B) & m2_relset_1(k2_funcop_1(A,C),A,B))) # label(t57_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2149 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C all D (r2_hidden(C,k1_relat_1(k5_funcop_1(B,D,A))) -> k1_binop_1(B,D,k1_funct_1(A,C)) = k1_funct_1(k5_funcop_1(B,D,A),C))))))) # label(t42_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2150 $T # label(dt_k4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2151 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (v2_binop_1(C,B) -> k7_funcop_1(B,A,C,k7_funcop_1(B,A,C,D,E),F) = k7_funcop_1(B,A,C,D,k2_binop_1(B,B,B,C,E,F))))))))))))))) # label(t78_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.83 2152 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (all E (m1_subset_1(E,B) -> (v3_binop_1(C,A) -> k8_funct_2(B,A,D,E) = k8_funct_2(B,A,k8_funcop_1(A,B,C,k8_funct_2(B,A,D,E),D),E)))))))))))) # label(t82_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2153 (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) -> m2_relset_1(k2_relat_1(D),B,C))))))))) # label(t72_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2154 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & -v1_xboole_0(C) & v1_funct_1(D) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) -> k1_funcop_1(D) = k10_funcop_1(A,B,C,D))) # label(redefinition_k10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2155 (all A k1_funcop_1(k12_funct_3(A)) = k12_funct_3(A)) # label(t9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2156 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B (r2_hidden(B,k1_relat_1(A)) -> v1_funct_1(k1_funct_1(A,B)) & v1_relat_1(k1_funct_1(A,B)))) <-> v1_funcop_1(A)))) # label(d6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2157 (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) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (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]. 28.21/27.84 2158 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_2(E,B,B) & m2_relset_1(E,B,B) & v1_funct_1(E) -> k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,k6_partfun1(B),E)) = k6_funcop_1(B,A,C,D,k7_funct_2(A,B,B,D,E)))))))))))) # label(t51_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2159 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (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) -> v1_funct_1(k3_funcop_1(C,D,E)) & m2_relset_1(k3_funcop_1(C,D,E),A,B) & v1_funct_2(k3_funcop_1(C,D,E),A,B))))))))))) # label(t47_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2160 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B k7_relat_1(k1_funcop_1(A),B) = k1_funcop_1(k7_relat_1(A,B))))) # label(t7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2161 $T # label(dt_k3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2162 $T # label(dt_k2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2163 (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)) -> 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]. 28.21/27.84 2164 $T # label(t33_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2165 (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) & v1_funct_2(E,B,A) & m1_relset_1(E,B,A) & v1_funct_1(E) & 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) -> v1_funct_1(k6_funcop_1(A,B,C,D,E)) & m2_relset_1(k6_funcop_1(A,B,C,D,E),B,A) & v1_funct_2(k6_funcop_1(A,B,C,D,E),B,A))) # label(dt_k6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2166 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> k13_funct_3(A,B) = k1_funcop_1(k13_funct_3(B,A)))))) # label(t6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2167 $T # label(t50_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2168 (all A all B all C (v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(C) & v1_funct_1(C) -> 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]. 28.21/27.84 2169 (all A all B all C k7_relat_1(k2_funcop_1(A,B),C) = k2_funcop_1(k3_xboole_0(A,C),B)) # label(t18_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2170 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C -(B != k1_xboole_0 & r2_hidden(C,k1_relat_1(A)) & k1_relat_1(k5_relat_1(k2_funcop_1(B,C),A)) = k1_xboole_0)))) # label(t24_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2171 (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) -> (all E (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> (v1_binop_1(C,B) -> k6_funcop_1(B,A,C,D,E) = k6_funcop_1(B,A,C,E,D)))))))))))) # label(t80_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2172 (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) -> k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,k6_partfun1(B),k6_partfun1(B))) = k6_funcop_1(B,A,C,D,D))))))))) # label(t53_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2173 (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) -> 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]. 28.21/27.84 2174 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_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]. 28.21/27.84 2175 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (r2_hidden(D,k1_relat_1(k3_funcop_1(C,A,B))) -> k1_binop_1(C,k1_funct_1(A,D),k1_funct_1(B,D)) = k1_funct_1(k3_funcop_1(C,A,B),D))))))))) # label(t28_funcop_1) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2176 (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]. 28.21/27.84 2177 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k1_funct_4(A,B)) & v1_relat_1(k1_funct_4(A,B)))) # label(dt_k1_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2178 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_partfun1(A,k1_funct_4(B,C)) -> r1_partfun1(A,C)))))))) # label(t28_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2179 (all A all B all C all D all E (-v1_xboole_0(E) -> (all F (-v1_xboole_0(F) -> (all G (v1_funct_1(G) & v1_funct_2(G,k2_zfmisc_1(A,B),E) & m2_relset_1(G,k2_zfmisc_1(A,B),E) -> (all H (m2_relset_1(H,k2_zfmisc_1(C,D),F) & v1_funct_2(H,k2_zfmisc_1(C,D),F) & v1_funct_1(H) -> 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]. 28.21/27.84 2180 (all A (v1_relat_1(A) & v1_funct_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]. 28.21/27.84 2181 (all A all B (v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(B) & v1_relat_1(A) -> A = k1_funct_4(A,A))) # label(idempotence_k1_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2182 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,B) -> B = k1_funct_4(B,A) & k1_funct_4(A,B) = B))))) # label(t79_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2183 (all A all B all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) -> m2_relset_1(k2_funct_4(D),k2_zfmisc_1(B,A),C) & v1_funct_2(k2_funct_4(D),k2_zfmisc_1(B,A),C) & v1_funct_1(k2_funct_4(D)))))) # label(t51_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2184 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(B)) & r1_partfun1(B,C) -> k1_funct_1(k1_funct_4(B,C),A) = k1_funct_1(B,A)))))) # label(t16_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2185 (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) -> (C != k1_xboole_0 -> k2_funct_4(k2_funct_4(D)) = D))) # label(t55_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2186 (all A all B (r1_tarski(A,B) <-> r1_tarski(k6_partfun1(A),k6_partfun1(B)))) # label(t4_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2187 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (r1_xboole_0(C,k1_relat_1(B)) -> k7_relat_1(k1_funct_4(A,B),C) = k7_relat_1(A,C))))))) # label(t76_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2188 (all A all B all C (v1_funct_1(C) & v1_relat_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]. 28.21/27.84 2189 (all A all B all C all D (A != B -> k1_funct_1(k4_funct_4(A,B,C,D),B) = D & k1_funct_1(k4_funct_4(A,B,C,D),A) = C)) # label(t66_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2190 (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(B,A) = k1_funct_4(A,B)))))) # label(t35_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2191 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r1_tarski(C,D) -> r1_tarski(k7_relat_1(k8_relat_1(A,C),B),k7_relat_1(k8_relat_1(A,D),B))))))) # label(t10_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2192 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r1_tarski(k2_relat_1(C),k1_relat_1(A)) & r1_tarski(k2_relat_1(D),k1_relat_1(B)) & r1_partfun1(A,B) -> k5_relat_1(k1_funct_4(C,D),k1_funct_4(A,B)) = k1_funct_4(k5_relat_1(C,A),k5_relat_1(D,B))))))))))) # label(t73_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2193 (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(k1_funct_4(A,B))) & r1_tarski(k1_relat_1(B),k1_relat_1(k1_funct_4(A,B))))))) # label(t11_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2194 (all A all B (v1_relat_1(B) & v1_funct_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]. 28.21/27.84 2195 (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)) -> k1_funct_1(C,A) = k1_funct_1(k1_funct_4(C,B),A)))))) # label(t12_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2196 (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]. 28.21/27.84 2197 (all A all B all C all D all E all F all G (v1_funct_1(G) & v1_funct_2(G,k2_zfmisc_1(A,B),C) & m2_relset_1(G,k2_zfmisc_1(A,B),C) -> (all H (v1_funct_2(H,k2_zfmisc_1(D,E),F) & m2_relset_1(H,k2_zfmisc_1(D,E),F) & v1_funct_1(H) -> -(C != k1_xboole_0 & F != k1_xboole_0 & -(v1_funct_1(k3_funct_4(G,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_2(k3_funct_4(G,H),k2_zfmisc_1(k2_zfmisc_1(A,D),k2_zfmisc_1(B,E)),k2_zfmisc_1(C,F)))))))) # label(t63_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2198 (all A all B all C all D all E (-v1_xboole_0(A) & m1_subset_1(D,A) & m1_subset_1(E,A) -> v1_funct_1(k5_funct_4(A,B,C,D,E)) & v1_funct_2(k5_funct_4(A,B,C,D,E),k2_tarski(B,C),A) & m2_relset_1(k5_funct_4(A,B,C,D,E),k2_tarski(B,C),A))) # label(dt_k5_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2199 (all A (v1_relat_1(A) & v1_funct_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]. 28.21/27.84 2200 $T # label(dt_k4_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2201 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B A = k1_funct_4(A,k7_relat_1(A,B))))) # label(t80_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2202 (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]. 28.21/27.84 2203 (all A all B all C (v1_relat_1(C) & v1_funct_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]. 28.21/27.84 2204 (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]. 28.21/27.84 2205 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> k1_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]. 28.21/27.84 2206 (all A all B all C all D (v1_funct_1(k4_funct_4(A,B,C,D)) & v1_relat_1(k4_funct_4(A,B,C,D)))) # label(fc1_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2207 (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(k1_funct_4(B,C))) <-> r2_hidden(A,k1_relat_1(B)) | r2_hidden(A,k1_relat_1(C))))))) # label(t13_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2208 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (v1_partfun1(D,A,B) -> k1_funct_4(C,D) = D))))) # label(t37_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2209 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_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]. 28.21/27.84 2210 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> k2_relat_1(k2_funct_4(C)) = k2_relat_1(C)))) # label(t48_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2211 (all A all B all C all D (A != C -> k4_funct_4(A,C,B,D) = k2_tarski(k4_tarski(A,B),k4_tarski(C,D)))) # label(t71_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2212 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> k7_relat_1(k1_funct_4(A,B),k1_relat_1(A)) = A))))) # label(t34_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2213 (all A (v1_funct_1(A) & v1_relat_1(A) -> r1_tarski(k2_funct_4(k2_funct_4(A)),A))) # label(t52_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2214 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(A),k2_relat_1(k1_funct_4(B,A))))))) # label(t19_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2215 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> ((all D all E all F all G (r2_hidden(k4_tarski(D,E),k1_relat_1(A)) & r2_hidden(k4_tarski(F,G),k1_relat_1(B)) -> 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 (r2_hidden(D,k1_relat_1(C)) <-> (exists E exists F exists G exists H (k4_tarski(k4_tarski(E,G),k4_tarski(F,H)) = D & r2_hidden(k4_tarski(G,H),k1_relat_1(B)) & r2_hidden(k4_tarski(E,F),k1_relat_1(A)))))) <-> C = k3_funct_4(A,B)))))))) # label(d3_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2216 (all A (v1_funct_1(A) & v1_relat_1(A) -> r1_tarski(k2_relat_1(k2_funct_4(A)),k2_relat_1(A)))) # label(t42_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2217 (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(k1_funct_4(C,B),A) = k1_funct_1(B,A)))))) # label(t14_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2218 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(k3_funct_4(A,B)),k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B))))))) # label(t59_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2219 (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) -> (C != k1_xboole_0 -> v1_funct_1(k2_funct_4(D)) & v1_funct_2(k2_funct_4(D),k2_zfmisc_1(B,A),C) & m2_relset_1(k2_funct_4(D),k2_zfmisc_1(B,A),C)))) # label(t50_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2220 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> B = k7_relat_1(k1_funct_4(A,B),k1_relat_1(B)))))) # label(t24_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2221 (all A all B all C all D all E (-v1_xboole_0(A) & m1_subset_1(E,A) & m1_subset_1(D,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]. 28.21/27.84 2222 (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) -> E = C & F = D | B = A)) # label(t72_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2223 (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(A),C) -> k7_relat_1(k1_funct_4(A,B),C) = k7_relat_1(B,C))))))) # label(t77_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2224 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k2_funct_4(A)) & v1_funct_1(k2_funct_4(A)))) # label(dt_k2_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2225 (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) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> k1_funct_4(C,D) = D)))))) # label(t40_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2226 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k2_funct_4(A) = 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)) & k4_tarski(E,D) = C))))))))) # label(d2_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2227 (all A (v1_funct_1(A) & v1_relat_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]. 28.21/27.84 2228 (all A all B all C all D all E (v1_funct_1(E) & v1_relat_1(E) -> (k1_relat_1(E) = k2_tarski(A,B) & D = k1_funct_1(E,B) & C = k1_funct_1(E,A) -> k4_funct_4(A,B,C,D) = E))) # label(t69_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2229 (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_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]. 28.21/27.84 2230 (all A -((all B all C -r1_tarski(A,k2_zfmisc_1(B,C))) & (all B -((all C all D k4_tarski(C,D) != B) & r2_hidden(B,A))))) # label(t1_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2231 (all A all B all C all D all E all F all G (v1_funct_1(G) & m2_relset_1(G,k2_zfmisc_1(A,B),C) -> (all H (m2_relset_1(H,k2_zfmisc_1(D,E),F) & v1_funct_1(H) -> v1_funct_1(k3_funct_4(G,H)) & m2_relset_1(k3_funct_4(G,H),k2_zfmisc_1(k2_zfmisc_1(A,D),k2_zfmisc_1(B,E)),k2_zfmisc_1(C,F)))))) # label(t62_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2232 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(k4_tarski(B,A),k1_relat_1(k2_funct_4(C))) <-> r2_hidden(k4_tarski(A,B),k1_relat_1(C))))) # label(t43_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2233 (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]. 28.21/27.84 2234 (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]. 28.21/27.84 2235 (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(A,C) = k1_funct_4(k1_funct_4(A,B),C)))))))) # label(t78_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2236 (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]. 28.21/27.84 2237 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k7_relat_1(k1_funct_4(A,B),k4_xboole_0(k1_relat_1(A),k1_relat_1(B))),A))))) # label(t25_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2238 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k1_relat_1(A),k1_relat_1(B)) -> B = k1_funct_4(A,B)))))) # label(t20_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2239 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,B),C) -> k2_funct_4(k2_funct_4(D)) = D)) # label(t54_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2240 (all A all B (v1_relat_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_funct_1(A) -> v1_funct_1(k3_funct_4(A,B)) & v1_relat_1(k3_funct_4(A,B)))) # label(dt_k3_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2241 (all A all B all C all D (r1_tarski(k2_funcop_1(A,B),k2_funcop_1(C,D)) -> k1_xboole_0 = A | B = D)) # label(t7_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2242 (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]. 28.21/27.84 2243 (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]. 28.21/27.84 2244 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C all D (r1_tarski(k1_relat_1(A),C) & r1_xboole_0(C,D) & r1_tarski(k1_relat_1(B),D) -> k7_relat_1(k1_funct_4(A,B),D) = B & A = k7_relat_1(k1_funct_4(A,B),C))))))) # label(t81_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2245 (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]. 28.21/27.84 2246 (all A (v1_funct_1(A) & v1_relat_1(A) -> k1_funct_4(A,k1_xboole_0) = A)) # label(t22_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2247 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> k1_funct_4(A,B) = k1_funct_4(B,A)))))) # label(t36_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2248 (all A all B all C k4_funct_4(A,B,C,C) = k2_funcop_1(k2_tarski(A,B),C)) # label(t68_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.84 2249 (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]. 28.21/27.85 2250 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (r1_xboole_0(k1_relat_1(B),C) & r1_tarski(k1_relat_1(A),C) -> A = k7_relat_1(k1_funct_4(A,B),C))))))) # label(t82_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.85 2251 (all A (v1_relat_1(A) & v1_funct_1(A) -> k1_funct_4(k1_xboole_0,A) = A)) # label(t21_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.85 2252 (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]. 28.21/27.85 2253 (all A all B k1_funct_4(k6_partfun1(A),k6_partfun1(B)) = k6_partfun1(k2_xboole_0(A,B))) # label(t23_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.85 2254 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> r1_tarski(k7_relat_1(k8_relat_1(A,C),B),C))) # label(t9_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.85 2255 (all A all 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) -> k2_funct_4(k2_funct_4(D)) = D)))) # label(t56_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.85 2256 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C k7_relat_1(k1_funct_4(A,B),C) = k1_funct_4(k7_relat_1(A,C),k7_relat_1(B,C))))))) # label(t75_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.85 2257 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k1_funct_4(A,B),k2_xboole_0(A,B)))))) # label(t30_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.85 2258 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> ((B = k1_xboole_0 -> A = k1_xboole_0) -> k1_funct_4(C,D) = D))))) # label(t38_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.85 2259 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(C,A,A) -> k1_funct_4(B,C) = C)))) # label(t39_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.85 2260 (all A all B all C all D all E (v1_relat_1(E) & v1_funct_1(E) -> (all F (v1_funct_1(F) & v1_relat_1(F) -> (r1_tarski(k1_relat_1(E),k2_zfmisc_1(A,B)) & r1_tarski(k1_relat_1(F),k2_zfmisc_1(C,D)) -> r1_tarski(k1_relat_1(k3_funct_4(E,F)),k2_zfmisc_1(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)))))))) # label(t60_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.85 2261 (all A all B all C all D (m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> m2_relset_1(k2_funct_4(D),k2_zfmisc_1(B,A),C) & v1_funct_1(k2_funct_4(D)))) # label(t49_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.21/27.85 2262 (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]. 28.21/27.85 2263 (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]. 28.21/27.85 2264 (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) -> (C = k1_funct_4(A,B) <-> k2_xboole_0(k1_relat_1(A),k1_relat_1(B)) = k1_relat_1(C) & (all D (r2_hidden(D,k2_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(B,D) = k1_funct_1(C,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]. 28.46/28.03 2265 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(k1_funct_4(A,B)),k2_xboole_0(k2_relat_1(A),k2_relat_1(B))))))) # label(t18_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.46/28.03 2266 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> m2_relset_1(k1_funct_4(C,D),A,B) & v1_funct_1(k1_funct_4(C,D)))))) # label(t41_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.46/28.03 2267 (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)) & r1_xboole_0(k1_relat_1(B),k1_relat_1(C)) -> k1_funct_1(B,A) = k1_funct_1(k1_funct_4(B,C),A)))))) # label(t17_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.46/28.03 2268 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (r1_tarski(k1_relat_1(A),k2_xboole_0(B,C)) -> k1_funct_4(k7_relat_1(A,B),k7_relat_1(A,C)) = A)))) # label(t74_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.46/28.03 2269 (all A all B all C all D (B != A -> k2_tarski(C,D) = k2_relat_1(k4_funct_4(A,B,C,D)))) # label(t67_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.46/28.03 2270 (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(A,C),k1_relat_1(E)) & r2_hidden(k4_tarski(B,D),k1_relat_1(F)) <-> 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]. 28.46/28.03 2271 $T # label(t3_funct_4) # label(axiom) # label(non_clause). [assumption]. 28.46/28.03 2272 (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]. 28.46/28.03 2273 (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)))) -> A = k1_xboole_0 | p1_s1_ordinal2(A)))) & p1_s1_ordinal2(k1_xboole_0) -> (all A (v3_ordinal1(A) -> p1_s1_ordinal2(A))) # label(s1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.03 2274 (all A r1_tarski(k3_ordinal2(A),A)) # label(t13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.03 2275 $T # label(t38_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.03 2276 (all A (v3_ordinal1(A) -> (all B (B = f1_s8_ordinal2(A) <-> (exists C (v1_funct_1(C) & 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)) = f3_s8_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) = f4_s8_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & f2_s8_ordinal2 = k1_funct_1(C,k1_xboole_0) & B = k1_ordinal2(C) & v5_ordinal1(C) & v1_relat_1(C))))))) -> f2_s8_ordinal2 = f1_s8_ordinal2(k1_xboole_0) # label(s8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.03 2277 (all A (v3_ordinal1(A) -> (all B ((exists C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & k1_ordinal2(C) = B & k1_ordinal1(A) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f5_s6_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 | k1_funct_1(C,D) = f6_s6_ordinal2(D,k2_ordinal1(C,D))))) & f4_s6_ordinal2 = k1_funct_1(C,k1_xboole_0))) <-> f2_s6_ordinal2(A) = B)))) & k1_relat_1(f1_s6_ordinal2) = f3_s6_ordinal2 & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f3_s6_ordinal2) -> k1_funct_1(f1_s6_ordinal2,k1_ordinal1(A)) = f5_s6_ordinal2(A,k1_funct_1(f1_s6_ordinal2,A))))) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & r2_hidden(A,f3_s6_ordinal2) -> k1_funct_1(f1_s6_ordinal2,A) = f6_s6_ordinal2(A,k2_ordinal1(f1_s6_ordinal2,A)) | k1_xboole_0 = A))) & (r2_hidden(k1_xboole_0,f3_s6_ordinal2) -> k1_funct_1(f1_s6_ordinal2,k1_xboole_0) = f4_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]. 28.46/28.03 2278 (all A (v3_ordinal1(A) -> (all B -((all C (v3_ordinal1(C) -> -(r1_ordinal1(A,C) & r2_hidden(C,B)))) & r2_hidden(A,k7_ordinal2(B)))))) # label(t29_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.03 2279 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(A) -> ((all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(C,k1_relat_1(A)) & r2_hidden(B,C) -> r2_hidden(k1_funct_1(A,B),k1_funct_1(A,C))))))) <-> v2_ordinal2(A)))) # label(d16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.03 2280 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) -> (all B (v3_ordinal1(B) -> (k10_ordinal2(A) = B <-> (exists C (v1_funct_1(C) & v5_ordinal1(C) & k9_ordinal2(C) = B & k1_relat_1(A) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(A)) -> k1_funct_1(C,D) = k7_ordinal2(k2_relat_1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),D))))))) & v1_ordinal2(C) & v1_relat_1(C)))))))) # label(d11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.03 2281 (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]. 28.46/28.03 2282 (exists A (v1_relat_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_1(A))) # label(rc2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.03 2283 $T # label(t40_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.03 2284 $T # label(t37_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.03 2285 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (f1_s14_ordinal2(A) = B <-> (exists C (v5_ordinal1(C) & v1_ordinal2(C) & B = k1_ordinal2(C) & k1_ordinal1(A) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f3_s14_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_xboole_0 = D | f4_s14_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & f2_s14_ordinal2 = k1_funct_1(C,k1_xboole_0) & v1_funct_1(C) & v1_relat_1(C)))))))) -> f1_s14_ordinal2(k1_xboole_0) = f2_s14_ordinal2 # label(s14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.03 2286 (exists A (v1_funct_1(A) & v1_ordinal2(A) & k1_relat_1(A) = f1_s3_ordinal2 & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s3_ordinal2) -> k1_funct_1(A,B) = f2_s3_ordinal2(B)))) & v5_ordinal1(A) & v1_relat_1(A))) # label(s3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.03 2287 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> v3_ordinal1(k14_ordinal2(A,B)))) # label(dt_k14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.03 2288 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> v3_ordinal1(k9_ordinal2(A)))) # label(dt_k9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.03 2289 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> (all C (v1_funct_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & v1_relat_1(C) -> ((all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k14_ordinal2(B,D) = k1_funct_1(C,D)))) & k1_relat_1(C) = A -> k8_ordinal2(C) = k14_ordinal2(B,A)))) | k1_xboole_0 = A))))) # label(t46_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.03 2290 (all A (v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> v3_ordinal1(k8_ordinal2(A)))) # label(dt_k8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.03 2291 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v1_ordinal2(A) <-> (exists B (r1_tarski(k2_relat_1(A),B) & v3_ordinal1(B)))))) # label(d8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.03 2292 (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]. 28.46/28.03 2293 (all A (v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(A) & v1_relat_1(A) -> v3_ordinal1(k12_ordinal2(A)))) # label(dt_k12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.04 2294 $T # label(dt_k2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.04 2295 (all A r1_tarski(k3_ordinal2(A),k2_ordinal2(A))) # label(t15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.04 2296 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k14_ordinal2(A,k1_ordinal1(B)) = k1_ordinal1(k14_ordinal2(A,B)))))) # label(t45_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.04 2297 $T # label(t39_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.04 2298 (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]. 28.46/28.04 2299 (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]. 28.46/28.04 2300 (all A (v3_ordinal1(A) -> r1_ordinal1(k3_tarski(A),A))) # label(t5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.04 2301 (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]. 28.46/28.04 2302 (all A (v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> v3_ordinal1(k11_ordinal2(A)))) # label(dt_k11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.04 2303 (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]. 28.46/28.04 2304 f2_s10_ordinal2 != k1_xboole_0 & (all A (v3_ordinal1(A) -> (r2_hidden(A,f2_s10_ordinal2) -> f3_s10_ordinal2(A) = k1_funct_1(f1_s10_ordinal2,A)))) & k1_relat_1(f1_s10_ordinal2) = f2_s10_ordinal2 & v4_ordinal1(f2_s10_ordinal2) & (all A (v3_ordinal1(A) -> (all B ((exists C (v1_relat_1(C) & v1_funct_1(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)) = f5_s10_ordinal2(D,k1_funct_1(C,D))))) & (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)))) & k1_funct_1(C,k1_xboole_0) = f4_s10_ordinal2 & k1_relat_1(C) = k1_ordinal1(A) & v5_ordinal1(C))) <-> B = f3_s10_ordinal2(A))))) -> f6_s10_ordinal2(f2_s10_ordinal2,f1_s10_ordinal2) = f3_s10_ordinal2(f2_s10_ordinal2) # label(s10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.04 2305 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (f3_s16_ordinal2(A) = B <-> (exists C (v1_funct_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & B = k1_ordinal2(C) & k1_funct_1(C,k1_xboole_0) = f4_s16_ordinal2 & (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))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> f6_s16_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D) | k1_xboole_0 = D))) & k1_ordinal1(A) = k1_relat_1(C) & v1_relat_1(C)))))))) & f2_s16_ordinal2 != k1_xboole_0 & k1_relat_1(f1_s16_ordinal2) = f2_s16_ordinal2 & (all A (v3_ordinal1(A) -> (r2_hidden(A,f2_s16_ordinal2) -> k1_funct_1(f1_s16_ordinal2,A) = f3_s16_ordinal2(A)))) & v4_ordinal1(f2_s16_ordinal2) -> f3_s16_ordinal2(f2_s16_ordinal2) = f6_s16_ordinal2(f2_s16_ordinal2,f1_s16_ordinal2) # label(s16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.04 2306 (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]. 28.46/28.04 2307 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> ((exists D (v1_relat_1(D) & v1_funct_1(D) & k1_ordinal1(B) = k1_relat_1(D) & k4_ordinal2 = k1_funct_1(D,k1_xboole_0) & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(B)) -> k1_funct_1(D,k1_ordinal1(E)) = k15_ordinal2(A,k1_funct_1(D,E))))) & (all E (v3_ordinal1(E) -> (r2_hidden(E,k1_ordinal1(B)) & v4_ordinal1(E) -> k1_xboole_0 = E | k12_ordinal2(k2_ordinal1(D,E)) = k1_funct_1(D,E)))) & k1_ordinal2(D) = C & v1_ordinal2(D) & v5_ordinal1(D))) <-> C = k16_ordinal2(A,B)))))))) # label(d20_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.04 2308 (exists A (v1_funct_1(A) & v5_ordinal1(A) & k1_relat_1(A) = f1_s2_ordinal2 & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s2_ordinal2) -> k1_funct_1(A,B) = f2_s2_ordinal2(B)))) & v1_relat_1(A))) # label(s2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.04 2309 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k14_ordinal2(k15_ordinal2(A,B),B) = k15_ordinal2(k1_ordinal1(A),B))))) # label(t53_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.04 2310 (all A (v3_ordinal1(A) -> k16_ordinal2(A,k4_ordinal2) = A & k16_ordinal2(k4_ordinal2,A) = k4_ordinal2)) # label(t63_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.04 2311 (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)) | k2_ordinal2(B) = k1_xboole_0)))) # label(t23_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.04 2312 (all A (v3_ordinal1(A) -> k3_tarski(k1_ordinal1(A)) = A)) # label(t2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.04 2313 $T # label(t20_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.04 2314 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> k7_ordinal2(k2_relat_1(A)) = k8_ordinal2(A) & k9_ordinal2(A) = k6_ordinal2(k2_relat_1(A)))) # label(t35_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.04 2315 (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]. 28.46/28.04 2316 $T # label(t12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.04 2317 (all A (A = k5_ordinal2 <-> r2_hidden(k1_xboole_0,A) & (all B (v3_ordinal1(B) -> (v4_ordinal1(B) & r2_hidden(k1_xboole_0,B) -> r1_tarski(A,B)))) & v3_ordinal1(A) & v4_ordinal1(A))) # label(d5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.04 2318 (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]. 28.46/28.04 2319 $T # label(t33_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.04 2320 (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]. 28.46/28.04 2321 (all A (v3_ordinal1(A) -> k1_ordinal1(A) = k7_ordinal2(k1_tarski(A)))) # label(t31_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.04 2322 (all A all B (v5_ordinal1(A) & v1_ordinal2(A) & v3_ordinal1(B) & v1_funct_1(A) & v1_relat_1(A) -> v1_ordinal1(k1_funct_1(A,B)) & v2_ordinal1(k1_funct_1(A,B)) & v3_ordinal1(k1_funct_1(A,B)))) # label(fc3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.04 2323 (all A all B (v3_ordinal1(A) & v1_relat_1(B) & v1_ordinal2(B) & v5_ordinal1(B) & v1_funct_1(B) -> v3_ordinal1(k13_ordinal2(A,B)))) # label(dt_k13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.04 2324 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v5_ordinal1(C) & v1_ordinal2(C) & k1_relat_1(C) = k1_relat_1(A) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(A)) -> k6_ordinal2(k2_relat_1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),D)))) = k1_funct_1(C,D)))) & k8_ordinal2(C) = B & v1_funct_1(C) & v1_relat_1(C))) <-> B = k11_ordinal2(A)))))) # label(d12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.04 2325 (all A (v3_ordinal1(A) -> k16_ordinal2(A,k1_xboole_0) = k4_ordinal2)) # label(t60_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.04 2326 (all A (v3_ordinal1(A) -> k2_ordinal2(A) = A)) # label(t10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.04 2327 $T # label(t6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.04 2328 (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]. 28.46/28.04 2329 (all A (v3_ordinal1(A) -> (all B (v1_ordinal2(B) & v5_ordinal1(B) & v1_funct_1(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]. 28.46/28.04 2330 (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) -> k1_funct_1(C,D) = k16_ordinal2(B,D)))) -> k12_ordinal2(C) = k16_ordinal2(B,A)))) | k1_xboole_0 = A))))) # label(t62_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.04 2331 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(B,C) -> A = k1_xboole_0 | r2_hidden(k15_ordinal2(B,A),k15_ordinal2(C,A))))))))) # label(t57_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.04 2332 (all A (v3_ordinal1(A) -> (all B (v1_funct_1(B) & v5_ordinal1(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]. 28.46/28.04 2333 (all A (v3_ordinal1(A) -> A = k14_ordinal2(A,k1_xboole_0))) # label(t44_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.04 2334 (all A (v3_ordinal1(A) -> k15_ordinal2(A,k1_xboole_0) = k1_xboole_0)) # label(t55_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.04 2335 $T # label(t8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.04 2336 (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]. 28.46/28.04 2337 (all A (v3_ordinal1(A) -> r1_tarski(k1_ordinal1(A),k1_zfmisc_1(A)))) # label(t3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.04 2338 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> A = k1_xboole_0 | (all C (v1_funct_1(C) & v1_ordinal2(C) & v5_ordinal1(C) & v1_relat_1(C) -> (k1_relat_1(C) = A & (all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k15_ordinal2(D,B) = k1_funct_1(C,D)))) -> k3_tarski(k8_ordinal2(C)) = k15_ordinal2(A,B))))))))) # label(t54_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.04 2339 (all A (v3_ordinal1(A) -> k1_xboole_0 = k15_ordinal2(k1_xboole_0,A))) # label(t52_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.04 2340 (all A (v3_ordinal1(A) -> (all B (m1_ordinal1(B,A) -> v1_ordinal2(B))))) # label(cc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.04 2341 (all A all B (v3_ordinal1(B) -> v1_funct_1(k2_funcop_1(A,B)) & v1_ordinal2(k2_funcop_1(A,B)) & v1_relat_1(k2_funcop_1(A,B)))) # label(fc4_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.04 2342 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (B = f4_s15_ordinal2(A) <-> (exists C (v1_relat_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & f1_s15_ordinal2 = k1_funct_1(C,k1_xboole_0) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> D = k1_xboole_0 | f3_s15_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f2_s15_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & k1_ordinal1(A) = k1_relat_1(C) & k1_ordinal2(C) = B & v1_funct_1(C)))))))) -> (all A (v3_ordinal1(A) -> f2_s15_ordinal2(A,f4_s15_ordinal2(A)) = f4_s15_ordinal2(k1_ordinal1(A)))) # label(s15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.04 2343 (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]. 28.46/28.04 2344 (all A (v3_ordinal1(A) -> (exists B ((exists C (v3_ordinal1(C) & v4_ordinal1(B) & v4_ordinal2(C) & k14_ordinal2(B,C) = A)) & v3_ordinal1(B))))) # label(t65_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.46/28.04 2345 (exists A (v1_relat_1(A) & v5_ordinal1(A) & (r2_hidden(k1_xboole_0,f1_s11_ordinal2) -> f2_s11_ordinal2 = k1_funct_1(A,k1_xboole_0)) & (all B (v3_ordinal1(B) -> (v4_ordinal1(B) & r2_hidden(B,f1_s11_ordinal2) -> k1_xboole_0 = B | k1_funct_1(A,B) = f4_s11_ordinal2(B,k2_ordinal1(A,B))))) & (all B (v3_ordinal1(B) -> (r2_hidden(k1_ordinal1(B),f1_s11_ordinal2) -> f3_s11_ordinal2(B,k1_funct_1(A,B)) = k1_funct_1(A,k1_ordinal1(B))))) & f1_s11_ordinal2 = k1_relat_1(A) & v1_ordinal2(A) & v1_funct_1(A))) # label(s11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.73/28.37 2346 (all A (v3_ordinal1(A) -> k14_ordinal2(A,k4_ordinal2) = k1_ordinal1(A))) # label(t48_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.73/28.37 2347 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (B = f2_s12_ordinal2(A) <-> (exists C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & k1_relat_1(C) = k1_ordinal1(A) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f5_s12_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (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_funct_1(C,k1_xboole_0) = f4_s12_ordinal2 & B = k1_ordinal2(C)))))))) & (r2_hidden(k1_xboole_0,f3_s12_ordinal2) -> k1_funct_1(f1_s12_ordinal2,k1_xboole_0) = f4_s12_ordinal2) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f3_s12_ordinal2) -> f5_s12_ordinal2(A,k1_funct_1(f1_s12_ordinal2,A)) = k1_funct_1(f1_s12_ordinal2,k1_ordinal1(A))))) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & r2_hidden(A,f3_s12_ordinal2) -> A = k1_xboole_0 | f6_s12_ordinal2(A,k2_ordinal1(f1_s12_ordinal2,A)) = k1_funct_1(f1_s12_ordinal2,A)))) & f3_s12_ordinal2 = k1_relat_1(f1_s12_ordinal2) -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s12_ordinal2)) -> f2_s12_ordinal2(A) = k1_funct_1(f1_s12_ordinal2,A)))) # label(s12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.73/28.37 2348 (all A r1_tarski(k2_ordinal2(A),A)) # label(t9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.73/28.37 2349 (all A (v3_ordinal1(A) -> A = k15_ordinal2(k4_ordinal2,A) & k15_ordinal2(A,k4_ordinal2) = A)) # label(t56_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.73/28.37 2350 (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]. 28.73/28.37 2351 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> k7_ordinal2(k2_relat_1(A)) = k8_ordinal2(A))) # label(d9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.73/28.37 2352 (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]. 28.73/28.37 2353 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> ((exists D (v1_relat_1(D) & v1_funct_1(D) & v5_ordinal1(D) & v1_ordinal2(D) & k1_ordinal2(D) = C & A = k1_funct_1(D,k1_xboole_0) & (all E (v3_ordinal1(E) -> (r2_hidden(E,k1_ordinal1(B)) & v4_ordinal1(E) -> k1_funct_1(D,E) = k8_ordinal2(k2_ordinal1(D,E)) | E = k1_xboole_0))) & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(B)) -> k1_funct_1(D,k1_ordinal1(E)) = k1_ordinal1(k1_funct_1(D,E))))) & k1_ordinal1(B) = k1_relat_1(D))) <-> C = k14_ordinal2(A,B)))))))) # label(d18_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.73/28.37 2354 (all A all B (v3_ordinal1(B) -> ((all C (v3_ordinal1(C) -> (r1_tarski(k2_ordinal2(A),C) -> r1_ordinal1(B,C)))) & r1_tarski(k2_ordinal2(A),B) <-> k7_ordinal2(A) = B))) # label(d7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.73/28.37 2355 (all A r1_ordinal1(k6_ordinal2(A),k7_ordinal2(A))) # label(t32_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.73/28.37 2356 (exists A (v2_ordinal1(A) & v4_ordinal1(A) & v3_ordinal1(A) & v1_ordinal1(A))) # label(rc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.73/28.37 2357 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) -> k6_ordinal2(k2_relat_1(A)) = k9_ordinal2(A))) # label(d10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.73/28.37 2358 $T # label(t43_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.84/28.41 2359 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v3_ordinal1(B) & v1_ordinal2(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]. 28.84/28.41 2360 (all A v3_ordinal1(k7_ordinal2(A))) # label(dt_k7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.84/28.41 2361 (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]. 28.84/28.41 2362 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -((exists C (v1_funct_1(C) & v5_ordinal1(C) & k1_ordinal1(f1_s13_ordinal2) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(f1_s13_ordinal2)) & v4_ordinal1(D) -> k1_funct_1(C,D) = f4_s13_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s13_ordinal2)) -> f3_s13_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & k1_funct_1(C,k1_xboole_0) = f2_s13_ordinal2 & k1_ordinal2(C) = B & v1_ordinal2(C) & v1_relat_1(C))) & B != A & (exists C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & k1_ordinal2(C) = A & k1_relat_1(C) = k1_ordinal1(f1_s13_ordinal2) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(f1_s13_ordinal2)) & v4_ordinal1(D) -> k1_funct_1(C,D) = f4_s13_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s13_ordinal2)) -> f3_s13_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & f2_s13_ordinal2 = k1_funct_1(C,k1_xboole_0) & v1_ordinal2(C)))))))) # label(s13_ordinal2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 28.84/28.41 2363 (exists A (v3_ordinal1(A) & (exists B (v1_relat_1(B) & v5_ordinal1(B) & A = k1_ordinal2(B) & k1_ordinal1(f1_s13_ordinal2) = k1_relat_1(B) & f2_s13_ordinal2 = k1_funct_1(B,k1_xboole_0) & (all C (v3_ordinal1(C) -> (r2_hidden(k1_ordinal1(C),k1_ordinal1(f1_s13_ordinal2)) -> f3_s13_ordinal2(C,k1_funct_1(B,C)) = k1_funct_1(B,k1_ordinal1(C))))) & (all C (v3_ordinal1(C) -> (r2_hidden(C,k1_ordinal1(f1_s13_ordinal2)) & v4_ordinal1(C) -> k1_funct_1(B,C) = f4_s13_ordinal2(C,k2_ordinal1(B,C)) | k1_xboole_0 = C))) & v1_ordinal2(B) & v1_funct_1(B))))) # label(s13_ordinal2_AndRHS) # label(axiom) # label(non_clause). [assumption]. 28.84/28.41 2364 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> v3_ordinal1(k16_ordinal2(A,B)))) # label(dt_k16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.84/28.41 2365 $T # label(t41_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.84/28.41 2366 (all A k6_ordinal2(A) = k1_setfam_1(k2_ordinal2(A))) # label(d6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.84/28.41 2367 $T # label(t42_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.84/28.41 2368 (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]. 28.84/28.41 2369 (all A (v3_ordinal1(A) -> (all B ((exists C (v1_funct_1(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_s9_ordinal2(D,k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> k1_funct_1(C,D) = f3_s9_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & k1_funct_1(C,k1_xboole_0) = f1_s9_ordinal2 & k1_relat_1(C) = k1_ordinal1(A) & v5_ordinal1(C) & v1_relat_1(C))) <-> f4_s9_ordinal2(A) = B)))) -> (all A (v3_ordinal1(A) -> f4_s9_ordinal2(k1_ordinal1(A)) = f2_s9_ordinal2(A,f4_s9_ordinal2(A)))) # label(s9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.84/28.41 2370 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> ((exists D (v5_ordinal1(D) & v1_ordinal2(D) & k1_funct_1(D,k1_xboole_0) = k1_xboole_0 & (all E (v3_ordinal1(E) -> (v4_ordinal1(E) & r2_hidden(E,k1_ordinal1(A)) -> k1_funct_1(D,E) = k3_tarski(k8_ordinal2(k2_ordinal1(D,E))) | E = k1_xboole_0))) & (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))))) & k1_relat_1(D) = k1_ordinal1(A) & C = k1_ordinal2(D) & v1_funct_1(D) & v1_relat_1(D))) <-> C = k15_ordinal2(A,B)))))))) # label(d19_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.85/28.49 2371 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> k1_funct_1(A,k3_tarski(k1_relat_1(A))) = k1_ordinal2(A))) # label(d1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.85/28.49 2372 $T # label(t21_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.85/28.49 2373 $T # label(t64_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.85/28.49 2374 (all A v3_ordinal1(k6_ordinal2(A))) # label(dt_k6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.85/28.49 2375 f1_s4_ordinal2 = k1_relat_1(f5_s4_ordinal2) & f1_s4_ordinal2 = k1_relat_1(f6_s4_ordinal2) & (r2_hidden(k1_xboole_0,f1_s4_ordinal2) -> k1_funct_1(f6_s4_ordinal2,k1_xboole_0) = f2_s4_ordinal2) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & r2_hidden(A,f1_s4_ordinal2) -> k1_funct_1(f6_s4_ordinal2,A) = f4_s4_ordinal2(A,k2_ordinal1(f6_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) -> k1_xboole_0 = A | f4_s4_ordinal2(A,k2_ordinal1(f5_s4_ordinal2,A)) = k1_funct_1(f5_s4_ordinal2,A)))) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f1_s4_ordinal2) -> 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) -> f2_s4_ordinal2 = k1_funct_1(f5_s4_ordinal2,k1_xboole_0)) -> f6_s4_ordinal2 = f5_s4_ordinal2 # label(s4_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.85/28.49 2376 (all A (v3_ordinal1(A) -> k7_ordinal2(A) = A)) # label(t26_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.85/28.49 2377 $T # label(dt_k3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.85/28.49 2378 (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]. 28.85/28.49 2379 (all A all B -((exists C (v1_funct_1(C) & k1_ordinal2(C) = A & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(f1_s7_ordinal2)) -> f4_s7_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D) | D = k1_xboole_0))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s7_ordinal2)) -> f3_s7_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & f2_s7_ordinal2 = k1_funct_1(C,k1_xboole_0) & k1_relat_1(C) = k1_ordinal1(f1_s7_ordinal2) & v5_ordinal1(C) & v1_relat_1(C))) & A != B & (exists C (v1_funct_1(C) & v5_ordinal1(C) & k1_relat_1(C) = k1_ordinal1(f1_s7_ordinal2) & k1_funct_1(C,k1_xboole_0) = f2_s7_ordinal2 & (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) -> (r2_hidden(D,k1_ordinal1(f1_s7_ordinal2)) & v4_ordinal1(D) -> k1_funct_1(C,D) = f4_s7_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & B = k1_ordinal2(C) & v1_relat_1(C))))) # label(s7_ordinal2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 28.85/28.49 2380 (exists A exists B (v1_relat_1(B) & v1_funct_1(B) & (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))))) & (all C (v3_ordinal1(C) -> (v4_ordinal1(C) & r2_hidden(C,k1_ordinal1(f1_s7_ordinal2)) -> k1_funct_1(B,C) = f4_s7_ordinal2(C,k2_ordinal1(B,C)) | k1_xboole_0 = C))) & k1_funct_1(B,k1_xboole_0) = f2_s7_ordinal2 & k1_ordinal1(f1_s7_ordinal2) = k1_relat_1(B) & k1_ordinal2(B) = A & v5_ordinal1(B))) # label(s7_ordinal2_AndRHS) # label(axiom) # label(non_clause). [assumption]. 28.85/28.49 2381 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(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))))) <-> v3_ordinal2(A)))) # label(d17_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2382 (all A all B ((all C (r2_hidden(C,B) <-> r2_hidden(C,A) & (exists D (D = C & v4_ordinal1(D) & v3_ordinal1(D))))) <-> B = k3_ordinal2(A))) # label(d3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2383 $T # label(dt_k5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2384 (all A (v3_ordinal1(A) -> (all B (v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) & v1_relat_1(B) -> (k1_xboole_0 != A -> ((all C (v3_ordinal1(C) -> (all D (v3_ordinal1(D) -> -((all E (v3_ordinal1(E) -> -((all F (v3_ordinal1(F) -> (r1_ordinal1(E,F) & r2_hidden(F,k1_relat_1(B)) -> r2_hidden(k1_funct_1(B,F),D) & r2_hidden(C,k1_funct_1(B,F))))) & r2_hidden(E,k1_relat_1(B))))) & r2_hidden(A,D) & r2_hidden(C,A)))))) <-> r1_ordinal2(A,B))) & (A = k1_xboole_0 -> ((exists C ((all D (v3_ordinal1(D) -> (r1_ordinal1(C,D) & r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(B,D) = k1_xboole_0))) & r2_hidden(C,k1_relat_1(B)) & v3_ordinal1(C))) <-> r1_ordinal2(A,B))))))) # label(d13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2385 (all A (r2_hidden(A,k5_ordinal2) <-> v4_ordinal2(A))) # label(d21_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2386 (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]. 28.85/28.50 2387 (all A (v3_ordinal1(A) -> A = k14_ordinal2(k1_xboole_0,A))) # label(t47_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2388 $T # label(dt_k1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2389 (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]. 28.85/28.50 2390 (exists A (v1_relat_1(A) & v5_ordinal1(A) & f1_s5_ordinal2 = k1_relat_1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(k1_ordinal1(B),f1_s5_ordinal2) -> f3_s5_ordinal2(B,k1_funct_1(A,B)) = k1_funct_1(A,k1_ordinal1(B))))) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s5_ordinal2) & v4_ordinal1(B) -> k1_funct_1(A,B) = f4_s5_ordinal2(B,k2_ordinal1(A,B)) | B = k1_xboole_0))) & (r2_hidden(k1_xboole_0,f1_s5_ordinal2) -> k1_funct_1(A,k1_xboole_0) = f2_s5_ordinal2) & v1_funct_1(A))) # label(s5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2391 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k16_ordinal2(A,k1_ordinal1(B)) = k15_ordinal2(A,k16_ordinal2(A,B)))))) # label(t61_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2392 $T # label(t36_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2393 (all A all B ((all C (r2_hidden(C,A) & v3_ordinal1(C) <-> r2_hidden(C,B))) <-> B = k2_ordinal2(A))) # label(d2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2394 $T # label(t18_ordinal2) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2395 (all A all B all C (v1_finset_1(A) & v1_finset_1(C) & v1_finset_1(B) -> v1_finset_1(k3_zfmisc_1(A,B,C)))) # label(t20_finset_1) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2396 $T # label(t1_finset_1) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2397 $T # label(t2_finset_1) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2398 (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]. 28.85/28.50 2399 $T # label(t4_finset_1) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2400 (all A -(v1_finset_1(A) & k1_xboole_0 != A & (all B -((all C (r2_hidden(C,A) -> r1_tarski(B,C))) & r2_hidden(B,A))) & v6_ordinal1(A))) # label(t30_finset_1) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2401 (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]. 28.85/28.50 2402 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v1_finset_1(A) -> v1_finset_1(k9_relat_1(B,A))))) # label(t17_finset_1) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2403 (all A all B (v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k2_xboole_0(A,B)))) # label(fc9_finset_1) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2404 (all A all B all C (v1_finset_1(A) & v1_finset_1(B) & v1_finset_1(C) -> v1_finset_1(k3_zfmisc_1(A,B,C)))) # label(fc15_finset_1) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2405 (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]. 28.85/28.50 2406 (all A all B (v1_finset_1(A) & v1_finset_1(B) -> v1_finset_1(k5_xboole_0(A,B)))) # label(t28_finset_1) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2407 (all A -(v1_finset_1(A) & v6_ordinal1(A) & (all B -((all C (r2_hidden(C,A) -> r1_tarski(C,B))) & r2_hidden(B,A))) & k1_xboole_0 != A)) # label(t31_finset_1) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2408 (all A all B (v1_finset_1(k2_zfmisc_1(A,B)) -> v1_finset_1(B) | A = k1_xboole_0)) # label(t23_finset_1) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2409 (all A (v1_finset_1(k1_zfmisc_1(A)) <-> v1_finset_1(A))) # label(t24_finset_1) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2410 $T # label(t9_finset_1) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2411 (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]. 28.85/28.50 2412 (all A all B all C all D (v1_finset_1(A) & v1_finset_1(B) & v1_finset_1(C) & v1_finset_1(D) -> v1_finset_1(k4_zfmisc_1(A,B,C,D)))) # label(fc16_finset_1) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2413 (all A ((exists B (v1_relat_1(B) & v1_funct_1(B) & k2_relat_1(B) = A & r2_hidden(k1_relat_1(B),k5_ordinal2))) <-> v1_finset_1(A))) # label(d1_finset_1) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2414 (all A all B all C v1_finset_1(k1_enumset1(A,B,C))) # label(fc3_finset_1) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2415 (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]. 28.85/28.50 2416 (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]. 28.85/28.50 2417 (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]. 28.85/28.50 2418 (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]. 28.85/28.50 2419 $T # label(t12_finset_1) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2420 $T # label(t10_finset_1) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2421 (exists A (-v1_xboole_0(A) & v1_finset_1(A))) # label(rc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2422 (all A exists B (v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v2_ordinal1(B) & v4_ordinal2(B) & v1_finset_1(B) & v3_ordinal1(B) & v1_ordinal1(B) & m1_subset_1(B,k1_zfmisc_1(A)))) # label(rc2_finset_1) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2423 (all A all B (-v1_xboole_0(k2_tarski(A,B)) & v1_finset_1(k2_tarski(A,B)))) # label(fc2_finset_1) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2424 (all A all B (v1_finset_1(k2_zfmisc_1(B,A)) -> v1_finset_1(B) | A = k1_xboole_0)) # label(t22_finset_1) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2425 (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]. 28.85/28.50 2426 (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]. 28.85/28.50 2427 (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]. 28.85/28.50 2428 (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]. 28.85/28.50 2429 (all A all B (v1_funct_1(A) & v1_finset_1(B) & v1_relat_1(A) -> v1_finset_1(k9_relat_1(A,B)))) # label(fc13_finset_1) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2430 (all A all B (v1_finset_1(A) & v1_finset_1(B) -> v1_finset_1(k2_zfmisc_1(A,B)))) # label(t19_finset_1) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2431 $T # label(t8_finset_1) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2432 $T # label(t5_finset_1) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2433 (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]. 28.85/28.50 2434 $T # label(t3_finset_1) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2435 (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]. 28.85/28.50 2436 (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]. 28.85/28.50 2437 (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]. 28.85/28.50 2438 (exists A (v1_funct_1(A) & k1_relat_1(A) = f1_s1_finset_1 & (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) -> k1_funct_1(A,B) = f3_s1_finset_1(B))))) & v1_relat_1(A))) # label(s1_finset_1) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2439 p1_s2_finset_1(k1_xboole_0) & (all A all B (p1_s2_finset_1(B) & r1_tarski(B,f1_s2_finset_1) & r2_hidden(A,f1_s2_finset_1) -> p1_s2_finset_1(k2_xboole_0(B,k1_tarski(A))))) & v1_finset_1(f1_s2_finset_1) -> p1_s2_finset_1(f1_s2_finset_1) # label(s2_finset_1) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2440 (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]. 28.85/28.50 2441 (all A (v1_xboole_0(A) -> v1_finset_1(A))) # label(cc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2442 $T # label(t7_finset_1) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2443 (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]. 28.85/28.50 2444 (all A (v1_finset_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> -(B != k1_xboole_0 & (all C -(r2_hidden(C,B) & (all D (r1_tarski(C,D) & r2_hidden(D,B) -> D = C))))))))) # label(t18_finset_1) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2445 (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]. 28.85/28.50 2446 (all A (v1_finset_1(k3_tarski(A)) <-> v1_finset_1(A) & (all B (r2_hidden(B,A) -> v1_finset_1(B))))) # label(t25_finset_1) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2447 (all A (v1_relat_1(A) & v1_funct_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]. 28.85/28.50 2448 $T # label(t11_finset_1) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2449 (all A (-v1_xboole_0(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(A)) & v1_finset_1(B) & -v1_xboole_0(B))))) # label(rc3_finset_1) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2450 (all A (-v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)))) # label(fc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2451 $T # label(t6_finset_1) # label(axiom) # label(non_clause). [assumption]. 28.85/28.50 2452 (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]. 28.94/28.50 2453 (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]. 28.94/28.50 2454 (all A (r2_hidden(A,a_0_22_fraenkel) <-> (exists B exists C (m1_subset_1(C,f2_s13_fraenkel) & p1_s13_fraenkel(B,C) & A = f4_s13_fraenkel(B,C) & m1_subset_1(B,f1_s13_fraenkel))))) # label(fraenkel_a_0_22_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.50 2455 (exists A ((all B (m1_subset_1(B,f1_s24_fraenkel) -> ((exists C (m1_subset_1(C,f2_s24_fraenkel) & p1_s24_fraenkel(B,C) & B = f4_s24_fraenkel(C) & r2_hidden(C,f3_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]. 28.94/28.50 2456 (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]. 28.94/28.50 2457 (all A all B all C (-v1_xboole_0(B) & m1_fraenkel(C,A,B) -> (all D (m2_fraenkel(D,A,B,C) <-> m1_subset_1(D,C))))) # label(redefinition_m2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.50 2458 (all A ((exists B (m1_subset_1(B,f1_s9_fraenkel) & p2_s9_fraenkel(B) & r2_hidden(B,f3_s9_fraenkel) & A = k8_funct_2(f1_s9_fraenkel,f2_s9_fraenkel,f5_s9_fraenkel,B))) <-> r2_hidden(A,a_0_17_fraenkel))) # label(fraenkel_a_0_17_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.50 2459 (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]. 28.94/28.50 2460 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> m1_fraenkel(k2_setwiseo(k1_zfmisc_1(k2_zfmisc_1(A,B)),C),A,B))) # label(t10_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.50 2461 (all A all B (v1_finset_1(A) & v1_finset_1(B) -> v1_fraenkel(k1_funct_2(A,B)) & v1_finset_1(k1_funct_2(A,B)))) # label(fc2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.50 2462 (all A ((exists B (A = f2_s14_fraenkel(B) & p1_s14_fraenkel(B) & p2_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]. 28.94/28.50 2463 (all A (m1_subset_1(A,f1_s5_fraenkel) -> f3_s5_fraenkel(A) = f2_s5_fraenkel(A))) -> a_0_9_fraenkel = a_0_8_fraenkel # label(s5_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.50 2464 (all A (r2_hidden(A,a_0_3_fraenkel) <-> (exists B exists C (m1_subset_1(C,f2_s2_fraenkel) & p2_s2_fraenkel(B,C) & A = f3_s2_fraenkel(B,C) & m1_subset_1(B,f1_s2_fraenkel))))) # label(fraenkel_a_0_3_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.50 2465 $T # label(t12_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.50 2466 (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]. 28.94/28.50 2467 (all A ((exists B (p2_s3_fraenkel(B) & A = f2_s3_fraenkel(B) & m1_subset_1(B,f1_s3_fraenkel))) <-> r2_hidden(A,a_0_5_fraenkel))) # label(fraenkel_a_0_5_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.50 2468 (all A (-v1_xboole_0(A) -> (all B all C all D (m2_fraenkel(D,B,A,k1_fraenkel(B,A)) -> k7_relat_1(D,C) = k7_relat_1(D,k3_xboole_0(B,C)))))) # label(t15_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.50 2469 (all A ((exists B (p2_s1_fraenkel(B) & A = f2_s1_fraenkel(B) & m1_subset_1(B,f1_s1_fraenkel))) <-> r2_hidden(A,a_0_1_fraenkel))) # label(fraenkel_a_0_1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.50 2470 (all A (m1_subset_1(A,f1_s16_fraenkel) -> (all B (m1_subset_1(B,f2_s16_fraenkel) -> -((all C (m1_subset_1(C,f1_s16_fraenkel) -> -(p2_s16_fraenkel(C,B) & f3_s16_fraenkel(C,B) = f3_s16_fraenkel(A,B)))) & p1_s16_fraenkel(A,B)))))) -> r1_tarski(a_0_30_fraenkel,a_0_31_fraenkel) # label(s16_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.50 2471 (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]. 28.94/28.50 2472 (all A ((exists B exists C (m1_subset_1(C,f2_s4_fraenkel) & A = f3_s4_fraenkel(B,C) & p2_s4_fraenkel(B,C) & m1_subset_1(B,f1_s4_fraenkel))) <-> r2_hidden(A,a_0_7_fraenkel))) # label(fraenkel_a_0_7_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.50 2473 (all A (-v1_xboole_0(A) -> (all B all C all D (r1_tarski(D,A) & r1_tarski(C,B) -> (all E (m1_subset_1(E,k1_funct_2(C,D)) -> m2_relset_1(E,B,A) & v1_funct_1(E))) | k1_funct_2(C,D) = k1_xboole_0)))) # label(t6_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.50 2474 (all A ((all B (r2_hidden(B,A) -> v1_funct_1(B) & v1_relat_1(B))) <-> v1_fraenkel(A))) # label(d1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.50 2475 (all A ((exists B (p1_s10_fraenkel(B) & A = B & m1_subset_1(B,f1_s10_fraenkel))) <-> r2_hidden(A,a_0_18_fraenkel))) # label(fraenkel_a_0_18_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.50 2476 $T # label(t1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.50 2477 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(B,f3_s25_fraenkel) = k7_relat_1(A,f3_s25_fraenkel) -> f5_s25_fraenkel(A) = f5_s25_fraenkel(B)))))) -> v1_finset_1(a_0_40_fraenkel) # label(s25_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.50 2478 (exists A (-v1_xboole_0(A) & v1_fraenkel(A))) # label(rc1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.50 2479 (all A (m1_subset_1(A,f1_s8_fraenkel) -> (all B (m1_subset_1(B,f2_s8_fraenkel) -> f3_s8_fraenkel(A,B) = f3_s8_fraenkel(B,A))))) & (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]. 28.94/28.50 2480 (all A (m1_subset_1(A,f1_s4_fraenkel) -> (all B (m1_subset_1(B,f2_s4_fraenkel) -> (p1_s4_fraenkel(A,B) <-> p2_s4_fraenkel(A,B)))))) -> a_0_7_fraenkel = a_0_6_fraenkel # label(s4_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.50 2481 (all A ((exists B exists C (m1_subset_1(C,f2_s20_fraenkel) & f4_s20_fraenkel = C & p1_s20_fraenkel(B,C) & f3_s20_fraenkel(B,C) = A & 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]. 28.94/28.50 2482 (all A (v1_fraenkel(A) -> (all B (r1_tarski(B,A) -> v1_fraenkel(B))))) # label(t17_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.50 2483 (all A (r2_hidden(A,a_0_9_fraenkel) <-> (exists B (m1_subset_1(B,f1_s5_fraenkel) & p1_s5_fraenkel(B) & A = f3_s5_fraenkel(B))))) # label(fraenkel_a_0_9_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.50 2484 (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]. 28.94/28.50 2485 $T # label(t4_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.50 2486 (all A ((exists B (m1_subset_1(B,f1_s14_fraenkel) & B = A & p2_s14_fraenkel(B))) <-> r2_hidden(A,a_0_25_fraenkel))) # label(fraenkel_a_0_25_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.50 2487 (all A (m1_subset_1(A,f1_s6_fraenkel) -> (p1_s6_fraenkel(A) -> f2_s6_fraenkel(A) = f3_s6_fraenkel(A)))) -> a_0_11_fraenkel = a_0_10_fraenkel # label(s6_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.50 2488 $T # label(t9_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.50 2489 (all A (r2_hidden(A,a_0_24_fraenkel) <-> (exists B (m1_subset_1(B,f1_s14_fraenkel) & r2_hidden(B,a_0_25_fraenkel) & p1_s14_fraenkel(B) & A = f2_s14_fraenkel(B))))) # label(fraenkel_a_0_24_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2490 (all A ((exists B exists C (A = f3_s16_fraenkel(B,C) & p2_s16_fraenkel(B,C) & m1_subset_1(C,f2_s16_fraenkel) & m1_subset_1(B,f1_s16_fraenkel))) <-> r2_hidden(A,a_0_31_fraenkel))) # label(fraenkel_a_0_31_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2491 (all A (r2_hidden(A,a_0_32_fraenkel) <-> (exists B (A = f3_s17_fraenkel(B) & p1_s17_fraenkel(B) & r2_hidden(f3_s17_fraenkel(B),f2_s17_fraenkel) & m1_subset_1(B,f1_s17_fraenkel))))) # label(fraenkel_a_0_32_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2492 (all A ((exists B (f2_s3_fraenkel(B) = A & p1_s3_fraenkel(B) & m1_subset_1(B,f1_s3_fraenkel))) <-> r2_hidden(A,a_0_4_fraenkel))) # label(fraenkel_a_0_4_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2493 (all A all B exists C m1_fraenkel(C,A,B)) # label(existence_m1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2494 (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_2(A,f1_s26_fraenkel,f2_s26_fraenkel) & m2_relset_1(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))))) & v1_funct_1(A))) # label(s26_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2495 (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]. 28.94/28.51 2496 (all A (m1_subset_1(A,f1_s27_fraenkel) -> -((all B (m1_subset_1(B,f2_s27_fraenkel) -> -p1_s27_fraenkel(A,B))) & r2_hidden(A,f3_s27_fraenkel)))) -> (exists A (m2_fraenkel(A,f1_s27_fraenkel,f2_s27_fraenkel,k1_fraenkel(f1_s27_fraenkel,f2_s27_fraenkel)) & (all B (m1_subset_1(B,f1_s27_fraenkel) -> (r2_hidden(B,f3_s27_fraenkel) -> p1_s27_fraenkel(B,k8_funct_2(f1_s27_fraenkel,f2_s27_fraenkel,A,B))))))) # label(s27_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2497 (all A ((exists B (f2_s6_fraenkel(B) = A & p1_s6_fraenkel(B) & m1_subset_1(B,f1_s6_fraenkel))) <-> r2_hidden(A,a_0_10_fraenkel))) # label(fraenkel_a_0_10_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2498 (all A ((exists B (m1_subset_1(B,f1_s21_fraenkel) & r2_hidden(B,f2_s21_fraenkel) & A = f3_s21_fraenkel(B))) <-> r2_hidden(A,a_0_38_fraenkel))) # label(fraenkel_a_0_38_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2499 (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]. 28.94/28.51 2500 (all A (r2_hidden(A,a_0_30_fraenkel) <-> (exists B exists C (m1_subset_1(C,f2_s16_fraenkel) & p1_s16_fraenkel(B,C) & A = f3_s16_fraenkel(B,C) & m1_subset_1(B,f1_s16_fraenkel))))) # label(fraenkel_a_0_30_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2501 (all A all B v1_fraenkel(k1_funct_2(A,B))) # label(fc1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2502 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_fraenkel(k1_tarski(A)))) # label(t8_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2503 (all A ((exists B (m1_subset_1(B,f1_s18_fraenkel) & A = f3_s18_fraenkel(B) & p1_s18_fraenkel(B) & -r2_hidden(f3_s18_fraenkel(B),f2_s18_fraenkel))) <-> r2_hidden(A,a_0_33_fraenkel))) # label(fraenkel_a_0_33_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2504 (all A (m1_subset_1(A,f1_s19_fraenkel) -> (all B (m1_subset_1(B,f2_s19_fraenkel) -> (p2_s19_fraenkel(A,B) <-> p1_s19_fraenkel(A,B) & f4_s19_fraenkel = B))))) -> a_0_35_fraenkel = a_0_34_fraenkel # label(s19_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2505 $T # label(t2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2506 (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]. 28.94/28.51 2507 (all A (r2_hidden(A,a_0_11_fraenkel) <-> (exists B (f3_s6_fraenkel(B) = A & p1_s6_fraenkel(B) & m1_subset_1(B,f1_s6_fraenkel))))) # label(fraenkel_a_0_11_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2508 (all A (r2_hidden(A,a_0_16_fraenkel) <-> (exists B (m1_subset_1(B,f1_s9_fraenkel) & k8_funct_2(f1_s9_fraenkel,f2_s9_fraenkel,f4_s9_fraenkel,B) = A & p1_s9_fraenkel(B) & r2_hidden(B,f3_s9_fraenkel))))) # label(fraenkel_a_0_16_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2509 (all A ((exists B exists C (m1_subset_1(C,f2_s19_fraenkel) & f3_s19_fraenkel(B,C) = A & p2_s19_fraenkel(B,C) & m1_subset_1(B,f1_s19_fraenkel))) <-> r2_hidden(A,a_0_34_fraenkel))) # label(fraenkel_a_0_34_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2510 (all A (r2_hidden(A,a_0_6_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s4_fraenkel) & f3_s4_fraenkel(B,C) = A & p1_s4_fraenkel(B,C) & m1_subset_1(C,f2_s4_fraenkel))))) # label(fraenkel_a_0_6_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2511 (all A ((exists B (p1_s20_fraenkel(B,f4_s20_fraenkel) & f3_s20_fraenkel(B,f4_s20_fraenkel) = A & m1_subset_1(B,f1_s20_fraenkel))) <-> r2_hidden(A,a_0_37_fraenkel))) # label(fraenkel_a_0_37_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2512 v1_finset_1(f2_s21_fraenkel) -> v1_finset_1(a_0_38_fraenkel) # label(s21_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2513 (all A all B all C (m1_fraenkel(C,A,B) & -v1_xboole_0(B) -> (exists D m2_fraenkel(D,A,B,C)))) # label(existence_m2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2514 (all A (v1_fraenkel(A) -> (all B (m1_subset_1(B,A) -> v1_funct_1(B) & v1_relat_1(B))))) # label(cc1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2515 $T # label(t7_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2516 (all A (r2_hidden(A,a_0_21_fraenkel) <-> (exists B (A = B & p2_s13_fraenkel(B) & r2_hidden(B,a_0_22_fraenkel) & m1_subset_1(B,f3_s13_fraenkel))))) # label(fraenkel_a_0_21_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2517 (all A ((exists B (m1_subset_1(B,f1_s19_fraenkel) & f3_s19_fraenkel(B,f4_s19_fraenkel) = A & p1_s19_fraenkel(B,f4_s19_fraenkel))) <-> r2_hidden(A,a_0_35_fraenkel))) # label(fraenkel_a_0_35_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2518 $T # label(t13_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2519 (all A all B (-v1_xboole_0(B) -> k1_fraenkel(A,B) = k1_funct_2(A,B))) # label(redefinition_k1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2520 (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) -> -((all C (m1_subset_1(C,f1_s23_fraenkel) -> (r2_hidden(C,f2_s23_fraenkel) & p1_s23_fraenkel(C,B) -> p1_s23_fraenkel(B,C)))) & p1_s23_fraenkel(B,A) & r2_hidden(B,f2_s23_fraenkel))))))) # label(s23_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2521 (all A ((exists B (p1_s1_fraenkel(B) & A = f2_s1_fraenkel(B) & m1_subset_1(B,f1_s1_fraenkel))) <-> r2_hidden(A,a_0_0_fraenkel))) # label(fraenkel_a_0_0_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2522 (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) & f3_s8_fraenkel(B,C) = A & p1_s8_fraenkel(B,C))))) # label(fraenkel_a_0_14_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2523 (all A all B all C (m1_fraenkel(C,A,B) & -v1_xboole_0(B) -> (all D (m2_fraenkel(D,A,B,C) -> v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B))))) # label(dt_m2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2524 (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]. 28.94/28.51 2525 (all A all B all C (-v1_xboole_0(C) & v1_fraenkel(C) -> (m1_fraenkel(C,A,B) <-> (all D (m1_subset_1(D,C) -> v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D)))))) # label(d2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2526 (all A ((exists B exists C (p1_s15_fraenkel(B,C) & r2_hidden(B,a_0_28_fraenkel) & f3_s15_fraenkel(B,C) = A & m1_subset_1(C,f2_s15_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]. 28.94/28.51 2527 (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]. 28.94/28.51 2528 (all A (m1_subset_1(A,f1_s9_fraenkel) -> (r2_hidden(A,f3_s9_fraenkel) -> (p2_s9_fraenkel(A) <-> p1_s9_fraenkel(A))))) & k7_relat_1(f4_s9_fraenkel,f3_s9_fraenkel) = k7_relat_1(f5_s9_fraenkel,f3_s9_fraenkel) -> a_0_17_fraenkel = a_0_16_fraenkel # label(s9_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2529 (all A (r2_hidden(A,a_0_13_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s7_fraenkel) & f4_s7_fraenkel(B,C) = A & p1_s7_fraenkel(B,C) & m1_subset_1(C,f2_s7_fraenkel))))) # label(fraenkel_a_0_13_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2530 (all A (m1_subset_1(A,f1_s3_fraenkel) -> (p2_s3_fraenkel(A) <-> p1_s3_fraenkel(A)))) -> a_0_5_fraenkel = a_0_4_fraenkel # label(s3_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2531 (all A ((exists B exists C (m1_subset_1(B,f1_s13_fraenkel) & A = f4_s13_fraenkel(B,C) & p2_s13_fraenkel(f4_s13_fraenkel(B,C)) & p1_s13_fraenkel(B,C) & m1_subset_1(C,f2_s13_fraenkel))) <-> r2_hidden(A,a_0_23_fraenkel))) # label(fraenkel_a_0_23_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2532 v1_finset_1(f4_s22_fraenkel) & v1_finset_1(f3_s22_fraenkel) -> v1_finset_1(a_0_39_fraenkel) # label(s22_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2533 (all A (r2_hidden(A,a_0_28_fraenkel) <-> (exists B (m1_subset_1(B,f1_s15_fraenkel) & B = A & p2_s15_fraenkel(B))))) # label(fraenkel_a_0_28_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2534 (all A ((exists B exists C (m1_subset_1(C,f2_s15_fraenkel) & p1_s15_fraenkel(B,C) & p2_s15_fraenkel(B) & f3_s15_fraenkel(B,C) = A & m1_subset_1(B,f1_s15_fraenkel))) <-> r2_hidden(A,a_0_29_fraenkel))) # label(fraenkel_a_0_29_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2535 (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 (k7_relat_1(F,C) = E & m2_fraenkel(F,B,A,k1_fraenkel(B,A)))))) | k1_funct_2(C,D) = k1_xboole_0)))) # label(t14_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2536 (all A ((exists B exists C (m1_subset_1(C,f2_s11_fraenkel) & p1_s11_fraenkel(B,C) & f3_s11_fraenkel(B,C) = A & m1_subset_1(B,f1_s11_fraenkel))) <-> r2_hidden(A,a_0_19_fraenkel))) # label(fraenkel_a_0_19_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2537 (all A (r2_hidden(A,a_0_39_fraenkel) <-> (exists B exists C (m1_subset_1(C,f2_s22_fraenkel) & A = f5_s22_fraenkel(B,C) & r2_hidden(C,f4_s22_fraenkel) & r2_hidden(B,f3_s22_fraenkel) & m1_subset_1(B,f1_s22_fraenkel))))) # label(fraenkel_a_0_39_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2538 (all A (r2_hidden(A,a_0_12_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s7_fraenkel) & m1_subset_1(C,f2_s7_fraenkel) & A = f3_s7_fraenkel(B,C) & p1_s7_fraenkel(B,C))))) # label(fraenkel_a_0_12_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2539 (all A ((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))) <-> r2_hidden(A,a_0_15_fraenkel))) # label(fraenkel_a_0_15_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2540 (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 (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (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,C,F) = k8_funct_2(A,B,D,F)))))))))))))) # label(t3_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2541 (all A (r2_hidden(A,a_0_20_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s12_fraenkel) & m1_subset_1(C,f2_s12_fraenkel) & p1_s12_fraenkel(B,C) & A = f3_s12_fraenkel(B,C))))) # label(fraenkel_a_0_20_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2542 (all A (m1_subset_1(A,f1_s7_fraenkel) -> (all B (m1_subset_1(B,f2_s7_fraenkel) -> f3_s7_fraenkel(A,B) = f4_s7_fraenkel(A,B))))) -> a_0_13_fraenkel = a_0_12_fraenkel # label(s7_fraenkel) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2543 (all A (r2_hidden(A,a_0_0_numbers) <-> (exists B (A = B & np__0 = k1_funct_1(B,k13_arytm_3) & m1_subset_1(B,k1_funct_2(k2_tarski(np__0,k13_arytm_3),k1_numbers)))))) # label(fraenkel_a_0_0_numbers) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2544 $T # label(dt_k1_numbers) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2545 $T # label(dt_k3_numbers) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2546 $T # label(dt_k4_numbers) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2547 $T # label(dt_k2_numbers) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2548 (all A (-v1_xboole_0(A) & v1_xreal_0(A) & -v2_xreal_0(A) -> v1_xcmplx_0(A) & v1_xreal_0(A) & v3_xreal_0(A))) # label(cc6_xreal_0) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2549 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> 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]. 28.94/28.51 2550 (all A all B (-v2_xreal_0(B) & v1_xreal_0(B) & v2_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(fc17_xreal_0) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2551 (exists A (v1_xboole_0(A) & -v2_xreal_0(A) & -v3_xreal_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A))) # label(rc4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2552 (all A all B (-v3_xreal_0(B) & v1_xreal_0(B) & -v2_xreal_0(A) & v1_xreal_0(A) -> v1_xreal_0(k3_xcmplx_0(B,A)) & -v2_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]. 28.94/28.51 2553 (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]. 28.94/28.51 2554 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) & v2_xreal_0(A) -> v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & -v2_xreal_0(k6_xcmplx_0(B,A)) & v3_xreal_0(k6_xcmplx_0(B,A)) & -v1_xboole_0(k6_xcmplx_0(B,A)))) # label(fc18_xreal_0) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2555 (all A (v1_xreal_0(A) & v3_xreal_0(A) -> -v2_xreal_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A) & -v1_xboole_0(A))) # label(cc5_xreal_0) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2556 (all A all B (v1_xreal_0(B) & -v3_xreal_0(B) & v2_xreal_0(A) & v1_xreal_0(A) -> -v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v2_xreal_0(k2_xcmplx_0(B,A)) & -v3_xreal_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)))) # label(fc10_xreal_0) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2557 (all A (v1_xreal_0(A) & v2_xreal_0(A) -> -v3_xreal_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A) & -v1_xboole_0(A))) # label(cc3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2558 (exists A (v1_xcmplx_0(A) & -v3_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(A) & -v1_xboole_0(A))) # label(rc2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2559 (exists A (v1_xcmplx_0(A) & v1_xreal_0(A))) # label(rc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2560 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) & -v2_xreal_0(A) -> -v3_xreal_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc23_xreal_0) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2561 (all A (v1_xboole_0(A) & v1_xreal_0(A) -> -v2_xreal_0(A) & -v3_xreal_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A))) # label(cc7_xreal_0) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2562 (all A (v1_xreal_0(A) & -v3_xreal_0(A) -> v1_xreal_0(k4_xcmplx_0(A)) & -v2_xreal_0(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)))) # label(fc14_xreal_0) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2563 (all A all B (-v3_xreal_0(B) & v1_xreal_0(B) & -v3_xreal_0(A) & 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]. 28.94/28.51 2564 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & -v3_xreal_0(B) & -v3_xreal_0(A) -> -v3_xreal_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc24_xreal_0) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2565 (all A (v1_xreal_0(A) & -v3_xreal_0(A) & -v1_xboole_0(A) -> v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A))) # label(cc4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2566 (all A all B (v1_xreal_0(A) & -v3_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)) & -v2_xreal_0(k3_xcmplx_0(A,B)))) # label(fc21_xreal_0) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2567 (all A (v1_xreal_0(A) & -v2_xreal_0(A) -> v1_xcmplx_0(k4_xcmplx_0(A)) & -v3_xreal_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)))) # label(fc13_xreal_0) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2568 (all A all B (v1_xreal_0(A) & -v3_xreal_0(A) & -v3_xreal_0(B) & v1_xreal_0(B) -> v1_xcmplx_0(k7_xcmplx_0(A,B)) & -v3_xreal_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)))) # label(fc29_xreal_0) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2569 (all A all B (v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & -v3_xreal_0(B) -> v1_xreal_0(k2_xcmplx_0(A,B)) & -v3_xreal_0(k2_xcmplx_0(A,B)) & v2_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]. 28.94/28.51 2570 (all A all B (v1_xreal_0(A) & -v3_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) -> -v2_xreal_0(k7_xcmplx_0(B,A)) & v1_xreal_0(k7_xcmplx_0(B,A)) & v1_xcmplx_0(k7_xcmplx_0(B,A)))) # label(fc28_xreal_0) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2571 (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]. 28.94/28.51 2572 (all A (r2_hidden(A,k1_numbers) <-> v1_xreal_0(A))) # label(d1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2573 (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]. 28.94/28.51 2574 (all A all B (v3_xreal_0(A) & -v2_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)) & -v2_xreal_0(k2_xcmplx_0(A,B)) & -v1_xboole_0(k2_xcmplx_0(A,B)))) # label(fc11_xreal_0) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2575 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> v1_xreal_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)))) # label(fc3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2576 (all A all B (v1_xreal_0(B) & -v2_xreal_0(B) & v3_xreal_0(A) & v1_xreal_0(A) -> v1_xreal_0(k2_xcmplx_0(B,A)) & -v2_xreal_0(k2_xcmplx_0(B,A)) & v3_xreal_0(k2_xcmplx_0(B,A)) & 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]. 28.94/28.51 2577 (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(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_xboole_0(k6_xcmplx_0(B,A)))) # label(fc20_xreal_0) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2578 (all A (v1_xreal_0(A) & -v3_xreal_0(A) & -v2_xreal_0(A) -> v1_xboole_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A))) # label(cc8_xreal_0) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2579 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)))) # label(fc6_xreal_0) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2580 (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]. 28.94/28.51 2581 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) & -v3_xreal_0(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(fc16_xreal_0) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2582 (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]. 28.94/28.51 2583 (all A all B (v1_xreal_0(A) & -v2_xreal_0(B) & v1_xreal_0(B) & -v2_xreal_0(A) -> -v2_xreal_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)))) # label(fc8_xreal_0) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2584 (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]. 28.94/28.51 2585 (all A (v1_xreal_0(A) -> v1_xreal_0(k5_xcmplx_0(A)) & v1_xcmplx_0(k5_xcmplx_0(A)))) # label(fc2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2586 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)))) # label(fc4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2587 (all A all B (v1_xreal_0(A) & -v2_xreal_0(B) & v1_xreal_0(B) & -v3_xreal_0(A) -> -v3_xreal_0(k6_xcmplx_0(A,B)) & v1_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]. 28.94/28.51 2588 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) & -v2_xreal_0(A) -> -v3_xreal_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) & v1_xcmplx_0(k7_xcmplx_0(A,B)))) # label(fc30_xreal_0) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2589 (all A (v1_xreal_0(A) -> v1_xcmplx_0(A))) # label(cc2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2590 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) -> (r1_xreal_0(A,B) <-> (exists C ((exists D (k4_tarski(np__0,D) = B & r1_arytm_2(D,C) & A = k4_tarski(np__0,C) & m1_subset_1(D,k2_arytm_2))) & m1_subset_1(C,k2_arytm_2))))) & -(-(r2_hidden(A,k2_arytm_2) & r2_hidden(B,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))) & -(r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) <-> r1_xreal_0(A,B))) & (r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_arytm_2) -> (r1_xreal_0(A,B) <-> (exists C (m1_subset_1(C,k2_arytm_2) & (exists D (m1_subset_1(D,k2_arytm_2) & C = A & r1_arytm_2(C,D) & D = B)))))))))) # label(d2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2591 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & -v3_xreal_0(B) & v3_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(fc19_xreal_0) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2592 (all A all B (-v3_xreal_0(A) & -v2_xreal_0(B) & v1_xreal_0(B) & v1_xreal_0(A) -> v1_xcmplx_0(k7_xcmplx_0(A,B)) & -v2_xreal_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)))) # label(fc27_xreal_0) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2593 (all A (v1_xreal_0(A) & -v3_xreal_0(A) -> v1_xcmplx_0(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(A)) & -v3_xreal_0(k5_xcmplx_0(A)))) # label(fc26_xreal_0) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2594 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> r1_xreal_0(A,B) | r1_xreal_0(B,A))) # label(connectedness_r1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2595 (all A (v4_ordinal2(A) -> v1_xreal_0(A))) # label(cc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2596 (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]. 28.94/28.51 2597 $T # label(t10_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2598 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(A,k1_int_1(A)) & v1_int_1(A)) & -(-v1_int_1(A) & r1_xreal_0(A,k1_int_1(A))))) # label(t48_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2599 (all A (v1_xreal_0(A) -> v1_int_1(k2_int_1(A)))) # label(dt_k2_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2600 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(k4_int_1(A),np__0) & v1_int_1(A)) & -(r1_xreal_0(k4_int_1(A),np__0) & -v1_int_1(A)))) # label(t72_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2601 (all A (v1_xreal_0(A) -> (v1_int_1(A) <-> np__0 = k4_int_1(A)))) # label(t71_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2602 $T # label(t31_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2603 (all A (v1_xreal_0(A) -> k4_int_1(A) = k3_int_1(A))) # label(redefinition_k4_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2604 (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(k2_xcmplx_0(A,D),k2_xcmplx_0(B,E),C)))))))))))) # label(t37_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2605 (all A (v1_xreal_0(A) -> (v1_int_1(A) <-> A = k2_int_1(A)))) # label(t54_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2606 (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]. 28.94/28.51 2607 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> (k1_int_1(A) = B <-> -r1_xreal_0(B,k6_xcmplx_0(A,np__1)) & r1_xreal_0(B,A)))))) # label(d4_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2608 (all A (v1_xreal_0(A) -> v1_xcmplx_0(k3_int_1(A)) & v1_xreal_0(k3_int_1(A)))) # label(fc10_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2609 (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]. 28.94/28.51 2610 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (B = np__1 & np__1 = A | k1_real_1(np__1) = A & B = k1_real_1(np__1) <-> np__1 = k3_xcmplx_0(A,B)))))) # label(t22_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2611 $T # label(t30_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2612 $T # label(t27_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2613 (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]. 28.94/28.51 2614 (all A all B (v1_int_1(A) & v1_int_1(B) -> v1_int_1(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)))) # label(fc1_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2615 (all A (v1_xreal_0(A) -> (v1_int_1(A) <-> k1_int_1(A) = k2_int_1(A)))) # label(t59_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2616 (all A (v1_xreal_0(A) -> k1_int_1(k1_int_1(A)) = k1_int_1(A))) # label(t63_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2617 (all A (v1_int_1(A) -> k5_int_1(A,np__0) = np__0)) # label(t75_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2618 (all A (v1_xreal_0(A) -> -((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> A != B & A != k1_real_1(B))) & v1_int_1(A)))) # label(t8_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.51 2619 p1_s2_int_1(f1_s2_int_1) & (all A (v1_int_1(A) -> (r1_xreal_0(f1_s2_int_1,A) & p1_s2_int_1(A) -> p1_s2_int_1(k2_xcmplx_0(A,np__1))))) -> (all A (v1_int_1(A) -> (r1_xreal_0(f1_s2_int_1,A) -> p1_s2_int_1(A)))) # label(s2_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2620 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> ((exists C (v1_int_1(C) & B = k3_xcmplx_0(A,C))) <-> r2_int_1(A,B)))))) # label(d9_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2621 (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]. 28.94/28.52 2622 (all A (r2_hidden(A,k4_numbers) <-> v1_int_1(A))) # label(d2_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2623 (all A (v1_xreal_0(A) -> -(r1_xreal_0(k2_int_1(A),k1_int_1(A)) & -v1_int_1(A)) & -(-r1_xreal_0(k2_int_1(A),k1_int_1(A)) & v1_int_1(A)))) # label(t60_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2624 (all A (v1_int_1(A) -> r1_int_1(A,np__0,A) & r1_int_1(np__0,A,A))) # label(t33_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2625 (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]. 28.94/28.52 2626 (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]. 28.94/28.52 2627 (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) -> C = B | r1_xreal_0(C,k6_xcmplx_0(A,np__1)) | r1_xreal_0(B,k6_xcmplx_0(A,np__1))))))))) # label(t44_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2628 $T # label(t73_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2629 (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]. 28.94/28.52 2630 (all A (v1_xreal_0(A) -> k2_int_1(A) = k1_int_1(k2_int_1(A)))) # label(t62_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2631 (all A (v1_xreal_0(A) -> (all B (v4_ordinal2(B) -> (A = B | A = k4_xcmplx_0(B) -> v1_int_1(A)))))) # label(t7_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2632 (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]. 28.94/28.52 2633 (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]. 28.94/28.52 2634 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_int_1(k6_xcmplx_0(A,B)))) # label(fc9_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2635 (all A all B (v1_int_1(B) & v1_int_1(A) -> v1_int_1(k6_int_1(A,B)))) # label(dt_k6_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2636 (all A (v1_xreal_0(A) -> (k2_int_1(A) = k1_int_1(A) <-> k2_int_1(A) != k2_xcmplx_0(k1_int_1(A),np__1)))) # label(t66_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2637 (all A all B (v1_int_1(A) & v1_int_1(B) -> v1_xreal_0(k3_xcmplx_0(A,B)) & v1_int_1(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc2_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2638 (exists A v1_int_1(A)) # label(rc2_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2639 (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]. 28.94/28.52 2640 $T # label(t6_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2641 $T # label(t15_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2642 (all A all B (v1_int_1(B) & v1_int_1(A) -> v1_int_1(k5_int_1(A,B)))) # label(dt_k5_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2643 (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]. 28.94/28.52 2644 (all A (v1_int_1(A) -> v1_xcmplx_0(k4_xcmplx_0(A)) & v1_int_1(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)))) # label(fc3_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2645 (all A (v1_xreal_0(A) -> -(-v1_int_1(A) & r1_xreal_0(k2_int_1(A),A)) & -(-r1_xreal_0(k2_int_1(A),A) & v1_int_1(A)))) # label(t55_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2646 (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]. 28.94/28.52 2647 (all A (v1_xreal_0(A) -> -r1_xreal_0(k2_xcmplx_0(k2_int_1(A),np__1),A) & -r1_xreal_0(k2_int_1(A),k6_xcmplx_0(A,np__1)))) # label(t57_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2648 $T # label(t2_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2649 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (np__1 = B & A = k1_real_1(np__1) | A = np__1 & k1_real_1(np__1) = B <-> k3_xcmplx_0(A,B) = k1_real_1(np__1)))))) # label(t23_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2650 $T # label(t24_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2651 (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) & k3_xcmplx_0(A,B) = C -> r1_int_1(D,E,A)))))))))))) # label(t41_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2652 (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]. 28.94/28.52 2653 $T # label(t9_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2654 (all A (v1_xreal_0(A) -> k1_int_1(A) = k2_int_1(k1_int_1(A)))) # label(t65_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2655 (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]. 28.94/28.52 2656 (all A (m1_subset_1(A,k5_numbers) -> v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & -v2_xreal_0(k4_xcmplx_0(A)) & v1_int_1(k4_xcmplx_0(A)))) # label(fc5_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2657 $T # label(t3_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2658 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> -((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(r1_xreal_0(np__1,C) & C = k6_xcmplx_0(B,A)))) & -r1_xreal_0(B,A)))))) # label(t78_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2659 $T # label(t46_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2660 $T # label(t67_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2661 (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]. 28.94/28.52 2662 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> k2_int_1(k2_xcmplx_0(A,B)) = k2_xcmplx_0(k2_int_1(A),B))))) # label(t58_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2663 (all A (v1_xreal_0(A) -> v1_int_1(k1_int_1(A)))) # label(dt_k1_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2664 (all A (v1_xreal_0(A) -> -r1_xreal_0(np__1,k4_int_1(A)) & r1_xreal_0(np__0,k4_int_1(A)))) # label(t69_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2665 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (r1_xreal_0(A,B) & r1_xreal_0(A,C) -> r1_xreal_0(k2_xcmplx_0(A,np__1),C) | C = B | r1_xreal_0(k2_xcmplx_0(A,np__1),B)))))))) # label(t45_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2666 (all A (v4_ordinal2(A) -> v1_int_1(A))) # label(cc3_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2667 $T # label(t26_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2668 (all A (v1_xreal_0(A) -> (np__0 != A -> k1_int_1(k7_xcmplx_0(A,A)) = np__1))) # label(t74_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2669 (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]. 28.94/28.52 2670 $T # label(t1_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2671 $T # label(dt_k3_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2672 $T # label(t53_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2673 (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]. 28.94/28.52 2674 (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]. 28.94/28.52 2675 (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]. 28.94/28.52 2676 (all A (v1_xreal_0(A) -> (v1_int_1(A) -> v1_int_1(k2_xcmplx_0(A,np__1)) & v1_int_1(k6_xcmplx_0(A,np__1))))) # label(t17_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2677 (all A (v1_xreal_0(A) -> (k1_int_1(A) = A <-> v1_int_1(A)))) # label(t47_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2678 (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]. 28.94/28.52 2679 (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]. 28.94/28.52 2680 (all A (v1_int_1(A) -> (p1_s6_int_1(A) -> r1_xreal_0(A,f1_s6_int_1)))) & (exists A (v1_int_1(A) & p1_s6_int_1(A))) -> (exists A (v1_int_1(A) & p1_s6_int_1(A) & (all B (v1_int_1(B) -> (p1_s6_int_1(B) -> r1_xreal_0(B,A)))))) # label(s6_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2681 (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]. 28.94/28.52 2682 $T # label(t5_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2683 $T # label(t29_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2684 $T # label(t14_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2685 (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]. 28.94/28.52 2686 (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]. 28.94/28.52 2687 $T # label(t56_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2688 $T # label(t49_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2689 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> ((exists D (v1_int_1(D) & k3_xcmplx_0(C,D) = k6_xcmplx_0(A,B))) <-> r1_int_1(A,B,C)))))))) # label(d3_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2690 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (B = np__0 -> np__0 = k6_int_1(A,B)) & (B != np__0 -> k6_xcmplx_0(A,k3_xcmplx_0(k5_int_1(A,B),B)) = k6_int_1(A,B)))))) # label(d8_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2691 $T # label(t4_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2692 $T # label(t13_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2693 (all A (v1_int_1(A) -> (A != np__0 -> k5_int_1(A,A) = np__1))) # label(t76_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2694 $T # label(t12_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2695 (all A all B (m1_subset_1(A,k5_numbers) & v1_int_1(B) -> v1_int_1(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)))) # label(fc6_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2696 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (k2_xcmplx_0(B,A) = C -> r1_xreal_0(B,C)))))))) # label(t19_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2697 (all A (v1_int_1(A) -> v1_xreal_0(A) & v1_xcmplx_0(A))) # label(cc4_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2698 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> (-r1_xreal_0(k2_xcmplx_0(A,np__1),B) & r1_xreal_0(A,B) <-> k2_int_1(A) = B))))) # label(d5_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2699 (exists A (v1_int_1(A) & p1_s5_int_1(A))) & (all A (v1_int_1(A) -> (p1_s5_int_1(A) -> r1_xreal_0(f1_s5_int_1,A)))) -> (exists A (p1_s5_int_1(A) & (all B (v1_int_1(B) -> (p1_s5_int_1(B) -> r1_xreal_0(A,B)))) & v1_int_1(A))) # label(s5_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2700 $T # label(t28_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2701 (all A all B (v1_int_1(A) & v1_int_1(B) -> r2_int_1(A,A))) # label(reflexivity_r2_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2702 (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]. 28.94/28.52 2703 $T # label(t25_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2704 (all A all B (m1_subset_1(A,k5_numbers) & v1_int_1(B) -> v1_xreal_0(k3_xcmplx_0(B,A)) & v1_int_1(k3_xcmplx_0(B,A)) & v1_xcmplx_0(k3_xcmplx_0(B,A)))) # label(fc7_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2705 (all A (m1_subset_1(A,k4_numbers) -> v1_int_1(A))) # label(cc1_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2706 (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]. 28.94/28.52 2707 (all A (k4_numbers = A <-> (all B (-(all C (m2_subset_1(C,k1_numbers,k5_numbers) -> B != C & k1_real_1(C) != B)) <-> r2_hidden(B,A))))) # label(d1_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2708 (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]. 28.94/28.52 2709 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (r1_int_1(k2_xcmplx_0(A,C),B,C) <-> r1_int_1(A,B,C)))))))) # label(t42_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2710 $T # label(t11_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2711 (all A (v1_int_1(A) -> np__0 = k6_int_1(A,A))) # label(t77_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2712 (all A all B (v1_int_1(B) & v1_int_1(A) -> 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(fc4_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2713 (all A (m1_subset_1(A,k5_numbers) -> v1_ordinal1(A) & v2_ordinal1(A) & -v3_xreal_0(A) & v1_int_1(A) & v1_xreal_0(A) & v1_xcmplx_0(A) & v4_ordinal2(A) & v3_ordinal1(A))) # label(cc2_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2714 (all A all B (v1_int_1(B) & m1_subset_1(A,k5_numbers) -> v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v1_int_1(k6_xcmplx_0(B,A)))) # label(fc8_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2715 (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]. 28.94/28.52 2716 (all A (v1_xreal_0(A) -> (r1_xreal_0(np__0,A) -> r1_xreal_0(np__0,k2_int_1(A)) & r1_xreal_0(np__0,k1_int_1(A)) & m2_subset_1(k2_int_1(A),k1_numbers,k5_numbers) & m2_subset_1(k1_int_1(A),k1_numbers,k5_numbers)))) # label(t80_int_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2717 (all A (v1_membered(A) -> ((all B (v1_xcmplx_0(B) -> r2_hidden(B,A))) -> A = k2_numbers))) # label(t11_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2718 (all A (v4_membered(A) -> (all B (v4_membered(B) -> (r1_xboole_0(A,B) <-> (all C (v1_int_1(C) -> -(r2_hidden(C,A) & r2_hidden(C,B))))))))) # label(d19_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2719 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> v2_membered(k2_tarski(A,B)) & v1_membered(k2_tarski(A,B)))) # label(fc13_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2720 (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]. 28.94/28.52 2721 (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]. 28.94/28.52 2722 (all A (v2_membered(A) -> r1_tarski(A,k1_numbers))) # label(t2_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2723 (all A all B (v1_xcmplx_0(A) & v1_xcmplx_0(B) -> v1_membered(k2_tarski(A,B)))) # label(fc12_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2724 (all A all B (v5_membered(A) & v5_membered(B) -> v2_membered(k5_xboole_0(A,B)) & v3_membered(k5_xboole_0(A,B)) & v4_membered(k5_xboole_0(A,B)) & v5_membered(k5_xboole_0(A,B)) & v1_membered(k5_xboole_0(A,B)))) # label(fc46_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2725 (all A all B (v5_membered(A) -> v5_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v1_membered(k3_xboole_0(B,A)))) # label(fc36_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2726 (all A (v5_membered(A) -> (all B (v5_membered(B) -> (r1_tarski(A,B) <-> (all C (v4_ordinal2(C) -> (r2_hidden(C,A) -> r2_hidden(C,B))))))))) # label(d10_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2727 (all A all B (v3_membered(A) & v3_membered(B) -> v1_membered(k5_xboole_0(A,B)) & v3_membered(k5_xboole_0(A,B)) & v2_membered(k5_xboole_0(A,B)))) # label(fc44_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2728 (all A (v4_membered(A) -> (all B (m1_subset_1(B,A) -> v1_xcmplx_0(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B))))) # label(cc13_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2729 (all A (m1_subset_1(A,k1_zfmisc_1(k2_numbers)) -> v1_membered(A))) # label(cc5_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2730 (all A all B (v4_membered(A) & v4_membered(B) -> 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]. 28.94/28.52 2731 (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]. 28.94/28.52 2732 (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]. 28.94/28.52 2733 (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]. 28.94/28.52 2734 (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]. 28.94/28.52 2735 (all A all B (v3_membered(B) -> (r1_tarski(A,B) -> v3_membered(A)))) # label(t18_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2736 (all A (v1_xreal_0(A) -> v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)))) # label(fc8_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2737 (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]. 28.94/28.52 2738 (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]. 28.94/28.52 2739 (all A all B (v3_membered(A) -> v3_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v1_membered(k3_xboole_0(A,B)))) # label(fc31_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2740 (all A (v1_membered(A) & -v1_xboole_0(A) -> (exists B (v1_xcmplx_0(B) & r2_hidden(B,A))))) # label(t6_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2741 (all A (v2_membered(A) -> v1_membered(A))) # label(cc4_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2742 (all A (v4_membered(A) & -v1_xboole_0(A) -> (exists B (v1_int_1(B) & r2_hidden(B,A))))) # label(t9_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2743 (all A (v2_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v2_membered(B) & v1_membered(B))))) # label(cc17_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2744 (all A all B (v5_membered(A) -> v1_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) & v5_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)))) # label(fc35_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2745 (all A all B (v1_membered(B) -> (r1_tarski(A,B) -> v1_membered(A)))) # label(t16_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2746 (all A (m1_subset_1(A,k1_zfmisc_1(k5_numbers)) -> v4_membered(A) & v5_membered(A) & v3_membered(A) & v2_membered(A) & v1_membered(A))) # label(cc9_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2747 (all A all B (v4_membered(A) -> v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)))) # label(fc33_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2748 (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]. 28.94/28.52 2749 (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]. 28.94/28.52 2750 (all A all B all C (v1_int_1(C) & v1_int_1(B) & v1_int_1(A) -> v2_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)) & v4_membered(k1_enumset1(A,B,C)) & v1_membered(k1_enumset1(A,B,C)))) # label(fc20_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2751 (all A all B all C (v1_xreal_0(C) & v1_xreal_0(B) & v1_xreal_0(A) -> v2_membered(k1_enumset1(A,B,C)) & v1_membered(k1_enumset1(A,B,C)))) # label(fc18_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2752 (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]. 28.94/28.52 2753 (all A (v1_membered(A) -> (all B (v1_membered(B) -> ((all C (v1_xcmplx_0(C) -> (r2_hidden(C,A) <-> r2_hidden(C,B)))) <-> A = B))))) # label(d11_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2754 (all A all B (v1_membered(A) -> v1_membered(k3_xboole_0(A,B)))) # label(fc27_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2755 (all A all B (v4_membered(B) & r2_hidden(B,A) -> v4_membered(k1_setfam_1(A)))) # label(t29_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2756 (all A all B (r2_hidden(B,A) & v1_membered(B) -> v1_membered(k1_setfam_1(A)))) # label(t26_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2757 (exists A ((all B (v1_rat_1(B) -> (p1_s3_membered(B) <-> r2_hidden(B,A)))) & v3_membered(A))) # label(s3_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2758 (all A all B (v4_membered(A) & v4_membered(B) -> v1_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)))) # label(fc25_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2759 (all A (v3_membered(A) -> (all B (v3_membered(B) -> (r1_tarski(A,B) <-> (all C (v1_rat_1(C) -> (r2_hidden(C,A) -> r2_hidden(C,B))))))))) # label(d8_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2760 (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]. 28.94/28.52 2761 (all A (v5_membered(A) -> r1_tarski(A,k5_numbers))) # label(t5_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2762 (all A (v1_membered(A) -> r1_tarski(A,k2_numbers))) # label(t1_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2763 (all A (v5_membered(A) -> v4_membered(A))) # label(cc1_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2764 (all A (v3_membered(A) <-> (all B (r2_hidden(B,A) -> v1_rat_1(B))))) # label(d3_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2765 (all A all B (v1_membered(A) -> v1_membered(k4_xboole_0(A,B)))) # label(fc37_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2766 (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]. 28.94/28.52 2767 (all A all B (v2_membered(A) & v2_membered(B) -> v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)))) # label(fc23_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2768 (all A (m1_subset_1(A,k1_zfmisc_1(k4_numbers)) -> v1_membered(A) & v2_membered(A) & v4_membered(A) & v3_membered(A))) # label(cc8_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2769 (all A (v1_xcmplx_0(A) -> v1_membered(k1_tarski(A)))) # label(fc7_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2770 (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]. 28.94/28.52 2771 (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]. 28.94/28.52 2772 (all A (v4_membered(A) -> r1_tarski(A,k4_numbers))) # label(t4_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2773 (all A (v4_membered(A) -> (all B (v4_membered(B) -> ((all C (v1_int_1(C) -> (r2_hidden(C,A) <-> r2_hidden(C,B)))) <-> B = A))))) # label(d14_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2774 (all A ((all B (r2_hidden(B,A) -> v1_int_1(B))) <-> v4_membered(A))) # label(d4_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2775 (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]. 28.94/28.52 2776 (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]. 28.94/28.52 2777 (all A all B (v4_ordinal2(A) & v4_ordinal2(B) -> v2_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) & v5_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v1_membered(k2_tarski(A,B)))) # label(fc16_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2778 (all A ((all B (r2_hidden(B,A) -> v1_xcmplx_0(B))) <-> v1_membered(A))) # label(d1_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2779 (all A all B (v1_int_1(B) & v1_int_1(A) -> v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v1_membered(k2_tarski(A,B)))) # label(fc15_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2780 (all A all B (v3_membered(A) -> v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) & v1_membered(k4_xboole_0(A,B)))) # label(fc39_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2781 (all A (v3_membered(A) -> (all B (v3_membered(B) -> (B = A <-> (all C (v1_rat_1(C) -> (r2_hidden(C,A) <-> r2_hidden(C,B))))))))) # label(d13_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2782 (all A (v2_membered(A) <-> (all B (r2_hidden(B,A) -> v1_xreal_0(B))))) # label(d2_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2783 (all A (v5_membered(A) & -v1_xboole_0(A) -> (exists B (v4_ordinal2(B) & r2_hidden(B,A))))) # label(t10_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2784 (all A all B all C (v4_ordinal2(B) & v4_ordinal2(C) & v4_ordinal2(A) -> v2_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)) & v5_membered(k1_enumset1(A,B,C)) & v4_membered(k1_enumset1(A,B,C)) & v1_membered(k1_enumset1(A,B,C)))) # label(fc21_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.52 2785 (all A (v4_membered(A) -> v3_membered(A))) # label(cc2_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2786 (all A all B (v5_membered(B) & v5_membered(A) -> v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v5_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) & v1_membered(k2_xboole_0(A,B)))) # label(fc26_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2787 (all A (v1_rat_1(A) -> v1_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)))) # label(fc9_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2788 (all A (v5_membered(A) -> (all B (m1_subset_1(B,A) -> v1_xcmplx_0(B) & v4_ordinal2(B) & v1_int_1(B) & v1_rat_1(B) & v1_xreal_0(B))))) # label(cc14_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2789 (all A (v2_membered(A) -> (all B (v2_membered(B) -> ((all C (v1_xreal_0(C) -> (r2_hidden(C,B) <-> r2_hidden(C,A)))) <-> B = A))))) # label(d12_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2790 (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]. 28.94/28.53 2791 (all A (v1_membered(A) -> (all B (v1_membered(B) -> (r1_xboole_0(A,B) <-> (all C (v1_xcmplx_0(C) -> -(r2_hidden(C,B) & r2_hidden(C,A))))))))) # label(d16_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2792 (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]. 28.94/28.53 2793 (all A all B (v5_membered(B) -> (r1_tarski(A,B) -> v5_membered(A)))) # label(t20_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2794 (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]. 28.94/28.53 2795 (all A ((all B (r2_hidden(B,A) -> v4_ordinal2(B))) <-> v5_membered(A))) # label(d5_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2796 (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)) & v3_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)))) # label(fc19_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2797 (all A (v3_membered(A) -> (all B (v3_membered(B) -> (r1_xboole_0(A,B) <-> (all C (v1_rat_1(C) -> -(r2_hidden(C,A) & r2_hidden(C,B))))))))) # label(d18_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2798 (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]. 28.94/28.53 2799 (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]. 28.94/28.53 2800 (all A (m1_subset_1(A,k1_zfmisc_1(k3_numbers)) -> v1_membered(A) & v3_membered(A) & v2_membered(A))) # label(cc7_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2801 (all A all B (v3_membered(B) & v3_membered(A) -> 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]. 28.94/28.53 2802 (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]. 28.94/28.53 2803 (all A (v5_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v1_membered(B) & v2_membered(B) & v3_membered(B) & v5_membered(B) & v4_membered(B))))) # label(cc20_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2804 (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]. 28.94/28.53 2805 (exists A ((all B (v1_int_1(B) -> (p1_s4_membered(B) <-> r2_hidden(B,A)))) & v4_membered(A))) # label(s4_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2806 (all A all B (v1_membered(A) -> v1_membered(k3_xboole_0(B,A)))) # label(fc28_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2807 (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]. 28.94/28.53 2808 (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]. 28.94/28.53 2809 (all A (v3_membered(A) -> v2_membered(A))) # label(cc3_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2810 (exists A (-v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v5_membered(A) & v4_membered(A))) # label(rc1_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2811 (all A (v5_membered(A) -> (all B (v5_membered(B) -> (A = B <-> (all C (v4_ordinal2(C) -> (r2_hidden(C,A) <-> r2_hidden(C,B))))))))) # label(d15_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2812 (all A all B (v5_membered(A) -> v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) & v5_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)) & v1_membered(k4_xboole_0(A,B)))) # label(fc41_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2813 (all A all B (v4_membered(A) -> v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)))) # label(fc40_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2814 (all A (v2_membered(A) -> (all B (v2_membered(B) -> (r1_xboole_0(A,B) <-> (all C (v1_xreal_0(C) -> -(r2_hidden(C,A) & r2_hidden(C,B))))))))) # label(d17_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2815 (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]. 28.94/28.53 2816 (all A (v4_membered(A) -> ((all B (v1_int_1(B) -> r2_hidden(B,A))) -> A = k4_numbers))) # label(t14_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2817 (all A (v3_membered(A) -> (all B (m1_subset_1(B,A) -> v1_rat_1(B) & v1_xreal_0(B) & v1_xcmplx_0(B))))) # label(cc12_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2818 (all A all B (v4_membered(B) -> (r1_tarski(A,B) -> v4_membered(A)))) # label(t19_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2819 (all A (v4_ordinal2(A) -> v4_membered(k1_tarski(A)) & v5_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v1_membered(k1_tarski(A)))) # label(fc11_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2820 (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]. 28.94/28.53 2821 (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]. 28.94/28.53 2822 (exists A (v2_membered(A) & (all B (v1_xreal_0(B) -> (r2_hidden(B,A) <-> p1_s2_membered(B)))))) # label(s2_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2823 (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]. 28.94/28.53 2824 (all A (v1_membered(A) -> (all B (v1_membered(B) -> ((all C (v1_xcmplx_0(C) -> (r2_hidden(C,A) -> r2_hidden(C,B)))) <-> r1_tarski(A,B)))))) # label(d6_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2825 (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]. 28.94/28.53 2826 (all A all B (v2_membered(B) -> (r1_tarski(A,B) -> v2_membered(A)))) # label(t17_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2827 (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]. 28.94/28.53 2828 (all A (v3_membered(A) -> r1_tarski(A,k3_numbers))) # label(t3_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2829 (all A (v1_xboole_0(A) -> v5_membered(A) & v4_membered(A) & v3_membered(A) & v2_membered(A) & v1_membered(A))) # label(cc15_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2830 (all A all B (v1_rat_1(B) & v1_rat_1(A) -> v3_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v1_membered(k2_tarski(A,B)))) # label(fc14_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2831 (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]. 28.94/28.53 2832 (all A (v1_int_1(A) -> v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)))) # label(fc10_membered) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2833 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) & r1_tarski(A,k1_relat_1(B)) -> r2_wellord2(A,k9_relat_1(B,A))))) # label(t60_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2834 $T # label(t9_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2835 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (r2_hidden(A,B) <-> -r1_tarski(B,A)))))) # label(t14_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2836 (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]. 28.94/28.53 2837 (all A np__1 = k4_card_1(k1_tarski(A))) # label(t79_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2838 (all A (v1_finset_1(A) -> v2_ordinal1(k1_card_1(A)) & v3_ordinal1(k1_card_1(A)) & v1_card_1(k1_card_1(A)) & v1_finset_1(k1_card_1(A)) & v1_ordinal1(k1_card_1(A)))) # label(fc2_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2839 (all A (k1_xboole_0 = A <-> r2_wellord2(A,k1_xboole_0))) # label(t46_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2840 $T # label(t31_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2841 (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]. 28.94/28.53 2842 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r1_tarski(k1_card_1(A),k1_card_1(B)) <-> r1_xreal_0(A,B)))))) # label(t72_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2843 $T # label(t37_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2844 (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]. 28.94/28.53 2845 $T # label(d4_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2846 (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]. 28.94/28.53 2847 $T # label(t17_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2848 (all A exists B (r2_wellord2(A,B) & v3_ordinal1(B))) # label(t4_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2849 (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]. 28.94/28.53 2850 $T # label(t53_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2851 (all A v1_card_1(k2_card_1(A))) # label(dt_k2_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2852 $T # label(t11_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2853 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_wellord2(A,B) -> A = B))))) # label(t64_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2854 (all A all B all C all D (r2_wellord2(A,B) & r2_hidden(C,A) & r2_hidden(D,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]. 28.94/28.53 2855 $T # label(d2_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2856 (all A (v3_ordinal1(A) -> r1_ordinal1(k1_card_1(A),A))) # label(t24_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2857 (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]. 28.94/28.53 2858 $T # label(t10_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2859 (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]. 28.94/28.53 2860 $T # label(t3_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2861 $T # label(t6_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2862 (exists A v1_card_1(A)) # label(rc1_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2863 $T # label(t75_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2864 $T # label(d3_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2865 (all A (m1_subset_1(A,k5_numbers) -> v3_ordinal1(A) & v1_xreal_0(A) & v1_card_1(A) & -v3_xreal_0(A) & v1_finset_1(A) & v1_xcmplx_0(A) & v4_ordinal2(A) & v2_ordinal1(A) & v1_ordinal1(A))) # label(cc3_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2866 (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]. 28.94/28.53 2867 (all A all B (v1_card_1(B) -> ((all C (v1_card_1(C) -> (r2_hidden(k1_card_1(A),C) -> r1_tarski(B,C)))) & r2_hidden(k1_card_1(A),B) <-> k2_card_1(A) = B))) # label(d6_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2868 (all A all B ((exists C (v1_funct_1(C) & r1_tarski(k2_relat_1(C),B) & A = k1_relat_1(C) & v2_funct_1(C) & v1_relat_1(C))) <-> r1_tarski(k1_card_1(A),k1_card_1(B)))) # label(t26_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2869 $T # label(t18_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2870 (all A v1_card_1(k1_card_1(A))) # label(dt_k1_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2871 $T # label(d9_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2872 (all A all B (r2_wellord2(A,B) <-> k1_card_1(B) = k1_card_1(A))) # label(t21_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2873 (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]. 28.94/28.53 2874 $T # label(dt_k3_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2875 (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]. 28.94/28.53 2876 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(k3_card_1(A),k3_card_1(B)) <-> r2_hidden(A,B)))))) # label(t41_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2877 (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]. 28.94/28.53 2878 (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]. 28.94/28.53 2879 (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_ordinal1(A,B)))))) # label(t56_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2880 $T # label(t70_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2881 (all A (v1_finset_1(A) -> k1_card_1(A) = k4_card_1(A))) # label(redefinition_k4_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2882 (all A (v3_ordinal1(A) -> (all 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_xboole_0 = D | k1_funct_1(C,D) = k1_card_1(k8_ordinal2(k2_ordinal1(C,D)))))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k2_card_1(k3_tarski(k1_tarski(k1_funct_1(C,D)))) = k1_funct_1(C,k1_ordinal1(D))))) & k1_funct_1(C,k1_xboole_0) = k1_card_1(k5_numbers) & B = k1_ordinal2(C) & v1_funct_1(C))) <-> B = k3_card_1(A))))) # label(d8_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2883 (all A -r2_wellord2(A,k1_zfmisc_1(A))) # label(t29_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2884 (all A k1_card_1(k1_tarski(A)) = k4_ordinal2) # label(t50_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2885 (all A (v3_ordinal1(A) -> r2_hidden(A,k2_card_1(A)))) # label(t36_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2886 (exists A (v1_ordinal1(A) & v1_card_1(A) & v1_finset_1(A) & v3_ordinal1(A) & v2_ordinal1(A))) # label(rc2_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2887 (all A all B (v1_card_1(B) -> (k1_card_1(A) = B <-> r2_wellord2(A,B)))) # label(d5_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2888 $T # label(t15_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2889 $T # label(t5_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2890 $T # label(t2_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2891 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (r2_hidden(A,B) <-> r1_tarski(A,B) & B != A))))) # label(t13_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2892 (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]. 28.94/28.53 2893 (all A (v3_ordinal1(A) -> v1_card_1(k3_card_1(A)) & v3_ordinal1(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]. 28.94/28.53 2894 (all A all B (r1_tarski(k1_zfmisc_1(A),B) -> -r2_wellord2(A,B) & r2_hidden(k1_card_1(A),k1_card_1(B)))) # label(t45_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2895 $T # label(t77_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2896 $T # label(t57_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2897 (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]. 28.94/28.53 2898 $T # label(t1_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2899 $T # label(t55_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2900 (all A (v1_card_1(A) -> r2_hidden(A,k2_card_1(A)))) # label(t32_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2901 $T # label(t16_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2902 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k1_card_1(A) = k1_card_1(B) -> A = B))))) # label(t71_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2903 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k1_ordinal1(A) = k1_nat_1(A,np__1))) # label(t52_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2904 (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]. 28.94/28.53 2905 $T # label(t62_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2906 (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]. 28.94/28.53 2907 $T # label(t63_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2908 (all A (v1_finset_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k1_card_1(B) = k1_card_1(A) <-> B = k4_card_1(A)))))) # label(d11_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2909 (all A all B (r2_wellord2(A,k1_tarski(B)) <-> (exists C k1_tarski(C) = A))) # label(t48_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2910 (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]. 28.94/28.53 2911 $T # label(t67_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2912 $T # label(t20_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2913 (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) -> ((all B (v1_card_1(B) -> (r2_hidden(B,A) -> p1_s1_card_1(B)))) & v2_card_1(A) -> A = k1_xboole_0 | p1_s1_card_1(A)))) & p1_s1_card_1(k1_xboole_0) -> (all A (v1_card_1(A) -> p1_s1_card_1(A))) # label(s1_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2914 (all A r2_hidden(k1_card_1(k1_xboole_0),k2_card_1(A))) # label(t33_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2915 (all A all B (r1_tarski(k1_card_1(A),k1_card_1(B)) <-> (exists C (v1_funct_1(C) & r1_tarski(A,k2_relat_1(C)) & k1_relat_1(C) = B & v1_relat_1(C))))) # label(t28_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2916 $T # label(d10_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2917 $T # label(t12_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2918 (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]. 28.94/28.53 2919 (all A all B (k1_card_1(B) = k1_card_1(A) -> k2_card_1(A) = k2_card_1(B))) # label(t34_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2920 (all A all B all C all D (r1_xboole_0(C,D) & r2_wellord2(B,D) & r2_wellord2(A,C) & r1_xboole_0(A,B) -> r2_wellord2(k2_xboole_0(A,B),k2_xboole_0(C,D)))) # label(t58_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2921 (all A (r2_hidden(A,k5_ordinal2) -> v1_card_1(A))) # label(t65_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2922 (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]. 28.94/28.53 2923 (all A (v1_finset_1(A) & v1_card_1(A) -> (exists B (k1_card_1(B) = A & m2_subset_1(B,k1_numbers,k5_numbers))))) # label(t86_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2924 (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]. 28.94/28.53 2925 (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]. 28.94/28.53 2926 (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]. 28.94/28.53 2927 (all A (m1_subset_1(A,k5_numbers) -> v3_ordinal1(A) & v1_xcmplx_0(A) & -v3_xreal_0(A) & v1_card_1(A) & v1_xreal_0(A) & v4_ordinal2(A) & v2_ordinal1(A) & v1_ordinal1(A))) # label(cc2_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2928 (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]. 28.94/28.53 2929 (all A (v1_finset_1(A) -> v1_finset_1(k2_card_1(A)))) # label(t82_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2930 (all A all B ((exists C k1_tarski(C) = A) <-> k1_card_1(k1_tarski(B)) = k1_card_1(A))) # label(t49_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2931 (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]. 28.94/28.53 2932 (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]. 28.94/28.53 2933 $T # label(t19_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2934 $T # label(t7_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2935 $T # label(t54_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2936 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (k3_card_1(B) = k3_card_1(A) -> B = A))))) # label(t42_card_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.53 2937 (exists A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(B,k2_finseq_1(f1_s2_finseq_1)) -> k1_funct_1(A,B) = f2_s2_finseq_1(B)))) & k3_finseq_1(A) = f1_s2_finseq_1)) # label(s2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2938 $T # label(t70_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2939 $T # label(t22_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2940 (exists A (v2_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2941 (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) -> (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(A,C) = k1_funct_1(B,C)))) -> B = A))))) # label(t18_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2942 (all A all B (m1_finseq_1(B,A) -> v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B))) # label(dt_m1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2943 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_xreal_0(A,B) -> k5_subset_1(k5_numbers,k2_finseq_1(B),k2_finseq_1(A)) = k2_finseq_1(A)))))) # label(t9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2944 (all A k5_finseq_1(A) = k1_tarski(k4_tarski(np__1,A))) # label(d5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2945 (all A (v1_finset_1(A) <-> (exists B (v1_relat_1(B) & A = k2_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B))))) # label(t73_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2946 (all A all B all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (np__2 = k3_finseq_1(C) & k1_funct_1(C,np__2) = B & k1_funct_1(C,np__1) = A <-> k10_finseq_1(A,B) = C))) # label(t61_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2947 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (k2_finseq_1(A) = k2_finseq_1(B) -> A = B))))) # label(t8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2948 (all A (v1_relat_1(A) -> ((exists B (m2_subset_1(B,k1_numbers,k5_numbers) & k2_finseq_1(B) = k1_relat_1(A))) <-> v1_finseq_1(A)))) # label(d2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2949 (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_tarski(A,B) -> r1_xreal_0(k3_finseq_1(A),k3_finseq_1(B))))))) # label(t84_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2950 $T # label(dt_k1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2951 $T # label(dt_k5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2952 (all A (v1_relat_1(A) -> v1_relat_1(k17_finseq_1(A)))) # label(dt_k17_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2953 $T # label(t1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2954 $T # label(t30_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2955 $T # label(t2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2956 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (k3_finseq_1(A) = np__0 <-> A = k1_xboole_0))) # label(t25_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2957 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> A = k1_funct_1(k7_finseq_1(B,k9_finseq_1(A)),k1_nat_1(k3_finseq_1(B),np__1)))) # label(t59_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2958 (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) -> -(A = D & 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]. 28.94/28.54 2959 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> A = k1_funct_1(k7_finseq_1(k9_finseq_1(A),B),np__1))) # label(t58_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2960 (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) -> -(C = k1_nat_1(k3_finseq_1(A),D) & r2_hidden(D,k4_finseq_1(B)))))))))))) # label(t38_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2961 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> A = k4_card_1(k1_card_1(A)) & k4_card_1(A) = A)) # label(t78_finseq_1_AndLHS) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2962 (all A (v4_ordinal2(A) -> A = k4_card_1(k2_finseq_1(A)))) # label(t78_finseq_1_AndRHS) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2963 (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) -> (k2_relat_1(B) = k2_relat_1(A) & v2_funct_1(A) & v2_funct_1(B) -> k3_finseq_1(B) = k3_finseq_1(A)))))) # label(t65_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2964 (all A exists B (m1_finseq_1(B,A) & v1_xboole_0(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_finset_1(B) & v2_funct_1(B) & v1_relat_1(B))) # label(rc4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2965 (all A -(v1_finset_1(A) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> -r2_wellord2(A,k2_finseq_1(B)))))) # label(t77_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2966 (all A (v4_ordinal2(A) -> k2_finseq_1(A) = k1_finseq_1(A))) # label(redefinition_k2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2967 (all A k9_finseq_1(A) = k5_finseq_1(A)) # label(redefinition_k9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2968 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (k3_finseq_1(A) = np__0 <-> A = k6_finseq_1(B))))) # label(t32_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2969 (all A all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> -((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(A = k4_tarski(C,k1_funct_1(B,C)) & r2_hidden(C,k4_finseq_1(B))))) & r2_hidden(A,B)))) # label(t16_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2970 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) -> v1_finset_1(k1_relat_1(A)))) # label(fc17_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2971 (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_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) -> -(r1_xreal_0(k3_finseq_1(A),k3_finseq_1(C)) & (all E (v1_funct_1(E) & v1_finseq_1(E) & v1_relat_1(E) -> C != k7_finseq_1(A,E))) & k7_finseq_1(A,B) = k7_finseq_1(C,D)))))))))) # label(t64_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2972 (all A exists B m1_finseq_1(B,A)) # label(existence_m1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2973 (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]. 28.94/28.54 2974 (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]. 28.94/28.54 2975 (all A (v1_relat_1(k9_finseq_1(A)) & v1_funct_1(k9_finseq_1(A)))) # label(dt_k9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2976 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> k4_finseq_1(A) = k1_relat_1(A))) # label(redefinition_k4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2977 $T # label(t13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2978 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_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> p1_s3_finseq_1(A))) # label(s3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2979 (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]. 28.94/28.54 2980 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B all C (p1_s1_finseq_1(A,B) & p1_s1_finseq_1(A,C) & r2_hidden(A,k2_finseq_1(f1_s1_finseq_1)) -> C = B)))) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> -((all B -p1_s1_finseq_1(A,B)) & r2_hidden(A,k2_finseq_1(f1_s1_finseq_1))))) -> (exists A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(B,k2_finseq_1(f1_s1_finseq_1)) -> p1_s1_finseq_1(B,k1_funct_1(A,B))))) & k4_finseq_1(A) = k2_finseq_1(f1_s1_finseq_1))) # label(s1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2981 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (B = k9_finseq_1(A) <-> k1_funct_1(B,np__1) = A & k1_relat_1(B) = k2_finseq_1(np__1)))) # label(d8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2982 $T # label(t67_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2983 (all A (v1_relat_1(A) & v1_funct_1(A) & v2_finseq_1(A) -> v1_relat_1(k15_finseq_1(A)) & v1_funct_1(k15_finseq_1(A)) & v1_finset_1(k15_finseq_1(A)) & v1_finseq_1(k15_finseq_1(A)))) # label(fc10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2984 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (k1_xboole_0 = A <-> k1_xboole_0 = k2_relat_1(A)))) # label(t27_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2985 (all A all B (v1_relat_1(A) & v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) & -v1_xboole_0(B) & v1_finseq_1(A) & v1_funct_1(A) -> -v1_xboole_0(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) & v1_relat_1(k7_finseq_1(A,B)))) # label(fc13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2986 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> A = k7_finseq_1(k1_xboole_0,A) & A = k7_finseq_1(A,k1_xboole_0))) # label(t47_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2987 (exists A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A))) # label(rc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2988 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(A),k2_relat_1(k7_finseq_1(B,A))))))) # label(t43_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2989 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k1_relat_1(A) = k2_finseq_1(B) <-> B = k3_finseq_1(A)))))) # label(d3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2990 $T # label(dt_k11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2991 (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]. 28.94/28.54 2992 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r2_hidden(A,k2_finseq_1(B)) <-> r1_xreal_0(np__1,A) & r1_xreal_0(A,B)))))) # label(t3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2993 (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) -> (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]. 28.94/28.54 2994 (all A (v4_ordinal2(A) -> v1_finset_1(k1_finseq_1(A)))) # label(fc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2995 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r2_hidden(k2_xcmplx_0(B,C),k2_finseq_1(k2_xcmplx_0(A,C))) -> r2_hidden(B,k2_finseq_1(k2_xcmplx_0(A,C))) & r2_hidden(B,k2_finseq_1(A)) | r1_xreal_0(B,np__0)))))))) # label(t82_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2996 (all A all B (m1_finseq_1(B,A) -> v1_xboole_0(k16_finseq_1(A,B,np__0)) & v1_funct_1(k16_finseq_1(A,B,np__0)) & v1_finset_1(k16_finseq_1(A,B,np__0)) & v1_finseq_1(k16_finseq_1(A,B,np__0)) & v2_funct_1(k16_finseq_1(A,B,np__0)) & v1_relat_1(k16_finseq_1(A,B,np__0)))) # label(fc15_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2997 (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 (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,C) & r1_xreal_0(C,k3_finseq_1(B)) -> k1_funct_1(B,C) = k1_funct_1(k7_finseq_1(A,B),k1_nat_1(k3_finseq_1(A),C))))))))) # label(t86_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2998 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> -((all B (m1_subset_1(B,f1_s5_finseq_1) -> -p1_s5_finseq_1(A,B))) & r2_hidden(A,k2_finseq_1(f2_s5_finseq_1))))) -> (exists A (k4_finseq_1(A) = k2_finseq_1(f2_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))))) & m2_finseq_1(A,f1_s5_finseq_1))) # label(s5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 2999 (all 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(B),k1_relat_1(A)) -> v1_relat_1(k5_relat_1(B,A)) & v1_funct_1(k5_relat_1(B,A)) & v1_finseq_1(k5_relat_1(B,A))))))) # label(t20_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 3000 (all A (v4_ordinal2(A) -> A = np__0 | r2_hidden(A,k2_finseq_1(A)))) # label(t5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 3001 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> A = k7_relat_1(k7_finseq_1(A,B),k4_finseq_1(A)))))) # label(t33_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 3002 (all A m2_finseq_1(k14_finseq_1(A),k5_numbers)) # label(dt_k14_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 3003 (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]. 28.94/28.54 3004 (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]. 28.94/28.54 3005 (all A k1_tarski(k4_tarski(np__1,A)) = k9_finseq_1(A)) # label(t52_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 3006 (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) -> (C = k7_finseq_1(A,B) <-> k2_finseq_1(k1_nat_1(k3_finseq_1(A),k3_finseq_1(B))) = k4_finseq_1(C) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(B)) -> k1_funct_1(B,D) = k1_funct_1(C,k1_nat_1(k3_finseq_1(A),D))))) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(A)) -> k1_funct_1(A,D) = k1_funct_1(C,D))))))))))) # label(d7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 3007 (all A ((exists B (v4_ordinal2(B) & r1_tarski(A,k2_finseq_1(B)))) -> (all B (m2_finseq_1(B,k5_numbers) -> (k2_relat_1(B) = A & (all C (v4_ordinal2(C) -> (all D (v4_ordinal2(D) -> (all E (v4_ordinal2(E) -> (all F (v4_ordinal2(F) -> -(-r1_xreal_0(D,C) & r1_xreal_0(F,E) & F = k1_funct_1(B,D) & E = k1_funct_1(B,C) & r1_xreal_0(D,k3_finseq_1(B)) & r1_xreal_0(np__1,C)))))))))) <-> B = k14_finseq_1(A)))))) # label(d13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 3008 (all A all B all C (m1_finseq_1(B,A) & m1_finseq_1(C,A) -> k7_finseq_1(B,C) = k8_finseq_1(A,B,C))) # label(redefinition_k8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 3009 $T # label(t34_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 3010 (all A (v1_xboole_0(k6_finseq_1(A)) & m2_finseq_1(k6_finseq_1(A),A))) # label(dt_k6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 3011 (all A (v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)))) # label(fc4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 3012 (all A exists B (m1_relset_1(B,k5_numbers,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B))) # label(rc2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 3013 $T # label(dt_k10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 3014 (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]. 28.94/28.54 3015 (all A all B all C (v1_relat_1(k11_finseq_1(A,B,C)) & v1_funct_1(k11_finseq_1(A,B,C)) & v1_finseq_1(k11_finseq_1(A,B,C)) & v1_finset_1(k11_finseq_1(A,B,C)))) # label(fc8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 3016 (all A all B all C (k7_finseq_1(k9_finseq_1(A),k10_finseq_1(B,C)) = k11_finseq_1(A,B,C) & k7_finseq_1(k10_finseq_1(A,B),k9_finseq_1(C)) = k11_finseq_1(A,B,C))) # label(t60_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 3017 (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]. 28.94/28.54 3018 (exists A (v1_funct_1(A) & v1_finset_1(A) & v1_relat_1(A) & -v1_xboole_0(A))) # label(rc7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 3019 (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(np__1,C) & r1_xreal_0(C,k3_finseq_1(A)) -> k1_funct_1(A,C) = k1_funct_1(k7_finseq_1(A,B),C)))))))) # label(t85_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 3020 (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) -> k3_finseq_1(k7_finseq_1(A,B)) = k1_nat_1(k3_finseq_1(A),k3_finseq_1(B)))))) # label(t35_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 3021 (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 (m2_finseq_1(k7_finseq_1(A,B),C) -> m2_finseq_1(B,C) & m2_finseq_1(A,C))))))) # label(t50_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 3022 (all A (v4_ordinal2(A) -> k2_finseq_1(A) = k4_xboole_0(k2_finseq_1(k2_xcmplx_0(A,np__1)),k1_tarski(k2_xcmplx_0(A,np__1))))) # label(t12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 3023 (all A r2_hidden(k1_xboole_0,k13_finseq_1(A))) # label(t66_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 3024 (all A (v1_relat_1(A) & v1_funct_1(A) & v2_finseq_1(A) -> k15_finseq_1(A) = k5_relat_1(k14_finseq_1(k1_relat_1(A)),A))) # label(d14_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 3025 (all A all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (A = k1_funct_1(B,np__1) & np__1 = k3_finseq_1(B) <-> k9_finseq_1(A) = B))) # label(t57_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 3026 (all A ((exists B (r1_tarski(A,k2_finseq_1(B)) & m2_subset_1(B,k1_numbers,k5_numbers))) -> (A = k1_xboole_0 <-> k1_xboole_0 = k14_finseq_1(A)))) # label(t72_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 3027 (all A all B (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) & v1_funct_1(A) -> v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)))) # label(dt_k7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 3028 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v4_ordinal2(C) -> (r1_xreal_0(C,k3_finseq_1(k7_finseq_1(A,B))) -> r1_xreal_0(C,k3_finseq_1(A)) | k1_funct_1(k7_finseq_1(A,B),C) = k1_funct_1(B,k6_xcmplx_0(C,k3_finseq_1(A)))))))))) # label(t37_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.54 3029 (exists A (v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_relat_1(A) & v1_xboole_0(A))) # label(rc6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3030 (all A all B (v1_funct_1(k10_finseq_1(A,B)) & v1_relat_1(k10_finseq_1(A,B)))) # label(fc5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3031 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> v2_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(t68_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3032 (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) & C = B & v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C))))) # label(s4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3033 $T # label(t51_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3034 $T # label(t28_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3035 (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 (v1_relat_1(E) & C = k1_funct_1(E,np__1) & (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)))) & k1_funct_1(E,k3_finseq_1(E)) = D & r1_xreal_0(np__1,k3_finseq_1(E)) & v1_finseq_1(E) & v1_funct_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]. 28.94/28.55 3036 (all A all B all C k7_finseq_1(k7_finseq_1(k9_finseq_1(A),k9_finseq_1(B)),k9_finseq_1(C)) = k11_finseq_1(A,B,C)) # label(d10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3037 (all A exists B m2_finseq_1(B,A)) # label(existence_m2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3038 (all A -v1_xboole_0(k13_finseq_1(A))) # label(fc9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3039 (all A (v4_ordinal2(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> v1_relat_1(k7_relat_1(B,k2_finseq_1(A))) & v1_funct_1(k7_relat_1(B,k2_finseq_1(A))) & v1_finseq_1(k7_relat_1(B,k2_finseq_1(A))))))) # label(t19_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3040 $T # label(dt_k13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3041 (all A (v1_funct_1(A) & v2_finseq_1(A) & v1_relat_1(A) -> k1_relat_1(A) = k2_relat_1(k14_finseq_1(k1_relat_1(A))))) # label(t71_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3042 (all A all B all C (v1_relat_1(k11_finseq_1(A,B,C)) & v1_funct_1(k11_finseq_1(A,B,C)))) # label(fc6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3043 (all A k1_xboole_0 = k6_finseq_1(A)) # label(d6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3044 (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]. 28.94/28.55 3045 (all A all B all C all D (v1_relat_1(D) & v1_finseq_1(D) & v1_funct_1(D) -> (B = k1_funct_1(D,np__2) & k1_funct_1(D,np__3) = C & A = k1_funct_1(D,np__1) & np__3 = k3_finseq_1(D) <-> D = k11_finseq_1(A,B,C)))) # label(t62_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3046 (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]. 28.94/28.55 3047 (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]. 28.94/28.55 3048 $T # label(t49_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3049 (all A all B (v1_relat_1(k10_finseq_1(A,B)) & v1_finset_1(k10_finseq_1(A,B)) & v1_finseq_1(k10_finseq_1(A,B)) & v1_funct_1(k10_finseq_1(A,B)))) # label(fc7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3050 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((exists B (m2_subset_1(B,k1_numbers,k5_numbers) & r1_tarski(k1_relat_1(A),k2_finseq_1(B)))) <-> v2_finseq_1(A)))) # label(d12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3051 (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]. 28.94/28.55 3052 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(A),k2_relat_1(k7_finseq_1(A,B))))))) # label(t42_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3053 (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]. 28.94/28.55 3054 (exists A (-v1_xboole_0(A) & v1_finseq_1(A) & v1_finset_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3055 (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]. 28.94/28.55 3056 $T # label(t54_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3057 (all A (v4_ordinal2(A) -> k2_xboole_0(k2_finseq_1(A),k1_tarski(k2_xcmplx_0(A,np__1))) = k2_finseq_1(k2_xcmplx_0(A,np__1)))) # label(t11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3058 (all A all B (v4_ordinal2(B) -> ((exists C (r1_xreal_0(np__1,C) & r1_xreal_0(C,B) & A = C & m2_subset_1(C,k1_numbers,k5_numbers))) <-> r2_hidden(A,a_1_0_finseq_1(B))))) # label(fraenkel_a_1_0_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3059 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> m1_subset_1(k4_finseq_1(A),k1_zfmisc_1(k5_numbers)))) # label(dt_k4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3060 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> k7_finseq_1(k7_finseq_1(A,B),C) = k7_finseq_1(A,k7_finseq_1(B,C)))))))) # label(t45_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3061 (all A (-v1_xboole_0(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_relat_1(k5_finseq_1(A)))) # label(fc12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3062 (exists A (v1_finseq_1(A) & v1_finset_1(A) & v2_funct_1(A) & v1_funct_1(A) & v1_relat_1(A) & v1_xboole_0(A))) # label(rc3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3063 $T # label(t31_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3064 (all A all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (k1_tarski(A) = k2_relat_1(B) & k4_finseq_1(B) = k2_finseq_1(np__1) <-> B = k9_finseq_1(A)))) # label(t55_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3065 (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_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (k7_finseq_1(C,B) = k7_finseq_1(A,B) | k7_finseq_1(B,C) = k7_finseq_1(B,A) -> A = C))))))) # label(t46_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3066 (all A all B (v1_funct_1(A) & -v1_xboole_0(B) & v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) & v1_finseq_1(A) & v1_relat_1(A) -> -v1_xboole_0(k7_finseq_1(B,A)) & v1_relat_1(k7_finseq_1(B,A)) & v1_finseq_1(k7_finseq_1(B,A)) & v1_finset_1(k7_finseq_1(B,A)) & v1_funct_1(k7_finseq_1(B,A)))) # label(fc14_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3067 (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]. 28.94/28.55 3068 (all A all B (m2_finseq_1(B,A) -> (all C (v4_ordinal2(C) -> (r1_xreal_0(C,k3_finseq_1(B)) -> C = k3_finseq_1(k16_finseq_1(A,B,C))))))) # label(t80_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3069 (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]. 28.94/28.55 3070 (all A all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (m1_finseq_1(B,A) <-> r1_tarski(k2_relat_1(B),A)))) # label(d4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3071 (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]. 28.94/28.55 3072 (all A (v1_finset_1(A) & v1_relat_1(A) -> v1_finset_1(k2_relat_1(A)))) # label(fc11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3073 (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]. 28.94/28.55 3074 (all A (v2_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k15_finseq_1(A)) & v1_relat_1(k15_finseq_1(A)))) # label(dt_k15_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3075 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> -(k1_xboole_0 != A & (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C k7_finseq_1(B,k9_finseq_1(C)) != A)))))) # label(t63_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3076 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers))) # label(dt_k3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3077 (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]. 28.94/28.55 3078 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) -> m2_finseq_1(k12_finseq_1(A,B),A))) # label(dt_k12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3079 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> v1_funct_1(k7_relat_1(B,A)) & v1_relat_1(k8_relat_1(A,B)) & v2_finseq_1(k8_relat_1(A,B)) & v1_funct_1(k8_relat_1(A,B)) & v2_finseq_1(k7_relat_1(B,A)) & v1_relat_1(k7_relat_1(B,A)))) # label(t69_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3080 (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) -> k2_xboole_0(k2_relat_1(A),k2_relat_1(B)) = k2_relat_1(k7_finseq_1(A,B)))))) # label(t44_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3081 (all A all B (B = k13_finseq_1(A) <-> (all C (m2_finseq_1(C,A) <-> r2_hidden(C,B))))) # label(d11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3082 (all A (v1_finseq_1(A) & v1_funct_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]. 28.94/28.55 3083 $T # label(t53_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3084 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k1_card_1(k2_finseq_1(A)) = k1_card_1(A))) # label(t76_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3085 (all A (v4_ordinal2(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) -> (r1_xreal_0(A,k3_finseq_1(B)) & C = k7_relat_1(B,k2_finseq_1(A)) -> k2_finseq_1(A) = k4_finseq_1(C) & k3_finseq_1(C) = A))))))) # label(t21_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3086 (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]. 28.94/28.55 3087 (all A m2_finseq_1(k1_xboole_0,A)) # label(t29_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3088 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) -> k12_finseq_1(A,B) = k5_finseq_1(B))) # label(redefinition_k12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3089 (all A (v1_relat_1(A) & v1_funct_1(A) -> -((all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> -r1_tarski(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]. 28.94/28.55 3090 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (k7_finseq_1(A,B) = k1_xboole_0 -> A = k1_xboole_0 & B = k1_xboole_0))))) # label(t48_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3091 (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]. 28.94/28.55 3092 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (k1_xboole_0 = A <-> k1_xboole_0 = k4_finseq_1(A)))) # label(t26_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3093 (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 (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(C,k4_finseq_1(A)) -> k1_funct_1(A,C) = k1_funct_1(B,C)))) & k4_finseq_1(B) = k4_finseq_1(A) -> B = A))))) # label(t17_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3094 (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]. 28.94/28.55 3095 (all A all B (m2_finseq_1(B,A) -> v1_funct_1(B) & v1_finseq_1(B) & m2_relset_1(B,k5_numbers,A))) # label(dt_m2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3096 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (k1_tarski(A) = k2_relat_1(B) & np__1 = k3_finseq_1(B) <-> B = k9_finseq_1(A)))) # label(t56_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3097 (all A all B all C (v4_ordinal2(C) & m1_finseq_1(B,A) -> m2_finseq_1(k16_finseq_1(A,B,C),A))) # label(dt_k16_finseq_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3098 (all A (v1_relat_1(A) -> (all B (r8_orders_1(A,B) <-> r9_orders_1(k4_relat_1(A),B))))) # label(t166_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3099 $T # label(t60_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3100 (all A (v1_relat_1(A) -> (all B all C (r1_orders_1(A,B) & r1_tarski(C,B) -> r1_orders_1(A,C))))) # label(t128_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3101 (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]. 28.94/28.55 3102 (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]. 28.94/28.55 3103 $T # label(t58_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3104 (all A all B (v1_relat_1(B) -> (r7_relat_2(B,A) <-> r6_relat_2(B,A) & r1_relat_2(B,A)))) # label(t92_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3105 (all A (v1_relat_1(A) -> (all B (v6_relat_2(A) & r7_orders_1(A,B) -> r9_orders_1(A,B))))) # label(t159_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3106 $T # label(t144_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3107 (all A (v1_relat_1(A) -> (all B (r2_wellord1(A,B) -> r3_orders_1(A,B) & r2_orders_1(A,B) & r1_orders_1(A,B))))) # label(t124_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3108 $T # label(t39_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3109 (all A (v1_relat_1(A) -> (v1_relat_2(A) & v8_relat_2(A) & v4_relat_2(A) <-> v2_orders_1(A)))) # label(d4_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3110 (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]. 28.94/28.55 3111 (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]. 28.94/28.55 3112 $T # label(t43_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3113 $T # label(t15_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3114 (all A (v1_relat_1(A) -> (v3_orders_1(A) <-> v1_relat_2(A) & v8_relat_2(A) & v6_relat_2(A) & v4_relat_2(A)))) # label(d5_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3115 $T # label(t170_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3116 (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]. 28.94/28.55 3117 $T # label(t68_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3118 (all A (v1_relat_1(A) -> (all B (r8_orders_1(A,B) & v4_relat_2(A) -> r6_orders_1(A,B))))) # label(t158_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3119 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> v1_orders_1(A) & v3_orders_1(A) & v2_orders_1(A)))) # label(t107_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3120 $T # label(t69_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3121 $T # label(t10_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3122 (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) | B = C)) <-> r9_orders_1(A,B))))) # label(d14_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3123 $T # label(t32_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3124 (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]. 28.94/28.55 3125 (all A (v1_relat_1(A) -> (all B (r6_orders_1(A,B) <-> r7_orders_1(k4_relat_1(A),B))))) # label(t164_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3126 (all A (v1_relat_1(A) -> (all B (r2_orders_1(A,B) -> v1_relat_2(k2_wellord1(A,B)) & v4_relat_2(k2_wellord1(A,B)) & v1_partfun1(k2_wellord1(A,B),B,B) & m2_relset_1(k2_wellord1(A,B),B,B) & v8_relat_2(k2_wellord1(A,B)))))) # label(t141_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3127 $T # label(t147_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3128 $T # label(t171_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3129 $T # label(t80_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3130 (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]. 28.94/28.55 3131 $T # label(t49_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3132 (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]. 28.94/28.55 3133 $T # label(t90_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3134 $T # label(t53_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3135 $T # label(t45_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3136 $T # label(t57_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3137 $T # label(t87_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3138 (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]. 28.94/28.55 3139 (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]. 28.94/28.55 3140 (all A (v1_relat_1(A) -> (all B (r4_orders_1(A,B) <-> r5_orders_1(k4_relat_1(A),B))))) # label(t151_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3141 (all A (v1_relat_1(A) -> (all B (r9_orders_1(A,B) <-> r8_orders_1(k4_relat_1(A),B))))) # label(t165_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3142 $T # label(t36_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3143 (all A all B all C (v1_relat_1(C) -> (r4_relat_2(C,A) & r1_tarski(B,A) -> r4_relat_2(C,B)))) # label(t94_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3144 $T # label(t102_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3145 $T # label(t9_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3146 (all A (v1_relat_1(A) -> (all B (r3_orders_1(A,B) <-> r1_relat_2(A,B) & r6_relat_2(A,B) & r4_relat_2(A,B) & r8_relat_2(A,B))))) # label(d8_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3147 $T # label(t145_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3148 (all A (-v1_xboole_0(A) -> (-r2_hidden(k1_xboole_0,A) -> (all B (v1_funct_1(B) & v1_funct_2(B,A,k3_tarski(A)) & m2_relset_1(B,A,k3_tarski(A)) -> (m1_orders_1(B,A) <-> (all C (r2_hidden(C,A) -> r2_hidden(k1_funct_1(B,C),C))))))))) # label(d1_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3149 $T # label(t25_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3150 (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]. 28.94/28.55 3151 (all A (v1_relat_1(A) -> (all B all C (r2_hidden(B,C) & r9_orders_1(A,B) & v1_relat_2(A) & r1_tarski(C,k3_relat_1(A)) -> r5_orders_1(A,C))))) # label(t162_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3152 $T # label(t83_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3153 (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]. 28.94/28.55 3154 (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]. 28.94/28.55 3155 $T # label(t101_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3156 $T # label(t37_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3157 $T # label(t155_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3158 (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]. 28.94/28.55 3159 $T # label(t40_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3160 (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]. 28.94/28.55 3161 $T # label(t62_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3162 $T # label(t29_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3163 $T # label(t21_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3164 (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]. 28.94/28.55 3165 (all A -(k1_xboole_0 != A & (all B -((all C -(r2_hidden(C,A) & (all D (r2_hidden(D,B) -> r1_tarski(D,C))))) & v6_ordinal1(B) & r1_tarski(B,A))) & (all B -((all C -(r1_tarski(B,C) & B != C & r2_hidden(C,A))) & r2_hidden(B,A))))) # label(t175_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3166 $T # label(t61_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3167 (all A (v1_relat_1(A) -> (all B (r8_orders_1(A,B) <-> r2_hidden(B,k3_relat_1(A)) & (all C (r2_hidden(C,k3_relat_1(A)) -> B = C | r2_hidden(k4_tarski(C,B),A))))))) # label(d13_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3168 $T # label(t1_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3169 $T # label(t117_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3170 $T # label(t72_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3171 $T # label(t35_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3172 (all A all B (v4_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v1_relat_2(B) -> A = k3_relat_1(B))) # label(t100_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3173 $T # label(t48_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3174 (all A -((all B (v6_ordinal1(B) & r1_tarski(B,A) -> B = k1_xboole_0 | r2_hidden(k3_tarski(B),A))) & (all B -(r2_hidden(B,A) & (all C -(r1_tarski(B,C) & B != C & r2_hidden(C,A))))) & k1_xboole_0 != A)) # label(t177_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3175 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B -(v1_finset_1(B) & r1_tarski(B,k2_relat_1(A)) & (all C -(v1_finset_1(C) & B = k9_relat_1(A,C) & r1_tarski(C,k1_relat_1(A)))))))) # label(t195_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.55 3176 (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) & B != C)) <-> r6_orders_1(A,B))))) # label(d11_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.56 3177 $T # label(t42_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.56 3178 $T # label(t148_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.56 3179 (all A (v1_relat_1(A) -> (all B ((all C -(r2_hidden(C,k3_relat_1(A)) & B != C & r2_hidden(k4_tarski(C,B),A))) & r2_hidden(B,k3_relat_1(A)) <-> r7_orders_1(A,B))))) # label(d12_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.56 3180 (all A all B (v4_relat_2(B) & v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v1_relat_2(B) -> A = k5_relset_1(A,A,B) & A = k4_relset_1(A,A,B))) # label(t99_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.56 3181 (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]. 28.94/28.56 3182 $T # label(t81_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.56 3183 (all A all B (v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v4_relat_2(B) & v1_relat_2(B) -> (v6_relat_2(B) -> v3_orders_1(B)))) # label(t112_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.56 3184 (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]. 28.94/28.56 3185 (all A all B all C (v1_relat_1(C) -> (r8_relat_2(C,A) & r1_tarski(B,A) -> r8_relat_2(C,B)))) # label(t95_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.56 3186 $T # label(t153_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.56 3187 $T # label(t63_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.56 3188 $T # label(t123_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.56 3189 (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]. 28.94/28.56 3190 $T # label(t59_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.56 3191 (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]. 28.94/28.56 3192 $T # label(t26_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.56 3193 $T # label(t65_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.56 3194 $T # label(t84_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.56 3195 $T # label(t74_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.56 3196 (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]. 28.94/28.56 3197 (all A (v1_relat_1(A) -> (v1_relat_2(A) & v8_relat_2(A) <-> v1_orders_1(A)))) # label(d3_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.56 3198 (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) -> v1_orders_1(B))) # label(t111_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.56 3199 (all A all B (v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v4_relat_2(B) & v1_relat_2(B) -> v2_orders_1(B))) # label(t110_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.56 3200 (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]. 28.94/28.56 3201 $T # label(t169_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.56 3202 (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]. 28.94/28.56 3203 $T # label(t16_orders_1) # label(axiom) # label(non_clause). [assumption]. 28.94/28.56 3204 (all A all B all C all D all E (v1_relat_2(E) & v1_partfun1(E,A,A) & m2_relset_1(E,A,A) & v8_relat_2(E) & v4_relat_2(E) -> (r2_hidden(B,A) & r2_hidden(C,A) & r2_hidden(k4_tarski(B,C),E) & r2_hidden(k4_tarski(C,D),E) & r2_hidden(D,A) -> r2_hidden(k4_tarski(B,D),E)))) # label(t14_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3205 (all A -((all B (m1_subset_1(B,f1_s2_orders_1) -> (all C (m1_subset_1(C,f1_s2_orders_1) -> -(-p1_s2_orders_1(C,B) & -p1_s2_orders_1(B,C) & r2_hidden(C,A) & r2_hidden(B,A)))))) & (all B (m1_subset_1(B,f1_s2_orders_1) -> (exists C (-p1_s2_orders_1(B,C) & r2_hidden(C,A) & m1_subset_1(C,f1_s2_orders_1))))) & r1_tarski(A,f1_s2_orders_1))) & (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 (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) -> p1_s2_orders_1(A,A))) -> (exists A ((all B (m1_subset_1(B,f1_s2_orders_1) -> -(p1_s2_orders_1(B,A) & B != A))) & m1_subset_1(A,f1_s2_orders_1))) # label(s2_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3206 (all A (v1_relat_1(A) -> (all B all C (v1_relat_2(A) & r1_tarski(C,k3_relat_1(A)) & r8_orders_1(A,B) & r2_hidden(B,C) -> r4_orders_1(A,C))))) # label(t161_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3207 $T # label(t73_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3208 $T # label(t64_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3209 (all A (v1_relat_1(A) -> (all B all C (r1_tarski(C,B) & r6_relat_2(A,B) -> r6_relat_2(A,C))))) # label(t186_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3210 $T # label(t89_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3211 (all A (-v1_xboole_0(A) -> r2_hidden(A,k1_orders_1(A)))) # label(t7_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3212 (all A (-v1_xboole_0(A) -> (all B (m1_orders_1(B,A) -> m2_relset_1(B,A,k3_tarski(A)) & v1_funct_2(B,A,k3_tarski(A)) & v1_funct_1(B))))) # label(dt_m1_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3213 $T # label(t156_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3214 $T # label(t70_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3215 (all A (m1_subset_1(A,f1_s1_orders_1) -> (all B (m1_subset_1(B,f1_s1_orders_1) -> (all C (m1_subset_1(C,f1_s1_orders_1) -> (p1_s1_orders_1(A,B) & p1_s1_orders_1(B,C) -> p1_s1_orders_1(A,C)))))))) & (all A -(r1_tarski(A,f1_s1_orders_1) & (all B (m1_subset_1(B,f1_s1_orders_1) -> (all C (m1_subset_1(C,f1_s1_orders_1) -> -(r2_hidden(B,A) & r2_hidden(C,A) & -p1_s1_orders_1(C,B) & -p1_s1_orders_1(B,C)))))) & (all B (m1_subset_1(B,f1_s1_orders_1) -> (exists C (-p1_s1_orders_1(C,B) & r2_hidden(C,A) & m1_subset_1(C,f1_s1_orders_1))))))) & (all A (m1_subset_1(A,f1_s1_orders_1) -> (all B (m1_subset_1(B,f1_s1_orders_1) -> (p1_s1_orders_1(A,B) & p1_s1_orders_1(B,A) -> B = A))))) & (all A (m1_subset_1(A,f1_s1_orders_1) -> p1_s1_orders_1(A,A))) -> (exists 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) & A != B))))) # label(s1_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3216 $T # label(t71_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3217 (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]. 29.02/28.66 3218 $T # label(t23_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3219 $T # label(t55_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3220 $T # label(t3_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3221 $T # label(t28_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3222 (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]. 29.02/28.66 3223 (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]. 29.02/28.66 3224 (all A (v1_orders_1(k6_partfun1(A)) & v2_orders_1(k6_partfun1(A)))) # label(t120_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3225 (all A (-v1_xboole_0(A) -> (exists B m1_orders_1(B,A)))) # label(existence_m1_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3226 $T # label(t31_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3227 (all A (v1_relat_1(A) -> (all B (r4_orders_1(A,B) <-> (all C -(r1_tarski(C,B) & v3_orders_1(k2_wellord1(A,C)) & (all D -((all E (r2_hidden(E,C) -> r2_hidden(k4_tarski(E,D),A))) & r2_hidden(D,B))))))))) # label(d9_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3228 $T # label(t41_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3229 (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]. 29.02/28.66 3230 $T # label(t11_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3231 (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]. 29.02/28.66 3232 (all A (v1_relat_1(A) -> (all B ((all C -(r1_tarski(C,B) & v3_orders_1(k2_wellord1(A,C)) & (all D -(r2_hidden(D,B) & (all E (r2_hidden(E,C) -> r2_hidden(k4_tarski(D,E),A))))))) <-> r5_orders_1(A,B))))) # label(d10_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3233 (all A (v1_relat_1(A) -> (v2_orders_1(A) -> v1_orders_1(A)))) # label(t109_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3234 $T # label(t85_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3235 $T # label(t8_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3236 $T # label(t46_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3237 (all A (-((exists B (r2_hidden(B,A) & k1_xboole_0 != B)) & k1_xboole_0 = k3_tarski(A)) & -(k3_tarski(A) != k1_xboole_0 & (all B -(r2_hidden(B,A) & k1_xboole_0 != B))))) # label(t91_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3238 (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]. 29.02/28.66 3239 (all A (-v1_xboole_0(A) -> -v1_xboole_0(k1_orders_1(A)))) # label(fc1_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3240 (all A (v1_relat_1(A) -> (all B all C (r1_tarski(C,B) & r2_wellord1(A,B) -> r2_wellord1(A,C))))) # label(t187_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3241 (all A (v1_relat_1(A) -> (all B k4_relat_1(k2_wellord1(A,B)) = k2_wellord1(k4_relat_1(A),B)))) # label(t193_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3242 (all A (v1_relat_1(A) -> (all B (r3_orders_1(A,B) -> v1_relat_2(k2_wellord1(A,B)) & v8_relat_2(k2_wellord1(A,B)) & m2_relset_1(k2_wellord1(A,B),B,B) & v1_partfun1(k2_wellord1(A,B),B,B) & v4_relat_2(k2_wellord1(A,B)))))) # label(t142_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3243 (all A (v1_relat_1(A) -> (all B -(B = k3_relat_1(A) & (all C -r6_orders_1(A,C)) & r4_orders_1(A,B) & r2_orders_1(A,B))))) # label(t173_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3244 $T # label(t52_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3245 $T # label(t67_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3246 $T # label(t50_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3247 (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]. 29.02/28.66 3248 $T # label(t86_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3249 $T # label(t167_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3250 (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]. 29.02/28.66 3251 (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]. 29.02/28.66 3252 (all A (v1_relat_1(A) -> (all B -(r2_orders_1(A,B) & (all C -r7_orders_1(A,C)) & r5_orders_1(A,B) & B = k3_relat_1(A))))) # label(t174_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3253 $T # label(t38_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3254 (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]. 29.02/28.66 3255 (all A all B (v4_relat_2(B) & v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v1_relat_2(B) -> r1_orders_1(B,A))) # label(t139_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3256 (all A -((all B -((all C -((all D (r2_hidden(D,B) -> r1_tarski(C,D))) & r2_hidden(C,A))) & v6_ordinal1(B) & r1_tarski(B,A))) & (all B -(r2_hidden(B,A) & (all C -(r2_hidden(C,A) & C != B & r1_tarski(C,B))))) & k1_xboole_0 != A)) # label(t176_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3257 (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]. 29.02/28.66 3258 (all A (v1_relat_1(A) -> (all B -(r4_orders_1(A,B) & k1_xboole_0 = B)))) # label(t149_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3259 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (r1_tarski(A,B) <-> r2_hidden(A,k1_orders_1(B))))))) # label(t5_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3260 $T # label(t30_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3261 $T # label(dt_k1_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3262 $T # label(t17_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3263 (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]. 29.02/28.66 3264 (all A all B all C (v4_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v8_relat_2(C) & 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]. 29.02/28.66 3265 $T # label(t18_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3266 (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]. 29.02/28.66 3267 (all A (v1_relat_1(A) -> (all B (r1_tarski(B,k3_relat_1(A)) & v1_relat_2(A) -> B = k3_relat_1(k2_wellord1(A,B)))))) # label(t181_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3268 (all A -((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) -> r2_hidden(k1_setfam_1(B),A) | B = k1_xboole_0)) & A != k1_xboole_0)) # label(t178_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3269 (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]. 29.02/28.66 3270 (all A all B (v4_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v1_relat_2(B) -> r2_orders_1(B,A))) # label(t140_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3271 $T # label(t168_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3272 (all A all B all C all D (m2_relset_1(D,A,A) & v1_partfun1(D,A,A) & v8_relat_2(D) & v4_relat_2(D) & v1_relat_2(D) -> (r2_hidden(C,A) & r2_hidden(k4_tarski(B,C),D) & r2_hidden(k4_tarski(C,B),D) & r2_hidden(B,A) -> B = C))) # label(t13_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3273 $T # label(t27_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3274 (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]. 29.02/28.66 3275 $T # label(t56_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3276 $T # label(t51_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3277 $T # label(t34_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3278 $T # label(t118_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.66 3279 $T # label(t33_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3280 $T # label(t44_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3281 $T # label(t19_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3282 $T # label(t154_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3283 $T # label(t78_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3284 $T # label(t103_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3285 $T # label(t76_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3286 $T # label(t47_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3287 $T # label(t66_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3288 (all A all B (v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> A = k3_relat_1(B))) # label(t97_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3289 (all A (v1_relat_1(A) -> (all B -(k3_relat_1(A) = B & (all C (v1_relat_1(C) -> -(r1_tarski(A,C) & r3_orders_1(C,B) & k3_relat_1(C) = B))) & r2_orders_1(A,B))))) # label(t179_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3290 $T # label(t122_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3291 (all A (v1_relat_1(A) -> (all B (r1_relat_2(A,B) & r4_relat_2(A,B) & r8_relat_2(A,B) <-> r2_orders_1(A,B))))) # label(d7_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3292 $T # label(t79_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3293 $T # label(t22_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3294 $T # label(t54_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3295 $T # label(t2_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3296 $T # label(t75_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3297 $T # label(t20_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3298 $T # label(t82_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3299 (all A (v1_relat_1(A) -> (all B (r1_orders_1(A,B) <-> r8_relat_2(A,B) & r1_relat_2(A,B))))) # label(d6_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3300 $T # label(t121_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3301 $T # label(t88_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3302 (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]. 29.02/28.67 3303 $T # label(t77_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3304 (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]. 29.02/28.67 3305 (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]. 29.02/28.67 3306 $T # label(t24_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3307 (all A (v1_relat_1(A) -> (all B (r2_wellord1(A,B) -> v1_relat_2(k2_wellord1(A,B)) & v4_relat_2(k2_wellord1(A,B)) & v8_relat_2(k2_wellord1(A,B)) & m2_relset_1(k2_wellord1(A,B),B,B) & v1_partfun1(k2_wellord1(A,B),B,B))))) # label(t143_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3308 (all A (v1_relat_1(A) -> (all B -(B = k1_xboole_0 & r5_orders_1(A,B))))) # label(t150_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3309 (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]. 29.02/28.67 3310 $T # label(t172_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3311 $T # label(t116_orders_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3312 $T # label(t10_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3313 (all A all B (v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) -> k6_partfun1(A) = k4_eqrel_1(A,k6_partfun1(A),B))) # label(t17_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3314 (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]. 29.02/28.67 3315 (all A all B (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> ((exists C k6_eqrel_1(A,B,C) = A) -> k1_eqrel_1(A) = B))) # label(t35_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3316 (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))) & (k1_xboole_0 != A -> (m1_eqrel_1(B,A) <-> k5_setfam_1(A,B) = A & (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r2_hidden(C,B) -> C != k1_xboole_0 & (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> -(r2_hidden(D,B) & -r1_xboole_0(C,D) & D != C)))))))))) # label(d6_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3317 (all A (v3_relat_2(k1_eqrel_1(A)) & v8_relat_2(k1_eqrel_1(A)) & v1_partfun1(k1_eqrel_1(A),A,A) & v1_relat_2(k1_eqrel_1(A)) & v1_relat_1(k1_eqrel_1(A)))) # label(fc2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3318 (all A all B (v1_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> -(B = k1_xboole_0 & (exists C r2_hidden(C,A))))) # label(t14_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3319 (all A all B (v3_relat_2(B) & v8_relat_2(B) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) -> m1_subset_1(k7_eqrel_1(A,B),k1_zfmisc_1(k1_zfmisc_1(A))))) # label(dt_k7_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3320 (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_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]. 29.02/28.67 3321 (all A k2_zfmisc_1(A,A) = k1_eqrel_1(A)) # label(d1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3322 (all A all B all C (v3_relat_2(C) & v1_partfun1(C,A,A) & m1_relset_1(C,A,A) & v8_relat_2(C) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & 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]. 29.02/28.67 3323 (all A all B all C (v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v3_relat_2(C) & v8_relat_2(C) & v1_partfun1(C,A,A) & m1_relset_1(C,A,A) & v8_relat_2(B) & v3_relat_2(B) -> k4_eqrel_1(A,B,B) = B)) # label(idempotence_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3324 (all A all B all C all D all E (v1_relat_2(E) & v8_relat_2(E) & v1_partfun1(E,A,A) & m2_relset_1(E,A,A) & v3_relat_2(E) -> (r2_hidden(B,k6_eqrel_1(A,E,C)) & r2_hidden(D,k6_eqrel_1(A,E,C)) -> r2_hidden(k4_tarski(B,D),E)))) # label(t30_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3325 (all A m2_relset_1(k1_eqrel_1(A),A,A)) # label(dt_k1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3326 (all A all B all C (m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v8_relat_2(C) & v3_relat_2(C) -> (all D (r2_hidden(D,A) -> (r2_hidden(B,k6_eqrel_1(A,C,D)) <-> k6_eqrel_1(A,C,D) = k6_eqrel_1(A,C,B)))))) # label(t31_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3327 (all A (v1_relat_2(k1_eqrel_1(A)) & v1_partfun1(k1_eqrel_1(A),A,A) & v1_relat_1(k1_eqrel_1(A)))) # label(fc1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3328 (all A all B all C all D (m2_relset_1(D,A,A) & v1_partfun1(D,A,A) & v3_relat_2(D) -> (r2_hidden(k4_tarski(B,C),D) -> r2_hidden(k4_tarski(C,B),D)))) # label(t12_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3329 (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]. 29.02/28.67 3330 $T # label(t21_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3331 $T # label(t9_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3332 (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) -> k5_eqrel_1(A,C,B) = k5_eqrel_1(A,B,C))) # label(commutativity_k5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3333 (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]. 29.02/28.67 3334 (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]. 29.02/28.67 3335 (all A all B (m1_eqrel_1(B,A) -> (exists C (v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & B = k7_eqrel_1(A,C) & v8_relat_2(C) & v3_relat_2(C))))) # label(t43_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3336 (all A all B all C (m1_relset_1(B,A,A) & m1_relset_1(C,A,A) -> k2_eqrel_1(A,B,B) = B)) # label(idempotence_k2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3337 $T # label(t15_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3338 (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 (v8_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v3_relat_2(C) -> (all D (v8_relat_2(D) & v1_partfun1(D,A,A) & m2_relset_1(D,A,A) & v3_relat_2(D) -> (k3_eqrel_1(A,B,C) = D -> (all E -(k6_eqrel_1(A,B,E) != k6_eqrel_1(A,D,E) & k6_eqrel_1(A,D,E) != k6_eqrel_1(A,C,E) & r2_hidden(E,A)))))))))) # label(t37_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3339 (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]. 29.02/28.67 3340 (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]. 29.02/28.67 3341 (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]. 29.02/28.67 3342 $T # label(d2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3343 $T # label(t8_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3344 (all A all B all C (v3_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v3_relat_2(C) & v8_relat_2(C) & v1_partfun1(C,A,A) & m1_relset_1(C,A,A) & v8_relat_2(B) -> v3_relat_2(k4_eqrel_1(A,B,C)) & v8_relat_2(k4_eqrel_1(A,B,C)) & v1_partfun1(k4_eqrel_1(A,B,C),A,A) & m2_relset_1(k4_eqrel_1(A,B,C),A,A))) # label(dt_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3345 (all A all B all C (m1_relset_1(B,A,A) & v3_relat_2(C) & v8_relat_2(C) & m1_relset_1(C,A,A) & v1_partfun1(C,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> B = k5_eqrel_1(A,B,B))) # label(idempotence_k5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3346 (all 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) & v3_relat_2(k1_eqrel_1(A)))) # label(t7_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3347 (all A all B (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> m1_eqrel_1(k7_eqrel_1(A,B),A))) # label(t42_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3348 (all A all B (m2_relset_1(B,A,A) -> (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) <-> v1_relat_2(B) & A = k3_relat_1(B) & v8_relat_2(B) & v3_relat_2(B)))) # label(t16_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3349 $T # label(t39_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3350 (all A all B all C all D (v3_relat_2(D) & m2_relset_1(D,A,A) & v1_partfun1(D,A,A) & v1_relat_2(D) -> (r2_hidden(k4_tarski(B,C),D) <-> r2_hidden(B,k6_eqrel_1(A,D,C))))) # label(t27_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3351 $T # label(t2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3352 $T # label(t26_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3353 (all A all B (v3_relat_2(B) & v8_relat_2(B) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) -> k8_eqrel_1(A,B) = k7_eqrel_1(A,B))) # label(redefinition_k8_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3354 (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) -> k4_eqrel_1(A,B,k5_eqrel_1(A,B,C)) = B)))) # label(t24_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3355 (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 (v8_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v3_relat_2(C) -> -(C != k1_eqrel_1(A) & k1_eqrel_1(A) != B & k1_eqrel_1(A) = k3_eqrel_1(A,B,C)))))) # label(t38_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3356 (all A all B (v1_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v3_relat_2(B) -> (all C (r2_hidden(C,A) -> r2_hidden(C,k6_eqrel_1(A,B,C)))))) # label(t28_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3357 (all A exists B m1_eqrel_1(B,A)) # label(existence_m1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3358 $T # label(t41_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3359 (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]. 29.02/28.67 3360 (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]. 29.02/28.67 3361 (all A (r1_relat_2(k6_partfun1(A),A) & r8_relat_2(k6_partfun1(A),A) & r3_relat_2(k6_partfun1(A),A))) # label(t4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3362 (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]. 29.02/28.67 3363 (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) -> v3_relat_2(C) & v8_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A))) -> v8_relat_2(k6_setfam_1(k2_zfmisc_1(A,A),B)) & v1_partfun1(k6_setfam_1(k2_zfmisc_1(A,A),B),A,A) & m2_relset_1(k6_setfam_1(k2_zfmisc_1(A,A),B),A,A) & v3_relat_2(k6_setfam_1(k2_zfmisc_1(A,A),B)) | B = k1_xboole_0))) # label(t19_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3364 $T # label(t3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3365 (all A all B all C (v3_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v8_relat_2(C) -> (all D (r2_hidden(D,A) -> (r2_hidden(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]. 29.02/28.67 3366 (all A all B (v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) -> B = k5_eqrel_1(A,B,B))) # label(t22_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3367 (all A all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) & v1_relat_2(B) -> (all C -(r2_hidden(C,A) & (all D -r2_hidden(C,k6_eqrel_1(A,B,D))))))) # label(t29_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3368 (all A all B (v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) -> (all C (v3_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v8_relat_2(C) -> (all D (v3_relat_2(D) & m2_relset_1(D,A,A) & v1_partfun1(D,A,A) & v8_relat_2(D) -> (k5_eqrel_1(A,B,C) = D <-> r1_tarski(k3_eqrel_1(A,B,C),D) & (all E (v8_relat_2(E) & m2_relset_1(E,A,A) & v1_partfun1(E,A,A) & v3_relat_2(E) -> (r1_tarski(k3_eqrel_1(A,B,C),E) -> r1_tarski(D,E))))))))))) # label(d3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3369 (all A all B (-v1_xboole_0(A) & v3_relat_2(B) & v8_relat_2(B) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) -> -v1_xboole_0(k7_eqrel_1(A,B)))) # label(fc3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3370 $T # label(t1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3371 (all A all B all C (v3_relat_2(B) & v8_relat_2(B) & m1_relset_1(C,A,A) & v1_partfun1(C,A,A) & v8_relat_2(C) & v3_relat_2(C) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) -> v3_relat_2(k5_eqrel_1(A,B,C)) & v1_partfun1(k5_eqrel_1(A,B,C),A,A) & m2_relset_1(k5_eqrel_1(A,B,C),A,A) & v8_relat_2(k5_eqrel_1(A,B,C)))) # label(dt_k5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3372 (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) & m1_relset_1(C,A,A) & v1_partfun1(C,A,A) & v8_relat_2(C) & v3_relat_2(C) -> k4_eqrel_1(A,C,B) = k4_eqrel_1(A,B,C))) # label(commutativity_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3373 (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]. 29.02/28.67 3374 (all A all B all C (v3_relat_2(C) & v1_partfun1(C,B,B) & m2_relset_1(C,B,B) & v8_relat_2(C) -> -(r2_hidden(A,k7_eqrel_1(B,C)) & (all D (m1_subset_1(D,B) -> k6_eqrel_1(B,C,D) != A))))) # label(t45_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3375 (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(C,A) & -r1_xboole_0(k6_eqrel_1(A,B,C),k6_eqrel_1(A,B,D)) & k6_eqrel_1(A,B,D) != k6_eqrel_1(A,B,C) & r2_hidden(D,A))))) # label(t32_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3376 (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 (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 (r2_hidden(E,A) & k6_eqrel_1(A,B,E) = D)))))))))) # label(d5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3377 (all A all B (v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> (all C (v3_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v8_relat_2(C) -> k5_eqrel_1(A,B,k4_eqrel_1(A,B,C)) = B)))) # label(t25_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3378 (all A all B all C (v1_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) -> (r2_hidden(B,A) -> r2_hidden(k4_tarski(B,B),C)))) # label(t11_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3379 (all A all B (m1_eqrel_1(B,A) -> v1_setfam_1(B))) # label(cc2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3380 (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(B,C) & p1_s1_eqrel_1(A,B) -> p1_s1_eqrel_1(A,C))) & (all A all B (p1_s1_eqrel_1(A,B) -> p1_s1_eqrel_1(B,A))) -> (exists A ((all B all C (r2_hidden(B,f1_s1_eqrel_1) & p1_s1_eqrel_1(B,C) & r2_hidden(C,f1_s1_eqrel_1) <-> r2_hidden(k4_tarski(B,C),A))) & m2_relset_1(A,f1_s1_eqrel_1,f1_s1_eqrel_1) & v1_partfun1(A,f1_s1_eqrel_1,f1_s1_eqrel_1) & v8_relat_2(A) & v3_relat_2(A))) # label(s1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3381 (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 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]. 29.02/28.67 3382 (all A all B (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> (A = k1_xboole_0 -> k7_eqrel_1(A,B) = k1_xboole_0))) # label(t40_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3383 (all A all B (r2_hidden(B,A) -> k6_eqrel_1(A,k1_eqrel_1(A),B) = A)) # label(t34_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3384 (all A all B (m2_relset_1(B,A,A) -> (exists C ((all D (v3_relat_2(D) & m2_relset_1(D,A,A) & v1_partfun1(D,A,A) & v8_relat_2(D) -> (r1_tarski(B,D) -> r1_tarski(C,D)))) & r1_tarski(B,C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v8_relat_2(C) & v3_relat_2(C))))) # label(t20_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3385 (all A all B all C (m1_relset_1(B,A,A) & m1_relset_1(C,A,A) -> k3_eqrel_1(A,B,B) = B)) # label(idempotence_k3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3386 (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 (v3_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v8_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]. 29.02/28.67 3387 (all A all B (v3_relat_2(B) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) -> m1_eqrel_1(k8_eqrel_1(A,B),A))) # label(dt_k8_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3388 $T # label(t5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3389 (all A all B all C all D (v3_relat_2(D) & m2_relset_1(D,B,B) & v1_partfun1(D,B,B) & v8_relat_2(D) -> (all E (v8_relat_2(E) & m2_relset_1(E,B,B) & v1_partfun1(E,B,B) & v3_relat_2(E) -> (r2_hidden(A,B) -> ((exists F (v1_relat_1(F) & v1_funct_1(F) & r1_xreal_0(np__1,k3_finseq_1(F)) & k1_funct_1(F,np__1) = A & k1_funct_1(F,k3_finseq_1(F)) = C & (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,G) -> r2_hidden(k4_tarski(k1_funct_1(F,G),k1_funct_1(F,k1_nat_1(G,np__1))),k3_eqrel_1(B,D,E)) | r1_xreal_0(k3_finseq_1(F),G)))) & v1_finseq_1(F))) <-> r2_hidden(k4_tarski(A,C),k5_eqrel_1(B,D,E)))))))) # label(t36_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3390 (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]. 29.02/28.67 3391 (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]. 29.02/28.67 3392 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B all C -r2_hidden(k4_tarski(B,C),k1_relat_1(A))) -> k3_funct_5(A) = k1_xboole_0 & k1_xboole_0 = k5_funct_5(A)))) # label(t34_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3393 (all A all B all C (r1_xboole_0(A,B) -> r2_wellord2(k1_funct_2(k2_xboole_0(A,B),C),k2_zfmisc_1(k1_funct_2(A,C),k1_funct_2(B,C))) & k1_card_1(k2_zfmisc_1(k1_funct_2(A,C),k1_funct_2(B,C))) = k1_card_1(k1_funct_2(k2_xboole_0(A,B),C)))) # label(t69_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3394 $T # label(dt_k2_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3395 (all A all B all C (r2_hidden(k4_tarski(A,B),C) -> r2_hidden(B,k2_funct_5(C)) & r2_hidden(A,k1_funct_5(C)))) # label(t4_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3396 (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]. 29.02/28.67 3397 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> -(k2_zfmisc_1(A,B) != k1_xboole_0 & (all E (v1_funct_1(E) & v1_relat_1(E) -> -(E = k1_funct_1(k3_funct_5(D),C) & k1_relat_1(E) = B & r1_tarski(k2_relat_1(E),k2_relat_1(D)) & (all F (r2_hidden(F,B) -> k1_funct_1(E,F) = k1_funct_1(D,k4_tarski(C,F))))))) & r2_hidden(C,A) & k2_zfmisc_1(A,B) = k1_relat_1(D)))) # label(t36_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3398 (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]. 29.02/28.67 3399 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (C = k1_funct_1(k3_funct_5(B),A) & r2_hidden(A,k1_relat_1(k3_funct_5(B))) -> k2_funct_5(k3_xboole_0(k1_relat_1(B),k2_zfmisc_1(k1_tarski(A),k2_funct_5(k1_relat_1(B))))) = k1_relat_1(C) & r1_tarski(k1_relat_1(C),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)))))))) # label(t38_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3400 (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]. 29.02/28.67 3401 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k2_zfmisc_1(A,B) = k1_relat_1(C) & k3_funct_5(D) = k3_funct_5(C) & k1_relat_1(D) = k2_zfmisc_1(A,B) -> D = C))))) # label(t51_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.67 3402 (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(A,k1_funct_2(B,C))) = k1_card_1(k1_funct_2(k2_zfmisc_1(A,B),C)))) # label(t70_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3403 (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]. 29.02/28.68 3404 (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(k2_zfmisc_1(C,C)) = k1_card_1(k1_funct_2(k2_tarski(A,B),C)))) # label(t73_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3405 $T # label(dt_k1_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3406 (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(D) = k3_funct_5(C) & r1_tarski(k1_relat_1(D),k2_zfmisc_1(A,B)) & r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> C = D))))) # label(t59_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3407 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k4_funct_5(A) = B <-> (all C ((exists D exists E (v1_relat_1(E) & v1_funct_1(E) & (exists F (C = k4_tarski(D,F) & r2_hidden(F,k1_relat_1(E)) & k1_funct_1(A,D) = E & r2_hidden(D,k1_relat_1(A)))))) <-> r2_hidden(C,k1_relat_1(B)))) & (all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(C,k1_relat_1(B)) & D = k1_funct_1(A,k1_mcart_1(C)) -> k1_funct_1(B,C) = k1_funct_1(D,k2_mcart_1(C)))))))))) # label(d4_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3408 $T # label(t14_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3409 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B -(v1_relat_1(k1_funct_1(A,B)) & v1_funct_1(k1_funct_1(A,B)) & r2_hidden(B,k1_relat_1(A)))) -> k1_xboole_0 = k4_funct_5(A) & k1_xboole_0 = k6_funct_5(A)))) # label(t35_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3410 (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]. 29.02/28.68 3411 (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]. 29.02/28.68 3412 (all A (v1_funct_1(A) & v1_relat_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]. 29.02/28.68 3413 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_relat_1(C),k1_funct_2(A,B)) -> k1_relat_1(k4_funct_5(C)) = k2_zfmisc_1(k1_relat_1(C),A) & k1_relat_1(k6_funct_5(C)) = k2_zfmisc_1(A,k1_relat_1(C))))) # label(t33_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3414 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k5_funct_5(A)) & v1_funct_1(k5_funct_5(A)))) # label(dt_k5_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3415 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (D = k1_funct_1(k3_funct_5(C),A) & r2_hidden(k4_tarski(A,B),k1_relat_1(C)) -> k1_funct_1(D,B) = k1_funct_1(C,k4_tarski(A,B)) & r2_hidden(B,k1_relat_1(D))))))) # label(t27_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3416 (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)) & k4_funct_5(D) = k4_funct_5(C) & r1_tarski(k2_relat_1(D),k1_funct_2(A,B)) -> A = k1_xboole_0 | C = D))))) # label(t53_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3417 (all A all B all C (k1_card_1(k1_funct_2(A,k2_zfmisc_1(B,C))) = k1_card_1(k2_zfmisc_1(k1_funct_2(A,B),k1_funct_2(A,C))) & r2_wellord2(k1_funct_2(A,k2_zfmisc_1(B,C)),k2_zfmisc_1(k1_funct_2(A,B),k1_funct_2(A,C))))) # label(t71_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3418 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(C) = k2_zfmisc_1(A,B) -> k1_relat_1(k5_funct_5(C)) = B & k1_relat_1(k3_funct_5(C)) = A | k1_xboole_0 = k2_zfmisc_1(A,B)))) # label(t31_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3419 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_relat_1(C),k4_partfun1(A,B)) -> r1_tarski(k1_relat_1(k6_funct_5(C)),k2_zfmisc_1(A,k1_relat_1(C))) & r1_tarski(k1_relat_1(k4_funct_5(C)),k2_zfmisc_1(k1_relat_1(C),A))))) # label(t44_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3420 (all A (v1_relat_1(A) -> k1_relat_1(A) = k1_funct_5(A) & k2_funct_5(A) = k2_relat_1(A))) # label(t21_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3421 (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_funct_5(k1_relat_1(A))) & (all D (v1_funct_1(D) & v1_relat_1(D) -> -(D = k1_funct_1(B,C) & k2_funct_5(k3_xboole_0(k1_relat_1(A),k2_zfmisc_1(k1_tarski(C),k2_funct_5(k1_relat_1(A))))) = k1_relat_1(D) & (all E (r2_hidden(E,k1_relat_1(D)) -> k1_funct_1(A,k4_tarski(C,E)) = k1_funct_1(D,E)))))))) & k1_relat_1(B) = k1_funct_5(k1_relat_1(A)) <-> k3_funct_5(A) = B))))) # label(d3_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3422 (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(k5_funct_5(B),A) = C & r2_hidden(A,k1_relat_1(k5_funct_5(B))) -> r1_tarski(k1_relat_1(C),k1_funct_5(k1_relat_1(B))) & (all D (r2_hidden(D,k1_relat_1(C)) -> k1_funct_1(C,D) = k1_funct_1(B,k4_tarski(D,A)) & r2_hidden(k4_tarski(D,A),k1_relat_1(B)))) & r1_tarski(k2_relat_1(C),k2_relat_1(B)) & k1_relat_1(C) = k1_funct_5(k3_xboole_0(k1_relat_1(B),k2_zfmisc_1(k1_funct_5(k1_relat_1(B)),k1_tarski(A))))))))) # label(t41_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3423 (all A all B all C all D (k1_card_1(C) = k1_card_1(D) & k1_card_1(B) = k1_card_1(A) -> k1_card_1(k1_funct_2(B,D)) = k1_card_1(k1_funct_2(A,C)))) # label(t68_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3424 (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(A,B),k1_relat_1(k4_funct_5(C))) & r2_hidden(k1_funct_1(D,B),k2_relat_1(k4_funct_5(C))) & k1_funct_1(k4_funct_5(C),k4_tarski(A,B)) = k1_funct_1(D,B)))))) # label(t45_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3425 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k5_funct_5(C) = k5_funct_5(D) & r1_tarski(k1_relat_1(D),k2_zfmisc_1(A,B)) & r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> C = D))))) # label(t60_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3426 (all A ((all B all C -r2_hidden(k4_tarski(B,C),A)) -> k2_funct_5(A) = k1_xboole_0 & k1_xboole_0 = k1_funct_5(A))) # label(t17_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3427 (all A all B (k2_funct_5(k2_xboole_0(A,B)) = k2_xboole_0(k2_funct_5(A),k2_funct_5(B)) & k2_xboole_0(k1_funct_5(A),k1_funct_5(B)) = k1_funct_5(k2_xboole_0(A,B)))) # label(t6_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3428 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r1_tarski(k2_relat_1(C),k4_partfun1(A,B)) & k6_funct_5(C) = k6_funct_5(D) & r1_tarski(k2_relat_1(D),k4_partfun1(A,B)) -> C = D | 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]. 29.02/28.68 3429 (all A k1_tarski(k1_xboole_0) = k1_funct_2(k1_xboole_0,A)) # label(t64_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3430 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_relat_1(C),k1_funct_2(A,B)) -> A = k1_xboole_0 | k5_funct_5(k6_funct_5(C)) = C & k3_funct_5(k4_funct_5(C)) = C))) # label(t55_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3431 (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]. 29.02/28.68 3432 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k1_funct_1(k5_funct_5(C),B) = D & r2_hidden(k4_tarski(A,B),k1_relat_1(C)) -> r2_hidden(A,k1_relat_1(D)) & k1_funct_1(D,A) = k1_funct_1(C,k4_tarski(A,B))))))) # label(t29_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3433 (exists A (v1_relat_1(A) & k1_relat_1(A) = f1_s1_funct_5 & (all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(B,f1_s1_funct_5) -> k1_funct_1(A,B) = f2_s1_funct_5(B)))) & v1_funct_1(A))) # label(s1_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3434 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(A,k1_relat_1(k3_funct_5(B))) -> v1_relat_1(k1_funct_1(k3_funct_5(B),A)) & v1_funct_1(k1_funct_1(k3_funct_5(B),A))))) # label(t37_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3435 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> -(k2_zfmisc_1(A,B) != k1_xboole_0 & k1_relat_1(D) = k2_zfmisc_1(A,B) & r2_hidden(C,B) & (all E (v1_funct_1(E) & v1_relat_1(E) -> -(A = k1_relat_1(E) & (all F (r2_hidden(F,A) -> k1_funct_1(E,F) = k1_funct_1(D,k4_tarski(F,C)))) & r1_tarski(k2_relat_1(E),k2_relat_1(D)) & k1_funct_1(k5_funct_5(D),C) = E)))))) # label(t39_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3436 (all A (k1_xboole_0 = k2_funct_5(A) | k1_xboole_0 = k1_funct_5(A) -> (all B all C -r2_hidden(k4_tarski(B,C),A)))) # label(t18_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3437 (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)) & D = k1_funct_1(C,A) -> r2_hidden(k4_tarski(B,A),k1_relat_1(k6_funct_5(C))) & r2_hidden(k1_funct_1(D,B),k2_relat_1(k6_funct_5(C))) & k1_funct_1(D,B) = k1_funct_1(k6_funct_5(C),k4_tarski(B,A))))))) # label(t46_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3438 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(k4_tarski(A,B),k1_relat_1(C)) -> r2_hidden(A,k1_relat_1(k3_funct_5(C))) & v1_relat_1(k1_funct_1(k3_funct_5(C),A)) & v1_funct_1(k1_funct_1(k3_funct_5(C),A))))) # label(t26_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3439 (all A all B (-(k1_xboole_0 = A & k2_zfmisc_1(B,A) = k1_xboole_0 & k2_zfmisc_1(A,B) = k1_xboole_0) -> B = k1_funct_5(k2_zfmisc_1(B,A)) & B = k2_funct_5(k2_zfmisc_1(A,B)))) # label(t11_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3440 (all A (k1_xboole_0 = k1_funct_5(A) <-> k1_xboole_0 = k2_funct_5(A))) # label(t19_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3441 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k5_funct_5(C) = k5_funct_5(D) & k1_relat_1(D) = k2_zfmisc_1(A,B) & k2_zfmisc_1(A,B) = k1_relat_1(C) -> D = C))))) # label(t52_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3442 (all A all B (k1_card_1(k1_funct_2(k1_tarski(B),A)) = k1_card_1(A) & r2_wellord2(A,k1_funct_2(k1_tarski(B),A)))) # label(t65_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3443 (all A all B all C (A != B -> r2_wellord2(k1_funct_2(C,k2_tarski(A,B)),k1_zfmisc_1(C)) & k1_card_1(k1_funct_2(C,k2_tarski(A,B))) = k1_card_1(k1_zfmisc_1(C)))) # label(t72_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3444 (all A all B (k1_funct_5(k1_tarski(k4_tarski(A,B))) = k1_tarski(A) & k1_tarski(B) = k2_funct_5(k1_tarski(k4_tarski(A,B))))) # label(t15_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3445 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r1_tarski(k2_relat_1(C),k1_funct_2(A,B)) & r1_tarski(k2_relat_1(D),k1_funct_2(A,B)) & k6_funct_5(C) = k6_funct_5(D) -> D = C | k1_xboole_0 = A))))) # label(t54_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3446 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(C) = k2_zfmisc_1(A,B) -> k6_funct_5(k5_funct_5(C)) = C & k4_funct_5(k3_funct_5(C)) = C))) # label(t56_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3447 (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]. 29.02/28.68 3448 (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]. 29.02/28.68 3449 (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]. 29.02/28.68 3450 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> k4_funct_5(k3_funct_5(C)) = C & k6_funct_5(k5_funct_5(C)) = C))) # label(t57_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3451 (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]. 29.02/28.68 3452 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_relat_1(C),k4_partfun1(A,B)) -> r2_hidden(k1_xboole_0,k2_relat_1(C)) | C = k5_funct_5(k6_funct_5(C)) & C = k3_funct_5(k4_funct_5(C))))) # label(t58_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3453 (all A (v1_relat_1(A) & v1_funct_1(A) -> k2_funct_4(k4_funct_5(A)) = k6_funct_5(A))) # label(d6_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3454 (all A all B all C (r1_tarski(A,k2_zfmisc_1(B,C)) -> r1_tarski(k1_funct_5(A),B) & r1_tarski(k2_funct_5(A),C))) # label(t13_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3455 (all A all B ((all C ((exists D r2_hidden(k4_tarski(C,D),A)) <-> r2_hidden(C,B))) <-> k1_funct_5(A) = B)) # label(d1_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3456 (all A all B all C all D (r2_wellord2(A,B) & r2_wellord2(C,D) -> k1_card_1(k1_funct_2(B,D)) = k1_card_1(k1_funct_2(A,C)) & r2_wellord2(k1_funct_2(A,C),k1_funct_2(B,D)))) # label(t67_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3457 (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]. 29.02/28.68 3458 $T # label(t25_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3459 (all A (v1_funct_1(A) & v1_relat_1(A) -> k5_funct_5(A) = k3_funct_5(k2_funct_4(A)))) # label(d5_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3460 $T # label(t2_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3461 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(C) = k2_zfmisc_1(A,B) -> r1_tarski(k2_relat_1(k3_funct_5(C)),k1_funct_2(B,k2_relat_1(C))) & r1_tarski(k2_relat_1(k5_funct_5(C)),k1_funct_2(A,k2_relat_1(C)))))) # label(t42_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3462 (all A all B (r1_tarski(A,B) -> r1_tarski(k1_funct_5(A),k1_funct_5(B)) & r1_tarski(k2_funct_5(A),k2_funct_5(B)))) # label(t5_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3463 (all A (v1_funct_1(A) & v1_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))) & r1_tarski(k2_relat_1(k3_funct_5(A)),k4_partfun1(k2_funct_5(k1_relat_1(A)),k2_relat_1(A))))) # label(t43_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3464 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(k5_funct_5(B))) -> v1_relat_1(k1_funct_1(k5_funct_5(B),A)) & v1_funct_1(k1_funct_1(k5_funct_5(B),A))))) # label(t40_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.02/28.68 3465 (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]. 29.02/28.68 3466 (all A all B all C all D (k2_tarski(B,D) = k2_funct_5(k2_tarski(k4_tarski(A,B),k4_tarski(C,D))) & k1_funct_5(k2_tarski(k4_tarski(A,B),k4_tarski(C,D))) = k2_tarski(A,C))) # label(t16_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3467 $T # label(t24_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3468 $T # label(t3_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3469 $T # label(t23_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3470 (all A (v1_funct_1(A) & v1_relat_1(A) -> k2_funct_5(k1_relat_1(A)) = k1_funct_5(k1_relat_1(k2_funct_4(A))) & k1_funct_5(k1_relat_1(A)) = k2_funct_5(k1_relat_1(k2_funct_4(A))))) # label(t20_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3471 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),k1_relat_1(C)) -> r2_hidden(B,k1_relat_1(k5_funct_5(C))) & v1_funct_1(k1_funct_1(k5_funct_5(C),B)) & v1_relat_1(k1_funct_1(k5_funct_5(C),B))))) # label(t28_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3472 $T # label(t22_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3473 (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(k2_relat_1(D),k4_partfun1(A,B)) & k4_funct_5(D) = k4_funct_5(C) & r1_tarski(k2_relat_1(C),k4_partfun1(A,B)) -> r2_hidden(k1_xboole_0,k2_relat_1(C)) | C = D | r2_hidden(k1_xboole_0,k2_relat_1(D))))))) # label(t61_funct_5) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3474 (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]. 29.12/28.69 3475 (all A k1_xboole_0 = k2_finseq_2(np__0,A)) # label(t72_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3476 (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]. 29.12/28.69 3477 (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]. 29.12/28.69 3478 (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]. 29.12/28.69 3479 (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 (v1_relat_1(D) & v1_funct_1(D) -> (k4_funcop_1(D,B,A) = C & r1_tarski(k2_zfmisc_1(k2_relat_1(B),k1_tarski(A)),k1_relat_1(D)) -> k3_finseq_1(C) = k3_finseq_1(B)))))))) # label(t83_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3480 (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(k1_tarski(A),k2_relat_1(B)),k1_relat_1(C)) -> v1_funct_1(k5_funcop_1(C,A,B)) & v1_finseq_1(k5_funcop_1(C,A,B)) & v1_relat_1(k5_funcop_1(C,A,B))))))) # label(t80_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3481 (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]. 29.12/28.69 3482 (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]. 29.12/28.69 3483 (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]. 29.12/28.69 3484 (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) -> k3_funcop_1(D,E,k6_finseq_1(B)) = k6_finseq_1(C) & k6_finseq_1(C) = k3_funcop_1(D,k6_finseq_1(A),F))))))))))))) # label(t87_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3485 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_1_finseq_2(B)) <-> (exists C exists D (m1_subset_1(C,B) & m1_subset_1(D,B) & A = k10_finseq_1(C,D)))))) # label(fraenkel_a_1_1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3486 (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]. 29.12/28.69 3487 (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_finseq_1(C) & v1_funct_1(C) -> (k3_finseq_1(B) = k3_finseq_1(A) & r1_tarski(B,C) & r1_tarski(A,C) -> B = A))))))) # label(t149_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3488 (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_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) -> (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]. 29.12/28.69 3489 (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]. 29.12/28.69 3490 (all A (v4_ordinal2(A) -> k4_finseq_1(k1_finseq_2(A)) = k2_finseq_1(A))) # label(t54_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3491 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_2(E,k2_zfmisc_1(A,B),C) & v1_funct_1(E) -> (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]. 29.12/28.69 3492 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(A,B)) -> (all D (m1_subset_1(D,B) -> D = k1_funct_1(k8_finseq_1(B,C,k12_finseq_1(B,D)),k1_nat_1(A,np__1)))))))))) # label(t136_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3493 (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(D,B) & A = k11_finseq_1(C,D,E) & m1_subset_1(E,B) & m1_subset_1(C,B)))))) # label(fraenkel_a_1_2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3494 (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]. 29.12/28.69 3495 (all A (v4_ordinal2(A) -> (all B k2_finseq_1(A) = k4_finseq_1(k2_finseq_2(A,B))))) # label(t68_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3496 (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]. 29.12/28.69 3497 (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_1(G) & v1_funct_2(G,k2_zfmisc_1(A,B),C) & m2_relset_1(G,k2_zfmisc_1(A,B),C) -> (all H (m2_finseq_1(H,A) -> (H = k10_finseq_1(D,E) -> k10_finseq_1(k2_binop_1(A,B,C,G,D,F),k2_binop_1(A,B,C,G,E,F)) = k4_funcop_1(G,H,F)))))))))))))))))) # label(t101_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3498 (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) & v1_funct_2(H,k2_zfmisc_1(A,B),C) & m2_relset_1(H,k2_zfmisc_1(A,B),C) -> (all I (m2_finseq_1(I,A) -> (all J (m2_finseq_1(J,B) -> (J = k10_finseq_1(F,G) & I = k10_finseq_1(D,E) -> k10_finseq_1(k2_binop_1(A,B,C,H,D,F),k2_binop_1(A,B,C,H,E,G)) = k3_funcop_1(H,I,J)))))))))))))))))))))) # label(t89_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3499 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (-v1_xboole_0(C) -> (all D (m2_finseq_1(D,C) -> (all E (v1_funct_2(E,k2_finseq_1(A),k2_finseq_1(B)) & m2_relset_1(E,k2_finseq_1(A),k2_finseq_1(B)) & v1_funct_1(E) -> (r1_xreal_0(B,k3_finseq_1(D)) -> m2_finseq_1(k1_partfun1(k2_finseq_1(A),k2_finseq_1(B),k5_numbers,C,E,D),C) | np__0 = B & A != np__0))))))))))) # label(t49_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3500 (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]. 29.12/28.69 3501 (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 -> k2_finseq_1(A) = k5_subset_1(k5_numbers,k2_finseq_1(B),k2_finseq_1(C))))))))) # label(t2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3502 (all A all B (v4_ordinal2(A) -> v1_relat_1(k2_finseq_2(A,B)) & v1_funct_1(k2_finseq_2(A,B)) & v1_finseq_1(k2_finseq_2(A,B)))) # label(dt_k2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3503 (all A (v4_ordinal2(A) -> (all B k3_finseq_1(k2_finseq_2(A,B)) = A))) # label(t69_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3504 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> -((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(r2_hidden(C,k4_finseq_1(B)) & k1_funct_1(B,C) = A))) & r2_hidden(A,k2_relat_1(B))))) # label(t11_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3505 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,B) -> (all H (v1_funct_2(H,k2_zfmisc_1(A,B),C) & m2_relset_1(H,k2_zfmisc_1(A,B),C) & v1_funct_1(H) -> (all I (m2_finseq_1(I,B) -> (k11_finseq_1(E,F,G) = I -> k5_funcop_1(H,D,I) = k11_finseq_1(k2_binop_1(A,B,C,H,D,E),k2_binop_1(A,B,C,H,D,F),k2_binop_1(A,B,C,H,D,G))))))))))))))))))))) # label(t96_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3506 $T # label(t53_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3507 (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(A,k4_finseq_1(k7_finseq_1(B,C)))))))))) # label(t18_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3508 $T # label(t29_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3509 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_2(B,A,k4_finseq_2(np__3,A)) -> (exists C ((exists D (m1_subset_1(D,A) & (exists E (m1_subset_1(E,A) & B = k11_finseq_1(C,D,E))))) & m1_subset_1(C,A))))))) # label(t123_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3510 (all A all B all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m2_finseq_1(E,C) -> (all F (v1_funct_2(F,C,D) & m2_relset_1(F,C,D) & v1_funct_1(F) -> (E = k10_finseq_1(A,B) -> k1_partfun1(k5_numbers,C,C,D,E,F) = k10_finseq_1(k1_funct_1(F,A),k1_funct_1(F,B))))))))))) # label(t40_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3511 (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) & 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]. 29.12/28.69 3512 (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 (k8_finseq_1(B,D,k12_finseq_1(B,E)) = C & m1_subset_1(E,B))) & m2_finseq_2(D,B,k4_finseq_2(A,B)))))))))) # label(t137_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3513 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (-v1_xboole_0(C) -> a_3_0_finseq_2(A,B,C) = k4_finseq_2(k1_nat_1(A,B),C))))))) # label(t125_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3514 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,B) -> (all E (v1_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) -> (all F (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) -> (E = k4_funcop_1(F,G,D) -> k3_finseq_1(E) = k3_finseq_1(G)))))))))))))))) # label(t98_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3515 (all A (v4_ordinal2(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,B) -> (A != np__0 -> (all D (m1_subset_1(D,k2_finseq_1(A)) -> C = k1_funct_1(k2_finseq_2(A,C),D)))))))))) # label(t71_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3516 (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 (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]. 29.12/28.69 3517 (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 & D = k8_finseq_1(B,C,D))))))))) # label(t115_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3518 (all A (v4_ordinal2(A) -> v1_funct_2(k1_finseq_2(A),k2_finseq_1(A),k2_finseq_1(A)) & v3_funct_2(k1_finseq_2(A),k2_finseq_1(A),k2_finseq_1(A)) & m2_relset_1(k1_finseq_2(A),k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_1(k1_finseq_2(A)))) # label(t65_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3519 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> v1_funct_1(B) & v1_funct_2(B,k4_finseq_1(B),A) & m2_relset_1(B,k4_finseq_1(B),A))))) # label(t30_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3520 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m2_relset_1(E,k2_zfmisc_1(B,C),D) & v1_funct_2(E,k2_zfmisc_1(B,C),D) & v1_funct_1(E) -> (all F (m2_finseq_2(F,B,k4_finseq_2(A,B)) -> (all G (m2_finseq_2(G,C,k4_finseq_2(A,C)) -> m2_finseq_2(k3_funcop_1(E,F,G),D,k4_finseq_2(A,D)))))))))))))))) # label(t140_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3521 (all A all B all C (v4_ordinal2(B) -> ((exists D (m2_finseq_2(D,C,k3_finseq_2(C)) & A = D & B = k3_finseq_1(D))) <-> r2_hidden(A,a_2_0_finseq_2(B,C))))) # label(fraenkel_a_2_0_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3522 $T # label(t12_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3523 (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]. 29.12/28.69 3524 (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]. 29.12/28.69 3525 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C all D (r2_hidden(D,k1_relat_1(A)) & r2_hidden(C,k1_relat_1(A)) & r2_hidden(B,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]. 29.12/28.69 3526 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_2(B,A,k4_finseq_2(np__2,A)) -> (exists C ((exists D (B = k10_finseq_1(C,D) & m1_subset_1(D,A))) & m1_subset_1(C,A))))))) # label(t120_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3527 $T # label(t7_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3528 (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]. 29.12/28.69 3529 (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]. 29.12/28.69 3530 (all A all B all C all D (m2_subset_1(C,k1_numbers,k5_numbers) & -v1_xboole_0(D) & m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(A,a_3_0_finseq_2(B,C,D)) <-> (exists E exists F (m2_finseq_2(E,D,k4_finseq_2(B,D)) & m2_finseq_2(F,D,k4_finseq_2(C,D)) & A = k8_finseq_1(D,E,F)))))) # label(fraenkel_a_3_0_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3531 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> -(k3_finseq_1(C) = k1_nat_1(A,B) & (all D (v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) -> (all E (v1_funct_1(E) & v1_finseq_1(E) & v1_relat_1(E) -> -(C = k7_finseq_1(D,E) & B = k3_finseq_1(E) & A = k3_finseq_1(D))))))))))))) # label(t25_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3532 (all A k2_finseq_2(np__1,A) = k9_finseq_1(A)) # label(t73_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3533 (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]. 29.12/28.69 3534 (all A (v4_ordinal2(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> k5_relat_1(k1_finseq_2(A),B) = k7_relat_1(B,k2_finseq_1(A)))))) # label(t63_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3535 (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]. 29.12/28.69 3536 (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 -> k4_funcop_1(H,I,G) = k11_finseq_1(k2_binop_1(A,B,C,H,D,G),k2_binop_1(A,B,C,H,E,G),k2_binop_1(A,B,C,H,F,G))))))))))))))))))))) # label(t102_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3537 $T # label(t67_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3538 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all 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_funct_1(B) -> v1_funct_1(k5_relat_1(B,A)) & v1_finseq_1(k5_relat_1(B,A)) & v1_relat_1(k5_relat_1(B,A)))))) # label(t44_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3539 (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]. 29.12/28.69 3540 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k7_finseq_1(k1_finseq_2(A),k12_finseq_1(k5_numbers,k1_nat_1(A,np__1))) = k1_finseq_2(k1_nat_1(A,np__1)))) # label(t60_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3541 (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]. 29.12/28.69 3542 (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]. 29.12/28.69 3543 $T # label(t106_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3544 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (A != np__0 -> (all B (m1_subset_1(B,k2_finseq_1(A)) -> B = k1_funct_1(k1_finseq_2(A),B)))))) # label(t57_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3545 (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) & k3_finseq_1(F) = B & k3_finseq_1(E) = A))))) & k3_finseq_1(D) = k1_nat_1(A,B)))))))))) # label(t26_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3546 (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 (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r1_tarski(k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B)),k1_relat_1(D)) & C = k3_funcop_1(D,A,B) -> 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]. 29.12/28.69 3547 (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]. 29.12/28.69 3548 $T # label(dt_m1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3549 (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_funct_1(k5_relat_1(C,B)) & v1_finseq_1(k5_relat_1(C,B))))))))) # label(t43_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3550 (all A all B (-v1_xboole_0(B) -> ((exists C (m1_subset_1(C,B) & k12_finseq_1(B,C) = A)) <-> r2_hidden(A,a_1_0_finseq_2(B))))) # label(fraenkel_a_1_0_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3551 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (v1_finseq_1(E) & v1_funct_1(E) & v1_relat_1(E) -> (all F (v1_funct_1(F) & 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,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]. 29.12/28.69 3552 (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]. 29.12/28.69 3553 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(C,k4_finseq_1(A)) -> r2_hidden(k1_funct_1(A,C),B)))) -> m2_finseq_1(A,B))))) # label(t14_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3554 (all A exists B m1_finseq_2(B,A)) # label(existence_m1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3555 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> k1_funct_2(k2_finseq_1(A),B) = k4_finseq_2(A,B))))) # label(t111_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3556 (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) -> B = k5_relat_1(k1_finseq_2(A),B)))))) # label(t64_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3557 (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]. 29.12/28.69 3558 $T # label(t17_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3559 (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]. 29.12/28.69 3560 (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]. 29.12/28.69 3561 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k4_finseq_1(A),k4_finseq_1(A)) & v3_funct_2(C,k4_finseq_1(A),k4_finseq_1(A)) & m2_relset_1(C,k4_finseq_1(A),k4_finseq_1(A)) -> (k5_relat_1(C,A) = B -> k3_finseq_1(B) = k3_finseq_1(A)))))))) # label(t48_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3562 (all A (m1_finseq_2(k3_finseq_2(A),A) & -v1_xboole_0(k3_finseq_2(A)))) # label(dt_k3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3563 (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_2(J,k2_zfmisc_1(A,B),C) & m2_relset_1(J,k2_zfmisc_1(A,B),C) & v1_funct_1(J) -> (all K (m2_finseq_1(K,A) -> (all L (m2_finseq_1(L,B) -> (K = k11_finseq_1(D,E,F) & L = k11_finseq_1(G,H,I) -> 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]. 29.12/28.69 3564 $T # label(t103_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3565 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k3_square_1(np__0,A) = np__0 & k4_square_1(A,np__0) = A & k4_square_1(np__0,A) = A & np__0 = k3_square_1(A,np__0))) # label(t6_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3566 (all A (v4_ordinal2(A) -> k6_partfun1(k2_finseq_1(A)) = k1_finseq_2(A))) # label(d1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3567 (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) & v1_funct_2(E,B,C) & m2_relset_1(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]. 29.12/28.69 3568 (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]. 29.12/28.69 3569 (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]. 29.12/28.69 3570 (all 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) -> (r1_tarski(k2_zfmisc_1(k2_relat_1(B),k1_tarski(A)),k1_relat_1(C)) -> v1_funct_1(k4_funcop_1(C,B,A)) & v1_finseq_1(k4_funcop_1(C,B,A)) & v1_relat_1(k4_funcop_1(C,B,A))))))) # label(t82_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3571 (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]. 29.12/28.69 3572 (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)) & k1_nat_1(B,np__1) != A & r2_hidden(A,k2_finseq_1(k1_nat_1(B,np__1)))))))) # label(t8_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.69 3573 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) -> (all C (-v1_xboole_0(C) & m1_finseq_2(C,B) -> -v1_xboole_0(C) & m1_finseq_2(C,A))))))) # label(t107_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3574 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (-v1_xboole_0(C) -> (all D (m2_finseq_2(D,C,k4_finseq_2(k1_nat_1(A,B),C)) -> (exists E ((exists F (k8_finseq_1(C,E,F) = D & m2_finseq_2(F,C,k4_finseq_2(B,C)))) & m2_finseq_2(E,C,k4_finseq_2(A,C)))))))))))) # label(t126_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3575 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C) -> (k7_relat_1(C,k2_finseq_1(A)) = B & r1_xreal_0(k3_finseq_1(C),A) -> B = C))))))) # label(t23_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3576 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (k2_finseq_1(A) = B -> (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]. 29.12/28.70 3577 (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]. 29.12/28.70 3578 (all A all B (-v1_xboole_0(B) & m1_finseq_2(B,A) -> (all C (m2_finseq_2(C,A,B) <-> m1_subset_1(C,B))))) # label(redefinition_m2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3579 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B k7_finseq_1(k2_finseq_2(A,B),k9_finseq_1(B)) = k2_finseq_2(k1_nat_1(A,np__1),B)))) # label(t74_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3580 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (-v1_xboole_0(C) -> (k4_finseq_2(B,C) = k4_finseq_2(A,C) -> A = B))))))) # label(t130_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3581 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B)),k1_relat_1(C)) -> v1_relat_1(k3_funcop_1(C,A,B)) & v1_funct_1(k3_funcop_1(C,A,B)) & v1_finseq_1(k3_funcop_1(C,A,B))))))))) # label(t78_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3582 (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]. 29.12/28.70 3583 (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]. 29.12/28.70 3584 (all A (-v1_xboole_0(A) -> a_1_0_finseq_2(A) = k4_finseq_2(np__1,A))) # label(t116_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3585 (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_1(G) & v1_funct_2(G,k2_zfmisc_1(A,B),C) & m2_relset_1(G,k2_zfmisc_1(A,B),C) -> (all H (m2_finseq_1(H,B) -> (H = k10_finseq_1(E,F) -> 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]. 29.12/28.70 3586 (all A exists B (-v1_xboole_0(B) & m1_finseq_2(B,A))) # label(rc1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3587 (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]. 29.12/28.70 3588 (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_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)))) -> C = B))))))) # label(t10_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3589 (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]. 29.12/28.70 3590 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) & v3_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) -> (r1_xreal_0(A,k3_finseq_1(B)) & k5_relat_1(D,B) = C -> k3_finseq_1(C) = A))))))))) # label(t47_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3591 (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]. 29.12/28.70 3592 (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]. 29.12/28.70 3593 (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]. 29.12/28.70 3594 (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]. 29.12/28.70 3595 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_finseq_1(A),B) & v1_funct_2(C,k2_finseq_1(A),B) & v1_funct_1(C) -> m2_finseq_1(C,B))))))) # label(t28_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3596 (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]. 29.12/28.70 3597 (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)) -> k10_finseq_1(k1_funct_1(A,B),k1_funct_1(A,C)) = k5_relat_1(k10_finseq_1(B,C),A))))) # label(t145_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3598 (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]. 29.12/28.70 3599 (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_finseq_1(C) & v1_funct_1(C) -> (all D k7_finseq_1(C,k9_finseq_1(D)) != B))) & k1_nat_1(A,np__1) = k3_finseq_1(B)))))) # label(t21_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3600 (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) -> B != k8_finseq_1(A,C,k12_finseq_1(A,D))))))))))) # label(t22_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3601 (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_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) -> (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]. 29.12/28.70 3602 $T # label(t108_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3603 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,B) -> (all F (m2_relset_1(F,k2_zfmisc_1(A,B),C) & v1_funct_2(F,k2_zfmisc_1(A,B),C) & v1_funct_1(F) -> (all G (m2_finseq_1(G,B) -> (k12_finseq_1(B,E) = G -> k5_funcop_1(F,D,G) = k12_finseq_1(C,k2_binop_1(A,B,C,F,D,E))))))))))))))))) # label(t94_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3604 (all A all B all C k1_enumset1(A,B,C) = k2_relat_1(k11_finseq_1(A,B,C))) # label(t148_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3605 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (B = k7_relat_1(C,k2_finseq_1(A)) -> k3_finseq_1(B) = k3_square_1(A,k3_finseq_1(C))))))))) # label(t24_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3606 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(A,B)) -> (all D (v1_funct_1(D) & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) & v3_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]. 29.12/28.70 3607 (all A all B all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) & v1_finseq_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]. 29.12/28.70 3608 (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)) -> k4_finseq_1(C) = k2_finseq_1(A))))))) # label(t144_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3609 (all A all B (m1_subset_1(B,k4_finseq_2(np__0,A)) -> B = k6_finseq_1(A))) # label(t113_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3610 (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) -> k6_xcmplx_0(B,A) = k2_square_1(np__0,k6_xcmplx_0(B,A))))))) # label(t4_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3611 (all A all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (all D (m2_finseq_1(D,A) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (k1_partfun1(k5_numbers,A,A,B,D,E) = C -> k3_finseq_1(C) = k3_finseq_1(D)))))))))) # label(t37_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3612 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m2_finseq_1(C,B) -> m2_finseq_1(C,A))))))) # label(t27_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3613 (all 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) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (C = k5_funcop_1(D,A,B) & r1_tarski(k2_zfmisc_1(k1_tarski(A),k2_relat_1(B)),k1_relat_1(D)) -> k3_finseq_1(B) = k3_finseq_1(C)))))))) # label(t81_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3614 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,B) -> (all F (v1_funct_1(F) & m2_relset_1(F,k2_zfmisc_1(B,C),D) & v1_funct_2(F,k2_zfmisc_1(B,C),D) -> (all G (m2_finseq_2(G,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]. 29.12/28.70 3615 (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) -> (D = k9_finseq_1(A) -> k9_finseq_1(k1_funct_1(E,A)) = k1_partfun1(k5_numbers,B,B,C,D,E)))))))))) # label(t39_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3616 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (k2_finseq_1(A) = B -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (all D (m2_finseq_1(D,B) -> (r1_xreal_0(A,k3_finseq_1(C)) -> v1_finseq_1(k5_relat_1(D,C)) & v1_funct_1(k5_relat_1(D,C)) & v1_relat_1(k5_relat_1(D,C)))))))))))) # label(t34_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3617 (all A k3_finseq_2(A) = k13_finseq_1(A)) # label(redefinition_k3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3618 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,B) -> (all E (m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_2(E,k2_zfmisc_1(A,B),C) & v1_funct_1(E) -> (all F (m2_finseq_1(F,A) -> m2_finseq_1(k4_funcop_1(E,F,D),C))))))))))))) # label(t97_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3619 (all A (v4_ordinal2(A) -> k3_finseq_1(k1_finseq_2(A)) = A)) # label(t55_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3620 (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]. 29.12/28.70 3621 (all A all B (m1_finseq_2(B,A) & -v1_xboole_0(B) -> r1_tarski(B,k3_finseq_2(A)))) # label(t105_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3622 (all A k2_finseq_2(np__3,A) = k11_finseq_1(A,A,A)) # label(t76_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3623 (all A (-v1_xboole_0(A) -> k3_tarski(a_1_3_finseq_2(A)) = k3_finseq_2(A))) # label(t128_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3624 (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]. 29.12/28.70 3625 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (m2_relset_1(C,k4_finseq_1(A),k4_finseq_1(A)) & v1_funct_2(C,k4_finseq_1(A),k4_finseq_1(A)) & v1_funct_1(C) -> (k5_relat_1(C,A) = B & k4_finseq_1(A) = k2_relat_1(C) -> k3_finseq_1(B) = k3_finseq_1(A)))))))) # label(t46_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3626 (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_2(G,D,E) & m2_relset_1(G,D,E) & v1_funct_1(G) -> (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]. 29.12/28.70 3627 (all A all B all C (m2_finseq_1(C,A) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> m2_finseq_1(k1_partfun1(k5_numbers,A,A,B,C,D),B))))) # label(t36_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3628 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_finseq_1(D) & v1_funct_1(D) & v1_relat_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_2(E,k2_zfmisc_1(A,B),C) -> (all F (m2_finseq_1(F,A) -> (all G (m2_finseq_1(G,B) -> (k3_finseq_1(F) = k3_finseq_1(G) & k3_funcop_1(E,F,G) = D -> k3_finseq_1(D) = k3_finseq_1(G) & k3_finseq_1(D) = k3_finseq_1(F)))))))))))))))) # label(t86_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3629 p1_s2_finseq_2(k6_finseq_1(f1_s2_finseq_2)) & (all A (m2_finseq_1(A,f1_s2_finseq_2) -> (all B (m1_subset_1(B,f1_s2_finseq_2) -> (p1_s2_finseq_2(A) -> p1_s2_finseq_2(k8_finseq_1(f1_s2_finseq_2,A,k12_finseq_1(f1_s2_finseq_2,B)))))))) -> (all A (m2_finseq_1(A,f1_s2_finseq_2) -> p1_s2_finseq_2(A))) # label(s2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3630 (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,A) -> (all H (m2_finseq_1(H,B) -> (k12_finseq_1(B,E) = H & k12_finseq_1(A,D) = G -> k12_finseq_1(C,k2_binop_1(A,B,C,F,D,E)) = k3_funcop_1(F,G,H)))))))))))))))))) # label(t88_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3631 (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]. 29.12/28.70 3632 (all A all B (m1_finseq_2(B,A) & -v1_xboole_0(B) -> (exists C m2_finseq_2(C,A,B)))) # label(existence_m2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3633 (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]. 29.12/28.70 3634 (all A k2_finseq_2(np__2,A) = k10_finseq_1(A,A)) # label(t75_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3635 (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)) -> v1_finseq_1(k5_relat_1(D,C)) & v1_funct_1(k5_relat_1(D,C)) & v1_relat_1(k5_relat_1(D,C)) | np__0 != A & B = np__0))))))))) # label(t42_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3636 (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]. 29.12/28.70 3637 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_2(E,k2_zfmisc_1(A,B),C) & v1_funct_1(E) -> k5_funcop_1(E,D,k6_finseq_1(B)) = k6_finseq_1(C))))))))))) # label(t93_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3638 (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]. 29.12/28.70 3639 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (all D (v1_funct_2(D,k5_numbers,B) & m2_relset_1(D,k5_numbers,B) & v1_funct_1(D) -> (C = k2_partfun1(k5_numbers,B,D,k2_finseq_1(A)) -> k3_finseq_1(C) = A))))))))) # label(t32_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3640 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,B) -> (all F (v1_funct_2(F,k2_zfmisc_1(A,B),C) & m2_relset_1(F,k2_zfmisc_1(A,B),C) & v1_funct_1(F) -> (all G (m2_finseq_1(G,A) -> (G = k12_finseq_1(A,D) -> k4_funcop_1(F,G,E) = k12_finseq_1(C,k2_binop_1(A,B,C,F,D,E))))))))))))))))) # label(t100_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3641 (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) -> (r1_tarski(k2_relat_1(A),k1_relat_1(C)) & k5_relat_1(A,C) = B -> k3_finseq_1(A) = k3_finseq_1(B)))))))) # label(t33_finseq_2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3642 (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]. 29.12/28.70 3643 (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]. 29.12/28.70 3644 (all A (v1_card_1(A) -> (all B ((all C (r2_hidden(C,B) -> r2_hidden(k1_card_1(C),A))) & v6_ordinal1(B) -> r1_tarski(k1_card_1(k3_tarski(B)),A))))) # label(t62_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3645 (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]. 29.12/28.70 3646 (all A all B all C k2_xboole_0(k5_card_3(C,A),k5_card_3(C,B)) = k5_card_3(C,k2_xboole_0(A,B))) # label(t27_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3647 (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) -> (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(k6_card_3(A),k6_card_3(B))))))) # label(t43_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3648 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> k5_card_3(A,k1_tarski(B)) = k1_tarski(k1_funct_1(B,A)))) # label(t25_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3649 (exists A (v1_card_3(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc1_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3650 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k1_relat_1(C)) & r2_hidden(A,k1_relat_1(C)) -> B = A | r1_xboole_0(k1_funct_1(k2_card_3(C),A),k1_funct_1(k2_card_3(C),B))))) # label(t13_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3651 $T # label(t2_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3652 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 (r2_hidden(A,f1_s3_card_3) & (all B (r2_hidden(B,f1_s3_card_3) -> p1_s3_card_3(A,B))))) # label(s3_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3653 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> k1_xboole_0 = k4_card_3(B) | k5_card_3(A,k4_card_3(B)) = k1_funct_1(B,A)))) # label(t22_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3654 (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]. 29.12/28.70 3655 (all A all B k2_funcop_1(A,k1_card_1(B)) = k1_card_3(k2_funcop_1(A,B))) # label(t10_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3656 (all A (v1_card_1(A) -> np__1 = k7_card_3(k2_funcop_1(k1_xboole_0,A)))) # label(t49_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3657 $T # label(t5_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3658 (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]. 29.12/28.70 3659 $T # label(t41_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3660 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C (r2_hidden(C,k1_relat_1(B)) -> r2_hidden(k1_funct_1(A,C),k1_funct_1(B,C)))) & k1_relat_1(A) = k1_relat_1(B) <-> r2_hidden(A,k4_card_3(B))))))) # label(t18_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3661 (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]. 29.12/28.70 3662 $T # label(t21_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3663 (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]. 29.12/28.70 3664 (all A (v1_relat_1(A) & v1_card_3(A) & v1_funct_1(A) -> k7_card_3(A) = k1_card_1(k4_card_3(A)))) # label(d8_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3665 (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]. 29.12/28.70 3666 (all A (v1_card_1(A) -> (all B A = k7_card_3(k2_funcop_1(k1_tarski(B),A))))) # label(t51_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3667 $T # label(t7_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3668 (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]. 29.12/28.70 3669 (all A (v1_funct_1(A) & v1_card_3(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_card_3(B) -> (r1_tarski(A,B) -> 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]. 29.12/28.70 3670 (all A all B (v1_card_1(B) -> v1_funct_1(k2_funcop_1(A,B)) & v1_card_3(k2_funcop_1(A,B)) & v1_ordinal2(k2_funcop_1(A,B)) & v1_relat_1(k2_funcop_1(A,B)))) # label(fc2_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3671 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & v1_setfam_1(B) -> -v1_xboole_0(k4_card_3(C)) & v1_fraenkel(k4_card_3(C)))) # label(fc4_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3672 (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]. 29.12/28.70 3673 (all A all B k4_card_3(k2_funcop_1(A,B)) = k1_funct_2(A,B)) # label(t20_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3674 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,B) -> r1_tarski(k3_card_3(A),k3_card_3(B))))))) # label(t35_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3675 $T # label(t6_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3676 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) -> (all B (r2_hidden(B,k1_relat_1(A)) -> k1_funct_1(A,B) = k1_card_1(k1_funct_1(k2_card_3(A),B)))))) # label(t40_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3677 (all A (v1_relat_1(A) & v1_funct_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]. 29.12/28.70 3678 (all A (v1_funct_1(A) & v1_card_3(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_card_3(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> r1_tarski(k1_funct_1(A,C),k1_funct_1(B,C)))) & k1_relat_1(A) = k1_relat_1(B) -> r1_tarski(k7_card_3(A),k7_card_3(B))))))) # label(t45_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3679 (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)) -> r1_tarski(k1_funct_1(A,C),k1_funct_1(B,C)))) & k1_relat_1(B) = k1_relat_1(A) -> r1_tarski(k4_card_3(A),k4_card_3(B))))))) # label(t38_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3680 (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]. 29.12/28.70 3681 (all A all B all C (k5_card_3(A,B) = C <-> (all D (r2_hidden(D,C) <-> (exists E (v1_relat_1(E) & v1_funct_1(E) & D = k1_funct_1(E,A) & r2_hidden(E,B))))))) # label(d6_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3682 (all A all B k2_card_3(k2_funcop_1(k1_tarski(A),B)) = k2_funcop_1(k1_tarski(A),k2_zfmisc_1(B,k1_tarski(A)))) # label(t12_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3683 $T # label(dt_k5_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3684 $T # label(t23_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3685 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(k1_mcart_1(A),k1_funct_1(B,k2_mcart_1(A))) & A = k4_tarski(k1_mcart_1(A),k2_mcart_1(A)) & r2_hidden(k2_mcart_1(A),k1_relat_1(B)) <-> r2_hidden(A,k3_card_3(k2_card_3(B)))))) # label(t33_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.70 3686 (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]. 29.12/28.70 3687 (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]. 29.12/28.70 3688 (exists A (f1_s4_card_3 = k1_relat_1(A) & (all B (r2_hidden(B,f1_s4_card_3) -> (all C (p1_s4_card_3(B,C) & r2_hidden(C,f2_s4_card_3(B)) <-> r2_hidden(C,k1_funct_1(A,B)))))) & v1_funct_1(A) & v1_relat_1(A))) # label(s4_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3689 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (k4_card_3(A) = 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)))) & C = D & v1_funct_1(D) & v1_relat_1(D))))))))) # label(d5_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3690 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) -> v1_card_1(k6_card_3(A)))) # label(dt_k6_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3691 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) -> (all B (v1_card_3(B) & v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(A) = k1_relat_1(B) & (all C (r2_hidden(C,k1_relat_1(A)) -> r2_hidden(k1_funct_1(A,C),k1_funct_1(B,C)))) -> r2_hidden(k6_card_3(A),k7_card_3(B))))))) # label(t56_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3692 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) -> (r2_hidden(k1_xboole_0,k2_relat_1(A)) <-> k7_card_3(A) = np__0))) # label(t44_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3693 (all A -(v6_ordinal1(A) & (all B -(r1_tarski(B,A) & (all C -((all D -(r2_hidden(D,C) & (all E (r2_hidden(E,C) -> r1_tarski(D,E))))) & C != k1_xboole_0 & r1_tarski(C,B))) & k3_tarski(B) = k3_tarski(A))))) # label(t61_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3694 (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]. 29.12/28.71 3695 (all A all B (v1_card_3(A) & v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)) & v1_card_3(k7_relat_1(A,B)))) # label(fc1_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3696 (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]. 29.12/28.71 3697 (all A (v1_funct_1(A) & v1_relat_1(A) -> (r2_hidden(k1_xboole_0,k2_relat_1(A)) <-> k4_card_3(A) = k1_xboole_0))) # label(t37_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3698 $T # label(t1_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3699 (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]. 29.12/28.71 3700 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_card_3(k1_card_3(A)) & v1_funct_1(k1_card_3(A)) & v1_relat_1(k1_card_3(A)))) # label(dt_k1_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3701 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> -(r2_hidden(A,k3_card_3(k2_card_3(B))) & (all C all D k4_tarski(C,D) != A)))) # label(t32_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3702 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(B,A) & p1_s2_card_3(A,B) -> B = A)) -> (exists A (r2_hidden(A,f1_s2_card_3) & (all B -(r2_hidden(B,f1_s2_card_3) & A != B & p1_s2_card_3(B,A))))) # label(s2_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3703 (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]. 29.12/28.71 3704 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v1_card_3(A) <-> (all B (r2_hidden(B,k1_relat_1(A)) -> v1_card_1(k1_funct_1(A,B))))))) # label(d1_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3705 $T # label(t4_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3706 (all A (v1_card_3(A) & v1_funct_1(A) & v1_relat_1(A) -> k6_card_3(A) = k1_card_1(k3_card_3(k2_card_3(A))))) # label(d7_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3707 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) -> A = k1_card_3(A))) # label(t8_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3708 (exists A (v1_relat_1(A) & (all B (r2_hidden(B,f1_s1_card_3) -> f2_s1_card_3(B) = k1_funct_1(A,B))) & f1_s1_card_3 = k1_relat_1(A) & v1_card_3(A) & v1_funct_1(A))) # label(s1_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3709 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) -> (all B (r2_hidden(B,k1_relat_1(A)) -> k1_card_1(k1_funct_1(A,B)) = k1_funct_1(A,B))))) # label(t39_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3710 $T # label(t42_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3711 $T # label(dt_k4_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3712 (all A (v1_card_1(A) -> np__0 = k6_card_3(k2_funcop_1(k1_xboole_0,A)))) # label(t48_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3713 (all A (v1_card_1(A) -> (all B A = k6_card_3(k2_funcop_1(k1_tarski(B),A))))) # label(t50_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3714 (all A k5_card_3(A,k1_xboole_0) = k1_xboole_0) # label(t24_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3715 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,B) -> r1_tarski(k2_card_3(A),k2_card_3(B))))))) # label(t34_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3716 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k2_card_3(A) = B <-> (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))) & k1_relat_1(B) = k1_relat_1(A)))))) # label(d3_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3717 (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]. 29.12/28.71 3718 (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]. 29.12/28.71 3719 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> k5_card_3(A,k2_tarski(B,C)) = k2_tarski(k1_funct_1(B,A),k1_funct_1(C,A)))))) # label(t26_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3720 (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) -> (r1_tarski(A,B) -> r1_tarski(k6_card_3(A),k6_card_3(B))))))) # label(t46_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3721 (all A (v1_relat_1(A) & v1_card_3(A) & v1_funct_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]. 29.12/28.71 3722 (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]. 29.12/28.71 3723 $T # label(dt_k3_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3724 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_card_3(B) & v1_funct_1(B) & v1_relat_1(B) -> (k1_card_3(A) = B <-> (all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(B,C) = k1_card_1(k1_funct_1(A,C)))) & k1_relat_1(B) = k1_relat_1(A)))))) # label(d2_card_3) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3725 (all A v1_ordinal1(k5_classes1(A))) # label(fc5_classes2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3726 (all A (v1_classes2(A) & -v1_xboole_0(A) -> k4_classes1(k2_ordinal2(A)) = A)) # label(t54_classes2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3727 (all A all B (v1_classes1(A) & r2_hidden(B,A) -> -r2_wellord2(B,A) & r2_hidden(k1_card_1(B),k1_card_1(A)))) # label(t1_classes2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3728 (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]. 29.12/28.71 3729 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & v1_classes2(A) -> k10_classes2(A,C,B) = k10_classes2(A,B,C))) # label(commutativity_k10_classes2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3730 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & v1_classes2(A) & -v1_xboole_0(A) -> k2_tarski(B,C) = k5_classes2(A,B,C))) # label(redefinition_k5_classes2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3731 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) & v1_classes2(A) -> m1_subset_1(k1_classes2(A,B),A))) # label(dt_k1_classes2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3732 (all A all B all C (r2_hidden(B,A) & r2_hidden(C,A) & v2_classes1(A) -> r2_hidden(k4_tarski(B,C),A))) # label(t4_classes2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3733 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (v1_classes2(B) & -v1_xboole_0(B) -> -(-r2_hidden(A,B) & -r2_hidden(B,A) & A != B))))) # label(t56_classes2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3734 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & v1_classes2(A) -> B = k8_classes2(A,B,B))) # label(idempotence_k8_classes2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3735 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (-v1_xboole_0(B) & v1_classes2(B) -> v1_classes2(k3_xboole_0(A,B)) & -v1_xboole_0(k3_xboole_0(A,B)) & v1_classes2(k2_xboole_0(A,B)) & -v1_xboole_0(k2_xboole_0(A,B)))))) # label(t61_classes2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3736 (all A (v2_classes1(A) -> v2_classes1(k4_classes1(k1_card_1(A))))) # label(t39_classes2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3737 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & v1_classes2(A) -> k5_classes2(A,C,B) = k5_classes2(A,B,C))) # label(commutativity_k5_classes2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3738 (all A (k1_card_1(k1_classes1(A)) != np__0 & v4_ordinal1(k1_card_1(k1_classes1(A))) & k1_card_1(k1_classes1(A)) != k1_xboole_0)) # label(t22_classes2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3739 (all A (v1_classes2(A) & -v1_xboole_0(A) -> v2_ordinal1(k2_ordinal2(A)) & v3_ordinal1(k2_ordinal2(A)) & v1_ordinal1(k2_ordinal2(A)))) # label(fc2_classes2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3740 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) -> (k1_relat_1(B) = A & (all C (v3_ordinal1(C) -> (r2_hidden(C,A) -> k16_classes2(C) = k1_funct_1(B,C)))) & v4_ordinal1(A) -> k16_classes2(A) = k15_classes2(k3_card_3(B)) | A = k1_xboole_0))))) # label(t78_classes2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3741 (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]. 29.12/28.71 3742 (all A all B all C (m1_subset_1(C,A) & m1_subset_1(B,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]. 29.12/28.71 3743 (all A all B all C (v1_classes2(C) & -v1_xboole_0(C) -> (r2_hidden(B,C) & r2_hidden(A,C) -> r2_hidden(k2_xboole_0(A,B),C) & r2_hidden(k5_xboole_0(A,B),C) & r2_hidden(k4_xboole_0(A,B),C) & r2_hidden(k3_xboole_0(A,B),C)))) # label(t66_classes2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3744 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & v1_classes2(B) -> (all C (-v1_xboole_0(C) & v1_classes2(C) -> (r2_hidden(A,B) & r2_hidden(B,C) -> r2_hidden(A,C)))))))) # label(t59_classes2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3745 (exists A (v1_ordinal1(A) & -v1_xboole_0(A) & v2_classes1(A) & v1_classes2(A) & v1_classes1(A))) # label(rc1_classes2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3746 $T # label(t73_classes2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3747 (all A all B (v2_classes1(A) & r2_hidden(B,A) -> r1_tarski(k1_classes1(B),A))) # label(t5_classes2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3748 (all A r1_tarski(k4_classes1(k1_card_1(k1_classes1(A))),k1_classes1(A))) # label(t29_classes2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3749 (all A all B -(r1_tarski(B,k4_classes1(k1_card_1(A))) & -r2_wellord2(B,k4_classes1(k1_card_1(A))) & -r2_hidden(B,k4_classes1(k1_card_1(A))) & v2_classes1(A))) # label(t37_classes2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3750 $T # label(t72_classes2) # label(axiom) # label(non_clause). [assumption]. 29.12/28.71 3751 (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]. 29.16/28.71 3752 $T # label(t74_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3753 (all A (v1_ordinal1(A) -> v1_classes2(k1_classes1(A)))) # label(t51_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3754 (all A (v1_ordinal1(A) -> v1_classes1(k1_classes1(A)) & v1_classes2(k1_classes1(A)) & v2_classes1(k1_classes1(A)) & -v1_xboole_0(k1_classes1(A)) & v1_ordinal1(k1_classes1(A)))) # label(fc6_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3755 (all A all B (v1_ordinal1(A) & r2_hidden(B,A) & v2_classes1(A) -> r2_hidden(k6_classes1(B),A))) # label(t30_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3756 (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]. 29.16/28.71 3757 (all A (v3_ordinal1(A) -> (all B ((exists C (v1_relat_1(C) & k1_ordinal1(A) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_classes1(k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k15_classes2(k3_card_3(k2_ordinal1(C,D))) = k1_funct_1(C,D) | k1_xboole_0 = D))) & k13_classes2 = k1_funct_1(C,k1_xboole_0) & k1_ordinal2(C) = B & v5_ordinal1(C) & v1_funct_1(C))) <-> B = k16_classes2(A))))) # label(d5_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3758 $T # label(dt_k16_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3759 (all A (v1_classes2(A) & -v1_xboole_0(A) -> v1_classes2(k1_classes1(A)) & -v1_xboole_0(k1_classes1(A)))) # label(t52_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3760 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> m1_subset_1(k7_classes2(A,B,C),A))) # label(dt_k7_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3761 (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]. 29.16/28.71 3762 $T # label(t68_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3763 (all A (v1_classes2(A) & -v1_xboole_0(A) -> k1_xboole_0 != k2_ordinal2(A) & v4_ordinal1(k2_ordinal2(A)))) # label(t55_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3764 (all A all B (v2_classes1(A) & r2_hidden(B,A) -> r2_hidden(k1_card_1(B),A))) # label(t12_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3765 (all A (v3_ordinal1(A) -> (all B (r2_hidden(A,k1_classes1(B)) -> r1_tarski(A,k1_classes1(B)) & r2_hidden(k1_ordinal1(A),k1_classes1(B)))))) # label(t7_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3766 (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]. 29.16/28.71 3767 (all A (v1_ordinal1(A) & v2_classes1(A) -> v1_classes2(A))) # label(cc3_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3768 (all A all B all C (v1_classes2(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k9_classes2(A,B,C) = k4_xboole_0(B,C))) # label(redefinition_k9_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3769 (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]. 29.16/28.71 3770 (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]. 29.16/28.71 3771 (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]. 29.16/28.71 3772 $T # label(t49_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3773 (all A all B (v1_classes2(A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> m1_subset_1(k2_classes2(A,B),A) & -v1_xboole_0(k2_classes2(A,B)))) # label(dt_k2_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3774 (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]. 29.16/28.71 3775 (all A (v2_classes1(A) -> k1_card_1(A) = k2_ordinal2(A))) # label(t10_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3776 (all A (-v1_xboole_0(k15_classes2(A)) & v1_classes2(k15_classes2(A)))) # label(dt_k15_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3777 (all A (v3_ordinal1(A) -> (all B -(v1_ordinal1(B) & (all C -(A = k6_classes1(C) & r2_hidden(C,B))) & r2_hidden(A,k6_classes1(B)))))) # label(t41_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3778 (all A (-v1_xboole_0(k1_classes1(A)) & v2_classes1(k1_classes1(A)) & v1_classes1(k1_classes1(A)))) # label(fc1_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3779 (all A (v2_classes1(A) -> v1_classes1(A))) # label(cc1_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3780 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> m1_subset_1(k11_classes2(A,B,C),A))) # label(dt_k11_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3781 (all A all B (v1_classes2(B) & -v1_xboole_0(B) -> (B = k15_classes2(A) <-> r1_tarski(A,B) & (all C (-v1_xboole_0(C) & v1_classes2(C) -> (r1_tarski(A,C) -> r1_tarski(B,C))))))) # label(d4_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3782 (all A (v3_ordinal1(A) -> k16_classes2(k1_ordinal1(A)) = k1_classes1(k16_classes2(A)))) # label(t76_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3783 (all A (v1_ordinal1(A) -> k4_classes1(k1_card_1(k1_classes1(A))) = k1_classes1(A))) # label(t46_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3784 (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]. 29.16/28.71 3785 (all A (v2_classes1(A) & v1_ordinal1(A) -> A = k4_classes1(k1_card_1(A)))) # label(t32_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3786 (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]. 29.16/28.71 3787 $T # label(t60_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3788 (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(k8_classes2(A,B,C),A))) # label(dt_k8_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3789 (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]. 29.16/28.71 3790 (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(k5_classes2(A,B,C),A))) # label(dt_k5_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3791 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & v1_classes2(A) & -v1_xboole_0(A) -> k8_classes2(A,B,C) = k8_classes2(A,C,B))) # label(commutativity_k8_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3792 (all A all B all C (v2_classes1(A) & r2_hidden(C,A) & r2_hidden(B,A) -> r2_hidden(k1_tarski(B),A) & r2_hidden(k2_tarski(B,C),A))) # label(t3_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3793 (all A (v3_ordinal1(A) -> (all B (r2_hidden(A,B) & v2_classes1(B) -> r2_hidden(k1_ordinal1(A),B) & r1_tarski(A,B))))) # label(t6_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3794 (all A k2_ordinal2(k1_classes1(A)) = k1_card_1(k1_classes1(A))) # label(t11_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3795 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> k7_classes2(A,B,C) = k2_xboole_0(B,C))) # label(redefinition_k7_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3796 (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]. 29.16/28.71 3797 (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]. 29.16/28.71 3798 (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]. 29.16/28.71 3799 (all A all B (-v1_xboole_0(B) & v1_classes2(B) -> (r2_hidden(A,B) -> r2_hidden(k3_tarski(A),B) & r2_hidden(k1_setfam_1(A),B) & r2_hidden(k1_zfmisc_1(A),B)))) # label(t65_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3800 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (k16_classes2(B) = k16_classes2(A) -> A = B))))) # label(t81_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3801 (all A (-v1_xboole_0(A) & v1_classes2(A) -> r2_hidden(k1_xboole_0,A))) # label(t62_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3802 (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]. 29.16/28.71 3803 (all A (v1_classes2(A) & -v1_xboole_0(A) -> v3_ordinal1(k2_ordinal2(A)))) # label(t50_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3804 (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]. 29.16/28.71 3805 (all A all B (v1_classes2(A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k1_classes2(A,B) = k1_tarski(B))) # label(redefinition_k1_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3806 (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]. 29.16/28.71 3807 (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(k9_classes2(A,B,C),A))) # label(dt_k9_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3808 (all A (-v1_xboole_0(A) & v1_classes2(A) -> r1_tarski(k13_classes2,A) & r1_tarski(k1_classes1(k1_xboole_0),A) & r1_tarski(k16_classes2(k1_xboole_0),A))) # label(t79_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3809 (all A (v3_ordinal1(A) -> (all B (r2_hidden(A,k2_ordinal2(B)) & v2_classes1(B) -> r2_hidden(k1_card_1(k4_classes1(A)),k1_card_1(B)) & r2_hidden(k4_classes1(A),B))))) # label(t26_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3810 (all A (v2_classes1(A) -> v4_ordinal1(k1_card_1(A)))) # label(t20_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3811 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(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)))) -> k3_card_3(A) = k4_classes1(k1_relat_1(A))))) # label(t25_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3812 (all A all B all C (v1_classes2(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> B = k7_classes2(A,B,B))) # label(idempotence_k7_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3813 (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(k10_classes2(A,B,C),A))) # label(dt_k10_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3814 (all A (v1_ordinal1(A) & v2_classes1(A) <-> v1_classes2(A))) # label(d1_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3815 (all A (v3_ordinal1(A) -> -v1_xboole_0(k16_classes2(A)) & v1_classes1(k16_classes2(A)) & v2_classes1(k16_classes2(A)) & v1_classes2(k16_classes2(A)) & v1_ordinal1(k16_classes2(A)))) # label(fc8_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3816 $T # label(t2_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.71 3817 (all A all B (-(-(v1_ordinal1(B) & r2_hidden(A,k1_classes1(B))) & -(r1_tarski(A,k1_classes1(B)) & r2_hidden(k1_card_1(A),k1_card_1(k1_classes1(B)))) & -(r1_tarski(A,k1_classes1(B)) & r2_hidden(A,k1_classes1(B)))) -> r1_tarski(k1_funct_2(A,k1_classes1(B)),k1_classes1(B)))) # label(t24_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3818 (all A all B all C (m1_subset_1(C,A) & m1_subset_1(B,A) & v1_classes2(A) & -v1_xboole_0(A) -> k2_zfmisc_1(B,C) = k11_classes2(A,B,C))) # label(redefinition_k11_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3819 (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]. 29.16/28.72 3820 (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]. 29.16/28.72 3821 (all A (-v1_xboole_0(A) & v1_classes2(A) -> -v1_xboole_0(k1_classes1(A)) & v1_classes1(k1_classes1(A)) & v2_classes1(k1_classes1(A)) & v1_classes2(k1_classes1(A)) & v1_ordinal1(k1_classes1(A)))) # label(fc3_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3822 (all A all B (m1_subset_1(B,A) & v1_classes2(A) & -v1_xboole_0(A) -> k3_classes2(A,B) = k3_tarski(B))) # label(redefinition_k3_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3823 (all A (v1_card_1(A) -> (all B (r2_hidden(A,k1_card_1(B)) & v2_classes1(B) -> r2_hidden(A,B))))) # label(t16_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3824 (all A (v2_classes1(A) & v1_ordinal1(A) -> r1_tarski(A,k4_classes1(k1_card_1(A))))) # label(t31_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3825 (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]. 29.16/28.72 3826 (all A (v3_ordinal1(A) -> v1_classes2(k1_classes1(A)))) # label(t53_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3827 (all A (v1_classes2(A) -> v1_ordinal1(A) & v1_classes1(A) & v2_classes1(A))) # label(cc2_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3828 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & v1_classes2(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]. 29.16/28.72 3829 (all A all B (m1_subset_1(B,A) & v1_classes2(A) & -v1_xboole_0(A) -> k1_zfmisc_1(B) = k2_classes2(A,B))) # label(redefinition_k2_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3830 (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(B,A)) & -(r1_tarski(B,A) & r2_hidden(k1_card_1(B),k1_card_1(A))))) # label(t23_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3831 (all A v2_classes1(k4_classes1(k1_card_1(k1_classes1(A))))) # label(t40_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3832 $T # label(t48_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3833 (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]. 29.16/28.72 3834 (all A (v3_ordinal1(A) -> v1_ordinal1(k4_classes1(A)))) # label(fc7_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3835 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> k6_classes2(A,B,C) = k4_tarski(B,C))) # label(redefinition_k6_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3836 (all A all B (v2_classes1(A) & v1_ordinal1(B) & r2_hidden(B,A) -> r2_hidden(B,k4_classes1(k1_card_1(A))))) # label(t43_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3837 (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]. 29.16/28.72 3838 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & v1_classes2(A) -> k3_xboole_0(B,C) = k8_classes2(A,B,C))) # label(redefinition_k8_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3839 (all A (v2_classes1(A) -> k1_card_1(A) = k1_card_1(k4_classes1(k1_card_1(A))))) # label(t35_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3840 (all A all B all C (m1_subset_1(C,A) & m1_subset_1(B,A) & v1_classes2(A) & -v1_xboole_0(A) -> m1_subset_1(k6_classes2(A,B,C),A))) # label(dt_k6_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3841 (all A (v2_classes1(A) -> A = k1_xboole_0 | v4_ordinal1(k1_card_1(A)) & k1_xboole_0 != k1_card_1(A) & np__0 != k1_card_1(A))) # label(t21_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3842 (all A (v3_ordinal1(A) -> -v1_xboole_0(k1_classes1(A)) & v1_classes1(k1_classes1(A)) & v1_classes2(k1_classes1(A)) & v2_classes1(k1_classes1(A)) & v1_ordinal1(k1_classes1(A)))) # label(fc4_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3843 (all A all B (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(B,A) -> k1_setfam_1(B) = k4_classes2(A,B))) # label(redefinition_k4_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3844 (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]. 29.16/28.72 3845 (all A all B all C (m1_subset_1(C,A) & m1_subset_1(B,A) & v1_classes2(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]. 29.16/28.72 3846 (all A (v2_classes1(A) -> r1_tarski(k4_classes1(k1_card_1(A)),A))) # label(t28_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3847 $T # label(t47_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3848 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (v1_classes2(B) & -v1_xboole_0(B) -> r1_tarski(A,B) | r2_hidden(B,A))))) # label(t57_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3849 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) & v1_classes2(A) -> m1_subset_1(k3_classes2(A,B),A))) # label(dt_k3_classes2) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3850 $T # label(t18_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3851 (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]. 29.16/28.72 3852 $T # label(t6_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3853 (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 <-> A = k12_qc_lang1(B))))))) # label(d23_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3854 (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]. 29.16/28.72 3855 (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]. 29.16/28.72 3856 (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]. 29.16/28.72 3857 (all A (m1_subset_1(A,k8_qc_lang1) -> ((exists B ((exists C ((exists D (k9_qc_lang1(C,D) = A & m1_qc_lang1(D,B))) & m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(B)))) & m2_subset_1(B,k1_numbers,k5_numbers))) <-> v2_qc_lang1(A)))) # label(d17_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3858 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A)) -> np__1 != k1_mcart_1(B) & np__2 != k1_mcart_1(B) & np__3 != k1_mcart_1(B) & k1_mcart_1(B) != np__0)))) # label(t48_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3859 $T # label(t41_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3860 $T # label(t28_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3861 $T # label(t8_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3862 $T # label(t17_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3863 (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]. 29.16/28.72 3864 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k1_zfmisc_1(k2_qc_lang1)) -> ((exists C (v1_funct_1(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) -> (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)) & (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)) & (v5_qc_lang1(D) -> k6_subset_1(k2_qc_lang1,k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,k21_qc_lang1(D)),k23_qc_lang1(k20_qc_lang1(D))) = k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,D)) & (v2_qc_lang1(D) -> a_1_2_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)))) <-> k24_qc_lang1(A) = B))))) # label(d29_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3865 (all A (m1_subset_1(A,k8_qc_lang1) -> k10_qc_lang1(A) = A)) # label(d12_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3866 $T # label(t40_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3867 (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]. 29.16/28.72 3868 $T # label(t31_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3869 (all A (m1_subset_1(A,k5_qc_lang1) -> (all B (m2_finseq_1(B,k1_qc_lang1) -> (k6_qc_lang1(A) = k3_finseq_1(B) -> 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]. 29.16/28.72 3870 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k13_qc_lang1(A,B) = k7_finseq_1(k7_finseq_1(k9_finseq_1(k4_tarski(np__2,np__0)),k10_qc_lang1(A)),k10_qc_lang1(B)))))) # label(d15_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3871 (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]. 29.16/28.72 3872 (all A (m1_subset_1(A,k8_qc_lang1) -> (v5_qc_lang1(A) <-> (exists B ((exists C (A = k14_qc_lang1(B,C) & m1_subset_1(C,k8_qc_lang1))) & m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)))))) # label(d20_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3873 $T # label(t22_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3874 (all A all B (m2_finseq_1(B,k1_qc_lang1) -> (r2_hidden(A,a_1_1_qc_lang1(B)) <-> (exists C (m2_subset_1(C,k1_numbers,k5_numbers) & 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))))) # label(fraenkel_a_1_1_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3875 (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]. 29.16/28.72 3876 (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]. 29.16/28.72 3877 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A)) -> k6_qc_lang1(B) = A)))) # label(t35_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3878 (all A (m1_subset_1(A,k8_qc_lang1) -> k12_qc_lang1(A) = k7_finseq_1(k9_finseq_1(k4_tarski(np__1,np__0)),k10_qc_lang1(A)))) # label(d14_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3879 $T # label(dt_k5_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3880 (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]. 29.16/28.72 3881 (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]. 29.16/28.72 3882 (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]. 29.16/28.72 3883 (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]. 29.16/28.72 3884 (all A all B (m1_subset_1(B,k8_qc_lang1) & m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k13_qc_lang1(A,B),k8_qc_lang1))) # label(dt_k13_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3885 $T # label(t24_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3886 (all A (r2_hidden(A,a_0_0_qc_lang1) <-> (exists B exists C (A = k4_tarski(B,C) & r1_xreal_0(np__7,B) & m2_subset_1(C,k1_numbers,k5_numbers) & m2_subset_1(B,k1_numbers,k5_numbers))))) # label(fraenkel_a_0_0_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3887 (all A all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(A,a_1_0_qc_lang1(B)) <-> (exists C (m1_subset_1(C,k5_qc_lang1) & k6_qc_lang1(C) = B & A = C))))) # label(fraenkel_a_1_0_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3888 $T # label(t15_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3889 (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]. 29.16/28.72 3890 $T # label(t43_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3891 $T # label(t19_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3892 (all A all B (m1_subset_1(B,k8_qc_lang1) -> ((exists C (A = k1_funct_1(k16_qc_lang1(B),C) & r2_hidden(k1_funct_1(k16_qc_lang1(B),C),k2_qc_lang1) & r1_xreal_0(C,k3_finseq_1(k16_qc_lang1(B))) & r1_xreal_0(np__1,C) & m2_subset_1(C,k1_numbers,k5_numbers))) <-> r2_hidden(A,a_1_2_qc_lang1(B))))) # label(fraenkel_a_1_2_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3893 (all A (m1_subset_1(A,k8_qc_lang1) -> -(v5_qc_lang1(A) & v2_qc_lang1(A)) & -(v3_qc_lang1(A) & v5_qc_lang1(A)) & -(v5_qc_lang1(A) & v4_qc_lang1(A)) & -(v4_qc_lang1(A) & v3_qc_lang1(A)) & -(v4_qc_lang1(A) & v2_qc_lang1(A)) & -(v3_qc_lang1(A) & v2_qc_lang1(A)))) # label(t51_qc_lang1_AndRHS_AndRHS_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3894 (all A (m1_subset_1(A,k8_qc_lang1) -> -(A != k11_qc_lang1 & -v2_qc_lang1(A) & -v4_qc_lang1(A) & -v5_qc_lang1(A) & -v3_qc_lang1(A)))) # label(t33_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3895 (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]. 29.16/28.72 3896 (all A (m1_subset_1(A,k8_qc_lang1) -> (v5_qc_lang1(A) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> ((exists C (m1_subset_1(C,k8_qc_lang1) & A = k14_qc_lang1(B,C))) <-> B = k20_qc_lang1(A))))))) # label(d26_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3897 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (k19_qc_lang1(A) = B <-> (exists C (k13_qc_lang1(C,B) = A & m1_subset_1(C,k8_qc_lang1))))))))) # label(d25_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.16/28.72 3898 (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]. 29.16/28.72 3899 (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]. 29.18/28.74 3900 $T # label(t27_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.18/28.74 3901 $T # label(t42_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.18/28.74 3902 (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]. 29.18/28.74 3903 $T # label(t29_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.18/28.74 3904 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) -> (all B (m1_subset_1(B,k8_qc_lang1) -> ((exists C (A = k13_qc_lang1(B,C) & m1_subset_1(C,k8_qc_lang1))) <-> k18_qc_lang1(A) = B)))))) # label(d24_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.18/28.74 3905 $T # label(t25_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.18/28.74 3906 (exists A (v1_funct_2(A,k8_qc_lang1,f1_s3_qc_lang1) & (all B (m1_subset_1(B,k8_qc_lang1) -> (v2_qc_lang1(B) -> k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,B) = f3_s3_qc_lang1(B)) & (v3_qc_lang1(B) -> f4_s3_qc_lang1(k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,k17_qc_lang1(B))) = k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,B)) & (v5_qc_lang1(B) -> k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,B) = f6_s3_qc_lang1(B,k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,k21_qc_lang1(B)))) & (v4_qc_lang1(B) -> k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,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)))))) & f2_s3_qc_lang1 = k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,k11_qc_lang1) & m2_relset_1(A,k8_qc_lang1,f1_s3_qc_lang1) & v1_funct_1(A))) # label(s3_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.18/28.74 3907 $T # label(t38_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.18/28.74 3908 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang1(A) -> (all B (m2_finseq_1(B,k1_qc_lang1) -> ((exists C ((exists D ((exists E (m1_qc_lang1(E,C) & A = k9_qc_lang1(D,E) & B = E)) & m2_subset_1(D,k5_qc_lang1,k7_qc_lang1(C)))) & m2_subset_1(C,k1_numbers,k5_numbers))) <-> k16_qc_lang1(A) = B)))))) # label(d22_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.18/28.74 3909 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang1(A) -> (all B (m1_subset_1(B,k5_qc_lang1) -> ((exists C (m2_subset_1(C,k1_numbers,k5_numbers) & (exists D (m1_qc_lang1(D,C) & (exists E (m2_subset_1(E,k5_qc_lang1,k7_qc_lang1(C)) & k9_qc_lang1(E,D) = A & B = E)))))) <-> B = k15_qc_lang1(A))))))) # label(d21_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.18/28.74 3910 (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]. 29.18/28.74 3911 (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]. 29.18/28.74 3912 (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]. 29.18/28.74 3913 $T # label(t11_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.18/28.74 3914 $T # label(t20_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.18/28.74 3915 $T # label(t3_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.18/28.74 3916 $T # label(t26_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.18/28.74 3917 $T # label(t12_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.18/28.74 3918 (all A (v1_qc_lang1(A) <-> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(B)) -> (all D (m1_qc_lang1(D,B) -> r2_hidden(k7_finseq_1(k12_finseq_1(k7_qc_lang1(B),C),D),A))))))) & r2_hidden(k9_finseq_1(k4_tarski(np__0,np__0)),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)))))) & (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)))) & m1_subset_1(A,k1_zfmisc_1(k13_finseq_1(k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)))))) # label(d9_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3919 $T # label(t5_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3920 (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]. 29.18/28.75 3921 (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]. 29.18/28.75 3922 (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]. 29.18/28.75 3923 (all A (m1_subset_1(A,k8_qc_lang1) -> (v5_qc_lang1(A) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (k21_qc_lang1(A) = B <-> (exists C (A = k14_qc_lang1(C,B) & m2_subset_1(C,k1_qc_lang1,k2_qc_lang1))))))))) # label(d27_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3924 (all A (m1_subset_1(A,k8_qc_lang1) -> np__0 = k1_mcart_1(k1_funct_1(k10_qc_lang1(k11_qc_lang1),np__1)) & -((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> -m2_subset_1(k1_funct_1(k10_qc_lang1(A),np__1),k5_qc_lang1,k7_qc_lang1(B)))) & v2_qc_lang1(A)) & (v3_qc_lang1(A) -> k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) = np__1) & (v4_qc_lang1(A) -> np__2 = k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1))) & (v5_qc_lang1(A) -> k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) = np__3))) # label(t49_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3925 (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]. 29.18/28.75 3926 (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]. 29.18/28.75 3927 (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))))) & p1_s1_qc_lang1(k11_qc_lang1) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A)) -> (all C (m1_qc_lang1(C,A) -> p1_s1_qc_lang1(k9_qc_lang1(B,C)))))))) -> (all A (m1_subset_1(A,k8_qc_lang1) -> p1_s1_qc_lang1(A))) # label(s1_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3928 (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]. 29.18/28.75 3929 (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]. 29.18/28.75 3930 $T # label(t30_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3931 $T # label(t32_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3932 $T # label(t7_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3933 (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]. 29.18/28.75 3934 $T # label(t16_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3935 (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]. 29.18/28.75 3936 $T # label(t9_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3937 (all A (-v1_xboole_0(A) -> ((all B (-v1_xboole_0(B) -> (v1_qc_lang1(B) -> r1_tarski(A,B)))) & v1_qc_lang1(A) <-> k8_qc_lang1 = A))) # label(d10_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3938 (all A (m1_subset_1(A,k2_qc_lang1) -> k1_tarski(A) = k23_qc_lang1(A))) # label(redefinition_k23_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3939 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k7_finseq_1(k7_finseq_1(k9_finseq_1(k4_tarski(np__3,np__0)),k12_finseq_1(k2_qc_lang1,A)),k10_qc_lang1(B)) = k14_qc_lang1(A,B))))) # label(d16_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3940 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (k10_qc_lang1(A) = k7_finseq_1(k10_qc_lang1(B),C) -> k10_qc_lang1(B) = k10_qc_lang1(A)))))))) # label(t37_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3941 $T # label(t13_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3942 $T # label(dt_k1_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3943 (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(k21_qc_lang1(A)) & v5_qc_lang1(A) -> p1_s2_qc_lang1(A)) & (v4_qc_lang1(A) & p1_s2_qc_lang1(k19_qc_lang1(A)) & p1_s2_qc_lang1(k18_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]. 29.18/28.75 3944 (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]. 29.18/28.75 3945 (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) -> k9_qc_lang1(B,C) = k7_finseq_1(k12_finseq_1(k7_qc_lang1(A),B),C))))))) # label(t23_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3946 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang1(A) -> k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) != np__1 & 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__3 & k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) != np__0))) # label(t50_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3947 $T # label(t39_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3948 $T # label(t14_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3949 (all A (m1_subset_1(A,k8_qc_lang1) -> ((exists B (A = k12_qc_lang1(B) & m1_subset_1(B,k8_qc_lang1))) <-> v3_qc_lang1(A)))) # label(d18_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3950 $T # label(t44_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3951 (all A (m1_subset_1(A,k8_qc_lang1) -> (np__0 = k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) -> A = k11_qc_lang1) & (np__2 = k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) -> v4_qc_lang1(A)) & (np__3 = k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) -> v5_qc_lang1(A)) & ((exists B (m2_subset_1(B,k1_numbers,k5_numbers) & m2_subset_1(k1_funct_1(k10_qc_lang1(A),np__1),k5_qc_lang1,k7_qc_lang1(B)))) -> v2_qc_lang1(A)) & (k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) = np__1 -> v3_qc_lang1(A)))) # label(t36_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3952 (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]. 29.18/28.75 3953 $T # label(t10_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3954 (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]. 29.18/28.75 3955 $T # label(t12_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3956 (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]. 29.18/28.75 3957 $T # label(t35_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3958 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (all E (m1_subset_1(E,k8_qc_lang1) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (k14_qc_lang1(F,E) = k8_qc_lang2(A,B,C,D) -> A = F & E = k6_qc_lang2(B,C,D)))))))))))))) # label(t28_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3959 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m2_subset_1(D,k1_qc_lang1,k2_qc_lang1) -> (all E (m2_subset_1(E,k1_qc_lang1,k2_qc_lang1) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (k6_qc_lang2(D,F,B) = k6_qc_lang2(C,E,A) -> E = F & A = B & C = D))))))))))))) # label(t21_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3960 (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]. 29.18/28.75 3961 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k19_qc_lang1(k13_qc_lang1(A,B)) = B & k18_qc_lang1(k13_qc_lang1(A,B)) = A)))) # label(t5_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3962 $T # label(t44_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3963 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> ((exists C (m2_subset_1(C,k1_numbers,k5_numbers) & (exists D (v1_relat_1(D) & v1_funct_1(D) & r1_xreal_0(np__1,C) & (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> -((all F (m1_subset_1(F,k8_qc_lang1) -> (all G (m1_subset_1(G,k8_qc_lang1) -> -(r1_qc_lang2(F,G) & k1_funct_1(D,k1_nat_1(E,np__1)) = G & k1_funct_1(D,E) = F))))) & -r1_xreal_0(C,E) & r1_xreal_0(np__1,E)))) & k1_funct_1(D,C) = B & A = k1_funct_1(D,np__1) & k3_finseq_1(D) = C & v1_finseq_1(D))))) <-> r2_qc_lang2(A,B)))))) # label(d21_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3964 (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)) & k8_qc_lang2(A,B,C,D) = k14_qc_lang1(A,k6_qc_lang2(B,C,D)))))))))) # label(t26_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3965 $T # label(t70_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3966 (all A all B all C all D (m1_subset_1(A,k2_qc_lang1) & m1_subset_1(B,k2_qc_lang1) & m1_subset_1(D,k8_qc_lang1) & m1_subset_1(C,k2_qc_lang1) -> m1_subset_1(k8_qc_lang2(A,B,C,D),k8_qc_lang1))) # label(dt_k8_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3967 (all A (m1_subset_1(A,k8_qc_lang1) -> (r2_qc_lang2(A,k11_qc_lang1) <-> A = k11_qc_lang1))) # label(t99_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3968 (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]. 29.18/28.75 3969 (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]. 29.18/28.75 3970 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k15_qc_lang2(k3_qc_lang2(A,B)) = k2_xboole_0(k2_xboole_0(k15_qc_lang2(A),k15_qc_lang2(B)),k2_enumset1(k12_qc_lang1(B),k12_qc_lang1(A),k13_qc_lang1(k12_qc_lang1(A),k12_qc_lang1(B)),k3_qc_lang2(A,B))))))) # label(t114_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3971 (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]. 29.18/28.75 3972 (all A (m1_subset_1(A,k8_qc_lang1) -> (v1_qc_lang2(A) -> v3_qc_lang1(A) & v4_qc_lang1(k17_qc_lang1(A)) & v3_qc_lang1(k18_qc_lang1(k17_qc_lang1(A))) & v3_qc_lang1(k19_qc_lang1(k17_qc_lang1(A))) & v2_qc_lang2(A)))) # label(t49_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3973 (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]. 29.18/28.75 3974 (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]. 29.18/28.75 3975 (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]. 29.18/28.75 3976 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (k3_qc_lang2(C,D) = k3_qc_lang2(A,B) -> B = D & C = A))))))))) # label(t16_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3977 (all A all B (m1_subset_1(A,k8_qc_lang1) & m1_subset_1(B,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]. 29.18/28.75 3978 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (-(-(r2_qc_lang2(B,C) & r3_qc_lang2(A,B)) & -(r1_qc_lang2(B,C) & r2_qc_lang2(A,B)) & -(r1_qc_lang2(B,C) & r3_qc_lang2(A,B)) & -(r3_qc_lang2(B,C) & r1_qc_lang2(A,B)) & -(r2_qc_lang2(B,C) & r1_qc_lang2(A,B)) & -(r3_qc_lang2(B,C) & r2_qc_lang2(A,B))) -> r3_qc_lang2(A,C)))))))) # label(t83_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3979 (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]. 29.18/28.75 3980 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang2(A) -> v3_qc_lang1(A) & v3_qc_lang1(k21_qc_lang1(k17_qc_lang1(A))) & v5_qc_lang1(k17_qc_lang1(A))))) # label(t52_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3981 (all A (m1_subset_1(A,k8_qc_lang1) -> (k15_qc_lang2(A) = k1_tarski(A) <-> A = k11_qc_lang1 | v2_qc_lang1(A)))) # label(t116_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3982 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (B = k15_qc_lang2(A) <-> (all C (r2_hidden(C,B) <-> (exists D (m1_subset_1(D,k8_qc_lang1) & r2_qc_lang2(D,A) & D = C)))))))) # label(d23_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3983 $T # label(t43_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3984 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (r2_hidden(B,k15_qc_lang2(C)) -> r2_hidden(A,k15_qc_lang2(C)) | -r1_qc_lang2(A,B) & -r2_qc_lang2(A,B) & -r3_qc_lang2(A,B)))))))) # label(t120_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3985 (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]. 29.18/28.75 3986 (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]. 29.18/28.75 3987 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r1_xreal_0(k3_finseq_1(k10_qc_lang1(B)),k3_finseq_1(k10_qc_lang1(A))) & r1_qc_lang2(A,B)))))) # label(t71_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3988 (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]. 29.18/28.75 3989 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A)) -> (all C (m1_qc_lang1(C,A) -> k1_tarski(k9_qc_lang1(B,C)) = k15_qc_lang2(k9_qc_lang1(B,C)))))))) # label(t108_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3990 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> v5_qc_lang1(k6_qc_lang2(A,B,C)) & k21_qc_lang1(k6_qc_lang2(A,B,C)) = k14_qc_lang1(B,C) & k20_qc_lang1(k6_qc_lang2(A,B,C)) = A)))))) # label(t25_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3991 (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]. 29.18/28.75 3992 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v4_qc_lang1(A) -> (B = k18_qc_lang1(A) | B = k19_qc_lang1(A) <-> r1_qc_lang2(B,A))))))) # label(t66_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3993 (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]. 29.18/28.75 3994 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (r3_qc_lang2(A,k14_qc_lang1(C,B)) <-> r2_qc_lang2(A,B)))))))) # label(t91_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 3995 (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]. 29.18/28.75 3996 (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]. 29.18/28.75 3997 (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]. 29.18/28.75 3998 (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]. 29.18/28.75 3999 (all A (m1_subset_1(A,k8_qc_lang1) -> k2_xboole_0(k15_qc_lang2(A),k1_tarski(k12_qc_lang1(A))) = k15_qc_lang2(k12_qc_lang1(A)))) # label(t110_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 4000 $T # label(t102_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 4001 $T # label(t106_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 4002 (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 & B = k11_qc_lang2(k3_qc_lang2(A,B)) & k17_qc_lang1(k3_qc_lang2(A,B)) = k13_qc_lang1(k12_qc_lang1(A),k12_qc_lang1(B)))))) # label(t45_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 4003 (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]. 29.18/28.75 4004 (all A (m1_subset_1(A,k8_qc_lang1) -> (v3_qc_lang1(A) -> k15_qc_lang2(A) = k2_xboole_0(k15_qc_lang2(k17_qc_lang1(A)),k1_tarski(A))))) # label(t117_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.75 4005 (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) -> k7_qc_lang2(B,C,D) = E & A = F))))))))))))) # label(t31_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4006 (all A (m1_subset_1(A,k8_qc_lang1) -> k18_qc_lang1(k17_qc_lang1(A)) = k12_qc_lang2(A))) # label(d16_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4007 $T # label(t9_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4008 (all A (m1_subset_1(A,k8_qc_lang1) -> ((exists B ((exists C (A = k4_qc_lang2(B,C) & 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]. 29.18/28.76 4009 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (k14_qc_lang1(A,C) = k14_qc_lang1(B,D) -> B = A & C = D))))))))) # label(t6_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4010 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> k2_xboole_0(k15_qc_lang2(A),k1_tarski(k14_qc_lang1(B,A))) = k15_qc_lang2(k14_qc_lang1(B,A)))))) # label(t112_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4011 (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]. 29.18/28.76 4012 (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]. 29.18/28.76 4013 (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) -> A = C & k5_qc_lang2(B,D) = E))))))))))) # label(t24_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4014 $T # label(t37_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4015 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v5_qc_lang1(A) -> (B = k21_qc_lang1(A) <-> r1_qc_lang2(B,A))))))) # label(t67_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4016 (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(k9_qc_lang2(A,B,C,D)) & v4_qc_lang2(k7_qc_lang2(A,B,D)))))))))) # label(t38_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4017 (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 (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> k14_qc_lang1(C,A) != B)) & (all C (m1_subset_1(C,k8_qc_lang1) -> k13_qc_lang1(C,A) != B & B != k13_qc_lang1(A,C))))))))) # label(d20_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4018 (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]. 29.18/28.76 4019 (all A all B (m1_subset_1(B,k8_qc_lang1) & m1_subset_1(A,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]. 29.18/28.76 4020 (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]. 29.18/28.76 4021 (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) & G = B))))))))))))))) # label(t32_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4022 (all A (m1_subset_1(A,k8_qc_lang1) -> (v3_qc_lang2(A) -> v4_qc_lang1(A) & v2_qc_lang2(k18_qc_lang1(A)) & v2_qc_lang2(k19_qc_lang1(A))))) # label(t51_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4023 $T # label(t68_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4024 $T # label(t69_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4025 (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) -> (B = A | A = C <-> r1_qc_lang2(A,k13_qc_lang1(B,C))))))))) # label(t62_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4026 (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]. 29.18/28.76 4027 (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]. 29.18/28.76 4028 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang2(A) <-> (exists B ((exists C (k2_qc_lang2(B,C) = A & m1_subset_1(C,k8_qc_lang1))) & m1_subset_1(B,k8_qc_lang1)))))) # label(d11_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4029 (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) -> D = C & H = G & A = B & F = E))))))))))))))))) # label(t27_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4030 (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]. 29.18/28.76 4031 (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]. 29.18/28.76 4032 (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]. 29.18/28.76 4033 $T # label(t11_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4034 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) -> k13_qc_lang1(k18_qc_lang1(A),k19_qc_lang1(A)) = A))) # label(t4_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4035 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (k13_qc_lang1(C,D) = k13_qc_lang1(A,B) -> C = A & B = D))))))))) # label(t3_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4036 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> A = k13_qc_lang2(k4_qc_lang2(A,B)) & k2_qc_lang2(B,A) = k19_qc_lang1(k4_qc_lang2(A,B)) & k18_qc_lang1(k4_qc_lang2(A,B)) = k2_qc_lang2(A,B) & k14_qc_lang2(k4_qc_lang2(A,B)) = B)))) # label(t47_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4037 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m2_subset_1(D,k1_qc_lang1,k2_qc_lang1) -> (all E (m2_subset_1(E,k1_qc_lang1,k2_qc_lang1) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (k7_qc_lang2(D,F,B) = k7_qc_lang2(C,E,A) -> D = C & E = F & B = A))))))))))))) # label(t23_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4038 (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]. 29.18/28.76 4039 $T # label(d17_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4040 (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]. 29.18/28.76 4041 $T # label(t42_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4042 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k12_qc_lang2(k2_qc_lang2(A,B)) = A & k13_qc_lang1(A,k12_qc_lang1(B)) = k17_qc_lang1(k2_qc_lang2(A,B)) & B = k11_qc_lang2(k2_qc_lang2(A,B)))))) # label(t46_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4043 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r1_qc_lang2(B,A) & v2_qc_lang1(A)))))) # label(t64_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4044 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(B)) -> (all D (m1_qc_lang1(D,B) -> (r2_qc_lang2(A,k9_qc_lang1(C,D)) <-> k9_qc_lang1(C,D) = A))))))))) # label(t100_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4045 (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]. 29.18/28.76 4046 $T # label(t41_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4047 (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]. 29.18/28.76 4048 (all A all B (m1_subset_1(B,k8_qc_lang1) & m1_subset_1(A,k8_qc_lang1) -> -r3_qc_lang2(A,A))) # label(irreflexivity_r3_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4049 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (k12_qc_lang1(A) = k12_qc_lang1(B) -> A = B))))) # label(t1_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4050 (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]. 29.18/28.76 4051 (all A (m1_subset_1(A,k8_qc_lang1) -> k13_qc_lang2(A) = k12_qc_lang2(k18_qc_lang1(A)))) # label(d18_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4052 (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]. 29.18/28.76 4053 (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]. 29.18/28.76 4054 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k2_xboole_0(k2_xboole_0(k15_qc_lang2(A),k15_qc_lang2(B)),k5_enumset1(k12_qc_lang1(B),k13_qc_lang1(A,k12_qc_lang1(B)),k2_qc_lang2(A,B),k12_qc_lang1(A),k13_qc_lang1(B,k12_qc_lang1(A)),k2_qc_lang2(B,A),k4_qc_lang2(A,B))) = k15_qc_lang2(k4_qc_lang2(A,B)))))) # label(t115_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4055 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> k6_qc_lang2(B,C,D) = k21_qc_lang1(k8_qc_lang2(A,B,C,D)) & k20_qc_lang1(k8_qc_lang2(A,B,C,D)) = A & v5_qc_lang1(k8_qc_lang2(A,B,C,D)))))))))) # label(t33_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4056 (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]. 29.18/28.76 4057 (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 & F = E & H = G & B = A))))))))))))))))) # label(t30_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4058 (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]. 29.18/28.76 4059 (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]. 29.18/28.76 4060 $T # label(t34_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4061 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k15_qc_lang2(k2_qc_lang2(A,B)) = 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))))))) # label(t113_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4062 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v3_qc_lang1(A) -> (r1_qc_lang2(B,A) <-> B = k17_qc_lang1(A))))))) # label(t65_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4063 $T # label(dt_k15_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4064 (all A (m1_subset_1(A,k8_qc_lang1) -> (k11_qc_lang1 = A <-> r1_qc_lang2(A,k1_qc_lang2)))) # label(t61_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4065 $T # label(t39_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4066 (all A (m1_subset_1(A,k8_qc_lang1) -> (v3_qc_lang2(A) -> A = k4_qc_lang2(k13_qc_lang2(A),k14_qc_lang2(A))))) # label(t55_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4067 (all A (m1_subset_1(A,k8_qc_lang1) -> k17_qc_lang1(k12_qc_lang1(A)) = A)) # label(t2_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4068 (all A (m1_subset_1(A,k8_qc_lang1) -> ((exists B ((exists C (A = k5_qc_lang2(B,C) & m1_subset_1(C,k8_qc_lang1))) & m2_subset_1(B,k1_qc_lang1,k2_qc_lang1))) <-> v4_qc_lang2(A)))) # label(d13_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4069 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (r2_qc_lang2(A,B) | r2_qc_lang2(A,C) <-> r3_qc_lang2(A,k13_qc_lang1(B,C))))))))) # label(t89_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4070 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> r3_qc_lang2(B,k3_qc_lang2(A,B)) & r3_qc_lang2(A,k3_qc_lang2(A,B)) & r3_qc_lang2(k12_qc_lang1(B),k3_qc_lang2(A,B)) & 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]. 29.18/28.76 4071 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k13_qc_lang1(k2_qc_lang2(A,B),k2_qc_lang2(B,A)) = k4_qc_lang2(A,B))))) # label(d4_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4072 $T # label(t40_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4073 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) -> k2_xboole_0(k2_xboole_0(k15_qc_lang2(k18_qc_lang1(A)),k15_qc_lang2(k19_qc_lang1(A))),k1_tarski(A)) = k15_qc_lang2(A)))) # label(t118_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4074 (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]. 29.18/28.76 4075 (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) -> B = G & E = k14_qc_lang1(C,D) & F = A))))))))))))))) # label(t29_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4076 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> k8_qc_lang2(A,B,C,D) = k14_qc_lang1(A,k6_qc_lang2(B,C,D)))))))))) # label(d8_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4077 (all A all B all C all D (m1_subset_1(A,k2_qc_lang1) & m1_subset_1(B,k2_qc_lang1) & m1_subset_1(D,k8_qc_lang1) & m1_subset_1(C,k2_qc_lang1) -> m1_subset_1(k9_qc_lang2(A,B,C,D),k8_qc_lang1))) # label(dt_k9_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4078 (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]. 29.18/28.76 4079 (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) -> C = D & B = A))))))))) # label(t19_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4080 (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]. 29.18/28.76 4081 (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]. 29.18/28.76 4082 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r2_qc_lang2(A,B) & B != A <-> r3_qc_lang2(A,B)))))) # label(d22_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4083 (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]. 29.18/28.76 4084 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (k4_qc_lang2(A,B) = k4_qc_lang2(C,D) -> B = D & A = C))))))))) # label(t18_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4085 (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]. 29.18/28.76 4086 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k20_qc_lang1(k14_qc_lang1(A,B)) = A & k21_qc_lang1(k14_qc_lang1(A,B)) = B)))) # label(t8_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4087 $T # label(t57_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4088 (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]. 29.18/28.76 4089 (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]. 29.18/28.76 4090 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r3_qc_lang2(A,B) & r2_qc_lang2(B,A)))))) # label(t79_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4091 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> k6_qc_lang2(A,B,C) = k14_qc_lang1(A,k14_qc_lang1(B,C)))))))) # label(d6_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4092 (all A (m1_subset_1(A,k8_qc_lang1) -> (v1_qc_lang2(A) <-> (exists B (m1_subset_1(B,k8_qc_lang1) & (exists C (A = k3_qc_lang2(B,C) & m1_subset_1(C,k8_qc_lang1)))))))) # label(d10_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4093 (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]. 29.18/28.76 4094 (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) & k7_qc_lang2(A,B,C) = k5_qc_lang2(A,k5_qc_lang2(B,C)))))))) # label(t20_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4095 (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]. 29.18/28.76 4096 (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]. 29.18/28.76 4097 (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]. 29.18/28.76 4098 (all A (m1_subset_1(A,k8_qc_lang1) -> (r2_qc_lang2(A,k1_qc_lang2) <-> A = k11_qc_lang1 | k1_qc_lang2 = A))) # label(t101_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4099 (all A (m1_subset_1(A,k8_qc_lang1) -> (v5_qc_lang1(A) -> k15_qc_lang2(A) = k2_xboole_0(k15_qc_lang2(k21_qc_lang1(A)),k1_tarski(A))))) # label(t119_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4100 (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) -> C = A & D = B))))))))) # label(t17_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4101 (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]. 29.18/28.76 4102 $T # label(t36_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4103 $T # label(t15_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4104 (all A (m1_subset_1(A,k8_qc_lang1) -> k11_qc_lang2(k18_qc_lang1(A)) = k14_qc_lang2(A))) # label(d19_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4105 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r2_qc_lang2(B,A) & r2_qc_lang2(A,B) -> B = A))))) # label(t78_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4106 (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]. 29.18/28.76 4107 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> k9_cqc_lang = k17_cqc_lang(k9_cqc_lang,A))) # label(t28_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4108 (all A all B all C (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k7_qc_lang1(A)) & m1_qc_lang1(C,A) & v1_cqc_lang(C,A) -> 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]. 29.18/28.76 4109 (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) -> k20_qc_lang1(B) = A | k17_cqc_lang(B,A) = k14_qc_lang1(k20_qc_lang1(B),k17_cqc_lang(k21_qc_lang1(B),A))))))) # label(t36_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4110 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v2_qc_lang1(B) -> k9_qc_lang1(k15_qc_lang1(B),k4_cqc_lang(k16_qc_lang1(B),k6_cqc_lang(k3_qc_lang3(np__0),A))) = k17_cqc_lang(B,A)))))) # label(t29_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4111 $T # label(t9_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4112 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m1_qc_lang1(B,A) -> (v1_cqc_lang(B,A) & m1_qc_lang1(B,A) <-> a_2_1_cqc_lang(A,B) = k1_xboole_0 & a_2_0_cqc_lang(A,B) = k1_xboole_0))))) # label(t15_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4113 (all A all B k3_cqc_lang(A,B) = k2_funcop_1(k1_tarski(A),B)) # label(d2_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4114 $T # label(t1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4115 $T # label(t14_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4116 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> k17_cqc_lang(k13_qc_lang1(B,C),A) = k13_qc_lang1(k17_cqc_lang(B,A),k17_cqc_lang(C,A)))))))) # label(t34_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4117 (all A all B (m1_subset_1(B,k7_cqc_lang) & m1_subset_1(A,k2_qc_lang1) -> k15_cqc_lang(A,B) = k14_qc_lang1(A,B))) # label(redefinition_k15_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4118 (all A all B (v1_relat_1(k3_cqc_lang(A,B)) & v1_funct_1(k3_cqc_lang(A,B)))) # label(fc1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4119 (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]. 29.18/28.76 4120 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (m2_subset_1(k13_qc_lang1(A,B),k8_qc_lang1,k7_cqc_lang) <-> m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) & m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)))))) # label(t19_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4121 (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]. 29.18/28.76 4122 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m1_subset_1(B,f1_s7_cqc_lang) -> (B = f2_s7_cqc_lang(A) <-> (exists C (v1_funct_1(C) & v1_funct_2(C,k7_cqc_lang,f1_s7_cqc_lang) & f3_s7_cqc_lang = k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k9_cqc_lang) & (all D (m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) -> (all E (m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (all H (m1_qc_lang1(H,G) & v1_cqc_lang(H,G) -> (all I (m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G)) -> f4_s7_cqc_lang(G,I,H) = k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k8_cqc_lang(G,I,H)) & f8_s7_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,D)) = k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k15_cqc_lang(F,D)) & k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k11_cqc_lang(D,E)) = f7_s7_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,E)) & f5_s7_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,D)) = k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k10_cqc_lang(D)))))))))))))) & k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,A) = B & m2_relset_1(C,k7_cqc_lang,f1_s7_cqc_lang)))))))) -> f5_s7_cqc_lang(f2_s7_cqc_lang(f6_s7_cqc_lang)) = f2_s7_cqc_lang(k10_cqc_lang(f6_s7_cqc_lang)) # label(s7_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.76 4123 (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]. 29.18/28.76 4124 (all A all B all C all D all E (m1_subset_1(E,A) & m1_subset_1(D,A) & -v1_xboole_0(A) -> k2_cqc_lang(A,B,C,D,E) = k1_cqc_lang(B,C,D,E))) # label(redefinition_k2_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.77 4125 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k17_cqc_lang(k12_qc_lang1(B),A) = k12_qc_lang1(k17_cqc_lang(B,A)))))) # label(t32_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.77 4126 (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]. 29.18/28.77 4127 (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]. 29.18/28.77 4128 (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]. 29.18/28.77 4129 (all A all B (m1_subset_1(B,k7_cqc_lang) & m1_subset_1(A,k7_cqc_lang) -> k12_cqc_lang(A,B) = k2_qc_lang2(A,B))) # label(redefinition_k12_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.77 4130 (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]. 29.18/28.77 4131 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m1_subset_1(B,f1_s8_cqc_lang) -> ((exists C (v1_funct_1(C) & (all D (m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) -> (all E (m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (all H (v1_cqc_lang(H,G) & m1_qc_lang1(H,G) -> (all I (m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G)) -> k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s8_cqc_lang(G,I,H) & f6_s8_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,E)) = k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k11_cqc_lang(D,E)) & f9_s8_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,D)) = k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k15_cqc_lang(F,D)) & 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)))))))))))))) & f3_s8_cqc_lang = k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k9_cqc_lang) & B = k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,A) & m2_relset_1(C,k7_cqc_lang,f1_s8_cqc_lang) & v1_funct_2(C,k7_cqc_lang,f1_s8_cqc_lang))) <-> f2_s8_cqc_lang(A) = B))))) -> 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]. 29.18/28.77 4132 (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]. 29.18/28.77 4133 (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]. 29.18/28.77 4134 (all A all B (m1_subset_1(A,k2_qc_lang1) & m1_subset_1(B,k7_cqc_lang) -> k16_cqc_lang(A,B) = k5_qc_lang2(A,B))) # label(redefinition_k16_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.77 4135 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m1_subset_1(B,f1_s5_cqc_lang) -> (f2_s5_cqc_lang(A) = B <-> (exists C (v1_funct_1(C) & v1_funct_2(C,k7_cqc_lang,f1_s5_cqc_lang) & m2_relset_1(C,k7_cqc_lang,f1_s5_cqc_lang) & B = k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,A) & k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k9_cqc_lang) = f3_s5_cqc_lang & (all D (m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) -> (all E (m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (all H (v1_cqc_lang(H,G) & m1_qc_lang1(H,G) -> (all I (m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G)) -> f6_s5_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,E)) = k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k11_cqc_lang(D,E)) & k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,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,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,k8_cqc_lang(G,I,H)) = f4_s5_cqc_lang(G,I,H)))))))))))))))))))) -> f3_s5_cqc_lang = f2_s5_cqc_lang(k9_cqc_lang) # label(s5_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.77 4136 (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) -> (k4_cqc_lang(A,B) = C <-> (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)))))) & k3_finseq_1(C) = k3_finseq_1(A)))))))) # label(d3_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.77 4137 $T # label(t25_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.77 4138 (all A (m1_subset_1(A,k8_qc_lang1) -> (k1_xboole_0 = k6_qc_lang3(A) & k5_qc_lang3(A) = k1_xboole_0 <-> m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)))) # label(t13_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.77 4139 (all A all B (m1_subset_1(A,k8_qc_lang1) & m1_subset_1(B,k2_qc_lang1) -> m1_subset_1(k17_cqc_lang(A,B),k8_qc_lang1))) # label(dt_k17_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.77 4140 (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]. 29.18/28.77 4141 (all A all B (m1_subset_1(B,k2_qc_lang1) & m1_subset_1(A,k4_qc_lang1) -> v1_funct_1(k6_cqc_lang(A,B)) & m2_relset_1(k6_cqc_lang(A,B),k4_qc_lang1,k1_qc_lang1))) # label(dt_k6_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.77 4142 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m1_qc_lang1(B,A) -> (v1_cqc_lang(B,A) <-> r1_tarski(k2_relat_1(B),k2_qc_lang1)))))) # label(d5_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.77 4143 $T # label(t12_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.77 4144 $T # label(t27_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.77 4145 (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]. 29.18/28.77 4146 (all A (-(-r2_hidden(A,k4_qc_lang1) & -r2_hidden(A,k2_qc_lang1) & -r2_hidden(A,k3_qc_lang1)) <-> r2_hidden(A,k1_qc_lang1))) # label(t7_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.77 4147 (all A all B B = k1_funct_1(k3_cqc_lang(A,B),A)) # label(t6_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.77 4148 (exists A ((exists B (m2_relset_1(B,k7_cqc_lang,f1_s4_cqc_lang) & A = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,f2_s4_cqc_lang) & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,k9_cqc_lang) = f3_s4_cqc_lang & (all C (m2_subset_1(C,k8_qc_lang1,k7_cqc_lang) -> (all D (m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) -> (all E (m2_subset_1(E,k1_qc_lang1,k2_qc_lang1) -> (all F (m2_subset_1(F,k1_numbers,k5_numbers) -> (all G (v1_cqc_lang(G,F) & m1_qc_lang1(G,F) -> (all H (m2_subset_1(H,k5_qc_lang1,k7_qc_lang1(F)) -> k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,k15_cqc_lang(E,C)) = f7_s4_cqc_lang(E,k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,C)) & f6_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,C),k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,D)) = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,k11_cqc_lang(C,D)) & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,k10_cqc_lang(C)) = f5_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,C)) & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,k8_cqc_lang(F,H,G)) = f4_s4_cqc_lang(F,H,G))))))))))))) & v1_funct_2(B,k7_cqc_lang,f1_s4_cqc_lang) & v1_funct_1(B))) & m1_subset_1(A,f1_s4_cqc_lang))) # label(s4_cqc_lang_AndLHS) # label(axiom) # label(non_clause). [assumption]. 29.18/28.77 4149 (all A (m1_subset_1(A,f1_s4_cqc_lang) -> (all B (m1_subset_1(B,f1_s4_cqc_lang) -> -((exists C (v1_funct_1(C) & v1_funct_2(C,k7_cqc_lang,f1_s4_cqc_lang) & m2_relset_1(C,k7_cqc_lang,f1_s4_cqc_lang) & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,f2_s4_cqc_lang) = A & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k9_cqc_lang) = f3_s4_cqc_lang & (all D (m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) -> (all E (m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (all H (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,k15_cqc_lang(F,D)) = f7_s4_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D)) & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,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)) & f5_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D)) = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k10_cqc_lang(D)))))))))))))))) & A != B & (exists C (v1_funct_2(C,k7_cqc_lang,f1_s4_cqc_lang) & m2_relset_1(C,k7_cqc_lang,f1_s4_cqc_lang) & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,f2_s4_cqc_lang) = B & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k9_cqc_lang) = f3_s4_cqc_lang & (all D (m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) -> (all E (m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (all H (v1_cqc_lang(H,G) & m1_qc_lang1(H,G) -> (all I (m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G)) -> f4_s4_cqc_lang(G,I,H) = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k8_cqc_lang(G,I,H)) & 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)) & f7_s4_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D)) = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k15_cqc_lang(F,D)) & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k10_cqc_lang(D)) = f5_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D)))))))))))))) & v1_funct_1(C)))))))) # label(s4_cqc_lang_AndRHS) # label(axiom) # label(non_clause). [assumption]. 29.18/28.77 4150 $T # label(t8_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.77 4151 $T # label(dt_k3_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.77 4152 (all A all B (v1_funct_1(B) & m1_relset_1(B,k4_qc_lang1,k1_qc_lang1) & m1_finseq_1(A,k1_qc_lang1) -> m2_finseq_1(k4_cqc_lang(A,B),k1_qc_lang1))) # label(dt_k4_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.77 4153 (all A all B (m1_subset_1(A,k2_qc_lang1) & m1_subset_1(B,k7_cqc_lang) -> m2_subset_1(k16_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang))) # label(dt_k16_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.77 4154 (all A all B (m1_subset_1(B,k2_qc_lang1) & m1_subset_1(A,k4_qc_lang1) -> k6_cqc_lang(A,B) = k3_cqc_lang(A,B))) # label(redefinition_k6_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.77 4155 (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]. 29.18/28.77 4156 (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 (r1_xreal_0(np__1,D) & r2_hidden(k1_funct_1(C,D),k4_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_0_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.77 4157 (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]. 29.18/28.78 4158 $T # label(t26_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4159 (all A all B (m1_subset_1(B,k7_cqc_lang) & m1_subset_1(A,k2_qc_lang1) -> m2_subset_1(k15_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang))) # label(dt_k15_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4160 (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]. 29.18/28.78 4161 $T # label(t2_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4162 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k4_qc_lang1) -> v1_funct_1(k3_cqc_lang(B,A)) & m2_relset_1(k3_cqc_lang(B,A),k4_qc_lang1,k1_qc_lang1))))) # label(t10_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4163 (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]. 29.18/28.78 4164 (all A all B (m1_subset_1(A,k7_cqc_lang) & m1_subset_1(B,k7_cqc_lang) -> k11_cqc_lang(A,B) = k13_qc_lang1(A,B))) # label(redefinition_k11_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4165 (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]. 29.18/28.78 4166 (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 (m2_subset_1(D,k1_numbers,k5_numbers) & r1_xreal_0(np__1,D) & r1_xreal_0(D,k3_finseq_1(C)) & r2_hidden(k1_funct_1(C,D),k3_qc_lang1) & A = k1_funct_1(C,D)))))) # label(fraenkel_a_2_1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4167 (all A all B (k1_tarski(A) = k1_relat_1(k3_cqc_lang(A,B)) & k1_tarski(B) = k2_relat_1(k3_cqc_lang(A,B)))) # label(t5_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4168 (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) -> (a_2_0_cqc_lang(A,C) = k1_xboole_0 & k1_xboole_0 = a_2_1_cqc_lang(A,C) <-> m2_subset_1(k9_qc_lang1(B,C),k8_qc_lang1,k7_cqc_lang)))))))) # label(t17_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4169 (all A all B all C all D all E (-v1_xboole_0(A) & m1_subset_1(E,A) & m1_subset_1(D,A) -> m1_subset_1(k2_cqc_lang(A,B,C,D,E),A))) # label(dt_k2_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4170 k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,k9_cqc_lang) = f4_s3_cqc_lang & k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,k9_cqc_lang) = f4_s3_cqc_lang & (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (v1_cqc_lang(E,D) & m1_qc_lang1(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)) & 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,k10_cqc_lang(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,k15_cqc_lang(C,A)) & f7_s3_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,A),k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,B)) = k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,k11_cqc_lang(A,B)))))))))))))) & (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)) -> f6_s3_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,A)) = k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,k10_cqc_lang(A)) & k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,k15_cqc_lang(C,A)) = f8_s3_cqc_lang(C,k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,A)) & k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,k11_cqc_lang(A,B)) = f7_s3_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,A),k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,B)) & f5_s3_cqc_lang(D,F,E) = k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,k8_cqc_lang(D,F,E)))))))))))))) -> f3_s3_cqc_lang = f2_s3_cqc_lang # label(s3_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4171 $T # label(t4_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4172 (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]. 29.18/28.78 4173 $T # label(dt_k1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4174 (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) -> (C = k17_cqc_lang(A,B) <-> (exists D (v1_funct_2(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) -> (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)))) & (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)) & (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)) & (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)) & k9_cqc_lang = k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,k9_cqc_lang))) & m2_relset_1(D,k8_qc_lang1,k8_qc_lang1) & v1_funct_1(D)))))))))) # label(d6_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4175 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (k20_qc_lang1(B) = A & v5_qc_lang1(B) -> B = k17_cqc_lang(B,A)))))) # label(t35_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4176 (all A all B (m1_subset_1(B,k7_cqc_lang) & m1_subset_1(A,k7_cqc_lang) -> m2_subset_1(k11_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang))) # label(dt_k11_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4177 (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 (m2_relset_1(F,k4_qc_lang1,k1_qc_lang1) & v1_funct_1(F) -> (r1_xreal_0(A,k3_finseq_1(E)) & r1_xreal_0(np__1,A) & D = k4_cqc_lang(E,F) & F = k6_cqc_lang(C,B) -> (C != k1_funct_1(E,A) -> k1_funct_1(E,A) = k1_funct_1(D,A)) & (k1_funct_1(E,A) = C -> B = k1_funct_1(D,A))))))))))))))) # label(t11_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4178 (all A all B all C (m1_subset_1(A,k5_numbers) & m1_qc_lang1(B,A) & m1_relset_1(C,k4_qc_lang1,k1_qc_lang1) & v1_funct_1(C) -> k4_cqc_lang(B,C) = k5_cqc_lang(A,B,C))) # label(redefinition_k5_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4179 (all A all B all C all D ((A = B -> C = k1_cqc_lang(A,B,C,D)) & (B != A -> k1_cqc_lang(A,B,C,D) = D))) # label(d1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4180 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> k17_cqc_lang(B,A) = B)))) # label(t40_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4181 (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) -> k9_qc_lang1(B,C) = k8_cqc_lang(A,B,C))) # label(redefinition_k8_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4182 $T # label(t3_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4183 (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]. 29.18/28.78 4184 (all A (r2_hidden(A,a_0_0_cqc_lang) <-> (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))))) # label(fraenkel_a_0_0_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4185 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (B != A -> k17_cqc_lang(k14_qc_lang1(A,C),B) = k14_qc_lang1(A,k17_cqc_lang(C,B))))))))) # label(t38_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4186 (all A all B (m1_subset_1(A,k7_cqc_lang) & m1_subset_1(B,k7_cqc_lang) -> k13_cqc_lang(A,B) = k3_qc_lang2(A,B))) # label(redefinition_k13_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4187 (all A (m1_subset_1(A,k5_numbers) -> (exists B (v1_funct_1(B) & v1_cqc_lang(B,A) & v1_finseq_1(B) & v1_relat_1(B) & m1_qc_lang1(B,A))))) # label(rc1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4188 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m1_subset_1(B,f1_s6_cqc_lang) -> ((exists C (v1_funct_1(C) & (all D (m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) -> (all E (m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (all H (m1_qc_lang1(H,G) & v1_cqc_lang(H,G) -> (all I (m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G)) -> k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s6_cqc_lang(G,I,H) & k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k11_cqc_lang(D,E)) = f9_s6_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,E)) & f10_s6_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,D)) = k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k15_cqc_lang(F,D)) & k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k10_cqc_lang(D)) = f8_s6_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,D)))))))))))))) & f2_s6_cqc_lang = k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k9_cqc_lang) & k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,A) = B & m2_relset_1(C,k7_cqc_lang,f1_s6_cqc_lang) & v1_funct_2(C,k7_cqc_lang,f1_s6_cqc_lang))) <-> B = f3_s6_cqc_lang(A)))))) -> f4_s6_cqc_lang(f5_s6_cqc_lang,f6_s6_cqc_lang,f7_s6_cqc_lang) = f3_s6_cqc_lang(k8_cqc_lang(f5_s6_cqc_lang,f6_s6_cqc_lang,f7_s6_cqc_lang)) # label(s6_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4189 (all A all B all C (m1_subset_1(A,k5_numbers) & v1_funct_1(C) & m1_relset_1(C,k4_qc_lang1,k1_qc_lang1) & 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]. 29.18/28.78 4190 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m1_subset_1(B,f1_s9_cqc_lang) -> (f2_s9_cqc_lang(A) = B <-> (exists C (v1_funct_1(C) & v1_funct_2(C,k7_cqc_lang,f1_s9_cqc_lang) & k8_funct_2(k7_cqc_lang,f1_s9_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 (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,k10_cqc_lang(D)) = f5_s9_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,D)) & f7_s9_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,D)) = k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k15_cqc_lang(F,D)) & f6_s9_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,E)) = k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k11_cqc_lang(D,E)) & f4_s9_cqc_lang(G,I,H) = k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k8_cqc_lang(G,I,H)))))))))))))) & k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k9_cqc_lang) = f3_s9_cqc_lang & m2_relset_1(C,k7_cqc_lang,f1_s9_cqc_lang)))))))) -> 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]. 29.18/28.78 4191 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (m1_qc_lang1(E,D) & v1_cqc_lang(E,D) -> (all F (m2_subset_1(F,k5_qc_lang1,k7_qc_lang1(D)) -> (p1_s1_cqc_lang(A) -> p1_s1_cqc_lang(k10_cqc_lang(A))) & (p1_s1_cqc_lang(A) & p1_s1_cqc_lang(B) -> p1_s1_cqc_lang(k11_cqc_lang(A,B))) & (p1_s1_cqc_lang(A) -> p1_s1_cqc_lang(k15_cqc_lang(C,A))) & p1_s1_cqc_lang(k8_cqc_lang(D,F,E)) & p1_s1_cqc_lang(k9_cqc_lang))))))))))))) -> (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> p1_s1_cqc_lang(A))) # label(s1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4192 (exists A ((all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> (all C (m2_subset_1(C,k8_qc_lang1,k7_cqc_lang) -> (all D (m2_subset_1(D,k1_qc_lang1,k2_qc_lang1) -> (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (all F (v1_cqc_lang(F,E) & m1_qc_lang1(F,E) -> (all G (m2_subset_1(G,k5_qc_lang1,k7_qc_lang1(E)) -> k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k8_cqc_lang(E,G,F)) = f3_s2_cqc_lang(E,G,F) & k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k10_cqc_lang(B)) = f4_s2_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,B)) & k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k15_cqc_lang(D,B)) = f6_s2_cqc_lang(D,k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,B)) & f5_s2_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,B),k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,C)) = k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k11_cqc_lang(B,C)))))))))))))) & k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k9_cqc_lang) = f2_s2_cqc_lang & m2_relset_1(A,k7_cqc_lang,f1_s2_cqc_lang) & v1_funct_2(A,k7_cqc_lang,f1_s2_cqc_lang) & v1_funct_1(A))) # label(s2_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4193 (all A all B (m1_subset_1(B,k7_cqc_lang) & m1_subset_1(A,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]. 29.18/28.78 4194 (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]. 29.18/28.78 4195 (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]. 29.18/28.78 4196 (all A all B all C all D (v1_funct_1(C) & m1_pboole(D,B) & v2_relat_1(D) & m1_relset_1(C,A,B) & v1_funct_2(C,A,B) & -v1_xboole_0(B) -> k5_relat_1(C,D) = k8_pboole(A,B,C,D))) # label(redefinition_k8_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4197 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> m1_pboole(k12_pboole(A,B,C),A))) # label(dt_k12_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4198 (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]. 29.18/28.78 4199 (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]. 29.18/28.78 4200 (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]. 29.18/28.78 4201 $T # label(t90_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4202 (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]. 29.18/28.78 4203 (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]. 29.18/28.78 4204 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r1_pboole(A,B,C) & r1_pboole(A,B,D) -> r4_pboole(A,C,D)))))))) # label(t10_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4205 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r4_pboole(A,B,k3_pboole(A,C,D)) -> r4_pboole(A,B,D) & r4_pboole(A,B,C)))))))) # label(t111_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4206 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k4_pboole(A,B,k2_pboole(A,C,B)),k1_pboole(A)) & r6_pboole(A,k4_pboole(A,B,k2_pboole(A,B,C)),k1_pboole(A)))))) # label(t67_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4207 (all A all B (m1_pboole(B,A) -> ((all C (r2_hidden(C,A) -> v1_xboole_0(k1_funct_1(B,C)))) <-> v3_relat_1(B)))) # label(d15_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4208 (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]. 29.18/28.78 4209 (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]. 29.18/28.78 4210 (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]. 29.18/28.78 4211 (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]. 29.18/28.78 4212 (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]. 29.18/28.78 4213 $T # label(t117_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4214 (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]. 29.18/28.78 4215 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> k2_pboole(A,k4_pboole(A,B,C),k4_pboole(A,C,B)) = k5_pboole(A,B,C))))) # label(d12_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4216 (exists A (v3_relat_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc1_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4217 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> (C = B <-> r6_pboole(A,B,C)))) # label(redefinition_r6_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4218 (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]. 29.18/28.78 4219 (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]. 29.18/28.78 4220 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k3_pboole(A,k2_pboole(A,B,C),B),B) & r6_pboole(A,k3_pboole(A,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,B,k2_pboole(A,B,C)),B))))) # label(t36_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4221 (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]. 29.18/28.78 4222 (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]. 29.18/28.78 4223 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r1_pboole(A,B,C) & r2_pboole(A,C,D) -> r1_pboole(A,B,D)))))))) # label(t9_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4224 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k4_pboole(A,B,k3_pboole(A,B,C)),k4_pboole(A,B,C)) & r6_pboole(A,k4_pboole(A,B,k3_pboole(A,C,B)),k4_pboole(A,B,C)))))) # label(t76_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4225 (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]. 29.18/28.78 4226 (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]. 29.18/28.78 4227 $T # label(t93_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4228 (all A all B (m1_pboole(B,A) -> r2_pboole(A,k1_pboole(A),B))) # label(t49_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4229 (all A all B (m1_pboole(B,A) -> ((all C (r2_hidden(C,A) -> k1_funct_1(B,C) = k1_xboole_0)) -> B = k1_pboole(A)))) # label(t6_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4230 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,k3_pboole(A,C,D)) -> r2_pboole(A,B,C) & r2_pboole(A,B,D)))))))) # label(t44_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4231 (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) & r4_pboole(A,B,D) & r2_pboole(A,B,C) -> r4_pboole(A,C,E)))))))))) # label(t110_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4232 (all A all B all C (m1_pboole(B,A) & m1_subset_1(C,A) & v2_relat_1(B) & -v1_xboole_0(A) -> -v1_xboole_0(k1_funct_1(B,C)))) # label(fc2_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4233 (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]. 29.18/28.78 4234 (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]. 29.18/28.78 4235 $T # label(t30_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4236 (all A all B (m2_relset_1(B,k5_numbers,k3_finseq_2(k1_tarski(A))) & v1_funct_2(B,k5_numbers,k3_finseq_2(k1_tarski(A))) & v1_funct_1(B) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k8_funct_2(k5_numbers,k3_finseq_2(k1_tarski(A)),B,C) = k2_finseq_2(C,A))) <-> B = k9_pboole(A)))) # label(d20_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4237 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r4_pboole(A,B,C) | r4_pboole(A,B,D) -> r4_pboole(A,B,k2_pboole(A,C,D))))))))) # label(t106_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4238 (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]. 29.18/28.78 4239 (all A m1_pboole(k1_pboole(A),A)) # label(dt_k1_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4240 $T # label(t131_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4241 (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]. 29.18/28.78 4242 $T # label(d2_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4243 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> k2_pboole(A,B,B) = B)) # label(idempotence_k2_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4244 (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]. 29.18/28.78 4245 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> r7_pboole(A,B,B))) # label(reflexivity_r7_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.78 4246 (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]. 29.18/28.79 4247 (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]. 29.18/28.79 4248 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,k3_finseq_2(A)) -> ((all D (m2_finseq_2(D,A,k3_finseq_2(A)) -> k1_funct_1(C,D) = k4_card_3(k5_relat_1(D,B)))) <-> C = k6_pboole(A,B)))))) # label(d19_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4249 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) & r2_pboole(A,C,B) <-> r6_pboole(A,B,C)))))) # label(d13_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4250 $T # label(t33_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4251 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,D,C) & r2_pboole(A,B,C) -> r2_pboole(A,k2_pboole(A,B,D),C)))))))) # label(t18_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4252 (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]. 29.18/28.79 4253 (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]. 29.18/28.79 4254 (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]. 29.18/28.79 4255 (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]. 29.18/28.79 4256 (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]. 29.18/28.79 4257 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,k4_pboole(A,B,C),D) & r2_pboole(A,k4_pboole(A,C,B),D) -> r2_pboole(A,k5_pboole(A,B,C),D)))))))) # label(t99_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4258 (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]. 29.18/28.79 4259 (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]. 29.18/28.79 4260 (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]. 29.18/28.79 4261 (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]. 29.18/28.79 4262 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,k2_pboole(A,B,C),D) -> r2_pboole(A,C,D) & r2_pboole(A,B,D)))))))) # label(t43_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4263 (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]. 29.18/28.79 4264 (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]. 29.18/28.79 4265 (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) -> m1_pboole(k7_pboole(A,B,C,D),A))) # label(dt_k7_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4266 (all A all B (m1_pboole(B,A) & v2_relat_1(B) -> v1_funct_1(k6_pboole(A,B)) & -v3_relat_1(k6_pboole(A,B)) & v2_relat_1(k6_pboole(A,B)) & v1_relat_1(k6_pboole(A,B)))) # label(fc1_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4267 (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]. 29.18/28.79 4268 (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]. 29.18/28.79 4269 (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]. 29.18/28.79 4270 (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]. 29.18/28.79 4271 (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]. 29.18/28.79 4272 (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]. 29.18/28.79 4273 (exists A (m1_pboole(A,f1_s4_pboole) & (all B (r2_hidden(B,f1_s4_pboole) -> k1_funct_1(A,B) = f2_s4_pboole(B))))) # label(s4_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4274 (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]. 29.18/28.79 4275 $T # label(t14_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4276 (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]. 29.18/28.79 4277 (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) & (all E (m1_pboole(E,A) -> (r2_pboole(A,E,C) & r2_pboole(A,E,D) -> r2_pboole(A,E,B)))) <-> r6_pboole(A,B,k3_pboole(A,C,D))))))))) # label(t29_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4278 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> ((all D (m1_pboole(D,A) -> (r1_pboole(A,D,B) -> r1_pboole(A,D,C)))) <-> r7_pboole(A,B,C)))))) # label(d14_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4279 (all A all B (m2_relset_1(k10_pboole(A,B),A,k1_tarski(B)) & v1_funct_2(k10_pboole(A,B),A,k1_tarski(B)) & v1_funct_1(k10_pboole(A,B)))) # label(dt_k10_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4280 (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]. 29.18/28.79 4281 (all A (m2_relset_1(k9_pboole(A),k5_numbers,k3_finseq_2(k1_tarski(A))) & v1_funct_2(k9_pboole(A),k5_numbers,k3_finseq_2(k1_tarski(A))) & v1_funct_1(k9_pboole(A)))) # label(dt_k9_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4282 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> m1_pboole(k3_pboole(A,B,C),A))) # label(dt_k3_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4283 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_relat_1(A) -> v1_setfam_1(k2_relat_1(A))))) # label(t1_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4284 (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) & r6_pboole(A,k3_pboole(A,C,D),k1_pboole(A)) -> r6_pboole(A,B,k1_pboole(A))))))))) # label(t51_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4285 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> ((all D (r2_hidden(D,A) -> k1_funct_1(C,D) = k1_funct_1(B,D))) -> C = B))))) # label(t3_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4286 (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]. 29.18/28.79 4287 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> -(r4_pboole(A,B,B) & k1_pboole(A) = B))))) # label(t140_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4288 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> m1_pboole(k4_pboole(A,B,C),A))) # label(dt_k4_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4289 (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]. 29.18/28.79 4290 (all A exists B m1_pboole(B,A)) # label(existence_m1_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4291 (all A all B (m1_pboole(B,A) -> r6_pboole(A,k2_pboole(A,B,k1_pboole(A)),B) & r6_pboole(A,k2_pboole(A,k1_pboole(A),B),B))) # label(t53_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4292 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k3_pboole(A,B,k3_pboole(A,B,C)),k3_pboole(A,B,C)) & r6_pboole(A,k3_pboole(A,k3_pboole(A,B,C),C),k3_pboole(A,B,C)))))) # label(t48_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4293 (all A (m1_pboole(A,k1_xboole_0) -> A = k1_xboole_0)) # label(t134_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4294 (all A all B all C (-v1_xboole_0(A) & m1_pboole(B,A) & m1_pboole(C,A) -> (r3_pboole(A,B,C) -> -r3_pboole(A,C,B)))) # label(antisymmetry_r3_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4295 (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]. 29.18/28.79 4296 (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]. 29.18/28.79 4297 (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]. 29.18/28.79 4298 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r6_pboole(A,k2_pboole(A,B,C),k1_pboole(A)) -> r6_pboole(A,C,k1_pboole(A)) & r6_pboole(A,B,k1_pboole(A))))))) # label(t54_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4299 (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]. 29.18/28.79 4300 $T # label(t125_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4301 $T # label(t13_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4302 (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]. 29.18/28.79 4303 (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]. 29.18/28.79 4304 $T # label(t31_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4305 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (v2_relat_1(B) & r2_pboole(A,B,C) -> v2_relat_1(C)))))) # label(t143_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4306 (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]. 29.18/28.79 4307 (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]. 29.18/28.79 4308 (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]. 29.18/28.79 4309 (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]. 29.18/28.79 4310 (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]. 29.18/28.79 4311 (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]. 29.18/28.79 4312 (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]. 29.18/28.79 4313 (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]. 29.18/28.79 4314 (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]. 29.18/28.79 4315 (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]. 29.18/28.79 4316 (all A all B (m1_pboole(B,A) & v2_relat_1(B) -> (exists C (m4_pboole(C,A,B) & v1_funct_1(C) & v2_relat_1(C) & v1_relat_1(C))))) # label(rc5_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4317 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B all C k5_relat_1(k2_finseq_2(A,B),k2_funcop_1(k1_tarski(B),C)) = k2_finseq_2(A,C)))) # label(t152_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4318 (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]. 29.18/28.79 4319 (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]. 29.18/28.79 4320 (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]. 29.18/28.79 4321 (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]. 29.18/28.79 4322 (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]. 29.18/28.79 4323 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> k2_pboole(A,C,B) = k2_pboole(A,B,C))) # label(commutativity_k2_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4324 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k3_pboole(A,k4_pboole(A,B,C),C),k1_pboole(A)) & r6_pboole(A,k3_pboole(A,C,k4_pboole(A,B,C)),k1_pboole(A)))))) # label(t69_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4325 (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]. 29.18/28.79 4326 (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]. 29.18/28.79 4327 $T # label(t107_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4328 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> (all C (m1_subset_1(C,k2_relat_1(B)) -> (exists D (C = k1_funct_1(B,D) & r2_hidden(D,A))))))))) # label(t150_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4329 (all A all B (m1_pboole(B,A) -> ((all C -(v1_xboole_0(k1_funct_1(B,C)) & r2_hidden(C,A))) <-> v2_relat_1(B)))) # label(d16_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4330 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k4_pboole(A,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]. 29.18/28.79 4331 (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]. 29.18/28.79 4332 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (D = k3_pboole(A,B,C) <-> (all E (r2_hidden(E,A) -> k1_funct_1(D,E) = k3_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E))))))))))) # label(d8_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4333 (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) -> r2_pboole(A,B,k3_pboole(A,C,D))))))))) # label(t19_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4334 (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]. 29.18/28.79 4335 (all A all B (m1_pboole(B,A) -> (v2_pboole(B,A) <-> v2_relat_1(B)))) # label(redefinition_v2_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4336 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> B = k3_pboole(A,B,B))) # label(idempotence_k3_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4337 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r4_pboole(A,B,C) <-> (all D -(r1_xboole_0(k1_funct_1(B,D),k1_funct_1(C,D)) & r2_hidden(D,A)))))))) # label(d10_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4338 (all A (v1_relat_1(A) & v1_funcop_1(A) & v1_funct_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) -> ((all D (r2_hidden(D,k1_relat_1(C)) -> k1_funct_1(C,D) = k5_relat_1(k1_funct_1(A,D),k1_funct_1(B,D)))) & k3_xboole_0(k1_relat_1(A),k1_relat_1(B)) = k1_relat_1(C) <-> C = k13_pboole(A,B)))))))) # label(d24_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4339 (all A all B (v1_relat_1(A) & v1_funcop_1(A) & v1_relat_1(B) & v1_funcop_1(B) & v1_funct_1(B) & v1_funct_1(A) -> v1_relat_1(k13_pboole(A,B)) & v1_funct_1(k13_pboole(A,B)) & v1_funcop_1(k13_pboole(A,B)))) # label(dt_k13_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4340 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> k5_pboole(A,B,C) = k5_pboole(A,C,B))) # label(commutativity_k5_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4341 (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]. 29.18/28.79 4342 (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]. 29.18/28.79 4343 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> (all D (m3_pboole(D,A,B,C) -> m1_pboole(D,A))))) # label(dt_m3_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4344 $T # label(t32_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4345 (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]. 29.18/28.79 4346 (all A exists B (v1_funct_1(B) & v1_funcop_1(B) & v1_relat_1(B) & m1_pboole(B,A))) # label(rc4_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4347 (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)) <-> (all E (m1_pboole(E,A) -> (r2_pboole(A,D,E) & r2_pboole(A,C,E) -> r2_pboole(A,B,E)))) & r2_pboole(A,D,B) & r2_pboole(A,C,B)))))))) # label(t28_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4348 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r5_pboole(A,E,C) & r5_pboole(A,D,B) & r6_pboole(A,k2_pboole(A,B,C),k2_pboole(A,D,E)) -> r6_pboole(A,D,C) & r6_pboole(A,E,B)))))))))) # label(t124_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4349 (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]. 29.18/28.79 4350 (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]. 29.18/28.79 4351 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> (r5_pboole(A,B,C) -> r5_pboole(A,C,B)))) # label(symmetry_r5_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4352 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> -r4_pboole(A,k1_pboole(A),B) & -r4_pboole(A,B,k1_pboole(A)))))) # label(t138_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4353 (all A (-v1_xboole_0(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C all D (m1_pboole(D,k1_tarski(C)) -> (k2_funcop_1(k1_tarski(C),A) = D -> k1_funct_2(k2_finseq_1(B),A) = k1_funct_1(k7_pboole(k5_numbers,k3_finseq_2(k1_tarski(C)),k9_pboole(C),k6_pboole(k1_tarski(C),D)),B)))))))) # label(t153_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4354 (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]. 29.18/28.79 4355 (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]. 29.18/28.79 4356 (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]. 29.18/28.79 4357 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> (r6_pboole(A,B,C) -> r6_pboole(A,C,B)))) # label(symmetry_r6_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4358 (all A all B k1_xboole_0 = k1_funct_1(k1_pboole(B),A)) # label(t5_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4359 (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]. 29.18/28.79 4360 (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]. 29.18/28.79 4361 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r5_pboole(A,C,D) & r2_pboole(A,B,D) & r2_pboole(A,B,C) -> r6_pboole(A,B,k1_pboole(A))))))))) # label(t123_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4362 (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]. 29.18/28.79 4363 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k2_pboole(A,k3_pboole(A,B,C),B),B) & r6_pboole(A,k2_pboole(A,k3_pboole(A,C,B),B),B) & r6_pboole(A,k2_pboole(A,B,k3_pboole(A,C,B)),B) & r6_pboole(A,k2_pboole(A,B,k3_pboole(A,B,C)),B))))) # label(t37_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4364 (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]. 29.18/28.79 4365 (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]. 29.18/28.79 4366 (all A k2_funcop_1(A,k1_xboole_0) = k1_pboole(A)) # label(d6_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4367 (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]. 29.18/28.79 4368 (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]. 29.18/28.79 4369 (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]. 29.18/28.79 4370 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v3_relat_1(A) <-> k1_xboole_0 = A | k2_relat_1(A) = k1_tarski(k1_xboole_0)))) # label(t2_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4371 (all A all B (m1_pboole(B,A) -> (all C (v1_funcop_1(C) & m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> ((all E (r2_hidden(E,A) -> k9_relat_1(k1_funct_1(C,E),k1_funct_1(B,E)) = k1_funct_1(D,E))) <-> k14_pboole(A,B,C) = D))))))) # label(d25_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4372 (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]. 29.18/28.79 4373 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> -(r4_pboole(A,B,C) & (all D (m1_pboole(D,A) -> -(r1_pboole(A,D,C) & r1_pboole(A,D,B))))))))) # label(t11_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4374 (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,C,B),C) & r6_pboole(A,k2_pboole(A,B,C),C)))))) # label(t24_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4375 (all A exists B (m1_pboole(B,A) & v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B))) # label(rc3_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4376 (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]. 29.18/28.79 4377 (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]. 29.18/28.79 4378 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r2_pboole(A,B,C) & r2_pboole(A,D,E) -> r2_pboole(A,k2_pboole(A,B,D),k2_pboole(A,C,E))))))))))) # label(t22_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4379 (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]. 29.18/28.79 4380 (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]. 29.18/28.79 4381 (all A exists B (v1_relat_1(B) & v1_funct_1(B) & v3_relat_1(B) & m1_pboole(B,A))) # label(rc2_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.79 4382 (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]. 29.18/28.80 4383 (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]. 29.18/28.80 4384 (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]. 29.18/28.80 4385 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r1_pboole(A,B,k3_pboole(A,C,D)) <-> r1_pboole(A,B,C) & r1_pboole(A,B,D)))))))) # label(t8_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.80 4386 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (v3_relat_1(B) & r2_pboole(A,C,B) -> v3_relat_1(C)))))) # label(t142_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.80 4387 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (m2_pboole(C,A,B) <-> (all D (r2_hidden(D,A) -> m1_subset_1(k1_funct_1(C,D),k1_funct_1(B,D))))))))) # label(d17_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.80 4388 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> ((all E (r2_hidden(E,A) -> v1_funct_1(k1_funct_1(D,E)) & m2_relset_1(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E)) & v1_funct_2(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E)))) <-> m3_pboole(D,A,B,C)))))))) # label(d18_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.80 4389 (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]. 29.18/28.80 4390 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (k2_pboole(A,B,C) = D <-> (all E (r2_hidden(E,A) -> k1_funct_1(D,E) = k2_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E))))))))))) # label(d7_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.80 4391 (all A all B all C (m1_pboole(C,A) & v1_funcop_1(C) & m1_pboole(B,A) -> m1_pboole(k14_pboole(A,B,C),A))) # label(dt_k14_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.80 4392 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (v2_relat_1(B) & r7_pboole(A,B,C) -> v2_relat_1(C)))))) # label(t145_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.80 4393 (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]. 29.18/28.80 4394 (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) -> k2_zfmisc_1(k1_funct_1(B,E),k1_funct_1(C,E)) = k1_funct_1(D,E)))))))))) # label(d21_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.80 4395 (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]. 29.18/28.80 4396 (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]. 29.18/28.80 4397 (all A -((all B -p1_s3_pboole(A,B)) & r2_hidden(A,f1_s3_pboole))) -> (exists A ((all B (r2_hidden(B,f1_s3_pboole) -> p1_s3_pboole(B,k1_funct_1(A,B)))) & m1_pboole(A,f1_s3_pboole))) # label(s3_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.80 4398 (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]. 29.18/28.80 4399 (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]. 29.18/28.80 4400 (exists A ((all B (m1_subset_1(B,f1_s5_pboole) -> k1_funct_1(A,B) = f2_s5_pboole(B))) & m1_pboole(A,f1_s5_pboole))) # label(s5_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.80 4401 (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]. 29.18/28.80 4402 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,k2_pboole(A,C,D)) & r6_pboole(A,k3_pboole(A,B,D),k1_pboole(A)) -> r2_pboole(A,B,C)))))))) # label(t56_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.80 4403 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k2_pboole(A,B,k4_pboole(A,C,B)),k2_pboole(A,B,C)) & r6_pboole(A,k2_pboole(A,k4_pboole(A,C,B),B),k2_pboole(A,C,B)))))) # label(t73_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.80 4404 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r6_pboole(A,k3_pboole(A,B,C),k1_pboole(A)) <-> r6_pboole(A,k4_pboole(A,B,C),B)))))) # label(t77_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.80 4405 (all A all B all C all D (v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_pboole(D,B) & v2_relat_1(D) & v1_funct_1(C) & -v1_xboole_0(B) -> v2_relat_1(k8_pboole(A,B,C,D)) & m1_pboole(k8_pboole(A,B,C,D),A))) # label(dt_k8_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.80 4406 (all A all B (m1_pboole(B,A) -> (all C (v2_relat_1(C) & m1_pboole(C,A) -> ((all D (m1_pboole(D,A) -> (r1_pboole(A,D,B) <-> r1_pboole(A,D,C)))) -> r6_pboole(A,C,B)))))) # label(t147_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.80 4407 (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]. 29.18/28.80 4408 (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]. 29.18/28.80 4409 (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]. 29.18/28.80 4410 (all A all B k2_funcop_1(A,B) = k10_pboole(A,B)) # label(redefinition_k10_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.80 4411 (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]. 29.18/28.80 4412 (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]. 29.18/28.80 4413 (all A all B all C all D (-v1_xboole_0(B) & v1_funct_1(C) & m1_relset_1(C,A,B) & m1_pboole(D,B) & v1_funct_2(C,A,B) -> k5_relat_1(C,D) = k7_pboole(A,B,C,D))) # label(redefinition_k7_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.80 4414 (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]. 29.18/28.80 4415 (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]. 29.18/28.80 4416 (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]. 29.18/28.80 4417 (all A all B (m1_pboole(B,A) -> -(r5_pboole(A,B,B) & B != k1_pboole(A)))) # label(t122_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.80 4418 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) -> r6_pboole(A,k3_pboole(A,C,B),B) & r6_pboole(A,k3_pboole(A,B,C),B)))))) # label(t25_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.80 4419 (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]. 29.18/28.80 4420 (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]. 29.18/28.80 4421 (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) & k3_pboole(A,C,D) = k1_pboole(A) & r3_pboole(A,B,C)))))))))) # label(t137_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.80 4422 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (D = k4_pboole(A,B,C) <-> (all E (r2_hidden(E,A) -> k1_funct_1(D,E) = k4_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E))))))))))) # label(d9_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.80 4423 (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]. 29.18/28.80 4424 $T # label(d1_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.80 4425 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k2_pboole(A,B,k3_pboole(A,C,D)),k3_pboole(A,k2_pboole(A,B,C),k2_pboole(A,B,D))) & r6_pboole(A,k2_pboole(A,k3_pboole(A,C,D),B),k3_pboole(A,k2_pboole(A,C,B),k2_pboole(A,D,B))))))))) # label(t39_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.80 4426 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r4_pboole(A,B,C) & r2_pboole(A,C,D) -> r4_pboole(A,B,D)))))))) # label(t108_pboole) # label(axiom) # label(non_clause). [assumption]. 29.18/28.80 4427 (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]. 29.18/28.80 4428 (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]. 29.18/28.80 4429 (exists 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) & v1_funct_1(A))) # label(s8_multop_1) # label(axiom) # label(non_clause). [assumption]. 29.18/28.80 4430 (all A all B all C all D all E all F all G all H all I all J (-v1_xboole_0(B) & -v1_xboole_0(E) & m1_relset_1(F,k4_zfmisc_1(A,B,C,D),E) & m1_subset_1(J,D) & m1_subset_1(I,C) & m1_subset_1(H,B) & m1_subset_1(G,A) & v1_funct_2(F,k4_zfmisc_1(A,B,C,D),E) & v1_funct_1(F) & -v1_xboole_0(D) & -v1_xboole_0(C) & -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]. 29.18/28.80 4431 (all A (m1_subset_1(A,f1_s1_multop_1) -> (all B (m1_subset_1(B,f2_s1_multop_1) -> (all C (m1_subset_1(C,f3_s1_multop_1) -> (exists D (p1_s1_multop_1(A,B,C,D) & m1_subset_1(D,f4_s1_multop_1))))))))) -> (exists A (v1_funct_1(A) & (all B (m1_subset_1(B,f1_s1_multop_1) -> (all C (m1_subset_1(C,f2_s1_multop_1) -> (all D (m1_subset_1(D,f3_s1_multop_1) -> p1_s1_multop_1(B,C,D,k8_funct_2(k3_zfmisc_1(f1_s1_multop_1,f2_s1_multop_1,f3_s1_multop_1),f4_s1_multop_1,A,k4_domain_1(f1_s1_multop_1,f2_s1_multop_1,f3_s1_multop_1,B,C,D))))))))) & m2_relset_1(A,k3_zfmisc_1(f1_s1_multop_1,f2_s1_multop_1,f3_s1_multop_1),f4_s1_multop_1) & v1_funct_2(A,k3_zfmisc_1(f1_s1_multop_1,f2_s1_multop_1,f3_s1_multop_1),f4_s1_multop_1))) # label(s1_multop_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.80 4432 (all A (-v1_xboole_0(A) -> (all B all C all D all E all F (v1_funct_1(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) -> (all G (v1_funct_1(G) & v1_funct_2(G,k4_zfmisc_1(B,C,D,E),A) & m2_relset_1(G,k4_zfmisc_1(B,C,D,E),A) -> ((all H all I all J all K (r2_hidden(I,C) & r2_hidden(K,E) & r2_hidden(J,D) & 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)))) -> G = F))))))) # label(t6_multop_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.80 4433 $T # label(dt_k1_multop_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.80 4434 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C all D k1_funct_1(A,k3_mcart_1(B,C,D)) = k1_multop_1(A,B,C,D)))) # label(d1_multop_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.80 4435 (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]. 29.26/28.80 4436 (all A all B all C all D all E all F all G all H (-v1_xboole_0(C) & 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(D) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k2_multop_1(A,B,C,D,E,F,G,H) = k1_multop_1(E,F,G,H))) # label(redefinition_k2_multop_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.80 4437 (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 (m2_relset_1(F,k3_zfmisc_1(B,C,D),A) & v1_funct_2(F,k3_zfmisc_1(B,C,D),A) & v1_funct_1(F) -> ((all G all H all I (r2_hidden(G,B) & r2_hidden(H,C) & r2_hidden(I,D) -> k1_funct_1(F,k3_mcart_1(G,H,I)) = k1_funct_1(E,k3_mcart_1(G,H,I)))) -> E = F))))))) # label(t2_multop_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.80 4438 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (m2_relset_1(F,k4_zfmisc_1(A,B,C,D),E) & v1_funct_2(F,k4_zfmisc_1(A,B,C,D),E) & v1_funct_1(F) -> (all G (v1_funct_1(G) & v1_funct_2(G,k4_zfmisc_1(A,B,C,D),E) & m2_relset_1(G,k4_zfmisc_1(A,B,C,D),E) -> ((all H (m1_subset_1(H,A) -> (all I (m1_subset_1(I,B) -> (all J (m1_subset_1(J,C) -> (all K (m1_subset_1(K,D) -> k4_multop_1(A,B,C,D,E,F,H,I,J,K) = k4_multop_1(A,B,C,D,E,G,H,I,J,K))))))))) -> G = F))))))))))))))) # label(t8_multop_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.80 4439 (exists A (v1_funct_1(A) & (all B (m1_subset_1(B,f1_s3_multop_1) -> (all C (m1_subset_1(C,f2_s3_multop_1) -> (all D (m1_subset_1(D,f3_s3_multop_1) -> 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) & v1_funct_2(A,k3_zfmisc_1(f1_s3_multop_1,f2_s3_multop_1,f3_s3_multop_1),f4_s3_multop_1))) # label(s3_multop_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.80 4440 (exists A (v1_funct_1(A) & v1_funct_2(A,k4_zfmisc_1(f1_s7_multop_1,f2_s7_multop_1,f3_s7_multop_1,f4_s7_multop_1),f5_s7_multop_1) & m2_relset_1(A,k4_zfmisc_1(f1_s7_multop_1,f2_s7_multop_1,f3_s7_multop_1,f4_s7_multop_1),f5_s7_multop_1) & (all B (m1_subset_1(B,f1_s7_multop_1) -> (all C (m1_subset_1(C,f2_s7_multop_1) -> (all D (m1_subset_1(D,f3_s7_multop_1) -> (all E (m1_subset_1(E,f4_s7_multop_1) -> f6_s7_multop_1(B,C,D,E) = k8_funct_2(k4_zfmisc_1(f1_s7_multop_1,f2_s7_multop_1,f3_s7_multop_1,f4_s7_multop_1),f5_s7_multop_1,A,k5_domain_1(f1_s7_multop_1,f2_s7_multop_1,f3_s7_multop_1,f4_s7_multop_1,B,C,D,E)))))))))))) # label(s7_multop_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.80 4441 (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_1(A) & v1_funct_2(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)))))))) & m2_relset_1(A,k3_zfmisc_1(f1_s2_multop_1,f1_s2_multop_1,f1_s2_multop_1),f1_s2_multop_1))) # label(s2_multop_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.80 4442 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C all D all E k1_funct_1(A,k4_mcart_1(B,C,D,E)) = k3_multop_1(A,B,C,D,E)))) # label(d2_multop_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.80 4443 $T # label(dt_k3_multop_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.80 4444 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,k3_zfmisc_1(A,B,C),D) & m2_relset_1(E,k3_zfmisc_1(A,B,C),D) -> (all F (v1_funct_1(F) & m2_relset_1(F,k3_zfmisc_1(A,B,C),D) & v1_funct_2(F,k3_zfmisc_1(A,B,C),D) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> k2_multop_1(A,B,C,D,F,G,H,I) = k2_multop_1(A,B,C,D,E,G,H,I))))))) -> E = F))))))))))))) # label(t4_multop_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.80 4445 (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_1(G) & m2_relset_1(G,k4_zfmisc_1(A,B,C,D),E) & v1_funct_2(G,k4_zfmisc_1(A,B,C,D),E) -> ((all H (m1_subset_1(H,A) -> (all I (m1_subset_1(I,B) -> (all J (m1_subset_1(J,C) -> (all K (m1_subset_1(K,D) -> k8_funct_2(k4_zfmisc_1(A,B,C,D),E,F,k5_domain_1(A,B,C,D,H,I,J,K)) = k8_funct_2(k4_zfmisc_1(A,B,C,D),E,G,k5_domain_1(A,B,C,D,H,I,J,K)))))))))) -> F = G))))))))))))))) # label(t7_multop_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.80 4446 $T # label(t5_multop_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.80 4447 (all A (m1_subset_1(A,f1_s6_multop_1) -> (all B (m1_subset_1(B,f1_s6_multop_1) -> (all C (m1_subset_1(C,f1_s6_multop_1) -> (all D (m1_subset_1(D,f1_s6_multop_1) -> (exists E (m1_subset_1(E,f1_s6_multop_1) & p1_s6_multop_1(A,B,C,D,E))))))))))) -> (exists A ((all B (m1_subset_1(B,f1_s6_multop_1) -> (all C (m1_subset_1(C,f1_s6_multop_1) -> (all D (m1_subset_1(D,f1_s6_multop_1) -> (all E (m1_subset_1(E,f1_s6_multop_1) -> p1_s6_multop_1(B,C,D,E,k4_multop_1(f1_s6_multop_1,f1_s6_multop_1,f1_s6_multop_1,f1_s6_multop_1,f1_s6_multop_1,A,B,C,D,E)))))))))) & m2_relset_1(A,k4_zfmisc_1(f1_s6_multop_1,f1_s6_multop_1,f1_s6_multop_1,f1_s6_multop_1),f1_s6_multop_1) & v1_funct_2(A,k4_zfmisc_1(f1_s6_multop_1,f1_s6_multop_1,f1_s6_multop_1,f1_s6_multop_1),f1_s6_multop_1) & v1_funct_1(A))) # label(s6_multop_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.80 4448 (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(B) & -v1_xboole_0(C) & -v1_xboole_0(D) & -v1_xboole_0(E) & v1_funct_1(F) & v1_funct_2(F,k4_zfmisc_1(A,B,C,D),E) & m1_subset_1(H,B) & m1_subset_1(J,D) & m1_subset_1(I,C) & m1_subset_1(G,A) & m1_relset_1(F,k4_zfmisc_1(A,B,C,D),E) -> 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]. 29.26/28.80 4449 (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 (p1_s5_multop_1(A,B,C,D,E) & m1_subset_1(E,f5_s5_multop_1))))))))))) -> (exists A ((all B (m1_subset_1(B,f1_s5_multop_1) -> (all C (m1_subset_1(C,f2_s5_multop_1) -> (all D (m1_subset_1(D,f3_s5_multop_1) -> (all E (m1_subset_1(E,f4_s5_multop_1) -> p1_s5_multop_1(B,C,D,E,k8_funct_2(k4_zfmisc_1(f1_s5_multop_1,f2_s5_multop_1,f3_s5_multop_1,f4_s5_multop_1),f5_s5_multop_1,A,k5_domain_1(f1_s5_multop_1,f2_s5_multop_1,f3_s5_multop_1,f4_s5_multop_1,B,C,D,E))))))))))) & m2_relset_1(A,k4_zfmisc_1(f1_s5_multop_1,f2_s5_multop_1,f3_s5_multop_1,f4_s5_multop_1),f5_s5_multop_1) & v1_funct_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) & v1_funct_1(A))) # label(s5_multop_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.80 4450 (all A all B all C all D all E all F all G all H (-v1_xboole_0(B) & -v1_xboole_0(C) & -v1_xboole_0(D) & v1_funct_1(E) & v1_funct_2(E,k3_zfmisc_1(A,B,C),D) & m1_subset_1(F,A) & m1_subset_1(G,B) & m1_subset_1(H,C) & m1_relset_1(E,k3_zfmisc_1(A,B,C),D) & -v1_xboole_0(A) -> m1_subset_1(k2_multop_1(A,B,C,D,E,F,G,H),D))) # label(dt_k2_multop_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.80 4451 $T # label(t1_multop_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.80 4452 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,k3_zfmisc_1(A,B,C),D) & m2_relset_1(E,k3_zfmisc_1(A,B,C),D) -> (all F (v1_funct_2(F,k3_zfmisc_1(A,B,C),D) & m2_relset_1(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) -> k8_funct_2(k3_zfmisc_1(A,B,C),D,E,k4_domain_1(A,B,C,G,H,I)) = k8_funct_2(k3_zfmisc_1(A,B,C),D,F,k4_domain_1(A,B,C,G,H,I)))))))) -> E = F))))))))))))) # label(t3_multop_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.80 4453 (all A all B (-v3_struct_0(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_struct_0(A) -> (all C (m1_struct_0(C,A,B) <-> m1_subset_1(C,B))))) # label(redefinition_m1_struct_0) # label(axiom) # label(non_clause). [assumption]. 29.26/28.80 4454 (all A all B (-v3_struct_0(A) & l1_struct_0(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_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]. 29.26/28.80 4455 (exists A (l1_struct_0(A) & -v3_struct_0(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption]. 29.26/28.80 4456 (all A all B (m1_subset_1(B,A) -> (all C all D (g2_struct_0(C,D) = g2_struct_0(A,B) -> C = A & B = D)))) # label(free_g2_struct_0) # label(axiom) # label(non_clause). [assumption]. 29.26/28.80 4457 (exists A l2_struct_0(A)) # label(existence_l2_struct_0) # label(axiom) # label(non_clause). [assumption]. 29.26/28.80 4458 (all A all B (l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & -v3_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]. 29.26/28.80 4459 (all A (v1_struct_0(g1_struct_0(A)) & l1_struct_0(g1_struct_0(A)))) # label(dt_g1_struct_0) # label(axiom) # label(non_clause). [assumption]. 29.26/28.80 4460 (all A all B (g1_struct_0(B) = g1_struct_0(A) -> A = B)) # label(free_g1_struct_0) # label(axiom) # label(non_clause). [assumption]. 29.26/28.80 4461 (all A (l1_struct_0(A) & -v3_struct_0(A) -> -v1_xboole_0(u1_struct_0(A)))) # label(fc1_struct_0) # label(axiom) # label(non_clause). [assumption]. 29.26/28.80 4462 (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]. 29.26/28.80 4463 (all A (-v3_struct_0(A) & l1_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]. 29.26/28.81 4464 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4465 (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]. 29.26/28.81 4466 (all A all B (-v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (exists C m1_struct_0(C,A,B)))) # label(existence_m1_struct_0) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4467 (all A (l2_struct_0(A) -> l1_struct_0(A))) # label(dt_l2_struct_0) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4468 (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) -> 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]. 29.26/28.81 4469 (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]. 29.26/28.81 4470 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4471 (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_struct_0(A,C,B) = k2_struct_0(A,B,C))) # label(commutativity_k2_struct_0) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4472 (all A all B (-v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) -> k1_tarski(B) = k1_struct_0(A,B))) # label(redefinition_k1_struct_0) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4473 (exists A (l1_struct_0(A) & v1_struct_0(A))) # label(rc1_struct_0) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4474 (exists A l1_struct_0(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4475 (exists A (v2_struct_0(A) & l2_struct_0(A))) # label(rc2_struct_0) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4476 (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]. 29.26/28.81 4477 (exists A (-v3_struct_0(A) & l2_struct_0(A))) # label(rc4_struct_0) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4478 (all A (l2_struct_0(A) -> (v2_struct_0(A) -> A = g2_struct_0(u1_struct_0(A),u2_struct_0(A))))) # label(abstractness_v2_struct_0) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4479 (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]. 29.26/28.81 4480 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,B,C) -> (all F (m1_cat_1(F,A,C,D) -> (v4_cat_1(k9_cat_1(A,B,C,D,E,F),A) -> k6_cat_1(A,B,C) = k1_xboole_0 | k1_xboole_0 = k6_cat_1(A,C,D) | v4_cat_1(F,A)))))))))))))) # label(t67_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4481 (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) <-> k6_cat_1(A,B,C) != k1_xboole_0 & k1_xboole_0 != k6_cat_1(A,C,B) & (exists D ((exists E (m1_cat_1(E,A,C,B) & 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(D,A,B,C)))))))))) # label(t81_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4482 (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]. 29.26/28.81 4483 $T # label(t16_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4484 (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]. 29.26/28.81 4485 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (v7_cat_1(C,A) & v7_cat_1(B,A) -> r1_cat_1(A,B,C)))))))) # label(t84_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4486 $T # label(t119_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4487 (all A all B all C all D all E all F (v1_funct_1(E) & v1_funct_1(F) & m1_relset_1(F,A,B) & v1_funct_2(F,A,B) & m1_relset_1(E,k2_zfmisc_1(B,B),B) & m1_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_1(D) & m1_relset_1(C,B,A) & v1_funct_2(C,B,A) & v1_funct_1(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> v1_cat_1(g1_cat_1(A,B,C,D,E,F)) & l1_cat_1(g1_cat_1(A,B,C,D,E,F)))) # label(dt_g1_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4488 (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]. 29.26/28.81 4489 (all A all B all 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)) = k1_relat_1(k1_cat_1(A,B,C)))) # label(t7_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4490 (all A all B all C all D (m1_subset_1(D,u1_cat_1(B)) & m1_subset_1(C,u1_cat_1(B)) & l1_cat_1(B) -> ((exists E (A = E & k3_cat_1(B,E) = D & C = k2_cat_1(B,E) & m1_subset_1(E,u2_cat_1(B)))) <-> r2_hidden(A,a_3_0_cat_1(B,C,D))))) # label(fraenkel_a_3_0_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4491 (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) & -r2_hidden(k4_cat_1(A,E,F),k6_cat_1(A,B,D)) & k6_cat_1(A,C,D) != k1_xboole_0))))))))))))) # label(t51_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4492 (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 (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]. 29.26/28.81 4493 (all A (l1_cat_1(A) & v2_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]. 29.26/28.81 4494 $T # label(t50_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4495 (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)) -> -(k6_cat_1(A,B,C) != k1_xboole_0 & k6_cat_1(A,B,D) = k1_xboole_0 & k1_xboole_0 != k6_cat_1(A,C,D)))))))))) # label(t52_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4496 (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]. 29.26/28.81 4497 (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) -> k6_cat_1(A,B,C) = k1_xboole_0 | v4_cat_1(D,A) | k6_cat_1(A,C,B) = k1_xboole_0))))))))))) # label(t68_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4498 (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]. 29.26/28.81 4499 $T # label(t5_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4500 (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]. 29.26/28.81 4501 (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))) -> k4_cat_1(A,B,C) = k1_funct_1(u5_cat_1(A),k4_tarski(C,B))))))))) # label(d4_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4502 (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]. 29.26/28.81 4503 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,B,C) -> (all F (m1_cat_1(F,A,C,D) -> (v3_cat_1(k9_cat_1(A,B,C,D,E,F),A) -> k6_cat_1(A,B,C) = k1_xboole_0 | k1_xboole_0 = k6_cat_1(A,C,D) | v3_cat_1(E,A)))))))))))))) # label(t62_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4504 $T # label(t12_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4505 $T # label(t79_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4506 (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 -> B = D & C = E | k6_cat_1(A,D,E) = k1_xboole_0 | k1_xboole_0 = k6_cat_1(A,B,C)))))))))))))))) # label(t24_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4507 (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]. 29.26/28.81 4508 (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)) -> 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]. 29.26/28.81 4509 (all A all B all C all D (m1_subset_1(D,k1_tarski(A)) -> (all E (m1_subset_1(E,k1_tarski(B)) -> k1_funct_1(k1_cat_1(A,B,C),k4_tarski(D,E)) = C)))) # label(t9_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4510 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,B,C) -> m2_cat_1(k7_funct_2(u2_cat_1(A),u2_cat_1(B),u2_cat_1(C),D,E),A,C))))))))))) # label(t110_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4511 $T # label(t95_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4512 (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)) -> -(k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)) = k1_xboole_0 & k6_cat_1(A,D,E) != k1_xboole_0))))))))))) # label(t126_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4513 (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]. 29.26/28.81 4514 (all A all B all C (m1_subset_1(C,u1_cat_1(k8_cat_1(A,B))) -> (all D (m1_subset_1(D,u1_cat_1(k8_cat_1(A,B))) -> k1_xboole_0 != k6_cat_1(k8_cat_1(A,B),C,D))))) # label(t38_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4515 (all A all B all C all D all E all F (m1_subset_1(B,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_subset_1(C,u1_cat_1(A)) & l1_cat_1(A) & v2_cat_1(A) -> m1_cat_1(k9_cat_1(A,B,C,D,E,F),A,B,D))) # label(dt_k9_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4516 (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) -> k1_tarski(G) != k6_cat_1(A,D,E))) & k1_tarski(F) = k6_cat_1(A,B,C) & r2_tarski(k6_cat_1(A,B,C),k6_cat_1(A,D,E))))))))))))))) # label(t27_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4517 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> r2_hidden(k5_cat_1(A,B),k6_cat_1(A,B,B)))))) # label(t55_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4518 (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(B,A) & r1_tarski(k2_funct_2(A,D,E,B),C) -> v1_funct_1(k2_partfun1(A,D,E,B)) & v1_funct_2(k2_partfun1(A,D,E,B),B,C) & m2_relset_1(k2_partfun1(A,D,E,B),B,C)))))) # label(t4_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4519 (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,B,C) = k1_xboole_0 | k1_xboole_0 = k6_cat_1(A,C,D) | v5_cat_1(k9_cat_1(A,B,C,D,E,F),A)))))))))))))) # label(t75_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4520 $T # label(t2_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4521 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (v6_cat_1(B,A) <-> (all C (m1_subset_1(C,u1_cat_1(A)) -> k1_xboole_0 != k6_cat_1(A,C,B) & (exists D ((all E (m1_cat_1(E,A,C,B) -> D = E)) & m1_cat_1(D,A,C,B)))))))))) # label(d15_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4522 $T # label(t106_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4523 (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 (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,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(t102_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4524 $T # label(t13_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4525 (all A all B all C all D all E all F (-v1_xboole_0(A) & v1_funct_1(C) & 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_xboole_0(B) -> (all G all H all I all J all K all L (g1_cat_1(A,B,C,D,E,F) = g1_cat_1(G,H,I,J,K,L) -> G = A & E = K & F = L & J = D & C = I & H = B)))) # label(free_g1_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4526 (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]. 29.26/28.81 4527 $T # label(t17_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4528 $T # label(t121_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4529 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,B,C) -> (all F (m1_cat_1(F,A,C,D) -> (v5_cat_1(F,A) & v5_cat_1(E,A) -> k1_xboole_0 = k6_cat_1(A,B,C) | k1_xboole_0 = k6_cat_1(A,C,D) | k11_cat_1(A,B,D,k9_cat_1(A,B,C,D,E,F)) = k9_cat_1(A,D,C,B,k11_cat_1(A,C,D,F),k11_cat_1(A,B,C,E))))))))))))))) # label(t77_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4530 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (all E (m1_subset_1(E,u2_cat_1(A)) -> (k2_cat_1(A,E) = k3_cat_1(A,D) -> k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)) = k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)) & 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(t99_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4531 (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]. 29.26/28.81 4532 (all A (l1_cat_1(A) -> (v1_cat_1(A) -> A = g1_cat_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))))) # label(abstractness_v1_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4533 (all A (l1_cat_1(A) -> -v1_xboole_0(u2_cat_1(A)))) # label(dt_u2_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4534 $T # label(t49_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4535 (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 -> k9_cat_1(A,B,C,C,D,k10_cat_1(A,C)) = D))))))))) # label(t57_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4536 (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]. 29.26/28.81 4537 (all A (l1_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)) & v1_funct_1(u4_cat_1(A)))) # label(dt_u4_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4538 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> v3_cat_1(k10_cat_1(A,B),A))))) # label(t64_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4539 (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)) -> k6_cat_1(A,B,C) = k1_xboole_0 | k6_cat_1(A,B,C) = k1_tarski(D)))))))))) # label(t26_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4540 (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]. 29.26/28.81 4541 (all A all B all C all D all E (l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & l1_cat_1(C) & m2_cat_1(D,A,B) & m2_cat_1(E,B,C) & v2_cat_1(C) & v2_cat_1(A) -> m2_cat_1(k14_cat_1(A,B,C,D,E),A,C))) # label(dt_k14_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4542 $T # label(t72_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4543 (all A all B all C all D (v2_cat_1(B) & m1_subset_1(D,u1_cat_1(A)) & m2_cat_1(C,A,B) & l1_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> m1_subset_1(k13_cat_1(A,B,C,D),u1_cat_1(B)))) # label(dt_k13_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4544 $T # label(t48_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4545 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,B,C) -> (all F (m1_cat_1(F,A,C,D) -> (v3_cat_1(E,A) & v3_cat_1(F,A) -> k1_xboole_0 = k6_cat_1(A,B,C) | k6_cat_1(A,C,D) = k1_xboole_0 | v3_cat_1(k9_cat_1(A,B,C,D,E,F),A)))))))))))))) # label(t61_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4546 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> -(k1_xboole_0 != k6_cat_1(A,C,B) & (exists E ((exists F (m1_cat_1(F,A,C,B) & k9_cat_1(A,C,B,C,E,D) = k10_cat_1(A,C) & E != F & k9_cat_1(A,B,C,B,D,F) = k10_cat_1(A,B))) & m1_cat_1(E,A,C,B))) & k6_cat_1(A,B,C) != k1_xboole_0))))))))) # label(t71_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4547 (all A all B (l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(A) -> (all C (m2_cat_1(C,A,B) -> v1_funct_1(C) & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)))))) # label(dt_m2_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.26/28.81 4548 (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]. 29.26/28.81 4549 (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]. 29.43/28.98 4550 $T # label(t14_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.98 4551 (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) -> k2_cat_1(A,B) = k2_cat_1(A,k4_cat_1(A,B,C)) & k3_cat_1(A,k4_cat_1(A,B,C)) = k3_cat_1(A,C)))))) & (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)) -> (k3_cat_1(A,C) = B -> C = k4_cat_1(A,C,k5_cat_1(A,B))))) & (all C (m1_subset_1(C,u2_cat_1(A)) -> (B = k2_cat_1(A,C) -> C = k4_cat_1(A,k5_cat_1(A,B),C)))) & B = k3_cat_1(A,k5_cat_1(A,B)))) & (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (k2_cat_1(A,D) = k3_cat_1(A,C) & k3_cat_1(A,B) = k2_cat_1(A,C) -> k4_cat_1(A,k4_cat_1(A,B,C),D) = k4_cat_1(A,B,k4_cat_1(A,C,D))))))))) & (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (r2_hidden(k4_tarski(C,B),k1_relat_1(u5_cat_1(A))) <-> k3_cat_1(A,B) = k2_cat_1(A,C)))))) -> v2_cat_1(A)))) # label(t29_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.98 4552 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_cat_1(F,A,B,C) -> (all G (m1_cat_1(G,A,C,D) -> (all H (m1_cat_1(H,A,D,E) -> -(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)) & k1_xboole_0 != k6_cat_1(A,D,E) & k6_cat_1(A,C,D) != k1_xboole_0 & k1_xboole_0 != k6_cat_1(A,B,C)))))))))))))))))) # label(t54_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.98 4553 $T # label(t53_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.98 4554 $T # label(t10_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.98 4555 (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]. 29.43/28.98 4556 (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]. 29.43/28.98 4557 $T # label(t3_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.98 4558 $T # label(t1_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.98 4559 (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(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]. 29.43/28.98 4560 (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]. 29.43/28.98 4561 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (v6_cat_1(B,A) -> v3_cat_1(D,A) | k1_xboole_0 = k6_cat_1(A,B,C)))))))))) # label(t90_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.98 4562 (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(B)) -> (k10_cat_1(B,E) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) -> k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D) = E))))))))))) # label(t103_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.98 4563 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> 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)) & k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)) = k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),k3_cat_1(A,D)))))))))) # label(t105_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.98 4564 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (v3_cat_1(B,A) <-> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (k4_cat_1(A,C,B) = k4_cat_1(A,D,B) & k2_cat_1(A,B) = k3_cat_1(A,D) & k2_cat_1(A,B) = k3_cat_1(A,C) & k2_cat_1(A,D) = k2_cat_1(A,C) -> C = D)))))))))) # label(d10_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.98 4565 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (r1_cat_1(A,B,C) & v7_cat_1(B,A) -> v7_cat_1(C,A)))))))) # label(t85_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.98 4566 $T # label(t30_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.98 4567 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (v6_cat_1(B,A) <-> (all C (m1_subset_1(C,u1_cat_1(A)) -> (exists D (m1_cat_1(D,A,C,B) & k1_tarski(D) = k6_cat_1(A,C,B)))))))))) # label(t86_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.98 4568 (exists A (v2_cat_1(A) & l1_cat_1(A))) # label(rc2_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.98 4569 (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]. 29.43/28.98 4570 (all A (l1_cat_1(A) -> -v1_xboole_0(u1_cat_1(A)))) # label(dt_u1_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.98 4571 (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]. 29.43/28.98 4572 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (k1_xboole_0 != k6_cat_1(A,B,C) -> k3_cat_1(A,D) = C & B = k2_cat_1(A,D)))))))))) # label(t23_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.98 4573 (all A all B (m1_subset_1(B,u1_cat_1(A)) & l1_cat_1(A) -> m1_subset_1(k5_cat_1(A,B),u2_cat_1(A)))) # label(dt_k5_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.98 4574 (exists A (v1_cat_1(A) & l1_cat_1(A))) # label(rc1_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.98 4575 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (k5_cat_1(A,C) = k5_cat_1(A,B) -> B = C))))))) # label(t45_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.98 4576 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),B) = k2_cat_1(A,B))))) # label(d2_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.98 4577 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> k13_cat_1(A,B,C,k2_cat_1(A,D)) = k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)) & k13_cat_1(A,B,C,k3_cat_1(A,D)) = k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)))))))))) # label(t109_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.98 4578 (all A all 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)) & v1_funct_1(k7_cat_1(A,B)))) # label(dt_k7_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.98 4579 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> ((all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (k3_cat_1(A,B) = k2_cat_1(A,C) & k2_cat_1(A,D) = k3_cat_1(A,B) & k4_cat_1(A,B,C) = k4_cat_1(A,B,D) & k3_cat_1(A,C) = k3_cat_1(A,D) -> D = C))))) <-> v4_cat_1(B,A)))))) # label(d11_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.98 4580 (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) -> (k2_relat_1(C) = u2_cat_1(B) & u1_cat_1(B) = k2_relat_1(k12_cat_1(A,B,C)) & v2_funct_1(C) <-> v8_cat_1(C,A,B)))))))) # label(d22_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.98 4581 (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) -> v3_cat_1(E,A) | k6_cat_1(A,C,B) = k1_xboole_0 | k6_cat_1(A,B,C) = k1_xboole_0))))))))))) # label(t63_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.98 4582 (all A (l1_cat_1(A) -> v1_funct_2(u3_cat_1(A),u2_cat_1(A),u1_cat_1(A)) & m2_relset_1(u3_cat_1(A),u2_cat_1(A),u1_cat_1(A)) & v1_funct_1(u3_cat_1(A)))) # label(dt_u3_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.98 4583 (all A all B all C all D all E (v2_cat_1(B) & l1_cat_1(B) & m1_subset_1(E,u1_cat_1(A)) & m1_subset_1(D,u1_cat_1(A)) & m2_cat_1(C,A,B) & l1_cat_1(A) & v2_cat_1(A) -> v1_funct_2(k16_cat_1(A,B,C,D,E),k6_cat_1(A,D,E),k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E))) & m2_relset_1(k16_cat_1(A,B,C,D,E),k6_cat_1(A,D,E),k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E))) & v1_funct_1(k16_cat_1(A,B,C,D,E)))) # label(dt_k16_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.98 4584 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (k1_tarski(D) = k6_cat_1(A,B,C) -> (all E (m1_cat_1(E,A,B,C) -> E = D))))))))))) # label(t25_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.98 4585 (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)) -> (r2_hidden(D,k6_cat_1(A,B,C)) <-> m1_cat_1(D,A,B,C))))))))))) # label(d7_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.98 4586 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (v7_cat_1(B,A) -> (all C (m1_cat_1(C,A,B,B) -> k10_cat_1(A,B) = C))))))) # label(t83_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.98 4587 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> B = k8_funct_2(u2_cat_1(A),u2_cat_1(A),k15_cat_1(A),B))))) # label(t115_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.98 4588 (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(E,B,C) & m2_cat_1(D,A,B) & l1_cat_1(C) & v2_cat_1(C) & l1_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]. 29.43/28.98 4589 (exists A l1_cat_1(A)) # label(existence_l1_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.98 4590 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> k3_cat_1(A,B) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),B))))) # label(d3_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.98 4591 (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)) -> (k1_xboole_0 != k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)) -> (all F (m1_cat_1(F,B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)) -> k1_xboole_0 != k6_cat_1(A,D,E) & (exists G (m1_cat_1(G,A,D,E) & k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,G) = F)))))))))))))))) # label(d23_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.98 4592 $T # label(t78_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.98 4593 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (k6_cat_1(A,D,E) != k1_xboole_0 -> (all F (m1_cat_1(F,A,D,E) -> k1_funct_1(k16_cat_1(A,B,C,D,E),F) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,F)))))))))))))) # label(t131_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.98 4594 $T # label(t80_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.98 4595 (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]. 29.43/28.98 4596 (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(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,G) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,F) -> G = F)))))))))) <-> v10_cat_1(C,A,B)))))))) # label(d24_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.99 4597 $T # label(t101_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.99 4598 (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,C,E) -> (all G (m1_cat_1(G,A,C,E) -> (k9_cat_1(A,B,C,E,D,F) = k9_cat_1(A,B,C,E,D,G) -> F = G | k6_cat_1(A,C,E) = k1_xboole_0))))))) <-> v4_cat_1(D,A))))))))))) # label(t65_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.99 4599 (all A all B all C (m1_subset_1(C,u1_cat_1(k8_cat_1(A,B))) -> (all D (m1_subset_1(D,u1_cat_1(k8_cat_1(A,B))) -> (all E (m1_subset_1(E,u1_cat_1(k8_cat_1(A,B))) -> (all F (m1_subset_1(F,u1_cat_1(k8_cat_1(A,B))) -> (all G (m1_cat_1(G,k8_cat_1(A,B),C,D) -> (all H (m1_cat_1(H,k8_cat_1(A,B),E,F) -> H = G)))))))))))) # label(t39_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.99 4600 $T # label(t120_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.99 4601 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,B,C) -> (v10_cat_1(E,B,C) & v10_cat_1(D,A,B) -> v10_cat_1(k14_cat_1(A,B,C,D,E),A,C)))))))))))) # label(t128_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.99 4602 $T # label(dt_l1_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.99 4603 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> ((exists C (m1_subset_1(C,u2_cat_1(A)) & 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)) & k2_cat_1(A,B) = k3_cat_1(A,C) & k2_cat_1(A,C) = k3_cat_1(A,B))) <-> v5_cat_1(B,A)))))) # label(d12_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.99 4604 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (k2_cat_1(A,B) = k3_cat_1(A,C) <-> r2_hidden(k4_tarski(B,C),k1_relat_1(u5_cat_1(A)))))))))) # label(t40_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.99 4605 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (k1_xboole_0 != k6_cat_1(A,B,C) -> (v5_cat_1(D,A) <-> k1_xboole_0 != k6_cat_1(A,C,B) & (exists E (m1_cat_1(E,A,C,B) & k10_cat_1(A,C) = k9_cat_1(A,C,B,C,E,D) & k10_cat_1(A,B) = k9_cat_1(A,B,C,B,D,E))))))))))))) # label(t70_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.99 4606 (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 ((all E (m1_cat_1(E,A,B,C) -> E = D)) & m1_cat_1(D,A,B,C)))))))))) # label(d16_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.99 4607 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (v5_cat_1(D,A) -> v5_cat_1(k11_cat_1(A,B,C,D),A) | k1_xboole_0 = k6_cat_1(A,B,C)))))))))) # label(t76_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.99 4608 (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]. 29.43/28.99 4609 (all A (v2_cat_1(A) & l1_cat_1(A) -> k15_cat_1(A) = k6_partfun1(u2_cat_1(A)))) # label(d21_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.99 4610 (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]. 29.43/28.99 4611 (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]. 29.43/28.99 4612 (all A (v2_cat_1(A) & l1_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]. 29.43/28.99 4613 (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)) -> (k3_cat_1(A,D) = C & B = k2_cat_1(A,D) <-> r2_hidden(D,k6_cat_1(A,B,C))))))))))) # label(t18_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.99 4614 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B) = k5_cat_1(A,B))))) # label(d5_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.99 4615 (all A all B (v1_cat_1(k8_cat_1(A,B)) & v2_cat_1(k8_cat_1(A,B)) & l1_cat_1(k8_cat_1(A,B)))) # label(dt_k8_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.99 4616 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,B,C) -> (v9_cat_1(E,B,C) & v9_cat_1(D,A,B) -> v9_cat_1(k14_cat_1(A,B,C,D,E),A,C)))))))))))) # label(t127_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.99 4617 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (k3_cat_1(A,B) = k2_cat_1(A,C) -> k2_cat_1(A,k4_cat_1(A,B,C)) = k2_cat_1(A,B) & k3_cat_1(A,C) = k3_cat_1(A,k4_cat_1(A,B,C))))))))) # label(t42_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.99 4618 (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]. 29.43/28.99 4619 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (v6_cat_1(B,A) & v6_cat_1(C,A) -> r1_cat_1(A,B,C)))))))) # label(t88_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.99 4620 (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) -> k6_cat_1(A,B,C) = k1_xboole_0 | (all E (m1_cat_1(E,A,C,B) -> (E = k11_cat_1(A,B,C,D) <-> k10_cat_1(A,C) = k9_cat_1(A,C,B,C,E,D) & k10_cat_1(A,B) = k9_cat_1(A,B,C,B,D,E))))))))))))) # label(d14_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.99 4621 $T # label(t31_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.99 4622 (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)) -> (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]. 29.43/28.99 4623 (all A all B all C (v1_funct_1(k1_cat_1(A,B,C)) & m2_relset_1(k1_cat_1(A,B,C),k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)))) # label(dt_k1_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.99 4624 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,B,C) -> (all F (m1_subset_1(F,u1_cat_1(A)) -> k8_funct_2(u1_cat_1(A),u1_cat_1(C),k12_cat_1(A,C,k14_cat_1(A,B,C,D,E)),F) = 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)))))))))))))) # label(t112_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.99 4625 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,B,C) -> (all F (m1_cat_1(F,A,C,D) -> (v4_cat_1(F,A) & v4_cat_1(E,A) -> k6_cat_1(A,B,C) = k1_xboole_0 | v4_cat_1(k9_cat_1(A,B,C,D,E,F),A) | k6_cat_1(A,C,D) = k1_xboole_0))))))))))))) # label(t66_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.99 4626 (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]. 29.43/28.99 4627 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> k10_cat_1(B,k13_cat_1(A,B,C,D)) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)))))))))) # label(t108_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.99 4628 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,B,C) -> (all F (m1_cat_1(F,A,C,D) -> -(k1_xboole_0 != k6_cat_1(A,B,C) & k1_xboole_0 != k6_cat_1(A,C,D) & k4_cat_1(A,E,F) != k9_cat_1(A,B,C,D,E,F)))))))))))))) # label(d13_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.99 4629 $T # label(t94_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.99 4630 (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(u2_cat_1(A),u2_cat_1(B),C,k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),D)) = k8_funct_2(u1_cat_1(B),u2_cat_1(B),u6_cat_1(B),E) & m1_subset_1(E,u1_cat_1(B)))))) -> (all D (m2_relset_1(D,u1_cat_1(A),u1_cat_1(B)) & v1_funct_2(D,u1_cat_1(A),u1_cat_1(B)) & v1_funct_1(D) -> (k12_cat_1(A,B,C) = D <-> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_subset_1(F,u1_cat_1(B)) -> (k8_funct_2(u1_cat_1(B),u2_cat_1(B),u6_cat_1(B),F) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),E)) -> k8_funct_2(u1_cat_1(A),u1_cat_1(B),D,E) = F))))))))))))))) # label(d19_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.99 4631 (exists A (v2_cat_1(A) & v1_cat_1(A) & l1_cat_1(A))) # label(rc3_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.99 4632 (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) | k1_xboole_0 = k6_cat_1(A,B,C)))))))))) # label(t73_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.99 4633 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> ((all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> k2_relat_1(k16_cat_1(A,B,C,D,E)) = k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)))))) <-> v9_cat_1(C,A,B)))))))) # label(t132_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.99 4634 $T # label(t114_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.99 4635 (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,D) = k3_cat_1(A,C) & k2_cat_1(A,C) = k3_cat_1(A,B) -> 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]. 29.43/28.99 4636 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (B = k2_cat_1(A,C) -> k4_cat_1(A,k5_cat_1(A,B),C) = C))))))) # label(t47_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.99 4637 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> k6_cat_1(A,k2_cat_1(A,B),k3_cat_1(A,B)) != k1_xboole_0)))) # label(t19_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.43/28.99 4638 (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)) -> (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]. 29.43/28.99 4639 $T # label(t130_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.45/28.99 4640 (all A (l1_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)) & v1_funct_1(u6_cat_1(A)))) # label(dt_u6_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.45/28.99 4641 (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]. 29.45/28.99 4642 (all A all B all 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)) & v1_funct_1(C) & l1_cat_1(B) & v2_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> v1_funct_1(k12_cat_1(A,B,C)) & v1_funct_2(k12_cat_1(A,B,C),u1_cat_1(A),u1_cat_1(B)) & m2_relset_1(k12_cat_1(A,B,C),u1_cat_1(A),u1_cat_1(B)))) # label(dt_k12_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.45/28.99 4643 (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]. 29.45/28.99 4644 (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 -> k9_cat_1(A,B,B,C,k10_cat_1(A,B),D) = D))))))))) # label(t58_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.45/28.99 4645 (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]. 29.45/28.99 4646 (all A (l1_cat_1(A) & v2_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)) -> ((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 (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),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))) & 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))))) & (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)))))))) <-> m2_cat_1(C,A,B)))))))) # label(d18_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.45/28.99 4647 $T # label(t11_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.45/28.99 4648 (all A all B all C (m1_subset_1(C,u1_cat_1(k8_cat_1(A,B))) -> A = C)) # label(t34_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.45/28.99 4649 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> r1_cat_1(A,B,B))))) # label(t91_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.45/28.99 4650 (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]. 29.45/28.99 4651 (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]. 29.45/28.99 4652 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> k13_cat_1(A,B,C,D) = k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D))))))))) # label(d20_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.45/28.99 4653 (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)) -> k10_cat_1(B,k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k2_cat_1(A,D))) & k10_cat_1(B,k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k3_cat_1(A,D))))))))))) # label(t98_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.49 4654 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> r1_tarski(k2_funct_2(u2_cat_1(A),u2_cat_1(B),C,k6_cat_1(A,D,E)),k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E))))))))))))) # label(t129_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.49 4655 (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]. 29.94/29.49 4656 (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)) -> (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]. 29.94/29.49 4657 $T # label(t20_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.49 4658 (all A (l1_cat_1(A) & v2_cat_1(A) -> m2_cat_1(k15_cat_1(A),A,A))) # label(dt_k15_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.49 4659 $T # label(t28_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.49 4660 (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 -> (v3_cat_1(D,A) <-> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_cat_1(F,A,E,B) -> (all G (m1_cat_1(G,A,E,B) -> (k9_cat_1(A,E,B,C,F,D) = k9_cat_1(A,E,B,C,G,D) -> k1_xboole_0 = k6_cat_1(A,E,B) | G = F))))))))))))))))) # label(t60_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.49 4661 (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]. 29.94/29.49 4662 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> ((exists D (v5_cat_1(D,A) & m1_cat_1(D,A,B,C))) & k1_xboole_0 != k6_cat_1(A,B,C) <-> r1_cat_1(A,B,C)))))))) # label(d17_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.49 4663 (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]. 29.94/29.49 4664 $T # label(t6_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.49 4665 (all A all B all C all D (v2_cat_1(A) & m1_cat_1(D,A,B,C) & m1_subset_1(C,u1_cat_1(A)) & m1_subset_1(B,u1_cat_1(A)) & l1_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]. 29.94/29.49 4666 (all A (l1_cat_1(A) -> (v2_cat_1(A) <-> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C) = B -> C = k1_funct_1(u5_cat_1(A),k4_tarski(C,k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B)))))) & (all C (m1_subset_1(C,u2_cat_1(A)) -> (B = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C) -> C = 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))))) & k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B)) = B & B = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B)))) & (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (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),u3_cat_1(A),D) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C) -> k1_funct_1(u5_cat_1(A),k4_tarski(D,k1_funct_1(u5_cat_1(A),k4_tarski(C,B)))) = k1_funct_1(u5_cat_1(A),k4_tarski(k1_funct_1(u5_cat_1(A),k4_tarski(D,C)),B))))))))) & (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),B) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C) -> 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) & 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)))))) & (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]. 29.94/29.50 4667 (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) & 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_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)) -> k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)) = k8_funct_2(u1_cat_1(A),u1_cat_1(B),D,k2_cat_1(A,E)) & k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)) = k8_funct_2(u1_cat_1(A),u1_cat_1(B),D,k3_cat_1(A,E)))) & (all E (m1_subset_1(E,u2_cat_1(A)) -> (all F (m1_subset_1(F,u2_cat_1(A)) -> (k2_cat_1(A,F) = k3_cat_1(A,E) -> k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k4_cat_1(A,E,F)) = k4_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,F))))))) -> m2_cat_1(C,A,B)))))))))) # label(t100_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4668 (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]. 29.94/29.50 4669 (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 (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)) -> 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)) -> (k3_cat_1(A,D) = k2_cat_1(A,E) -> k4_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k4_cat_1(A,D,E))))))) -> m2_cat_1(C,A,B)))))))) # label(t96_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4670 (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]. 29.94/29.50 4671 (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)) -> (k10_cat_1(B,E) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) -> E = k13_cat_1(A,B,C,D)))))))))))) # label(t107_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4672 (all A all B (v2_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & l1_cat_1(A) -> (exists C m2_cat_1(C,A,B)))) # label(existence_m2_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4673 $T # label(t15_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4674 (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) & k1_tarski(D) = k6_cat_1(A,B,C))))) <-> v7_cat_1(B,A)))))) # label(t82_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4675 (all A all B (m1_subset_1(B,u1_cat_1(A)) & l1_cat_1(A) & v2_cat_1(A) -> k5_cat_1(A,B) = k10_cat_1(A,B))) # label(redefinition_k10_cat_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4676 (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)) -> k3_lattices(A,k4_lattices(A,B,C),k4_lattices(A,B,D)) = k4_lattices(A,B,k3_lattices(A,C,D)))))))) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k4_lattices(A,k3_lattices(A,B,C),k3_lattices(A,B,D)) = k3_lattices(A,B,k4_lattices(A,C,D))))))))))) # label(t19_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4677 $T # label(t37_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4678 $T # label(t10_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4679 (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]. 29.94/29.50 4680 (exists A (v2_lattices(A) & l2_lattices(A))) # label(rc2_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4681 $T # label(t36_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4682 (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_lattices(A) & v6_lattices(A) -> k4_lattices(A,B,C) = k4_lattices(A,C,B))) # label(commutativity_k4_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4683 (all A all B all C (v4_lattices(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l2_lattices(A) & -v3_struct_0(A) -> k1_lattices(A,B,C) = k3_lattices(A,B,C))) # label(redefinition_k3_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4684 (all A (-v3_struct_0(A) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k4_lattices(A,k6_lattices(A),B) = B)))) # label(t43_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4685 $T # label(t8_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4686 (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)) -> k6_lattices(A) = k3_lattices(A,k7_lattices(A,B),B))))) # label(t48_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4687 (all A (l2_lattices(A) -> (v2_lattices(A) -> g2_lattices(u1_struct_0(A),u2_lattices(A)) = A))) # label(abstractness_v2_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4688 (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)) -> k4_lattices(A,k7_lattices(A,B),B) = k5_lattices(A))))) # label(t47_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4689 (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,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]. 29.94/29.50 4690 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> v1_lattices(g1_lattices(A,B)) & l1_lattices(g1_lattices(A,B)))) # label(dt_g1_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4691 (all A all B all C (-v3_struct_0(A) & l1_lattices(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) -> m1_subset_1(k2_lattices(A,B,C),u1_struct_0(A)))) # label(dt_k2_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4692 (all A all B all C (l1_lattices(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(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]. 29.94/29.50 4693 (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]. 29.94/29.50 4694 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v13_lattices(A) & v14_lattices(A) -> -v3_struct_0(A) & v15_lattices(A)))) # label(cc3_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4695 (all A all B all C (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(C) & m1_relset_1(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]. 29.94/29.50 4696 $T # label(t12_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4697 (exists A l1_lattices(A)) # label(existence_l1_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4698 (all A (l3_lattices(A) & -v3_struct_0(A) -> (v5_lattices(A) & v8_lattices(A) & v7_lattices(A) & v9_lattices(A) & v6_lattices(A) & v4_lattices(A) <-> v10_lattices(A)))) # label(d10_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4699 (all A (l2_lattices(A) & -v3_struct_0(A) -> m1_subset_1(k6_lattices(A),u1_struct_0(A)))) # label(dt_k6_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4700 (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)) -> k4_lattices(A,k4_lattices(A,k3_lattices(A,B,C),k3_lattices(A,C,D)),k3_lattices(A,D,B)) = k3_lattices(A,k3_lattices(A,k4_lattices(A,B,C),k4_lattices(A,C,D)),k4_lattices(A,D,B)))))))) -> v11_lattices(A)))) # label(t29_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4701 (all A (l2_lattices(A) -> l1_struct_0(A))) # label(dt_l2_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4702 (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)) -> k7_lattices(A,k4_lattices(A,B,C)) = k3_lattices(A,k7_lattices(A,B),k7_lattices(A,C)))))))) # label(t50_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4703 $T # label(t35_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4704 (exists A (v3_lattices(A) & -v3_struct_0(A) & l3_lattices(A))) # label(rc6_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4705 $T # label(t33_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4706 (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_lattices(A,B)) & v1_lattices(g1_lattices(A,B)))) # label(fc2_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4707 (all A (l3_lattices(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_lattices(A,B,k1_lattices(A,C,D)) = k1_lattices(A,k2_lattices(A,B,C),k2_lattices(A,B,D)))))))) <-> v11_lattices(A)))) # label(d11_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4708 (all A all B all C (v1_funct_1(B) & v1_funct_2(B,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) & v1_funct_1(C) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & -v1_xboole_0(A) -> v3_lattices(g3_lattices(A,B,C)) & -v3_struct_0(g3_lattices(A,B,C)))) # label(fc3_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4709 (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)) -> (r1_lattices(A,B,C) <-> C = k1_lattices(A,B,C)))))))) # label(d3_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4710 $T # label(t15_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4711 (exists A (v3_lattices(A) & v5_lattices(A) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v14_lattices(A) & v15_lattices(A) & v13_lattices(A) & v7_lattices(A) & v4_lattices(A) & -v3_struct_0(A) & l3_lattices(A))) # label(rc11_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4712 (all A (-v3_struct_0(A) & l3_lattices(A) & v8_lattices(A) & v6_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]. 29.94/29.50 4713 $T # label(t30_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4714 (all A (-v3_struct_0(A) & l3_lattices(A) -> (v16_lattices(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (exists C (m1_subset_1(C,u1_struct_0(A)) & r2_lattices(A,C,B)))))))) # label(d19_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4715 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v4_lattices(A) & v6_lattices(A) & v7_lattices(A) & v9_lattices(A) & v8_lattices(A) & v5_lattices(A) -> v10_lattices(A) & -v3_struct_0(A)))) # label(cc2_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4716 (all A all B all C (m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l2_lattices(A) & v4_lattices(A) & -v3_struct_0(A) -> m1_subset_1(k3_lattices(A,B,C),u1_struct_0(A)))) # label(dt_k3_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4717 $T # label(t3_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4718 (all A (v8_lattices(A) & l3_lattices(A) & v9_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]. 29.94/29.50 4719 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A) -> -v3_struct_0(A) & v17_lattices(A)))) # label(cc6_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4720 (all A all B all C (v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & -v3_struct_0(A) -> (r1_lattices(A,B,C) <-> r3_lattices(A,B,C)))) # label(redefinition_r3_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4721 (exists A l3_lattices(A)) # label(existence_l3_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4722 (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]. 29.94/29.50 4723 (all A all B (-v1_xboole_0(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) -> -v3_struct_0(g2_lattices(A,B)) & v2_lattices(g2_lattices(A,B)))) # label(fc1_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4724 (all A (l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v16_lattices(A) & l3_lattices(A) & v11_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (C = k7_lattices(A,B) <-> r2_lattices(A,C,B))))))))) # label(d21_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4725 (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)) -> B = k2_lattices(A,B,C) & B = k2_lattices(A,C,B))))))))) # label(d16_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4726 (all A (-v3_struct_0(A) & v14_lattices(A) & l3_lattices(A) & v10_lattices(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]. 29.94/29.50 4727 $T # label(t1_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4728 (exists A (l1_lattices(A) & -v3_struct_0(A) & v1_lattices(A))) # label(rc5_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4729 (all A (l1_lattices(A) -> l1_struct_0(A))) # label(dt_l1_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4730 $T # label(t38_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4731 (all A (l3_lattices(A) -> (v15_lattices(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v14_lattices(A) & v13_lattices(A)))) # label(cc4_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4732 (exists A (l3_lattices(A) & -v3_struct_0(A) & v5_lattices(A) & v6_lattices(A) & v11_lattices(A) & v13_lattices(A) & v15_lattices(A) & v17_lattices(A) & v16_lattices(A) & v14_lattices(A) & v10_lattices(A) & v9_lattices(A) & v8_lattices(A) & v7_lattices(A) & v4_lattices(A) & v3_lattices(A))) # label(rc13_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4733 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C all D (g2_lattices(C,D) = g2_lattices(A,B) -> D = B & C = A)))) # label(free_g2_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4734 (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)) -> (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]. 29.94/29.50 4735 (all A (-v3_struct_0(A) & v8_lattices(A) & l3_lattices(A) & v9_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_lattices(A,B,C) <-> k2_lattices(A,B,C) = B))))))) # label(t21_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4736 $T # label(t5_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4737 (all A (l3_lattices(A) -> (v11_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> v4_lattices(A) & v5_lattices(A) & v7_lattices(A) & v8_lattices(A) & v12_lattices(A) & v10_lattices(A) & v9_lattices(A) & v6_lattices(A) & -v3_struct_0(A)))) # label(cc7_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4738 (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]. 29.94/29.50 4739 (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_lattices(A,B,C) = k5_lattices(A) <-> r3_lattices(A,B,k7_lattices(A,C))))))))) # label(t52_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4740 $T # label(t14_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4741 (all A all B all C (v6_lattices(A) & l3_lattices(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & v9_lattices(A) & v8_lattices(A) & -v3_struct_0(A) -> r3_lattices(A,B,B))) # label(reflexivity_r3_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4742 (exists A (v3_lattices(A) & v4_lattices(A) & v5_lattices(A) & v8_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A) & v13_lattices(A) & v10_lattices(A) & v9_lattices(A) & v7_lattices(A) & v6_lattices(A) & -v3_struct_0(A) & l3_lattices(A))) # label(rc12_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4743 (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)) -> r3_lattices(A,k5_lattices(A),B))))) # label(t41_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4744 (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)) -> B = k2_lattices(A,B,k1_lattices(A,B,C)))))) <-> v9_lattices(A)))) # label(d9_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4745 $T # label(t11_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4746 $T # label(t24_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4747 (all A (l2_lattices(A) & -v3_struct_0(A) -> (v14_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k6_lattices(A) = B <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_lattices(A,B,C) = B & k1_lattices(A,C,B) = B)))))))) # label(d17_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4748 (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]. 29.94/29.50 4749 $T # label(t42_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4750 (all A all B all C (m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,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]. 29.94/29.50 4751 (exists A (l3_lattices(A) & v5_lattices(A) & v7_lattices(A) & v9_lattices(A) & v11_lattices(A) & v14_lattices(A) & v13_lattices(A) & v12_lattices(A) & v10_lattices(A) & v8_lattices(A) & v6_lattices(A) & v4_lattices(A) & v3_lattices(A) & -v3_struct_0(A))) # label(rc10_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4752 (all A (v10_lattices(A) & v11_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k4_lattices(A,k4_lattices(A,k3_lattices(A,B,C),k3_lattices(A,C,D)),k3_lattices(A,D,B)) = k3_lattices(A,k3_lattices(A,k4_lattices(A,B,C),k4_lattices(A,C,D)),k4_lattices(A,D,B)))))))))) # label(t34_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4753 (all A (-v3_struct_0(A) & l2_lattices(A) -> (v5_lattices(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (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))))))))))) # label(d5_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4754 (all A (l1_lattices(A) -> v1_funct_2(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & m2_relset_1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_1(u1_lattices(A)))) # label(dt_u1_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4755 (all A (l3_lattices(A) & -v3_struct_0(A) -> (v17_lattices(A) <-> v11_lattices(A) & v16_lattices(A) & v15_lattices(A)))) # label(d20_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4756 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v17_lattices(A) -> -v3_struct_0(A) & v11_lattices(A) & v16_lattices(A) & v15_lattices(A) & v14_lattices(A) & v13_lattices(A)))) # label(cc5_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4757 $T # label(t9_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4758 $T # label(t4_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4759 (all A (-v3_struct_0(A) & v4_lattices(A) & l2_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,C,B) & r1_lattices(A,B,C) -> C = B))))))) # label(t26_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4760 (all A (l3_lattices(A) -> l1_lattices(A) & l2_lattices(A))) # label(dt_l3_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4761 (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)) -> B = k7_lattices(A,k7_lattices(A,B)))))) # label(t49_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4762 (all A (l3_lattices(A) -> (v10_lattices(A) & -v3_struct_0(A) -> v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v4_lattices(A) & -v3_struct_0(A)))) # label(cc1_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.50 4763 (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]. 29.94/29.50 4764 $T # label(t7_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4765 $T # label(t13_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4766 $T # label(t2_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4767 (exists A l2_lattices(A)) # label(existence_l2_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4768 (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)) -> m1_subset_1(k1_lattices(A,B,C),u1_struct_0(A)))) # label(dt_k1_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4769 $T # label(t6_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4770 (exists A (v3_lattices(A) & l3_lattices(A))) # label(rc3_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4771 (all A (v7_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)) -> (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]. 29.94/29.51 4772 (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) -> v2_lattices(g2_lattices(A,B)) & l2_lattices(g2_lattices(A,B)))) # label(dt_g2_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4773 $T # label(t20_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4774 (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]. 29.94/29.51 4775 (exists A (l1_lattices(A) & -v3_struct_0(A) & v7_lattices(A) & v6_lattices(A) & v1_lattices(A))) # label(rc8_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4776 (all A all B all C (-v3_struct_0(A) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) -> k2_lattices(A,B,C) = k4_lattices(A,B,C))) # label(redefinition_k4_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4777 (all A (-v3_struct_0(A) & v6_lattices(A) & v9_lattices(A) & l3_lattices(A) & v8_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k4_lattices(A,B,B))))) # label(t18_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4778 (all A (-v3_struct_0(A) & l3_lattices(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattices(A,B,D) -> k2_lattices(A,k1_lattices(A,B,C),D) = k1_lattices(A,B,k2_lattices(A,C,D))))))))) <-> v12_lattices(A)))) # label(d12_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4779 $T # label(t16_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4780 (all A (l2_lattices(A) -> m2_relset_1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_2(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_1(u2_lattices(A)))) # label(dt_u2_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4781 (all A (l1_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_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]. 29.94/29.51 4782 (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)) -> (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]. 29.94/29.51 4783 (exists A (-v3_struct_0(A) & v2_lattices(A) & v5_lattices(A) & v4_lattices(A) & l2_lattices(A))) # label(rc7_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4784 (all A (-v3_struct_0(A) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k1_lattices(A,B,B))))) # label(t17_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4785 (exists A (l1_lattices(A) & v1_lattices(A))) # label(rc1_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4786 (all A all B all C (v1_funct_2(B,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) & v1_funct_1(C) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all D all E all F (g3_lattices(A,B,C) = g3_lattices(D,E,F) -> A = D & E = B & F = C)))) # label(free_g3_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4787 (all A all B (l3_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & -v3_struct_0(A) -> m1_subset_1(k7_lattices(A,B),u1_struct_0(A)))) # label(dt_k7_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4788 (all A all B (m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C all D (g1_lattices(C,D) = g1_lattices(A,B) -> B = D & A = C)))) # label(free_g1_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4789 (all A (l3_lattices(A) & -v3_struct_0(A) -> (v8_lattices(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_lattices(A,k2_lattices(A,B,C),C) = C))))))) # label(d8_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4790 (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,C,B) = k1_lattices(A,B,C))))) <-> v4_lattices(A)))) # label(d4_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4791 (all A (-v3_struct_0(A) & v14_lattices(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r3_lattices(A,B,k6_lattices(A)))))) # label(t45_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4792 $T # label(t28_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4793 (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)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_lattices(A,k2_lattices(A,B,C),D) = k2_lattices(A,B,k2_lattices(A,C,D)))))))) <-> v7_lattices(A)))) # label(d7_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4794 (all A (-v3_struct_0(A) & l2_lattices(A) -> (v14_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,B,C) = B & k1_lattices(A,C,B) = B))))))) # label(d14_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4795 (all A (v10_lattices(A) & v11_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)) -> 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]. 29.94/29.51 4796 (all A (-v3_struct_0(A) & l2_lattices(A) & v5_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattices(A,C,D) & r1_lattices(A,B,C) -> r1_lattices(A,B,D)))))))))) # label(t25_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4797 (exists A (l2_lattices(A) & v2_lattices(A) & -v3_struct_0(A))) # label(rc4_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4798 (all A (-v3_struct_0(A) & l1_lattices(A) -> ((exists B (m1_subset_1(B,u1_struct_0(A)) & (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_lattices(A,C,B) = B & B = k2_lattices(A,B,C))))) <-> v13_lattices(A)))) # label(d13_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4799 $T # label(t46_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4800 (exists A (l3_lattices(A) & -v3_struct_0(A) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v7_lattices(A) & v5_lattices(A) & v4_lattices(A) & v3_lattices(A))) # label(rc9_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4801 (all A (l3_lattices(A) & v13_lattices(A) & v10_lattices(A) & -v3_struct_0(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]. 29.94/29.51 4802 (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) <-> k1_lattices(A,C,B) = k6_lattices(A) & k5_lattices(A) = k2_lattices(A,B,C) & k5_lattices(A) = k2_lattices(A,C,B) & k1_lattices(A,B,C) = k6_lattices(A)))))))) # label(d18_lattices) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4803 (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]. 29.94/29.51 4804 (all A (l1_pre_topc(A) -> (exists B m1_pre_topc(B,A)))) # label(existence_m1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4805 (all A (l1_pre_topc(A) -> (v1_pre_topc(A) -> g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = A))) # label(abstractness_v1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4806 $T # label(t37_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4807 $T # label(t36_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4808 (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))) -> 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]. 29.94/29.51 4809 (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]. 29.94/29.51 4810 $T # label(t34_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4811 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_pre_topc(A,B) <-> k2_pre_topc(A) = k5_setfam_1(u1_struct_0(A),B)))))) # label(d8_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4812 (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_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))) & (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)) & v2_pre_topc(A) -> v3_pre_topc(B,A)))))) # label(t53_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4813 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -((all C (m1_subset_1(C,u1_struct_0(A)) -> -r2_hidden(C,B))) & B != k1_pre_topc(A)))))) # label(t41_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4814 (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]. 29.94/29.51 4815 (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]. 29.94/29.51 4816 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (C = D -> k3_xboole_0(k6_pre_topc(A,C),k2_pre_topc(B)) = k6_pre_topc(B,D)))))))))) # label(t47_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4817 (all A (l1_struct_0(A) -> k1_xboole_0 = k1_pre_topc(A))) # label(d2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4818 (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]. 29.94/29.51 4819 (all A all B all C all D (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) & 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]. 29.94/29.51 4820 (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]. 29.94/29.51 4821 (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]. 29.94/29.51 4822 (all A all B (v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v1_pre_topc(k3_pre_topc(A,B)) & v2_pre_topc(k3_pre_topc(A,B)))) # label(fc4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4823 $T # label(d4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4824 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) -> k6_pre_topc(A,B) = B) & (k6_pre_topc(A,B) = B & v2_pre_topc(A) -> v4_pre_topc(B,A)))))) # label(t52_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4825 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C all D (g1_pre_topc(A,B) = g1_pre_topc(C,D) -> B = D & C = A)))) # label(free_g1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4826 $T # label(t26_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4827 (all A (l1_struct_0(A) -> u1_struct_0(A) = k2_pre_topc(A))) # label(d3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4828 (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]. 29.94/29.51 4829 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (exists B (v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc6_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4830 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_xboole_0(B,C) & k4_subset_1(u1_struct_0(A),B,C) = k2_pre_topc(A) -> k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) = C))))))) # label(t25_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4831 (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]. 29.94/29.51 4832 $T # label(t33_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4833 $T # label(t2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4834 (all A all B all C all D (l1_struct_0(A) & l1_struct_0(B) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> 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]. 29.94/29.51 4835 (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]. 29.94/29.51 4836 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (r2_hidden(C,u1_struct_0(A)) -> (r2_hidden(C,k6_pre_topc(A,B)) <-> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,D) & v4_pre_topc(D,A) -> r2_hidden(C,D))))))))))) # label(t45_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4837 (all A all B all C all D (l1_struct_0(A) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) & l1_struct_0(B) -> 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]. 29.94/29.51 4838 $T # label(d7_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4839 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v5_pre_topc(C,A,B) <-> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v4_pre_topc(D,B) -> v4_pre_topc(k5_pre_topc(A,B,C,D),A))))))))))) # label(d12_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4840 $T # label(t3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4841 $T # label(t31_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4842 $T # label(t7_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4843 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k6_subset_1(u1_struct_0(A),k2_pre_topc(A),k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B)) = B)))) # label(t22_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4844 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> v4_pre_topc(C,A)))) -> v4_pre_topc(k6_setfam_1(u1_struct_0(A),B),A)))))) # label(t44_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4845 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) = C -> k2_pre_topc(A) = k4_subset_1(u1_struct_0(A),B,C)))))))) # label(t24_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4846 (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]. 29.94/29.51 4847 $T # label(t21_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4848 $T # label(t4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4849 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) <-> r2_hidden(B,u1_pre_topc(A))))))) # label(d5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4850 $T # label(t35_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4851 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (exists B (m1_pre_topc(B,A) & v1_pre_topc(B) & v2_pre_topc(B))))) # label(rc5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4852 (all A all B all C all D (l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> k5_pre_topc(A,B,C,D) = k10_relat_1(C,D))) # label(redefinition_k5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4853 (all A all B (l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> m1_subset_1(k6_pre_topc(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k6_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4854 $T # label(t9_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4855 $T # label(t19_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4856 (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]. 29.94/29.51 4857 (exists A l1_pre_topc(A)) # label(existence_l1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4858 (all A (l1_pre_topc(A) -> (v2_pre_topc(A) <-> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(B,u1_pre_topc(A)) -> r2_hidden(k5_setfam_1(u1_struct_0(A),B),u1_pre_topc(A))))) & (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,u1_pre_topc(A)) & r2_hidden(C,u1_pre_topc(A)) -> r2_hidden(k5_subset_1(u1_struct_0(A),B,C),u1_pre_topc(A))))))) & r2_hidden(u1_struct_0(A),u1_pre_topc(A))))) # label(d1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4859 $T # label(d11_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4860 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (exists B (m1_pre_topc(B,A) & v1_pre_topc(B) & -v3_struct_0(B))))) # label(rc4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4861 $T # label(t28_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.51 4862 $T # label(t6_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4863 (all A (l1_pre_topc(A) -> (exists B (v1_pre_topc(B) & m1_pre_topc(B,A))))) # label(rc3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4864 (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]. 29.94/29.52 4865 $T # label(t32_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4866 (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 (C = k3_xboole_0(D,k2_pre_topc(B)) & r2_hidden(D,u1_pre_topc(A)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))))))))))))) # label(d9_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4867 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> m1_pre_topc(k3_pre_topc(A,B),A) & v1_pre_topc(k3_pre_topc(A,B)))) # label(dt_k3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4868 (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]. 29.94/29.52 4869 $T # label(t8_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4870 $T # label(t20_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4871 (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 (r2_hidden(D,u1_struct_0(A)) -> ((all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(E,A) & r1_xboole_0(B,E) & r2_hidden(D,E)))) <-> r2_hidden(D,C)))) <-> C = k6_pre_topc(A,B)))))))) # label(d13_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4872 $T # label(t40_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4873 $T # label(t1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4874 $T # label(t29_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4875 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (exists C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & k6_setfam_1(u1_struct_0(A),C) = k6_pre_topc(A,B) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(D,C) <-> v4_pre_topc(D,A) & r1_tarski(B,D)))))))))) # label(t46_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4876 (all A (-v3_struct_0(A) & l1_struct_0(A) -> -v1_xboole_0(k2_pre_topc(A)))) # label(fc2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4877 (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)) -> ((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)))) & -v3_struct_0(A) <-> r2_hidden(C,k6_pre_topc(A,B))))))))) # label(t54_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4878 (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]. 29.94/29.52 4879 $T # label(t38_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4880 (all A (l1_struct_0(A) -> v1_xboole_0(k1_pre_topc(A)) & v1_membered(k1_pre_topc(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)))) # label(fc1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4881 $T # label(t11_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4882 (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]. 29.94/29.52 4883 (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]. 29.94/29.52 4884 (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]. 29.94/29.52 4885 (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]. 29.94/29.52 4886 $T # label(t30_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4887 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> v4_pre_topc(k2_pre_topc(A),A))) # label(fc5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4888 (all A all B (-v3_struct_0(A) & l1_pre_topc(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v1_pre_topc(k3_pre_topc(A,B)) & -v3_struct_0(k3_pre_topc(A,B)))) # label(fc3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4889 $T # label(t10_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4890 (exists A (v1_pre_topc(A) & l1_pre_topc(A))) # label(rc1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4891 (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]. 29.94/29.52 4892 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (v4_pre_topc(B,A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc7_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4893 (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]. 29.94/29.52 4894 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(k2_pre_topc(A) != B & k1_xboole_0 = k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B)) & -(k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) != k1_xboole_0 & B = k2_pre_topc(A)))))) # label(t23_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4895 (all A (l1_struct_0(A) -> u1_struct_0(A) = k2_pre_topc(A))) # label(t12_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4896 (all A (l1_pre_topc(A) -> l1_struct_0(A))) # label(dt_l1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4897 (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) -> (B = k2_pre_topc(C) <-> C = k3_pre_topc(A,B)))))))) # label(d10_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4898 (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 (v4_pre_topc(D,A) & C = k3_xboole_0(D,k2_pre_topc(B)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))))) <-> v4_pre_topc(C,B)))))))) # label(t43_pre_topc) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4899 $T # label(t17_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4900 $T # label(t3_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4901 (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]. 29.94/29.52 4902 (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]. 29.94/29.52 4903 (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]. 29.94/29.52 4904 $T # label(t10_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4905 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> k2_pre_topc(A) = k1_tops_1(A,k2_pre_topc(A)))) # label(t43_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4906 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_1(B,A) & v1_tops_1(C,A) & v3_pre_topc(C,A) -> v1_tops_1(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t82_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4907 (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]. 29.94/29.52 4908 (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]. 29.94/29.52 4909 $T # label(t7_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4910 $T # label(t9_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4911 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_tops_1(B,A) <-> r1_tarski(B,k6_pre_topc(A,k1_tops_1(A,B))) & r1_tarski(k1_tops_1(A,k6_pre_topc(A,B)),B)))))) # label(d6_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4912 (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]. 29.94/29.52 4913 (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]. 29.94/29.52 4914 (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]. 29.94/29.52 4915 (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]. 29.94/29.52 4916 $T # label(t33_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4917 (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]. 29.94/29.52 4918 (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]. 29.94/29.52 4919 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) & v3_tops_1(B,A) -> B = k1_xboole_0))))) # label(t97_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4920 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> v3_pre_topc(k2_pre_topc(A),A) & v4_pre_topc(k2_pre_topc(A),A))) # label(fc8_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4921 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) & v2_tops_1(B,A) -> v2_tops_1(B,A) & v3_tops_1(B,A)))))) # label(cc5_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4922 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(C,B) & v4_pre_topc(B,A) -> r1_tarski(k6_pre_topc(A,C),B)))))))) # label(t31_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4923 (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]. 29.94/29.52 4924 $T # label(t6_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4925 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tops_1(B,A) <-> v1_tops_1(k3_subset_1(u1_struct_0(A),B),A)))))) # label(d4_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4926 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (v1_xboole_0(B) & v4_pre_topc(B,A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v5_membered(B) & v2_tops_1(B,A) & v3_tops_1(B,A) & v4_membered(B) & v3_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc5_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4927 $T # label(t1_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4928 (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]. 29.94/29.52 4929 $T # label(t42_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4930 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k1_tops_1(A,k1_tops_1(A,B)) = k1_tops_1(A,B))))) # label(t45_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4931 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (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]. 29.94/29.52 4932 $T # label(t83_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4933 (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))) -> (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]. 29.94/29.52 4934 (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]. 29.94/29.52 4935 $T # label(t25_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4936 (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))) -> k5_subset_1(u1_struct_0(A),k1_tops_1(A,B),k1_tops_1(A,C)) = k1_tops_1(A,k5_subset_1(u1_struct_0(A),B,C)))))))) # label(t46_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4937 $T # label(t16_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4938 $T # label(t5_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4939 (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) -> 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]. 29.94/29.52 4940 (all A (l1_pre_topc(A) -> (exists B (v1_xboole_0(B) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v5_membered(B) & v2_tops_1(B,A) & v4_membered(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc4_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4941 $T # label(t98_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4942 $T # label(t89_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4943 $T # label(t19_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4944 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (exists B (v3_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc1_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4945 $T # label(t100_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4946 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> v3_tops_1(k2_tops_1(A,B),A)))))) # label(t95_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4947 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (B = k6_pre_topc(A,k1_tops_1(A,B)) <-> v5_tops_1(B,A)))))) # label(d7_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4948 (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]. 29.94/29.52 4949 $T # label(t60_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4950 (all A all B (v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(B,A) -> v3_pre_topc(k3_subset_1(u1_struct_0(A),B),A))) # label(fc3_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4951 (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]. 29.94/29.52 4952 (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]. 29.94/29.52 4953 (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]. 29.94/29.52 4954 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_1(B,A) <-> k6_pre_topc(A,B) = k2_pre_topc(A)))))) # label(d3_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4955 (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) & v3_pre_topc(C,A) -> v3_pre_topc(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t37_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4956 (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]. 29.94/29.52 4957 $T # label(t13_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4958 $T # label(t78_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4959 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_1(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(C != k1_xboole_0 & r1_xboole_0(B,C) & v3_pre_topc(C,A))))))))) # label(t80_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4960 (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]. 29.94/29.52 4961 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k6_pre_topc(A,B) = k4_subset_1(u1_struct_0(A),B,k2_tops_1(A,B)))))) # label(t65_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4962 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k6_pre_topc(A,k6_pre_topc(A,B)) = k6_pre_topc(A,B))))) # label(t26_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4963 (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(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t38_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4964 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) & v4_pre_topc(C,A) -> v4_pre_topc(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t36_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4965 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> v3_pre_topc(k1_pre_topc(A),A))) # label(t52_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4966 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(B,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]. 29.94/29.52 4967 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (k2_tops_1(A,B) = k6_subset_1(u1_struct_0(A),B,k1_tops_1(A,B)) <-> v4_pre_topc(B,A)))))) # label(t77_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4968 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k4_subset_1(u1_struct_0(A),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]. 29.94/29.52 4969 (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_pre_topc(B,A) & v4_pre_topc(B,A)))))) # label(cc1_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4970 (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]. 29.94/29.52 4971 (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]. 29.94/29.52 4972 (all A all B (v2_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> v3_pre_topc(k1_tops_1(A,B),A))) # label(fc6_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4973 (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]. 29.94/29.52 4974 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k2_tops_1(A,k3_subset_1(u1_struct_0(A),B)) = k2_tops_1(A,B))))) # label(t62_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4975 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> v3_pre_topc(k1_pre_topc(A),A) & v4_pre_topc(k1_pre_topc(A),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)) & v1_membered(k1_pre_topc(A)) & v1_xboole_0(k1_pre_topc(A)))) # label(fc7_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4976 (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) & v4_tops_1(D,B) -> v6_tops_1(D,B)) & (v6_tops_1(C,A) -> v3_pre_topc(C,A) & v4_tops_1(C,A)))))))))) # label(t107_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4977 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) & v3_tops_1(B,A) -> v3_pre_topc(B,A) & v4_pre_topc(B,A) & v1_membered(B) & v4_membered(B) & v2_tops_1(B,A) & v3_tops_1(B,A) & v5_membered(B) & v3_membered(B) & v2_membered(B) & v1_xboole_0(B)))))) # label(cc6_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4978 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v6_tops_1(C,A) & v6_tops_1(B,A) -> v6_tops_1(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t109_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4979 (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]. 29.94/29.52 4980 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k2_tops_1(A,k2_tops_1(A,k2_tops_1(A,B))) = k2_tops_1(A,k2_tops_1(A,B)))))) # label(t75_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4981 (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))) & r1_tarski(D,B) & r2_hidden(C,D) & v3_pre_topc(D,A)))))))))) # label(t57_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4982 $T # label(t99_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4983 (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]. 29.94/29.52 4984 (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) -> v2_tops_1(B,A)))))) # label(cc4_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4985 (all A all B (v2_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> v4_pre_topc(k6_pre_topc(A,B),A))) # label(fc2_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4986 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tops_1(B,A) & v4_pre_topc(C,A) & v2_tops_1(C,A) -> v2_tops_1(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t85_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4987 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (k6_subset_1(u1_struct_0(A),k6_pre_topc(A,B),B) = k2_tops_1(A,B) <-> v3_pre_topc(B,A)))))) # label(t76_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4988 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,k1_tops_1(A,C)) <-> (exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & r2_hidden(B,D) & r1_tarski(D,C) & v3_pre_topc(D,A)))))))) # label(t54_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4989 (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]. 29.94/29.52 4990 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_tops_1(B,A) -> k1_tops_1(A,k2_tops_1(A,B)) = k1_xboole_0))))) # label(t110_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4991 (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]. 29.94/29.52 4992 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> k6_pre_topc(A,B) = k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,B)))))))) # label(t59_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4993 (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]. 29.94/29.52 4994 $T # label(t4_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4995 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> v1_xboole_0(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v4_pre_topc(k1_pre_topc(A),A))) # label(fc1_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.52 4996 (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]. 29.94/29.52 4997 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) -> (k2_tops_1(A,B) = B <-> v3_tops_1(B,A))))))) # label(t94_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 4998 (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]. 29.94/29.53 4999 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) & v3_pre_topc(B,A) -> (v5_tops_1(B,A) <-> v6_tops_1(B,A))))))) # label(t105_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5000 (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]. 29.94/29.53 5001 (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),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B))) = k1_tops_1(A,B))))) # label(d1_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5002 (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]. 29.94/29.53 5003 $T # label(t24_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5004 (all A all B (l1_pre_topc(A) & v3_tops_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(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]. 29.94/29.53 5005 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & v3_pre_topc(B,A) & v4_pre_topc(B,A))))) # label(rc3_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5006 (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]. 29.94/29.53 5007 (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(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t35_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5008 (all A all B (v2_tops_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> v2_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) & v1_membered(k1_tops_1(A,B)) & v1_xboole_0(k1_tops_1(A,B)))) # label(fc10_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5009 $T # label(t28_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5010 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(C,A) & v4_pre_topc(B,A) -> k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,C)) = k5_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,C))))))))) # label(t34_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5011 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (B = k1_tops_1(A,k6_pre_topc(A,B)) <-> v6_tops_1(B,A)))))) # label(d8_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5012 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k2_tops_1(A,B),k6_pre_topc(A,B)))))) # label(t63_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5013 (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]. 29.94/29.53 5014 (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]. 29.94/29.53 5015 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(B,A) & v3_tops_1(C,A) -> v3_tops_1(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t90_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5016 (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,k6_pre_topc(A,k1_tops_1(A,B)))) = k6_pre_topc(A,k1_tops_1(A,B)))))) # label(t58_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5017 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) -> (v2_tops_1(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(k1_xboole_0 != C & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(D,A) & r1_xboole_0(B,D) & D != k1_xboole_0 & r1_tarski(D,C)))) & v3_pre_topc(C,A)))))))))) # label(t87_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5018 $T # label(t12_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5019 (all A (l1_struct_0(A) -> k3_subset_1(u1_struct_0(A),k2_pre_topc(A)) = k1_pre_topc(A))) # label(t8_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5020 (all A all B (v2_pre_topc(A) & l1_pre_topc(A) & v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v3_tops_1(k2_tops_1(A,B),A) & v2_tops_1(k2_tops_1(A,B),A))) # label(fc13_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5021 (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]. 29.94/29.53 5022 (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]. 29.94/29.53 5023 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (k3_subset_1(u1_struct_0(A),C) = k3_subset_1(u1_struct_0(A),B) -> C = B))))))) # label(t21_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5024 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v6_tops_1(B,A) -> k2_tops_1(A,B) = k2_tops_1(A,k6_pre_topc(A,B)) & k6_subset_1(u1_struct_0(A),k6_pre_topc(A,B),B) = k2_tops_1(A,k6_pre_topc(A,B))))))) # label(t104_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5025 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,k2_tops_1(A,B)) <-> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,D) & v3_pre_topc(D,A) -> -r1_xboole_0(k3_subset_1(u1_struct_0(A),B),D) & -r1_xboole_0(B,D))))))))))) # label(t61_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5026 (all A all B (l1_pre_topc(A) & v3_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v2_pre_topc(A) -> v3_tops_1(k2_tops_1(A,B),A) & v2_tops_1(k2_tops_1(A,B),A))) # label(fc12_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5027 (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]. 29.94/29.53 5028 (all A (l1_pre_topc(A) -> v1_membered(k1_tops_1(A,k1_pre_topc(A))) & v3_membered(k1_tops_1(A,k1_pre_topc(A))) & v5_membered(k1_tops_1(A,k1_pre_topc(A))) & v4_membered(k1_tops_1(A,k1_pre_topc(A))) & v2_membered(k1_tops_1(A,k1_pre_topc(A))) & v1_xboole_0(k1_tops_1(A,k1_pre_topc(A))))) # label(fc5_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5029 $T # label(t11_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5030 (all A (l1_pre_topc(A) -> v1_tops_1(k2_pre_topc(A),A))) # label(fc9_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5031 $T # label(t14_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5032 (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))) -> (v5_tops_1(C,A) -> v4_pre_topc(C,A) & v4_tops_1(C,A)) & (v4_tops_1(D,B) & v4_pre_topc(D,B) -> v5_tops_1(D,B)))))))))) # label(t106_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5033 (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]. 29.94/29.53 5034 $T # label(t18_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5035 (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]. 29.94/29.53 5036 (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]. 29.94/29.53 5037 (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]. 29.94/29.53 5038 $T # label(t15_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5039 $T # label(t23_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5040 (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]. 29.94/29.53 5041 (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(C,B) & v3_pre_topc(C,A) -> C = k1_xboole_0))) <-> v2_tops_1(B,A)))))) # label(t86_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5042 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (k1_tops_1(A,B) = k1_xboole_0 <-> v2_tops_1(B,A)))))) # label(t84_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5043 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,k6_pre_topc(A,B)) <-> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_hidden(C,D) & r1_xboole_0(B,D) & v3_pre_topc(D,A))))))))))) # label(t39_tops_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5044 (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)) -> (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]. 29.94/29.53 5045 (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) -> k10_finseq_1(B,C) = k7_rlvect_1(A,B,C))) # label(redefinition_k7_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5046 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)) = k9_rlvect_1(A,k8_rlvect_1(A,B,D,C)))))))))) # label(t87_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5047 (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]. 29.94/29.53 5048 (all A (m1_subset_1(A,k1_numbers) -> (all B (-v3_struct_0(B) & v7_rlvect_1(B) & l2_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (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]. 29.94/29.53 5049 (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,u1_struct_0(A)) -> (k5_rlvect_1(A,B) = B -> B = k1_rlvect_1(A)))))) # label(t33_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5050 $T # label(t4_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5051 $T # label(t13_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5052 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_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)) -> (np__3 = k3_finseq_1(B) & k1_funct_1(B,np__1) = C & E = k1_funct_1(B,np__3) & D = k1_funct_1(B,np__2) -> k9_rlvect_1(A,B) = k2_rlvect_1(A,k2_rlvect_1(A,C,D),E)))))))))))) # label(t97_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5053 $T # label(t88_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5054 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_rlvect_1(A,B,C) = k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A),u1_rlvect_1(A),k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C)))))))) # label(d3_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5055 (all A (l1_rlvect_1(A) & -v3_struct_0(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)) -> k2_rlvect_1(A,B,C) = k2_rlvect_1(A,C,B)))))))) # label(d5_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5056 (all A (l1_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)) -> (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]. 29.94/29.53 5057 (all A all B (m1_subset_1(B,u1_struct_0(A)) & l1_rlvect_1(A) & -v3_struct_0(A) -> m1_subset_1(k5_rlvect_1(A,B),u1_struct_0(A)))) # label(dt_k5_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5058 (exists A (-v3_struct_0(A) & v4_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & v2_rlvect_1(A) & l2_rlvect_1(A))) # label(rc6_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5059 (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 (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k6_rlvect_1(A,B,k6_rlvect_1(A,C,D)) = k4_rlvect_1(A,k6_rlvect_1(A,B,C),D))))))))) # label(t43_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5060 (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)) -> 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]. 29.94/29.53 5061 (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)) -> (np__1 = k3_finseq_1(B) -> k1_funct_1(B,np__1) = k9_rlvect_1(A,B)))))) # label(t95_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5062 $T # label(t11_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5063 (all A all B all C (-v3_struct_0(A) & v3_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_rlvect_1(A) -> k2_rlvect_1(A,B,C) = k4_rlvect_1(A,B,C))) # label(redefinition_k4_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5064 (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)) -> k5_rlvect_1(A,k2_rlvect_1(A,C,B)) = k9_rlvect_1(A,k7_rlvect_1(A,k5_rlvect_1(A,B),k5_rlvect_1(A,C))))))))) # label(t78_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5065 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k5_rlvect_1(A,B) = k6_rlvect_1(A,k1_rlvect_1(A),B))))) # label(t27_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5066 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k1_nat_1(k3_finseq_1(C),np__1) = k3_finseq_1(B) & k1_funct_1(B,k3_finseq_1(B)) = D & k7_relat_1(B,k4_finseq_1(C)) = C -> k9_rlvect_1(A,B) = k2_rlvect_1(A,k9_rlvect_1(A,C),D)))))))))) # label(t55_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5067 (all A (l2_rlvect_1(A) -> (v2_rlvect_1(A) -> A = g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A))))) # label(abstractness_v2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5068 (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)) -> k6_rlvect_1(A,k6_rlvect_1(A,k5_rlvect_1(A,B),C),D) = k5_rlvect_1(A,k9_rlvect_1(A,k8_rlvect_1(A,B,C,D))))))))))) # label(t71_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5069 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> B = k2_rlvect_1(A,B,k1_rlvect_1(A)))) <-> v5_rlvect_1(A)))) # label(d7_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 29.94/29.53 5070 (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]. 29.94/29.53 5071 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l1_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)) -> 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]. 29.94/29.53 5072 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (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]. 29.94/29.53 5073 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_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]. 29.94/29.53 5074 (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]. 29.94/29.53 5075 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(Alarm clock 120.22/120.07 Prover9 interrupted 120.22/120.07 EOF